Solutions of fractional nonlinear diffusion equation and first passage time: Influence of initial condition and diffusion coefficient

We investigate the solutions and the first passage time for anomalous diffusion processes governed by the fractional nonlinear diffusion equation with diffusion coefficient separable in time and space, D(t,x)=D(t)|x|^−θ, subject to absorbing boundary condition and the conventional initial condition p(x,0)=δ(x−x₀). We obtain explicit analytical expressions for the probability distribution, the first passage time distribution, the mean first passage time and the mean squared displacement, and discuss their behavior corresponding to different time dependent diffusion coefficients.     

Doubly Charmed Exotic Mesons

We discuss the mass spectrum of doubly charmed mesons as hadronic molecules composed by D and D^* meson. Considering the heavy quark symmetry and chiral symmetry, we introduce the one-boson ( ${\pi , \rho , \omega}$ ) exchange potential between D and D^* meson. For all possible quantum numbers I(J ^P ) with isospin I, total angular momentum J( ≤ 2) and parity P, we solve the fully coupled channel Schrödinger equation. We find that in many quantum numbers the bound and resonant states composed by D or D^* meson can exist near the DD, DD^* and D^*D^* thresholds.     

Regeneration of surface roughness by the Langevin equation using stochastic analysis on AFM image of a carbon fiber

A new method was developed using AFM images of a fiber surface to regenerate the surface roughness in 3D geometry, such as the cylindrical shape of a “model” fiber. The Langevin equation was used to derive the fluctuations of a carbon fiber surface image. The equation contains two quantities, D⁽¹⁾ (h) and D⁽²⁾ (h) which in physics represent drift and diffusion coefficients. Knowing this coefficient and adding a proper noise function, a similar surface of larger dimension with the same statistical properties of the initial data was created. The generated surface was mapped into cylindrical coordinates, then a mesh generated. The resulting reconstructed surface, input over the geometry of a cylindrical shape, can be implemented for finite element analysis of a single fiber surrounded by matrix and generalized to a many fiber model.     

The DD* interaction with isospin zero in an extended hidden gauge symmetry approach

The DD^* interaction via a ρ or ω exchange is constructed within an extended hidden gauge symmetry approach, where the strange quark is replaced by the charm quark in the SU(3) flavor space. With this DD^* interaction, a bound state slightly lower than the DD^* threshold is generated dynamically in the isospin zero sector by solving the Bethe-Salpeter equation in the coupled-channel approximation, which might correspond to the X(3872) particle announced by many collaborations. This formulism is also used to study the BB^* interaction, and a BB^* bound state with isospin zero is generated dynamically, which has no counterpart listed in the review of the Particle Data Group. Furthermore, the one-pion exchange between the D meson and the D^* is analyzed precisely, and we do not think the one-pion exchange potential need be considered when the Bethe-Salpeter equation is solved.     

A discussion of the relativistic equal-time equation

Ruan Tu-nan et al. [1] have proposed an equal-time equation for composite particles which is derived from Bethe-Salpeter (B-S) equation. Its advantage is that the kernel of this equation is a completely definite single rearrangement of the B-S irreducible kernel without any artificial assumptions. In this paper we shall give a further discussion of the properties of this equation. We discuss the behaviour of this equation as the mass of one of the two particles approaches the limitM ₂→∞ in the ladder approximation of single photon exchange. We show that up to orderO(α⁴) this equation is consistent with the Dirac equation. If the crossed two photon exchange diagrams are taken into account the difference between them is of orderO(α⁶).     

High-resolution FTIR measurement of the line parameters in the fundamental band of HI

The linestrengths and self-broadening coefficients are determined from high-resolution measurements for P(1)-P(10) and R(0)-R(15) lines in the fundamental vibration-rotation band of hydrogen iodide at different gas pressures in the range of 2-280 Torr. Dipole matrix elements are calculated from the linestrength data. New values of the Herman-Wallis coefficients obtained, C₁₀=0.1319, D₁₀=4.41×10^-3, are in a better agreement with theory than previously reported. A significant influence of the hyperfine splitting on the spectral line profiles is demonstrated.     

