New evidence for zero-temperature relaxation in a spin-polarized fermi liquid

Spin-echo experiments are reported for 3He-4He solutions under extremely high B/T conditions, B=14.75 T and T>or=1.73 mK. The 3He concentration x(3) was adjusted close to the value x(c) approximately 3.8% at which the spin-rotation parameter muM0 vanishes. In this way the transverse and longitudinal spin-diffusion coefficients D( perpendicular ),D( parallel ) were measured while keeping |muM(0)|<1. It is found that the temperature dependence of D( perpendicular ) deviates strongly from 1/T(2), with anisotropy temperature T(a)=4.26(+0.18)(-0.44) mK. This value is close to the theoretical prediction for dilute solutions and suggests that spin current relaxation remains finite as the temperature tends to zero.     

A reaction-diffusion equation for a cyclic system with three components

The one-dimensional reaction-diffusion equations for the process (D) $$A + B \to 2A,B + C \to 2B,C + A \to 2C$$ are extended to include the counteracting reactions (R) $$A + 2B \to 3B,B + 2C \to 3C,C + 2A \to 3A$$ which have a reaction rate α relative to the direct process (D). This process can be seen as a three-component version of the reaction which is described by the Fisher-Kolmogorov equation. The fixed points of the equations are studied as a function of α. It is shown that the equations admit solutions which consist of a series of traveling fronts. Other solutions exist which are traveling periodic waves. A very remarkable fact is that for these waves exact expressions can be constructed.     

KAM for the Quantum Harmonic Oscillator

In this paper we prove an abstract KAM theorem for infinite dimensional Hamiltonians systems. This result extends previous works of S.B. Kuksin and J. P?schel and uses recent techniques of H. Eliasson and S.B. Kuksin. As an application we show that some 1D nonlinear Schr?dinger equations with harmonic potential admits many quasi-periodic solutions. In a second application we prove the reducibility of the 1D Schr?dinger equations with the harmonic potential and a quasi periodic in time potential.     

对甲苯偶氮水杨基荧光酮应用于大豆酶解液中钼的形态分布研究

研究了新试剂对甲苯偶氮水杨基荧光酮(MBASF)与钼(Ⅵ)显色反应,以建立水解液中钼的形态分布测定方法。在盐酸介质中,对MBASF与钼(Ⅵ)发生灵敏的显色反应,形成稳定的红色配合物。配合物表观摩尔吸光系数达1.54 L·mol-1·cm-1,在0～12 μg·(25 mL)-1范围内钼(Ⅵ)服从比耳定律。除常见金属离子外,蛋白、多肽和氨基酸均有高的允许量。大豆酶解液A经等电点沉淀法除去未水解蛋白后得溶液B,溶液B经D301R树脂吸附后,分别采用pH 3.6和9.0的缓冲液洗脱分离得溶液C和D;A,B,C和D溶液分别用于光度法测定总钼、水解钼、结合态钼(多肽和氨基酸螯合态钼)和游离钼的含量。     

Constraints on Kaluza–Klein gravity from Gravity Probe B

Using measurements of geodetic precession from Gravity Probe B, we constrain possible departures from Einstein’s General Relativity for a spinning test body in Kaluza–Klein gravity with one additional space dimension. We consider the two known static and spherically symmetric solutions of the 5D field equations (the soliton and canonical metrics) and obtain new limits on the free parameters associated with each. The theory is consistent with observation but must be “close to 4D” in both cases.     

Functional Separable Solutions to Nonlinear Diffusion Equations by Group Foliation Method

We consider the functional separation of variables to the nonlinear diffusion equation with source and convection termut = (A(x)D(u)ux)x B(x)Q(u),Ax ≠ 0.The functional separation of variables to this equation is studied by using the group foliation method.A classification is carried out for the equations which admit the function separable solutions.As a consequence,some solutions to the resulting equations are obtained.     

Charged AdS black holes with finite electrodynamics in 4D Einstein-Gauss-Bonnet gravity

Using a modified expression for the electric potential in the context of T-duality [Gaete and Nicolini, Phys. Lett. B, 2022], we obtained an exact charged solution within the 4D Einstein-Gauss-Bonnet (4D EGB) theory of gravity in the presence of a cosmological constant. We show that the solution also exists in the regularized 4D EGB theory. Moreover, we point out a correspondence between the black hole solution in the 4D EGB theory and the solution in the non-relativistic Horava–Lifshitz theory. The black hole solution is regular and free from singularity. As a special case, we derive a class of well known solutions in the literature.     

