Surface polaritons in a dielectric at a boundary with a metal in a static electric field

The existence of surface polaritons in a dielectric at a boundary with an ideal metal or superconductor in a static electric field is predicted. The frequency regions in which polaritons exist are substantially different for opposite orientations of the electric field, so that a change in the direction of the field signifies “switching on” or “switching off” of surface polaritons with a fixed frequency. Pis'ma Zh. éksp. Teor. Fiz. 68, No. 12, 876–880 (25 December 1998)     

Drag on a sphere in a fluid

Summary The possible acceleration dependence of the drag on a sphere, executing a translatory motion in a fluid, is examined in detail. After revisiting the standard derivations of this dependence, it is pointed out that the result might be connected with the scheme of incompressible fluids. That the adoption of this scheme is crucial is made evident by showing that a striking contradiction would arise in compressible fluids. Next a procedure is applied which, in a suitable linear approximation, leads to an explicit expression for the drag in compressible fluids. The drag turns out to depend both on the present value and on the history of the speed of the sphere.

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Riassunto Si considera una sfera in moto traslatorio in un fluido e si esamina il problema dell’eventuale dipendenza della forza resistiva dall’accelerazione. Sulla base delle derivazioni classiche di tale dipendenza, si mette in evidenza che il risultato potrebbe essere conseguenza diretta dell’adozione del modello di fluido incomprimibile. Che tale modello sia realmente cruciale è provato anzitutto osservando che l’analoga trattazione, nel caso di fluidi comprimibili, conduce ad una contraddizione. Successivamente, seguendo un’opportuna approssimazione lineare, si perviene all’espressione esplicita della forza resistiva in un fluido comprimibile. Tale forza risulta dipendente sia dal valore attuale sia dalla storia della velocità della sfera.

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Резюме Рассматривается трансияционное движение сферы в жидкости и исследуется проблема эффективной зависимости силы сопротивления от ускорения. После анализа стандартных подходов для вывода этой зависимости отмечается, что исследуемый результат может быть связан с выбранной моделью несжимаемой жидкости. Тот факт, что выбор модели является сушественнум, иллюстрируется в случае сжимаемых жидкостей, где возникает противоречие. Затем развивается линейное приближение, которое приводит к явному выражению для сопротивления в сжимаемых жидкостях. Оказывается, что сопротивление зависит не только от скорости в данный момент, но и от истории скорости сферы.

     

Impurity diffusion in a gas flow in a channel

The impurity concentration N in a gas flow in a channel is approximately calculated. In a number of cases, the wall losses of impurities in the channel can be taken into account by introducing an effective lifetime τ that describes the diffusion drift of the impurity from the flow toward the walls.     

Excess entropy for a vacancy in a crystal

The following topics are discussed: (1) Within the harmonic theory a general expression is given for excess entropy of a localized detect in any crystal with cyclic boundary conditions and in the small perturbation limit. For a single vacancy defect Stripp and Kirkwood's formula is obtained, ΔS/k_B = d/2,d being the dimension of the space. For other localized defects the perturbation formula requires calculation of the unperturbed Green's matrix. (2) It is argued that the effect of free surface boundary conditions, as well as other surface changes, leaves ΔS effectively invariant. (3) Using the vacancy perturbation result for ΔS and Lawson's formula, a value for the vacancy formation volume is obtained only in terms of known measured parameters; this result is compared to experimental and other calculated values of ΔV_f. (4) If localized vibrational modes are present due to the vacancy, what effect these might have on ΔS, and, from this, what materials might be candidates for observing localized modes.     

