Weakly nonlinear waves in elastic rods have been studied by many authors. Most studies concentrated on smooth solutions only. However, when waves are of moderate length, non-smooth waves, such as peakons (or solitary shock waves), can arise (see Dai and Huo 2000). For strongly nonlinear waves (not assuming the smallness of the wave amplitude), as far as the authors are aware, only incompressibl...

An experimental investigation of shock wave induced heating and compression in planar targets relevant to direct-drive inertial confinement fusion (ICF) was conducted on the OMEGA laser system. A physical understanding of shock wave heating, radiative heating, and heating by energetic electrons in direct-drive ICF is necessary because the achievement of energy gain requires accurate control of ...

We reexamine stochastic Fermi acceleration (STFA) in the low energy (Newtonian) regime in the context of solar flares. The particle energization rate depends a dispersive term and a coherent gain term. The energy dependence of pitch angle scattering is important for determining the electron energy spectrum. For scattering by whistler wave turbulence, STFA produces a quasi-thermal spectrum. A se...

The propagation of magneto-thermoelastic disturbances in an elastic half-space caused by the application of a thermal shock on the stress-free bounding surface in contact with vacuum is investigated. The theory of thermoelasticity III proposed by Green and Naghdi is used to study the interaction between elastic, thermal, and magnetic fields. Small-time approximations of solutions for displaceme...

In this paper the quantum limit of heat transport induced by ultrashort laser pulses is discussed. The new quantum heat transport equation is derived. The relaxation time τ = h̄/mv h (vh = thermal wave velocity) and diffusion coefficient De = h̄/m are calculated.

The shock wave structure in a moderately dense gas is studied by numerically solving the one-dimensional Enskog kinetic equation. The numerical method is based on a combination of a nite difference scheme for the streaming term and a Monte Carlo quadrature technique to evaluate the collision integral. The obtained shock prooles are compared to the results of Navier-Stokes theory and to molecula...

We propose the following model equation, u(t) + 1/2(u(2)-uu(s))x = f(x,u(s)) that predicts chaotic shock waves, similar to those in detonations in chemically reacting mixtures. The equation is given on the half line, x<0, and the shock is located at x = 0 for any t ≥ 0. Here, u(s)(t) is the shock state and the source term f is taken to mimic the chemical energy release in detonations. This equa...

As all biologists appreciate, there is constant interaction between life and the environment, and temperature plays a critical role. It establishes distribution limits, it affects rates of function as well as the survival of organisms. Notoriously sensitive to temperature is plant growth. Critical steps in plant life such as germination, flowering and breaking of dormancy can be manipulated by ...

We consider the evolution of a tight binding wave packet propagating in a time dependent potential. If the potential evolves according to a stationary Markov process, we show that the square amplitude of the wave packet converges, after diffusive rescaling, to a solution of a heat equation.