On nonanalytic solitary waves formed by a nonlinear dispersion

We study the prototypical, genuinely nonlinear, K(m, n) equation, u_t ± a(u^m)_x + (uⁿ)_xxx = 0, a = const, which exhibits a number of remarkable dispersive effects. In particular, the distinguished subclass wherein m = n + 2 is transformed into a new, purely dispersive equation free of convection. In addition to compactons, the K(m, n) can support both kinks and solitons with an infinite slope(s), periodic waves and dark solitons with cusp(s) all being manifestations of nonlinear dispersion in action. For n < 0 the enhanced dispersion at the tail may generate algebraically decaying patterns.     

1-forms over the moduli space of irreducible connections defined by the spectrum of Dirac operators

Let (P) be the moduli space of irreducible connections of a G-principal bundle P over a closed Riemannian spin manifold M. Let D_A be the Dirac operator of M coupled to a connection A of P and f a smooth function on M. We consider a smooth variation A(u) of A with tangent vector ω and denote T_ω:= (D_A(u)−f) (u=0. The coefficients of the asymptotic expansion of trace (T_ω · e^-t(D_A−f)2) near t=0 define 1-forms a^(k)_f, K=0, 1, 2, … on (P). In this paper we calculate aa⁽⁰⁾_f, a⁽¹⁾_f, a⁽²⁾_f and study some of their properties. For instance using the 1-form a⁽²⁾_f for suitable functions f we obtain a foliation of codimension 5 of the space of G-instantons of S⁴.     

Generalized Einstein manifolds

A Finslerian manifold is called a generalized Einstein manifold (GEM) if the Ricci directional curvature R(u,u) is independent of the direction. Let F⁰(M, g_t) be a deformation of a compact n-dimensional Finslerian manifold preserving the volume of the unitary fibre bundle W(M). We prove that the critical points g₀ F⁰(g_t) of the integral I(g_t) on W(M) of the Finslerian scalar curvature (and certain functions of the scalar curvature) define a GEM. We give an estimate of the eigenvalues of Laplacian Δ defined on W(M) operating on the functions coming from the base when (M, g) is of minima fibration with a constant scalar curvature H admitting a conformal infinitesimal deformation (CID). We obtain λ ≥ H/(n − 1) (Δf = λf). If M is simply connected and λ = H/(n − 1), then (M, g) is Riemannian and is isometric to an n-sphere. We first calculate, in the general case, the formula of the second variationals of the integral I (g_t) for G = g₀, then for a CID we show that for certain Finslerian manifolds, I″(g₀) > 0. Applications to the gravitation and electromagnetism in general relativity are given. We prove that the spaces characterizing Einstein-Maxwell equations are GEMs.     

New variable separation solutions for the generalized nonlinear diffusion equations

The functionally generalized variable separation of the generalized nonlinear diffusion equations ut = A(u, ux)uxx +B(u, ux) is studied by using the conditional Lie–Ba¨cklund symmetry method. The variant forms of the considered equations,which admit the corresponding conditional Lie–Ba¨cklund symmetries, are characterized. To construct functionally generalized separable solutions, several concrete examples defined on the exponential and trigonometric invariant subspaces are provided.     

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.     

一类带扰动的Sine-Gordon方程的谱方法

研究一类具扰动的Sine-Gordon方程u_tt-u_xx+αsinu-βu_xxt=g(u),t>0,-∞< x< ∞的周期初值问题,提出了谱方法,并用先验估计方法作了误差估计,证明了近似方法的收敛性,并得到了该问题广义解的存在、唯一性。     

Effects of cation- or oxide ion-defect on conductivities of apatite-type La–Ge–O system ceramics

