Transverse instability of a plane front of fast impact ionization waves

The transverse instability of a plane front of fast impact ionization waves in p ⁺-n-n ⁺ semiconductor structures with a finite concentration of donors N in the n layer has been theoretically analyzed. It is assumed that the high velocity u of impact ionization waves is ensured owing to the avalanche multiplication of the uniform background of electrons and holes whose concentration ??_b ahead of the front is high enough for the continuum approximation to be applicable. The problem of the calculation of the growth rate s of a small harmonic perturbation with wavenumber k is reduced to the eigenvalue problem for a specific homogeneous Volterra equation of the second kind containing the sum of double and triple integrals of an unknown eigenfunction. This problem has been solved by the method of successive approximations. It has been shown that the function s(k) for small k values increases monotonically in agreement with the analytical theory reported in Thermal Engineering 58 (13), 1119 (2011), reaches a maximum s _M at k = k _M, then decreases, and becomes negative at k > k ₀₁. This behavior of the function s(k) for short-wavelength perturbations is due to a decrease in the distortion of the field owing to a finite thickness of the space charge region of the front and ??smearing?? of perturbation of concentrations owing to the transverse transport of charge carriers. The similarity laws for perturbations with k ? k _M have been established: at fixed ??_b values and the maximum field strength on the front E _0M, the growth rate s depends only on the ratio k/N and the boundary wavenumber k ₀₁ ?? N. The parameters s _M, k _M, and k ₀₁, which determine the perturbation growth dynamics and the upper boundary of the instability region for impact ionization waves, have been presented as functions of E _0M. These dependences indicate that the model of a plane impact ionization wave is insufficient for describing the operation of avalanche voltage sharpers and that fronts of fast streamers in the continuum approximation should be stable with respect to transverse perturbations in agreement with the previously reported numerical simulation results. The results have been confirmed by the numerical simulation of the evolution of small harmonic perturbations of the steady-state plane impact ionization wave.     

Description of radiative strength functions in deformed nuclei

Radiative strength functions ofE1- andM1-transitions from ground states of doubly even deformed nuclei to states near the neutron binding energyB _n are calculated within the quasiparticle-phonon nuclear model. The wave functions of excited states include one- and two-phonon components. The calculations were made with the Pauli principle being or not included in the two-phonon components of the wave functions. It is shown that the radiativeE1- andM1-strength functions as well as the widths of giant dipole resonances in deformed nuclei are slightly influenced by the two-phonon components of the wave functions and they can be calculated in the RPA. Thek _E1- andk _M1-values are calculated for some deformed nuclei of the rare-earth and actinide region. The calculated values ofk _E1 are 1.5–2 times larger and the values ofk _M1 are somewhat less than the average values obtained in [14] from the analysis of available experimental data.     

Primordial inflation and present-day cosmological constant from extra dimensions

A semiclassical gravitation model is outlined which makes use of the Casimir energy density of vacuum fluctuations in extra compactified dimensions to produce the present-day cosmological constant as ρ _Λ ∼M ⁸/M _P ⁴, where M _P is the Planck scale and M is the weak interaction scale. The model is based on (4+D)-dimensional gravity, with D=2 extra dimensions with radius b(t) curled up at the ADD length scale b ₀=M _P /M ²∼0.1 mm. Vacuum fluctuations in the compactified space perturb b ₀ very slightly, generating a small present-day cosmological constant.The radius of the compactified dimensions is predicted to be b ₀≈k ^1/40.09 mm (or equivalently M≈2.4 TeV/k ^1/8), where the Casimir energy density is k/b ⁴.Primordial inflation of our three-dimensional space occurs as in the cosmology of the ADD model as the inflaton b(t), which initially is on the order of 1/M∼10⁻¹⁷ cm, rolls down its potential to b ₀.     

