Finite volume Kolmogorov-Johnson-Mehl-Avrami theory

We study the Kolmogorov-Johnson-Mehl-Avrami theory of phase conversion in finite volumes. For the conversion time we find the relationship tau(con)=tau(nu)[1+f(d)(q)]. Here d is the space dimension, tau(nu) the nucleation time in the volume V, and f(d)(q) a scaling function. Its dimensionless argument is q=tau(ex)/tau(nu), where tau(ex) is an expansion time, defined to be proportional to the diameter of the volume divided by expansion speed. We calculate f(d)(q) in one, two, and three dimensions. The often considered limits of phase conversion via either nucleation or spinodal decomposition are found to be volume-size dependent concepts, governed by simple power laws for f(d)(q).     

First measurement of form factors of the decay Xi(0) --> Sigma(+)e(-)nu macro(e)

We present the first measurement of the form factor ratios g(1)/f(1) (direct axial vector to vector), g(2)/f(1) (second class current), and f(2)/f(1) (weak magnetism) for the decay Xi(0)-->Sigma(+)e(-)nu macro(e) using the KTeV (E799) beam line and detector at Fermilab. From the Sigma(+) polarization measured with the decay Sigma(+)-->p pi(0) and the e(-)-nu; correlation, we measure g(1)/f(1) to be 1.32+/-(0.21)(0.17)(stat)+/-0.05(syst), assuming the SU(3)(f) (flavor) values for g(2)/f(1) and f(2)/f(1). Our results are all consistent with exact SU(3)(f) symmetry.     

Testing the stability of fundamental constants with the 199Hg+ single-ion optical clock

Over a two-year duration, we have compared the frequency of the 199Hg+ 5d(10)6s (2)S(1/2)(F=0)<-->5d(9)6s(2) (2)D(5/2)(F=2) electric-quadrupole transition at 282 nm with the frequency of the ground-state hyperfine splitting in neutral 133Cs. These measurements show that any fractional time variation of the ratio nu(Cs)/nu(Hg) between the two frequencies is smaller than +/-7 x 10(-15) yr(-1) (1sigma uncertainty). According to recent atomic structure calculations, this sets an upper limit to a possible fractional time variation of g(Cs)(m(e)/m(p))alpha(6.0) at the same level.     

The equation of motion and gravitational radiation of a small extended spherically symmetric mass

On the basis of an approximation method developed in a previous paper the motion of an extended small mass on a gravitational background is investigated. The mass is described by a spherically symmetric rest mass distribution with some form of rigidity; the smallness of the mass is defined by the assumption that the radius of the mass is small compared with the change of the background . The equation of motion is yielded by integrating Einstein's conservation law of energy and momentum over the world tube of the mass. In the lowest mixed order (mixed of the background and the retarded potentials of the mass in lowest order) this equation is identical with the geodesic line linearized in . In the case when the motion on a static background generated by a localized matter distribution is finite, the gravitational radiation of the mass in lowest order is given.     

U(1) gauge-coupled Dirac equation and massless (QED)2 on a finite element

Toward the construction of the gauge theory on a lattice without species doubling, we formulate the U(1) gauge-coupled Dirac equation on a finite element in (d + 1)-dimensional space-time. For massless (QED)₂, we derive the vector current conservation and the axial anomaly. The reproduction of the axial anomaly indicates the resolution of the doubling problem.     

Upper limit on the diffuse flux of ultrahigh energy tau neutrinos from the Pierre Auger Observatory

The surface detector array of the Pierre Auger Observatory is sensitive to Earth-skimming tau neutrinos that interact in Earth's crust. Tau leptons from nu(tau) charged-current interactions can emerge and decay in the atmosphere to produce a nearly horizontal shower with a significant electromagnetic component. The data collected between 1 January 2004 and 31 August 2007 are used to place an upper limit on the diffuse flux of nu(tau) at EeV energies. Assuming an E(nu)(-2) differential energy spectrum the limit set at 90% C.L. is E(nu)(2)dN(nu)(tau)/dE(nu)<1.3 x 10(-7) GeV cm(-2) s(-1) sr(-1) in the energy range 2 x 10(17) eV< E(nu)< 2 x 10(19) eV.     

