Almost sure explosion of solutions to stochastic differential equations

This paper is concerned with the problem of explosive solutions for a class of stochastic differential equations. Our main results are presented as two theorems. Theorem 1 is concerned with the existence of explosive solutions with positive probability under certain sufficient conditions. With some additional mild conditions, it is shown in Theorem 2 that the explosion will occur almost surely. The methods of auxiliary functions and cycles are used in the proofs. Several remarks about their applications are given.     

Orbital angular momentum contribution to the magneto-optical behavior of a binuclear cobalt(II) complex

We report magnetic and magnetic circular dichroism investigations of a binuclear Co(II) compound. The Hamiltonian of the system involves an isotropic exchange interaction dealing with the real spins of cobalt(II) ions, spin-orbit coupling, and a low-symmetry crystal field acting within the (4)T(1g) ground manifold of each cobalt ion. It is shown that spin-orbit coupling between this ground term and the low-lying excited ones can be taken into consideration as an effective g factor in the Zeeman part of the Hamiltonian. The value of this g factor is estimated for the averaged experimental values of Racah and cubic ligand field parameters for high-spin cobalt(II). The treatment of the Hamiltonian is performed with the use of a irreducible tensor operator technique. The results of the calculation are in good agreement with experimental observations. Both a large effective g factor for the ground state and a large temperature-independent part of the magnetic susceptibility arise because of a strong orbital contribution to the magnetic behavior of the Co(II) dimer.     

Diffusion and criticality in undoped graphene with resonant scatterers

A general theory is developed to describe graphene with an arbitrary number of isolated impurities. The theory provides a basis for an efficient numerical analysis of the charge transport and is applied to calculate the Dirac-point conductivity σ of graphene with resonant scatterers. In the case of smooth resonant impurities the symmetry class is identified as DIII and σ grows logarithmically with increasing impurity concentration. For vacancies (or strong on-site potential impurities, class BDI) σ saturates at a constant value that depends on the vacancy distribution among two sublattices.     

Intermittency Expansions for Limit Lognormal Multifractals

The general intermittency expansion is developed for the probability distribution of the limit lognormal multifractal process introduced by Mandelbrot (in Rosenblatt M, Van Atta C (eds.) Statistical Models and Turbulence. Lecture Notes in Physics, vol. 12, p. 333. Springer, New York, 1972) and constructed explicitly by Bacry et al. (Phys Rev E 64:026103, 2001). The structure of expansion coefficients is shown to be determined solely by that of the Selberg integral. The coefficients are computed in terms of the values of the Riemann zeta function at positive integers. For application, an explicit formula for the negative integral moments of the process is given.      

Building Scattering Cross Sections from Resonance Wave Functions

A comparative discussion is presented for methods to evaluate simultaneously both resonance and background contributions to scattering.Permanent address: Inst. of Physics, St. Petersburg State University, St. Petersburg, Russia     

Wave processes in media with hysteretic nonlinearity. Part I

Two phenomenological models of hysteretic equations of state for media with imperfect elasticity are described and compared. On the basis of these equations, a theoretical study of nonlinear effects caused by the acoustic wave propagation in an unbounded medium is performed. The profiles, parameters, and spectra of waves are determined. The distinctive features of nonlinear wave processes in such media are revealed, so that these features can be used to choose the appropriate hysteretic equation of state for analytically describing the experimental data.     

Detection of weak signals against the background of artificial noise fields scattered by an inhomogeneous medium. I. Gaussian approximation

We consider an optimal procedure for weak signal detection against the background of scattered artificial noise fields within the framework of a Gaussian approximation. We focus on the specific problems of detection and adaptive recovery of the primary wave field at the inputs of a multichannel detector. Antiaircraft Command High School, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 9, pp. 1177–1194, September, 1998.     

Mixed micellization between natural and synthetic block copolymers: β-casein and Lutrol F-127

Amphiphilic block copolymers and mixtures of amphiphiles find broad applications in numerous technologies, including pharma, food, cosmetic and detergency. Here we report on the interactions between a biological charged diblock copolymer, β-casein, and a synthetic uncharged triblock copolymer, Lutrol F-127 (EO(101)PO(56)EO(101)), on their mixed micellization characteristics and the micelles' structure and morphology. Isothermal titration calorimetry (ITC) experiments indicate that mixed micelles form when Lutrol is added to monomeric as well as to assembled β-casein. The main driving force for the mixed micellization is the hydrophobic interactions. Above β-casein CMC, strong perturbations caused by penetration of the hydrophobic oxypropylene sections of Lutrol into the protein micellar core lead to disintegration of the micelles and reformation of mixed Lutrol/β-casein micelles. The negative enthalpy of micelle formation (ΔH) and cooperativity increase with raising β-casein concentration in solution. ζ-potential measurements show that Lutrol interacts with the protein micelles to form mixed micelles even below its critical micellization temperature (CMT). They further indicate that Lutrol effectively masks the protein charges, probably by forming a coating layer of the ethyleneoxide rich chains. Small-angle X-ray scattering (SAXS) and cryogenic-transmission electron microscopy (cryo-TEM) indicate relatively small changes in the oblate micellar shape, but do show swelling along the small axis of β-casein micelles in the presence of Lutrol, thereby confirming the formation of mixed micelles.     

Coherence times and Rabi oscillations in CaWO₄:Cr(5+) crystal

The coherence times of dopant pentavalent chromium ions in CaWO? single crystal (0.0006at.% Cr(5+)) were investigated both theoretically and experimentally. Temperature dependences of spin-lattice relaxation time T? and phase memory time T(M) were measured in the temperature range 6-30 K at high (94 GHz, W band) and low (3.5 GHz, S band) frequencies of electron spin resonance. It follows from T(M) calculations that phase relaxation of Cr(5+) ion arises mainly from magnetic dipole interactions between the chromium ions. Anomalously fast damping of Rabi oscillations is detected in both S- and W-band experiments. It is shown that this phenomenon is caused by microwave field inhomogeneity inside the resonator. Relations between the damping time of Rabi oscillations, Rabi frequency and the crystal sample size are obtained. Lumped-element resonators and smaller sample dimensions are suggested to lower spin dephasing during transient nutations.     

Improved linear response for stochastically driven systems

The recently developed short-time linear response algorithm, which predicts the average response of a nonlinear chaotic system with forcing and dissipation to small external perturbation, generally yields high precision of the response prediction, although suffers from numerical instability for long response times due to positive Lyapunov exponents. However, in the case of stochastically driven dynamics, one typically resorts to the classical fluctuation-dissipation formula, which has the drawback of explicitly requiring the probability density of the statistical state together with its derivative for computation, which might not be available with sufficient precision in the case of complex dynamics (usually a Gaussian approximation is used). Here, we adapt the short-time linear response formula for stochastically driven dynamics, and observe that, for short and moderate response times before numerical instability develops, it is generally superior to the classical formula with Gaussian approximation for both the additive and multiplicative stochastic forcing. Additionally, a suitable blending with classical formula for longer response times eliminates numerical instability and provides an improved response prediction even for long response times.