General solutions of the Monge-Ampère equation in n-dimensional space

It is shown that the general solution of a homogeneous Monge-Ampère equation in n-dimensional space is closely connected with the exactly (but only implicitly) integrable system ∂ξ_j/∂x₀ + Σ_k=1ⁿ⁻¹ ξ_k ∂ξ_j/∂x_k = 0 Using the explicit form of solution of this system it is possible to construct the general solution of the Monge-Ampère equation.     

Higher order elastic constants of alkali halides

The Coulomb, van der Waals and repulsive lattice sums occurring in the higher order elastic constants up to sixth order have been calculated for the rocksalt and cesium chloride structures. Numerical values of the static elastic constants up to sixth order based on a rigid ion model with van der Waals and Born-Mayer type central force interaction between first and second nearest neighbors are calculated for several alkali halides representing both structure types. Fair agreement with the available experimental third and fourth order elastic constant data is found.     

Anisotropic breathing shell model and phonons in NaCl structures

Callow, Diller and Norgett, in their investigations on the dynamics of alkali halides, have developed analytic potentials for the short range interactions between the anions and cations. These potentials consisting of Buckingham and van der Waals contributions have been determined from the elastic, dielectric constants and the equilibrium conditions of the lattice and are found to satisfactorily explain the defect properties of many halides. We employ the analytic potentials of Catlow et al. and use anisotropic breathing corrections for the computation on phonon dispersions and Debye-Waller factors of all NaCl structure alkali halides. The results of our study show that good agreement can be obtained with these more physical parameters.     

Total neutron cross sections and the nuclear Ramsauer effect (II). En = 0.5–42 MeV

Investigation at fourteen energies from 0.5 to 42 MeV and A 27 shows that a simple expression describes the σ_T(A,E) surface in the energy and mass number region mentioned above. For E 10 MeV the expression can be interpreted by the nuclear Ramsauer effect, while for E < 10 MeV a better approximation for the black-nucleus formula seems to be useful. The constant amplitude of oscillations suggests a weak volume absorption and a strong surface absorption.     

Evaluation of the spectroscopic constants of the modified rittner potential by the Simon-Parr-Finlan technique

A critical examination is shown of the modified Rittner potential by use of the Simon-Parr- Finlan (SPF) technique, including contributions from the polarisability of ions and the van der Waals term. We develop an equation for the SPF constants, which are related to spectroscopic constants and the polarisability of the constituent ions. Our analysis indicates excellent agreement for the dissociation energies of 20 alkali halides with available experimental data. We also cite theoretical values of the SPF coefficients Y₂₀ and Y₁₁ for the 20 alkali halides; these also compare favourably with experimental data.     

Study of superconducting state parameters of alkali–alkali binary alloys by a pseudopotential

A detailed study of the superconducting state parameters (SSP) viz. electron–phonon coupling strength λ, Coulomb pseudopotential μ^*, transition temperature T_C, isotope effect exponent and effective interaction strength N_OV of ten alkali–alkali binary alloys i.e. Li_1−xNa_x, Li_1−xK_x, Li_1−xRb_x, Li_1−xCs_x, Na_1−xK_x, Na_1−xRb_x, Na_1−xCs_x, K_1−xRb_x, K_1−xCs_x and Rb_1−xCs_x are made within the framework of the model potential formalism and employing the pseudo-alloy-atom (PAA) model for the first time. We use the Ashcroft’s empty core (EMC) model potential for evaluating the superconducting properties of alkali alloys. Five different forms of local field correction functions viz. Hartree (H), Taylor (T), Ichimaru–Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) are used to incorporate the exchange and correlation effects. A considerable influence of various exchange and correlation functions on λ and μ^* is found from the present study. Reasonable agreement with the theoretical values of the SSP of pure components is found (corresponding to the concentration x = 0 or 1). It is also concluded that nature of the SSP strongly depends on the value of the atomic volume Ω₀ of alkali–alkali binary alloys.     

Reduced s-d model with antiferromagnetically coupled impurity spins

An antiferromagnetic equivalent-neighbour Heisenberg interaction H_i between impurity spins is added to the reduced s-d Hamiltonian H_r previously introduced by simplifying the Kondo s-d exchange Hamiltonian H_K. Asymptotic mean-field theory is developed for H_r + H_i, in the presence and absence of external magnetic field, and applied to (La_1−xCe_x)Al₂ alloys. Specific heat c_i(T) and zero-field susceptibility χ_i(0,T) curves for (La_1−xCe_x)Al₂ are depicted. The coupling constants of H_r + H_i and conduction bandwidth are adjusted so that T_c temperatures for x = 0.2, 0.1 are equal to the experimental values. c_i(T) exhibits a jump at T_c and is decreasing for T < T_c. χ_i(0,T) has a first order pole at T_c which corresponds to the maximum of experimental susceptibility and χ_i(0,0) > 0. These results improve those obtained earlier on the grounds of H_r theory.     

