14,650 research outputs found
The free rigid body dynamics: generalized versus classic
In this paper we analyze the normal forms of a general quadratic Hamiltonian
system defined on the dual of the Lie algebra of real -
skew - symmetric matrices, where is an arbitrary real symmetric
matrix. A consequence of the main results is that any first-order autonomous
three-dimensional differential equation possessing two independent quadratic
constants of motion which admits a positive/negative definite linear
combination, is affinely equivalent to the classical "relaxed" free rigid body
dynamics with linear controls.Comment: 12 page
Kinetic and ion pairing contributions in the dielectric spectra of electrolyte aqueous solutions
Understanding dielectric spectra can reveal important information about the
dynamics of solvents and solutes from the dipolar relaxation times down to
electronic ones. In the late 1970s, Hubbard and Onsager predicted that adding
salt ions to a polar solution would result in a reduced dielectric permittivity
that arises from the unexpected tendency of solvent dipoles to align opposite
to the applied field. So far, this effect has escaped an experimental
verification, mainly because of the concomitant appearance of dielectric
saturation from which the Hubbard-Onsager decrement cannot be easily separated.
Here we develop a novel non-equilibrium molecular dynamics simulation approach
to determine this decrement accurately for the first time. Using a
thermodynamic consistent all-atom force field we show that for an aqueous
solution containing sodium chloride around 4.8 Mol/l, this effect accounts for
12\% of the total dielectric permittivity. The dielectric decrement can be
strikingly different if a less accurate force field for the ions is used. Using
the widespread GROMOS parameters, we observe in fact an {\it increment} of the
dielectric permittivity rather than a decrement. We can show that this
increment is caused by ion pairing, introduced by a too low dispersion force,
and clarify the microscopic connection between long-living ion pairs and the
appearance of specific features in the dielectric spectrum of the solution
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
Complete integrability versus symmetry
The purpose of this article is to show that on an open and dense set,
complete integrability implies the existence of symmetry
Emergent singular solutions of non-local density-magnetization equations in one dimension
We investigate the emergence of singular solutions in a non-local model for a
magnetic system. We study a modified Gilbert-type equation for the
magnetization vector and find that the evolution depends strongly on the length
scales of the non-local effects. We pass to a coupled density-magnetization
model and perform a linear stability analysis, noting the effect of the length
scales of non-locality on the system's stability properties. We carry out
numerical simulations of the coupled system and find that singular solutions
emerge from smooth initial data. The singular solutions represent a collection
of interacting particles (clumpons). By restricting ourselves to the
two-clumpon case, we are reduced to a two-dimensional dynamical system that is
readily analyzed, and thus we classify the different clumpon interactions
possible.Comment: 19 pages, 13 figures. Submitted to Phys. Rev.
Theory and simulations of rigid polyelectrolytes
We present theoretical and numerical studies on stiff, linear
polyelectrolytes within the framework of the cell model. We first review
analytical results obtained on a mean-field Poisson-Boltzmann level, and then
use molecular dynamics simulations to show, under which circumstances these
fail quantitatively and qualitatively. For the hexagonally packed nematic phase
of the polyelectrolytes we compute the osmotic coefficient as a function of
density. In the presence of multivalent counterions it can become negative,
leading to effective attractions. We show that this results from a reduced
contribution of the virial part to the pressure. We compute the osmotic
coefficient and ionic distribution functions from Poisson-Boltzmann theory with
and without a recently proposed correlation correction, and also simulation
results for the case of poly(para-phenylene) and compare it to recently
obtained experimental data on this stiff polyelectrolyte. We also investigate
ion-ion correlations in the strong coupling regime, and compare them to
predictions of the recently advocated Wigner crystal theories.Comment: 32 pages, 15 figures, proceedings of the ASTATPHYS-MEX-2001, to be
published in Mol. Phy
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
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
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