Matrix model in a class of time dependent supersymmetric backgrounds

We discuss the matrix model in a class of 11D time dependent supersymmetric backgrounds as obtained in [B. Chen, Phys. Lett. B 632 (2006) 393, hep-th/0508191]. We construct the matrix model action through the matrix regularization of the membrane action in the background. We show that the action is exact to all orders of fermionic coordinates. Furthermore we discuss the fuzzy sphere solutions in this background.     

Spatiotemporal chaos in the dynamics of buoyantly and diffusively unstable chemical fronts

Nonlinear dynamics resulting from the interplay between diffusive and buoyancy-driven Rayleigh-Taylor (RT) instabilities of autocatalytic traveling fronts are analyzed numerically for various values of the relevant parameters. These are the Rayleigh numbers of the reactant A and autocatalytic product B solutions as well as the ratio D=D(B)/D(A) between the diffusion coefficients of the two key chemical species. The interplay between the coarsening dynamics characteristic of the RT instability and the constant short wavelength modulation of the diffusive instability can lead in some regimes to complex dynamics dominated by irregular succession of birth and death of fingers. By using spectral entropy measurements, we characterize the transition between order and spatial disorder in this system. The analysis of the power spectrum and autocorrelation function, moreover, identifies similarities between the various spatial patterns. The contribution of the diffusive instability to the complex dynamics is discussed.     

Statistical mechanics of geophysical turbulence: application to jovian flows and Jupiter’s great red spot

We propose a parameterization of 2D geophysical turbulence in the form of a relaxation equation similar to a generalized Fokker–Planck equation [P.H. Chavanis, Phys. Rev. E 68 (2003) 036108]. This equation conserves circulation and energy and increases a generalized entropy functional determined by a prior vorticity distribution fixed by small-scale forcing [R. Ellis, K. Haven, B. Turkington, Nonlinearity 15 (2002) 239]. We discuss applications of this formalism to jovian atmosphere and Jupiter’s great red spot. We show that, in the limit of small Rossby radius where the interaction becomes short-range, our relaxation equation becomes similar to the Cahn–Hilliard equation describing phase ordering kinetics. This strengthens the analogy between the jet structure of the great red spot and a “domain wall”. Our relaxation equation can also serve as a numerical algorithm to construct arbitrary nonlinearly dynamically stable stationary solutions of the 2D Euler equation. These solutions can represent jets and vortices that emerge in 2D turbulent flows as a result of violent relaxation. Due to incomplete relaxation, the statistical prediction may fail and the system can settle on a stationary solution of the 2D Euler equation which is not the most mixed state. In that case, it can be useful to construct more general nonlinearly dynamically stable stationary solutions of the 2D Euler equation in an attempt to reproduce observed phenomena.     

Self-assembly of nanoparticles on the surface of ionic crystals: Structural properties

With a suitable combination of ligand-stabilised nanoparticle suspension and ionic salt solutions, it is possible to produce microcrystals that are coated with nanoparticles. The self-assembly process of coating microcrystals by gold nanoparticles (NP) is mediated by the crystal lattice. This is the so-called CLAMS process - a generic process for self-organisation of nanoparticles on the surface of crystals [M. Murugeshan, D. Cunningham, J.-L. Martnez-Albertos, R. Vrcelj, B.D. Moore, Chem. Commun. (2005) 2677]. We are exploring here the structural properties of these self-assembled structures by using different imaging techniques.     

Comment on “Do evanescent waves really exist in free space?”

In a recent paper [A.B. Katrich, Opt. Commun. 255 (2005) 169], Katrich has claimed that in a 2D free space evanescent waves do not exist because they are not exact solutions of the free space wave equation. We show that his conclusions are not valid, and that evanescent can indeed exist in free space.     

On the Entire Radial Solutions of the Chern–Simons SU(3) System

In this paper, we study the entire radial solutions of the self-dual equations arising from the relativistic SU(3) Chern–Simons model proposed by Kao and Lee (Phys Rev D 50:6626–6632, 1994) and Dunne (Phys Lett B 345:452–457, 1995; Nuclear Phys B 433:333–348, 1995). Understanding the structure of entire radial solutions is one of the fundamental issues for the system of nonlinear equations. In this paper, we prove that any entire radial solutions must be one of topological, non-topological and mixed type solutions, and completely classify the asymptotic behaviors at infinity of these solutions. Even for radial solutions, this classification has remained an open problem for many years. As an application of this classification, we prove that the two components u and v have intersection at most finite times.     