Higher-order elastic constants of La1.84Sr0.16CuO4 high-temperature superconductor

Finite deformation theory is used to obtain the strain energy density of a tetragonal 2–1–4-type single crystal of the high-temperature superconductor La_2−xSr_xCuO₄. The complete set of second and third-order elastic constants of the high-temperature superconductor La_2−xSr_xCuO₄ (x = 0.16) is calculated by taking into account the interactions between nine nearest-neighbour atoms in the lattice and using Mie–Grüneisen interatomic potential. For the sake of comparison we have also computed the values of these constants for x = 0.13–0.20. The values of third-order elastic constants of La_2−xSr_xCuO₄ (x = 0.13–0.20) are negative and their absolute magnitudes are one order higher than those of the second-order elastic constants.     

Magnetic behaviour of some Mn.III2.VI4 compounds and their alloys

Measurement of the magnetic susceptibility χ as a function of temperature were made on polycrystalline samples from the alloy systems Cd_1−zMn_zGa₂Se₄, Zn_1−zMn_zGa₂Se₄ and Cd_1−zMn_zIn₂Te₄ which had been subjected to various heat treatments. The 1/χ versus T curves indicated that for the Zn---Se alloys, for all values of z, samples slowly cooled to room temperature were antiferromagnetic showing ideal Curie-Weiss behaviour, but for samples quenched from 700°C the behaviour was a mixture of antiferromagnetic and spin-glass. For the Cd---Se alloys, samples from the range (0.6 < z < 1.0) showed very similar behaviour, but in the range (0 < z < 0.6) even the very slowly cooled samples showed a mixture of antiferromagnetic and spin-glass behaviour. For the Cd---Te alloys, all samples, however heat-treated, showed spin-glass form. Values of the Curie-Weiss constant Ф were determined from all of the 1/χ versus T curves, and by comparison with the T(z) phase diagrams for the different alloy systems, the values of Ф were correlated with the ordering of the Mn atoms on the cation lattice. It is shown that the experimental values of Ф can give a very convenient way of determining the type of ordering and the degree of order in such alloys.     

The Born repulsive parameters and dielectric behaviour of alkali halides

The dependence of the Born repulsive parameters of alkali halides on elastic and dielectric data has been discussed. The values of hardness parameter in alkali halides have been recalculated using the revised values of van der Waals energies. It is observed that the two sets of hardness parameter corresponding to elastic and dielectric data differ from each other but become compatible if an effective charge parameter for the ions is introduced. Its usefulness has been demonstrated by calculating the strain derivative of static dielectric constant of alkali halides.     

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.     

Determination of the inelastic mean free path of electrons in silver and copper by measurement and calculation of the elastic scattering coefficient

The inelastic mean free paths, λ, of electrons in polycrystalline Ag and Cu samples were determined for electron energies in the range 250–1500 eV by means of elastic peak electron spectroscopy (EPES). In this method the coefficient of elastic scattering of electrons, η_e, is measured. η_e is also calculated theoretically for different assumed values of λ. The value of λ giving the best agreement between the measured and calculated η_e is taken as the experimental one. the η_e measurements were performed for Ag and Cu samples cleaned by mechanical scraping only and for samples cleaned by ion bombardment in order to estimate the eventual influence of surface roughness on the η_e values. Additionally, different methods to calculate η_e theoretically are compared.     

Measurement of L X-ray production cross sections and Li subshell fluorescence yields

L_i (i=1, 2 and 3) X-ray production cross sections have been measured for 14 elements in the atomic number range 55≤Z≤81 at 15.73 keV. The values of L_i subshell fluorescence yields (ω₁, ω₂ and ω₃) have been determined using the presently measured X-ray production cross sections and the theoretical L_i subshell photoionization cross sections values, Coster–Kronig transition probabilities and radiative emission rates. The measured X-ray production (XRP) cross-sections and fluorescence yield values were compared with the theoretical and semi empirical values, respectively.     

