Location: Bond Graph Circulation @ 0e3a0f941e81 / BG_Modules.cellml

Author:
Soroush <ssaf006@aucklanduni.ac.nz>
Date:
2020-05-05 21:14:49+12:00
Desc:
added the matlab file for plots.
Permanent Source URI:
https://models.cellml.org/workspace/5e0/rawfile/0e3a0f941e81e6bf5e7e0bde25c808b2f8c16027/BG_Modules.cellml

<?xml version='1.0' encoding='UTF-8'?>
<model name="Vessel_BG_Units" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
    <!--//////////////////////////////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////////// non-BC Vessel ////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////////////////-->
    <component name="pv_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive Parameters-->
        <variable initial_value="0.004" name="mu" units="Js_per_m3"/>
        <variable initial_value="1050" name="rho" units="Js2_per_m5"/>
        <variable name="E" public_interface="in" units="J_per_m3"/>
        <variable name="E_m" public_interface="out" units="J_per_m3"/>
        <variable name="l" public_interface="in" units="metre"/>
        <variable name="length" public_interface="out" units="metre"/>
        <variable name="h" public_interface="out" units="metre"/>
        <variable name="thickness" public_interface="out" units="metre"/>
        <variable name="r" public_interface="in" units="metre"/>
        <variable name="radius" public_interface="out" units="metre"/>
        <variable name="I" public_interface="out" units="Js2_per_m6"/>
        <variable name="C" public_interface="out" units="m6_per_J"/>
        <variable name="R" public_interface="out" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <variable initial_value="0.2802" name="a" units="dimensionless"/>
        <variable initial_value="-505.3" name="b" units="per_m"/>
        <variable initial_value="0.1324" name="c" units="dimensionless"/>
        <variable initial_value="-11.14" name="d" units="per_m"/>
        <!-- State Variables-->
        <variable name="u_in" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="u_C" public_interface="out" units="J_per_m3"/>
        <variable name="v_out" public_interface="in" units="m3_per_s"/>
        <!-- Constitutive Relations-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>h</ci>
                <apply>
                    <times/>
                    <ci>r</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>a</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>b</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>c</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>d</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>C</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">3</cn>
                        </apply>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>E</ci>
                        <ci>h</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">8</cn>
                        <ci>mu</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">4</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>length</ci>
                <ci>l</ci>
            </apply>
            <apply>
                <eq/>
                <ci>E_m</ci>
                <ci>E</ci>
            </apply>
            <apply>
                <eq/>
                <ci>radius</ci>
                <ci>r</ci>
            </apply>
            <apply>
                <eq/>
                <ci>thickness</ci>
                <ci>h</ci>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u_in</ci>
                            <ci>u</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>R</ci>
                            <ci>v</ci>
                        </apply>
                    </apply>
                    <ci>I</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>u_C</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>v</ci>
                        <ci>v_out</ci>
                    </apply>
                    <ci>C</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v</ci>
                            <ci>v_out</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <!--&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;-//
&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;-//-->
    <component name="vp_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive Parameters-->
        <variable initial_value="0.004" name="mu" units="Js_per_m3"/>
        <variable initial_value="1050" name="rho" units="Js2_per_m5"/>
        <variable name="E" public_interface="in" units="J_per_m3"/>
        <variable name="E_m" public_interface="out" units="J_per_m3"/>
        <variable name="l" public_interface="in" units="metre"/>
        <variable name="length" public_interface="out" units="metre"/>
        <variable name="h" public_interface="out" units="metre"/>
        <variable name="thickness" public_interface="out" units="metre"/>
        <variable name="r" public_interface="in" units="metre"/>
        <variable name="radius" public_interface="out" units="metre"/>
        <variable name="I" public_interface="out" units="Js2_per_m6"/>
        <variable name="C" public_interface="out" units="m6_per_J"/>
        <variable name="R" public_interface="out" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <variable initial_value="0.2802" name="a" units="dimensionless"/>
        <variable initial_value="-505.3" name="b" units="per_m"/>
        <variable initial_value="0.1324" name="c" units="dimensionless"/>
        <variable initial_value="-11.14" name="d" units="per_m"/>
        <!-- State Variables-->
        <variable name="v_in" public_interface="in" units="m3_per_s"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="u_C" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u_out" public_interface="in" units="J_per_m3"/>
        <!-- Constitutive Relations-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>h</ci>
