22,986 research outputs found
Near field of an oscillating electric dipole and cross-polarization of a collimated beam of light: two sides of the same coin
We address the question of whether there exists a hidden relationship between
the near-field distribution generated by an oscillating electric dipole and the
so-called cross polarization of a collimated beam of light. We find that the
answer is affirmative by showing that the complex field distributions occurring
in both cases have a common physical origin: the requirement that the
electromagnetic fields must be transverse
A Variational Principle for Dissipative Fluid Dynamics
In the variational principle leading to the Euler equation for a perfect
fluid, we can use the method of undetermined multiplier for holonomic
constraints representing mass conservation and adiabatic condition. For a
dissipative fluid, the latter condition is replaced by the constraint
specifying how to dissipate. Noting that this constraint is nonholonomic, we
can derive the balance equation of momentum for viscous and viscoelastic fluids
by using a single variational principle. We can also derive the associated
Hamiltonian formulation by regarding the velocity field as the input in the
framework of control theory.Comment: 15 page
Vlasov equation and collisionless hydrodynamics adapted to curved spacetime
The modification of the Vlasov equation, in its standard form describing a
charged particle distribution in the six-dimensional phase space, is derived
explicitly within a formal Hamiltonian approach for arbitrarily curved
spacetime. The equation accounts simultaneously for the Lorentz force and the
effects of general relativity, with the latter appearing as the gravity force
and an additional force due to the extrinsic curvature of spatial
hypersurfaces. For an arbitrary spatial metric, the equations of collisionless
hydrodynamics are also obtained in the usual three-vector form
Modification of Coulomb's law in closed spaces
We obtain a modified version of Coulomb's law in two- and three-dimensional
closed spaces. We demonstrate that in a closed space the total electric charge
must be zero. We also discuss the relation between total charge neutrality of a
isotropic and homogenous universe to whether or not its spatial sector is
closed.Comment: 11 pages, 3 figure
Bichiral structure of feroelectric domain wall driven by flexoelectricity
The influence of flexoelectric coupling on the internal structure of neutral
domain walls in tetragonal phase of perovskite ferroelectrics is studied. The
effect is shown to lower the symmetry of 180-degree walls which are oblique
with respect to the cubic crystallographic axes, while {100} and {110} walls
stay "untouched". Being of the Ising type in the absence of the flexoelectric
interaction, the oblique domain walls acquire a new polarization component with
a structure qualitatively different from the classical Bloch-wall structure. In
contrast to the Bloch-type walls, where the polarization vector draws a helix
on passing from one domain to the other, in the flexoeffect-affected wall, the
polarization rotates in opposite directions on the two sides of the wall and
passes through zero in its center. Since the resulting polarization profile is
invariant upon inversion with respect to the wall center it does not brake the
wall symmetry in contrast to the classical Bloch-type walls. The flexoelectric
coupling lower the domain wall energy and gives rise to its additional
anisotropy that is comparable to that conditioned by the elastic anisotropy.
The atomic orderof- magnitude estimates shows that the new polarization
component P2 may be comparable with spontaneous polarization Ps, thus
suggesting that, in general, the flexoelectric coupling should be mandatory
included in domain wall simulations in ferroelectrics. Calculations performed
for barium titanate yields the maximal value of the P2, which is much smaller
than that of the spontaneous polarization. This smallness is attributed to an
anomalously small value of a component of the "strain-polarization"
elecrostictive tensor in this material
Some remarks about intrinsic parity in Ryder's derivation of the Dirac equation
This work is a comment on Ryder's derivation of the Dirac equation, with
emphasis on the physical contents of this equation: the notion of particles and
antiparticles according to the Stueckelberg-Feynman interpretation, the
opposite intrinsic parity between particles and antiparticles, and the spin.Comment: 4 pages, Revte
Hopf Algebras and Congruence Subgroups
We prove that the kernel of the natural action of the modular group on the
center of the Drinfel'd double of a semisimple Hopf algebra is a congruence
subgroup. To do this, we introduce a class of generalized Frobenius-Schur
indicators and endow it with an action of the modular group that is compatible
with the original one.Comment: 130 pages. Many new results added, remark by D. Nikshych included.
See also http://www.southalabama.edu/mathstat/personal_pages/sommerh
Theory of the Relativistic Brownian Motion. The (1+1)-Dimensional Case
We construct a theory for the 1+1-dimensional Brownian motion in a viscous
medium, which is (i) consistent with Einstein's theory of special relativity,
and (ii) reduces to the standard Brownian motion in the Newtonian limit case.
In the first part of this work the classical Langevin equations of motion,
governing the nonrelativistic dynamics of a free Brownian particle in the
presence of a heat bath (white noise), are generalized in the framework of
special relativity. Subsequently, the corresponding relativistic Langevin
equations are discussed in the context of the generalized Ito (pre-point
discretization rule) vs. the Stratonovich (mid-point discretization rule)
dilemma: It is found that the relativistic Langevin equation in the
Haenggi-Klimontovich interpretation (with the post-point discretization rule)
is the only one that yields agreement with the relativistic Maxwell
distribution. Numerical results for the relativistic Langevin equation of a
free Brownian particle are presented.Comment: see cond-mat/0607082 for an improved theor
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