Spatial-temporal dispersion of the kinetic coefficients near the Anderson transition

A generalization of the Vollhardt-Wölfle localization theory is proposed to make it possible to study the spatial-temporal dispersion of the kinetic coefficients of a d-dimensional disordered system in the low-frequency, long-wavelength range (ω?_F and q?k _F ). It is shown that the critical behavior of the generalized diffusion coefficient D(q,ω) near the Anderson transition agrees with the general Berezinskii-Gor’kov localization criterion. More precisely, on the metallic side of the transition the static diffusion coefficient D(q,0) vanishes at a mobility threshold λ _c common for all q: D(q, 0)∝t=(λ _c ?λ)/λ _c →0, where λ=1/(2π?_F τ) is a dimensionless coupling constant. On the insulator side, q≠0 D(q,ω)∝?iω as ω→0 for all finite q. Within these limits, the scale of the spatial dispersion of D(q,ω) decreases in proportion to t in the metallic phase and in proportion to ωξ ², where ξ is the localization length, in the insulator phase until it reaches its lower limit ～λ _F. The suppression of the spatial dispersion of D(q,ω) near the Anderson transition up to the atomic scale confirms the asymptotic validity of the Vollhardt-Wölfle approximation: D(q,ω)?D(ω) as |t|→0 and ω→0. By contrast, the scale of the spatial dispersion of the electrical conductivity in the insulator phase is of order of the localization length and diverges in proportion to |t|^?v as |t|→0.     

Martingales, detrending data, and the efficient market hypothesis

We discuss martingales, detrending data, and the efficient market hypothesis (EMH) for stochastic processes x(t) with arbitrary diffusion coefficients D(x,t). Beginning with x-independent drift coefficients R(t) we show that martingale stochastic processes generate uncorrelated, generally non-stationary increments. Generally, a test for a martingale is therefore a test for uncorrelated increments. A detrended process with an x-dependent drift coefficient is generally not a martingale, and so we extend our analysis to include the class of (x,t)-dependent drift coefficients of interest in finance. We explain why martingales look Markovian at the level of both simple averages and 2-point correlations. And while a Markovian market has no memory to exploit and presumably cannot be beaten systematically, it has never been shown that martingale memory cannot be exploited in 3-point or higher correlations to beat the market. We generalize our Markov scaling solutions presented earlier, and also generalize the martingale formulation of the EMH to include (x,t)-dependent drift in log returns. We also use the analysis of this paper to correct a misstatement of the ‘fair game’ condition in terms of serial correlations in Fama's paper on the EMH. We end with a discussion of Levy's characterization of Brownian motion and prove that an arbitrary martingale is topologically inequivalent to a Wiener process.     

Classification of <Emphasis Type="Italic">T</Emphasis>-odd asymmetries for prescission and evaporated light particles in ternary and quaternary nuclear fission induced by cold polarized neutrons

A unified mechanism of the emergence of T-odd ROT- and TRI-asymmetries is proposed for describing experimental T-odd asymmetry coefficients D(θ) in the angular distributions of prescission alphaparticles that are emitted in true ternary and quaternary nuclear fission reactions induced by cold polarized neutrons. The mechanism is related to the different ways in which the Coriolis interaction of the total spin of a polarized compound fissile nucleus with the orbital moment of alpha-particles affects even (for ROT-asymmetries) and odd (for TRI-asymmetries) components of the amplitude of an undisturbed angular distribution of emitted alpha-particles. Coefficients D_ROT(θ) and D_TRI(θ) derived with this mechanism for T-odd ROT- and TRI-asymmetries successfully describe the dependences of corresponding experimental coefficients for ²³⁵U and ²³⁹Pu nuclei over the range of angles θ, and for the ²³³U nucleus in the angular range of 60° < θ < 110°. It is explained why only ROT-type T-odd asymmetries emerge for evaporated neutrons and γ-quanta emitted by fission fragments in similar reactions if we allows for the Coriolis interaction of the total spin of the compound fissile nucleus with the orbital moments of the fission fragments and the wriggling vibrations of the above nucleus near its scission point.     

