Molecular theory ofK-vacancy production in heavy-ion-atom collisions at small impact parameters

1sσ vacancy production is calculated by approximating the 1sσ molecular wave function with an atomic 1s wave function for a chargeZ(R) centered at a distanceh(R) from the heavier nucleus.h(R) andZ(R) are determined by minimizing the 1sσ electronic energy. Previous calculations with the atomic semi-classical approximation (h=0,Z(R)=Z ₂, the target atomic number) showed that the probability of making CuK vacancies in 0.5- to 2-MeV/a.m.u. H⁺, D⁺, and He⁺+Cu collisions can be written asP(θ)=A(1+Bcosθ), whereθ is the scattering angle andA andB are constants forθ?10°. Although the recoil and dipole excitation contributions toP(θ) (which interfere destructively in the atomic theory) are independently smaller in the molecular calculations, similarB values are obtained.     

On the Solutions of the Yang-Baxter Equations with General Inhomogeneous Eight-Vertex R-Matrix: Relations with Zamolodchikov’s Tetrahedral Algebra

We present most general one-parametric solutions of the Yang-Baxter equations (YBE) for one spectral parameter dependent R _ij (u)-matrices of the six- and eight-vertex models, where the only constraint is the particle number conservation by mod(2). A complete classification of the solutions is performed. We have obtained also two spectral parameter dependent particular solutions R _ij (u,v) of YBE. The application of the non-homogeneous solutions to construction of Zamolodchikov’s tetrahedral algebra is discussed.     

Rotationally inelastic,classical scattering from an anisotropic rigid shell potential of rotation symmetry

Rotational excitation in collisions of structureless atoms and diatomic rigid rotor molecules interacting by a rigid potential shell is considered in classical mechanics. The double differential cross sectionJ(u ^*,θ) for final (over initial) relative velocityu ^*=ν′/ν and deflection byθ is analytically related to the shell form in the case of vanishing initial molecular rotation.J(u ^*,θ) exhibits the strong structure of “bulge” scattering or “orientational rainbows” which has been observed in the K?N₂ and K-CO systems and is expected to occur in rotationally inelastic collisions of many nonreactive systems under appropriate scattering conditions. The present results elucidate the nature of the sensitive and direct relation of bulge scattering to the anisotropy of the intermolecular potential.     

On the spaces of positive and negative frequency solutions of the Klein-Gordon equation in curved space-times

In a space-time $\text{(V}{}_{\mathrm{n}}\text{×}\text{R}\text{;g)}$ with V_n closed (n ≠ 2) satisfying certain global conditions, we can write the Klein-Gordon equation, relative to a suitable class of atlases, in the evolution form du/dt = T^-1(t)u, on Sobolev spaces K^l(V_n) = H^l(V_n) × H^l?1(V_n), where the spectrum of T^-1(t) is imaginary. Following papers by T. Kato and J. Kisyński we prove the existence of the evolution operator for this equation. The space $\text{K}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(V}{}_{\mathrm{n}}\text{)}$ has a natural strongly-symplectic structure ω. We determine the explicit form of complex-structure-positive operators of this structure. We prove that any two such operators, say J₁, J₂, are symplectically equivalent, (i.e. there is a symplectic transformation S such that J₂ = SJ₁S^-1). Spaces of positive and negative frequency solutions are then unique modulo symplectic equivalence. Each operator J determines a regular kernel on space-time which satisfies the properties of the kernel postulated by A. Lichnérowich in his program of quantization of fields in curved space-times. We carry out explicit calculations in the case of Robertson-Walker space-times. If an additional condition is satisfied by the given space-time, a unique complex-structure-positive operator can be selected in a natural way. This condition is satisfied by globally stationary space-times.     

Wigner Function of the Two-Mode Squeezing-Enhanced Vacuum State

We find the two-mode generalized squeezing operator with two parameters can be separated into the product of a ordinary squeezing operator S ₂(ξ) and a rotating operator R ₂(θ). Acting it on the two-mode vacuum state, one can get two-mode squeezing-enhanced vacuum state (TSEVS). Compared with the usual two-mode squeezed vacuum state, TSEVS exhibits stronger squeezing properties. With the help of the operator’s Weyl-ordering invariance under the similarity transformation, we derive the Wigner function of the TSEVS.     

