Entropic elasticity of two-dimensional self-avoiding percolation systems

The sol-gel transition is studied on a purely entropic two-dimensional model system consisting of hard spheres (disks) in which a fraction p of neighbors are tethered by inextensible bonds. We use a new method to measure directly the elastic properties of the system. We find that over a broad range of hard sphere diameters a the rigidity threshold is insensitive to a and indistinguishable from the percolation threshold p(c). Close to p(c), the shear modulus behaves as (p-p(c))(f), where the exponent f approximately 1. 3 is independent of a and is similar to the conductivity exponent in random resistor networks.     

Exact determination of all ground states of random field systems in polynomial time

An algorithm is developed which allows calculating all ground states of ferromagnetic and unfrustrated antiferromagnetic Ising systems with arbitrary site-dependent fields by transforming the system into an equivalent network and calculating the maximal flow. By a trial and error scheme a minimum cut is constructed which corresponds to a spin configuration. In this way each ground state is calculated with a finite probability. The algorithm is applied to site-diluted antiferromagnets in external magnetic fields. It is found that in this case its time complexity is approximately quadratic in the lattice size. As an application we calculate the distribution of overlaps between ground states of the site-diluted antiferromagnet in a strong magnetic field and we analyse the fractal structure of these ground states.     

Site percolation thresholds for Archimedean lattices

Precise thresholds for site percolation on eight Archimedean lattices are determined by the hull-walk gradient-percolation simulation method, with the results p(c)=0.697 043, honeycomb or (6(3)), 0.807 904 (3,12(2)), 0.747 806 (4,6,12), 0.729 724 (4,8(2)), 0.579 498 (3(4),6), 0.621 819 (3,4,6,4), 0.550 213 (3(3),4(2)), and 0.550 806 (3(2),4,3,4), with errors of about +/- 3 x 10(-6). [The remaining Archimedean lattices are the square (4(4)), triangular (3(6)), and Kagomé (3,6,3,6), for which p(c) is already known exactly or to a high degree of accuracy.] The numerical result for the (3,12(2)) lattice is consistent with the exact value [1-2 sin(pi/18)](1/2). The values of p(c) for all 11 Archimedean lattices, as well as a number of nonuniform lattices, are found to be well correlated by a nearly linear function of a generalized Scher-Zallen filling factor. This correlation is much more accurate than recently proposed correlations based solely upon coordination number.     

Diffusion in Lorentz lattice gas cellular automata: The honeycomb and quasi-lattices compared with the square and triangular lattices

We study numerically the nature of the diffusion process on a honeycomb and a quasi-lattice, where a point particle, moving along the bonds of the lattice, scatters from randomly placed scatterers on the lattice sites according to strictly deterministic rules. For the honeycomb lattice fully occupied by fixed rotators two (symmetric) isolated critical points appear to be present, with the same hyperscaling relation as for the square and the triangular lattices. No such points appear to exist for the quasi-lattice. A comprehensive comparison is made with the behavior on the previously studied square and triangular lattices. A great variety of diffusive behavior is found, ranging from propagation, superdiffusion, normal, quasi-normal, and anomalous, to absence of diffusion. The influence of the scattering rules as well as of the lattice structure on the diffusive behavior of a point particle moving on the all lattices studied so far is summarized.     

Shear waves in viscoelastic wormlike micellar fluids over a broad concentration range

Low frequency (61 Hz) shear wave speeds have been measured in viscoelastic wormlike micellar (WM) fluids for a concentration range of 20/12-500/300 mM CTAB/NaSAL where CTAB is the surfactant and NaSAL is the salt and the concentration ratio was fixed at 0.6 for all experiments. The birefringent property of the WM fluids was exploited to visually track the the shear pulse using crossed optical polarizing filters and high speed video. Several scalings of shear wave speed as a function of concentration were discovered: c(s) ~ √C for 20-200 mM and c(s) ~ C for higher concentrations, but with a break in the slope at 400 mM CTAB. Over this full concentration range, the shear wave speed varied from 0.08-0.7 m/s. The shear wave speed was also found to be sensitive to the time between fluid synthesis and measurement indicating a long equilibrium time. Further, comparison with elastic and loss moduli obtained from rheology data show that shear wave propagation is dominated by the elastic modulus for this frequency range. Also briefly discussed are potential applications of this fluid in elastography.     

Energy band structure and thermo-mechanical properties of tungsten and tungsten carbides as studied by the LMTO-ASA method

The calculations of the energy band structures of W (b.c.c. lattice), WC (f.c.c. and h.c.p. lattices) and W₂C have been performed by the LMTO-ASA method. The results of the band structure calculations have been used for the evaluations of the unit cell parameters, bulk moduli, Debye temperatures. The values obtained are in good agreement with the experimental data. It is shown that h.c.p. WC has the highest bulk modulus, while W₂C possess the highest density-of-states at the Fermi level. The calculations reveal a noticeable charge transfer from tungsten to carbon in WC, while the effective charges in W₂C are rather small.     