The green function of an infinite,fluid loaded membrane

In this paper the response of a fluid loaded plane structure (a membrane) to a concentrated line force excitation is considered in great detail. The normalized velocity response—here called the Green function G—depends upon a dimensionless range x₀=k_m|x|, where k_m is the free wavenumber on the membrane in a vacuum, on the Mach number $\text{M=}\text{k}{}_0\text{k}{}_{\mathrm{m}}$, the ratio of wave phase speed ω/k_m on the unloaded membrane to the sound speed ω/k₀, and on a parameter ? which can be regarded as a measure of fluid loading at the “coincidence” condition M=1. In the analogous problem involving a thin elastic plate, the corresponding parameter is independent of frequency and plate thickness and may be regarded as an intrinsic measure of fluid loading; moreover, in cases of common interest (steel in water, aluminium in air) that parameter is small. In the present paper, the asymptotic structure of G(x₀, M, ?) is therefore sought in the limit ? → 0. Naturally, no single asymptotic expansion can be expected to be valid throughout the (x₀, M) plane, and the programme therefore involves the delineation of regions of that plane in which distinct asymptotic results apply, the construction and discussion of those results, and the asymptotic matching (according to the procedures of the method of matched asymptotic expansions) of results holding in adjoining regions. The Fourier integral for G is broken into surface wave and acoustic components, and the asymptotic structure obtained for each. Previously obtained results for the behaviour at large distances are recovered, with a demonstration that very large distances indeed (x₀ ? ?^?2) may be needed for their validity for some ranges of M; and the drive point behaviour, of G(x₀=0, M, ?) as ? → 0 qua function of M, is shown to correspond to that already discussed in the literature. Elsewhere, in the covering of the whole (x₀, M) plane by different asymptotic expressions, a wide variety of analytical results is found, reflecting the achievement in different regions of different balances among the five competing physical mechanisms represented in the model: namely, structural stiffness, structural inertia, fluid pressures, fluid compressibility and fluid inertia. These different balances give rise to a wide variety of expressions for the phase and amplitude of the surface wave and acoustic components which can now be used to isolate the dominant structural and acoustic mechanisms at any point in the (x₀, M) plane.     

Brownian motion on a manifold as a limit of Brownian motions with drift

Let ?ⁿ be n-dimensional Euclidean space and let M ? ?ⁿ be a smooth compact m-dimensional Riemannian manifold (without boundary) embedded in ?ⁿ. By a Brownian motion on M we mean a Markovian process whose transition semigroup is defined by the generator ?½Δ_M, where Δ_M stands for the Laplace-Beltrami operator on M (see, e.g., [2]). This note extends a series of papers in which a measure generated by a Brownian motion on M on the space of trajectories (with values in M) can be represented as the weak limit of measures on the space of trajectories in the ambient space ?ⁿ (see [7–10]). Namely, we claim that a sequence of diffusion processes on ?n which are Brownian motions with drift (in the direction of the manifold) with infinitely increasing modulus converges in distribution to a Brownian motion on the manifold.     

Second-order corrections to correlations in muon capture

Muon capture by a nucleus with an arbitrary spin is considered. Second-order terms in 1/M in the effective weak-interaction Hamiltonian are taken into account. New terms in the Hamiltonian associated with the nucleon-nucleus potential are found. A general expression for the angular distribution of neutrinos (recoil nuclei) is derived for polarized muons and oriented target nuclei. Second-order contributions to the amplitudes M _u (k) are obtained. This allows one to calculate second-order corrections to any integral and correlation characteristics in muon capture that are expressed in terms of M _u (k).     

Geometrical Dissipation for Dynamical Systems

On a Riemannian manifold (M, g) we consider the k?+?1 functions F ₁, . . . , F _k , G and construct the vector fields that conserve F ₁, . . . , F _k and dissipate G with a prescribed rate. We study the geometry of these vector fields and prove that they are of gradient type on regular leaves corresponding to F ₁, . . . , F _k . By using these constructions we show that the cubic Morrison dissipation and the Landau-Lifschitz equation can be formulated in a unitary form.     

Effective biaxial modulus and strain energy density of ideally (h k l)-fiber-textured cubic polycrystalline films

The effective biaxial modulus (M_eff) and strain energy density (W) of cubic polycrystalline films with ideally (h k l) fiber textures are estimated using Vook-Witt (VW) grain interaction model and the data are compared with those derived from Voigt, Reuss and Voigt-Reuss-Hill (VRH) models. Numerical results show that the VW average of M_eff for ideally (1 0 0)- or (1 1 1)-fiber-textured films is identical to the VRH average of M_eff. For (1 1 0) and (1 1 2) planes, however, the VW average of M_eff for (1 1 0)-fiber-textured film is larger than that of (1 1 2)-fiber-textured film when the Zener anisotropic factor (A_R) is not equal to 1. Furthermore, M_eff and W exhibit incremental tendencies with the increase of the orientation factor (Γ_h k l) for the [h k l] axis when A_R > 1, implying that M_eff and W have the minimums on the (1 0 0) plane. Reversely, M_eff and W decrease with the increasing Γ_h k l when A_R < 1. This means that M_eff and W on (1 1 1) plane have the minimums.     

Ferrodistortiv geordnete tetragonal gedehnte AgIIF6-oktaeder in den verbindungen AgMIVF6[MIV = Sn,Zr]

From EPR measurements on polycrystalline samples of the complex flourides AgM^IVF₆ [M^IV = Sn, Zr] a coupling of tetragonal elongated AgF₆-octrahedral corresponding to an undisturbed ferrodistortive order can be deduced. The spectroscopic dáta (g-values and ligand field parameters) are consistent with reasonable covalency parameters (k_[, k_⊥) for the Ag^II-F-bonding.     