                <apply>
                    <times/>
                    <ci>r</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>a</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>b</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>c</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>d</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <!--C = 2{dimensionless}*pi*pow(r, 3{dimensionless})*l/(E*h);-->
            <apply>
                <eq/>
                <ci>C</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">3</cn>
                        </apply>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>E</ci>
                        <ci>h</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">8</cn>
                        <ci>mu</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">4</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>length</ci>
                <ci>l</ci>
            </apply>
            <apply>
                <eq/>
                <ci>E_m</ci>
                <ci>E</ci>
            </apply>
            <apply>
                <eq/>
                <ci>radius</ci>
                <ci>r</ci>
            </apply>
            <apply>
                <eq/>
                <ci>thickness</ci>
                <ci>h</ci>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u</ci>
                            <ci>u_out</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>R</ci>
                            <ci>v</ci>
                        </apply>
                    </apply>
                    <ci>I</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>u_C</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>v_in</ci>
                        <ci>v</ci>
                    </apply>
                    <ci>C</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v_in</ci>
                            <ci>v</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <!--&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;-//
&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;-//-->
    <component name="pp_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive Parameters-->
        <variable initial_value="0.004" name="mu" units="Js_per_m3"/>
        <variable initial_value="1050" name="rho" units="Js2_per_m5"/>
        <variable name="E" public_interface="in" units="J_per_m3"/>
        <variable name="E_m" public_interface="out" units="J_per_m3"/>
        <variable name="l" public_interface="in" units="metre"/>
        <variable name="length" public_interface="out" units="metre"/>
        <variable name="h" public_interface="out" units="metre"/>
        <variable name="thickness" public_interface="out" units="metre"/>
        <variable name="r" public_interface="in" units="metre"/>
        <variable name="radius" public_interface="out" units="metre"/>
        <variable name="I" public_interface="out" units="Js2_per_m6"/>
        <variable name="C" public_interface="out" units="m6_per_J"/>
        <variable name="R" public_interface="out" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <variable initial_value="0.2802" name="a" units="dimensionless"/>
        <variable initial_value="-505.3" name="b" units="per_m"/>
        <variable initial_value="0.1324" name="c" units="dimensionless"/>
        <variable initial_value="-11.14" name="d" units="per_m"/>
        <!-- State Variables-->
        <variable name="u_in" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="u_C" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="v_d" public_interface="out" units="m3_per_s"/>
        <variable name="u_out" public_interface="in" units="J_per_m3"/>
        <!-- Constitutive Relations-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>h</ci>
                <apply>
                    <times/>
                    <ci>r</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>a</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>b</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>c</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>d</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>C</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">3</cn>
                        </apply>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>E</ci>
                        <ci>h</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">8</cn>
                        <ci>mu</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">4</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>length</ci>
                <ci>l</ci>
            </apply>
            <apply>
                <eq/>
                <ci>E_m</ci>
                <ci>E</ci>
            </apply>
            <apply>
                <eq/>
                <ci>radius</ci>
                <ci>r</ci>
            </apply>
            <apply>
                <eq/>
                <ci>thickness</ci>
                <ci>h</ci>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u_in</ci>
                            <ci>u</ci>
                        </apply>
                        <apply>
                            <times/>
                            <apply>
                                <divide/>
                                <ci>R</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                            <ci>v</ci>
                        </apply>
                    </apply>
                    <apply>
                        <divide/>
                        <ci>I</ci>
                        <cn cellml:units="dimensionless">2</cn>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>u_C</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>v</ci>
                        <ci>v_d</ci>
                    </apply>
