Modification of the equation of state upon structural transition from two-dimensional branching of Ti<Subscript>2</Subscript> dimers to a three-dimensional Ti<Subscript>13</Subscript> cluster

The equations of state for a set of clusters Ti_n (n = 2–13) are derived using the method of scattered waves. The changeover from dimers to three-dimensional structures is considered a consequence of the sequential decrease in the degree of anharmonicity of the interatomic interaction potential in the clusters.     

Parametric interaction of space-charge waves in asymmetric thin-film <Emphasis Type="Italic">n</Emphasis>-GaAs structures

Based on a theory developed previously, parametric interaction between space-charge waves in thin-film semiconductor structures with negative differential conductivity is analyzed. The analysis is carried out in the approximation that the drift flux of charge carriers has a rigid boundary and under the assumption that the frequency of low-frequency pumping equals the cutoff frequency f _c of waves being amplified (f _c roughly equals 30 GHz in our case). For asymmetric structures, a general multimode set of coupled equations is reduced to a pair of differential equations for the excitation amplitudes of the fundamental space-charge mode at the signal frequency ω_s and idler frequency ω_i=ω_s−ω_p. The equations are solved numerically for n-GaAs-based structures, and the solution obtained is discussed.     

An analytical least squares solution applied to spectral series limit determinations

A method is derived to determine spectral series limits analytically. It is assumed that the graphical quantum defect solution (n?n^* vs ν_lim?ν) is approximately linear (for the correct ν_lim) so that a least-squares fit may be obtained. The problem reduces to a non-linear system of three equations in three unknowns (two least-squares coefficients and the series limit) with a unique solution found numerically. Least-squares errors are also obtained for each variable. Results using this method agree well with published values obtained by the traditional graphical method. This procedure provides an operational method for series-limit determinations, independent of the subjective problems involved with the graphical method.     

Propagation and interaction of ion-acoustic solitary waves in a quantum electron-positron-ion plasma

This paper discusses the existence of ion-acoustic solitary waves and their interaction in a dense quantum electron-positron-ion plasma by using the quantum hydrodynamic equations.The extended Poincar’e-Lighthill-Kuo perturbation method is used to derive the Korteweg-de Vries equations for quantum ion-acoustic solitary waves in this plasma.The effects of the ratio of positrons to ions unperturbation number density p and the quantum diffraction parameter H e (H p) on the newly formed wave during interaction,and the phase shift of the colliding solitary waves are studied.It is found that the interaction between two solitary waves fits linear superposition principle and these plasma parameters have significantly influence on the newly formed wave and phase shift of the colliding solitary waves.The investigations should be useful for understanding the propagation and interaction of ion-acoustic solitary waves in dense astrophysical plasmas (such as white dwarfs) as well as in intense laser-solid matter interaction experiments.     

Nichtlineare Wechselwirkung elektromagnetischer Wellen im Plasma mit konstantem Magnetfeld

The nonlinear interaction of waves in anisotropic plasmas is considered. Solving the hydrodynamics equations with a n-th order perturbation procedure, an equation for the nonlinear electric field is derived. The n-th order current produced by interaction of waves with lower order is represented by means of a nonlinear tensor of conductivity, which is calculated for n = 2. It is shown, that a miced plasma wave with combination frequencies is excited as the result of interaction of two transverse (ordinary) waves propagating perpendicular to the magnetic field.     

Thermodynamics of III–V solutions with n components

A method has been developed for the calculation of phase diagrams of III–V mixtures with more than three components. The equations for the chemical potentials, activity coefficients and the free energy of the mixture and for the liquidus- and iso-solidus-concentration lines are given. The parameters, needed for the calculation, are the temperature of fusion, heats of fusion, and the interaction parameters. The interaction parameters can be fitted to datas of the binary or quasi-binary phase diagrams, or can be calculated using the electronegativities, energies of sublimation and molar volumes of the constituent elements.Two approaches for a mixture with n components are given, which give in the ternary and binary case the known equations. The two possible cases of quaternary III–V solutions are discussed explicitly.     

Influence of spatial dispersion of the first and the second orders simultaneously on the parameters of natural waves in a uniaxial crystal

It is found for the first time that the coexistence of two principal and two additional natural waves and only one additional wave (in the absence of the second one) is impossible in the exact solution and in the approximate solution, respectively, of the problem formulated in the title, because Fresnel’s general equation beaks up into two independent equations for two principal and two additional waves. A probable relationship is found between the small parameters of spatial dispersion of the first (γ) and the second (α₀) orders (α₀/γ≈1) for the spectral region far from resonances, for which the refractive index of the third additional wave for α₀=0 is approximately equal to the refractive index of one of two additional waves for α₀≠0 and γ≠0, when the wave normal is directed along the optical axis of a uniaxial crystal.     

