Warm turbulence in the Boltzmann equation

We study the single-particle distributions of three-dimensional hard sphere gas described by the Boltzmann equation. We focus on the steady homogeneous isotropic solutions in thermodynamically open conditions, i.e. in the presence of forcing and dissipation. We observe nonequilibrium steady state solution characterized by a warm turbulence, that is an energy and particle cascade superimposed on the Maxwell-Boltzmann distribution. We use a dimensional analysis approach to relate the thermodynamic quantities of the steady state with the characteristics of the forcing and dissipation terms. In particular, we present an analytical prediction for the temperature of the system which we show to be dependent only on the forcing and dissipative scales. Numerical simulations of the Boltzmann equation support our analytical predictions.Comment: 4 pages, 5 figure

Quadratic invariants for discrete clusters of weakly interacting waves

We consider discrete clusters of quasi-resonant triads arising from a Hamiltonian three-wave equation. A cluster consists of N modes forming a total of M connected triads. We investigate the problem of constructing a functionally independent set of quadratic constants of motion. We show that this problem is equivalent to an underlying basic linear problem, consisting of finding the null space of a rectangular M × N matrix with entries 1, −1 and 0. In particular, we prove that the number of independent quadratic invariants is equal to J ≡ N − M* ≥ N − M, where M* is the number of linearly independent rows in Thus, the problem of finding all independent quadratic invariants is reduced to a linear algebra problem in the Hamiltonian case. We establish that the properties of the quadratic invariants (e.g., locality) are related to the topological properties of the clusters (e.g., types of linkage). To do so, we formulate an algorithm for decomposing large clusters into smaller ones and show how various invariants are related to certain parts of a cluster, including the basic structures leading to M* < M. We illustrate our findings by presenting examples from the Charney–Hasegawa–Mima wave model, and by showing a classification of small (up to three-triad) clusters

The Kelvin-wave cascade in the vortex filament model

The energy transfer mechanism in zero temperature superfluid turbulence of helium-4 is still a widely debated topic. Currently, the main hypothesis is that weakly nonlinear interacting Kelvin waves transfer energy to sufficiently small scales such that energy is dissipated as heat via phonon excitations. Theoretically, there are at least two proposed theories for Kelvin-wave interactions. We perform the most comprehensive numerical simulation of weakly nonlinear interacting Kelvin-waves to date and show, using a specially designed numerical algorithm incorporating the full Biot-Savart equation, that our results are consistent with nonlocal six-wave Kelvin wave interactions as proposed by L'vov and Nazarenko.Comment: 6 pages, 6 figure

Competition Between Stripes and Pairing in a t-t'-J Model

As the number of legs n of an n-leg, t-J ladder increases, density matrix renormalization group calculations have shown that the doped state tends to be characterized by a static array of domain walls and that pairing correlations are suppressed. Here we present results for a t-t'-J model in which a diagonal, single particle, next-near-neighbor hopping t' is introduced. We find that this can suppress the formation of stripes and, for t' positive, enhance the d_{x^2-y^2}-like pairing correlations. The effect of t' > 0 is to cause the stripes to evaporate into pairs and for t' < 0 to evaporate into quasi-particles. Results for n=4 and 6-leg ladders are discussed.Comment: Four pages, four encapsulated figure

Differential approximation for Kelvin-wave turbulence

I present a nonlinear differential equation model (DAM) for the spectrum of Kelvin waves on a thin vortex filament. This model preserves the original scaling of the six-wave kinetic equation, its direct and inverse cascade solutions, as well as the thermodynamic equilibrium spectra. Further, I extend DAM to include the effect of sound radiation by Kelvin waves. I show that, because of the phonon radiation, the turbulence spectrum ends at a maximum frequency $\omega^* \sim (\epsilon^3 c_s^{20} / \kappa^{16})^{1/13}$ where $\epsilon$ is the total energy injection rate, $c_s$ is the speed of sound and $\kappa$ is the quantum of circulation.Comment: Prepared of publication in JETP Letter

Effect of electron beam irradiation on thermal and mechanical properties of epoxy polymer

This study investigates the thermal and mechanical properties of epoxy polymer after exposure to different doses of electron beam irradiation. The epoxy polymer was prepared using epoxy-diane resin ED-20 cured by polyethylenepolyamine. The irradiation of the samples was carried out with doses of 30, 100 and 300 kGy. The effects of doses on thermal and mechanical properties of the epoxy polymer were investigated by the methods of thermal gravimetric analysis, tensile test, and dynamic mechanical analysis. The thermal properties of the epoxy polymer slightly increased after irradiation at the heating in air. The tensile strength and Young's modulus of the epoxy polymer increased by the action of electron beam up to dose of 100 kGy and then decreased. The elongation at break decreased with increasing the irradiation dose

Surface alignment and anchoring transitions in nematic lyotropic chromonic liquid crystal

The surface alignment of lyotropic chromonic liquid crystals (LCLCs) can be not only planar (tangential) but also homeotropic, with self-assembled aggregates perpendicular to the substrate, as demonstrated by mapping optical retardation and by three-dimensional imaging of the director field. With time, the homeotropic nematic undergoes a transition into a tangential state. The anchoring transition is discontinuous and can be described by a double-well anchoring potential with two minima corresponding to tangential and homeotropic orientation.Comment: Accepted for publication in Phys. Rev. Lett. (Accepted Wednesday Jun 02, 2010

Effect of electron beam irradiation on thermal and mechanical properties of epoxy polymer

This study investigates the thermal and mechanical properties of epoxy polymer after exposure to different doses of electron beam irradiation. The epoxy polymer was prepared using epoxy-diane resin ED-20 cured by polyethylenepolyamine. The irradiation of the samples was carried out with doses of 30, 100 and 300 kGy. The effects of doses on thermal and mechanical properties of the epoxy polymer were investigated by the methods of thermal gravimetric analysis, tensile test, and dynamic mechanical analysis. The thermal properties of the epoxy polymer slightly increased after irradiation at the heating in air. The tensile strength and Young's modulus of the epoxy polymer increased by the action of electron beam up to dose of 100 kGy and then decreased. The elongation at break decreased with increasing the irradiation dose