Theory of elastic interaction between colloidal particles in the nematic cell in the presence of the external electric or magnetic field

The Green function method developed in Ref.[S. B. Chernyshuk and B. I. Lev, Phys. Rev. E \textbf{81}, 041707 (2010)] is used to describe elastic interactions between axially symmetric colloidal particles in the nematic cell in the presence of the external electric or magnetic field. General formulas for dipole-dipole, dipole-quadrupole and quadrupole-quadrupole interactions in the homeotropic and planar nematic cells with parallel and perpendicular field orientations are obtained. A set of new results has been predicted: 1) \textit{Deconfinement effect} for dipole particles in the homeotropic nematic cell with negative dielectric anisotropy $\Delta\epsilon<0$ and perpendicular to the cell electric field, when electric field is approaching it's Frederiks threshold value $E\Rightarrow E_{c}$. This means cancellation of the confinement effect found in Ref. [M.Vilfan et al. Phys.Rev.Lett. {\bf 101}, 237801, (2008)] for dipole particles near the Frederiks transition while it remains for quadrupole particles. 2) New effect of \textit{attraction and stabilization} of the particles along the electric field parallel to the cell planes in the homeotropic nematic cell with $\Delta\epsilon<0$ . The minimun distance between two particles depends on the strength of the field and can be ordinary for . 3) Attraction and repulsion zones for all elastic interactions are changed dramatically under the action of the external field.Comment: 15 pages, 17 figure

Elastic interaction between colloidal particles in confined nematic liquid crystals

The theory of elastic interaction of micron size axially symmetric colloidal particles immersed into confined nematic liquid crystal has been proposed. General formulas are obtained for the self energy of one colloidal particle and interaction energy between two particles in arbitrary confined NLC with strong anchoring condition on the bounding surface. Particular cases of dipole-dipole interaction in the homeotropic and planar nematic cell with thickness $L$ are considered and found to be exponentially screened on far distances with decay length $\lambda_{dd}=\frac{L}{\pi}$. It is predicted that bounding surfaces in the planar cell crucially change the attraction and repulsion zones of usual dipole-dipole interaction. As well it is predicted that \textit{the decay length} in quadrupolar interaction is \textit{two times smaller} than for the dipolar case.Comment: 4 pages,2 figure

Poynting Vector Flow in a Circular Circuit

A circuit is considered in the shape of a ring, with a battery of negligible size and a wire of uniform resistance. A linear charge distribution along the wire maintains an electrostatic field and a steady current, which produces a constant magnetic field. Earlier studies of the Poynting vector and the rate of flow of energy considered only idealized geometries in which the Poynting vector was confined to the space within the circuit. But in more realistic cases the Poynting vector is nonzero outside as well as inside the circuit. An expression is obtained for the Poynting vector in terms of products of integrals, which are evaluated numerically to show the energy flow. Limiting expressions are obtained analytically. It is shown that the total power generated by the battery equals the energy flowing into the wire per unit time.Comment: 19 pages, 8 figure

Peculiarities of the Weyl - Wigner - Moyal formalism for scalar charged particles

A description of scalar charged particles, based on the Feshbach-Villars formalism, is proposed. Particles are described by an object that is a Wigner function in usual coordinates and momenta and a density matrix in the charge variable. It is possible to introduce the usual Wigner function for a large class of dynamical variables. Such an approach explicitly contains a measuring device frame. From our point of view it corresponds to the Copenhagen interpretation of quantum mechanics. It is shown how physical properties of such particles depend on the definition of the coordinate operator. The evolution equation for the Wigner function of a single-charge state in the classical limit coincides with the Liouville equation. Localization peculiarities manifest themselves in specific constraints on possible initial conditions.Comment: 16 pages, 2 figure

Thermal collapse of a granular gas under gravity

Free cooling of a gas of inelastically colliding hard spheres represents a central paradigm of kinetic theory of granular gases. At zero gravity the temperature of a freely cooling homogeneous granular gas follows a power law in time. How does gravity, which brings inhomogeneity, affect the cooling? We combine molecular dynamics simulations, a numerical solution of hydrodynamic equations and an analytic theory to show that a granular gas cooling under gravity undergoes thermal collapse: it cools down to zero temperature and condenses on the bottom of the container in a finite time.Comment: 4 pages, 12 eps figures, to appear in PR

Training-induced criticality in martensites

We propose an explanation for the self-organization towards criticality observed in martensites during the cyclic process known as `training'. The scale-free behavior originates from the interplay between the reversible phase transformation and the concurrent activity of lattice defects. The basis of the model is a continuous dynamical system on a rugged energy landscape, which in the quasi-static limit reduces to a sandpile automaton. We reproduce all the principal observations in thermally driven martensites, including power-law statistics, hysteresis shakedown, asymmetric signal shapes, and correlated disorder.Comment: 5 pages, 4 figure

Space-like and time-like pion electromagnetic form factor and Fock state components within the Light-Front dynamics

The simultaneous investigation of the pion electromagnetic form factor in the space- and time-like regions within a light-front model allows one to address the issue of non-valence components of the pion and photon wave functions. Our relativistic approach is based on a microscopic vector meson dominance (VMD) model for the dressed vertex where a photon decays in a quark-antiquark pair, and on a simple parametrization for the emission or absorption of a pion by a quark. The results show an excellent agreement in the space like region up to -10 $(GeV/c)^2$, while in time-like region the model produces reasonable results up to 10 $(GeV/c)^2$.Comment: 74 pages, 11 figures, use revtex