A theorem on the representation of the field of forced vibrations of a composite elastic system

A theorem on the representation of a vibration field of an elastic system comprising two subsystems is proved in a general form. It is assumed that the system is linear and the subsystems are rigidly connected and interact along a continuous surface S. According to the theorem, forced vibrations of the system can be represented in the form of the sum of two components, which are the solutions of two simpler auxiliary boundary-value problems. The first component is the field of vibrations of the isolated (separated or blocked along S) subsystems under the effect of preset external forces. The second component represents the forced vibrations of the junction of the subsystems, where the external forces are taken equal to zero and only the reaction forces obtained in solving the first auxiliary problem act at the surface S. The theorem is applied to the problem on the reflection and transmission of elastic waves through a junction of two media. It is demonstrated that the theorem utilization reduces the amount of calculations. Other applications are discussed.     

Alpha-Particles within Nuclei

We present a formalism describing the bound state of a large number of bosons and apply it to study nuclei consisting of A α particles. The method has its roots in a few-body approach and is based on the expansion of the many-body Faddeev components in Potential Harmonics, and the subsequent reduction of the Faddeev equation into a two-variable, integro-differential equation. For A → ∞ this equation is transformed into a new simpler integro-differential equation, which is easy to use in calculations for A up to as large as 1000. We use both integro-differential equations to investigate the behavior of nuclei subject to the assumption that they are composed of α particles. Various α α forces were employed. For the Ali-Bodmer potential we found that the A = 5 system (i.e. ²⁰Ne) is the most stable, while for the A = 10 system (i.e. ⁴⁰Ca) the binding energy has a maximum. The formalism predicts α-decay for larger nuclei, but the value of A where this begins to happen is strongly dependent on the α α potential.     

On dynamic image potential

Self consistent calculations for the dynamic image potential are carried out, taking the finite acceleration of the incoming charge into account. Results indicate that the effect of the inclusion of acceleration is rather small, and the simpler self consistent approach neglecting the acceleration and using a local speed approximation seems to be adequate. Our theoretical framework also provides a mathematical justification of the latter simpler approach which was earlier employed by Ray and Mahan in an ad hoc manner.     

Hyperspherical Coulomb spheroidal basis in the Coulomb three-body problem

A hyperspherical Coulomb spheroidal (HSCS) representation is proposed for the Coulomb three-body problem. This is a new expansion in the set of well-known Coulomb spheroidal functions. The orthogonality of Coulomb spheroidal functions on a constant-hyperradius surface ρ = const rather than on a constant-internuclear-distance surface R = const, as in the traditional Born-Oppenheimer approach, is a distinguishing feature of the proposed approach. Owing to this, the HSCS representation proves to be consistent with the asymptotic conditions for the scattering problem at energies below the threshold for three-body breakup: only a finite number of radial functions do not vanish in the limit of ρ→∞, with the result that the formulation of the scattering problem becomes substantially simpler. In the proposed approach, the HSCS basis functions are considerably simpler than those in the well-known adiabatic hyperspherical representation, which is also consistent with the asymptotic conditions. Specifically, the HSCS basis functions are completely factorized. Therefore, there arise no problems associated with avoided crossings of adiabatic hyperspherical terms.     

On simplifying ‘incremental remap’–based transport schemes

The flux-form incremental remapping transport scheme introduced by Dukowicz and Baumgardner [1] converts the transport problem into a remapping problem. This involves identifying overlap areas between quadrilateral flux-areas and regular square grid cells which is non-trivial and leads to some algorithm complexity. In the simpler swept area approach (originally introduced by Hirt et al. [2]) the search for overlap areas is eliminated even if the flux-areas overlap several regular grid cells. The resulting simplified scheme leads to a much simpler and robust algorithm.     

Power absorbed by a subsystem in the response theory

A macroscopic system which consists of a set of interacting subsystems in an external field is considered. A convenient formula is derived for the mean energy Q_j absorbed per unit time by a subsystem. The expression obtained for Q_j takes into account that in general the Hamiltonian H of such a system does not coincide with the sum of the Hamiltonians of the subsystems H_j; Q_j appears to be the same for various possible definitions of H_j's.     

