Statics and dynamics of phase segregation in multicomponent fermion gas

We investigate the statics and dynamics of spatial phase segregation process of a mixture of fermion atoms in a harmonic trap using the density functional theory. The kinetic energy of the fermion gas is written in terms of the density and its gradients. Several cases have been studied by neglecting the gradient terms (the Thomas-Fermi limit) which are then compared with the Monte-Carlo results using the full gradient corrected kinetic energy. A linear instability analysis has been performed using the random-phase approximation. Near the onset of instability, the fastest unstable mode for spinodal decomposition is found to occur at q = 0. However, in the strong coupling limit, many more modes with q ≈ K _F decay with comparable time scales. Received 12 September 2001 Published online 24 September 2002 RID="a" ID="a"e-mail: k1@sharif.edu RID="b" ID="b"Permanent address: Dr. Vijay Kumar Foundation, 45 Bazaar Street, K.K. Nagar (West), Chennai 600 078, India.     

Perturbation theory for the radial distribution function

Perturbation theory is used to consider expansions for the radial distribution function, g ₂(r), of a fluid with a soft core. We consider the Lennard-Jones (12, 6) potential and divide it into repulsive and attractive regions. In the repulsive region we expand the function exp (β u(r))g ₂(r) about a hard sphere value. For the first-order contribution of the attractive region we consider a simple approximation to the exact analytical expression. The resulting g ₂(r) is accurate at densities below about ρσ ³=0·5.     

Thermodynamic perturbation theory for the (12-6-n) fluids

A perturbation method in which attractive forces are taken as perturbation of the repulsive (reference) forces is applied to calculate the thermodynamic properties of (12-6-n) fluids in terms of the properties of hard-sphere fluid. The numerical values of the thermodynamic properties (free energy per particle, compressibility and excess internal energy) for a range of temperature and density are given for (12-6-8) fluids. Further, two perturbation schemes are adopted to evaluate the total radial distribution function using the EXP version of the optimized cluster theory (OCT). The numerical results are reliable as reported at two states (T* = 1·036,ρ* = 0·65 andT* = 0·719ρ* = 0·85) for the (12-6-8) fluid and the Lennard-Jones (12-6) fluid as well.     

Simulation of molecular orientational dynamics in a model polar fluid

A molecular dynamics simulation of a Stockmayer fluid with μ* = 1·0, ρ* = 0·7 and T* = 1·13 (±0·03) is reported. In addition to evaluations of a number of static properties, orientational time correlation functions C_l (t) = <P(cos δθ(t))> were calculated for l = 1 through 4 ; P_l is a Legendre polynomial and δθ(t) is the angle of reorientation of the dipole in time t. These time correlation functions are characteristic of nearly free rotation and agree well with curves calculated from a perturbation theory for the memory functions that utilizes the simulated value of the mean square torque. The angular velocity autocorrelation function for this fluid was also simulated and compared with perturbation theory. Agreement is not good, primarily because of the presence of a pronounced long time tail in the simulated function. The relationship between these results and those of other simulations and theories is discussed.     

Scalar Field in the Bianchi I: Noncommutative Classical and Quantum Cosmology

Using the ADM formalism in the minisuperspace, we obtain the commutative and noncommutative exact classical solutions and exact wave function to the Wheeler-DeWitt equation with an arbitrary factor ordering, for the anisotropic Bianchi type I cosmological model, coupled to a scalar field, cosmological term and barotropic perfect fluid. We introduce noncommutative scale factors, considering that all minisuperspace variables q ⁱ do not commute, so the symplectic structure was modified. In the classical regime, it is shown that the anisotropic parameter β _±nc and the field φ, for some value in the λ _eff cosmological term and noncommutative θ parameter, present a dynamical isotropization up to a critical cosmic time t _c ; after this time, the effects of isotropization in the noncommutative minisuperspace seems to disappear. In the quantum regimen, the probability density presents a new structure that corresponds to the value of the noncommutativity parameter.     

On the initial stage of spinodal decomposition

A consistent theory describing the initial stage of spinodal decomposition of a two-component system is proposed. It is shown that the structure factor S(q, t) has two maxima as a function of wavenumber at this stage. The main maximum point q₊ varies with time, first moving from q_saddle to q_m (given by expressions (22) and (12), respectively) and then back after the turning point in time given by (26) is passed. The other maximum point is localized at q ≈ 0, and the corresponding peak amplitude is virtually independent of time. The characteristics of the main maximum are sensitive to the existence of the “zero” peak. Available experimental observations support the predictions of the theory.     