Bernstein-Greene-Kruskal modes in a three-dimensional plasma

Bernstein-Greene-Kruskal modes in a three-dimensional (3D) unmagnetized plasma are constructed. It is shown that 3D solutions that depend only on energy do not exist. However, 3D solutions that depend on energy and additional constants of motion (such as angular momentum) do exist. Exact analytical as well as numerical solutions are constructed assuming spherical symmetry, and their properties are contrasted with those of 1D solutions. Possible extensions to solutions with cylindrical symmetry with or without a finite magnetic guide field are discussed.     

A Revisit on the Derivation of the Particular Solution for the Differential Operator ∆2 ± λ2

In this paper, we applied the polyharmonic splines as the basis functions to derive particular solutions for the differential operator ∆² ± λ². Similar to the derivation of fundamental solutions, it is non-trivial to derive particular solutions for higher order differential operators. In this paper, we provide a simple algebraic factorization approach to derive particular solutions for these types of differential operators in 2D and 3D. The main focus of this paper is its simplicity in the sense that minimal mathematical background is required for numerically solving higher order partial differential equations such as thin plate vibration. Three numerical examples in both 2D and 3D are given to validate particular solutions we derived.     

Structural elements and collapse regimes in 3D flows on a slope

The mechanisms and structural elements of an instability whose development results in the collapse of flow fragments have been studied in the scope of the Hamilton version of the “shallow water” 3D model on a slope. The study indicated that the 3D model differs from its 2D analog in a more varied set of collapsing solutions. In particular, the solutions describing anisotropic collapse, during which the area of a collapsing fragment in contact with the slope contracts into a segment rather than a point, exist together with the solutions describing radially symmetric (isotropic) collapse.     

On the second-moment condition of Stillinger and Lovett

The Stillinger-Lovett second-moment condition of electrolyte solutions is derived rigorously and simply from only some reasonable (but apparently never proven rigorously) assumptions concerning the asymptotic form of the direct correlation function and the Ornstein-Zernike equation. The derivation suggests that this condition is not the first member of a hierarchy of moment conditions and that there exists no simple result for a fourth-moment condition.Alfred P. Sloan Fellow.This work was partially supported by a grant from the National Institutes of Health, RO1 GM 20800-03 (to D.A.M.), by the Research Foundation of the State University of New York (USAEC Contract No. AT (30-1) 3668B) and the USAFOSR under Grant No. 68-1416B (to J.G.), and by the Petroleum Research Fund (A.S.).     

Baryon duality solutions with the harmonic-oscillator spectrum and the amplitude signs in πN→πΔ

By constructing exact exchange-degenerate solutions of baryons with the harmonic-oscillator spectrum for a set of reactions MB→M′B′, MB → M′D′ and MD → M′D′, we investigate the duality constraints on the amplitude signs in MB → M′D′. It is shown that the amplitude signs determined by duality are consistent with those predicted by the extended version of SU(6)_W symmetry with the universal dominance of the ΔL_Z = 0 or ΔL_Z = ±1 amplitude in the mesonic transitions of the baryons.     

Three-dimensional fundamental solutions for one-dimensional hexagonal quasicrystal with piezoelectric effect

In this paper, a set of 3D general solutions to static problems of 1D hexagonal piezoelectric quasicrystals is obtained by introducing two displacement functions and utilizing the rigorous operator theory. All the physical quantities are expressed by five quasi-harmonic functions. Based on the general solutions and with the help of the superposition principle, fundamental solutions for infinite/half-infinite spaces are presented by trial-and-error technique. The general solutions can be conveniently used to solve the boundary value problems regarding dislocations, cracks and inhomogeneities. The fundamental solutions are of primary significance to development of numerical codes such as boundary element method.     

Abundant solutions of Wick-type stochastic fractional 2D KdV equations

A modified fractional sub-equation method is applied to Wick-type stochastic fractional two-dimensional （2D） KdV equations. With the help of a Hermit transform, we obtain a new set of exact stochastic solutions to Wick-type stochastic fractional 2D KdV equations in the white noise space. These solutions include exponential decay wave solutions, soliton wave solutions, and periodic wave solutions. Two examples are explicitly given to illustrate our approach.