Optimal lattice configurations for interacting spatially extended particles

We investigate lattice energies for radially symmetric, spatially extended particles interacting via a radial potential and arranged on the sites of a two-dimensional Bravais lattice. We show the global minimality of the triangular lattice among Bravais lattices of fixed density in two cases: In the first case, the distribution of mass is sufficiently concentrated around the lattice points, and the mass concentration depends on the density we have fixed. In the second case, both interacting potential and density of the distribution of mass are described by completely monotone functions in which case the optimality holds at any fixed density.     

Superlight small bipolarons in the presence of a strong Coulomb repulsion

We study a lattice bipolaron on a staggered triangular ladder and triangular and hexagonal lattices with both long-range electron-phonon interaction and strong Coulomb repulsion using a novel continuous-time quantum Monte Carlo algorithm to solve the two-particle Coulomb-Fr?hlich model. The algorithm is preceded by an exact integration over phonon degrees of freedom, and as such is extremely efficient. The bipolaron effective mass and radius are computed. Bipolarons on lattices constructed from triangular plaquettes have a novel crablike motion, and are small but very light over a wide range of parameters. We discuss the conditions under which such particles may form a Bose-Einstein condensate with high transition temperature, proposing a route to room temperature superconductivity.     

Complete condensation in a zero range process on scale-free networks

We study a zero range process on scale-free networks in order to investigate how network structure influences particle dynamics. The zero range process is defined with the rate p(n) = n(delta) at which particles hop out of nodes with n particles. We show analytically that a complete condensation occurs when delta < or = delta(c) triple bond 1/(gamma-1) where gamma is the degree distribution exponent of the underlying networks. In the complete condensation, those nodes whose degree is higher than a threshold are occupied by macroscopic numbers of particles, while the other nodes are occupied by negligible numbers of particles. We also show numerically that the relaxation time follows a power-law scaling tau approximately L(z) with the network size L and a dynamic exponent z in the condensed phase.     

Thermodynamic perturbation theory for polydisperse colloidal suspensions using orthogonal polynomial expansions

We present a method for calculating the thermodynamic and structural properties of a polydisperse liquid by means of a thermodynamic perturbation theory: the optimized random phase approximation (ORPA). The approach is an extension of a method proposed recently by one of us for an integral equation application [Phys. Rev. E 54, 4411 (1996)]. The method is based on expansions of all sigma-dependent functions in the orthogonal polynomials p(i)(sigma) associated with the weight function f(Sigma)(sigma), where sigma is a random variable (in our case the size of the particles) with distribution f(Sigma)(sigma). As in the one-component or general N-component case, one can show that the solution of the ORPA is equivalent to the minimization of a suitably chosen functional with respect to variations of the direct correlation functions. To illustrate the method, we study a polydisperse system of square-well particles; extension to other hard-core or soft-core systems is straightforward.     

Cluster analysis and finite-size scaling for Ising spin systems

Based on the connection between the Ising model and a correlated percolation model, we calculate the distribution function for the fraction (c) of lattice sites in percolating clusters in subgraphs with n percolating clusters, f(n)(c), and the distribution function for magnetization (m) in subgraphs with n percolating clusters, p(n)(m). We find that f(n)(c) and p(n)(m) have very good finite-size scaling behavior and that they have universal finite-size scaling functions for the model on square, plane triangular, and honeycomb lattices when aspect ratios of these lattices have the proportions 1:square root[3]/2:square root[3]. The complex structure of the magnetization distribution function p(m) for the system with large aspect ratio could be understood from the independent orientations of two or more percolation clusters in such a system.     

More on shear modulus collapse of lattices at high pressure

In his recent paper, Shear modulus collapse of lattices at high pressure, J. Phys. Cond. Matt. 16 (2004) L125, V.V. Kechin claims that the zero temperature shear modulus of a metallic solid vanishes at a high critical pressure, and the critical pressures for this shear modulus collapse lie in the range 0-250 Mbar for elemental metals. Here we demonstrate that Kechin's arguments contain an erroneous assumption, and therefore, do not prove that all metals become mechanically unstable at high pressures. Ab initio calculations and experimental results on a number of solids are analyzed to confirm our conclusion.     

Measurement of the shear strength of a charge density wave

We have explored the shear plasticity of charge density waves (CDWs) in NbSe3 samples with cross sections having a single microfabricated thickness step. Shear stresses along the step result from thickness-dependent CDW pinning. For small thickness differences the CDW depins elastically at the volume average depinning field. For large thickness differences the thicker, more weakly pinned side depins first via plastic shear, and shear plasticity contributes substantial dissipation well above the depinning field. A simple model describes the qualitative features of our data and yields a value for the CDW's shear strength of approximately 9.5 x 10(3) Nm(-2). This value is orders of magnitude smaller than the CDW's longitudinal modulus but much larger than corresponding values for flux line lattices, and in part explains the relative coherence of the CDW response.     

Diffusion and propagation in triangular Lorentz lattice gas cellular automata

The diffusion process of point particles moving on regular triangular and random lattices, randomly occupied with stationary scatterers (a Lorentz lattice gas cellular automaton), is studied, for strictly deterministic scattering rules, as a function of the concentration of the scatterers. In addition to the normal and various kinds of retarded diffusion found before on the regular square lattice, straight-line propagation through the scatterers is observed.     

