Showing papers in "Physica A-statistical Mechanics and Its Applications in 1982"
TL;DR: The Penrose pattern as discussed by the authors is a tiling of two-dimensional and of three-dimensional space by identical tiles of two kinds (acute and obtuse rhombi with α = 72° and 144° in two dimensions and acute rhombohedra withα = 63.43° and 116.57° in three dimensions).
Abstract: The Penrose pattern is a tiling of two-dimensional and of three-dimensional space by identical tiles of two kinds (acute and obtuse rhombi with α = 72° and 144° in two dimensions and acute and obtuse rhombohedra with α = 63.43° and 116.57° in three dimensions). The two-dimensional pattern is a section through that in three dimensions. When joining (or recursion) rules are prescribed, the pattern is unique and non-periodic. It has local five-fold axes and thus represents a structure outside the formalism of classical crystallography and might be designated a quasi-lattice.
305 citations
TL;DR: In this article, a general scheme is presented to evaluate the mobility tensors of an arbitrary number of spheres, immersed in a viscous fluid, in a power series expansion in R-1, where R is a typical distance between spheres.
Abstract: A general scheme is presented to evaluate the mobility tensors of an arbitrary number of spheres, immersed in a viscous fluid, in a power series expansion in R-1, where R is a typical distance between spheres. Some general properties of these (translational and rotational) mobility tensors are discussed. Explicit expressions are derived up to order R-7. To this order, hydrodynamic interactions between two, three and four spheres contribute.
302 citations
TL;DR: In this article, the theory of gravity is considered from the little group viewpoint, which leads to a theory with a constraint, which is equivalent to general relativity with an arbitrary cosmological term.
Abstract: The theory of gravity is considered from the little group viewpoint. This leads to a theory with a constraint, which is equivalent to general relativity with an arbitrary cosmological term. With this framework (i) the cosmological constant cannot be put into the Lagrangian but it appears as an integration constant. (ii) The gravitational Lagrangian automatically takes the form of a finite polynomial of the metric. (iii) The so-called conformal factor is fixed, which removes an apparent difficulty in carrying out path integrals.
277 citations
TL;DR: In this article, the liquid-crystalline ordering in the solution of persistent chains which length, L, is comparable with the length of the effective Kuhn segment, l, is considered by means of a generalization of the Onsager method.
Abstract: The liquid-crystalline ordering in the solution of persistent chains which length, L, is comparable with the length of the effective Kuhn segment, l, is considered by means of a generalization of the Onsager method. The orientational entropy for this case is calculated using the method proposed by I.M. Lifshitz (for another problem) in 1968. It is shown that a slight flexibility of the persistent chain is sufficient for the complete change in the properties of the liquid-crystalline transition: for example, at L l ∼0.1 these properties are more similar to those which are characteristic for the semi-flexible limit ( L l ⪢1), than for the rigid rod limit ( L l ⪡1), although at such L l the geometric form of the macromolecule is much closer to the rodlike one.
230 citations
TL;DR: In this paper, the critical behavior of the q-state Potts model was investigated using finite-size scaling and transfer matrix methods, and an effective algorithm to compute the dominant eigenvalues of this essentially nonsymmetric transfer matrix was developed.
Abstract: We investigate the critical behaviour of the two-dimensional, q-state Potts model, using finite-size scaling and transfer matrix methods. For the continuous transition range (0 These results for continuous q were obtained from a transfer matrix constructed for a generalized Whitney polynomial representing the Potts models. An effective algorithm to compute the dominant eigenvalues of this essentially nonsymmetric transfer matrix is developed.
218 citations
TL;DR: In this paper, the ground state properties of the one-dimensional spin-s (12⩽s <∞) anisotropic XYZ antiferromagnet in a magnetic field of arbitrary direction were studied.
Abstract: This is a study of the ground-state properties of the one-dimensional spin-s (12⩽s<∞) anisotropic XYZ antiferromagnet in a magnetic field of arbitrary direction. It provides the first rigorous results for the general case of this model in non-zero field. By exact calculations we find the existence of an ellipsoidal surface h = hN in field space where the ground state is of the classical two-sublattice Neel type with non-zero antiferromagnetic long-range order. At hN there are no correlated quantum fluctuations. We give upper and lower bounds for the critical field hc where antiferromagnetic long-range order is suppressed by the field. The zero-temperature phase diagrams are discussed for a few representative cases.