False Euro (FEUR) exchange rate correlated behaviors and investment strategy

We have searched for correlations and anticorrelations with respect to currencies as CHF, DKK, JPY, and USD in order to understand the EUR behavior. In order to do so we have invented a false euro (FEUR) dating back to 1993 and have derived simulated exchange rates of the FEUR. Within the Detrended Fluctuation Analysis (DFA) statistical method we have obtained the power law behavior describing the rms. deviation of the fluctuations as a function of time. We have compared the time-dependent exponent for these four exchange rates, and observe the role of the DEM, and the other currencies forming the EUR. A simple investment strategy based on the local DFA technique shows one can obtain appreciable gains, even taking into account some modest transaction fee. We compare the time dependent α exponent of the DFA for various exchange rates as in a correlation matrix for estimating respective influences. Received 31 August 2000     

Collision-induced first overtone band of D2 in binary mixtures D2-X where X is Ar, Kr, and Xe

Enhancement spectra of the collision-induced absorption in the first overtone region 5500-6750 cm⁻¹ of D₂ in the D₂-Ar, D₂-Kr, and D₂-Xe binary mixtures were studied at 298 K for base densities of D₂ in the range 55-251 amagat and for partial densities of Ar, Kr, and Xe in the range 46-384 amagat. The observed spectra consist of the following quadrupolar transitions: O₂(3), O₂(2), Q₂ (J), J = 1-5 and S₂ (J), J = 0-5 of D₂. Binary and ternary absorption coefficients were determined from the integrated absorption coefficients of the band. Profile analyses of the spectra were carried out using the Birnbaum-Cohen (BC) lineshape function and characteristic lineshape parameters were determined from the analyses.     

Kinetic Theory and Lax Equations for Shock Clustering and Burgers Turbulence

We study shock statistics in the scalar conservation law ? _t u+? _x f(u)=0, x∈?, t>0, with a convex flux f and spatially random initial data. We show that the Markov property (in x) is preserved for a large class of random initial data (Markov processes with downward jumps and derivatives of Lévy processes with downward jumps). The kinetics of shock clustering is then described completely by an evolution equation for the generator of the Markov process u(x,t), x∈?. We present four distinct derivations for this evolution equation, and show that it takes the form of a Lax pair. The Lax equation admits a spectral parameter as in Manakov (Funct. Anal. Appl. 10:328–329, 1976), and has remarkable exact solutions for Burgers equation (f(u)=u ²/2). This suggests the kinetic equations of shock clustering are completely integrable.     

Dynamic properties of water in silicalite-1 powder

Self-diffusion of D₂O in partially filled silicalite-1 crystals was studied at 25°C by ²H nuclear magnetic resonance (NMR) with bipolar field gradient pulses and longitudinal Eddy-current-delay. For the first time, reliable experimental diffusion data for this system were obtained. Analysis of NMR diffusion decays revealed the presence of a continuous distribution of apparent self-diffusion coefficients (SDCs) of water, ranging from 10⁻⁷ to ∼10⁻¹⁰ m²/s, which include values much higher and lower than that of bulk water (∼10⁻⁹ m²/s) in liquid phase. The observed distribution of SDC changes with variation of the diffusion time in the range of 10–200 ms. A two-site Kärger exchange model was successfully fitted to the data. Finally, the water distribution and exchange in silicalite-1 pores were described by taking into account (a) a gas-like phase in the zeolite pores, a gas-like phase in mesopores and an intercrystalline gas-like phase and (b) intercrystalline liquid droplets with intermediate exchange rate with the other phases. The other phases experience fast exchange on the NMR diffusion time scale. Diffusion coefficients and mean residence times of water in some of these states were estimated.     

Sorption, desorption and extraction of uranium from some sands under dynamic conditions

Sorption, desorption and extraction behavior of uranium in various fluvial sands of domestic origin were investigated in continuous dynamic column experiments. For the sorption of U(VI) an aqueous 10⁻⁴M UO₂(NO₃)₂ solution was used at a flow rate of about 0,3 cm³/min. Desorption was carried out with demineralized water, and the extraction with 10⁻²M Na₂CO₃ solution following desorption. The retardation coefficients (R) and hydrodynamic dispersion coefficients (D_d), were determined using an ADE equation. From the experimentally determined values of R, bulk density and porosity, the distribution coefficients (K_d) of the UO₂ ² species have been calculated for the respective processes. The extent of U sorption in sands, as well as the proportion of desorbed and extracted U from these sands, was also calculated.     