Interaction of long magnetoacoustic waves in cosmic plasma with turbulence

The interaction of fast magnetoacoustic (FMA) waves in a plasma with particle concentration n_t∼n_i∼1 cm⁻³ is studied with allowance for Alfvén modes, which simulates turbulence. Equations that describe three-wave interaction of FMAs are derived and a method is indicated for constructing some stationary structures that form in the spatial synchronism of interacting FMA waves. The applicability of the inverse scattering problem method to the problem of the interaction of FMA waves in a turbulent plasma is discussed. Chechen State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, p. 3–9, September, 1997.     

On the criterion for effectiveness of wave linear transformation in a smoothly inhomogeneous medium and of nonadiabatic transitions during atomic collisions

A universal criterion for effectiveness of linear transformation of waves with locally close characteristic exponents in smoothly inhomogeneous media is obtained. The same criterion is applicable for estimating the effectiveness of nonadiabatic transitions in slow atomic collisions. The formalism developed for an analysis of the linear interaction of waves is based of the WKB asymptotic form of the solution of a scalar nth order ordinary differential equation. The obtained criterion can be applied in any practical problem for drawing a conclusion about the effectiveness of the linear interaction of modes if only the characteristic equation of waves in a homogeneous medium and the coefficients of the initial differential equation are known. In this case, the solution of the problem is reduced to elementary arithmetic calculations.     

Transmission waveguide resonator with dissipative and polarization-sensitive elements

The diffraction of E_p and H_p waves due to the inhomogeneous step expansion of a planar waveguide is analyzed. The resonant region consists of magnetodielectric layers, a resistive film, and a grating of parallel metal strips. The eigenmodes of the system are defined by the method of moments on the basis of equivalent boundary conditions and scattering characteristics. The solution is represented in the form of infinite systems of linear algebraic equations. The grating considerably increases the Q-factor of the trapped modes for H_p waves, decreases the velocity of such waves and affects differently the degree of intermode (E_p⇆E_n, H_p⇆H_n) transformation of the fields. A film with average conductance adds some dissipative losses but retains the dispersion dependences by selective action on the Q-factor of the trapped modes. The distinct boundary between attenuation and propagation regimes is absent. State University, Kharkov, Ukraine. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 7, pp. 926–936, July, 1998.     

Computing the Scaling Exponents in Fluid Turbulence from First Principles: Demonstration of Multiscaling

We develop a consistent closure procedure for the calculation of the scaling exponents ζ _n of the nth-order correlation functions in fully developed hydro-dynamic turbulence, starting from first principles. The closure procedure is constructed to respect the fundamental rescaling symmetry of the Euler equation. The starting point of the procedure is an infinite hierarchy of coupled equations that are obeyed identically with respect to scaling for any set of scaling exponents ζ _n . This hierarchy was discussed in detail in a recent publication by V. S. L'vov and I. Procaccia. The scaling exponents in this set of equations cannot be found from power counting. In this paper we present in detail the lowest non-trivial closure of this infinite set of equations, and prove that this closure leads to the determination of the scaling exponents from solvability conditions. The equations under consideration after this closure are nonlinear integro-differential equations, reflecting the nonlinearity of the original Navier–Stokes equations. Nevertheless they have a very special structure such that the determination of the scaling exponents requires a procedure that is very similar to the solution of linear homogeneous equations, in which amplitudes are determined by fitting to the boundary conditions in the space of scales. The renormalization scale that is necessary for any anomalous scaling appears at this point. The Hölder inequalities on the scaling exponents select the renormalization scale as the outer scale of turbulence L. We demonstrate that the solvability condition of our equations leads to non-Kolmogorov values of the scaling exponents ζ _n . Finally, we show that this solutions is a first approximation in a systematic series of improving approximations for the calculation of the anomalous exponents in turbulence.     

Cylindrical solitons in shallow water of variable depth

Summary The propagation and the interaction of cylindrical solitons in shallow vater of variable depth are studied. Starting from the cylindrically symmetric version of the equations describing long waves in a beach, a Korteweg-de Vries equation type ψ_τ+6ψψ_ξ+ψ_ξξξ=−Γ(τ)ψ is derived. Since no exact analytical solution has been found to date for this equation, some remarkable cases in which the equation takes up a tractable form are analysed. Finally the interaction between cylindrical imploding and expanding waves is considered and the phase shifts caused by the head-on collision are given. This work was supported by CNR-GNFM.     

Stationary Propagation of Coupled Nonlinear High Frequency Waves and Ion-Acoustic Waves in a Plasma

Stationary solutions of the coupled equations for high frequency transverse waves in a plasma and for the low frequency ion motion (T_e?T_i) are investigated numerically. The use of the nonlinear hydrodynamic equations instead of the linear wave equation for ion acoustic waves allows to look for solutions without restrictions of the Mach number M = V/c_s (V group velocity, c_s ion acoustic velocity) and the ratio ω/ω_pe (ω frequency of the HF-field, ω_pe electron plasma frequency at the undisturbed region). In particular, supersonic soliton-like solutions with n/n_o > 1 were found. Dispersion effects due to charge separation are not included.     

