Asymptotic upper bound of density for two-particle annihilating exclusion

We consider a stochastic process which presents an evolution of particles of two types on ^d with annihilations between particles of opposite types. Initially, at each site of ^d , independently of the other sites, we put a particle with probability 21 and assign to it one of two types with equal chances. Each particle, independently from the others, waits an exponential time with mean 1, chooses one of its neighboring sites on the lattice ^d with equal probabilities, and jumps to the site chosen. If the site to which a particle attempts to move is occupied by another particle of the same type, the jump is suppressed; if it is occupied by a particle of the opposite type, then both are annihilated and disappear from the system. The considered process may serve as a model for the chemical reaction A+B inert. The paper concerns an upper bound of(t), the density of particles in the system at timet. We prove that(t)<t -d/ when t>t() for all>0 in the dimensionsd4 and asymptotically(t) ^–1 in the higher dimensions. In our proofs, we used the ideas and the technique developed by Bramson and Lebowitz and the tools which are customarily used to study a symmetric exclusion process.     

Asymptotic behavior of densities for two-particle annihilating random walks

Consider the system of particles on ^d where particles are of two types—A andB—and execute simple random walks in continuous time. Particles do not interact with their own type, but when anA-particle meets aB-particle, both disappear, i.e., are annihilated. This system serves as a model for the chemical reactionA+B inert. We analyze the limiting behavior of the densities _A (t) and _B (t) when the initial state is given by homogeneous Poisson random fields. We prove that for equal initial densities _A (0)= _B (0) there is a change in behavior fromd4, where _A (t)= _B (t)C/t ^d /4, tod4, where _A (t)= _B (t)C/tast. For unequal initial densities _A (0)< _B (0), _A (t)e ^–cl ind=1, _A (t)e ^–Ct/logt ind=2, and _A (t)e ^–Ct ind3. The termC depends on the initial densities and changes withd. Techniques are from interacting particle systems. The behavior for this two-particle annihilation process has similarities to those for coalescing random walks (A+AA) and annihilating random walks (A+Ainert). The analysis of the present process is made considerably more difficult by the lack of comparison with an attractive particle system.     

Charge density at the nucleus and radial behavior of ground state for lithium-like ions with Z = 21 to 30

By using the full-core plus correlation (FCPC) type wave functions, the accurate charge densities ρ(0) at the nucleus and the radial expectation values of the ground states for the lithium-like systems with Z = 21 to 30 are obtained. The determinantal conditions and the electron-nucleus cusp condition are used to calculate the inequalities of the upper and the lower bounds to ρ(0) with two or more expectation values. These inequalities, derived by Angulo and Dehesa [Phys. Rev. A 44 1516 (1991)], are verified to be also valid for these ions with higher nuclear charge. The present results show that the wave functions used in this paper are satisfactory in the whole configuration space for these ions with higher nuclear charge.     

Path integrals and lower bounds for density matrices

Feynman has established a variational principle for the coordinate space representation of the canonical density matrix. It uses real trial actions in place of the actual real action. This principle is extended by dividing the original temperature interval, using matrix multiplication, and trial actions that depend on the end points. The result is a series of better lower bounds. A detailed analysis is made of the soluble harmonic oscillator case using free particle and mean path trial actions.Work supported by a grant from the National Science Foundation.     

类锂离子（Z = 21~30）1s22s和1s22p态近核处电子密度的下限

应用行列式条件和电子-原子核尖点(cusp)条件计算了核电荷数Z=21-30的类锂离子1s22s和1s22p态近核处电子密度的理论下限.该下限由Angulo和 Dehesa等人推导(见Phys. Rev. A 42 641 (1990)）的包含两个或者更多径向期待值的不等式给出. 结果表明,该下限对于高核电荷离子也同样适用,而且其品质要好于以前所知道的;计算中所用的波函数在这些具有较高核电荷离子体系的整个组态空间中都是准确可靠的.     