180 citations
TL;DR: In this article, a special case of kink dynamics of nonlinear wave equations is found to reduce to the Toda lattice dynamics, which corresponds to the momentum conservation law for wave equations.
Abstract: A certain class of nonlinear evolution equations of one space dimension which permits kink type solutions and includes one-dimensional time-dependent Ginzburg-Landau (TDGL) equations and certain nonlinear wave equations is studied in some strong coupling approximation where the problem can be reduced to the study of kink dynamics. A detailed study is presented for the case of TDGL equation with possible applications to the late stage kinetics of order-disorer phase transitions and spinodal decompositions. A special case of kink dynamics of nonlinear wave equations is found to reduce to the Toda lattice dynamics. A new conservation law for dissipative systems is found which corresponds to the momentum conservation law for wave equations.
166 citations
TL;DR: In this paper, the response of multivariable linear systems to Levy fluctuations is examined explicitly as a function of time using the characteristic function, the fractional moments of the process are determined and the nature of the product rule obeyed by the characteristic functions of a general linear dynamical system is elucidated.
Abstract: We have examined the response of multivariable linear systems to Levy fluctuations The characteristic function of the response is obtained explicitly as a function of time Using the characteristic function, the fractional moments of the process are determined The nature of the product rule obeyed by the characteristic function of a general linear dynamical system is elucidated
113 citations
TL;DR: In this article, a systematic treatment of the equation of motion of the classical anisotropic Heisenberg spin chain is given, both in the discrete case and in the continuum limit, in which the spins associated with the lattice sites m are replaced by a spin density S(x, t), which is a function of the time t and the position x on the chain.
Abstract: A systematic treatment is given of the equation of motion of the classical anisotropic Heisenberg spin chain, both in the discrete case and in the continuum limit in which the spins Sm(t) associated with the lattice sites m are replaced by a spin density S(x, t), which is a function of the time t and the position x on the chain. In the case of axial symmetry the equation of motion for the spins is shown to be equivalent to a new equation in terms of one real variable, i.e. qm(t) in the discrete case q(x, t) in the continuum limit. (From the treatment by A.E. Borovik it follows that the new equation of motion for q(x, t) is completely integrible in the special case of quadratic anisotropy.) Explicit expressions are given for the Lagrangians, both in the ferromagnetic and in the antiferromagnetic case. The relation with the nonlinear Schrodinger equation on the one hand and the sine-Gordon equation on the other hand is discussed in some detail.
101 citations
TL;DR: In this paper, the N -particle Smoluchowski equation is solved exactly for a system of spherical Brownian particles interacting through hard-core potentials to first order in the volume concentration φ.
Abstract: The N -particle Smoluchowski equation is solved exactly for a system of spherical Brownian particles interacting through hard-core potentials to first order in the volume concentration φ. The self-diffusion coefficient is found to be given by D s = D 0 (1−2 φ ), where D 0 is the free diffusion constant. The hydrodynamic interaction is then taken into account in a perturbative way. Using the Oseen approximation, D s = D 0 (1−0.09 φ ) is found, whereas the improved form for the hydrodynamic interaction due to Felderhof gives D s = D 0 (1−1.89 φ ).
90 citations
TL;DR: In this article, the authors formulate the solution of the linear Navier-Stokes equations for steady, incompressible flow about a spherical particle as an expansion of scattered waves, and find spherical force multipoles from the amplitudes of the incident waves with the aid of a resistance matrix, which is expressed in terms of the scattering coefficients of the particle.
Abstract: We formulate the solution of the linear Navier-Stokes equations for steady, incompressible flow about a spherical particle as an expansion of scattered waves. The amplitudes of the outgoing waves are simply related to a set of spherical force multipoles. These multipoles are found from the amplitudes of the incident waves with the aid of a resistance matrix, which is expressed in terms of the scattering coefficients of the particle.
