Bianchi type I in f(T) gravitational theories

A tetrad field that is homogeneous and anisotropic which contains two unknown functions A(t) and B(t) of cosmic time is applied to the field equations of f(T), where T is the torsion scalar, T = T~μ_(νρ)S_μ~(νρ). We calculate the equation of continuity and rewrite it as a product of two brackets, the first is a function of f(T) and the second is a function of the two unknowns A(t) and B(t). We use two different relations between the two unknown functions A(t) and B(t) in the second bracket to solve it. Both of these relations give constant scalar torsion and solutions coincide with the de Sitter one. So,another assumption related to the contents of the matter fields is postulated. This assumption enables us to drive a solution with a non-constant value of the scalar torsion and a form of f(T) which represents ΛCDM.     

Exact operator solutions to Euler hamiltonians

It is nearly impossible in general to solve exactly the quantum-mechanical Heisenberg equations of motion when these operator equations are non-linear. However, in this paper we show how to obtain exact closed-form solutions for the operators p(t) and q(t) for any Euler hamiltonian (one that be expressed a function of pq).     

Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schrödinger equation

We make a quantitative study on the soliton interactions in the nonlinear Schrödinger equation (NLSE) and its variable-coefficient (vc) counterpart. For the regular two-soliton and double-pole solutions of the NLSE, we employ the asymptotic analysis method to obtain the expressions of asymptotic solitons, and analyze the interaction properties based on the soliton physical quantities (especially the soliton accelerations and interaction forces); whereas for the bounded two-soliton solution, we numerically calculate the soliton center positions and accelerations, and discuss the soliton interaction scenarios in three typical bounded cases. Via some variable transformations, we also obtain the inhomogeneous regular two-soliton and double-pole solutions for the vcNLSE with an integrable condition. Based on the expressions of asymptotic solitons, we quantitatively study the two-soliton interactions with some inhomogeneous dispersion profiles, particularly discuss the influence of the variable dispersion function f(t) on the soliton interaction dynamics.     

Scaling probability, key to the equilibrium statistical volume distribution in foams

The equilibrium statistical volume distribution in foams, which has been previously demonstrated to be the so-called log-normal, is accounted on probability grounds by a scaling law on the bubble's volume time-evolution. This law states that the conditional probability for a given bubble to have the volume v(t + Δt), he assumption that it was v(t), to depend solely on the relationship v(t + Δt)/v(t), and in particular, to be independent of the time t. The theoretical results, however, allow to go further. Indeed, since the time dependece of its parameters (expectation and variance) are given functions of time, only two parameters are necessary to describe completely the foam.     

Deux trajectoires de regge dans la reaction πp → πn

The possibility of describing the high-energy reaction π⁻p^→π⁰n with two Regge trajectories (t) and _'(t) is studied in more detail. These trajectories are assumed to be exactly linear in t, with (t) constrained to pass through (m²) = 1. We examine hypotheses in which (t) obeys either the Gell-Mann mechanism or the Chew mechanism, and in which '(t) is or is not a conspiring trajectory. The model is in good agreement with the data in practically all cases; greater experimental accuracy would be necessary to distinguish between the various hypothesis. Predictions are given for the neutron polarization at |t| < 1 GeV².     

On generalized Bäcklund transformations for equations describing pseudo-spherical surfaces

It is shown that each one-parameter subgroup of SL(2,R) gives rise to a local correspondence theorem between suitably generic solutions of arbitrary scalar equations describing pseudo-spherical surfaces. Thus, if appropriate genericity conditions are satisfied, there exist local transformations between any two solutions of scalar equations arising as integrability conditions of sl(2,R)-valued linear problems.

A complete characterization of evolution equations u_t=K(x,t,u,u_x,…,u_x^k) which are of strictly pseudo-spherical type is also provided.     

On the Riemann–Hilbert problem of a generalized derivative nonlinear Schrödinger equation

In this work,we present a unified transformation method directly by using the inverse scattering method for a generalized derivative nonlinear Schr?dinger(DNLS)equation.By establishing a matrix Riemann-Hilbert problem and reconstructing potential function q(x,t)from eigenfunctions{Gj(x,t,η)}3/1 in the inverse problem,the initial-boundary value problems for the generalized DNLS equation on the half-line are discussed.Moreover,we also obtain that the spectral functions f(η),s(η),F(η),S(η)are not independent of each other,but meet an important global relation.As applications,the generalized DNLS equation can be reduced to the Kaup-Newell equation and Chen-Lee-Liu equation on the half-line.     