                    <ci>C</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v</ci>
                            <ci>v_d</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_d</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u</ci>
                            <ci>u_out</ci>
                        </apply>
                        <apply>
                            <times/>
                            <apply>
                                <divide/>
                                <ci>R</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                            <ci>v_d</ci>
                        </apply>
                    </apply>
                    <apply>
                        <divide/>
                        <ci>I</ci>
                        <cn cellml:units="dimensionless">2</cn>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <!--//////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////// input-BC Vessel ///////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////////////////-->
    <component name="vv_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive Parameters-->
        <variable initial_value="0.004" name="mu" units="Js_per_m3"/>
        <variable initial_value="1050" name="rho" units="Js2_per_m5"/>
        <variable name="E" public_interface="in" units="J_per_m3"/>
        <variable name="E_m" public_interface="out" units="J_per_m3"/>
        <variable name="l" public_interface="in" units="metre"/>
        <variable name="length" public_interface="out" units="metre"/>
        <variable name="h" public_interface="out" units="metre"/>
        <variable name="thickness" public_interface="out" units="metre"/>
        <variable name="r" public_interface="in" units="metre"/>
        <variable name="radius" public_interface="out" units="metre"/>
        <variable name="I" public_interface="out" units="Js2_per_m6"/>
        <variable name="C" public_interface="out" units="m6_per_J"/>
        <variable name="R" public_interface="out" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <variable initial_value="0.2802" name="a" units="dimensionless"/>
        <variable initial_value="-505.3" name="b" units="per_m"/>
        <variable initial_value="0.1324" name="c" units="dimensionless"/>
        <variable initial_value="-11.14" name="d" units="per_m"/>
        <!-- State Variables-->
        <variable name="v_in" public_interface="in" units="m3_per_s"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="u_C" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u_d" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="u_C_d" public_interface="out" units="J_per_m3"/>
        <variable name="v_out" public_interface="in" units="m3_per_s"/>
        <!-- Constitutive Relations-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>h</ci>
                <apply>
                    <times/>
                    <ci>r</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>a</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>b</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>c</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>d</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>C</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">3</cn>
                        </apply>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>E</ci>
                        <ci>h</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">8</cn>
                        <ci>mu</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">4</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>length</ci>
                <ci>l</ci>
            </apply>
            <apply>
                <eq/>
                <ci>E_m</ci>
                <ci>E</ci>
            </apply>
            <apply>
                <eq/>
                <ci>radius</ci>
                <ci>r</ci>
            </apply>
            <apply>
                <eq/>
                <ci>thickness</ci>
                <ci>h</ci>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u</ci>
                            <ci>u_d</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>R</ci>
                            <ci>v</ci>
                        </apply>
                    </apply>
                    <ci>I</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>u_C</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>v_in</ci>
                        <ci>v</ci>
                    </apply>
                    <apply>
                        <divide/>
                        <ci>C</ci>
                        <cn cellml:units="dimensionless">2</cn>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>u_C_d</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>v</ci>
                        <ci>v_out</ci>
                    </apply>
                    <apply>
                        <divide/>
                        <ci>C</ci>
                        <cn cellml:units="dimensionless">2</cn>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v_in</ci>
                            <ci>v</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_d</ci>
                <apply>
                    <plus/>
                    <ci>u_C_d</ci>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v</ci>
                            <ci>v_out</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <!--//////////////////////////////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////// output-BC Vessel ///////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////////////////-->
    <component name="pp_BC_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive Parameters-->
        <variable initial_value="0.004" name="mu" units="Js_per_m3"/>
        <variable initial_value="1050" name="rho" units="Js2_per_m5"/>
        <variable name="E" public_interface="in" units="J_per_m3"/>