Calculating the low temperature vapour line by Monte Carlo

A combination of canonical and grand-canonical ensemble Monte Carlo calculations, together with the virial expansion, have been used to calculate the thermodynamic properties of the liquid/vapour co-existence curve of the (6 : 12) Lennard-Jones fluid for reduced temperatures, [Ttilde] ? 1·1. The results for the liquid density and energy and the latent heat of vaporization are believed to be precise, with the exception of the point at [Ttilde]=1·1 which may lie outside the range of the function fitting the liquid phase Monte Carlo data. The liquid density and the saturated vapour pressure are in very good agreement with the results of perturbation theory. The latent heat of vaporization does not agree well with the experimental data for argon though the fit to liquid density and internal energy is good.     

Computational materials design of filled tetrahedral compound magnetic semiconductors

Based on first-principles calculations within the density functional theory, materials design of filled tetrahedral compound magnetic semiconductors is proposed. By using the Korringa–Kohn–Rostoker coherent potential approximation, electronic structures of Mn-doped LiZnAs, LiZnP and LiZnN are calculated. First, by estimating free energy, phase diagrams of these systems are predicted. It is shown that these systems are phase separating systems and favor spinodal decomposition. However, by introducing Li vacancies, spinodal decomposition is strongly suppressed and Mn can be doped up to high concentration. Moreover, the introduced Li vacancies induce ferromagnetic interaction between Mn and thus we can expect high Curie temperature (T_C) in these systems. To see the chemical trend, electronic structure and T_C of Li(Zn, Cr)As are also calculated.     

Ab‐initio thermodynamic calculations of Mg2BIV (BIV = Si,Ge, Sn) solid solutions

The thermodynamic properties of ternary Mg₂B^IV (B^IV = Si, Ge, Sn) solid solutions were first calculated by the ab‐initio density functional method. The results showed that there exist composition regions with d²G /dx² < 0 in Mg₂Si_1–x Sn_x and Mg₂Ge_1–x Sn_x systems, implying the possibility of spinodal decomposition of the pseudobinary solid solutions. It is suggested that the spinodal decomposition would be a potential way to obtain Mg₂B^IV based bulk in‐situ nanocomposites with reduced grain sizes and enhanced phonon scattering, and hence an improved thermoelectric figure of merit. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nuclear spin lattice relaxation and electric field gradient in liquid indium

We have measured the nuclear spin lattice relaxation time in liquid indium from 130°C to 300°C to be: 1/T ₁=(1.98 × 0.0082T) × 10³ sec^-1. The relaxation rate consists of two significant parts: (1/T ₁) _K from the nuclear magnetic hyperfine interaction, and (1/T ₁) _Q from the nuclear quadrupole interaction. We calculate (1/T ₁) _K from the the modified Korringa relation using a correction factor of order unity for electron-electron interactions. The hyperfine term is linear in T and accounts for the second term in 1/T ₁. Within experimental error the remaining rate, (1/T ₁) _Q , is temperature independent, and theoretically varies as the product of the square of the electric field gradient, q, and τ_c, a typical time between field gradient fluctuations. Making use of the x-ray RDF, we construct a simple model for liquid indium and calculate the ionic and electronic contributions, q _I and q _E, to the electric field gradient, to be q _I=1.4 × 10²⁴/cm³ and q _E=8.5 × 10²⁴/cm³. The calculation of q _E assumes covalent bonding between nearest neighbours. Taking q _I and q _E to be of opposite sign, we find that the correlation time τ_c is 1.6 × 10^-13 sec. When we further identify τ _c with the correlation time for diffusion in a three-dimensional random walk, we are able to calculate the r.m.s. jump distance, Δr _D, involved in self-diffusion, Δr _D=0.38 Å. This value is consistent with the x-ray peak width of 0.38 Å which we used earlier to calculate the electric field gradient.     