Mass-energy distribution of fragments within Langevin dynamics of fission induced by heavy ions

A stochastic approach based on four-dimensional Langevin fission dynamics is applied to calculating mass-energy distributions of fragments originating from the fission of excited compound nuclei. In the model under investigation, the coordinate K representing the projection of the total angular momentum onto the symmetry axis of the nucleus is taken into account in addition to three collective shape coordinates introduced on the basis of the {c, h, ??} parametrization. The evolution of the orientation degree of freedom (K mode) is described by means of the Langevin equation in the overdamped regime. The tensor of friction is calculated under the assumption of the reducedmechanismof one-body dissipation in the wall-plus-window model. The calculations are performed for two values of the coefficient that takes into account the reduction of the contribution from the wall formula: k _s = 0.25 and k _s = 1.0. Calculations with a modified wall-plus-window formula are also performed, and the quantity measuring the degree to which the single-particle motion of nucleons within the nuclear system being considered is chaotic is used for k _s in this calculation. Fusion-fission reactions leading to the production of compound nuclei are considered for values of the parameter Z ²/A in the range between 21 and 44. So wide a range is chosen in order to perform a comparative analysis not only for heavy but also for light compound nuclei in the vicinity of the Businaro-Gallone point. For all of the reactions considered in the present study, the calculations performed within four-dimensional Langevin dynamics faithfully reproduce mass-energy and mass distributions obtained experimentally. The inclusion of the K mode in the Langevin equation leads to an increase in the variances of mass and energy distributions in relation to what one obtains from three-dimensional Langevin calculations. The results of the calculations where one associates k _s with the measure of chaoticity in the single-particle motion of nucleons within the nuclear system under study are in good agreement for variances of mass distributions. The results of calculations for the correlations between the prescission neutron multiplicity and the fission-fragment mass, ??n _pre(M)??, and between, this multiplicity and the kinetic energy of fission fragments, ??n _pre(E _k )??, are also presented.     

Quantifying the complexity of geodesic paths on curved statistical manifolds through information geometric entropies and Jacobi fields

We characterize the complexity of geodesic paths on a curved statistical manifold M_s through the asymptotic computation of the information geometric complexity V_Ms and the Jacobi vector field intensity J_Ms. The manifold M_s is a 2l-dimensional Gaussian model reproduced by an appropriate embedding in a larger 4l-dimensional Gaussian manifold and endowed with a Fisher-Rao information metric g_μν(Θ) with non-trivial off-diagonal terms. These terms emerge due to the presence of a correlational structure (embedding constraints) among the statistical variables on the larger manifold and are characterized by macroscopic correlational coefficients r_k. First, we observe a power law decay of the information geometric complexity at a rate determined by the coefficients r_k and conclude that the non-trivial off-diagonal terms lead to the emergence of an asymptotic information geometric compression of the explored macrostates Θ on M_s. Finally, we observe that the presence of such embedding constraints leads to an attenuation of the asymptotic exponential divergence of the Jacobi vector field intensity.     

On the spin assignment to the 268 keV state in Au197

It is shown that the recent internal conversion data favour theI=1/2 value if the penetration effects inM1 conversion are fully taken into account. The 191 keV transition is found to be anM1 +E0 mixture with 41 (2)%E0, although the measuredK conversion coefficient is smaller than the theoreticalβ _k(M1) value.     

Bivariate distributions in statistical spectroscopy studies: Fixed-J level densities,fixed-J averages and spin cut-off factors

Analytical studies with the TBRE ensemble, supplemented by numerical calculations with realistic interactions show that for large particle numbers, the bivariate cumulants (k _rs ) defined for the Hamiltonian operator (H) and theJ _z operator, are very small; ∥k _rs ∥?0.3 for 3≦r+s≦6. As a result the expansions around a bivariate normal density are meaningful for the fixed-M densities (ρ(E,M)). We adopt a bivariate Edgeworth expansion forρ(E,M) and give a compact form for the same. Finally using thisρ(E,M) (which also define fixed-J densities uniquely), new series expansions are given for fixed-M (and hence for fixed-J) averages of the powers ofH and also for the spin cut-off factors.     

