We argue that the celebrated Stefan condition on the moving interphase, accepted in mathematical physics up to now, can not be imposed if energy sources are spatially distributed in the volume. A method based on Tikhonov and Samarskii's ideas for numerical solution of the problem is developed. Mathematical modelling of energy relaxation of some processes useful in modern ion beam technologies i...

We claim that the celebrated Stefan condition on the moving interphase, accepted in mathematical physics, can not be imposed if energy sources are spatially distributed in the volume. A method based on Tikhonov and Samarskii ideas for numerical solution of the problem is developed. Mathematical modelling of energy relaxation of some processes useful in modern ion beam technologies is fulfilled....

Mathematical modeling of thermal effects on steady state dynamics of microresonators, utilizing an analytical approach is studied. Thermal phenomena has two distinct effects, which in this report are called, thermal damping and temperature relaxation. In this part of a two-part report we investigate the thermal damping and its effects on microresonator dynamics. To do this, first the reduced or...

We study a refined framework of parameterized complexity theory where the parameter dependence of fixed-parameter tractable algorithms is not arbitrary, but restricted by a function in some familyF . For every family F of functions, this yields a notion of F -fixed parameter tractability. If F is the class of all polynomially bounded functions, then F -fixed parameter tractability coincides wit...

A mathematical model is described to investigate the damping moment of weakly nonlinear roll and yaw motions of a floating body in time domain under the action of sinusoidal waves. The mathematical formulation for added mass moment of inertia and damping is presented by approximating time-dependent coefficients and forcing moments when small distortion holds. Using perturbation technique, we ob...

In this article, the sliding mode control of frequency load control of power systems is studied. The study areaconsists of a system of water and heat. First, a mathematical model of the proposed system disturbances ismade and then sliding control mode for frequency load control is provided. By the system simulation andsliding mode control, it can be shown that the damping of oscillations is wel...

Using molecular dynamics based on Langevin equations with a coordinate- and velocity-dependent damping coefficient, we study the frictional properties of a thin layer of "soft" lubricant (where the interaction within the lubricant is weaker than the lubricant-substrate interaction) confined between two solids. At low driving velocities the system demonstrates stick-slip motion. The lubricant ma...