Theorie der spontanen Magnetisierung kleiner ferromagnetischer Teilchen

With a modified conception of the Néel sublattices a molecular field theory is developed for small ferromagnetic particles. They are treated as a system of neighboring shells. These are supposed to consist each of atoms with equal average properties and are coupled to the next neighbors by an (exchange-) interaction. To simplify the numerical calculations the model was further modified by taking together all shells of the interior to form a core. Calculations of the temperature dependence of the spontaneous magnetization and of Curie-temperatures have been done for some particle forms and sizes of the f.c.c., b.c.c. and hexagonal lattices. The results are discussed and compared to experimental data of other authors from small particles of nickel, iron and cobalt.     

Anisotropic states of two-dimensional electrons in high magnetic fields

We study the collective states formed by two-dimensional electrons in Landau levels of index n > or = near half filling. By numerically solving the self-consistent Hartree-Fock (HF) equations for a set of oblique two-dimensional lattices, we find that the stripe state is an anisotropic Wigner crystal (AWC), and determine its precise structure for varying values of the filling factor. Calculating the elastic energy, we find that the shear modulus of the AWC is small but finite (nonzero) within the HF approximation. This implies, in particular, that the long-wavelength magnetophonon mode in the stripe state vanishes q(3/2) like as in an ordinary Wigner crystal, and not like q(5/2) as was found in previous studies where the energy of shear deformations was neglected.     

ANALYSIS OF PARTICLE-PARTICLE FORCES IN ELECTRORHEOLOGICAL FLUIDS

The Rayleigh identity, based on a multipole expansion theory, is extended to analyse the forces between particles in an electrorheological system. The shear modulus for chains of particles arrayed on a square lattice is calculated. It is found that the modulus increases linearly with the ratio of dielectric constants of the dispersed particles to that of the continuous phase; as the ratio becomes larger, contrary to the expectations from a simple dipole approximation, the modulus would saturate. In the case of conducting particles, the modulus varies with the frequency of the applied field. In a limiting case of perfectly conducting particles, the conductivity is also considered. It is found that the particle-particle forces are extremely sensitive to their separations from each other.     

The thermodynamics of elastic deformation—I: Equation of state for solids

The isobaric and isothermal volume derivatives of In B, In μ and In μ' are investigated, where B, μ and μ' are the isothermal bulk modulus and the two shear moduli, respectively, of a cubic crystal. In the case of the bulk modulus, the temperature independence of αB (where α is the volume thermal expansion) for a large number of materials, ensures that the derivatives are constant and approximately equal, while for the shear moduli, evidence is advanced that the isothermal derivatives are constant along an isotherm, but not along an isobar except at high temperatures near the melting point. The relationships satisfied by the bulk modulus enable the explicit temperature and pressure dependence of the molar volume, V, thermal expansion, and bulk modulus to be determined. The most adequate representation of the volume dependence of the Grüneisen parameter, γ, appears to be that γ/V is independent of volume between the Debye and melting temperatures.     

Ferromagnetism in the Hubbard model: instability of the Nagaoka state on the triangular,honeycomb and kagome lattices

In order to analyse the lattice dependence of ferromagnetism in the two-dimensional Hubbard model we investigate the instability of the fully polarised ferromagnetic ground state (Nagaoka state) on the triangular, honeycomb and kagome lattices. We mainly focus on the local instability, applying single spin flip variational wave functions which include majority spin correlation effects. The question of global instability and phase separation is addressed in the framework of Hartree-Fock theory. We find a strong tendency towards Nagaoka ferromagnetism on the non-bipartite lattices (triangular, kagome) for more than half filling. For the triangular lattice we find the Nagaoka state to be unstable above a critical density of n = 1.887 at U = ∞, thereby significantly improving former variational results. For the kagome lattice the region where ferromagnetism prevails in the phase diagram widely exceeds the flat band regime. Our results even allow the stability of the Nagaoka state in a small region below half filling. In the case of the bipartite honeycomb lattice several disconnected regions are left for a possible Nagaoka ground state.     

Spectral degeneracy of the lattice dirac equation as a function of lattice shape

We investigate the free Dirac equation in 2 + 1 dimensions on square, triangular, and hexagonal lattices. For each lattice the spectrum exhibits a degeneracy not present in the continuum limit. In the square and hexagonal cases there is a 4-fold degeneracy corresponding to 2 independent symmetries of the Hamiltonian; the degeneracy is eliminated by diagonalizing these symmetries and projecting onto the subspace characterized by a particular pair of eigenvalues. For the triangular case the degeneracy is 6-fold, but the naive Hamiltonian does not possess enough symmetry to eliminate the degeneracy. Certain ambiguities in the lattice Hamiltonian are pointed out and by the addition of terms which vanish in the continuum limit, it is cast in a form with sufficient symmetry to remove the degeneracy entirely, just as was done for the hexagonal and square lattices. It is found that after elimination of the spectral degeneracy the Hamiltonians for the hexagonal and triangular lattices are identical. The solutions to these theories are shown to have the correct continuum limit.