类锂离子(Z=21～30)1s~22s和1s~22p态近核处电子密度的下限(英文)

应用行列式条件和电子-原子核尖点(cusp)条件计算了核电荷数Z=21～30的类锂离子1s~22s和1s~2p态近核处电子密度的理论下限.该下限由Angulo和Dehesa等人推导(见Phys.Rev.A 42 641(1990))的包含两个或者更多径向期待值的不等式给出.结果表明,该下限对于高核电荷离子也同样适用,而且其品质要好于以前所知道的;计算中所用的波函数在这些具有较高核电荷离子体系的整个组态空间中都是准确可靠的.     

External Fields, Density Functionals, and the Gibbs Inequality

By combining the upper and lower bounds to the free energy as given by the Gibbs inequality for two systems with the same intermolecular interactions but with external fields differing from each other only in a finite region of space , we show that the corresponding equilibrium densities must also differ from each other somewhere in . We note that the basic equations of density functional theory arise naturally from a simple rearrangement and reinterpretation of the terms in the upper bound Gibbs inequality for such systems and briefly discuss some of the complications that occur when the intermolecular interactions of the two systems also differ.     

电流变液系统流动的渐近估计

根据电流变液中球形颗粒的运动模型，研究了颗粒质量很小时，电流变液中颗粒运动的渐近状态，利用微分不等式理论，给出了相应运动的渐近估计. 关键词： 电流变液 微分不等式理论 渐近估计     

Classical solution of the nonlinear Boltzmann equation in allR 3: Asymptotic behavior of solutions

Proof is given of the existence of a classical solution to the nonlinear Boltzmann equation in allR ³. The solution, which is global in time, exists if the initial data go to zero fast enough at infinity and the mean free path is sufficiently large. The solution is smooth in the space variable if the initial value is smooth. The asymptotic behavior of solutions is also given. It is shown that ast the solution to the Boltzmann equation can be approximated by the solution to the free motion problem.     

Exact solution of the master equation for the asymmetric exclusion process

Using the Bethe ansatz, we obtain the exact solution of the master equation for the totally asymmetric exclusion process on an infinite one-dimensional lattice. We derive explicit expressions for the conditional probabilitiesP(x₁,...,x_N;t/y ₁,...,y_N; 0) of findingN particles on lattices sitesx ₁,...,x_N at timet with initial occupationy ₁,...,y_N at timet=0.     

Asymptotic behavior of solutions to the coagulation-fragmentation equations. II. Weak fragmentation

The discrete coagulation-fragmentation equations are a model for the kinetics of cluster growth in which clusters can coagulate via binary interactions to form larger clusters or fragment to form smaller ones. The assumptions made on the fragmentation coefficients have the physical interpretation that surface effects are important. Our results on the asymptotic behavior of solutions generalize the corresponding results of Ball, Carr, and Penrose for the Becker-Doring equation.Dedicated to Oliver Penrose on the occasion of his 65th birthday     

On the Validations of the Asymptotic Matching Conjectures

In this paper we review the asymptotic matching conjectures for r-regular bipartite graphs, and their connections in estimating the monomer-dimer entropies in d-dimensional integer lattice and Bethe lattices. We prove new rigorous upper and lower bounds for the monomer-dimer entropies, which support these conjectures. We describe a general construction of infinite families of r-regular tori graphs and give algorithms for computing the monomer-dimer entropy of density p, for any p∈[0,1], for these graphs. Finally we use tori graphs to test the asymptotic matching conjectures for certain infinite r-regular bipartite graphs.     

Quantum uncertainty relations of Tsallis relative α entropy coherence based on MUBs

In this paper,we discuss quantum uncertainty relations of Tsallis relative α entropy coherence for a single qubit system based on three mutually unbiased bases.For α∈[1/2,1)U(1,2],the upper and lower bounds of sums of coherence are obtained.However,the above results cannot be verified directly for any α∈(0,1/2).Hence,we only consider the special case of α=1/n+1,where n is a positive integer,and we obtain the upper and lower bounds.By comparing the upper and lower bounds,we find that the upper bound is equal to the lower bound for the special α=1/2,and the differences between the upper and the lower bounds will increase as α increases.Furthermore,we discuss the tendency of the sum of coherence,and find that it has the same tendency with respect to the different θ or φ,which is opposite to the uncertainty relations based on the Rényi entropy and Tsallis entropy.     

