Production of X-radiation in the Crab nebula

It is suggested that the X-rays from the Crab nebula are due to the synchrotron radiation of electrons of energy ～4×10¹² eV in the magnetic field of the central region of the nebula, the magnetic field being enhanced by hydromagnetic waves. The consistency of the model with experimental X-ray observations and the energetics of the nebula are shown.     

On the refined modeling of the force distribution in a bistable magnetoelastic energy harvesting system due to a magnetic field

Abstract: The problem of a bistable magnetoelastic beam under base excitation was discussed in [1] under the aspect of chaotic behaviour in mechanical systems. Three decades later the system was used in [2] to design an energy harvesting system which performs well under harmonic excitation for a broad range of excitation frequencies due to its bistability. The initial modeling was tailored to obtain a model with one degree of freedom based on the assumption that the magnetic force acts on the beam tip only. A more appropriate model can be found when considering a distributed force along the beam. The authors present the force distribution on a ferromagnetic beam due to the magnetic field of two permanent magnets. A semi-analytic method is used to compute the magnetic field. The force distribution can in future be used to derive a refined nonlinear dynamical model for the ferromagnetic elastic beam. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

String field theory: From high energy to cosmology

We review recent achievements and open questions in string field theory. We comment on the history of the construction of the covariant gauge-invariant string field formulation and briefly consider possible applications of string field theory in D-brane physics and cosmology.     

Generalized eigenvalue decomposition of the field autocorrelation in correlation diffusion of photons in turbid media

We propose a novel numerical method based on a generalized eigenvalue decomposition for solving the diffusion equation governing the correlation diffusion of photons in turbid media. Medical imaging modalities such as diffuse correlation tomography and ultrasound‐modulated optical tomography have the (elliptic) diffusion equation parameterized by a time variable as the forward model. Hitherto, for the computation of the correlation function, the diffusion equation is solved repeatedly over the time parameter. We show that the use of a certain time‐independent generalized eigenfunction basis results in the decoupling of the spatial and time dependence of the correlation function, thus allowing greater computational efficiency in arriving at the forward solution. Besides presenting the mathematical analysis of the generalized eigenvalue problem on the basis of spectral theory, we put forth the numerical results that compare the proposed numerical method with the standard technique for solving the diffusion equation. Copyright © 2012 John Wiley & Sons, Ltd.     

Parapositronium atom in the field of annihilation and optical photons as a nonlinear quantum system

A parapositronium atom in an optical laser field is described beyond the perturbation theory framework by a closed system of Heisenberg equations on operators of atoms and photons. Wwe consider the annihilation of the parapositronium atom, which starts from one or two quantum states; optical quantum transitions between these states are caused by one or two optical photons. Mean occupation numbers of these states are governed by a system of two nonlinear equations. We investigated particular stationary and nonstationary solutions of this system and find that annihilation photons substantially affect the annihilation process. We show that definite optical laser radiation may stabilize the parapositronium atom and make its lifetime hundreds of times longer than the lifetime of the free parapositronium atom in the 1s state. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 124, No. 1, pp. 148–168, July, 2000.     

A mathematical study of energy dissipation due to atrioventricular valve vibration

A mathematical model of the dynamic response of atrioventricular valve leaflets to the systolic pressure pulse is used to calculate the resultant energy dissipation under the action of viscous damping. The energy dissipated from mitral and tricuspid leaflets is compared, and the effects of leaflet size, closing velocity, the magnitude of the damping force, and the rate of change of the atrioventricular pressure gradient are investigated. The results are interpreted in relation to experimentally documented first heart sound determinants.     

Calculation of the magnetic field due to a bioelectric current dipole in an ellipsoid

The bioelectric current dipole model is important both theoretically and computationally in the study of electrical activity in the brain and stomach due to the resemblance of the shape of these two organs to an ellipsoid. To calculate the magnetic field B due to a dipole in an ellipsoid, one must evaluate truncated series expansions involving ellipsoidal harmonics , which are products of Lamé functions. In this article, we extend a strictly analytic model (G. Dassios and F. Kariotou, J. Math. Phys. 44 (2003), 220–241), where B was computed from an ellipsoidal harmonic expansion of order 2. The present derivations show how the field can be evaluated to arbitrary order using numerical procedures for evaluating the roots of Lamé polynomials of degree 5 or higher. This can be accomplished using an optimization technique for solving nonlinear systems of equations, which allows one to acquire an understanding of the truncation error associated with the harmonic series expansion used for the calculation. Funding was provided by the National Institute of Health, Grant No. 1RO1 DK 58697 and by the Veterans’ Affairs Research Service.     

