Percolation model of SHF breakdown in a dielectric

A percolation model of gas-discharge evolution is described in the cellular automaton paradigm, which makes it possible to overcome difficulties associated with the complex geometry of discharge structures. The two-dimensional case is considered, when the potential of the discharge region is zero and the potential on the outer boundary varies harmonically. Both linear and circular polarization of the external field is allowed. Typical fractal structures are derived, and their fractal dimension is calculated by two methods.Translated from Matematicheskie Modeli Estestvoznaniya, Published by Moscow University, Moscow, 1995, pp. 10–16.     

Determination of the strength of the bonds between the fibers in cellulose compositions

It has been shown that the magnitude of the tensile strength of the bonds between the fibers in cellulose compositions can be determined from data obtained by measuring the tensile strength of a specimen at standard and zero length. The influence of the thickness of the material on some of its strength and optical characteristics has been studied. It has been confirmed experimentally that there is a functional relationship between the tensile strength of the bonds between the fibers and the magnitude of the light-scattering coefficient in the cellulose compositions studied.     

Reciprocity between partitions and compositions

The Ramanujan Journal - In this paper, we extend the work of Andrews, Beck and Hopkins by considering partitions and compositions with bounded gaps between each pair of consecutive parts. We show...     

A nondestructive method of testing the mechanical strength anisotropy of cellulose compositions

A nondestructive method of testing the mechanical tensile strength anisotropy of cellulose compositions from the coefficients of reflection of polarized shf waves is described. Equations for finding the reflection coefficient from the measured value of the SWR of the shf wave are presented. It is shown that there is a close linear correlation between the mechanical strength anisotropy and the anisotropy of the shfwave reflection coefficient.     

The electrically induced stress in the dielectric of a transmission coaxial line

The electrically induced stress in the dielectric material of a rectangular coaxial line with a centered inner cross is investigated by use of a conformal mapping method in complex plane. The electric field is analytically expressed through elliptic functions. The components of the stress parallel and perpendicular to the electric field are computed. The location where the maximum stress occurs is determined. The centered strip line and square coaxial line are discussed as sample problems. The stress distribution in dielectric is improved through electrostriction coefficient when the dependence of permittivity on strain is considered. This methodology can be applicable to other transmission lines.     

Soft supersymmetry breaking as a spontaneous breaking in the auxiliary sector

Soft supersymmetry breaking is accomplished as a spontaneous symmetry breaking by extending the auxiliary field content of the model. The renormalization procedure in such models is discussed. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 117, No. 2, pp. 325–329, November, 1998.     

Effect of fillers on the sensitivity of epoxide compositions to stress concentrations in the glassy state

The results are presented of a study of the effect of mica and annealed and unannealed quartz on the strength characteristics of epoxide compositions and on their sensitivity to stress concentrations in the glassy state. It was established that the positive effect of the fillers on the properties of the polymeric compositions in the glassy state becomes apparent in a reduction of the sensitivity of these materials to stress concentrations.Institute of Physical Chemistry, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 929–931, September–October, 1973.     

Certain correlations between the physico-chemical properties and breaking characteristics of polyvinyl alcohol fibers

The experimental correlation between the structural orientation of polyvinyl alcohol fibers and their breaking characteristics is discussed and explained.Leningrad Branch, All-Union Scientific-Research Institute of Synthetic Fibers. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 349–351, March–April, 1969.     

A relation between long-range correlation and dielectric anomaly

A double-well potential model is established to explain the dielectric anomaly of ferroelectrics. The dielectric constant consists of two parts. One part is independent of the long-range correlation, following 1/T law. The other part originates from the long-range correlation, and can be described by the correlation length well. The deviation from Curie-Weiss law in a small size sample originates from the decrease of the long-range correlation. Project supported by the Climbing Program of Foundamental Research of China.     

Casimir force between metal plate and dielectric plate

The Casimir effect between metal plate and dielectric plate is discussed with 1 + 1-dimensional potential model without using cut-off method. Calculation shows that the Casimir force between metal plate and dielectric plate is determined not only by the potentialV ₀, the dielectric thickness and the distancea between the metal plate and dielectric plate, but also by the dimension of the vessel. Whena is far less than the dimension of the vessel, the Casimir forceF _c ∝a ^-1; converselyF _c ∝a ^-2 This result is significant for Casimir force experiment.     

The relationship between stress and deformation of polymers in the linear stress state

The relation between stress, strain and strain rate is proposed as a means of describing the deformation properties of polymers. The equation describes the stress-strain curve, aftereffect, and stress relaxation in polymers. The theoretical conclusions are in good agreement with the results of creep tests on kapron (nylon-6).Mekhanika Polimerov, Vol. 1, No. 5, pp. 25–29, 1965     

Correlation between the strength and relaxation properties of polymers in the rubbery state

The molecular nature of the processes of fracture and relaxation of polymers in the rubbery state is examined. Allowance for the activating influence of mechanical stress and temperature leads to the obtaining of certain relaxations which describe, more accurately than the existing ones, the temperature-stress dependences of the rupture life and the activation energy of the various molecular processes.     

Correlation between the strength and thermal conductivity of glass-reinforced plastics

The effect of changes in the component ratio and porosity of glass-reinforced plastics on their strength and thermal conductivity is considered. A correlation is shown to exist between the bending strength and thermal conductivity of a glass laminate.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 749–751, July–August, 1969.     

Relations between the strain and stress tensors in successive biaxial tension

The manner of applying the load is one of the main factors governing the formation of the principal strains and their limiting values. Starting from the theory of local strains, relations between the strain and stress tensors are formulated for both simple and complex loading. It is shown that the principal strains associated with a given stress state vary depending upon the loading path.Mekhanika Polimerov, Vol. 1, No. 3, pp. 43–51, 1965     

Cyclic compositions and cycles of the hypercube

The partition graph of a positive integer n, \(P_n\), is the graph whose vertices are the cyclic compositions of n and two vertices are adjacent if one composition is obtained from the other one by replacing two cyclically consecutive parts by their sum. In this paper we introduce and investigate the notions of singular cyclic composition and singular edge of \(P_n\). We associate with every singular edge and every cycle of \(P_n\), whose vertices are aperiodic cyclic compositions of n, a cycle or a set of disjoint cycles of equal length of the hypercube \(Q_n\).     

The connection between dielectric susceptibility and weight by volume of vitreous plastics

Experimental results of measurements of dielectric susceptibilities of vitreous plastics by use of SHF electromagnetic waves are presented. A connection is shown between the dielectric susceptibility over the specimen as it depends on the technological pressing process.V. I. Ul'yanov (Lenin) Leningrad Electrotechnical Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1133–1135, November–December, 1972.     

Wave propagation and breaking in multidimensional magnetogasdynamic flows

Summary The theory of shocks evolving from weak discontinuities is applied to magnetogasdynamics and worked out in detail for two situations: a spherical disturbance propagating into a uniform magnetic field, and a planar disturbance propagating in the field of a current-carrying wire. For both cases, shock formation is delayed as the magnetoacoustic speed of propagation approaches the Alfvén speed. This agrees with the fact that Alfvén waves do not steepen to form shocks.

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Résumé On applique à la magnétogasdynamique la théorie des ondes de choc produites par l'évolution des discontinuités faibles. On présente des résultats sur la formation de chocs par des ondes magnétoacoustiques. Lorsque la vitesse de propagation de ces ondes se rapproche de la vitesse d'Alfvén, l'apparition des chocs est retardée, en accord avec le résultat bien connu que les ondes d'Alfvén ne se transforment pas pour former des chocs.

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Research supported in part by Grant No. AFOSR-73-2561.