455 research outputs found
Quantized representation of some nonlinear integrable evolution equations on the soliton sector
The Hirota algorithm for solving several integrable nonlinear evolution
equations is suggestive of a simple quantized representation of these equations
and their soliton solutions over a Fock space of bosons or of fermions. The
classical nonlinear wave equation becomes a nonlinear equation for an operator.
The solution of this equation is constructed through the operator analog of the
Hirota transformation. The classical N-solitons solution is the expectation
value of the solution operator in an N-particle state in the Fock space.Comment: 12 page
Decomposition driven interface evolution for layers of binary mixtures: I. Model derivation and stratified base states
A dynamical model is proposed to describe the coupled decomposition and
profile evolution of a free surface film of a binary mixture. An example is a
thin film of a polymer blend on a solid substrate undergoing simultaneous phase
separation and dewetting. The model is based on model-H describing the coupled
transport of the mass of one component (convective Cahn-Hilliard equation) and
momentum (Navier-Stokes-Korteweg equations) supplemented by appropriate
boundary conditions at the solid substrate and the free surface.
General transport equations are derived using phenomenological
non-equilibrium thermodynamics for a general non-isothermal setting taking into
account Soret and Dufour effects and interfacial viscosity for the internal
diffuse interface between the two components. Focusing on an isothermal setting
the resulting model is compared to literature results and its base states
corresponding to homogeneous or vertically stratified flat layers are analysed.Comment: Submitted to Physics of Fluid
HI Bright Galaxies in the Southern Zone of Avoidance
A blind survey for HI bright galaxies in the southern Zone of Avoidance, (212
deg < l < 36 deg; |b| < 5 deg), has been made with the 21 cm multibeam receiver
on the Parkes 64 m radiotelescope. The survey, sensitive to normal spiral
galaxies to a distance of about 40 Mpc and more nearby dwarfs, detected 110
galaxies. Of these, 67 have no counterparts in the NASA/IPAC Extragalactic
Database. In general, the uncataloged galaxies lie behind thicker obscuration
than do the cataloged objects. All of the newly-discovered galaxies have HI
flux integrals more than an order of magnitude lower than the Circinus galaxy.
The survey recovers the Puppis cluster and foreground group (Kraan-Korteweg &
Huchtmeier 1992), and the Local Void remains empty. The HI mass function
derived for the sample is satisfactorily fit by a Schechter function with
parameters alpha = 1.51 +- 0.12, Phi* = 0.006 +- 0.003, and log M* = 9.7 +-
0.10.Comment: To appear in The Astronomical Journa
Free Energy Minimizers for a Two--Species Model with Segregation and Liquid-Vapor Transition
We study the coexistence of phases in a two--species model whose free energy
is given by the scaling limit of a system with long range interactions (Kac
potentials) which are attractive between particles of the same species and
repulsive between different species.Comment: 32 pages, 1 fig, plain tex, typeset twic
Two-way FSI modelling of blood flow through CCA accounting on-line medical diagnostics in hypertension
Flow parameters can induce pathological changes in the arteries. We propose a
method to asses those parameters using a 3D computer model of the flow in the Common
Carotid Artery. Input data was acquired using an automatic 2D ultrasound wall tracking
system. This data has been used to generate a 3D geometry of the artery. The diameter and wall
thickness have been assessed individually for every patient, but the artery has been taken as a
75mm straight tube. The Young’s modulus for the arterial walls was calculated using the pulse
pressure, diastolic (minimal) diameter and wall thickness (IMT). Blood flow was derived from
the pressure waveform using a 2-parameter Windkessel model. The blood is assumed to be
non-Newtonian. The computational models were generated and calculated using commercial
code. The coupling method required the use of Arbitrary Lagrangian-Euler formulation to
solve Navier-Stokes and Navier-Lamè equations in a moving domain. The calculations showed
that the distention of the walls in the model is not significantly different from the
measurements. Results from the model have been used to locate additional risk factors, such as
wall shear stress or circumferential stress, that may predict adverse hypertension
complications
Three-dimensional gravity-capillary solitary waves in water of finite depth and related problems
Vector-soliton collision dynamics in nonlinear optical fibers
We consider the interactions of two identical, orthogonally polarized vector
solitons in a nonlinear optical fiber with two polarization directions,
described by a coupled pair of nonlinear Schroedinger equations. We study a
low-dimensional model system of Hamiltonian ODE derived by Ueda and Kath and
also studied by Tan and Yang. We derive a further simplified model which has
similar dynamics but is more amenable to analysis. Sufficiently fast solitons
move by each other without much interaction, but below a critical velocity the
solitons may be captured. In certain bands of initial velocities the solitons
are initially captured, but separate after passing each other twice, a
phenomenon known as the two-bounce or two-pass resonance. We derive an analytic
formula for the critical velocity. Using matched asymptotic expansions for
separatrix crossing, we determine the location of these "resonance windows."
Numerical simulations of the ODE models show they compare quite well with the
asymptotic theory.Comment: 32 pages, submitted to Physical Review
Asymptotic models for the generation of internal waves by a moving ship, and the dead-water phenomenon
This paper deals with the dead-water phenomenon, which occurs when a ship
sails in a stratified fluid, and experiences an important drag due to waves
below the surface. More generally, we study the generation of internal waves by
a disturbance moving at constant speed on top of two layers of fluids of
different densities. Starting from the full Euler equations, we present several
nonlinear asymptotic models, in the long wave regime. These models are
rigorously justified by consistency or convergence results. A careful
theoretical and numerical analysis is then provided, in order to predict the
behavior of the flow and in which situations the dead-water effect appears.Comment: To appear in Nonlinearit
Higher order corrections for shallow-water solitary waves: elementary derivation and experiments
We present an elementary method to obtain the equations of the shallow-water
solitary waves in different orders of approximation. The first two of these
equations are solved to get the shapes and propagation velocities of the
corresponding solitary waves. The first-order equation is shown to be
equivalent to the Korteweg-de Vries (KdV) equation, while the second-order
equation is solved numerically. The propagation velocity found for the solitary
waves of the second-order equation coincides with a known expression, but it is
obtained in a simpler way. By measuring the propagation velocity of solitary
waves in the laboratory, we demonstrate that the second-order theory gives a
considerably improved fit to experimental results.Comment: 15 pages, 8 EPS figures, uses IOP class file for LaTeX2e, slightly
revised versio
Anomalous wave reflection from the interface of two strongly nonlinear granular media
Granular materials exhibit a strongly nonlinear behaviour affecting the
propagation of information in the medium. Dynamically self-organized strongly
nonlinear solitary waves are the main information carriers in granular chains.
Here we report the first experimental observation of the dramatic change of
reflectivity from the interface of two granular media triggered by a noncontact
magnetically induced initial precompression. It may be appropriate to name this
phenomenon the "acoustic diode" effect. Based on numerical simulations, we
explain this effect by the high gradient of particle velocity near the
interface.Comment: 14 pages, 3 figure
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