TL;DR: In this paper, the results of molecular dynamics calculations of the two-dimensional one-component plasma with logarithmic interactions between the particles are reported, and a solid-fluid transition is observed for Γ = q 2 kT ≈ 135.
Abstract: We report the results of molecular dynamics calculations of the two-dimensional one-component plasma with logarithmic interactions between the particles. A solid-fluid transition is observed for Γ = q 2 kT ≈ 135 . The hysteresis observed on traversing the transition region indicates that the transition is first order. The velocity autocorrelation function shows marked oscillations in the strong coupling region, with a frequency, almost independent of Γ, close to the plasma frequency.
Abstract: An extension of Faxen's theorem is given for the case that n spheres move with arbitrary velocities through a fluid in non-uniform steady flow. Explicit expressions for the friction- and mutual friction tensors, valid to order R-3, where R is a typical distance between spheres, are obtained together with this extension. These expressions contain 2-, 3- and 4-sphere contributions. Brownian motion of n spheres as a consequence of fluid fluctuations is discussed on the basis of the relationships derived.
TL;DR: In this paper, the free boson gas with Dirichlet boundary conditions in d-dimensional Euclidean space was investigated and three types of condensation when the mean density ρ exceeds a critical value ρc, depending on how the bulk limit is taken.
Abstract: We investigate the free boson gas with Dirichlet boundary conditions in d-dimensional Euclidean space. For d > 2 we find three types of condensation when the mean density ρ exceeds a critical value ρc, depending on how the bulk limit is taken.
TL;DR: In this article, the creeping flow equations for two spherically symmetric particles immersed in an incompressible fluid are solved in a two-center expansion of spherical waves scattered from each of the particles.
Abstract: We solve the creeping flow equations for two spherically symmetric particles immersed in an incompressible fluid. The flow pattern outside the particles is analyzed in a two-center expansion of spherical waves scattered from each of the particles. Hence we construct the friction matrix which relates the forces, the torques and symmetric force dipole moments to the imposed flow velocities and their linear derivatives at the particle centers.
TL;DR: In this paper, the authors discuss the possibility that, besides periodic and quasiperiodic crystals, there exist turbulent crystals as thermodynamic equilibrium states at non-zero temperature, which would not be invariant under translation, but would differ from other crystals by the fuzziness of some diffraction peaks.
Abstract: We discuss the possibility that, besides periodic and quasiperiodic crystals, there exist turbulent crystals as thermodynamic equilibrium states at non-zero temperature. Turbulent crystals would not be invariant under translation, but would differ from other crystals by the fuzziness of some diffraction peaks. Turbulent crystals could appear by breakdown of long range order in quasiperiodic crystals with two independent modulations.
TL;DR: In this paper, the general formalism of master equations is used together with a projection which preserves the pure states to derive a class of non-linear Schrodinger-like equations.
Abstract: The general formalism of master equations is used together with a projection which preserves the pure states to derive a class of non-linear Schrodinger-like equations. The result is applied to a spin- 1 2 coupled to a bath of two-level systems and the Bloch equations are recovered. Finally we make a connection with Sz-Nagy's theorem on the dilations of contracting semi-groups.
TL;DR: In this article, diffusion coefficients, D12, and thermal diffusion factors, αT, are reported for the systems He-N2, Ne-N 2, Ar N 2, Kr N 2 and Xe N 2; the D12 values were measured over the temperature range 275-323 K and the αT values at 300 K.
Abstract: Diffusion coefficients, D12, and thermal diffusion factors, αT, are reported for the systems He-N2, Ne-N2, Ar-N2, Kr-N2 and Xe-N2; the D12 values were measured over the temperature range 275–323 K and the αT values at 300 K. The diffusion coefficients were combined with accurate second virial coefficient data to obtain (m, 6, 8) potential parameters and these values, together with existing potential parameters, were used to calculate αT values for comparison with experiment.
TL;DR: In this paper, the Fourier transform of the pair correlation functions is computed in the two-dimensional square lattice, using the nearest-neighbors square as the basic cluster, and the correlation functions are given up to the order 7 in the inverse temperature.
