Atomistic simulation of site preference, Curie temperature, and lattice vibration of Nd2Co7 - xFex

The effects of Fe substitution for Co on the structural stability and the site preference of intermetallics Nd 2 Co 7-x Fe x with a hexagonal Ce 2 Ni 7-type structure are studied by using a series of interatomic pair potentials.In Nd 2 Co 7-x Fe x,Fe atoms are substituted for Co atoms with a strong preference for the 6h sites and the order of site preference is 6h,4e,4f,2a,and 12k.Calculated lattice parameters are found to be consistent with the reported results in the literature.The variation behaviour of the Curie temperature of Nd 2 Co 7-x Fe x is explained qualitatively by the exchange interaction model.The properties related to lattice vibration,such as phonon density of states and Debye temperature,are first evaluated for the Nd 2 Co 7-x Fe x compounds.     

Thermodynamic potentials and thermodynamic relations in nonextensive thermodynamics

The generalized Gibbs free energy and enthalpy are derived in the framework of nonextensive thermodynamics by using the concept of the physical temperature and the physical pressure. Some relations of the thermodynamical potentials are changed due to the difference between the physical temperature and the inverse of Lagrange multiplier. We derive the thermodynamical relation between the heat capacities at a constant volume and at a constant pressure using the generalized thermodynamical potential. We find that it has a different form from the traditional one in Gibbs thermodynamics. But, the expressions of the heat capacities in this framework using the generalized thermodynamical potentials are still the same as the traditional one.     

带有无界势和一般时间频率的非周期离散非线性Schr#246;dinger方程：无穷多个孤立子

本文研究下面的非周期离散非线性Schrödinger 方程：
-Δu_n + v_nu_n - ωun = g_n（u_n）,n ∈ Z,
其中V = {v_n}_n∈Z 和g_n 都是非周期的,当|n| → +∞ 时,v_n → +∞,并且时间频率ω ∈ R 可以满足下面的任何一种情形：（1）ω 属于算子-Δ + V 的一个有限谱间隔;（2）ω < inf σ（-Δ + V）;（3）ω ∈ σ（-Δ+ V）,其中σ（-Δ+ V）表示-Δ+ V的谱. 本文将用一些局部条件（在无穷远或零处）来代替一些全局条件. 利用变化的喷泉定理,当非线性项在无穷远处是超线性时,本文得到这个方程的无穷多个非平凡孤立子,并且,也得到指数衰减的孤立子的存在性.     

The Vlasov-Poisson-Boltzmann system for non-cutof hard potentials

This paper is concerned with the construction of globally smooth solutions near a given global Maxwellian to the Cauchy problem of the Vlasov-Poisson-Boltzmann system for non-cutof hard potentials in three space dimensions without the neutral condition imposed on the initial perturbation.Our analysis is based on the time-weighted energy method and some delicate estimates.     

Singular Continuous Spectrum for a Class of Substitution Hamiltonians II

We consider discrete one-dimensional Schrödinger operators with aperiodic potentials generated by primitive substitutions. Using the three-block version of Gordon's criterion, we establish purely singular continuous spectrum with probability one provided that the potentials have index greater than three. It is also shown that one cannot use this criterion to prove uniform results.     

Smoothness of the Solution of the Spatially Homogeneous Boltzmann Equation without Cutoff

Abstract

For regularized hard potentials cross sections, the solution of the spatially homogeneous Boltzmann equation without angular cutoff lies in Schwartz's space 𝒮(? ^N ) for all (strictly positive) time. The proof is presented in full detail for the two-dimensional case, and for a moderate singularity of the cross section. Then we present those parts of the proof for the general case, where the dimension, or the strength of the singularity play an essential role.     

Radii of Redox Components from Absolute Redox Potentials Compared with Covalent and Aqueous Ionic Radii

Aqueous standard potentials, referred to that of the SHE as zero, were recently shown to vary linearly with gaseous ionization potentials, with the absolute potential of SHE as the intercept. This enabled arriving at the absolute redox potentials of elements. Here, the distances between the oxidized and reduced forms in aqueous solutions have been evaluated. From the linear dependence of these distances on the covalent radii of atoms, the radii of the redox components have been obtained. The latter also vary linearly with the aqueous ionic radii estimated earlier from ion‐water distances, and indicate the presence of aqueous molecular anions.     

Electrical resistivity of the alkaline earth metals Ca,Sr and Ba in the 50–300K temperature region

The computed values of the temperature dependent electrical resistivity is presented for the alkaline earth metals Ca, Sr and Ba. Numerical values of the mean free paths obtained using a finite mean free path approach is also reported. The structure factor has been evaluated using experimental values for the phonon spectra while local model potentials were used for the form factors. Our numerical results compare favourably with experiments.     

Quantum model for the price dynamics: The problem of smoothness of trajectories

We apply methods of quantum mechanics to mathematical modelling of price dynamics in a financial market. We propose to describe behavioral financial factors (e.g., expectations of traders) by using the pilot wave (Bohmian) model of quantum mechanics. Our model is a quantum-like model of the financial market, cf. with works of W. Segal, I.E. Segal, E. Haven. In this paper we study the problem of smoothness of price-trajectories in the Bohmian financial model. We show that even the smooth evolution of the financial pilot wave ψ(t,x) (representing expectations of traders) can induce jumps of prices of shares.