7,445 research outputs found
Two-component {CH} system: Inverse Scattering, Peakons and Geometry
An inverse scattering transform method corresponding to a Riemann-Hilbert
problem is formulated for CH2, the two-component generalization of the
Camassa-Holm (CH) equation. As an illustration of the method, the multi -
soliton solutions corresponding to the reflectionless potentials are
constructed in terms of the scattering data for CH2.Comment: 22 pages, 3 figures, draft, please send comment
Induced activation in accelerator components
The residual activity induced in particle accelerators is a serious issue from the point of view of radiation safety as the long-lived radionuclides produced by fast or moderated neutrons and impact protons cause problems of radiation exposure for staff involved in the maintenance work and when decommissioning the facility. This paper presents activation studies of the magnets and collimators in the High Energy Beam Transport line of the European Spallation Source due to the backscattered neutrons from the target and also due to the direct proton interactions and their secondaries. An estimate of the radionuclide inventory and induced activation are predicted using the GEANT4 code
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
Nanomechanics of a magnetic shuttle device
We show that self sustained mechanical vibrations in a model magnetic shuttle device can be driven by both the charge and the spin accumulated on the movable central island of the device. Different scenarios for how spin- and charge-induced shuttle instabilities may develop are discussed and shown to depend on whether there is a Coulomb blockade of tunneling or not. The crucial role of electronic spin flips in a magnetically driven shuttle is established and shown to cause giant magnetoresistance and dynamic magnetostriction effects
Coupling of nitrogen-vacancy centers in diamond to a GaP waveguide
The optical coupling of guided modes in a GaP waveguide to nitrogen-vacancy
(NV) centers in diamond is demonstrated. The electric field penetration into
diamond and the loss of the guided mode are measured. The results indicate that
the GaP-diamond system could be useful for realizing coupled microcavity-NV
devices for quantum information processing in diamond.Comment: 4 pages 4 figure
An Integrable Shallow Water Equation with Linear and Nonlinear Dispersion
We study a class of 1+1 quadratically nonlinear water wave equations that
combines the linear dispersion of the Korteweg-deVries (KdV) equation with the
nonlinear/nonlocal dispersion of the Camassa-Holm (CH) equation, yet still
preserves integrability via the inverse scattering transform (IST) method.
This IST-integrable class of equations contains both the KdV equation and the
CH equation as limiting cases. It arises as the compatibility condition for a
second order isospectral eigenvalue problem and a first order equation for the
evolution of its eigenfunctions. This integrable equation is shown to be a
shallow water wave equation derived by asymptotic expansion at one order higher
approximation than KdV. We compare its traveling wave solutions to KdV
solitons.Comment: 4 pages, no figure
A note on multi-dimensional Camassa-Holm type systems on the torus
We present a -component nonlinear evolutionary PDE which includes the
-dimensional versions of the Camassa-Holm and the Hunter-Saxton systems as
well as their partially averaged variations. Our goal is to apply Arnold's
[V.I. Arnold, Sur la g\'eom\'etrie diff\'erentielle des groupes de Lie de
dimension infinie et ses applications \`a l'hydrodynamique des fluides
parfaits. Ann. Inst. Fourier (Grenoble) 16 (1966) 319-361], [D.G. Ebin and J.E.
Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid.
Ann. of Math. 92(2) (1970) 102-163] geometric formalism to this general
equation in order to obtain results on well-posedness, conservation laws or
stability of its solutions. Following the line of arguments of the paper [M.
Kohlmann, The two-dimensional periodic -equation on the diffeomorphism group
of the torus. J. Phys. A.: Math. Theor. 44 (2011) 465205 (17 pp.)] we present
geometric aspects of a two-dimensional periodic --equation on the
diffeomorphism group of the torus in this context.Comment: 14 page
Selective decay by Casimir dissipation in fluids
The problem of parameterizing the interactions of larger scales and smaller
scales in fluid flows is addressed by considering a property of two-dimensional
incompressible turbulence. The property we consider is selective decay, in
which a Casimir of the ideal formulation (enstrophy in 2D flows, helicity in 3D
flows) decays in time, while the energy stays essentially constant. This paper
introduces a mechanism that produces selective decay by enforcing Casimir
dissipation in fluid dynamics. This mechanism turns out to be related in
certain cases to the numerical method of anticipated vorticity discussed in
\cite{SaBa1981,SaBa1985}. Several examples are given and a general theory of
selective decay is developed that uses the Lie-Poisson structure of the ideal
theory. A scale-selection operator allows the resulting modifications of the
fluid motion equations to be interpreted in several examples as parameterizing
the nonlinear, dynamical interactions between disparate scales. The type of
modified fluid equation systems derived here may be useful in modelling
turbulent geophysical flows where it is computationally prohibitive to rely on
the slower, indirect effects of a realistic viscosity, such as in large-scale,
coherent, oceanic flows interacting with much smaller eddies
Integrable discretizations of some cases of the rigid body dynamics
A heavy top with a fixed point and a rigid body in an ideal fluid are
important examples of Hamiltonian systems on a dual to the semidirect product
Lie algebra . We give a Lagrangian derivation of
the corresponding equations of motion, and introduce discrete time analogs of
two integrable cases of these systems: the Lagrange top and the Clebsch case,
respectively. The construction of discretizations is based on the discrete time
Lagrangian mechanics on Lie groups, accompanied by the discrete time Lagrangian
reduction. The resulting explicit maps on are Poisson with respect to
the Lie--Poisson bracket, and are also completely integrable. Lax
representations of these maps are also found.Comment: arXiv version is already officia
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