We study the time scale T to equipartition in a 1D lattice of N masses coupled by quartic nonlinear (hard) springs (the Fermi-Pasta-Ulam beta model). We take the initial energy to be either in a single mode gamma or in a package of low-frequency modes centered at gamma and of width deltagamma, with both gamma and deltagamma proportional to N. These initial conditions both give, for finite energ...

Most applications of time-dependent density-functional theory (TDDFT) use the adiabatic local-density approximation (ALDA) for the dynamical exchange-correlation potential V(xc)(r,t). An exact (i.e., nonadiabatic) extension of the ground-state LDA into the dynamical regime leads to a V(xc)(r,t) with a memory, which causes the electron dynamics to become dissipative. To illustrate and explain th...

Switching of the direction of flagella rotations is the key control mechanism governing the chemotactic activity of E. coli and many other bacteria. Power-law distributions of switching times are most peculiar because their emergence cannot be deduced from simple thermodynamic arguments. Recently it was suggested that by adding finite-time correlations into Gaussian fluctuations regulating the ...

We generalize the simplest kinetically constrained model of a glass-forming liquid by softening kinetic constraints, allowing them to be violated with a small rate. We demonstrate that this model supports a first-order dynamical (space-time) phase transition between active (fluid) and inactive (glass) phases. The first-order phase boundary in this softened model ends in a finite-temperature dyn...

Given a general thermodynamic process which carries a system from one equilibrium state to another, we construct a quantity whose average, over an ensemble of microscopic realizations of the process, depends only on these end states, even if at intermediate times the system is out of equilibrium. This result leads directly to a statistical statement of the Clausius-Duhem inequality, and can be ...

in this paper, the problem of finite time stabilization for guidance system is investigated and a novel nonlinear guidance law against maneuvering targets is proposed based on the principles of parallel navigation. the proposed law is developed using two variable structure control techniques. by applying finite time integral sliding mode and combining it with terminal sliding mode, a new guidan...

In this paper a new nonlinear guidance law with finite time convergence is proposed. The second order integrated guidance and control loop is formulated considering a first order control loop dynamics. By transforming the state equations to the normal form, a finite time stabilizer feedback linearization technique is proposed to guarantee the finite time convergence of the system states to zero...

Black holes are arguably the most extreme regions of universe. Yet, they also utterly inaccessible to experimentation, and even just indirect observation poses significant technical challenges. The phenomenological approach thermodynamics is uniquely suited explore at least some physical properties such scenarios, this has motivated study so-called holographic engines. We show that efficiency a...