A series of apatite-type La–Ge–O ceramics were prepared and their cation-defect at the 4f+6h sites and oxide ion-defect at 2a site were investigated. In La_xGe₆O_12+1.5x ceramics of x=6–12, the higher conductivities were obtained in the region of apatite composition, La_x(GeO₄)₆O_1.5x−12 (x=8–9.33), and the highest conductivity was achieved for La₉(GeO₄)₆O_1.5 (x=9), where the number of cation (La³⁺) occupying the 4f+6h sites is 9 and the number of oxide ion occupying the 2a site is 1.5. The ceramics with cation- and oxide ion-defects were La_9−0.66xSr_x(GeO₄)₆O_1.5 (x=0–1), La_9−1.33xZr_x(GeO₄)₆O_1.5 (x=0–1), La_9−xSr_x(GeO₄)₆O_1.5−0.5x (x=0–3), La_9−xZr_x(GeO₄)₆O_1.5+0.5x (x=0–1), La_x(GeO₄)_3x−21(AsO₄)_27−3xO_1.5 (x=0–3), La_x(GeO₄)_33−3x(AlO₄)_3x−27O_1.5 (x=0–3), La₉(GeO₄)_6−x (AlO₄)_xO_1.5−0.5x (x=0–3), La₉(GeO₄)_6−x(AsO₄)_xO_1.5+0.5x (x=0–1), La_9.33−xSr_x(GeO₄)₆O_2−0.5x (x=0–1.2) and La_x(GeO₄)_4.5(AlO₄)_1.5O_1.5x−12.75 (x=8.8–9.83), which were prepared by the partial substitution of La³⁺and GeO₄⁴⁻of the basic apatite La₉(GeO₄)₆O_1.5 with Sr²⁺ or Zr⁴⁺ and AlO₄⁵⁻ or AsO₄³⁻. Such substitutions lowered the conductivity of La₉(GeO₄)₆O_1.5. These results were discussed by the electrostatic interaction between Sr²⁺, Zr⁴⁺, AlO₄⁵⁻ or AsO₄³⁻ and oxide ion as a conductive species.     

Contribution of asymmetric strange–antistrange sea to the Paschos–Wolfenstein relation

The NuTeV Collaboration reported a value of sin²θ_w measured in neutrino–nucleon deep inelastic scattering, and found that the value is three standard deviations from the standard model prediction. This result is obtained under the assumption that the strange quark–antiquark sea of nucleons are symmetric, and that the up and down quark distributions are symmetric with the simultaneous interchange of u↔d and p↔n. We discuss the contribution of asymmetric strange–antistrange sea to the Paschos–Wolfenstein relation in the extraction of weak mixing angle sin²θ_w. We also point out that the contribution of asymmetric strange–antistrange sea should remove roughly 30–80% of the discrepancy between the NuTeV result and other determinations of sin²θ_w when using the light-cone meson–baryon model to calculate the contribution of the strange–antistrange sea.     

Projective and affine connections on S and integrable systems

It is known that the Korteweg–de Vries (KdV) equation is a geodesic flow of an L² metric on the Bott–Virasoro group. This can also be interpreted as a flow on the space of projective connections on S¹. The space of differential operators Δ⁽ⁿ⁾=∂ⁿ+u₂∂ⁿ⁻²++u_n form the space of extended or generalized projective connections. If a projective connection is factorizable Δ⁽ⁿ⁾=(∂−((n+1)/2−1)p₁)(∂+(n−1)/2p_n) with respect to quasi primary fields p_i’s, then these fields satisfy ∑_i=1ⁿ((n+1)/2−i)p_i=0. In this paper we discuss the factorization of projective connection in terms of affine connections. It is shown that the Burgers equation and derivative non-linear Schrödinger (DNLS) equation or the Kaup–Newell equation is the Euler–Arnold flow on the space of affine connections.     

Effects of the dust size distribution in one-dimensional quantum dusty plasma

The effects of the dust size distribution in ultracold quantum dusty plasmas are investigated. The amplitude φ_m and width ω of quantum dust acoustic waves are studied with different dust size distributions in the system. The φ_m and ω of the quantum dust acoustic waves are found to increase as the total number density increases. The φ_m and ω are greater for unusual dusty plasmas than for typical dusty plasmas. Moreover, as the Fermi temperature of the dust grains increases, the φ_m of the wave decreases. The ω of quantum dust acoustic waves increases as the speed u₀ of the wave increases.     