多金属氧酸盐α-Na7H[GaW9Fe3(H2O)3O37]·16H2O合成和光谱

合成了α Na7H[GaW9Fe3 (H2 O) 3 O3 7]·16H2 O(简写为α GaW9Fe3 ,以下类同 )通过红外、紫外、元素分析、光电子能谱、极谱等手段进行了表征 ,并对该配合物的红外、紫外、元素分析、光电子能谱进行分析。配合物的红外光谱都出现了Keggin杂多阴离子所具有的νas(W—Oa—W ) ,νas(W—Ob—W ) ,νas(W—Oc—W) 和νas(W—Od—W ) 四种基本特征振动峰 ,表明所合成配合物也具有Keggin结构。所合成的配合物的紫外光谱都在2 10和 2 6 8nm附近有两个荷移跃迁带 ,分别对应于Od—W的 pπ dπ 荷移跃迁和Ob/Oc的 pπ dπ 荷移跃迁。Ob/Oc 的 pπ dπ荷移跃迁为特征吸收峰。GaW9和GaW9Fe3 都有一个 4电子还原波 ,且E1/ 2 比GaW9更负 ,因此所合成的配合物GaW9Fe3 为α体。GaW9Fe3 室温的磁矩比有效磁矩纯自旋值 6 0 3× 10 -2 3 A·m2 低 ,这暗示了杂多阴离子的三金属簇中 3个铁原子间存在反铁磁性自旋交换作用。对M ssbauer谱进行了分析 ,铁与桥氧之间形成了d pπ键 ,铁的d轨道与桥氧的 p轨道发生了重叠 ,p ,d电子之间产生了反磁性交换。因此M ssbauer谱是研究配合物磁性的有效手段。对该配合物的红外、紫外、光电子能谱、M ssbauer谱进行分析。为深入研究磁性与配合物结构的关系 ,为进一步研究其作为功能材     

Neutrino-lepton masses, Zee scalars, and muon g-2

Evidence for neutrino oscillations points to the existence of tiny but finite neutrino masses. Such masses may be naturally generated via radiative corrections in models, such as the Zee model, where a singlet Zee scalar plays a key role. We minimally extend the Zee model by including a right-handed singlet neutrino nu(R). The radiative Zee mechanism can be protected by a simple U(1)(X) symmetry involving only the nu(R) and a Zee scalar. We further construct a class of models with a single horizontal U(1)(FN) (à la Froggatt-Nielsen) such that the mass patterns of the neutrinos and leptons are naturally explained. We then analyze the muon anomalous magnetic moment (g(mu)-2) and the flavor changing mu-->egamma decay. The nu(R) interaction in our minimal extension is found to induce the BNL g(mu)-2 anomaly, with a light charged Zee scalar of mass 100-300 GeV.     

On the Incompressible Fluid Limit and the Vortex Motion Law of the Nonlinear Schrödinger Equation

The nonlinear Schr?dinger equation (NLS) has been a fundamental model for understanding vortex motion in superfluids. The vortex motion law has been formally derived on various physical grounds and has been around for almost half a century. We study the nonlinear Schr?dinger equation in the incompressible fluid limit on a bounded domain with Dirichlet or Neumann boundary condition. The initial condition contains any finite number of degree ± 1 vortices. We prove that the NLS linear momentum weakly converges to a solution of the incompressible Euler equation away from the vortices. If the initial NLS energy is almost minimizing, we show that the vortex motion obeys the classical Kirchhoff law for fluid point vortices. Similar results hold for the entire plane and periodic cases, and a related complex Ginzburg–Landau equation. We treat as well the semi-classical (WKB) limit of NLS in the presence of vortices. In this limit, sound waves propagate through steady vortices. Received: 1 December 1997 / Accepted: 27 June 1998     

Semianalytic solution of the Kramers exit problem for a small ferromagnetic particle

The distribution Q(t) of magnetization reversal times in a small uniaxial particle is computed here directly from Brown's Fokker-Planck equation. Constant applied field and axial symmetry are assumed. The Laplace transform of Q(t) has the form Q(z)=F(1)(z)/F(2)(z) where the regular functions F(i)(z) are defined by a solution of a Volterra integral equation. A separate integral equation is derived for the function dF(2)(z)/dz, and the poles and residues of Q(z) may then be found numerically with arbitary precision.     

Subcritical crack growth: the microscopic origin of Paris' law

We investigate the origin of Paris' law, which states that the velocity of a crack at subcritical load grows like a power law, da/dt ~ (DeltaK)(m), where DeltaK is the stress-intensity-factor amplitude. Starting from a damage-accumulation function proportional to (Deltasigma)(gamma), Deltasigma being the stress amplitude, we show analytically that the asymptotic exponent m can be expressed as a piecewise-linear function of the exponent gamma, namely, m=6-2gamma for gamma or =gamma(c), reflecting the existence of a critical value gamma(c)=2. We perform numerical simulations to confirm this result for finite sizes. Finally, we introduce bounded disorder in the breaking thresholds and find that below gamma(c) disorder is relevant, i.e., the exponent m is changed, while above gamma(c) disorder is irrelevant.     

Probing possible decoherence effects in atmospheric neutrino oscillations

It is shown that the results of the Super-Kamiokande atmospheric neutrino experiment, interpreted in terms of nu(mu)<-->nu(tau) flavor transitions, can probe possible decoherence effects induced by new physics (e.g., by quantum gravity) with high sensitivity, supplementing current laboratory tests based on kaon oscillations and on neutron interferometry. By varying the (unknown) energy dependence of such effects, one can either obtain strong limits on their amplitude or use them to find an unconventional solution to the atmospheric nu anomaly based solely on decoherence.     