About a nonadditivity of energy and entropy

The mathematical expression of nonadditivity X(1 ?? 2) = X(1) + X(2) + ??X(1)X(2) has been frequently used for the development of statistical physics for nonadditive system, where X is entropy or energy, and ?? is hoped to be a parameter characterising the nonadditive property of the composite system (1 ?? 2). Here we show that this relationship cannot hold exactly. In general, ?? in this expression inevitably depends on how a given system with constant X(1 ?? 2) is divided into subsystems 1 and 2. Hence mathematical problems may arise when it is used to characterise the nonadditivity of the system. Nevertheless, under some conditions, it is possible to use it as a good approximation.     

Clustering aspects of light exotic nuclei

The discovery of light nuclei with neutron halos has opened new perspectives for nuclear structure and a possibility to study genuine few-body aspects of matter. A number of borromean systems where the system is bound but where no binary subsystems are bound, are realized by nature in the context of nuclei,¹¹Li being the nucleus which has had most recent attention. Although a large number of calculations have addressed the detailed structure of the¹¹Li neutron halo, no single model has yet explained all the data presently available. This is in part due to uncertainties in then+⁹Li interaction. For⁶He, also a borromean system, where then+core interaction is known, the best three-body and reaction models succeed in reproducing the data. In the¹¹Li case, a major uncertainty concerns the effect of possible 1s intruder states.     

An approximate method for calculating scattering and absorption of light by fractal aggregates

A simplified version of the coupled dipole method (CDM) is proposed which allows one to reduce the initial system of 3N×3N equations to a simpler system of N×N equations. The method neglects depolarization effects in the interaction of dipoles but, unlike the mean field approximation, it takes into account local fluctuations of the scalar amplitudes of the excited dipole moments. Simple analytic solutions are obtained for integrated cross sections averaged over aggregate orientations. It is shown by the example of ballistic fractal aggregates that this method provides the accuracy close to that of a standard CDM, being substantially less time-consuming. In the case of biospheres, the approximate method is compared with the exact results of the multipole expansion.     

Field Theoretic Formulation of Kinetic Theory: Basic Development

We show how kinetic theory, the statistics of classical particles obeying Newtonian dynamics, can be formulated as a field theory. The field theory can be organized to produce a self-consistent perturbation theory expansion in an effective interaction potential. The need for a self-consistent approach is suggested by our interest in investigating ergodic-nonergodic transitions in dense fluids. The formal structure we develop has been implemented in detail for the simpler case of Smoluchowski dynamics. One aspect of the approach is the identification of a core problem spanned by the variables ?? the number density and B a response density. In this paper we set up the perturbation theory expansion with explicit development at zeroth and first order. We also determine all of the cumulants in the noninteracting limit among the core variables ?? and B.     

Simulation studies of gas-liquid transitions in two dimensions via a subsystem-block-density distribution analysis

The finite-size scaling analysis of the density distribution function of subsystems of a system studied at constant total density is studied by a comparative investigation of two models: (i) the nearest-neighbor lattice gas model on the square lattice, choosing a total lattice size of 64×64 sites. (ii) The two-dimensional off-lattice Lennard-Jones system (truncated at a distance of 2.5 σ, σ being the range parameter of the interaction) withN=4096 particles, applying the NVT ensemble. In both models, the density distribution functionP _L (ρ) is obtained forL×L subsystems for a wide range of temperaturesT, subblock linear dimensionsL and average densities <ρ>. Particular attention is paid to the question whether accurate estimates of critical temperatureT _c and critical density ρ _c can be obtained. In the lattice gas model these critical parameters are known exactly and the limitations of the approach can thus be definitively asserted. The final estimates for the Lennard Jones problem areT _c =0.47±0.01 (in units of the Lennard Jones energy ε) and ρ _c (in units of σ²), a comparison with previous estimates is made.     

Conditional Mutual Information and Commutator

A simpler approach to the characterization of vanishing conditional mutual information is presented. Some remarks are given as well. More specifically, relating the conditional mutual information to a commutator is a very promising approach towards the approximate version of SSA. That is, it is conjectured that small conditional mutual information implies small perturbation of quantum Markov chain.     

On a generalized peaceful coexistence of special relativity and quantum mechanics

The result that quantum nonlocality is causal because it cannot be used to transfer classical information across spacelike intervals is extended to entangled n-partite systems (n⩾2). We show that correlations between any m (0<m<n) of the subsystems is independent of unitary operations performed on any other k subsystems and/or (projective, nondegenerate) measurement operations performed on any other l (n−m⩽l,k<n) subsystems. This corroborates the peaceful coexistence of quantum mechanics and special relativity, and is in keeping with the understanding that the total information in an entangled system is locally inaccessible.     

