Related papers: Energy in one dimensional linear waves in a string
We consider the dynamics of vortex strings and sound waves in superfluids in the phenomenological Landau-Ginzburg equation. We first derive the vortex equation where the velocity of a vortex is determined by the average fluid velocity and…
Heat and energy are conceptually different, but often are assumed to be the same without justification. An effective method for investigating diffusion properties in equilibrium systems is discussed. With this method, we demonstrate that…
We present results from a systematic numerical study of structural properties of an unforced, incompressible, homogeneous, and isotropic three-dimensional turbulent fluid with an initial energy spectrum that develops a cascade of kinetic…
The first article in a two-part series (the second article being [arXiv:2205.13197]) assumes a weak local energy decay estimate holds and proves that solutions to the linear wave equation with variable coefficients in $\mathbb R^{1+3}$,…
We prove the existence of small solitary waves for one-dimensional lattices of particles that each repel every other particle with a force that decays as a power of distance. For force exponents $\alpha+1$ with $\frac43<\alpha<3$, we employ…
Key issues of classical and quantum strings in gravitational plane waves, shock waves and spacetime singularities are synthetically understood. This includes the string mass and mode number excitations, energy-momentum tensor, scattering…
We describe an extracurricular learning path on waves focused on energy transfer. The advantages of introducing mechanical waves by using the Shive wave machine and laboratory activities are presented. Laboratories are realized by inquiry,…
We consider wave models with lower order terms and recollect some recent results on energy and dispersive estimates for their solution based on symbolic type estimates for coefficients and partly stabilisation conditions. The exposition is…
We study the propagation of waves in a medium in which the wave velocity fluctuates randomly in time. We prove that at long times, the statistical distribution of the wave energy is log-normal, with the average energy growing exponentially.…
Ocean wave energy is a new renewable energy resource which is going to become one of the reliable and alternative resources for fossil fuels during recent decades. The majority of studies have focused on extract wave energy at an effective…
A single-wavenumber representation of nonlinear energy spectrum, i.e., stretching energy spectrum is found in elastic-wave turbulence governed by the F\"oppl-von K\'arm\'an (FvK) equation. The representation enables energy decomposition…
The paper gives a description of wave propagation in discrete-periodic one-dimensional media with block structure. For one-dimensional problems mathematical models are proposed that describe block structures in the form of a mass chain or…
We investigate the behavior of classical closed strings in a gravitational wave burst and discover an intriguing resonant behavior where the energy absorbed by the strings is crucially dependent on the amplitude and frequency of the…
We study the energy loss of a heavy quark propagating through the matter produced in the collision of two sheets of energy [1]. Even though this matter is initially far-from-equilibrium we find that, when written in terms of the energy…
We obtain systematic approximations for the modes of vibration of a string of variable density, which is held fixed at its ends. These approximations are obtained iteratively applying three theorems which are proved in the paper and which…
We calculate the fluctuations in the current and energy densities for the case of a quantized, minimally coupled, massless, complex scalar field around a straight and infinitesimally thin cosmic string carrying magnetic flux. At zero…
Gravitational wave signatures from cosmic strings are analyzed numerically. Cosmic string networks form during phase transistions in the early universe and these networks of long cosmic strings break into loops that radiate energy in the…
We investigate the diffusive properties of energy fluctuations in a one-dimensional diatomic chain of hard-point particles interacting through a square--well potential. The evolution of initially localized infinitesimal and finite…
Starting from three-dimensional nonlinear elasticity under the restriction of incompressibility, we derive reduced models to capture the behavior of strings in response to external forces. Our $\Gamma$-convergence analysis of the…
A closed-form expression for the amplitudes of source waves in 2D discrete lattice with local and linear (waveguides) defects is derived. The numerical implementation of this analytic expression is demonstrated by several examples.