35,823 research outputs found
Universality of Sea Wave Growth and Its Physical Roots
Modern day studies of wind-driven sea waves are usually focused on wind
forcing rather than on the effect of resonant nonlinear wave interactions. The
authors assume that these effects are dominating and propose a simple
relationship between instant wave steepness and time or fetch of wave
development expressed in wave periods or lengths. This law does not contain
wind speed explicitly and relies upon this asymptotic theory. The validity of
this law is illustrated by results of numerical simulations, in situ
measurements of growing wind seas and wind wave tank experiments. The impact of
the new vision of sea wave physics is discussed in the context of conventional
approaches to wave modeling and forecasting.Comment: submitted to Journal of Fluid Mechanics 24-Sep-2014, 34 pages, 10
figure
Resolving the Schwarzschild singularity in both classic and quantum gravity
The Schwarzschild singularity's resolution has key values in cracking the key
mysteries related with black holes, the origin of their horizon entropy and the
information missing puzzle involved in their evaporations. We provide in this
work the general dynamic inner metric of collapsing stars with horizons and
with non-trivial radial mass distributions. We find that static central
singularities are not the final state of the system. Instead, the final state
of the system is a periodically zero-cross breathing ball. Through 3+1
decomposed general relativity and its quantum formulation, we establish a
functional Schr\"odinger equation controlling the micro-state of this breathing
ball and show that, the system configuration with all the matter concentrating
on the central point is not the unique eigen-energy-density solution. Using a
Bohr-Sommerfield like "orbital" quantisation assumption, we show that for each
black hole of horizon radius , there are about
allowable eigen-energy-density profile. This
naturally leads to physic interpretations for the micro-origin of horizon
entropy, as well as solutions to the information missing puzzle involved in
Hawking radiations.Comment: 19 pages, 5 figures, final published versio
Wave envelopes with second-order spatiotemporal dispersion: II. Modulational instabilities and dark Kerr solitons
A simple scalar model for describing spatiotemporal dispersion of pulses, beyond the classic “slowly-varying envelopes + Galilean boost” approach, is studied. The governing equation has a cubic nonlinearity and we focus here mainly on contexts with normal group-velocity dispersion. A complete analysis of continuous waves is reported, including their dispersion relations and modulational instability characteristics. We also present a detailed derivation of exact analytical dark solitons, obtained by combining direct-integration methods with geometrical transformations. Classic results from conventional pulse theory are recovered as-ymptotically from the spatiotemporal formulation. Numerical simulations test new theoretical predictions for modulational instability, and examine the robustness of spatiotemporal dark solitons against perturbations to their local pulse shape
Simulation of flows with violent free surface motion and moving objects using unstructured grids
This is the peer reviewed version of the following article: [Löhner, R. , Yang, C. and Oñate, E. (2007), Simulation of flows with violent free surface motion and moving objects using unstructured grids. Int. J. Numer. Meth. Fluids, 53: 1315-1338. doi:10.1002/fld.1244], which has been published in final form at https://doi.org/10.1002/fld.1244. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.A volume of fluid (VOF) technique has been developed and coupled with an incompressible Euler/Navier–Stokes solver operating on adaptive, unstructured grids to simulate the interactions of extreme waves and three-dimensional structures. The present implementation follows the classic VOF implementation for the liquid–gas system, considering only the liquid phase. Extrapolation algorithms are used to obtain velocities and pressure in the gas region near the free surface. The VOF technique is validated against the classic dam-break problem, as well as series of 2D sloshing experiments and results from SPH calculations. These and a series of other examples demonstrate that the ability of the present approach to simulate violent free surface flows with strong nonlinear behaviour.Peer ReviewedPostprint (author's final draft
On the Localized superluminal Solutions to the Maxwell Equations
In the first part of this article the various experimental sectors of physics
in which Superluminal motions seem to appear are briefly mentioned, after a
sketchy theoretical introduction. In particular, a panoramic view is presented
of the experiments with evanescent waves (and/or tunneling photons), and with
the "Localized superluminal Solutions" (SLS) to the wave equation, like the
so-called X-shaped waves. In the second part of this paper we present a series
of new SLSs to the Maxwell equations, suitable for arbitrary frequencies and
arbitrary bandwidths: some of them being endowed with finite total energy.
Among the others, we set forth an infinite family of generalizations of the
classic X-shaped wave; and show how to deal with the case of a dispersive
medium. Results of this kind may find application in other fields in which an
essential role is played by a wave-equation (like acoustics, seismology,
geophysics, gravitation, elementary particle physics, etc.). This e-print, in
large part a review, was prepared for the special issue on "Nontraditional
Forms of Light" of the IEEE JSTQE (2003); and a preliminary version of it
appeared as Report NSF-ITP-02-93 (KITP, UCSB; 2002). Further material can be
found in the recent e-prints arXiv:0708.1655v2 [physics.gen-ph] and
arXiv:0708.1209v1 [physics.gen-ph]. The case of the very interesting (and more
orthodox, in a sense) subluminal Localized Waves, solutions to the wave
equations, will be dealt with in a coming paper. [Keywords: Wave equation; Wave
propagation; Localized solutions to Maxwell equations; Superluminal waves;
Bessel beams; Limited-dispersion beams; Electromagnetic wavelets; X-shaped
waves; Finite-energy beams; Optics; Electromagnetism; Microwaves; Special
relativity]Comment: LaTeX paper of 37 pages, with 20 Figures in jpg [to be processed by
PDFlatex
Part I. The Cosmological Vacuum from a Topological Perspective
This article examines how the physical presence of field energy and
particulate matter can be interpreted in terms of the topological properties of
space-time. The theory is developed in terms of vector and matrix equations of
exterior differential systems, which are not constrained by tensor
diffeomorphic equivalences. The first postulate defines the field properties (a
vector space continuum) of the Cosmological Vacuum in terms of matrices of
basis functions that map exact differentials into neighborhoods of exterior
differential 1-forms (potentials). The second postulate requires that the field
equations must satisfy the First Law of Thermodynamics dynamically created in
terms of the Lie differential with respect to a process direction field acting
on the exterior differential forms that encode the thermodynamic system. The
vector space of infinitesimals need not be global and its compliment is used to
define particle properties as topological defects embedded in the field vector
space. The potentials, as exterior differential 1-forms, are not (necessarily)
uniquely integrable: the fibers can be twisted, leading to possible Chiral
matrix arrays of certain 3-forms defined as Topological Torsion and Topological
Spin. A significant result demonstrates how the coefficients of Affine Torsion
are related to the concept of Field excitations (mass and charge); another
demonstrates how thermodynamic evolution can describe the emergence of
topological defects in the physical vacuum.Comment: 70 pages, 5 figure
Anisotropic and dispersive wave propagation within strain-gradient framework
In this paper anisotropic and dispersive wave propagation within linear
strain-gradient elasticity is investigated. This analysis reveals significant
features of this extended theory of continuum elasticity. First, and contrarily
to classical elasticity, wave propagation in hexagonal (chiral or achiral)
lattices becomes anisotropic as the frequency increases. Second, since
strain-gradient elasticity is dispersive, group and energy velocities have to
be treated as different quantities. These points are first theoretically
derived, and then numerically experienced on hexagonal chiral and achiral
lattices. The use of a continuum model for the description of the high
frequency behavior of these microstructured materials can be of great interest
in engineering applications, allowing problems with complex geometries to be
more easily treated
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