Morphological characterization of spinodal decomposition kinetics

The time evolution of the morphology of homogeneous phases during spinodal decomposition is described using a family of morphological measures known as Minkowski functionals. They provide the characteristic length scale L of patterns in a convenient, statistically robust, and computationally inexpensive way. They also allow one to study the scaling behavior of the content, shape, and connectivity of spatial structures and to define the crossover from the early stage decomposition to the late stage domain growth. We observe the scaling behavior with , , and depending on the viscosity of the fluid. When approaching the spinodal density , we recover the prediction for the early time spinodal decomposition. Received 3 March 1998     

Anisotropic Universe Models with Perfect Fluid and Dark Energy with Time Varying G and Λ

We have investigated general Bianchi type I cosmological models which containing a perfect fluid and dark energy with time varying G and Λ that have been presented. The perfect fluid is taken to be one obeying the equation of state parameter, i.e., p=ωρ; whereas the dark energy density is considered to be either modified polytropic or the Chaplygin gas. Cosmological models admitting both power-law which is explored in the presence of perfect fluid and dark energy too. We reconstruct gravitational parameter G, cosmological term Λ, critical density ρ _c , density parameter Ω, cosmological constant density parameter Ω _Λ and deceleration parameter q for different equation of state. The present study will examine non-linear EOS with a general nonlinear term in the energy density.     

Thermodynamic and structural properties of liquids modelled by ‘2-Lennard-Jones centres’ pair potentials

Molecular dynamics calculations have been carried out for model liquid systems of N (=108 or 256) molecules interacting through two Lennard-Jones (12–6) centres coinciding with the positions of the atomic masses (the ‘atom-atom’ pair potential). The objectives were (a) to study the dependence of the properties on the molecular anisotropy defined by the reduced distance l*=l/σ between the centres in the range 0·5–0·8; and (b) to compare the computed quantities with those of real liquids (F₂, Cl₂, Br₂, CO₂). This paper deals with thermodynamic and structural features. Time-dependent correlations will be treated in a future communication.

In the liquid region not too far from the triple point the energy and pressure isochores are well represented by straight lines, the slopes of which increase with density and anisotropy. Thermodynamically consistent expressions for the energy and pressure as functions of density and temperature have been obtained for each system.

With Lennard-Jones parameters adjusted so as to secure the best overall fit, the agreement between experimental and computed thermodynamic properties is very satisfactory for F₂ (l*=0·505), quite good for Cl₂ and Br₂ (l*=0·608–0·63), but rather poor for CO₂ (l*=0·793). The ‘interatomic distances’ are close to the experimental values.

The static structural correlations are discussed in terms of the pair-correlation functions (pcf) g _A(r*) for the separation between ‘atoms’, the first few functions g_ll'm (R*) which arise from the expansion of the g(R*, θ₁, θ₂, φ₁₂) in spherical harmonics, and the pcf's for certain special near-neighbour configurations. The computed atom-atom structure factor is compared with the experimental data for liquid Br₂.

Mean square forces and torques have been evaluated and are related to some experimental results.     

HfV2·Hx中扩散导致的1H核自旋弛豫 近邻无规行步处理

对氢合金HfV₂·H_x中¹H核自旋弛豫起主导的因素是偶极相互作用,研究的核心是如何理论计算¹H在基质晶格中扩散造成偶极相互作用涨落的谱密度。我们把Torrey同核偶极作用近邻无规扩散行步理论推广到同核、异核偶极作用并存的情况;并就中子衍射提供的HfV₂·H_x结构(C-15)参数计算了确定谱密度J_q^HH(ω)和J_q^HV(ω)(q=0,1,2)所需的G_HH(k,y)和G_HV(k,y)。引用以前别人的核磁共振实验数据,依照我们的理论分析计算扩散激活能和H在间隙位上的振动频率;与他们用唯象理论获得的相应数值对比,结果是满意的。 关键词：     

Density Fluctuations as Precursors of Crystallization in Polyamide 6,6 Using Time-Resolved X-Ray Scattering Techniques

In the present study, attempts are made to throw light on the mechanisms leading to primary nucleation in polymer crystallization. Previous studies in this field are not conclusive. Aiming to investigate the induction period prior to crystallization, time-resolved simultaneous small- and wide-angle X-ray scattering (SAXS and WAXS) measurements have been made in situ for polyamide 6,6, while it was crystallized from the melt. For this polymer, it is confirmed that at a low supercooling (ΔT≈28°C), during the induction period, a well-resolved SAXS pattern appears. The time evolution of this scattering pattern can be described by the kinetics of spinodal decomposition, as previously reported for the glass crystallization of PEKK and TPI. According to this analysis, a value for the most probable scattering vector q of density fluctuations at around 0.43 nm^?1 is found. It corresponds to a characteristic wavelength of 14.7 nm of long-range density fluctuations growing with time.     