A Pati–Salam model from branes

We explore the possibility of embedding the Pati–Salam model in the context of Type I brane models. We study a generic model with U(4)_C×U(2)_L×U(2)_R gauge symmetry and matter fields compatible with a Type I brane configuration. Examining the anomaly cancellation conditions of the surplus abelian symmetries we find an alternative hypercharge embedding that is compatible with a low string/brane scale of the order of 5–7 TeV, when the U(4)_C and U(2)_R brane stack couplings are equal. Proton stability is assured as baryon number is associated to a global symmetry remnant of the broken abelian factors. It is also shown that this scenario can accommodate an extra low energy abelian symmetry that can be associated to lepton number. The issue of fermion and especially neutrino masses is also discussed.     

Temperature dependence of the critical current in YBa2Cu3O7−δ and Bi2Sr2Ca1Cu2O8 Josephson junctions

We have studied the stationary Josephson effect on YBa₂Cu₃O_7−δ (T_c=90 K) and Bi₂Sr₂Ca₁Cu₂ O₈ (T_c=80 K and 87 K for two samples of different origin) ceramic based junctions. The temperature dependence of the critical current near T_c has been found as I_c≈(T_c-T) for the Y-Ba-Cu-O samples indicating that they should be classified as S-N-I-N-S type junctions. The I-V curves of the Bi-Sr-Ca-Cu samples show the typical behaviour of S-I-S structures. Using Ambegaokar-Baratoff's theory for Bi₂Sr₂Ca₁Cu₂O₈, the temperature dependence of the superconducting state gap Δ(T) was calculated and it was evaluated that 1.452Δ(0)/k_BT_c3.5.     

一类演化方程的高稳定性的差分格式

考虑一类演化方程u_t=au∂_2k+1(其中a是常数,u∂_2k+1=∂^2k+1u/∂x^2k+1,k=1,2……)的有限差分解法。构造了两类具有高稳定性的显式差分格式。并用引入耗散项的方法建立了两类半显式差分格式,它们是无条件稳定的且可显式地进行计算。     

Magnetic properties of the Bi1.95Sr2.05−xLaxCuOy (Bi-2201) superconducting phase

We have investigated the reversible mixed-state magnetization M of three lanthanum substituted Bi_1.95Sr_2.05−xLa_xCuO_y (Bi-2201) ceramic samples having different critical temperatures T_c ranging from 20.0 to 35.5 K. As for the Bi₂Sr₂CaCu₂O_8+δ (Bi-2212) phase, we found that anisotropy of Bi-2201 is large. A manifestation of this anisotropy is the field independent magnetization M^* observed at a temperature T^*. In the framework of the London model, and including thermal fluctuations of vortices, we found for the temperature dependence of the penetration depth λ_ab(T) = λ_ab(0)[1 − (T/T_c0)ⁿ]^−1/2, with n 1.7 and λ_ab (T = 0) 4000 Å. The estimated upper critical fields μ₀H_c2,c are of the order of 10 T. We observe a peculiar negative slope M/T at low temperature and sufficiently high external magnetic field. This feature seems to be a characteristic of the Bi-2201 phase. However, we do not know whether it is associated with the superconducting mixed-state. A small amount of magnetic impurities could also be responsible for this behavior. Finally, the behavior of the reversible magnetization of the Bi-2201 samples investigated, which are situated at the optimal and in the overdoped region, did not indicate any unusual temperature dependence for the upper critical field H_c2,c.     

Probing the isospin dependent in-medium nucleon–nucleon cross section by nucleon emissions

The effects of the symmetry potential and the isospin dependent in-medium nucleon–nucleon (NN) cross section on the number of proton(neutron) emissions N_p(N_n) are studied respectively within an isospin-dependent quantum molecular dynamics (IQMD) model. The isospin dependent in-medium NN cross section is found to have a strong influence on N_p(N_n) but N_p(N_n) is not sensitive to the symmetry potential for the neutron-deficient colliding system at relatively high energies. We propose to make use of the N_p(N_n) as a probe to extract information on the isospin dependent in-medium NN cross section.     