Abstract: The cluster variation method is used to obtain approximate free energy functions for a binary system in an inhomogeneous field, in order to calculate the Fourier transform of the pair correlation functions. In the two-dimensional square lattice, using the nearest-neighbors square as the basic cluster, the correlation functions are correctly given up to the order 7 in the inverse temperature. The effect of second-neighbor pairs and many-body interactions is investigated.
TL;DR: In this paper, the authors study random walks on d-dimensional lattices with periodically distributed traps and derive general expressions for the total probability that the walk ends in a trap and for the moments of the number of steps made before this happens if it does happen.
Abstract: We study random walks on d-dimensional lattices with periodically distributed traps in which the walker has a finite probability per step of disappearing from the lattice and a finite probability of escaping from a trap. General expressions are derived for the total probability that the walk ends in a trap and for the moments of the number of steps made before this happens if it does happen. The analysis is extended to lattices with more types of traps and to a model where the trapping occurs during special steps. Finally, the Green's function at the origin G(0; z) for a finite lattice with periodic boundary conditions, which enters into the main expressions, is studied more closely. A generalization of an expression for G(0; 1) for the square lattice given by Montroll to values of z different from, but close to, 1 is derived.
TL;DR: In this article, a model of the nonlinear Boltzmann equation is presented that is exactly solvable for all initial conditions, and the model has the following desirable properties: (i) conservation of the number of particles; (ii) energy conservation; (iii) nonlinearity; (iv) positivity of distribution functions; and (v) unique equilibrium state.
Abstract: In one space and one time dimension, a model of the nonlinear Boltzmann equation is presented that is exactly solvable for all initial conditions. Furthermore, this model has the following desirable properties: (i) conservation of the number of particles; (ii) energy conservation; (iii) nonlinearity; (iv) positivity of distribution functions; and (v) unique equilibrium state (for any given density) which is approached as t → ∞ for most physically interesting initial conditions. Some of the simple properties of this model are studied.
TL;DR: In this paper, a thermodynamic description of a liquid-vapour interface with singular densities and currents at the dividing surface is given, as well as the equilibrium correlation functions for e.g.
Abstract: We formulate a scheme describing the fluctuations of a liquid-vapour interface. This is done using a thermodynamic description of the system with singular densities and currents at the dividing surface. Equilibrium (equal time) correlation functions for e.g. the interfacial temperature and the location of the dividing surface are given. Landau-Lifshitz equations are formulated for the interfacial densities. These equations, as well as the boundary conditions, contain random contributions to the currents which are Gaussian and white. Fluctuations-dissipation theorems for these random currents are given.
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TL;DR: In this article, the basic relations of the Weyl-Wigner representation of quantum mechanics are reviewed and it is stressed that this representation is unique and based on a phase-space operator which corresponds to an observable in Dirac's sense.
Abstract: The basic relations of the Weyl-Wigner representation of quantum mechanics are reviewed. It is stressed that this representation is unique and based on a phase-space operator which corresponds to an observable in Dirac's sense.
TL;DR: In this article, the Maier-Saupe theory was used to calculate the order parameters and elastic constants for liquid crystals with disc-like molecules. But the results were restricted to the case when the molecules are neither rod-like nor disc-shaped.
Abstract: Using a previously developed theory of nematic liquid crystals we present a calculation of the order parameters and elastic constants for those liquid crystals which consist of disc-like molecules. We obtain a simple inversion as compared to rod-like molecules. In addition we remark that the Maier-Saupe theory can be considered as describing the intermediate case, in which the molecules are neither rod-like nor disc-like. They have a form such that the mutually excluded volume of a pair of molecules is always a sphere, but with a radius which depends on the relative orientation of their symmetry axes.
TL;DR: The time dependent longitudinal dispersion of Brownian particles, suspended in a fluid in unidirectional steady or oscillatory motion is calculated on the basis of the equivalence of Langevin and Fokker-Planck formalisms.
Abstract: The time dependent longitudinal dispersion of Brownian particles, suspended in a fluid in unidirectional steady or oscillatory motion is calculated on the basis of the equivalence of Langevin and Fokker-Planck formalisms. In particular, a series expansion for the effective longitudinal diffusion coefficient is obtained. The method is applied to flows between plane parallel plates and flows in a cylindrical tube.
