Critical behavior of self-avoiding walks on fractals

Using a new graph counting technique suitable for self-similar fractals, exact 18th-order series expansions for SAWs on some Sierpinski carpets are generated. From them, the critical fugacityx _c and critical exponents _SAW and _SAW are obtained. The results show a linear dependence of the critical fugacity with the average number of bonds per site of the lattices studied. We find for some carpets with low lacunarity that _SAW<0.75, thus violating the relation _SAW(fractal) > _SAW (d) for SAWs on the fractals which are embedded in ad-dimensional Euclidean space.     

Study of the Β decay of6He with allowance for second-class currents and the antineutrino mass

The effects of the rest mass of the electron antineutrino are studied with allowance for the induced tensor form-factor F_c of the second-class current according to the Weinberg classification during the decay of the⁶He nucleus. We calculate the contribution of m and F_c to the electron-antineutron angular correlation coefficient A_e and the degree of longitudinal polarization P_e of the decay electrons. When m is nonzero, the coefficient A_e tends asymptotically to zero both at the beginning and endpoint of the spectrum, whether or not the second-class currents are taken into account. The series of qualitatively new experiments planned for the near future to measure the e- correlation for pure Gamow-Teller transitions (the⁶He nucleus could be a suitable nucleus here) with an accuracy of the order of 1% would allow the available estimate of the form-factor F_c to be improved substantially.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 62–67. September, 1989.     

Riccati-coupled similarity shock wave solutions for multispeed discrete Boltzmann models

We study nonstandard shock wave similarity solutions for three multispeed discrete Boltzmann models: (1) the square 8_i, model with speeds 1 and 2 with thex axis along one median, (2) the Cabannes cubic 14_i model with speeds 1 and 3 and thex axis perpendicular to one face, and (3) another 14_i, model with speeds 1 and 2. These models have five independent densities and two nonlinear Riccati-coupled equations. The standard similarity shock waves, solutions of scalar Riccati equations, are monotonic and the same behavior holds for the conservative macroscopic quantities. First, we determine exact similarity shock-wave solutions of coupled Riccati equations and we observe nonmonotonic behavior for one density and a smaller effect for one conservative macroscopic quantity when we allow a violation of the microreversibility. Second, we obtain new results on the Whitham weak shock wave propagation. Third, we solve numerically the corresponding dynamical system, with microreversibility satisfied or not, and we also observe the analogous nonmonotonic behavior.     

Electron cyclotron instability

The paper presents a study of the dependence of initiation and development of instability on the cyclotron frequency of electrons in a homogeneous plasma with cold ions and electrons forming two beams which move in the direction of, and opposite to, that of a constant magnetic field. It is demonstrated that for ^{2 2} , the instability can already arise at _pe ² _ce ² , and a brief comparison with the experimental results is carried out.The authors take this opportunity to thank Dr. M. Seidl for his valuable comments and stimulating discussions on this paper.     

Spin interaction with an ideal Fermi gas

We consider the equilibrium dynamics of a system consisting of a spin interacting with an ideal Fermi gas on the lattice , 3. We present two examples: when this system is unitarily equivalent to an ideal Fermi gas or to a spin in an ideal Fermi gas without interaction between them.     

Long-wave optical absorption in electron-bombarded GaAs

The absorption spectra of n- and p-type GaAs bombarded with 2-MeV electrons at T=300K were studied in the spectral range from 0.2 eV to Eg. It was found that shallow radiation-defect levels E_c – 0.01 eV and E_c + (0.06–0.1) eV were formed. The structureless character of the absorption in the region h < Eg in electron-bombarded gallium arsenide specimens was shown to be due to the distinctive features of photoionization of deep levels and the strong electron-phonon interaction in this material.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 93–97, July, 1981.     

ВЛИЯНИЕ ОСВЕЩЕНИЯ НА ПРОВОДИМОСТЬ И ФОТОПРОВОДИМОСТЬ З АКИСИ МЕДИ

, Cu₂O - 130–200 °C - . . - . , , , , - , - . - . - .     

К определению самопр оизволъной иамагниченности В об ласти точки кыри

. . , .     

