The Adiabatic Transport of Bose-Einstein Condensates in a Double-Well Trap: Case a Small Nonlinearity

A complete adiabatic transport of Bose-Einstein condensate in a double-well trap is investigated within the Landau-Zener (LZ) and Gaussian Landau-Zener (GLZ) schemes for the case of a small nonlinearity, when the atomic interaction is weaker than the coupling. The schemes use the constant (LZ) and time-dependent Gaussian (GLZ) couplings. The mean field calculations show that LZ and GLZ suggest essentially different transport dynamics. Significant deviations from the case of a strong coupling are discussed.Comment: 6 pages, 3 figures, to be published in Laser Physic

Quark mass correction to the string potential

A consistent method for calculating the interquark potential generated by the relativistic string with massive ends is proposed. In this approach the interquark potential in the model of the Nambu--Goto string with point--like masses at its ends is calculated. At first the calculation is done in the one--loop approximation and then the variational estimation is performed. The quark mass correction results in decreasing the critical distance (deconfinement radius). When quark mass decreases the critical distance also decreases. For obtaining a finite result under summation over eigenfrequencies of the Nambu--Goto string with massive ends a suitable mode--by--mode subtraction is proposed. This renormalization procedure proves to be completely unique. In the framework of the developed approach the one--loop interquark potential in the model of the relativistic string with rigidity is also calculated.Comment: 34 pages, LATE

Acoustic Probing of the Jamming Transition in an Unconsolidated Granular Medium

Experiments with acoustic waves guided along the mechanically free surface of an unconsolidated granular packed structure provide information on the elasticity of granular media at very low pressures that are naturally controlled by the gravitational acceleration and the depth beneath the surface. Comparison of the determined dispersion relations for guided surface acoustic modes with a theoretical model reveals the dependencies of the elastic moduli of the granular medium on pressure. The experiments confirm recent theoretical predictions that relaxation of the disordered granular packing through non-affine motion leads to a peculiar scaling of shear rigidity with pressure near the jamming transition corresponding to zero pressure. Unexpectedly, and in disagreement with the most of the available theories, the bulk modulus depends on pressure in a very similar way to the shear modulus

Twist Mode in Spherical Alkali Metal Clusters

A remarkable orbital quadrupole magnetic resonance, so-called twist mode, is predicted in alkali metal clusters where it is represented by $I^{\pi}=2^-$ low-energy excitations of valence electrons with strong M2 transitions to the ground state. We treat the twist by both macroscopic and microscopic ways. In the latter case, the shell structure of clusters is fully exploited, which is crucial for the considered size region ($8\le N_e\le 1314$). The energy-weighted sum rule is derived for the pseudo-Hamiltonian. In medium and heavy spherical clusters the twist dominates over its spin-dipole counterpart and becomes the most strong multipole magnetic mode.Comment: 8 pages, 4 figures, to be published in Phys. Rev. Lett., v.85, n.15, 200

Застосування регресійної моделі коефіцієнта використання каналів для формування плану розподілу навантаження в мережі

Introduction. Method of problem solutions of management, design and quality evaluation using mathematical models coefficient utilization of channels (CUC) in standard form has several inconveniences. It is connected with fact models used analytical expressions that are not derivatives and don’t explicitly get some parameters dependence by others. Formulation of the problem. Objective is obtain approximate analytical coefficient dependence channel utilization ratio of the load, the number of channels and allowable probability of loss requests on branches network. This ratio reflects essence of processes occurring in network with a high level of adequacy and differentiated range of values explored. Solution. The problem definition of empirical relationships is conducted by two stages. At the first stage the general form of analytical expressions was determined (7). In the second stage best settings analytical expressions were calculated. The calculation results are represented in Tables 1 and 2. Analysis of the CUC is carried by the first derivative functions. Results. Analytical dependences of the CCC were obtained. They allow you to remove indeterminacy in the solution of nonlinear equations. This nonlinear system describes the requirements for quality of service in connection direction. This reduces the requested channel resource in the network. That allows providing a certain quality of service in connection direction.При решении задач управления, проектирования и оценки качества обслуживания в телекоммуникационных сетях нередко используется математическая модель коэффициента использования каналов. Однако, ее использование в стандартном виде имеет ряд неудобств. Это связано с тем, что используемые в модели аналитические выражения не дифференцируемы и не позволяют в явном виде выражать зависимость одних параметров через другие. В статье предложена аппроксимация математической модели коэффициента использования каналов приближенными дифференцируемыми функциями на базе математического аппарата регрессионного анализа. Даны рекомендации по использованию полученных результатов в ходе решения сетевых задач.При вирішенні завдань управління, проектування і оцінки якості обслуговування в телекомунікаційних мережах нерідко використовується математична модель коефіцієнта використання каналів. Однак, її використання в стандартному вигляді має ряд незручностей. Це пов'язано з тим, що в моделі використовуються аналітичні вирази, які не мають похідні і не дозволяють в явному вигляді отримувати залежність одних параметрів через інші. У статті запропонована апроксимація математичної моделі коефіцієнта використання каналів наближеними диференційованими функціями на базі математичного апарату регресійного аналізу. Надано рекомендації щодо використання отриманих результатів в ході вирішення мережевих задач

Importance of motivation to study and teaching of mathematics

Стаття присвячена аналізу ролі мотивації в математичній підготовці студентів.This article analyzes the role of motivation in the mathematical training of students.Статья посвящена анализу роли мотивации в математической подготовке студентов

Does J/ψ→π+π−J/\psi \rightarrow \pi^{+} \pi^{-} fix the Electromagnetic Form Factor Fπ(t)F_{\pi}(t) at t=MJ/ψ2t=M_{J/\psi}^2?

We show that the $J/\psi \rightarrow \pi^{+} \pi^{-}$ decay is a reliable source of information for the electromagnetic form factor of the pion at $t=M_{J/\psi}^2=9.6 {\rm GeV}^2$ by using general arguments to estimate, or rather, put upper bounds on, the background processes that could spoil this extraction. We briefly comment on the significance of the resulting $F_{\pi}(M_{J/\psi}^2)$.Comment: 10 pages revtex manuscript, one figure--not included, U. of MD PP #94-00

Mean field theory for global binding systematics

We review some possible improvements of mean field theory for application to nuclear binding systematics. Up to now, microscopic theory has been less successful than models starting from the liquid drop in describing accurately the global binding systematics. We believe that there are good prospects to develop a better global theory, using modern forms of energy density functionals and treating correlation energies systematically by the RPA.Comment: RevTex, 17 pages, 5 eps figures. To be published in Yadernaya Fizika, special edition for the 90th birthday of Professor A.B. Migda

Radiation reaction for multipole moments

We propose a Poincare-invariant description for the effective dynamics of systems of charged particles by means of intrinsic multipole moments. To achieve this goal we study the effective dynamics of such systems within two frameworks -- the particle itself and hydrodynamical one. We give a relativistic-invariant definition for the intrinsic multipole moments both pointlike and extended relativistic objects. Within the hydrodynamical framework we suggest a covariant action functional for a perfect fluid with pressure. In the case of a relativistic charged dust we prove the equivalence of the particle approach to the hydrodynamical one to the problem of radiation reaction for multipoles. As the particular example of a general procedure we obtain the effective model for a neutral system of charged particles with dipole moment.Comment: 12 pages, 1 figure, RevTeX 4; references updated, minor textual correction