TL;DR: In this paper, the authors extend the theory of van der Waals and of Fisk and Widom for the interfacial density profile below the critical temperature to the one-phase region above critical temperature.
Abstract: The gravitational field induces density gradients in gases near the critical point. These density gradients are usually evaluated with the assumption that the relationship between the local density and local chemical potential is the same as for a macroscopic system in thermodynamic equilibrium. Very close to the critical point the assumption of local equilibrium ceases to be valid. In this paper we obtain the actual density profiles including nonlocal effects. For this purpose we extend the theory of van der Waals and of Fisk and Widom for the interfacial density profile below the critical temperature to the one-phase region above the critical temperature. The nonlocal effects in the density profiles are found to be significant in temperature intervals that are accessible with currently available experimental techniques for temperature control.
TL;DR: In this article, a cross-supersonic beam apparatus measurements have been performed on the total cross section as a function of velocity in the thermal range for scattering of Ne, Ar, Kr and Xe by Ne, Kr, Xe, and Ar.
Abstract: In a crossed supersonic beam apparatus measurements have been performed on the total cross section as a function of velocity in the thermal range for scattering of Ne, Ar, Kr and Xe by Ar, Kr and Xe. Apart from glory structure in the total cross section also ratios of absolute values of the non-glory total cross sections have been measured. For the analysis four quantities are introduced which are characteristic for the main aspects of total cross section data viz. the absolute value of the total cross section, the velocity dependence of the non-glory total cross section, the position of the glories and their amplitude. The four quantities are directly related to specific properties of the interaction. The various potentials proposed in the literature are tested correspondingly. The validity of combination rules for ϵ, rm and Qngl is examined. It is demonstrated that the long range noble gas interactions do not reduce to the same form.
TL;DR: In this article, a formal mode coupling theory for hydrodynamic systems is presented, which includes contributions from all powers of the hydrodynamics of the system, and applied to nonequilibrium steady state systems.
Abstract: We construct a formal mode coupling theory for hydrodynamic systems which includes contributions from all powers of the hydrodynamic variables. This theory is applied to nonequilibrium steady state systems. A generalization of the local equilibrium distribution is used to describe the nonequilibrium state. This distribution independently constrains all moments of the hydrodynamic variables. The infinite hierarchy of equations for the moments of the hydrodynamic variables is truncated using an inverse system size expansion. Explicit results are obtained for the time correlation functions of fluids with a linear temperature gradient or a linear shear. These results agree with previous studies of these steady states.
TL;DR: In this paper, collective diffusion and self-diffusion in a polydisperse suspension of macroparticles are considered and a multispecies projection formalism for the density fluctuations is derived.
Abstract: We consider collective diffusion and self-diffusion in a polydisperse suspension of macroparticles. Using the generalized Smoluchowski equation to describe the interacting suspension we extend Ackerson's work to derive a multispecies projection formalism for the density fluctuations. We include 2-body direct potential interactions as well as accurate 2-body hydrodynamic interactions. We take the long wavelength low density limit of this formalism to obtain an expression for the memory matrix expressed in terms of 2-body interactions and propagators. We show how memory contributions can arise to first order in density from the fact that the correct mobility tensors are not divergenceless.
TL;DR: In this paper, the rotational relaxation is described to the first order in the Sonine polynomial expansion of nonequilibrium distribution functions by the well known Wang Chang, Uhlenbeck, and De Boer expression.
Abstract: Rotational relaxation, related to the experimentally accessible volume viscosity, is described to the first order in the Sonine polynomial expansion of nonequilibrium distribution functions by the well known Wang Chang, Uhlenbeck, and De Boer expression. By a classical trajectory evaluation of a classical limit of this expression, using a recently proposed anisotropic inter-molecular potential for N2-N2, results are obtained for the rotational relaxation cross section. A corresponding expression including second order Sonine terms is also investigated. The second order results are found to differ significantly from the first order treatment (by about 18% at room temperature) and to agree very well with ultrasonic measurements over a temperature range from 77 K to 293 K.