[PDE & Applications seminar] Prof. Igor Andrianov and Dr. Fajar Kusumo Colloquium talks

10 October 2023 16:00 till 17:15 - Location: Lecture hall Ampere, EEMCS Building | Add to my calendar

Investigation of electrically actuated geometrically nonlinear micro and nano beams and plates
I.V. Andrianov, RWTH Aachen University, Germany

Oscillations of the electrically actuated micro and nano beams and plates are considered, described by strongly nonlinear differential equations.
One of the essentially nonlinear effects is the pull-in phenomenon, i.e., the transition of the oscillatory regime to the attraction one. This effect is considered on the basis of various approximate models. In particular, the error of replacing the original nonlinearity by its expansion in the Maclaurin series is estimated. It is shown that such an approximation can only be used for voltage values that are far from critical. A simple and physically clear algorithm for determining the voltage values at which the system suddenly collapses is proposed. This algorithm is based on the
criterion consisting in the merging of points of a stable (center) and an unstable (saddle) equilibrium. Comparison with the results of calculations based on other methods shows sufficient accuracy of the proposed algorithm. The electrically activated oscillations are considered taking
into account the geometric nonlinearity within the framework of the Kirchhoff and Berger models. The effect of geometric non-linearity on pull-in values is studied. It is shown that neglect of this factor can lead to significant errors. Influence of Casimir and van der Waals forces on the pullin value is also studied. It is shown that the dependence of the pullin value on the initial displacements is almost linear. Analytical estimation for the initial displacements and velocities which guarantees oscillatory character of motion is proposed.

Torus and Homoclinic Bifurcations in a Cell Repair Regulation Model for Metastatic Nasopharyngeal Carcinoma
Fajar Adi Kusumo (joint work with Ario Wiraya)

Nasopharyngeal carcinoma (NPC) is a tumor that grows on nasopharyngeal epithelial cells. There are some proteins that play important roles in the regulation of cell repair for metastatic NPC, i.e., ATM, p53, MDM2, and DSB. In this paper, we construct a mathematical model that shows the interactions between such proteins and study the behavior of NPC in a long time period. The model is a four-dimensional system of first-order ODEs that has a 16-dimensional parameter space. In this case, we consider the appearance of attracting patterns of the solutions near the steady-state conditions. We use the codimension 1 and codimension 2 bifurcations analysis to study the role of several important parameters for the metastasis of NPC and study the possibilities of the system to have chaotic solutions. The appearance of a chaotic solution shows the irregularity of the system due to the changes of the initial conditions. It is important to understand the metastasis behavior NPC and to determine the treatment strategies.