Dark Solitons for the Defocusing Cubic Nonlinear Schrödinger Equation with the Spatially Periodic Potential and Nonlinearity

We study the existence of dark solitons of the defocusing cubic nonlinear Schrödinger (NLS) eqaution with the spatially-periodic potential and nonlinearity. Firstly, we propose six families of upper and lower solutions of the dynamical systems arising from the stationary defocusing NLS equation. Secondly, by regarding a dark soliton as a heteroclinic orbit of the Poincaré map, we present some constraint conditions for the periodic potential and nonlinearity to show the existence of stationary dark solitons of the defocusing NLS equation for six different cases in terms of the theory of strict lower and upper solutions and the dynamics of planar homeomorphisms. Finally, we give the explicit dark solitons of the defocusing NLS equation with the chosen periodic potential and nonlinearity.     

On the use of variational methods for solving Boltzmann equations involving non-Hermitian operators

Variational principles yielding upper and lower bounds on transport coefficients can readily be applied to the Boltzmann equation, provided it has the form of a linear, inhomogeneous integrodifferential equation with a Hermitian operator acting on the deviation from equilibrium of the distribution function. In transport problems involving a magnetic field or an alternating electric field, this operator is non-Hermitian. By suitably transforming the transport equation, we show how Variational principles may still give upper and lower bounds. The bounds are used for considering the frequency-dependent conductivity associated with a general scattering operator, and the longitudinal magnetoresistivity in the relaxation time approximation for the scattering operator. Explicit results are presented for (1) the frequency-dependent conductivity of a charged Fermi liquid and (2) the longitudinal magnetoresistivity for a weakly anisotropic Fermi surface.     

Asymptotic behavior of correlation functions for electric potential and field fluctuations in a classical one- component plasma

The correlations of the electric potential fluctuations in a classical one-component plasma are studied for large distances between the observation points. The two-point correlation function for these fluctuations is known to decay slowly for large distances, even if exponential clustering holds for the charge correlation functions. In this paper the asymptotic behavior of the generalk-point electric potential correlation functions is analyzed. Each of these correlation functions can be split into a reducible part, which is given by a sum of products of lower-order correlation functions, and a remaining irreducible part. It is shown, on the basis of an exponential clustering hypothesis for the charge correlation functions, that for allk3 the irreducible parts of the electric potential correlation functions decay faster than any inverse power of the distance, if one or more of the observation points move far away from the others. Hence, the two-point electric potential correlation function is the only one with a slow algebraic decay. The same statement holds for the correlation functions of the electric field fluctuations.     

Asymptotic solution for a perturbed mechanism of western boundary undercurrents in the Pacific

This paper consider a class of perturbed mechanism for the western boundary undercurrents in the Pacific. The model of generalized governing equations is studied. Using the perturbation method, it constructs the asymptotic solution of the model. And the accuracy of asymptotic solution is proved by the theory of differential inequalities. Thus the uniformly valid asymptotic expansions of the solution are obtained.     

The abrupt changes in the yellowed fibril density in the Linen of Turin

The present investigation is an attempt to explain the abrupt changes in the yellowed fibril density (or image intensity) values in the dorsal part of the Shroud of Turin body image. The interested areas are the ones at the base of the shoulders and the buttocks. These rapid changes in the body image intensity are not anomalies of the linen manufacture. They can be explained with the original presence of aromas and/or burial ointments.     

核ANC和激发态中子晕

利用转移反应¹¹B(d,p)¹²B和¹²C(d,p)¹³C抽取¹²B<—>¹¹B+n和¹³C<—>¹²C+n重叠函数的核渐近归一化常数,计算了¹²B和¹³C核中价中子密度分布的均方根半径及其在核外的几率.实验结果表明,¹²B的第二(J^π=2^－),第三(J^π=1^－)激发态和13C的第一(J^π=1/2⁺)激发态为中子晕态,而¹³C的第三(J^π=5/2⁺)激发态是中子皮态.考察了库仑势和角动量对晕形成的阻碍效应.提出了均方根半径对于有效核子分离能的统一的标度定律.