9,058 research outputs found
Variational Principles for Lagrangian Averaged Fluid Dynamics
The Lagrangian average (LA) of the ideal fluid equations preserves their
transport structure. This transport structure is responsible for the Kelvin
circulation theorem of the LA flow and, hence, for its convection of potential
vorticity and its conservation of helicity.
Lagrangian averaging also preserves the Euler-Poincar\'e (EP) variational
framework that implies the LA fluid equations. This is expressed in the
Lagrangian-averaged Euler-Poincar\'e (LAEP) theorem proven here and illustrated
for the Lagrangian average Euler (LAE) equations.Comment: 23 pages, 3 figure
Ground state of two unlike charged colloids: An analogy with ionic bonding
In this letter, we study the ground state of two spherical macroions of
identical radius, but asymmetric bare charge ((Q_{A}>Q_{B})). Electroneutrality
of the system is insured by the presence of the surrounding divalent
counterions. Using Molecular Dynamics simulations within the framework of the
primitive model, we show that the ground state of such a system consists of an
overcharged and an undercharged colloid. For a given macroion separation the
stability of these ionized-like states is a function of the difference
((\sqrt{N_{A}}-\sqrt{N_{B}})) of neutralizing counterions (N_{A}) and (N_{B}).
Furthermore the degree of ionization, or equivalently, the degree of
overcharging, is also governed by the distance separation of the macroions. The
natural analogy with ionic bonding is briefly discussed.Comment: published versio
Spatiotemporal patterns and agro-ecological risk factors for cutaneous and renal glomerular vasculopathy (Alabama Rot) in dogs in the UK
Seasonal outbreaks of cutaneous and renal glomerular vasculopathy (CRGV) have been reported annually in UK dogs since 2012, yet the aetiology of the disease remains unknown. The objectives of this study were to explore whether any breeds had an increased or decreased risk of being diagnosed with CRGV, and to report on age and sex distributions of CRGV cases occurring in the UK. Multivariable logistic regression was used to compare 101 dogs diagnosed with CRGV between November 2012 and May 2017 with a denominator population of 446,453 dogs from the VetCompass database. Two Kennel Club breed groups—hounds (odds ratio (OR) 10.68) and gun dogs (OR 9.69)—had the highest risk of being diagnosed with CRGV compared with terriers, while toy dogs were absent from among CRGV cases. Females were more likely to be diagnosed with CRGV (OR 1.51) as were neutered dogs (OR 3.36). As well as helping veterinarians develop an index of suspicion for the disease, better understanding of the signalment risk factors may assist in the development of causal models for CRGV and help identify the aetiology of the disease
An integrable shallow water equation with peaked solitons
We derive a new completely integrable dispersive shallow water equation that
is biHamiltonian and thus possesses an infinite number of conservation laws in
involution. The equation is obtained by using an asymptotic expansion directly
in the Hamiltonian for Euler's equations in the shallow water regime. The
soliton solution for this equation has a limiting form that has a discontinuity
in the first derivative at its peak.Comment: LaTeX file. Figure available from authors upon reques
Signalment risk factors for cutaneous and renal glomerular vasculopathy (Alabama rot) in dogs in the UK
Seasonal outbreaks of cutaneous and renal glomerular vasculopathy (CRGV) have been reported annually in UK dogs since 2012, yet the aetiology of the disease remains unknown. The objectives of this study were to explore whether any breeds had an increased or decreased risk of being diagnosed with CRGV, and to report on age and sex distributions of CRGV cases occurring in the UK. Multivariable logistic regression was used to compare 101 dogs diagnosed with CRGV between November 2012 and May 2017 with a denominator population of 446,453 dogs from the VetCompass database. Two Kennel Club breed groups—hounds (odds ratio (OR) 10.68) and gun dogs (OR 9.69)—had the highest risk of being diagnosed with CRGV compared with terriers, while toy dogs were absent from among CRGV cases. Females were more likely to be diagnosed with CRGV (OR 1.51) as were neutered dogs (OR 3.36). As well as helping veterinarians develop an index of suspicion for the disease, better understanding of the signalment risk factors may assist in the development of causal models for CRGV and help identify the aetiology of the disease
Equilibrium solutions of the shallow water equations
A statistical method for calculating equilibrium solutions of the shallow
water equations, a model of essentially 2-d fluid flow with a free surface, is
described. The model contains a competing acoustic turbulent {\it direct}
energy cascade, and a 2-d turbulent {\it inverse} energy cascade. It is shown,
nonetheless that, just as in the corresponding theory of the inviscid Euler
equation, the infinite number of conserved quantities constrain the flow
sufficiently to produce nontrivial large-scale vortex structures which are
solutions to a set of explicitly derived coupled nonlinear partial differential
equations.Comment: 4 pages, no figures. Submitted to Physical Review Letter
Effects of electromagnetic waves on the electrical properties of contacts between grains
A DC electrical current is injected through a chain of metallic beads. The
electrical resistances of each bead-bead contacts are measured. At low current,
the distribution of these resistances is large and log-normal. At high enough
current, the resistance distribution becomes sharp and Gaussian due to the
creation of microweldings between some beads. The action of nearby
electromagnetic waves (sparks) on the electrical conductivity of the chain is
also studied. The spark effect is to lower the resistance values of the more
resistive contacts, the best conductive ones remaining unaffected by the spark
production. The spark is able to induce through the chain a current enough to
create microweldings between some beads. This explains why the electrical
resistance of a granular medium is so sensitive to the electromagnetic waves
produced in its vicinity.Comment: 4 pages, 5 figure
Lagrangian analysis of alignment dynamics for isentropic compressible magnetohydrodynamics
After a review of the isentropic compressible magnetohydrodynamics (ICMHD)
equations, a quaternionic framework for studying the alignment dynamics of a
general fluid flow is explained and applied to the ICMHD equations.Comment: 12 pages, 2 figures, submitted to a Focus Issue of New Journal of
Physics on "Magnetohydrodynamics and the Dynamo Problem" J-F Pinton, A
Pouquet, E Dormy and S Cowley, editor
Colloidal electrophoresis: Scaling analysis, Green-Kubo relation, and numerical results
We consider electrophoresis of a single charged colloidal particle in a
finite box with periodic boundary conditions, where added counterions and salt
ions ensure charge neutrality. A systematic rescaling of the electrokinetic
equations allows us to identify a minimum set of suitable dimensionless
parameters, which, within this theoretical framework, determine the reduced
electrophoretic mobility. It turns out that the salt-free case can, on the Mean
Field level, be described in terms of just three parameters. A fourth
parameter, which had previously been identified on the basis of straightforward
dimensional analysis, can only be important beyond Mean Field. More complicated
behavior is expected to arise when further ionic species are added. However,
for a certain parameter regime, we can demonstrate that the salt-free case can
be mapped onto a corresponding system containing additional salt. The
Green-Kubo formula for the electrophoretic mobility is derived, and its
usefulness demonstrated by simulation data. Finally, we report on
finite-element solutions of the electrokinetic equations, using the commercial
software package COMSOL.Comment: To appear in Journal of Physics: Condensed Matter - special issue on
occasion of the CODEF 2008 conferenc
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