Free energy of the spherical mean field model

We compute at any temperature the free energy of the multi p-spin spherical model when only terms for p even are considered. Work partially supported by an NSF grant     

The sound field due to a periodic array of forced wave-bearing strips

A compressible fluid in a two-dimensional half-space (y >0) is bounded by a plane surface (y = 0) which is acousticallyhard except for a set of periodically arranged strips S_n givenby nd – a < x < nd + a, y = 0 with n = 0, 1, 2,....The velocity potential Re {(x, y)exp(–it)} satisfies theHelmholtz wave equation in the fluid region y>0, with /y= 0 on the plane y = 0, x S_n. The boundary condition on thepistons S_n is taken to have the form where the prescribed forcing function V(x) is the same on eachstrip, so that V(x + nd) = V(x), and the operators L and M arepolynomial functions of the second derivative ²/x². This boundarycondition includes the possibilities of an elastic plate, amembrane, or an impedance surface for S_n. When the separationdistance d is much greater than the strip width 2a and wavelength2/k, the problem is reduced to that of finding the potential_p due to a single piston S_o set in a rigid baffle, togetherwith a potential _c subject to a similar condition with forcingfunctions exp (ikx) in place of V(x). The problem is generalizedto allow for the possibility of a phased forcing function V(x),such that V(x + nd) = exp (ißnd)V(x), where ßis a given constant.     

Defining the integers in large rings of a number field using one universal quantifier

Julia Robinson gave a first-order definition of the set of integers in the rational numbers by a formula (∀∃∀∃)(F = 0) where the ∀-quantifiers run over a total of 8 variables and F is polynomial. We show that for a large class of number fields, not including , for every ε > 0 there exist a set of primes of natural density exceeding 1 − ε such that can be defined as a subset of the “large” subring

An asymptotic expansion for perturbations in the displacement field due to the presence of thin interfaces

We rigorously derive an asymptotic expansion for two-dimensional displacement field associated with thin elastic inclusion having no uniform thickness. Our approach is based on layer potential techniques through integral representation formulas of the fields. We extend these techniques to determine a relationship between traction–displacement measurements and the shape of the thin inclusion.     

Kernel formula approach to the universal Whitham hierarchy

Based on the kernel formula proposed by Carroll and Kodama, we derive the dispersionless Hirota equations of the universal Whitham hierarchy. We also verify the associativity equations in this hierarchy from the dispersionless Hirota equations and give a realization of the associative algebra with the structure constants expressed in terms of residue formulas.     

The asymptotic properties of the motions of satellites in a central field due to internal dissipation

A satellite in the form of a system of bodies that does not have the property of a gyrostat in the general case is considered. An algorithm for determining all the equilibrium configurations of the system that correspond to steady motions in a central gravitational field and an algorithm for analysing their stability are given. A method based on Routh's first theorem is used to investigate the asymptotic stability of the steady motions in the unconstrained problem. Three effects caused by internal dissipation are established in a model example: stabilization of the satellites in a neighbourhood of rotations about a normal to the orbital plane, which is codirectional with the axis of the largest moment of inertia, evolution of elliptic orbits into circular orbits, and capture of the satellites in resonant oscillatory modes of motion.     

Proton emission from nuclei due to neutron interactions

The energy spectra of protons emitted in neutron bombardment of Al²⁷ is analysed in terms of the statistical model and volume direct interaction. It is found that the diffuseness of the nuclear potential or the form of level density used does not alter the shape of the energy spectra very much. The available experimental data agree fairly well with theory. The contribution of direct interaction is seen to be small and hence does not alter the general shape of the spectra. The direct interaction cross-section obtained from the measurements of the angular distribution in the case of iron and copper agree reasonably well with theory.     

Transitions from bursting to spiking due to depolarizing current in the Chay neuronal model

Distinct transitions of firing activities from bursting to spiking induced by the depolarizing current I are explored near the Hopf bifurcations in the Chay neuronal system. The period-1 “circle/homoclinic” bursting at one rest state makes a transition slowly to repetitive spiking with the parameter I increasing. However, the “Hopf/homoclinic” bursting via a “fold/homoclinic” hysteresis loop at another rest state may transit to continuous spiking abruptly by increasing I.     

Applying the universal iterative process to some problems of mechanics

The iterative universal process, which was introduced by the author some years ago, is applied to quasilinear boundary value problems in elasticity and filtration. It is proved that the method converges both in weak (energy) and strong (C ^γ(γ > 0)). Some results concerning the existence of weak and regular solutions are proved. The proof is based on general results such as the Korn inequality for weighted spaces and the method of elastic solutions.The main results also contain the Hölder continuity of displacements for elasto-plastic media with hardening.     

On the Sprindžuk-Weissauer approach to universal Hilbert subsets

The works of both Sprindžuk (1979–80) and Weissauer (1980) consider the relation between Hilbert subsets of Q and sets consisting of powers of primes. A comparison of their results leads to generalizations and new proofs devoid of eitherp-adic diophantine approximation or of nonstandard arithmetic (§3 and §4). Results of Weissauer, giving new Hibertian infinite extensions of every Hilbertian field, receive short direct standard proofs, and a negative answer is given to a question of Roquette on the relation between Hilbert sets and value sets. Partially supported by a Fulbright-Hays research grant at Helsinki University, Fall semester, 1982.