A semi-inverse shape optimization problem in linear anti-plane shear

The design of a semi-infinite fillet for efficient stress transmission is considered. The problem is treated within the context of anti-plane shear deformations of a homogeneous, isotropic, linearly elastic solid. Under a remote state of simple shear, it is desired to determine the shape of the traction-free lateral boundaries of a symmetric plane domain so that the shear stress distribution on the finite end is as uniform as possible. A semi-inverse approach for a particular class of semi-infinite profiles is used to examine this issue.     

On a principle of virtual work for thermo-elastic bodies

A principle of virtual work is proposed for thermo-elastic bodies. From it are derived the equations of motion, the Cauchy stress principle and the Gibbs relations. The principle is also used to analyse the response of internally constrained bodies.     

On the macroscopic dynamics induced by a model wave-particle collision operator

The macroscopic dynamics of a kinetic equation involving a model wave-particle collision operator of plasma physics is investigated. The Chapman-Enskog asymptotics is first considered in the framework of a hydrodynamic scaling. The obtained macroscopic model still involves a kinetic variable, the particle energy in the rest frame of the fluid, but shares similarities with the compressible Navier-Stokes equation of gas dynamics. Then a diffusive scaling is examined under the hypothesis of small perturbations of a global equilibrium. In this case, the macroscopic model couples the usual incompressible Navier-Stokes with a diffusion equation for the energy distribution function of the particles, constrained by an extended version of the Boussinesq relation. In both cases, the effect of a Lorentz force term is developed, in the perspective of plasma physical modelling. Received June 16, 1997     

Prediction of CL-20 chemical degradation pathways,theoretical and experimental evidence for dependence on competing modes of reaction

Highest occupied and lowest unoccupied molecular orbital energies, formation energies, bond lengths and FTIR spectra all suggest competing CL-20 degradation mechanisms. This second of two studies investigates recalcitrant, toxic, aromatic CL-20 intermediates that absorb from 370 to 430?nm. Our earlier study (Struct. Chem., 15, 2004) revealed that these intermediates were formed at high OH^? concentrations via the chemically preferred pathway of breaking the C–C bond between the two cyclopentanes, thereby eliminating nitro groups, forming conjugated π bonds, and resulting in a pyrazine three-ring aromatic intermediate. In attempting to find and make dominant a more benign CL-20 transformation pathway, this current research validates hydroxylation results from both studies and examines CL-20 transformations via photo-induced free radical reactions. This article discusses CL-20 competing modes of degradation revealed through: computational calculation; UV/VIS and SF spectroscopy following alkaline hydrolysis; and photochemical irradiation to degrade CL-20 and its byproducts at their respective wavelengths of maximum absorption.     

The structure and electronic property of the smallest C20‐glycine and Gd‐encapsulated C20‐glycine derivatives with potentially biological activity

Theoretical calculations on interaction of the C₂₀ fullerene (consists solely by pentagons) with the smallest amino acid (glycine) were carried out using density‐functional theory method. The glycine molecule energetically prefers to interact with the Top‐site on the C₂₀ cage via its amino nitrogen (N) active site. The stable ordering of three active sites on glycine molecule is NH₂‐site > O‐site > OH‐site. Moreover, when the Gd atom is encapsulated to the center of C₂₀‐glycine, the cage volume obviously increase ～24.8%; and the endohedral atom induces the generation of two strong bands in the partial density of states spectra, which could cause the effect on optical properties. Additionally, it is also found that the modified C₂₀‐glycine derivative by Gd atom can reduce the thermodynamic and kinetic stabilities. It could be expected that the study may provide a theoretical reference in exploring their intrinsic feature structurally to antitumor activity. © 2012 Wiley Periodicals, Inc.     

Gaps in the number of generators of monomial Togliatti systems

Let $I_{d,n}?k[x_0,?,x_n]$ be a minimal monomial Togliatti system of forms of degree d. In [4], Mezzetti and Miró-Roig proved that the minimal number of generators $\mu (I_{d,n})$ of $I_{d,n}$ lies in the interval $[2n+1,\left(\begin{array}{c}n+d?1\\ n?1\end{array}\right)]$. In this paper, we prove that for $n\ge 4$ and $d\ge 3$, the integer values in $[2n+3,3n?1]$ cannot be realized as the number of minimal generators of a minimal monomial Togliatti system. We classify minimal monomial Togliatti systems $I_{d,n}?k[x_0,?,x_n]$ of forms of degree d with $\mu (I_{d,n})=2n+2$ or 3n (i.e. with the minimal number of generators reaching the border of the non-existence interval). Finally, we prove that for $n=4$, $d\ge 3$ and $\mu \in [9,\left(\begin{array}{c}d+3\\ 3\end{array}\right)]?\{11\}$ there exists a minimal monomial Togliatti system $I_{d,n}?k[x_0,?,x_n]$ of forms of degree d with $\mu (I_{n,d})=\mu$.     

On the Lipschitz equivalence of self‐affine sets

Recently Lipschitz equivalence of self‐similar sets on 201800041:mana201800041-math-0001" class="section_image" src="/cms/asset/b769a572-c904-4a34-915d-314d61115455/mana201800041-math-0001.png"> has been studied extensively in the literature. However for self‐affine sets the problem is more awkward and there are very few results. In this paper, we introduce a w‐Lipschitz equivalence by repacing the Euclidean norm with a pseudo‐norm w. Under the open set condition, we prove that any two totally disconnected integral self‐affine sets with a common matrix are w‐Lipschitz equivalent if and only if their digit sets have equal cardinality. The main methods used are the technique of pseudo‐norm and Gromov hyperbolic graph theory on iterated function systems.     

Mixing time of an unaligned Gibbs sampler on the square

The paper concerns a particular example of the Gibbs sampler and its mixing efficiency. Coordinates of a point are rerandomized in the unit square ${[0,1]}^2$ to approach a stationary distribution with density proportional to $exp(?A^2{(u?v)}^2)$ for $(u,v)\in {[0,1]}^2$ with some large parameter $A$.Diaconis conjectured the mixing time of this process to be $O\left(A^2\right)$ which we confirm in this paper. This improves on the currently known $O(exp\left(A^2\right))$ estimate.