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Active matter taps into external energy sources to power its own processes. Systems of passive particles ordinarily lack this capacity, but can become active if the constituent particles interact with each other nonreciprocally. By…
We construct the gravitational energy-momentum pseudo-tensor of up to fourth-order conformally invariant theories of gravity. Then we linearize the pseudo-tensor and use its average over a macroscopic region to find the energy and momentum…
Detonation propagation in the limit of highly spatially discretized energy sources is investigated. The model of this problem begins with a medium consisting of a calorically perfect gas with a prescribed energy release per unit mass. The…
This paper is devoted to the stabilization of the incompressible Euler equation with free surface. We study the damping of two-dimensional gravity waves by an absorbing beach where the water-wave energy is dissipated by using the variations…
This paper addresses deep-water gravity waves of finite amplitude generated by an initial disturbance to the water. It is assumed that the horizontal dimensions of the initially disturbed body of the water are much larger than the magnitude…
The equations for waves on the surface of an irrotational incompressible fluid are derived in the coordinates of the velocity potential/stream function. The low frequency shallow water approximation for these waves is derived for a varying…
Effective theory arguments are used to derive the most general energy-momentum tensor of a relativistic viscous fluid with an arbitrary equation of state (in the absence of other conserved currents) that is first-order in the derivatives of…
In this paper we study the existence of global-in-time energy solutions to the Cauchy problem for the Euler-Poisson-Darboux equation, with a power nonlinearity: $$u_{tt}-u_{xx} + \frac\mu{t}\,u_t = |u|^p \,, \quad t>t_0, \…
In these lecture notes we discuss the solution theory of geometric wave equations as they arise in Lorentzian geometry: for a normally hyperbolic differential operator the existence and uniqueness properties of Green functions and Green…
Elastic waves with transverse polarization inside incidence plane can create longitudinal surface wave (LSW) after reflection from a free surface. At a critical incidence angle this LSW accumulates energy density, which can be orders of…
This article investigates the spacetime of two colliding sandwich gravitational waves, focusing on evaluating gravitational energy before and after the collision. In the framework of the Teleparallel Equivalent of General Relativity (TEGR),…
The energy localization hypothesis of the author that energy is localized in non-vanishing regions of the energy-momentum tensor implies that gravitational waves do not carry energy in vacuum. If substantiated, this has significant…
Few rigorous results are derived for fully developed turbulence. By applying the scaling properties of the Navier-Stokes equation we have derived a relation for the energy spectrum valid for unforced or decaying isotropic turbulence. We…
The data of simultaneous measurements of the surface displacement produced by propagating planar waves in experimental flume and of the dynamic pressure beneath the waves are compared with the theoretical predictions based on different…
The present article is the third part of a series of papers devoted to the shallow water wave modelling. In this part, we investigate the derivation of some long wave models on a deformed sphere. We propose first a suitable for our purposes…
This work analyses the homogeneous isotropic turbulence by means of the equivalence between Euler and Lagrange representations of motion, adopting the bifurcation rates associated with Navier--Stokes and kinematic equations, and an…
We find that the energy-momentum tensor of electromagnetic waves in media is very similar to that of ordinary fluids, and concepts such as density, pressure, and energy transfer rate can be similarly defined. On this basis, we conducted a…
Two methods to treat wave breaking in the framework of the Hamiltonian formulation of free-surface potential flow are presented, tested, and validated. The first is an extension of Kennedy et al (2000)'s eddy-viscosity approach originally…
This paper is devoted to the stabilization of the water-wave equations with surface tension through of an external pressure acting on a small part of the free surface. It is proved that the energy decays to zero exponentially in time,…
We derive expressions for the energy, linear momentum, and angular momentum content of circularly polarized Laguerre-Gaussian wave-packets propagating in free space. The vectorial nature of the electromagnetic field is taken into account,…