The generalised Huggins-Mayer form of born repulsive potentials for NaCl-type alkali halides

The generalised Huggins-Mayer form of Born repulsive potentials for NaCl-type alkali halides have been re-evaluated using more reliable, recently published thermodynamic data and van der Waals energy coefficients. As with older versions of these potentials excellent agreement between model and experimental values of interionic distance and cohesive energy is achieved. Further, the earlier shortcomings in the failure of the stability condition and predicted elastic constants are significantly reduced. For the majority of salts the new short-range interactions have stronger van der Waals attractions and slider repulsions. The model gives average crystal radii for the alkali ions about ~0.3 Å larger than traditional free ion radii and ~0.08 Å larger than Tosi-Fumi crystal radii. The predicted halogen crystal radii are correspondingly smaller by the same amounts.     

Landau damping in degenerate solid state plasmas

Helicon waves are found useful for studying Landau damping in degenerate plasmas. The damping is analyzed as the phase velocity of the wave is increased from ω/q v_F to ω/q v_F. There is no first-orderlike transition at ω/q = V_F. In the collisionless limit, the damping tends to zero as ω/q → v_F. For finite collision times τ it does not vanish for ω/q > v_F. Nonlocal corrections to the wavelength exhibit a peak at ω/q = V_F, which degenerates into a shoulder for ωτ 100.     

Swendsen-Wang simulation of Ising spins and a precise definition of critical clusters

A recent ultrafast simulation of Ising spins (σ_i = ± 1) utilizes a random + to − flip-over of duly defined decoupled blocks of spins. We show that the random dynamics alone suffices to prove the correspondence of the blocks with “critical clusters” describing thermal (magnetic) fluctuation. (The precise requirement is σ_iσ_i = 1, for a pair of spins inside a block, and σ_iσ_j = 0, for a σ_i inside and σ_j, outside.) The present approach helps to extend the study of critical clusters, and also ultrafast simulation, to the case of nonzero magnetization. Finite critical clusters constitute always a ± symmetric set and are very different (much smaller) than continuous domains of similarly oriented spins.     

Fluctuation-induced attraction of vortices in anisotropic superconductors

We study the fluctuation-induced attraction of vortices for continuous anisotropic superconductors by using quantum statistical physics. In the low temperature or quantum limit, only the low-lying modes are relevant, the induced short-range attractive potential is proportional to (k_BT)³K₁(ΓR/λ), while in high temperature or classical limit, the induced attractive potential reduced to long-range van der Waals type k_BT/R⁴ for two vortices separated by a distance R.     

On the NSR formulation of string theory on AdS5×S

We discuss the NSR formulation of the superstring action on AdS₅×S⁵ proposed recently by Kallosh and Tseytlin in the Green-Schwarz formalism. We show that the stress-energy tensor corresponding to the NSR action for AdS superstring contains the branelike terms, corresponding to exotic massless vertex operators (referred to as the branelike vertices)- the 5-form e^φψ_m1ψ_m5 and the 3-form ∂(e^φψ_m1ψ_m3), multiplied by ∂X_m. The corresponding sigma-model action has the manifest SO(1,3)×SO(6) invariance of superstring theory on AdS₅×S⁵. We argue that adding the branelike terms is equivalent to curving the space-time to obtain the AdS₅×S⁵ background. We commence the study of the proposed NSR sigma-model by analyzing the scattering amplitudes involving the branelike vertex operators. The analysis shows quite an unusual momentum dependence of these scattering amplitudes.     

Phase segregation of LixMn2O4 (0.6<x<1) in non-equilibrium reduction processes

Chemical synthesis routes to Li_xMn₂O₄ (0.15≤x≤1) in non-equilibrium reduction processes were developed to carry out detailed structural analysis. Non-equilibrium Li_xMn₂O₄ (0.15≤x≤1) samples were prepared by chemical lithiation of λ-MnO₂ with LiI for 24 h; longer than 1 week was needed to reach true equilibrium at room temperature. The samples were characterized by X-ray diffraction analysis. The phase diagram was different from that in the equilibrium state; three cubic phases (phases A, B and C) were observed for Li_xMn₂O₄ (0.15≤x≤1). There were two regions of two-phase coexistence: the region of 0.25<x<0.55 (phase B+phase C) and 0.6<x<1.0 (phase A+phase B). In the compositional range of 0.6<x<1.0, the lattice constants of phases A and B change with the lithium composition, this indicates that it is a structural anomaly with a metastable two-phase character in non-equilibrium reduction processes.