Inverse scattering with non-overdetermined data

Let A(β,α,k) be the scattering amplitude corresponding to a real-valued potential which vanishes outside of a bounded domain D⊂R³. The unit vector α is the direction of the incident plane wave, the unit vector β is the direction of the scattered wave, k>0 is the wave number. The governing equation for the waves is [∇²+k²−q(x)]u=0 in R³. For a suitable class M of potentials it is proved that if Aq₁(−β,β,k)=Aq₂(−β,β,k),∀β∈S², ∀k∈(k₀,k₁), and q₁, q₂∈M, then q₁=q₂. This is a uniqueness theorem for the solution to the inverse scattering problem with backscattering data. It is also proved for this class of potentials that if , ∀k∈(k₀,k₁), and q₁, q₂∈M, then q₁=q₂. Here is an arbitrarily small open subset of S², and |k₀−k₁|>0 is arbitrarily small.     

The Yang-Lee distribution for a class of lattice gases

Classical lattice gases moving on a simple cubic lattice are considered. The lattice is assumed to grow only one-dimensionally. The gas particles have hard cores (of diameter greater than the lattice spacing) and are further subject to interactions of finite range and finite order. The interactions outside the hard cores may be represented as the components of av-dimensional vector, ?, which is initially allowed to be complex. Using a transfer matrix technique, an asymptotic expression is obtained for the grand canonical pressure (at complex values of the inverse absolute temperature β and the fugacityz). Let λ₁ ... λ _M denote the eigenvalues of the transfer matrix. Define ? to be aD*-interaction if and only if the quotients, λ _j /λ _k , 1≦j<k≦M, regarded as functions of β,z (with ? fixed) arenonconstant. In this paper it is assumed that there exists at least one allowable D*-interaction. With this assumption, the main result is that ifF denotes the set of interaction vectors for which the distribution, Ω, of limit points of zeros of the grand partition function in the complexz-plane at fixed β (res. complex β-plane at fixedz) contains a domain, thenF contains no product setA ₁×...×A _v ,A _k ??, 1≦k≦v unless one or more of theA _k consists of (at most) isolated points. This implies that the set of vectors for which Ω consists of arcs is dense in the set of all allowable vectors (in the usual topology for ?v).     

Measurements of Hk and Ms in thin magnetic films by the angular dependence of the planar Hall effect

It is shown that the angular dependences of the planar Hall effect measured with infinite magnetic field and with magnetic field H⩾H_k have an intersection point and this fact is enough for measuring the anisotropy field H_k applying the method presented by Pastor, Ferreiro and Torres in J. Magn. Magn. Mat. 53 (1986) 349, 62 (1986) 101. The scaling of the Hall tension U proportional to M²_s in mV/Am^-1 gives a possibility for calculating the M_s-values of the films. These assumptions are verified for NiFe- and NiFeGe films with a uniaxial magnetic anisotropy.     

Solid H2: Has the quadrupolar glass phase a well-defined transition?

We report measurements of the NMR lineshape, the second and fourth moments (M₂ and M₄), and of the longitudinal relaxation tine in H₂ single crystals. Although a sharp phase transition cannot be excluded, our results for ortho concentrations between 0.15 and 0.4 suggest rather a continuous freezing of rotational motion to a “glass state” as T decreases. In this regime; the NMR spectrum is found to be very nearly isotropic.     

Discontinuities in disordered systems

The entropyS _T (j) of a two-dimensional Ising spin glass with an independent distribution of the random couplingp(J)=x·δ(J+1)+(1-x)δ(J-j) is discontinuous for temperatureT=0 and rationalj>0 and continuous elsewhere. The integrated density of frequenciesk _M (ω ²) of an one-dimensional chain of coupled oscillators with an independent distribution of the random massesp(m)=x·δ(m-1)+(1-x)δ(m-M) has the same behaviour, whereω ² corresponds toj andM to 1/T. The discontinuity points for infiniteM are, for sufficiently large but finiteM, special, frequencies, wherek _M (ω ²) has a Lifshitz singularity.     

Symmetry analysis in neutron diffraction studies of magnetic structures: 5. Polarization effects in the scattering of neutrons by magnetic structures

It is shown that both the cross section of elastic scattering by a magnetic structure and the polarization vector of the scattered neutrons beam are described by a set of complex axial vectors M^L. They depend on the vectors of atomic magnetic moments in a primitive cell of the crystal and the wave-vector star of the magnetic structure. Particularly, the intensity of a magnetic Bragg reflection and the polarization vector of the scattered beam of that reflection are determined only by a vector M^L connected with an arm star contribution of the magnetic structure and corresponding to the wave vector k_L of a star {k}. A single magnetic reflection allows one to determinean arm contribution of the magnetic structure if one uses polarization effects and an expansion of the magnetic structure over the basis functions of the irreducible representation of the crystal space group. In the general case minimal number of necessary reflections for the total determination of a magnetic crystal is equal to the arm number of the wave-vector star. All analyses here have been done for the single domain magnetic structure. The polarization phenomena will not be observed for many cases where there is a uniform distribution of domains.