Related papers: Energy in one dimensional linear waves in a string
Many complex systems exhibit hydrodynamic (or macroscopic) behavior at large scales characterized by few variables such as the particle number density, temperature and pressure obeying a set of hydrodynamic (or macroscopic) equations. Does…
We experimentally investigate the dynamics of water cooled from below at 0^oC and heated from above. Taking advantage of the unusual property that water's density maximum is at about 4^oC, this set-up allows us to simulate in the laboratory…
We examine the motion of a relativistic charged particle in a constant magnetic field perturbed by gravitational waves incident along the direction of the magnetic field. We apply a generalized energy conservation law to compute the…
String vibration represents an active field of research in acoustics. Small-amplitude vibration is often assumed, leading to simplified physical models that can be simulated efficiently. However, the inclusion of nonlinear phenomena due to…
I provide a pedagogical introduction to the notion of pseudomomentum for waves in a medium, and show how changes in pseudomomentum may sometimes be used to compute real forces. I then explain how these ideas apply to sound waves in a fluid.…
We revisit some issues about existence and regularity for the wave equation in noncylindrical domains. Using a method of diffeomorphisms, we show how, through increasing regularity assumptions, the existence of weak solutions, their…
Inertial range energy transfer in three dimensional fully developed binary fluid turbulence is studied under the assumption of statistical homogeneity. Using two point statistics, exact relations corresponding to the energy cascade are…
Conventional textbook treatments on electromagnetic wave propagation consider the induced charge and current densities as "bound", and therefore absorb them into a refractive index. In principle it must also be possible to treat the medium…
Electromagnetic waves and fluids have locally conserved mechanical properties associated with them and we may expect these to exist for matter waves. We present a semiclassical description of the continuity equations relating to these…
We consider a one-dimensional array of particles interacting via an infinite well potential. We explore the properties of energy spreading from an initial state where only a group of particles has non-zero velocities while others are…
We consider the initial-value problem for the one-dimensional, time-dependent wave equation with positive, Lipschitz continuous coefficients, which are constant outside a bounded region. Under the assumption of compact support of the…
Experiments and numerical simulations reveal that in the forward cascade regime, the energy spectrum of two-dimensional turbulence with Ekman friction deviates from Kraichnan's prediction of $k^{-3}$ power spectrum. In this letter we…
Differential energy structure of a micro multi-charged-particle system and the beam internal potential energy is derived with consequent property and ecessary inference. Then by combining the energy differential structure with differential…
It is well known that although the group velocity of structured light pulses propagating in vacuum can be subluminal or superluminal, the upper limit of the energy flow velocity is c, the speed of light in vacuum. This inequality can be…
We investigate the energy growth and dissipation of wind-forced breaking waves at high wind speed using direct numerical simulations of the coupled air-water Navier-Stokes equations. A turbulent wind boundary layer drives the growth of a…
Lattice-based string formation algorithms can, at least in principle, be reduced to the study of the statistics of the corresponding aperiodic random walk. Since in three or more dimensions such walks are transient this approach necessarily…
In this paper, using Pao's conjecture [Y.-H. Pao, Phys. Fluids 11, 1371 (1968)], we derive expressions for the spectra and fluxes of kinetic energy and enstrophy for two-dimensional (2D) forced turbulence that extend beyond the inertial…
In this paper we study the Cauchy problem for doubly dissipative elastic waves in two space dimensions, where the damping terms consist of two different friction or structural damping. We derive energy estimates and diffusion phenomena with…
In this paper, a multi-dimensional fractional wave equation that describes propagation of the damped waves is introduced and analyzed. In contrast to the fractional diffusion-wave equation, the fractional wave equation contains fractional…
We propose a model for frequency-dependent damping in the linear wave equation. After proving well-posedness of the problem, we study qualitative properties of the energy. In the one-dimensional case, we provide an explicit analysis for…