In classical mechanics, Galilean covariance and the principle of relativity are completely equivalent and hold for all possible dynamical processes. In contrast, in relativistic physics the situation is much more complex. It will be shown that Lorentz covariance and the principle of relativity are not completely equivalent. The reason is that the principle of relativity actually only holds for ...

A method is presented to characterize general sound-absorbing materials through a pole-based identification of the equivalent fluid. This accomplished by 1) determining extended fluid material sample transfer function (TFM), 2) acoustic response poles effective density and compressibility, 3) build compressibility from associated local response. Real pole pairs describe dissipative medium (or e...

By introducing the notations of dissipative and strictly dissipative p-symmetrizers of initial-boundary-value problems for linear hyperbolic systems we formalize the dissipative integrals technique [A. Blokhin, Yu. Trakhinin, in Handbook of Mathematical Fluid Dynamics, Vol. 1, North-Holland, Amsterdam, 2002, pp. 545–652] applied earlier to shock waves and characteristic discontinuities for vari...

The area of analysis and control of linear parameter-varying (LPV) systems has received much recent attention because of its importance in developing systematic techniques for gain-scheduling. An LPV system resembles a linear system that nonlinearly depends on one or more time-varying parameters. Nonlinear systems are often modeled in the LPV system via the parameterized Jacobian linearization....

We consider a one-dimensional Ising model in a transverse magnetic field coupled to a dissipative heat bath. The phase diagram and the critical exponents are determined from extensive Monte Carlo simulations. It is shown that the character of the quantum phase transition is radically altered from the corresponding nondissipative model and the double well coupled to a dissipative heat bath with ...

We obtain a family of nonlinear maximum principles for linear dissipative nonlocal operators, that are general, robust, and versatile. We use these nonlinear bounds to provide transparent proofs of global regularity for critical SQG and critical d-dimensional Burgers equations. In addition we give applications of the nonlinear maximum principle to the global regularity of a slightly dissipative...

The problem of delay-dependent dissipative analysis and control for stochastic singular systems with state delay is investigated in this paper. Delay-dependent dissipative condition for the stochastic singular systems with state delay is obtained by employing singular stochastic Lyapunov and LMI-based methods. Based on this condition, a delay-dependent dissipative controller is presented. A num...