Dynamic shielding of a charge in a metal

A discussion of the shielding of a charged particle in a current-carrying conductor is given that is based on the linearized Thomas-Fermi approximation. An expression for the force on a particle of charge q is obtained from which the value of the electric field E_c in the conductor may be found:

$\text{E}{}_{\mathrm{c}}\text{=}\text{lim}\text{q→0}\text{F}{}_{\mathrm{q}}\text{/q}$

It is shown that the force on the particle has the form $\text{F}{}_{\mathrm{q}}\text{= q}\text{E}{}_0\text{× (1 + γ(}\text{q}\text{e}\text{) + …}$ to second order in the charge q, where E₀ is the electric field at large distances from q, e is the charge of the carrier, and γ is a material-dependent constant. The shielding correction has the character of a “wind-force,” and the electric field in the conductor is given by Ec = E₀.     

Diffusion of a Heteropolymer in a Multi-Interface Medium

We consider a heteropolymer, consisting of an i.i.d. concatenation of hydrophilic and hydrophobic monomers, in the presence of water and oil arranged in alternating layers. The heteropolymer is modelled by a directed path ( $\left( {i,S_i } \right)_{i \in \mathbb{N}_0 }$ , where the vertical component lives on $\mathbb{Z}$ , and the layers are horizontal with equal width. The path measure for the vertical component is given by that of simple random walk multiplied by an exponential weight factor that favors matches and disfavors mismatches between the monomers and the medium. We study the vertical motion of the heteropolymer as a function of its total length n when the width of the layers is d _n and the parameters in the exponential weight factor are such that the heteropolymer tends to stay close to an interface (“localized regime”). In the limit as n→∞ and under the condition that lim _n→∞ d _n /log log n=∞ and lim _n→∞ d _n /log n=0, we show that the vertical motion is a diffusive hopping between neighboring interfaces on a time scale exp[χd _n (1+o(1))], where χ is computed explicitly in terms of a variational problem. An analysis of this variational problem sheds light on the optimal hopping strategy.     

Formation of a bistructure of a solid in a computer experiment

Molecular-dynamics was used to investigate the structural changes occurring in a three-dimensional solid when the solid is transferred from an amorphous into a crystalline state. Crystal cells of a new type — pentadecahedrons with five square lateral faces and ten regular triangular faces at the vertices of a cell — were found for the first time in a computer experiment. It is shown that a bistructure consisting of crystal cells of different types, including cells with five-fold symmetry axes, are stable in the solid. Fiz. Tverd. Tela (St. Petersburg) 40, 1919–1924 (October 1998)     

Spin relaxation of triplet pyrene in a crystal and in a glass

We have investigated the EPR spectral lines of the photo-excited triplet state of pyrene-d-10 both in a fluorene single crystal and an ethanol glass matrix. In the crystal we have measured the width, shape and saturation parameters, λ′, a and B _{1/2 ^u} , of the ΔM = 1 lines from both sites in the cleavage plane, Y-Z, at 193 K and along the principal directions, X, Y, Z, between 143 K and 300 K. In the glass the same parameters have been measured for the six resonances of the absorption derivative at 77 K. We have used a general deconvolution procedure to extract the unresolved inhomogeneous and homogeneous broadenings, ΔB _G and ΔB _L ≡ 1/γT ₂, and the spin-lattice relaxation rate, T ₁ ^-1, from λ′, a and B _{1/2 ^u} for the different types of resonances. The use of Fourier-series expansions permits optimal utilization of the data and resolution of the terms of different symmetries for these quantities. The application of the method of moments, using assumed spin densities, permits the demonstration that the main contribution to the constant term of ΔB _G, but only a small part of its anisotropy, originates from the intramolecular hyperfine interactions. As T ₂ and T ₁ are of the same order of magnitude, we have assumed the same mechanism, i.e. modulation of the fine-structure tensor D, for both relaxation effects. A first-order semi-classical treatment leads to partial agreement between the main features of the calculated and observed orientation dependences if one assumes strongly anisotropic librations coupled to large modulations of D. This is consistent with the maximal libration amplitudes estimated from the differences between the D tensors measured in the crystal and in the glass. Variations with temperature are attributed to a competition between the increase of modulation amplitudes and decrease of correlation time with heating.     

