167,571 research outputs found
Do peaked solitary water waves indeed exist?
Many models of shallow water waves admit peaked solitary waves. However, it
is an open question whether or not the widely accepted peaked solitary waves
can be derived from the fully nonlinear wave equations. In this paper, a
unified wave model (UWM) based on the symmetry and the fully nonlinear wave
equations is put forward for progressive waves with permanent form in finite
water depth. Different from traditional wave models, the flows described by the
UWM are not necessarily irrotational at crest, so that it is more general. The
unified wave model admits not only the traditional progressive waves with
smooth crest, but also a new kind of solitary waves with peaked crest that
include the famous peaked solitary waves given by the Camassa-Holm equation.
Besides, it is proved that Kelvin's theorem still holds everywhere for the
newly found peaked solitary waves. Thus, the UWM unifies, for the first time,
both of the traditional smooth waves and the peaked solitary waves. In other
words, the peaked solitary waves are consistent with the traditional smooth
ones. So, in the frame of inviscid fluid, the peaked solitary waves are as
acceptable and reasonable as the traditional smooth ones. It is found that the
peaked solitary waves have some unusual and unique characteristics. First of
all, they have a peaked crest with a discontinuous vertical velocity at crest.
Especially, the phase speed of the peaked solitary waves has nothing to do with
wave height. In addition, the kinetic energy of the peaked solitary waves
either increases or almost keeps the same from free surface to bottom. All of
these unusual properties show the novelty of the peaked solitary waves,
although it is still an open question whether or not they are reasonable in
physics if the viscosity of fluid and surface tension are considered.Comment: 53 pages, 13 figures, 7 tables. Accepted by Communications in
Nonlinear Science and Numerical Simulatio
Optimization of Renormalization Group Flow
Renormalization group flow equations for scalar lambda Phi^4 are generated
using three classes of smooth smearing functions. Numerical results for the
critical exponent nu in three dimensions are calculated by means of a truncated
series expansion of the blocked potential. We demonstrate how the convergence
of nu as a function of the order of truncation can be improved through a fine
tuning of the smoothness of the smearing functions.Comment: 23 pages, 7 figure
Finding the one-loop soliton solution of the short-pulse equation by means of the homotopy analysis method
The homotopy analysis method is applied to the short-pulse equation in order to find an analytic approximation to the known exact solitary upright-loop solution. It is demonstrated that the approximate solution agrees well with the exact solution. This provides further evidence that the homotopy analysis method is a powerful tool for finding excellent approximations to nonlinear solitary waves
Statistical properties of solutions to the Navier-Stokes equation in the limit of vanishing viscosity
Presents a new approach to the Navier-Stokes turbulence. With the Gaussian soft constraint on the Navier-Stokes equation, the author derives the energy spectrum to be E(k) approximately k^-3 and k^-2 in two and three spatial dimensions respectively. The possible future developments are also pointed out
Book Review: Understanding commercial Law
This article reviews the book: “Understanding commercial Law”, by Philippa Gerbic and Leigh Miller
Hard Probe of Soft Matter Geometry and Fluctuations from RHIC to LHC
We report results on event-by-event hard probe of soft matter geometry and
fluctuations in heavy ion collisions. Geometric data ( of high
hadrons) from RHIC plus LHC clearly favors jet "monography" model with strong
near-Tc enhancement of jet-medium interaction strength which also implies a
less opaque medium at LHC. We also quantify the jet responses to all harmonic
anisotropy () and their manifestation in hard-soft
azimuthal correlations.Comment: 3 pages, 4 figures, contribution to CIPANP2012 Proceeding
Catastrophe and hope : the politics of the ancient capital and The city where the blood-red bat descended
Book Review: Hinde on Commercial Leases
This article reviews the book: “Hinde on Commercial Leases”, by G.W. Hinde
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