        <variable name="E_m" public_interface="out" units="J_per_m3"/>
        <variable name="l" public_interface="in" units="metre"/>
        <variable name="length" public_interface="out" units="metre"/>
        <variable name="h" public_interface="out" units="metre"/>
        <variable name="thickness" public_interface="out" units="metre"/>
        <variable name="r" public_interface="in" units="metre"/>
        <variable name="radius" public_interface="out" units="metre"/>
        <variable name="I" public_interface="out" units="Js2_per_m6"/>
        <variable name="I_e" public_interface="out" units="Js2_per_m6"/>
        <variable name="C" public_interface="out" units="m6_per_J"/>
        <variable name="R" public_interface="out" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <variable name="R_T" public_interface="in" units="Js_per_m6"/>
        <variable name="R_T_2" public_interface="out" units="Js_per_m6"/>
        <variable name="C_T" public_interface="in" units="m6_per_J"/>
        <variable initial_value="0.2802" name="a" units="dimensionless"/>
        <variable initial_value="-505.3" name="b" units="per_m"/>
        <variable initial_value="0.1324" name="c" units="dimensionless"/>
        <variable initial_value="-11.14" name="d" units="per_m"/>
        <variable name="alpha" public_interface="in" units="dimensionless"/>
        <!-- State Variables-->
        <variable name="u_in" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="u_C" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="u_T" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="v_T" public_interface="out" units="m3_per_s"/>
        <variable name="u_out" public_interface="in" units="J_per_m3"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>h</ci>
                <apply>
                    <times/>
                    <ci>r</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>a</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>b</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>c</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>d</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I_e</ci>
                <apply>
                    <times/>
                    <ci>I</ci>
                    <cn cellml:units="dimensionless" type="e-notation">1<sep/>-6</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>C</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">3</cn>
                        </apply>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>E</ci>
                        <ci>h</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">8</cn>
                        <ci>mu</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">4</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_T_2</ci>
                <apply>
                    <times/>
                    <cn cellml:units="dimensionless">4</cn>
                    <ci>R_T</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>length</ci>
                <ci>l</ci>
            </apply>
            <apply>
                <eq/>
                <ci>E_m</ci>
                <ci>E</ci>
            </apply>
            <apply>
                <eq/>
                <ci>radius</ci>
                <ci>r</ci>
            </apply>
            <apply>
                <eq/>
                <ci>thickness</ci>
                <ci>h</ci>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u_in</ci>
                            <ci>u</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>R</ci>
                            <ci>v</ci>
                        </apply>
                    </apply>
                    <ci>I</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>u_C</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>v</ci>
                        <ci>v_T</ci>
                    </apply>
                    <ci>C</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v</ci>
                            <ci>v_T</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_T</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <ci>u</ci>
                                <ci>u_out</ci>
                            </apply>
                            <ci>u_T</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>alpha</ci>
                            <ci>R_T</ci>
                            <ci>v_T</ci>
                        </apply>
                    </apply>
                    <ci>I_e</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>u_T</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>v_T</ci>
                        <apply>
                            <divide/>
                            <ci>u_T</ci>
                            <apply>
                                <times/>
                                <ci>alpha</ci>
                                <ci>R_T_2</ci>
                            </apply>
                        </apply>
                    </apply>
                    <ci>C_T</ci>
                </apply>
            </apply>
        </math>
    </component>
    <!--//////////////////////////////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////// output-BC Venous Vessel ////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////////////////-->
    <component name="pp_vBC_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive Parameters-->
        <variable initial_value="0.004" name="mu" units="Js_per_m3"/>
        <variable initial_value="1050" name="rho" units="Js2_per_m5"/>
        <variable name="E" public_interface="in" units="J_per_m3"/>
        <variable name="E_m" public_interface="out" units="J_per_m3"/>
        <variable name="l" public_interface="in" units="metre"/>
        <variable name="length" public_interface="out" units="metre"/>