Characteristics of a reflex discharge in hydrogen in a magnetic field

The properties of an extensive reflex discharge of large power with one heated and one cold cathode in a magnetic field of 10 to 1500 Gauss were measured. At a neutral hydrogen pressure of 10^–4 to 10^–3 torr a plasma column was obtained which was 100 cm long, 10 cm in diameter and had a density greater than 10^–11 cm^–3. The dependence of the radial profile of the potential in the plasma was measured by a heated probe, and the temperature and electron density by Langmuir probes calibrated by a microwave interferometer.The dependence of the origin of low-frequency rotational instability on the parameters of the discharge was studied and the measured critical magnetic field was compared with theory. Apart from this low-frequency instability, intensive oscillations were also found in the discharge current in a frequency band up to 30 MHz, and the dependence of their spectrum on the magnetic field was measured.     

Intermolecular interactions in acetonitrile in a liquid and in a low-temperature argon matrix

IR spectra of acetonitrile embedded in an argon matrix and in a liquid are recorded. IR spectra of specimens obtained with different concentrations of acetonitrile in argon are analyzed. The spectral region of C≡N vibrations of 2200–2300 cm⁻¹ with bands of monomers and possible associates is investigated. Overlap with the band of a hot transition on the low-frequency side is responsible for the pronounced asymmetry of the band ν(C≡N). To whom correspondence should be addressed. St. Petersburg State Institute of Precision Mechanics and Optics (Technical University), 14, Sablinskaya Str., St. Petersburg, 197101, Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 5, pp. 627–631, September–October, 1999.     

Thermodynamics of a Charged Particle in a Noncommutative Plane in a Background Magnetic Field

Landau system in noncommutative space has been considered. To take into account the issue of gauge invariance in noncommutative space, we incorporate the Seiberg-Witten map in our analysis. Generalised Bopp-shift transformation is then used to map the noncommutative system to its commutative equivalent system. In particular we have computed the partition function of the system and from this we obtained the susceptibility of the Landau system and found that the result gets modified by the spatial noncommutative parameter θ. We also investigate the de Hass–van Alphen effect in noncommutative space and observe that the oscillation of the magnetization and the susceptibility gets noncommutative corrections. Interestingly, the susceptibility in the noncommutative scenario is non-zero in the range of the magnetic field greater than the threshold value which is in contrast to its commutative counterpart. The results obtained are valid upto all orders in the noncommutative parameter θ.     

Dipolar excitons in a potential trap in a magnetic field

The conditions for observing the Zeeman spin splitting compensation in an exciton Bose gas have been investigated. The magnetoluminescence of spatially indirect, dipolar excitons in a 25-nm-wide GaAs/AlGaAs quantum well upon their accumulation in a lateral electrostatic trap has been studied in the Faraday geometry. The critical magnetic field B _cr below which the spin (paramagnetic) splitting of the luminescence line for a heavy-hole exciton at the trap center is almost completely compensated due to the exchange interaction in a dense Bose gas has been found to increase linearly with exciton concentration in qualitative agreement with the theory. Using a potential trap is fundamentally important. Incomplete compensation is observed in a homogeneous photoexcitation spot for dipolar excitons: the splitting is considerably smaller than that for a spatially direct exciton but differs noticeably from zero. The spin splitting compensation effect is observed only under neutral charge balance conditions—there is no Zeeman splitting suppression in a charged quantum well.     

Properties of a magnetic impurity in a metal

The effect of a polarized conduction-electron cloud back on a magnetic impurity dissolved in a metal is studied. It is shown that at a temperature T _c much higher than the Kondo temperature the system becomes unstable against symmetry breaking and that a state with 〈S _z 〉 ≠ 0 is established. The behavior of 〈 S _z 〉 is derived for all temperatures and magnetic fields except for a very narrow region around T _c and for very low temperatures. The minute role of Kondo-type processes in establishing the symmetry-broken state is pointed out. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 3, 184–189 (10 August 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Stagnation-point flow past a shrinking sheet in a nanofluid

