Magnetoplastic effects in solids

This paper is an overview of the studies into the effect of weak magnetic fields on the structure and mechanical properties of nonmagnetic solids of various nature (ionic, covalent, molecular, and metallic crystals, polymers, etc.). The various effects and aftereffects initiated by static, pulsed, and microwave magnetic fields that have been discovered over the past 15 years are classified and critically analyzed. The thermodynamic and kinetic aspects of the magnetic-field sensitivity of real solids with structural defects containing paramagnetic centers (electrons, holes, radicals, excitons, etc.) are discussed. Possible mechanisms for the effect of a weak magnetic field on the defect structure of crystals are considered. Special attention is given to the most developed chemical-physical theory of spin-dependent reactions between mobile particles and unpaired electrons. Interpretation of magnetoplastic effects is proposed in terms of the spin, electron, molecular, and dislocation dynamics of the complex multistage processes initiated by a magnetic field in a system of metastable structural defects.     

Thermodynamic and kinetic aspects of the weakening of ionic crystals by pulsed magnetic fields

The effect of short (10⁻² s) magnetic-field pulses (B=7 T) on the plastic flow of ionic crystals is investigated. The stages of the transition process stimulated by a field in the system of structural defects of the lattice are distinguished. The results are discussed from the standpoint of the thermodynamics and kinetics of processes in nonequilibrium systems. Fiz. Tverd. Tela (St. Petersburg) 39, 2016–2018 (November 1997)     

Identities of sums of commutative subalgebras

SiaR un'algebra associativa tale cheR=A+B conA, B sottoalgebre commutative. Si dimostra cheR soddisfa l'identitá polinomiale [[x,y],[z,t]]≡0 e che, seV é la varietá determinata da questa identitá,V é la piú piccola varietá contenente tutte le algebre somma di sottoalgebre commutative. Si determina inoltre la struttura delle algebre libere diV.

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Research supported in part by MURST of Italy.     

Reversible and irreversible magnetic-field-induced changes in the plastic properties of NaCl crystals

It is established that a weak magnetic field with induction B∼1 T gives rise to irreversible changes in NaCl crystals without freshly introduced dislocations, while a strong magnetic field with induction 16<B<35 T gives rise predominantly to reversible changes. It is inferred that there exist two different channels whereby a magnetic field influences the state of point defects. Fiz. Tverd. Tela (St. Petersburg) 40, 2065–2068 (November 1998)     

Model calculations in reconstructions of measured fields

The state of technological systems, such as reactions in a confined volume, are usually monitored with sensors within as well as outside the volume. To achieve the level of precision required by regulators, these data often need to be supplemented with the solution to a mathematical model of the process. The present work addresses an observed, and until now unexplained, convergence problem in the iterative solution in the application of the finite element method to boundary value problems. We use point group theory to clarify the cause of the non-convergence, and give rule problems. We use the appropriate and consistent orders of approximation on the boundary and within the volume so as to avoid non-convergence.     

Asymptotic Approximations for the Distributions of the Multinomial Goodness-of-Fit Statistics under Local Alternatives

N. Cressie and T. R. C. Read (1984, J. Roy. Statist. Soc. B46, 440–464) introduced a class of multinomial goodness-of-fit statistics R^a based on power divergence. All R^a have the same chi-square limiting distribution under null hypothesis and have the same noncentral chi-square limiting distribution under local alternatives. In this paper, we investigate asymptotic approximations for the distributions of R^a under local alternatives. We obtain an expression of approximation for the distribution of R^a under local alternatives. The expression consists of continuous and discontinuous terms. Using the continuous term of the expression, we propose a new approximation of the power of R^a. We call the approximation AE approximation. By numerical investigation of the accuracy of the AE approximation, we present a range of sample size n that the omission of the discontinuous term exercises only slight influence on power approximation of R^a. We find that the AE approximation is effective for a much wider range of the value of a than the other power approximations, except for an approximation method which requires high computer performance.     

Magnetohydrodynamic flow past a drop at low Reynolds and Hartmann numbers

The flow of an electrically conductive liquid past a solid spherical particle at low Reynolds and Hartmann numbers in longitudinal and transverse magnetic fields was first investigated in [1,2]. The effect of a weak magnetic field on the strength of the resistance of a conductive drop in a dielectric medium was considered in [3]. In the present paper we consider the motion of a conductive liquid drop in an electrically conductive medium and calculate the strength of the resistance in the Stokes approximation for an arbitrary orientation of the uniform magnetic field and in the Oseen approximation for the case in which the direction of the magnetic field coincides with the direction of the oncoming stream. As in the previous studies, we do not consider the possibility of the formation of a double layer on the interface between the phases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 19–25, November–December, 1978.The authors are grateful to G. I. Petrov and the participants in the seminar they conducted for their comments on the work.