The translation-rotation paradox in the nucleation theory

The factor of 10¹⁷ proposed by Lothe and Pound in the theory of nucleation of droplets from the vapor phase is studied using classical statistical mechanics. The controversial factor is derived from partition functions for an isolatedn-mer and for ann-molecular cluster imbedded in the bulk liquid phase. The rotational degrees of freedom have no place in, in agreement with Reiss, Katz, and Cohen's treatment. It is proved that the surface free energy of a cluster is proportional to the surface area. The estimate of what Lothe and Pound called the replacement term is different from those of previous authors. It is concluded that is written as a ratio = _g/_l, where _g and _l , are the volumes per molecule in the gas phase and in the liquid phase, respectively. For water at 300K, is approximately equal to 10₄.     

Hamiltonian formulation of general relativity in terms of Dirac spinors

The Dirac spinors and matrices are used in combination with the Arnowitt-Deser-Misner formalism in order to obtain yet another formulation of Hamiltonian general relativity, together with a new form of the Gauss-Codazzi equations. The relation with Ashtekar's variables is analyzed; it is shown, for instance, that the matrices are equivalent to the electric field variable. The electric and magnetic decomposition of the gravitational field is also studie using Dirac matrices.     

Hydromagnetic laminar flow of a conducting fluid in an annulus in presence of a radial magnetic field

The object of the present paper is to study the MHD effects on the laminar flow of a viscous, incompressible and conducting fluid in an annulus with arbitrary time-varying pressure gradient and arbitrary initial velocity in presence of a radial magnetic field. Using finite Hankel transform, solutions for both the unsteady and steady flows under different prescribed pressure gradients have been found out.Notation H a constant characterising the intensity of the magnetic field - p hydrostatic pressure - _e magnetic permeability - coefficient of viscosity - kinematic coefficient of voscosity - conductivity of the medium - density - a radius of the inner cylinder - b radius of the outer cylinder - parameter - s positive root - J (sr) Bessel's function of first kind of ordergl - Y (sr) Bessel's function of second kind of order     

ЗАТУХАНИЕ КОЛЕБАНИЙ ЧАСТИЦ В ОБЩЕМ ПОЛЕ С ПЕРИОДИЧЕСКОЙ СТРУКТУРОЙ I

, , . , . .

---

The damping of particle oscillations in a general field with periodic structure I

A liner theory is derived, discussing the dynamics of particles in the region of an equilibrium orbit in a general electromagnetic field, which forms a periodic system. The total particle damping is determined from the Hamiltonian found and from dissipative forces brought out by a classical reaction radiation. Relations for the damping of the synchrotron oscillations are derived from the study of the appropriate phase space.

     

Radius of clusters at the percolation threshold: A position space renormalization group study

Using a direct position-space renormalization-group approach we study percolation clusters in the limits , wheres is the number of occupied elements in a cluster. We do this by assigning a fugacityK per cluster element; asK approaches a critical valueK _c , the conjugate variables . All exponents along the path (K–K _c ) 0 are then related to a corresponding exponent along the paths . We calculate the exponent , which describes how the radius of ans-site cluster grows withs at the percolation threshold, in dimensionsd=2, 3. Ind=2 our numerical estimate of =0.52±0.02, obtained from extrapolation and from cell-to-cell transformation procedures, is in agreement with the best known estimates. We combine this result with previous PSRG calculations for the connectedness-length exponent , to make an indirect test of cluster-radius scaling by calculating the scaling function exponent using the relation =/. Our result for is in agreement with direct Monte-Carlo calculations of , and thus supports the cluster-radius scaling assumption. We also calculate ind=3 for both site and bond percolation, using a cell of linear sizeb=2 on the simple-cubic lattice. Although the result of such small-cell calculations are at best only approximate, they nevertheless are consistent with the most recent numerical estimates.Supported in part by grants from ARO and ONR     

Knight shift,hyperfine field,NMR frequency and magnetization of a Neel-type nickel single crystal

The field dependence of the NMR line center frequency of naturally abundant⁶¹Ni has been studied with Néel-type nickel single crystals at 4.2 K. For internal fields H_i lower than H_is, which is the field necessary for complete magnetic saturation, a nonlinear correlation between and H_i was found due to changes of the orientation of the hyperfine field with H_i. For fields larger than H_is the linear variation lead to K=111.10^–4 for the Knight shift. Using available susceptibility data, we find _p=28.10^–6 emu/mole and _vv=92.10^–6 emu/mole.     