Symmetry enforced gauge invariance of nuclear magnetic shielding constants

E.S.R. experiments performed at 1·3 K by optical detection are reported for the photo-excited triplet state of palladiumporphin in a single crystal of n-octane, and the observation of a level anticrossing signal is described.

In the crystal the orbital degeneracy of the ³ E _u state of the free molecule is lifted by the crystal field and in n-octane the energy difference between the two orbital components |x> and |y> is found to be 58 ± 2 cm^-1. The spinorbit coupling (SOC) and the orbital Zeeman interaction couple the triplet manifolds of |x> and |y>, and for a proper understanding of the magnetic properties of these states it is necessary to work in the basis of the six spin-orbit functions deriving from the ³ E _u state of the free molecule. It is shown that either of the two triplet states can be described by an effective spin hamiltonian of the common form and expressions for the zero-field parameters D and E and the principal values of the g tensor are given. The experimental values of the parameters in the lowest triplet state are D = -24·38 ± 0·03 GHz, |E| = 320 ± 60 MHz, g _‖ = 1·677 ± 0·001 and g _⊥ = 1·989 ± 0·002. The matrix element of the SOC connecting the |x> and |y> triplet manifolds amounts to qZ = 15 ± 3 cm^-1 and the vibronic orbital angular momentum (in units of ?) in the ³ E _u state of the free molecule to qΛ = 1·5 ± 0·3. A tentative value of 0·63 for the orbital reduction factor q is obtained by comparison with a theoretical estimate of Λ. The value of q is indicative of weak Jahn-Teller coupling.     

The thermodynamics of symmetric two centre Lennard-Jones liquids

We have carried out molecular dynamic simulations for the thermodynamic properties of two centre Lennard-Jones fluids at lower densities and higher temperatures than have been studied previously, and have also made simulations for one additional shape. The results, together with results already given in the literature, are presented in a parameterized form which is very convenient to use in testing the simulation results against data for real liquids. Tables of second virial coefficients are also provided. We illustrate the use of our results by an analysis of pure liquid ethane, which is found to be well represented by such a model with L* = 0·67, ε/k = 137·5 K and σ = 3·506 Å. We also suggest that the experimental thermodynamic properties of suitable liquid mixtures can, with the aid of a theory for the equivalent pure liquid parameters (L _x *, ε _x , σ _x ), be satisfactorily interpreted using the general results given in this paper.     

Intermolecular potential for Ar+D2O from differential cross sections

Differential cross sections for the scattering of D₂O (velocity selected beam) by Ar (nozzle beam) were measured at kinetic energies, ē, of 13·5 × 10^-14 erg? and 17·0 × 10^-14 erg by the crossed molecular beam technique. The distributions were compared with differential cross sections calculated from Lennard-Jones (12, 6) and Kihara-Stockmayer trial potentials to determine the potential parameters.     

Quantum Group as Semi-infinite Cohomology

We obtain the quantum group SL _q (2) as semi-infinite cohomology of the Virasoro algebra with values in a tensor product of two braided vertex operator algebras with complementary central charges c+[`(c)]=26{c+\bar{c}=26}. Each braided VOA is constructed from the free Fock space realization of the Virasoro algebra with an additional q-deformed harmonic oscillator degree of freedom. The braided VOA structure arises from the theory of local systems over configuration spaces and it yields an associative algebra structure on the cohomology. We explicitly provide the four cohomology classes that serve as the generators of SL _q (2) and verify their relations. We also discuss the possible extensions of our construction and its connection to the Liouville model and minimal string theory.     

Absence of the partially ordered phase in theq-state models

We investigate theq-state models called (N ,N ) model using an infinitesimal Migdal-Kadanoff renormalization-group method. We distinguish two cases namely the isotropic model and the anisotropic model. The first one presents a critical value ofq,q _c such that forq _c we obtain an Ashkin-Teller phase diagrams while forq>q _c the partially ordered phase disappears then the model exhibits only phase transition between ferromagnetic phase and disordered one. The phase diagrams in the second case are qualitatively similar to one obtained forZ(6) model for all values ofq.