Effects of collision energy and rotational quantum number on stereodynamics of the reactions:H(~2S)+NH(v=0,j=0,2,5,10)→N(~4S)+H_2

The stereodynamical properties of H(~2S) + NH(v = 0,j = 0,2,5,10)→N(~4S) + H_2 reactions are studied in this paper by using the quasi-classical trajectory(QCT) method with different collision energies on the double many-body expansion(DMBE) potential energy surface(PES)(Poveda L A and Varandas A J C 2005 Phys.Chem.Chem.Phys.7 2867).In a range of collision energy from 2 to 20 kcal/mol,the vibrational rotational quantum numbers of the NH molecules are specifically investigated on v = 0 and j = 0,2,5,10 respectively.The distributions of P(θ_r),P(φ_r),P(θ_r,φ_r),(2π/σ)(dσ_(00)/dω_t)differential cross-section(DCSs) and integral cross-sections(ICSs) are calculated.The ICSs,computed for collision energies from 2 kcal/mol to 20 kcal/mol,for the ground state are in good agreement with the cited data.The results show that the reagent rotational quantum number and initial collision energy both have a significant effect on the distributions of the k-j',the k-k'-j',and the k-k' correlations.In addition,the DCS is found to be susceptible to collision energy,but it is not significantly affected by the rotational excitation of reagent.     

Oxygen overdoping in superconducting and non-superconducting Y1−xPrxBa2Cu3Oy

We present the evolution of magnetic and structural properties of Y_1−xPr_xBa₂Cu₃O_y (x0.5 and x=1) single crystals and polycrystalline materials when the oxygen concentration y is varied from under- to overdoping. We have found a monotonous evolution of the Pr Néel temperature for x=1 samples and a maximum of the superconducting critical temperature for the x0.5 samples. The structural properties as detected by X-ray diffraction and Raman spectroscopy show no instabilities when crossing the optimal doping region as was found in the x=0 material.     

Anomalous magnetotransport phenomena in θ-(BEDT-TTF)2I3

Anomalous magnetotransport phenomena have been observed in θ-(BEDT-TTF)₂I₃ crystals at temperatures below 15 K. The magnetoresistance M : (1) is a linear function of the magnetic field H, (2) is not affected by the angle between the electric current and the magnetic field, (3) but depends on the magnetic field orientation with respect to the crystal axis. Magnetoresistance is expressed as M = (aH²_a + bH²_b + cH²_c)₀^-3/2/H in terms of H = (H_a, H_b, H_c), the zero field resistivity ₀, and parameters a, b, and c which are independent of temperature and magnetic field. We have found that b a > c. Magnetoresistance up to 40 is observed for H = 7T along the b-axis at T = 1.5K.     

The effect of gallium substitution on the superconductivity of the BiSrCaCuO system

Magnetic susceptibility, X-ray diffraction and resistivity measurements of the system Bi_1.4Pb_0.6Sr₂Ca_2−xGa_xCu₃O_y are reported for 0 x 2. The high-T_c 2223 phase with a T_c of 107 K for x = 0 exists for x 0.3. The low-T_c 2212 phase with a T_c of 75 K for x = 0 exists for the full range of x. The highest values of the critical temperature and the largest volume fraction of the low-T_c phase in compounds with Ga occur for x = 0.5 ± 0.1. The identification of CaO by X-ray diffraction for x 0.6 indicates that Ga replaces Ca in the compound.     

Annealing effects on the magnetization of Co–Ni–B amorphous nanoparticles

Chemically prepared (Co_xNi_1−x)_1−yB_y (x=0.5, 0.75, 1; y≈0.4) amorphous fine particles were characterized by X-ray diffraction, DTA and TGA, and in situ magnetic measurement as a function of annealing temperature in an inert atmosphere. Magnetic measurement performed in as-prepared and 150°C annealed samples shows an increase of the saturation magnetization and magnetic moment after thermal treatment. Room temperature magnetization increases by factors of 3.5, 1.8, and 1.5, for x=0.5, 0.75, and 1, respectively. These measurements may indicate a local re-ordering of the amorphous phase at temperatures much lower than the full crystallization temperature.