Comparison of the texture functions describing the grain alignment in NdFeB magnets

Two types of Gaussian distribution function (`θ type’ and `tan θ type') describing the degree of grain alignment in sintered NdFeB magnets have been compared in the distribution coefficient σ (or σ_g), the distribution probability P(θ) and the grain alignment dependence of coercivity. The results show that when the grain alignment is good (the ratio of remanence-to-saturation polarization J_r/J_s⩾0.90), σ(σ_g) and P(θ) for the two types of Gaussian functions have similar variation tendencies, the calculated values of normalized coercivity based on the starting field theory are basically the same and are consistent with experiments. When the grain alignment is not good (J_r/J_s⩾0.80), the variation tendencies of σ and P(θ) are different. In addition, according to `tan θ type’ Gaussian function, the theoretical values of the normalized coercivity based on the starting field theory are still consistent with the experiments, but according to `θ type’ Gaussian function, the theoretical values seriously deviate from the experiments. This means that the `tan θ type’ Gaussian function is a better texture function for describing the grain alignment.     

New Analytical Solution of the Equilibrium Ampere’s Law Using the Walker’s Method: a Didactic Example

This work aims to demonstrate the analytical solution of the Grad-Shafranov (GS) equation or generalized Ampere’s law, which is important in the studies of self-consistent 2.5-D solution for current sheet structures. A detailed mathematical development is presented to obtain the generating function as shown by Walker (RSPSA 91, 410, 1915). Therefore, we study the general solution of the GS equation in terms of the Walker’s generating function in details without omitting any step. The Walker’s generating function g(ζ) is written in a new way as the tangent of an unspecified function K(ζ). In this trend, the general solution of the GS equation is expressed as exp(??2Ψ) =?4|K ^′(ζ)|²/cos²[K(ζ) ? K(ζ ^?)]. In order to investigate whether our proposal would simplify the mathematical effort to find new generating functions, we use Harris’s solution as a test, in this case K(ζ) = arctan(exp(i ζ)). In summary, one of the article purposes is to present a review of the Harris’s solution. In an attempt to find a simplified solution, we propose a new way to write the GS solution using g(ζ) = tan(K(ζ)). We also present a new analytical solution to the equilibrium Ampere’s law using g(ζ) = cosh(b ζ), which includes a generalization of the Harris model and presents isolated magnetic islands.     

Killing vector fields and the Einstein-Maxwell field equations with perfect fluid source

This paper is concerned with space-times that satisfy the Einstein-Maxwell field equations in the presence of a perfect fluid, which may be charged. We consider the following question. Suppose that the space-time admits a group of motions (isometries), i.e., that the metric is invariant under a group of transformations. Does it follow that the quantities that describe the source, i.e., the electromagnetic field tensorF _ij, the charge densityε, and the four-velocityu ⁱ, energy densityμ, and pressurep of the fluid, are invariant under the group? It is found that the behavior of these quantities under the group is strongly restricted. In particular in the case of the three-dimensional special orthogonal groupSO(3), which arises in the case of spherically symmetric space-times, it is found that the source quantities are invariant. On the other hand, it is established that there exist groups under whichF _ij is not necessarily invariant. The above question is also considered for the case of homothetic motions.     

Intrinsic coercivities of molecular beam epitaxy grown single-crystal Ni films on Ag buffer layer

Single-crystal Ni films were made by the molecular beam epitaxy (MBE) method on Si(1 0 0) and Si(1 1 0) substrates, respectively, with an 100 Å thick Ag buffer layer. The growth temperature T_S was 270 °C, and the film thickness t was 500 Å. From reflection high-energy electron diffraction (RHEED) patterns, the crystalline symmetries of the two films are clear and as expected. Intrinsic coercivities, H_C(1 0 0) and H_C(1 1 0), are plotted as a function of the angle of rotation ? around the crystal axes [1 0 0] and [1 1 0], respectively. The results show that both H_C(1 0 0) and H_C(1 1 0) exhibit mixed features of the crystalline (K_C) and the induced uniaxial magnetic (K_u) anisotropies. K_u is the magneto-elastic energy, due to lattice mismatch at the Ni/Ag interface. Moreover, the crystalline anisotropy fields, H_K(1 0 0) and H_K(1 1 0), and the induced anisotropy filed, H_u, can be calculated as a function of ?, respectively. Then, each H_C curve is fitted by the equation: H_C = H_o + H_K + H_u, where H_o is the isotropic pinning field. Meanwhile, domain structures were examined by the Bitter method, using Ferrofluid 707. On the Ni(1 0 0) film, we observed the charged cross-tie walls, and on the Ni(1 1 0) film, the un-charged Bloch walls.     