        <variable name="h" public_interface="out" units="metre"/>
        <variable name="thickness" public_interface="out" units="metre"/>
        <variable name="r" public_interface="in" units="metre"/>
        <variable name="radius" public_interface="out" units="metre"/>
        <variable name="I" public_interface="out" units="Js2_per_m6"/>
        <variable name="I_e" public_interface="out" units="Js2_per_m6"/>
        <variable name="C" public_interface="out" units="m6_per_J"/>
        <variable name="R" public_interface="out" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <variable name="R_T" public_interface="in" units="Js_per_m6"/>
        <variable name="C_T" public_interface="in" units="m6_per_J"/>
        <variable initial_value="0.2802" name="a" units="dimensionless"/>
        <variable initial_value="-505.3" name="b" units="per_m"/>
        <variable initial_value="0.1324" name="c" units="dimensionless"/>
        <variable initial_value="-11.14" name="d" units="per_m"/>
        <!-- State Variables-->
        <variable name="u_in" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="u_C" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="v_T" public_interface="out" units="m3_per_s"/>
        <variable name="u_out" public_interface="in" units="J_per_m3"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>h</ci>
                <apply>
                    <times/>
                    <ci>r</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>a</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>b</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>c</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>d</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I_e</ci>
                <apply>
                    <times/>
                    <ci>I</ci>
                    <cn cellml:units="dimensionless" type="e-notation">1<sep/>-6</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>C</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">3</cn>
                        </apply>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>E</ci>
                        <ci>h</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">8</cn>
                        <ci>mu</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">4</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>length</ci>
                <ci>l</ci>
            </apply>
            <apply>
                <eq/>
                <ci>E_m</ci>
                <ci>E</ci>
            </apply>
            <apply>
                <eq/>
                <ci>radius</ci>
                <ci>r</ci>
            </apply>
            <apply>
                <eq/>
                <ci>thickness</ci>
                <ci>h</ci>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u_in</ci>
                            <ci>u</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>R</ci>
                            <ci>v</ci>
                        </apply>
                    </apply>
                    <ci>I</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>u_C</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>v</ci>
                        <ci>v_T</ci>
                    </apply>
                    <ci>C</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <ci>v</ci>
                            <ci>v_T</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v_T</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u</ci>
                            <ci>u_out</ci>
                        </apply>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">3.0</cn>
                            <ci>R_T</ci>
                            <ci>v_T</ci>
                        </apply>
                    </apply>
                    <ci>I_e</ci>
                </apply>
            </apply>
        </math>
    </component>
    <!--/////////////////////////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////// Junctions //////////////////////////////////////////////
/////////////////////////////////////////////////////////////////////////////////////////////////////-->
    <!-- Bifurcation-->
    <component name="pv_jII_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive Parameters-->
        <variable initial_value="0.004" name="mu" units="Js_per_m3"/>
        <variable initial_value="1050" name="rho" units="Js2_per_m5"/>
        <variable name="E" public_interface="in" units="J_per_m3"/>
        <variable name="E_m" public_interface="out" units="J_per_m3"/>
        <variable name="l" public_interface="in" units="metre"/>
        <variable name="length" public_interface="out" units="metre"/>
        <variable name="h" public_interface="out" units="metre"/>
        <variable name="thickness" public_interface="out" units="metre"/>
        <variable name="r" public_interface="in" units="metre"/>
        <variable name="radius" public_interface="out" units="metre"/>
        <variable name="I" public_interface="out" units="Js2_per_m6"/>
        <variable name="C" public_interface="out" units="m6_per_J"/>
        <variable name="R" public_interface="out" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <variable initial_value="0.2802" name="a" units="dimensionless"/>
        <variable initial_value="-505.3" name="b" units="per_m"/>
        <variable initial_value="0.1324" name="c" units="dimensionless"/>
        <variable initial_value="-11.14" name="d" units="per_m"/>
        <!-- State Variables-->
        <variable name="u_in" public_interface="in" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="u_C" public_interface="out" units="J_per_m3"/>
        <variable name="v_out_1" public_interface="in" units="m3_per_s"/>
        <variable name="v_out_2" public_interface="in" units="m3_per_s"/>
        <!-- Constitutive Relations-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>h</ci>
