Moment Inequalities and High-Energy Tails for Boltzmann Equations with Inelastic Interactions

Journal of Statistical Physics - We study high-energy asymptotics of the steady velocity distributions for model kinetic equations describing various regimes in dilute granular flows. The main...     

Analogs of the Luzin-Danzhu and Cantor-Lebesgue theorems for double trigonometric series

Let ∥ · ∥ be some norm in R², Γ be the unit sphere induced in R² by this norm, and {Aj} a sequence of disjoint subsets of R₊ such that if ν ε A_j, then ν · Γ ∩ Z^N ≠ Ø. For series of the form $$\sum\nolimits_{j = 1}^\infty {} \sum\nolimits_{\parallel n\parallel \in A_j } {c_n e^{2\pi _i (n_1 x_1 + n_2 x_2 )} } $$ analogs of the Luzin-Danzhu and Cantor-Lebesgue theorems are established.     

Stresses in elastic conical tubes of transversely isotropic materials with spherical anisotropies under temperature and force loadings

Analytic solutions are proposed for a number of new problems on determining the state of stress of a transversely-isotropic hollow cone with spherical anisotropy. An exact solution of the problem of the axisymmetric deformation of a long conical tube (or continuous cone) from an elastic transversely-isotropic material with spherical anisotropy subjected to an axial force is obtained in a spherical coordinate system R, , θ, the material axis of symmetry is directed along the spherical radius R. A rigorous solution is given of the problem of the uniform heating of a conical tube of transversely-isotropic material with spherical anisotropy for particular values of Poisson's ratios; the material axis of symmetry is directed along the θ-axis. For arbitrary Poisson's ratios an asymptotic solution is found for the temperature problem for a tube with small conicity.     

Lifetime and relaxation processes in solid polymers

The relationship between relaxation processes and the fracture of solid polymers is examined with reference to the example of repeat loading with recovery. An investigation of polymethyl methacrylate, KAST-V glass laminate, and a Finnish polyester glass-reinforced plastic has shown that this lifetime may be considerably (several orders) shorter than that at the same level of constant stress. This is attributed to the time dependence of the structure-sensitive coefficient in the lifetime equation and is illustrated by means of a model that includes a Regel' fracture element.Moscow Lenin State Pedagogical Institute, Problem Laboratory of Polymer Physics. Translated from Mekhanika Polimerov, No. 4, pp. 629–635, July–August, 1969.     

Electrophoresis-Assisted Multilayer Assembly of Nanoparticles for Sensitive Lateral Flow Immunoassay**

Lateral flow immunoassay (LFIA) is a rapid, simple, and inexpensive point-of-need method. A major limitation of LFIA is a high limit of detection (LOD), which impacts its diagnostic sensitivity. To overcome this limitation, we introduce a signal-enhancement procedure that is performed after completing LFIA and involves controllably moving biotin- and streptavidin-functionalized gold nanoparticles by electrophoresis. The nanoparticles link to immunocomplexes forming multilayer aggregates on the test strip, thus, enhancing the signal. Here, we demonstrate lowering the LOD of hepatitis B surface antigen from approximately 8 to 0.12 ng mL⁻¹, making it clinically acceptable. Testing 118 clinical samples for hepatitis B showed that signal enhancement increased the diagnostic sensitivity of LFIA from 73 % to 98 % while not affecting its 95 % specificity. Electrophoresis-driven enhancement of LFIA is universal (antigen-independent), takes two minutes, and can be performed by an untrained person.     

The complex three-dimensional elastoplastic bending of a rod with a square cross-section

The complex three-dimensional bending of a long rod (with square cross-section) made of an isotropic ideally plastic and ideally cyclical material is investigated. The bending of the rod occurs due to the action of two moments, applied to its ends in such a way that the longitudinal deformation of the middle fibres of two neighbouring sides is described by a dashed line.     

Strong solutions of the Boltzmann equation in one spatial dimension

For the Boltzmann equation, the setting of a narrow shock tube implies that solutions $f(x,v,t)$ depend upon $v\in {\mathbb{R}}^3$, however they have one-dimensional spatial dependence. This Note discusses the case in which solutions are periodic in x, with controlled total energy and entropy, and such that the macroscopic density determined by the initial data is bounded. Our principal result is that the macroscopic density then remains bounded at all subsequent times, that is, this data gives rise to strong solutions which exist globally in time. Through a weak/strong uniqueness principle, these solutions are unique among the class of dissipative solutions. Additionally, we show that the flow of the Boltzmann equation propagates the moments in $v\in {\mathbb{R}}^3$ and derivatives in both $x_1\in {\mathbb{R}}^1$ and $v\in {\mathbb{R}}^3$ of the solution $f(x,v,t)$. Our main theorems are valid for Boltzmann collision kernels which are bounded, and which have a relative velocity cutoff. The proofs depend upon a new averaging property of the collision operator and integral inequalities based in turn on entropy and on the Bony functional. To cite this article: A. Biryuk et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

A new consistent discrete‐velocity model for the Boltzmann equation

This paper discusses the convergence of a new discrete‐velocity model to the Boltzmann equation. First the consistency of the collision integral approximation is proved. Based on this we prove the convergence of solutions for a modified model to renormalized solutions of the Boltzmann equation. In a numerical example, the solutions to the discrete problems are compared with the exact solution of the Boltzmann equation in the space‐homogeneous case. Copyright © 2002 John Wiley & Sons, Ltd.