Fast directional multilevel summation for oscillatory kernels based on Chebyshev interpolation

Many applications lead to large systems of linear equations with dense matrices. Direct matrix-vector products become prohibitive, since the computational cost increases quadratically with the size of the problem. By exploiting specific kernel properties fast algorithms can be constructed.A directional multilevel algorithm for translation-invariant oscillatory kernels of the type K(x, y) = G(x ? y)e^?k∣x?y∣, with G(x ? y) being any smooth kernel, will be presented. We will first present a general approach to build fast multipole methods (FMMs) based on Chebyshev interpolation and the adaptive cross approximation (ACA) for smooth kernels. The Chebyshev interpolation is used to transfer information up and down the levels of the FMM. The scheme is further accelerated by compressing the information stored at Chebyshev interpolation points using ACA and QR decompositions. This leads to a nearly optimal computational cost with a small pre-processing time due to the low computational cost of ACA. This approach is in particular faster than performing singular value decompositions.This does not address the difficulties associated with the oscillatory nature of K. For that purpose, we consider the following modification of the kernel K^u = K(x, y)e^??ku·(x?y), where u is a unit vector (see Brandt [1]). We proved that the kernel K^u can be interpolated efficiently when x ? y lies in a cone of direction u. This result is used to construct an FMM for the kernel K.Theoretical error bounds will be presented to control the error in the computation as well as the computational cost of the method. The paper ends with the presentation of 2D and 3D numerical convergence studies, and computational cost benchmarks.     

Electronic structure characteristic of carbon nanotubules

Electronic structure near the Fermi energy of single-shell carbon nanotubules has been studied within the framework of the tight-binding approximation. The electronic density of states (DOS) of tubules shows a structure consisting of many spike-like peaks. An analytical expression in a π-electron model is derived which predicts not only the energy gap (E _g ) of semiconducting tubules, but also the energy positions of those spike-like peaks in the π-DOS near the Fermi energy in any tubule. The limitation of the π-electron model in tubules is discussed by investigating the effect of σ-πmixing. The position of σ component edge in the DOS is also investigated as a function of tubule radius (R) and chiral angle (θ). It is found that this edge energy is very sensitive to θ and largely changes with R, because the dominant contribution of θ to its change is given by g(θ)/R in contrast to f(θ)/R ² for E _g .     

K + production inp-nucleus collisions

We present a non-perturbative dynamical study ofK ⁺ meson production in proton-nucleus collisions from 1.2 to 2.5 GeV bombarding energy. The dynamical evolution of the proton-nucleus collision is described by a transport equation of the Boltzmann-Uehling-Uhlenbeck type evolving phase-space distribution functions for nucleons, δ’s,N(1440)’s,N(1535)’s, poins and η’s with their isospin degrees of freedom. We incorporate all known sources forK ⁺ production and study their momentum and angular distributions, and the excitation function. We show that at lower energies (E _b<1.5 GeV)NΔ andNN* channels dominate the kaon yield for light systems, and the πN channel for heavy systems. At higher bombarding energies the directNN channel accounts for almost the whole cross-section.     

Congratulations to Akusticheskii Zhurnal on the occasion of its 50th anniversary. Vibrations of spherical inclusions in elastic solids

Variational principles are derived for the analysis of dynamical phenomena associated with spherical inclusions embedded in homogeneous isotropic elastic solids. The starting point is Hamilton’s principle, with the material properties assumed to vary only with the radial distance r from the origin. Attention is restricted to disturbances that are symmetric about the polar (z) axis, such that the nonzero displacement components in spherical coordinates, u _r and u_θ, are independent of the polar coordinate φ. The symmetry allows for a decoupling of the polar components, the nth of which is described by U _{r, n} (r, t)P _n (cosθ) and U_{θ, n}(r, t)dP _n /dθ. A variational principle is subsequently derived for the field quantities U _{r, n} and U_{θ, n}. Concepts analogous to those of the theory of matched asymptotic expansions are used to embellish the principle in order to allow for the damping associated with the outward radiation of elastic waves. Examples illustrating the use of the variational principle for formulating plausible lumped-parameter models are given for the cases of n = 0 and n = 1.     

Diffusion in very chaotic hamiltonian systems

We study nonintegrable hamiltonian dynamics: H(I,θ) = H₀(I) + kH₁(I,θ), for large k, that is, far from integrability. An integral representation is given for the conditional probability P(I,θ, t¦I₀, θ₀, t₀) that the system is at I, θ at t, given it was at I₀, θ₀ at t₀. By discretizing time into steps of size ?, we show how to evaluate physical observables for large k, fixed ?. An explicit calculation of a diffusion coefficient in a two degrees of freedom problem is reported. Passage to ? = 0, the original hamiltonian flow, is discussed.     