                <apply>
                    <times/>
                    <ci>r</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>a</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>b</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>c</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>d</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>C</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">3</cn>
                        </apply>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>E</ci>
                        <ci>h</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">8</cn>
                        <ci>mu</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">4</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>length</ci>
                <ci>l</ci>
            </apply>
            <apply>
                <eq/>
                <ci>E_m</ci>
                <ci>E</ci>
            </apply>
            <apply>
                <eq/>
                <ci>radius</ci>
                <ci>r</ci>
            </apply>
            <apply>
                <eq/>
                <ci>thickness</ci>
                <ci>h</ci>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u_in</ci>
                            <ci>u</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>R</ci>
                            <ci>v</ci>
                        </apply>
                    </apply>
                    <ci>I</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>u_C</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>v</ci>
                            <ci>v_out_1</ci>
                        </apply>
                        <ci>v_out_2</ci>
                    </apply>
                    <ci>C</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <ci>v</ci>
                                <ci>v_out_1</ci>
                            </apply>
                            <ci>v_out_2</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <!--&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;-//
&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;-//-->
    <!-- Merging-->
    <component name="vv_jII_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive Parameters-->
        <variable initial_value="0.004" name="mu" units="Js_per_m3"/>
        <variable initial_value="1050" name="rho" units="Js2_per_m5"/>
        <variable name="E" public_interface="in" units="J_per_m3"/>
        <variable name="E_m" public_interface="out" units="J_per_m3"/>
        <variable name="l" public_interface="in" units="metre"/>
        <variable name="length" public_interface="out" units="metre"/>
        <variable name="h" public_interface="out" units="metre"/>
        <variable name="thickness" public_interface="out" units="metre"/>
        <variable name="r" public_interface="in" units="metre"/>
        <variable name="radius" public_interface="out" units="metre"/>
        <variable name="I" public_interface="out" units="Js2_per_m6"/>
        <variable name="C" public_interface="out" units="m6_per_J"/>
        <variable name="R" public_interface="out" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <variable initial_value="0.2802" name="a" units="dimensionless"/>
        <variable initial_value="-505.3" name="b" units="per_m"/>
        <variable initial_value="0.1324" name="c" units="dimensionless"/>
        <variable initial_value="-11.14" name="d" units="per_m"/>
        <!-- State Variables-->
        <variable name="v_in_1" public_interface="in" units="m3_per_s"/>
        <variable name="v_in_2" public_interface="in" units="m3_per_s"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="u_C" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u_d" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="u_C_d" public_interface="out" units="J_per_m3"/>
        <variable name="v_out_1" public_interface="in" units="m3_per_s"/>
        <variable name="v_out_2" public_interface="in" units="m3_per_s"/>
        <!-- Constitutive Relations-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>h</ci>
                <apply>
                    <times/>
                    <ci>r</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>a</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>b</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>c</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>d</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>C</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">3</cn>
                        </apply>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>E</ci>
                        <ci>h</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">8</cn>
                        <ci>mu</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">4</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>length</ci>
                <ci>l</ci>
            </apply>
            <apply>
                <eq/>
                <ci>E_m</ci>
                <ci>E</ci>
            </apply>
            <apply>
                <eq/>
                <ci>radius</ci>
                <ci>r</ci>
            </apply>
            <apply>
                <eq/>
                <ci>thickness</ci>
                <ci>h</ci>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u</ci>
                            <ci>u_d</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>R</ci>
                            <ci>v</ci>
                        </apply>
                    </apply>
                    <ci>I</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>u_C</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <ci>v_in_1</ci>
                            <ci>v_in_2</ci>
                        </apply>
                        <ci>v</ci>
                    </apply>