Cyclotron instabilities of a two-component electron plasma

A study is made of instability at frequencies close to the electron cyclotron frequency _B and its multiples, subject to the presence of two different groups of electrons. It is shown that a mixture of hot and cold electrons ( _ph ² _pc ² ) in the region of frequencies s _B, s2 can be unstable with respect to waves of the flute type (k _z=0) with maximum increment _max ( _ph/_pc). _B, if there exists an interval of transversal velocities in whichF/ >0. When the curvature of the magnetic field is taken into account, even waves with _B can be unstable in such a plasma. The effect of spatial inhomogeneity of the hot component on flute-type instability and on two-beam cyclotron instability is also examined.The author extends his thanks to A. B. Mikhajlovskij for his valuable comments and discussions.     

Convective excitation of quasistatic waves in an inhomogeneous anisothermic plasma II. Nonlinear estimates

Nonlinear effects stabilizing the convective instabilities excited in an anisothermic plasma (T _etT _i) at the plasma boundaryaV_s/ _Bi) are discussed. Waves having in the linear theory (Part I) the highest growth rates ( _Bi) saturate at first. Being excited by a small part of slow plasma electrons ( _zTe) only, they saturate at a relatively low level. Further, surface waves with lower frequencies and higher phase velocities ( _ph/k_z) become dominant and a broadening of the plasma boundary occurs. For their saturation nonlinear interaction is more important than the quasilinear effects. During the time interval of several _Bi ^–1 the longest surface waves withk _yBi/V_s, _Bik_yV_s and _{ph Te} saturate at the absolutely highest level. The plasma boundary broadens in the meanwhile up toaV _s/_Bi. The wave energy is comparable to the whole energy connected with the longitudinal motion of the initially thermal electrons inside this boundary layer. The wave amplitude is large enough to trap the initially cold ions belonging to this layer and heat them up to energies comparable to those of the electron component. The heating process occurs again within several _Bi ^–1 and the Larmor radius of the ions is then comparable toV _s/_Bi. Further evolution of the system is governed by the unstable local perturbations.He leaves of absence from thePhysical and Technical Institute, Kharkov, USSR.     

Ionization wave in a longitudinal RF field

We investigate a stationary one-dimensional ionization wave produced in a cold gas by an alternating electric field of frequency (the field is parallel to the direction of propagation of the wave). Primary attention is given to specific features associated with the existence of a plasma resonance transition region at the front of the wave, where the electric-field amplitude and, therefore, the collisional ionization rate of the gas have a pronounced maximum at low electron-collision frequencies . We investigate analytically and calculate numerically the parameters of the wave, which is described by a nonlinear diffusion equation. It is shown that a made of ultrafast discharge propagation with ionization wave velocity V for /0 can be established in the gas due to resonance effects even if the external electric field has amplitude far below breakdown.Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 10, pp. 991–1000, October, 1995.     

Systematic study of muon transfer to sulphur dioxide

In a systematic study of the transfer process to sulphur dioxide, in seven different H₂ + SO₂ gas mixtures, the time spectra of the muonic sulphur X-rays yield muon transfer rates to the SO₂ molecule, deduced from the lifetimes of the p atoms, which agree all well with each other. The muonic oxygen time spectra show an additional structure as if p atoms of another kind were present. Reduced transfer rates_O are reproducible if one uses the model of ephemeral p atoms. The intensity ratios between the different kinds of p atoms are also discussed in the framework of this model and the one of black and white p atoms.     

Anomaly of the soft-mode damping function near phase-transition points due to interaction with acoustic phonons

An expression is derived for the anomalous part (T, ) of the soft-mode damping function due to third-order interaction between critical optical phonons and acoustic phonons. It is shown that in crystals with a large elastic viscosity the damping function of critical phonons can have stronger temperature anomalies near phase-transition points. The frequency dispersion of () is investigated; it is found that the damping is a maximum at =_o for the soft-mode vibrational dynamics and at =0 for the relaxational dynamics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 47–49, March, 1982.     

Calculation of the dependences of the sextic constants of H2O molecules on the quantum number v2

The paper gives a quantitative and qualitative explanation of the anomalously strong dependence of some sextic constants of the centrifugal distortion of the H₂O molecule on the flexural vibration mode N₂.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 75–80, September, 1984.