On the extraction of elastic neutron electromagnetic form factors from highQ 2 D(e,e′) scattering

The problem of extraction of the neutron magnetic form factor from highQ ² D(e, e′) data is considered. We calculate the inelastic contribution to the cross section using two models of the EMC effect and find that the extracted value ofG _Mn(Q ²) is not sensitive to the deuteron structure forQ ²≦6 GeV². At the same time accurate data atQ ²>10 GeV² and x≧ l would enable to establish presence of the EMC type effect for the deuteron.     

Theory of light scattering from a system of interacting Brownian particles

Starting from a N-particle diffusion equation for a system of N interacting spherical Brownian particles, a non-linear transport equation for concentration fluctuations δc(r, t) of the particles is derived. This dynamic equation is transformed into a hierarchy of equations for retarded propagators of increasing numbers of concentration fluctuations. A cluster expansion to lowest order in the average concentration results in a set of two coupled equations. The spectrum of light scattered by the interacting particles is in general not a Lorentzian, due to the non-linear term in the transport equation. For small scattering wave vectors k the width is D(ω)k², where ω is the transferred frequency. It is shown that D(0) = D_e, the effective diffusion coefficient. For a hardcore interaction potential the spectrum is Lorentzian and it is found that D_e = D₀(1 + φ), where D₀ is the diffusion constant for independent particles and φ the volume concentration of Brownian particles.     

Oxygen diffusion studies on (Y2O3)2(Sc2O3)9(ZrO2)89

The oxygen tracer diffusion coefficient (D?) has been measured for 9 mol% scandia 2 mol% yttria co-doped zirconia solid solution, (Y₂O₃)₂(Sc₂O₃)₉(ZrO₂)₈₉, using isotopic exchange and line scanning by Secondary Ion Mass Spectrometry, as a function of temperature. The values of the tracer diffusion coefficient are in the range of 10^? 8–10^? 7 cm² s^? 1 and the Arrhenius activation energy was calculated to be 0.9 eV; both valid in the temperature range of 600–900 °C. Electrical conductivity measurements were carried out using 2-probe and 4-probe AC impedance spectroscopy, and a 4-point DC method at various temperatures. There is a good agreement between the measured tracer diffusion coefficients (D?, Ea = 0.9 eV) and the diffusion coefficients calculated from the DC total conductivity data (D_σ, Ea = 1.0 eV), the latter calculated using the Nernst–Einstein relationship.     

Higher order field equations II; Limit properties of green's functions

In a previous paper wave propagation was studied according to a sixth-order partial differential equation involving a complex mass M. The corresponding Yang-Feldman integral equations (indicated as SM-YF-equations), were formulated using modified Green's functions G^M_R(x) and G^M_A(x), which then incorporate the partial differential equation together with certain boundary conditions. In this paper certain limit properties of these modified Green's functions are derived: (a) It is shown that for |M| → ∞ the Green's functions G^M_R(x) and G^M_A(x) approach the Green's functions Δ_R(x) and Δ_A(x) of the corresponding KG-equation (Klein-Gordon equation). (b) It is further shown that the asymptotic behaviour of G^M_A(x) and G^M_A(x) is the same as of Δ_R(x) and Δ_A(x) - and also the same as for D_R(x) and D_A(x) for t→ ± ∞, where D_R and D_A are the Green n's functions for the KG-equation with mass zero. It is essential to take limits in the sense of distribution theory in both cases (a) and (b). The property (b) indicates that the wave propagation properties of the SM-YF-equations, the KG-equation with finite mass and the KG-equation with mass zero are closely related in an asymptotic sense.     

A Gribov equation for the photon Green’s function

We present a derivation of the Gribov equation for the gluon/photon Green’s function D(q). Our derivation is based on the second derivative of the gauge-invariant quantity Trln?D(q), which we interpret as the gauge-boson ‘self-loop’. By considering the higher-order corrections to this quantity, we are able to obtain a Gribov equation which sums the logarithmically enhanced corrections. By solving this equation, we obtain the non-perturbative running coupling in both QCD and QED. In the case of QCD, α _S has a singularity in the space-like region corresponding to super-criticality, which is argued to be resolved in Gribov’s light-quark confinement scenario. For the QED coupling in the UV limit, we obtain a ∝ Q ² behavior for space-like Q ²=?q ². This implies the decoupling of the photon and an NJLVL-type effective theory in the UV limit.