                    <apply>
                        <divide/>
                        <ci>C</ci>
                        <cn cellml:units="dimensionless">2</cn>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>u_C_d</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>v</ci>
                            <ci>v_out_1</ci>
                        </apply>
                        <ci>v_out_2</ci>
                    </apply>
                    <apply>
                        <divide/>
                        <ci>C</ci>
                        <cn cellml:units="dimensionless">2</cn>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <apply>
                                <plus/>
                                <ci>v_in_1</ci>
                                <ci>v_in_2</ci>
                            </apply>
                            <ci>v</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_d</ci>
                <apply>
                    <plus/>
                    <ci>u_C_d</ci>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <ci>v</ci>
                                <ci>v_out_1</ci>
                            </apply>
                            <ci>v_out_2</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <!-- Vein Merging-->
    <component name="vp_jII_type">
        <variable name="t" public_interface="in" units="second"/>
        <!-- Constitutive Parameters-->
        <variable initial_value="0.004" name="mu" units="Js_per_m3"/>
        <variable initial_value="1050" name="rho" units="Js2_per_m5"/>
        <variable name="E" public_interface="in" units="J_per_m3"/>
        <variable name="E_m" public_interface="out" units="J_per_m3"/>
        <variable name="l" public_interface="in" units="metre"/>
        <variable name="length" public_interface="out" units="metre"/>
        <variable name="h" public_interface="out" units="metre"/>
        <variable name="thickness" public_interface="out" units="metre"/>
        <variable name="r" public_interface="in" units="metre"/>
        <variable name="radius" public_interface="out" units="metre"/>
        <variable name="I" public_interface="out" units="Js2_per_m6"/>
        <variable name="C" public_interface="out" units="m6_per_J"/>
        <variable name="R" public_interface="out" units="Js_per_m6"/>
        <variable name="R_v" public_interface="out" units="Js_per_m6"/>
        <variable initial_value="0.2802" name="a" units="dimensionless"/>
        <variable initial_value="-505.3" name="b" units="per_m"/>
        <variable initial_value="0.1324" name="c" units="dimensionless"/>
        <variable initial_value="-11.14" name="d" units="per_m"/>
        <!-- State Variables-->
        <variable name="v_in_1" public_interface="in" units="m3_per_s"/>
        <variable name="v_in_2" public_interface="in" units="m3_per_s"/>
        <variable name="u" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="u_C" public_interface="out" units="J_per_m3"/>
        <variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
        <variable name="u_out" public_interface="in" units="J_per_m3"/>
        <!-- Constitutive Relations-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>h</ci>
                <apply>
                    <times/>
                    <ci>r</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>a</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>b</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>c</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>d</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>C</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">3</cn>
                        </apply>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>E</ci>
                        <ci>h</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">8</cn>
                        <ci>mu</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">4</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R_v</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="second">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>length</ci>
                <ci>l</ci>
            </apply>
            <apply>
                <eq/>
                <ci>E_m</ci>
                <ci>E</ci>
            </apply>
            <apply>
                <eq/>
                <ci>radius</ci>
                <ci>r</ci>
            </apply>
            <apply>
                <eq/>
                <ci>thickness</ci>
                <ci>h</ci>
            </apply>
            <!-- Conservation Laws-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>v</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>u</ci>
                            <ci>u_out</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>R</ci>
                            <ci>v</ci>
                        </apply>
                    </apply>
                    <ci>I</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>u_C</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <ci>v_in_1</ci>
                            <ci>v_in_2</ci>
                        </apply>
                        <ci>v</ci>
                    </apply>
                    <ci>C</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u</ci>
                <apply>
                    <plus/>
                    <ci>u_C</ci>
                    <apply>
                        <times/>
                        <ci>R_v</ci>
                        <apply>
                            <minus/>
                            <apply>
                                <plus/>
                                <ci>v_in_1</ci>
                                <ci>v_in_2</ci>
                            </apply>
                            <ci>v</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
</model>