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<span style="font-size: 12pt;" class="">Değerli Liste Üyeleri,</span></div>
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Bu hafta (Şubat 12-16 haftası) Koç Üniversitesi ana kampüsünde (Rumeli Feneri Kampüsü’nde) </div>
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aşağıdaki <span style="font-size: 12pt;" class="">iki konuşma gerçekleşecek.</span></div>
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İlgilenen herkesi bekleriz.</div>
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Saygılarımla,</div>
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Emre Mengi</div>
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<div class="elementToProof"><span style="font-family: Calibri, sans-serif; font-size: 12pt; color: rgb(0, 32, 96);" class=""><b class="">KOÇ UNIVERSITY MATHEMATICS COLLOQUIUM</b></span></div>
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<span style="font-size: 12pt; color: rgb(0, 32, 96);" class=""><b class="">Speaker :</b> Volker Mehrmann, Technical University of Berlin</span></div>
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<span style="font-size: 12pt; color: rgb(0, 32, 96);" class=""><b class="">Title :</b> Energy based modeling, simulation and control of energy systems</span></div>
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<span style="font-size: 12pt; color: rgb(0, 32, 96);" class=""><b class="">Date :</b> Tuesday, February 13, 2024</span></p>
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<span style="font-size: 12pt; color: rgb(0, 32, 96);" class=""><b class="">Time :</b> 14:30-15:30</span></div>
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<span style="font-size: 12pt; color: rgb(0, 32, 96);" class=""><b class="">Place :</b> SCI 103 (Science Building 103)</span></div>
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<span style="font-size: 12pt; color: rgb(0, 32, 96);" class=""><b class="">Abstract: </b></span></div>
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<span style="font-size: 12pt; color: rgb(0, 32, 96);" class="">Most real world dynamical systems consist of subsystems from different physical domains, modelled by partial-differential equations, ordinary differential equations, and algebraic equations, combined
with input and output connections. To deal with such complex system, in recent years energy based modeling via the class of dissipative port-Hamiltonian (pH) descriptor systems has emerged as a very successful mathematical modeling methodology. The main reasons
are that the network based interconnection of pH systems is again pH, Galerkin projection in PDE discretization and model reduction preserve the pH structure and the physical properties are encoded in the geometric properties of the flow as well as the algebraic
properties of the equations. Furthermore, dissipative pH systems form a very robust representation under structured perturbations and directly indicate Lyapunov functions for stability analysis.</span></div>
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<span style="font-size: 12pt; color: rgb(0, 32, 96);" class="">Another advantage of energy based modeling via pH systems is that each separate model of a physical system can be a whole model catalog from which models can be chosen in an adaptive way within
simulation and optimization methods. </span></div>
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<span style="font-size: 12pt; color: rgb(0, 32, 96);" class="">We discuss the model class of constrained pH systems and show how many classical real world mathematical models in energy systems can be formulated in this class. We illustrate the results with
some real world examples from gas transport, district heating and power systems and point out emerging mathematical challenges.</span></div>
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<span style="font-family: Calibri, sans-serif; font-size: 12pt; color: rgb(0, 32, 96);" class=""><b class="">KOÇ UNIVERSITY MATH SEMINAR</b></span></div>
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<div style="margin: 0cm; direction: ltr; font-size: 11pt;" class=""><span style="font-size: 12pt; color: rgb(0, 32, 96);" class="">*******************************</span></div>
<div style="margin: 0cm; direction: ltr; font-size: 11pt;" class=""><span style="font-size: 12pt; color: rgb(0, 32, 96);" class=""><b class="">Speaker :</b> Volker Mehrmann, Technical University of Berlin</span></div>
<div style="margin: 0cm; direction: ltr; font-size: 11pt;" class=""><span style="font-size: 12pt; color: rgb(0, 32, 96);" class=""><b class="">Title :</b> Hypocoercivity, hypocontractivity and short-time decay of solutions to linear evolution
equations</span></div>
<p style="margin: 0cm 0cm 5pt; direction: ltr; font-size: 11pt;" class=""><span style="font-size: 12pt; color: rgb(0, 32, 96);" class=""><b class="">Date :</b> Thursday, February 15, 2024</span></p>
<div style="margin: 0cm; direction: ltr; font-size: 11pt;" class=""><span style="font-size: 12pt; color: rgb(0, 32, 96);" class=""><b class="">Time :</b> 14:30-15:30</span></div>
<div style="margin: 0cm; direction: ltr; font-size: 11pt;" class=""><span style="font-size: 12pt; color: rgb(0, 32, 96);" class=""><b class="">Place :</b> SCI 103 </span><span style="caret-color: rgb(0, 32, 96); color: rgb(0, 32, 96); font-size: 16px;" class="">(Science
Building 103)</span></div>
<p style="margin: 0cm; direction: ltr; font-size: 11pt;" class=""><span style="font-size: 12pt; color: rgb(0, 32, 96);" class=""> </span></p>
<div style="margin: 0cm; direction: ltr; font-size: 11pt;" class=""><span style="font-size: 12pt; color: rgb(0, 32, 96);" class=""><b class="">Abstract: </b></span></div>
<div style="margin: 0cm; direction: ltr; font-size: 11pt;" class=""><span style="font-size: 12pt; color: rgb(0, 32, 96);" class="">For linear evolution equations (in continuous-time and discrete-time) we revisit and extend the concepts of hypocoercivity and
hypocontractivity and give a detailed analysis of the relations of these concepts to (asymptotic) stability, as well as (semi-)dissipativity and (semi-)contractivity, respectively. On the basis of these results, the short-time decay behavior of the norm of
the fundamental solution matrix for linear continuous-time and discrete-time systems is characterized by an integer called hypocoercivity index or hypocontractivity index, respectively. The results extend to linear operators in Hilbert spaces and can be applied
to the analysis of anisotropic flows.</span></div>
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