频率对半导体器件热击穿影响的理论模型

针对半导体器件中的热击穿,通过分析已有的理论模型,把频率对器件热区热产生和热传导的影响引入理论模型.利用格林函数求解热传输方程,同时对余误差函数进行近似处理,求解得到热区温度以及器件烧毁功率与频率和脉冲宽度的表达式.通过数值分析,求解得到不同频率下器件烧毁功率随脉冲宽度的变化规律以及不同脉冲宽度下器件烧毁功率随频率的变化规律,同时给出了频率对器件烧毁功率影响的物理解释.     

Annealing dependence of magnetic properties in nanostructured Sm0.5Y0.5Co5

Nanocrystalline Sm_0.5Y_0.5Co₅ powders with high coercivity H_C and enhanced remanence M_r were prepared by mechanical milling and subsequent annealing. Annealing temperatures T ranging from 973 to 1173 K, and times t ranging from 1 to 5 min were used. X-ray diffraction (XRD) and DC-magnetization measurements were carried out to study the microstructure and magnetic properties of these samples. XRD patterns demonstrate that the average grain size D of the nanocrystalline powders depends on the annealing temperature T and time t: D ranges from 11 nm (for T=973 K and t=1 min) to 93 nm (for T=1173 K and t=5 min). Magnetic measurements performed at room temperature indicate high coercivity values (H_C>955 kA/m), and enhanced remanence (M_r/M_max>0.5) for all samples. A strong annealing-induced grain size dependence of these magnetic properties was found.     

Connection formulae for Painlevé V functions : II. The δ function Bose gas problem

We continue our study of those Painlevé V equations which admit a one-parameter family of solutions analytic at the origin and solve the global problem of connecting the 2-parameter expansion about t = 0 with the 2-parameter expansion valid for t → ± i∞. A special case of our results is applied to the study of the one-particle reduced density matrix of the one-dimensional gas of impenetrable bosons. We also use our results to obtain a 2-parameter connection formula for a class of Painlevé III functions.     

Magnetization temperature dependence in Fe/Cr superlattices

We report the temperature dependence of the saturation magnetization, M_s(T), of Fe(t)/Cr(40 Å) superlattices grown on MgO(1 0 0) and MgO(1 1 0) and its variation with Fe-layer thickness (5 Å<t<80 Å). The structure was characterized by X-ray diffraction. M_s(t) vs. T, as measured by DC magnetization and ferromagnetic resonance, show a large interface effect. The origins of this effect are discussed.     

计算自旋-s算子幺正演化矩阵ds(t)的新方法及其应用

提出了一种严格求解任意自旋-s算子幺正演化矩阵的方法,该方法不同于群论的方法和直接计算的方法,是一种间接的算法.方法的核心是利用两个系统表示的等价性：即自旋-s算子Hamiltonian量H_s=S_x与Heisenberg XX开链带相互作用J_n=n(N-n)的Hamiltonian量的等价性,由于存在这种等价性,自旋-s算子幺正演化矩阵的计算可通过Heisenberg XX开链中态的演化来实现.采用该方法计算了s=3/2,s=2和s=5/2时对应的幺正演化矩阵.由于初始态|sm〉在算子e^-itS_x下的演化实质上相当于对态|sm〉进行一个绕x轴转角为β＝t的转动,演化矩阵元d^s_m'm(t)=〈sm′|e^-itS_x|sm〉就是转动后的态e^-itS_x|sm〉在|sm′〉态上的投影值,所以在t＝π时刻的演化矩阵刚好对应Heisenberg XX开链上量子态的理想传输. 关键词： s算子')" href="#">自旋-s算子 幺正演化矩阵 量子态传输     

Nonergodicity and dynamical approach to the anharmonic oscillator

General lower bounds for the time average C^AA(∞)≡lim_T→∞(1/T)∝^T₀ C^AA(t) dt of the correlation C^AA(t)≡A(t)A(0)−A² of an arbitrary variable A are derived, which depend only on the temperature derivatives of the canonical averages of A and the Hamiltonian of the system. The bounds may be used to give good estimations for C^AA(∞) which is different from zero when A is nonergodic. It is important to take care of these terms when dynamical theories made for interacting systems are applied to isolated systems. We show explicitely that our recently developed dynamical approach to phonon systems with quartic anharmonicity yields excellent results for the corresponding isolated system, the anharmonic single well oscillator, when nonvanishing time averages are taken into account.     

How does the S11 N*(890) state emerge from a naive K-matrix fit?

We give a pedagogical analysis on K-matrix models describing the πN scattering amplitude, in S₁₁ channel at low energies. We show how the correct use of analyticity in the s-channel and crossing symmetry in t- and u-channels leads to a much improved analytic behavior in the negative s region, in agreement with the prediction from chiral perturbation amplitudes in its validity region. The analysis leads again to the conclusion that a genuine N*(890) resonance exists.     

