1,904 research outputs found
Skyrmion on a three--cylinder
The class of static, spherically symmetric, and finite energy hedgehog
solutions in the SU(2) Skyrme model is examined on a metric three-cylinder. The
exact analytic shape function of the 1-Skyrmion is found. It can be expressed
via elliptic integrals. Its energy is calculated, and its stability with
respect to radial and spherically symmetric deformations is analyzed. No other
topologically nontrivial solutions belonging to this class are possible on the
three-cylinder.Comment: v2: version accepted for publication in Phys. Rev.
Linear and multiplicative 2-forms
We study the relationship between multiplicative 2-forms on Lie groupoids and
linear 2-forms on Lie algebroids, which leads to a new approach to the
infinitesimal description of multiplicative 2-forms and to the integration of
twisted Dirac manifolds.Comment: to appear in Letters in Mathematical Physic
Exact Solutions of a Model for Granular Avalanches
We present exact solutions of the non-linear {\sc bcre} model for granular
avalanches without diffusion. We assume a generic sandpile profile consisting
of two regions of constant but different slope. Our solution is constructed in
terms of characteristic curves from which several novel predictions for
experiments on avalanches are deduced: Analytical results are given for the
shock condition, shock coordinates, universal quantities at the shock, slope
relaxation at large times, velocities of the active region and of the sandpile
profile.Comment: 7 pages, 2 figure
On the Green-Functions of the classical offshell electrodynamics under the manifestly covariant relativistic dynamics of Stueckelberg
In previous paper derivations of the Green function have been given for 5D
off-shell electrodynamics in the framework of the manifestly covariant
relativistic dynamics of Stueckelberg (with invariant evolution parameter
). In this paper, we reconcile these derivations resulting in different
explicit forms, and relate our results to the conventional fundamental
solutions of linear 5D wave equations published in the mathematical literature.
We give physical arguments for the choice of the Green function retarded in the
fifth variable .Comment: 16 pages, 1 figur
Locating Boosted Kerr and Schwarzschild Apparent Horizons
We describe a finite-difference method for locating apparent horizons and
illustrate its capabilities on boosted Kerr and Schwarzschild black holes. Our
model spacetime is given by the Kerr-Schild metric. We apply a Lorentz boost to
this spacetime metric and then carry out a 3+1 decomposition. The result is a
slicing of Kerr/Schwarzschild in which the black hole is propagated and Lorentz
contracted. We show that our method can locate distorted apparent horizons
efficiently and accurately.Comment: Submitted to Physical Review D. 12 pages and 22 figure
Non-equilibrium thermodynamics. IV: Generalization of Maxwell, Claussius-Clapeyron and Response Functions Relations, and the Prigogine-Defay Ratio for Systems in Internal Equilibrium
We follow the consequences of internal equilibrium in non-equilibrium systems
that has been introduced recently [Phys. Rev. E 81, 051130 (2010)] to obtain
the generalization of Maxwell's relation and the Clausius-Clapeyron relation
that are normally given for equilibrium systems. The use of Jacobians allow for
a more compact way to address the generalized Maxwell relations; the latter are
available for any number of internal variables. The Clausius-Clapeyron relation
in the subspace of observables show not only the non-equilibrium modification
but also the modification due to internal variables that play a dominant role
in glasses. Real systems do not directly turn into glasses (GL) that are frozen
structures from the supercooled liquid state L; there is an intermediate state
(gL) where the internal variables are not frozen. Thus, there is no single
glass transition. A system possess several kinds of glass transitions, some
conventional (L \rightarrow gL; gL\rightarrow GL) in which the state change
continuously and the transition mimics a continuous or second order transition,
and some apparent (L\rightarrow gL; L\rightarrow GL) in which the free energies
are discontinuous so that the transition appears as a zeroth order transition,
as discussed in the text. We evaluate the Prigogine-Defay ratio {\Pi} in the
subspace of the observables at these transitions. We find that it is normally
different from 1, except at the conventional transition L\rightarrow gL, where
{\Pi}=1 regardless of the number of internal variables.Comment: 42 pages, 3 figures, citations correcte
Effective capillary interaction of spherical particles at fluid interfaces
We present a detailed analysis of the effective force between two smooth
spherical colloids floating at a fluid interface due to deformations of the
interface. The results hold in general and are applicable independently of the
source of the deformation provided the capillary deformations are small so that
a superposition approximation for the deformations is valid. We conclude that
an effective long--ranged attraction is possible if the net force on the system
does not vanish. Otherwise, the interaction is short--ranged and cannot be
computed reliably based on the superposition approximation. As an application,
we consider the case of like--charged, smooth nanoparticles and
electrostatically induced capillary deformation. The resulting long--ranged
capillary attraction can be easily tuned by a relatively small external
electrostatic field, but it cannot explain recent experimental observations of
attraction if these experimental systems were indeed isolated.Comment: 23 page
Statistical Mechanics of Quantum-Classical Systems with Holonomic Constraints
The statistical mechanics of quantum-classical systems with holonomic
constraints is formulated rigorously by unifying the classical Dirac bracket
and the quantum-classical bracket in matrix form.
The resulting Dirac quantum-classical theory, which conserves the holonomic
constraints exactly, is then used to formulate time evolution and statistical
mechanics. The correct momentum-jump approximation for constrained system
arises naturally from this formalism. Finally, in analogy with what was found
in the classical case, it is shown that the rigorous linear response function
of constrained quantum-classical systems contains non-trivial additional terms
which are absent in the response of unconstrained systems.Comment: Submitted to Journal of Chemical Physic
Structure characterization of hard sphere packings in amorphous and crystalline states
The channel size distribution in hard sphere systems, based on the local
neighbor correlation of four particle positions, is investigated for all volume
fractions up to jamming. For each particle, all three particle combinations of
neighbors define channels, which are relevant for the concept of caging. The
analysis of the channel size distribution is shown to be very useful in
distinguishing between gaseous, liquid, partially and fully crystallized, and
glassy (random) jammed states. A common microstructural feature of four
coplanar particles is observed in crystalline and glassy jammed states,
suggesting the presence of "hidden" two-dimensional order in three-dimensional
random close packings.Comment: 5 pages, 5 figure
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