Stability for the Korteweg-de Vries equation by inverse scattering theory

The stability problems for the Korteweg-de Vries equation, where linear stability fails, are investigated by the inverse scattering method. A rather general solution u(t, x) of the K-dV equation is shown to depend, for fixed time t, continuously on the initial condition u(0, x). For a continuum solution u_c(t, x), this continuity holds uniformly in t (stability), but for a soliton solution this is not true. A soliton solution can be uniquely decomposed into a continuum and discrete (soliton) part: u(t, x) = u_e(t, x) + u_d(t, x). Then the perturbed solution u is close to u after a suitable t-dependent “shift” of the soliton part (form stability).     

Polarization and polarization transfer in the 2H(d,n)3He reaction at 10 MeV

Angular distributions of six polarization transfer coefficients $\text{K}{}_{\mathrm{x}}{}^{\mathrm{x\prime }}\text{(θ), k}{}_{\mathrm{x}}{}^{\mathrm{z\prime }}\text{(θ), K}{}_{\mathrm{z}}{}^{\mathrm{<mtext>x</mtext><mtext>?</mtext>}}\text{(θ), K}{}_{\mathrm{z}}{}^{\mathrm{<mtext>z</mtext><mtext>?</mtext>}}\text{(θ),}\text{and}\text{K}{}_{\mathrm{yy}}{}^{\mathrm{<mtext>y</mtext><mtext>?</mtext>}}\text{(θ)}$; of the four analyzing powers A_y(θ), A_xx(θ), A_yy(θ), and A_zz(θ); and of the polarization function P^ý(θ), have been measured atE_d = 10.00 MeV for the reaction ²H(d, n)³He. Measurements were made for neutron lab angles between 0° and 80° in 10° steps. Additionally the y-axis associated quantities were measured at θ_1ab = 99°. Most of the measured coefficients are large at some angles and all show considerable variation with angle.     

Absence of periodic solutions to scale invariant classical field theories

It is shown that in 3 + 1 Minkowski space classical field theories with energy-momentum θ_μν(x,t) satisfying θ₀₀(x,t) ? 0 and θ_μ^μ(x,t) = 0 have no finite energy periodic (or static) solutions. In particular this rules out classical glueball solutions. to Yang-Mills theories with compact gauge groups.     

de Broglie’s wave hypothesis from Fisher information

Seeking the unknown dynamics obeyed by a particle gives rise to the de Broglie wave representation, without the need for physical assumptions specific to quantum mechanics. The only required physical assumption is conservation of momentum μ. The particle, of mass m, moves through free space from an unknown source-plane position a to an unknown coordinate x in an aperture plane of unknown probability density p_X(x), and then to an output plane of observed position y=a+z. There is no prior knowledge of the probability laws or , with the particle momentum at the source. It is desired to (i) optimally estimate a, in the sense of a maximum likelihood (ML) estimate. The estimate is further optimized, by minimizing its error through (ii) maximizing the Fisher information about a that is received at y. Forming the ML estimate requires (iii) estimation of the likelihood law p_Z(z), which (iv) must obey positivity. The relation p_Z(z)≡|u(z)|²≥0 satisfies this. The same u(z) conveniently defines the Fisher channel capacity, a concept central to the principle of Extreme physical information (EPI). Its output u(z) achieves aims (i)-(iv). The output is parametrized by a free parameter K. For a choice K=0, the result is u(z)=δ(z), indicating classical motion. Or, for a finite, empirical choice K=? (Planck’s constant), u(z) obeys the familiar de Broglie representation as the Fourier transform of the particle’s probability amplitude function P(μ) on momentum μ. For a definite momentum μ,u(z) becomes a sinusoid of wavelength λ=h/μ, the de Broglie result.     

Bianchi Type-II Dark Energy Model in f(R,T) Gravity

The spatially homogeneous and totally anisotropic Bianchi Type-II space-time dark energy model with EoS parameter is considered in the presence of a perfect fluid source in the framework of f(R,T) gravity proposed by Harko et al. (Phys. Rev. D, 84:024020, 2011). With the help of special law of variation for Hubble’s parameter proposed by Berman (Nuovo Cimento B, 74:182, 1983) a dark energy cosmological model is obtained in this theory. We consider f(R,T) model and investigate the modification R+f(T) in Bianchi type-II cosmology with an appropriate choice of a function f(T)=λT. We use the power law relation between average Hubble parameter H and average scale factor R to find the solution. The assumption of constant deceleration parameter leads to two models of universe, i.e. power law model and exponential model. Some physical and kinematical properties of the model are also discussed.