Location: Cardiovascular Circulation @ d0d05dca8689 / BG_Modules.cellml
- Author:
- Soroush <ssaf006@aucklanduni.ac.nz>
- Date:
- 2021-12-09 13:57:24+13:00
- Desc:
- changed the valve
- Permanent Source URI:
- https://models.cellml.org/workspace/4ac/rawfile/d0d05dca86894705e03d7bad752782f5354d166a/BG_Modules.cellml
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<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>
<!-------------------------------------------------------------------------------//
-----------------------------------------------------------------------------//-->
<!-- 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>
<!-------------------------------------------------------------------------------//
-----------------------------------------------------------------------------//-->
<component name="adv_type">
<variable name="t" public_interface="in" units="second"/>
<!-- Parameters-->
<variable name="K" public_interface="in" units="m3_per_s"/>
<variable name="l" public_interface="in" units="metre"/>
<variable name="r" public_interface="in" units="metre"/>
<!-- State variables-->
<variable initial_value="0" name="q" public_interface="out" units="mole"/>
<variable name="q_in" public_interface="in" units="mole"/>
<variable name="v" public_interface="out" units="mol_per_s"/>
<variable name="v_out" public_interface="in" units="mol_per_s"/>
<!-- Conservation laws-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q</ci>
</apply>
<apply>
<minus/>
<ci>v</ci>
<ci>v_out</ci>
</apply>
</apply>
<!-- Constitutive relations-->
<apply>
<eq/>
<ci>v</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>K</ci>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>l</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>q_in</ci>
<ci>q</ci>
</apply>
</apply>
</apply>
</math>
</component>
<!-------------------------------------------------------------------------------//
-----------------------------------------------------------------------------//-->
<component name="pv_adv_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>
<!-- State variables-->
<variable initial_value="0" name="q" public_interface="out" units="mole"/>
<variable name="q_in" public_interface="in" units="mole"/>
<variable name="v_conc" public_interface="out" units="mol_per_s"/>
<variable name="v_conc_out" public_interface="in" units="mol_per_s"/>
<!-- Conservation laws-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q</ci>
</apply>
<apply>
<minus/>
<ci>v_conc</ci>
<ci>v_conc_out</ci>
</apply>
</apply>
<!-- Constitutive relations-->
<apply>
<eq/>
<ci>v_conc</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>v</ci>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>l</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>q_in</ci>
<ci>q</ci>
</apply>
</apply>
</apply>
</math>
</component>
<!-------------------------------------------------------------------------------//
-----------------------------------------------------------------------------//-->
<component name="pv_jII_adv_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>
<!-- State variables-->
<variable initial_value="0" name="q" public_interface="out" units="mole"/>
<variable name="q_in" public_interface="in" units="mole"/>
<variable name="v_conc" public_interface="out" units="mol_per_s"/>
<variable name="v_conc_out_1" public_interface="in" units="mol_per_s"/>
<variable name="v_conc_out_2" public_interface="in" units="mol_per_s"/>
<!-- Conservation laws-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>v_conc</ci>
<ci>v_conc_out_1</ci>
</apply>
<ci>v_conc_out_2</ci>
</apply>
</apply>
<!-- Constitutive relations-->
<apply>
<eq/>
<ci>v_conc</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>v</ci>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>l</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>q_in</ci>
<ci>q</ci>
</apply>
</apply>
</apply>
</math>
</component>
<!-------------------------------------------------------------------------------//
-----------------------------------------------------------------------------//-->
<component name="pp_BC_adv_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="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"/>
<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>
<!-- State variables-->
<variable initial_value="0" name="q" public_interface="out" units="mole"/>
<variable name="q_in" public_interface="in" units="mole"/>
<variable name="v_conc" public_interface="out" units="mol_per_s"/>
<variable name="v_conc_out" public_interface="in" units="mol_per_s"/>
<!-- Conservation laws-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q</ci>
</apply>
<apply>
<minus/>
<ci>v_conc</ci>
<ci>v_conc_out</ci>
</apply>
</apply>
<!-- Constitutive relations-->
<apply>
<eq/>
<ci>v_conc</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>v</ci>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>l</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>q_in</ci>
<ci>q</ci>
</apply>
</apply>
</apply>
</math>
</component>
<!-------------------------------------------------------------------------------//
-----------------------------------------------------------------------------//-->
<component name="vv_adv_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>
<!-- State variables-->
<variable initial_value="0" name="q" public_interface="out" units="mole"/>
<variable name="q_in" public_interface="in" units="mole"/>
<variable name="v_conc" public_interface="out" units="mol_per_s"/>
<variable name="v_conc_out" public_interface="in" units="mol_per_s"/>
<!-- Conservation laws-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q</ci>
</apply>
<apply>
<minus/>
<ci>v_conc</ci>
<ci>v_conc_out</ci>
</apply>
</apply>
<!-- Constitutive relations-->
<apply>
<eq/>
<ci>v_conc</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>v</ci>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>l</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>q_in</ci>
<ci>q</ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--//////////////////////////////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////// output-BC Vessel ///////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////////////////-->
<component name="pp_BC_X_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="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"/>
<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>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>
</model>