On the evolution of higher dimensional Heisenberg continuum spin systems

We consider the evolution of a classical Heisenberg ferromagnetic spin chain in its continuum limit in higher spatial dimensions. It is shown that the evolution of a radially symmetric chain could be identified with the motion of a helical space curve as in the linear case. The resulting invariant equations for the curvature (radial energy density) and torsion (related to current density) are shown to be equivalent to a generalized nonlinear Schrödinger equation, similar to the one derived by Ruijgrok and Jurkiewicz recently. Equivalent linear equations as well as special static solutions of point singular type are obtained. Similarity solutions, a class of which belong to Riccati type, are discussed in detail. For general higher dimensions, a potentially useful formulation is presented: Under stereographic projection of the unit sphere of spin, the equation of motion takes a neater form even with the inclusion of anisotropic interactions. Classes of explicit solutions are reported in higher dimensions. Propagating spin waves, static spin waves of point singular nature and of finite energy in some cases are also discussed.     

Kondo effect in quantum dots coupled to ferromagnetic leads

We study the Kondo effect in a quantum dot coupled to ferromagnetic leads and analyze its properties as a function of the spin polarization of the leads. Based on a scaling approach, we predict that for parallel alignment of the magnetizations in the leads the strong-coupling limit of the Kondo effect is reached at a finite value of the magnetic field. Using an equation of motion technique, we study nonlinear transport through the dot. For parallel alignment, the zero-bias anomaly may be split even in the absence of an external magnetic field. For antiparallel spin alignment and symmetric coupling, the peak is split only in the presence of a magnetic field, but shows a characteristic asymmetry in amplitude and position.     

Determination of the strange form factors of the Nucleon from nup, nup, and parity-violating e-->p elastic scattering

A new method of obtaining the strange form factors of the nucleon is presented, in which forward-angle parity-violating e-->p elastic scattering data are combined with nup and nu;p elastic scattering data to extract all three strange form factors: electric, magnetic, and axial (G(s)(E), G(s)(M), and G(s)(A)). In this Letter, nup and nu;p data from the Brookhaven E734 experiment are combined with the Jefferson Laboratory HAPPEX e-->p data to obtain two distinct solutions for the strange form factors at Q(2)=0.5 GeV2. More generally, combining the neutrino elastic scattering data from E734 with the existing and upcoming e-->p data will yield the strange form factors of the nucleon for Q2 of 0.45-1.05 GeV2. Measurement of G(s)(A) is crucial to the determination of the strange quark contribution to the nucleon spin Deltas.     

Evolution of particle-scale dynamics in an aging clay suspension

Multispeckle x-ray photon correlation spectroscopy was employed to characterize the slow dynamics of a suspension of highly charged, nanometer-sized disks. At wave vectors q corresponding to interparticle length scales, the dynamic structure factor follows a form f(q,t) approximately exp([-(t/tau)(beta)], where beta approximately 1.5. The relaxation time tau increases with the sample age t(a) approximately as tau approximately t(1.8)(a) and decreases with q as tau approximately q(-1). Such behavior is consistent with models that describe the dynamics in disordered elastic media in terms of strain from random, local structural rearrangements. The measured amplitude of f(q,t) varies with q in a manner that implies caged particle motion. The decrease in the range of this motion and an increase in suspension conductivity with increasing t(a) indicate a growth in interparticle repulsion as the mechanism for internal stress development implied by these models.     

Axial anomaly at finite temperature and finite density

TheU(1) axial anomaly in a hot fermion medium is investigated by using the real time Green's function method. After calculating the lowest order triangle diagrams, we find that finite temperature as well as finite fermion density does not affect the axial anomaly. The higher order corrections for the axial anomaly are discussed.     

Constraints on cosmological parameters from the analysis of the cosmic lens all sky survey radio-selected gravitational lens statistics

We derive constraints on cosmological parameters and the properties of the lensing galaxies from gravitational lens statistics based on the final Cosmic Lens All Sky Survey data. For a flat universe with a classical cosmological constant, we find that the present matter fraction of the critical density is Omega(m)=0.31(+0.27)(-0.14) (68%)+0.12-0.10 (syst). For a flat universe with a constant equation of state for dark energy w=p(x)(pressure)/rho(x)(energy density), we find w<-0.55(+0.18)(-0.11) (68%).     

Propagation-Dispersion Equation

A propagation-dispersion equation is derived for the first passage distribution function of a particle moving on a substrate with time delays. The equation is obtained as the hydrodynamic limit of the first visit equation, an exact microscopic finite difference equation describing the motion of a particle on a lattice whose sites operate as time-delayers. The propagation-dispersion equation should be contrasted with the advection-diffusion equation (or the classical Fokker–Planck equation) as it describes a dispersion process in time (instead of diffusion in space) with a drift expressed by a propagation speed with non-zero bounded values. The temporal dispersion coefficient is shown to exhibit a form analogous to Taylor's dispersivity. Physical systems where the propagation-dispersion equation applies are discussed.