QCD instantons and the soft pomeron

We study the rôle of semiclassical QCD vacuum solutions in high-energy scattering by considering the instanton contribution to hadronic cross sections. We propose a new type of instanton-induced interactions (“instanton ladder”) that leads to the rising with energy cross section σs^Δ of Regge type (the pomeron). We argue that this interaction may be responsible for the structure of the soft pomeron. The intercept Δ>0 is calculated. It has a nonanalytic dependence on the strong coupling constant, allowing a nonsingular continuation into the nonperturbative region. We derive the pomeron trajectory, which appears to be approximately linear in some range of (negative) momentum transfer t, but exhibits a curvature at small t. Possible rôle of instantons in multiparticle production is also discussed.     

1/f-type fluctuation of electron transmission in one-dimensional disordered systems

A universal feature of 1/f-type fluctuation is numerically observed in the system-size n dependence of the transmission amplitude t_n in various one-dimensional disordered systems. The power spectrum P(f) of the transmission coefficient T(n)=|t_n|² exhibits the power law of 1/f², irrespective to the type of disorder of the system whether it is of short-range or of long-range correlation. That of the phase θ_t(n) of t_n also does the universal power law of 1/f^1.4.     

Mean displacement moments and survival times in the trapping model with strong fields

The mean displacement moments for the strong field trapping model are calculated. Their asymptotic behaviour is Xⁿ(t) (V_efft)ⁿ, where V_eff is an effective drift velocity. This is in sharp contrast with the weak field case, for which Xⁿ(t) t^n/3. The mean survival (first passage) time and the upstream and downstream trapping probabilities are also obtained.     

The delay time of gravitational wave – gamma-ray burst associations

The first gravitational wave (GW) – gamma-ray burst (GRB) association, GW170817/GRB 170817A, had an offset in time, with the GRB trigger time delayed by ~1.7 s with respect to the merger time of the GW signal. We generally discuss the astrophysical origin of the delay time, Δt, of GW-GRB associations within the context of compact binary coalescence (CBC) – short GRB (sGRB) associations and GW burst – long GRB (lGRB) associations. In general, the delay time should include three terms, the time to launch a clean (relativistic) jet, Δt_jet; the time for the jet to break out from the surrounding medium, Δt_bo; and the time for the jet to reach the energy dissipation and GRB emission site, Δt_GRB. For CBC-sGRB associations, Δtjet and Δt_bo are correlated, and the final delay can be from 10 ms to a few seconds. For GWB-lGRB associations, Δt_jet and Δt_bo are independent. The latter is at least ~10 s, so that Δt of these associations is at least this long. For certain jet launching mechanisms of lGRBs, Δt can be minutes or even hours long due to the extended engine waiting time to launch a jet. We discuss the cases of GW170817/GRB 170817A and GW150914/GW150914-GBM within this theoretical framework and suggest that the delay times of future GW/GRB associations will shed light into the jet launching mechanisms of GRBs.     

Analytical result for dimensionally regularized massless master non-planar double box with one-leg off shell

The dimensionally regularized massless non-planar double box Feynman diagram with powers of propagators equal to one, one leg off the mass shell, i.e., with p₁²=q²≠0, and three legs on shell, p_i²=0, i=2,3,4, is analytically calculated for general values of q² and the Mandelstam variables s,t and u (not necessarily restricted by the physical condition s+t+u=q²). An explicit result is expressed through (generalized) polylogarithms, up to the fourth order, dependent on rational combinations of q²,s,t and u, and simple finite two- and three-fold Mellin–Barnes integrals of products of gamma functions which are easily numerically evaluated for arbitrary non-zero values of the arguments.     

Self-phase modulation via similariton solutions of the perturbed NLSE Modulation instability and induced self-steepening

The perturbed nonlinear Schrodinger equation (PNLSE) describes the pulse propagation in optical fibers, which results from the interaction of the higher-order dispersion effect, self-steepening (SS) and self-phase modulation (SPM). The challenge between these aforementioned phenomena may lead to a dominant one among them. It is worth noticing that the study of modulation instability (MI) leads to the inspection of dominant phenomena (DPh). Indeed, the MI triggers when the coefficient of DPh exceeds a critical value and it may occur that the interaction leads to wave compression. The PNLSE is currently studied in the literature, mainly on finding traveling wave solutions. Here, we are concerned with analyzing the similarity solutions of the PNLSE. The exact solutions are obtained via introducing similarity transformations and by using the extended unified method. The solutions are evaluated numerically and they are shown graphically. It is observed that the intensity of the pulses exhibits self steepening which progresses to shock soliton in ultra-short time (or near t = 0). Also, it is found that the real part of the solution exhibits self-phase modulation in time. The study of (MI) determines the critical value for the coefficients of SS, SPM, or high dispersivity to occur.