Generation and control of chaos in a Bose--Einstein condensate

For a Bose--Einstein condensate (BEC) confined in a double lattice consisting of two weak laser standing waves we find the Melnikov chaotic solution and chaotic region of parameter space by using the direct perturbation method. In the chaotic region, spatial evolutions of the chaotic solution and the corresponding distribution of particle number density are bounded but unpredictable between their superior and inferior limits. It is illustrated that when the relation k₁\approx k₂ between the two laser wave vectors is kept, the adjustment from k₂1 to k₂\ge k₁ can transform the chaotic region into regular one or the other way round. This suggests a feasible scheme for generating and controlling chaos, which could lead to an experimental observation in the near future.     

Measurements of theP 3/2-S 1/2-intervals in then=4,n=5 andn=6 states of ionized helium

TheP _3/2-S _1/2-intervals in then=4,n=5 andn=6 states of ionized helium have been measured by a radio frequency method, which permits to determine the disturbing electric fields in the interaction region and to correct their influences. The experimental results for theP _3/2-S _1/2 intervals in then=4,n=5 andn=6 states were (20,180.6±0.8) MHz, (10,332.9±1.4) MHz and (5,979.1±1.2) MHz respectively. From these intervals, the following indirect values for theS _1/2-P _1/2-Lambshifts can be deduced: (1,768.5±0.8) MHz in then=4 state, (905.0±1.4) MHz in then=5 state and (524.3±1.2) MHz in then=6 state. The results agree with the theoretical predictions. The static electric fields in the interaction region, ranging from 2 to 6 V/cm, increased with increasing electron excitation current, but were independent of the helium pressure within the range of 10 to 26 mTorr. All uncertainties are expressed as 68% confidence values.     

Exact stationary solution of a Fokker-Planck equation for multimode laser action including phase locking

We first derive the exact stationary solution of a Fokker-Planck equation where the complex drift coefficients are nonlinear functions of the variables, provided the drift and diffusion coefficients fulfill certain conditions. Then we apply the solution to

1. normal multimode action where no phase locking occurs at all.
2. phase locking in a laser with many axial modes having a narrow frequency spacing.

The atomic line which supports laser action may be homogeneously or inhomogeneously broadened. In case 1 the modes may be completely arbitrary, i.e. for instance running or standing waves. In case 2 we assume axial modes described by running waves. The treatment is valid in a region not too far below and not too far above laser threshold where the atomic variables adiabatically follow the motion of the lightfield variables. The drift coefficients are taken from the multimode Langevin equations ofHaken andSauermann. The diffusion coefficients are taken from a paper ofArzt et al. The only essential assumption is that the diffusion coefficients may be considered constant over the frequency range where modes participate in the laser process. If our results are specialized to single mode action we obtain Risken's solution.     

Gulyaev–Bleustein Waves in a Layered Structure of Piezoelectric – Periodic Granular High-Temperature Superconductor Structure

Bragg's interactions of Gulyaev–Bleustein surface waves with a periodic granular high-temperature superconducting medium are studied. Dispersion equations describing the characteristics of surface acoustoelectric waves are derived for piezoelectrics of 4 and 6mm symmetry. Resonance absorption of surface acoustoelectric waves is revealed near the critical temperature. The reflection coefficients for surface acoustoelectric waves in Ba₂Si₂TiO₃ from semi-finite and finite periodic high-temperature superconducting structures are calculated. The results obtained for this model problem can be used for solving similar problems for strong piezoelectrics (e.g., lithium niobate) and for designing tunable frequency selectors and transient bolometric photodetectors.     

Formulas for An- and Bn-solutions of WDVV equations

The simplest non-trivial solutions of WDVV equations are A_n-and B_n-potentials, which describe metrics of Saito on spaces of versal deformation of A_n-and B_n-singularities. These are some polynomials, which were known for n≤4. In this paper, we find the potentials for all A_n-and B_n-singularities. We give a recurrence formula for coefficients of KP and n-KdV hierarchy.     

The harmonic-map structure of the axially symmetric stationary Einstein equations

We systematically review the solutions of the vacuum Einstein equations for the axially symmetric stationary case which are harmonic maps. In particular, we show that the interesting part of the Kerr solution is a composition of a harmonic map intoH ₁ ² with a totally geodesic map fromH ₁ ² into SS(1,1). We also point out, relying on Sanchez' results, that there is an analogous structure for the Lorentz-domain cases involving cylindrical gravitational waves and colliding plane waves.