In this paper, the stagnation-point flow and heat transfer towards a shrinking sheet in a nanofluid is considered. The nonlinear system of coupled partial differential equations was transformed and reduced to a nonlinear system of coupled ordinary differential equations, which was solved numerically using the shooting method. Numerical results were obtained for the skin friction coefficient, the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the nanoparticle volume fraction φ, the shrinking parameter λand the Prandtl number Pr. Three different types of nanoparticles are considered, namely Cu, Al₂O₃ and TiO₂. It was found that nanoparticles of low thermal conductivity, TiO₂, have better enhancement on heat transfer compared to nanoparticles Al₂O₃ and Cu. For a particular nanoparticle, increasing the volume fraction φ results in an increase of the skin friction coefficient and the heat transfer rate at the surface. It is also found that solutions do not exist for larger shrinking rates and dual solutions exist when λ < −1.0.     

Plasmons at a hole in a screen

The field distribution and the spectrum of plasma eigenmodes are determined for a circular hole in a screen having the form of a hyperboloid of revolution. The spectrum of plasmons is obtained for a planar screen with a circular hole. The symmetric mode with m=1 can be excited in the field of a dipole oriented along the screen plane, whereas the antisymmetric mode with m=0 can be excited by a dipole perpendicular to the screen plane.     

Field structure in a photorefractive holographic grating in a planar waveguide

A theoretical investigation is made of the field structure in a holographic grating formed by TE₀ modes in a planar photorefractive waveguide by the photogalvanic recording mechanism. Waveguides with three characteristic refractive index profiles are considered, namely, a step function, a parabola, and a hyperbolic secant squared. A comparison is made between the light field distributions of TE₀ modes in waveguides having the different profiles. The field structure of the space charge in planar holographic gratings is analyzed for their initial formation phase. It is shown that the space charge field has a similar structure for all three waveguide types considered when planar photorefractive gratings are recorded by TE₀ modes.Institute of Automated Control Systems and Radio Electronics, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 85–92, November, 1993.     

Analysis of a penny-shaped crack in a magneto-electro-elastic medium

The solution for an ellipsoidal cavity in an infinite transversely isotropic magneto-electro-elastic medium under remotely applied axisymmetric, combined mechanical–electric–magnetic loading is derived. The exact solution for a penny-shaped crack is obtained by letting the minor axis of the ellipsoidal cavity approach zero. The results demonstrate that the stress intensity factor depends only on the applied mechanical loading, but the electric displacement intensity factor and the magnetic induction intensity factor depend on the applied combined loading, as well as the two ratios of β/α and γ/α. Parameter α is the ratio of the minor axis to the major axis of the ellipsoidal cavity, β is the ratio of the dielectric constant of the material in the cavity to the effective dielectric constant of the magneto-electro-elastic medium, and γ is the ratio of the magnetic permeability of the material in the cavity to the effective magnetic permeability of the magneto-electro-elastic medium. The two ratios characterize the permeability of the crack to electric and magnetic fields. Several limiting cases for β/α and γ/α are studied. A self-consistent method is adopted to determine the real crack opening α under the combined mechanical–electric–magnetic loading. The stress, electric displacement and magnetic induction intensity factors of a penny-shaped crack in BaTiO₃–CoFe₂O₄ composites are calculated for different volume fractions and different applied combined loadings.     

Time in a simple model of a physical system

We build a model of time starting from the primitive concept of base-setB≡{α _i |i∈I} of all physical systems, whose elements are called pre-particles α _i . We assume thatB is a denumerably infinite set. Particles or bodies are represented by the subsets of the power setP (B) of the base-setB. A physical system is represented by a set of particles. We introduce the distinction between evolving and non-evolving particles, and assume that the former are represented by those subsets ofP (B) which are chains. Making use of the above concepts we define the state of a particle and the indicator of the state of a particle with respect to a given state of the same or another particle. Then we define in terms of indicators the concepts of instant, time-set, degenerate time-set, event, and clock. For the time related to a given clock one has a set in which the order relation is is in general not connected. Some theorems are proved.