Schemes for performance of displacing Hadamard gate with coherent states

We propose an approach with displaced states to use it for rotations of base coherent states and squeezed coherent states. Our approach is based on representation of the coherent states in free-traveling fields in terms of displaced number states with arbitrary amplitude of displacement. Two optical schemes are developed for construction of Hadamard gate for the base states. One of the optical schemes is based on alternation of photon additions and displacement operators (in general case, N-photon additions and N?1-displacements are required) to generate displaced squeezed even/odd superposition of coherent states (SCSs) with high fidelity in dependency on type (computational zero or one) of the base input state. Another optical scheme uses two-photon subtracted squeezed coherent states to approximate outcome of the Hadamard gate for the base squeezed coherent states. Output states approximate with high fidelity either even squeezed SCS or odd SCS shifted relative to each other by some value. It enables to adjust the optical scheme for construction of the Hadamard gate being mainframe element for quantum computation with basic squeezed coherent states.     

Divergence cancellations in the renormalization of electroweak couplings

Cancellations of nonuniversal ultraviolet divergent contributions to the renormalization of couplingsvlW,vvZ,llZ (in the lowest nontrivial order) in theunitary (U) gauge of the Weinberg-Salam model are reconsidered. The expansion ofU-gauge Feynman diagrams into a set of simpler “secondary” graphs devised some time ago by Kummer and Lane is employed. It is shown that this approach reveals details of the cancellation mechanism which have not been discussed in previous treatments. The connection of cancellations in question with underlying gauge symmetry and the corresponding Higgs mechanism thus becomes more transparent.     

Ride quality and International Standard ISO 2631 “Guide for the evaluation of human exposure to whole-body vibration” : G. R. Allen. Paper 21. (30 pages, 13 figures, 22 references)

An exact solution is obtained for the normal vibration frequencies of a rectangular array of identical point-masses. The method of intermediate co-ordinate transformation, which was introduced in a previous article in this journal, makes it possible to treat the system as a coupled set of linear chains. By this means, the analysis can be made considerably simpler than the usual treatment. The result shows that the coupling of the normal modes of the separate chains is restricted to those modes having the same index numbers. Thus, the usual problem involving N₁ × N₁ secular determinant, where N₁ is the number of particles contained in each separate chain, is reduced to that involving only a 2 × 2 determinant. The calculation in the present article will serve as a basis for the vibrational analyses of more complicated problems involving two- and three-dimensional arrays of masses that are perturbed by “disorder”.     

Distribution function for systems far from thermal equilibrium

We present the general stationary solution of the Fokker-Planck equation for a system of interacting subsystems weakly coupled to reservoirs at different temperatures, T_j. For T_j = T, it reduces to the Boltzman distribution function.     

The decay h0 → A0 → A0A0: a complete one-loop calculation in the MSSM

In the minimal supersymmetric standard model the decay h⁰ → A⁰A⁰ of the light neutral scalar h⁰ is kinematically allowed for low values of tan β when radiative corrections to the neutral Higgs masses are taken into account. The width of this decay mode is revisited on the basis of a complete one-loop diagrammatic calculation. We give the analytical expressions and numerical results and compare them with the corresponding ones from the simpler and compact approximations of the effective potential method and the renormalization group approach.     

Electrohydrodynamic flow analysis in a circular cylindrical conduit using Least Square Method

In this article, Electrohydrodynamic flow (EHD flow) in a circular cylindrical conduit is studied by a semi-exact and high efficient weighted residual method called Least Square Method (LSM). A principle of LSM is briefly introduced and later is employed to solve the described problem. Furthermore, the effects of the Hartmann electric number (Ha) and the strength of nonlinearity (α) on velocity profiles are discussed and presented graphically. Results are compared with numerical solution and obtained residuals are compared with those of HAM which previously were done by Mastroberardino in Ref. [3]. Outcomes reveal that LSM has an excellent agreement with numerical solution; also depicted residual functions showed that LSM is more acceptable than HAM especially for large values of Ha and α numbers, also it is simpler and needs fewer computations.