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At least 217 records · Page 12Linked to original sources
arXiv2008

On optimal wavelet bases for the realization of microcanonical cascade processes

Multiplicative cascades are often used to represent the structure of multiscaling variables in many physical systems, specially turbulent flows. In processes of this kind, these variables can be understood as the result of a successive tranfer in cascade from large to small scales. For a given signal, only its optimal wavelet basis can represent it in such a way that the cascade relation between scales becomes explicit, i.e., it is geometrically achieved at each point of the system. Finding such a basis is a data-demanding, highly-complex task. In this paper we propose a formalism that allows to find the optimal wavelet in an efficient, less data-demanding way. We confirm the appropriateness of this approach by analyzing the results on synthetic signals constructed with prescribed optimal bases. Although we show the validity of our approach constrainted to given families of wavelets, it can be generalized for a continuous unconstrainted search scheme.

cond-mat.stat-mech↗
arXiv2009

Cooperative sequential adsorption with nearest-neighbor exclusion and next-nearest neighbor interaction

A model for cooperative sequential adsorption that incorporates nearest-neighbor exclusion and next-nearest neighbor interaction is presented. It is analyzed for the case of one-dimensional dimer and two-dimensional monomer adsorption. Analytic solutions found for certain values of the interaction strength are used to investigate jamming coverage and temporal approach to jamming in the one-dimensional case. In two dimensions, the series expansion of the coverage $θ(t)$ is presented and employed to provide estimates for the jamming coverage as a function of interaction strength. These estimates are supported by Monte Carlo simulation results.

cond-mat.stat-mech↗
arXiv2008

Further extensions of the high-temperature expansions for the two-dimensional classical XY model on the triangular and the square lattices

The high-temperature expansions for the spin-spin correlation function of the two-dimensional classical XY (planar rotator) model are extended by two terms, from order 24 through order 26, in the case of the square lattice, and by five terms, from order 15 through order 20, in the case of the triangular lattice. The data are analyzed to improve the current estimates of the critical parameters of the models.

hep-lat↗
arXiv2008

Multiparameter statistical models from $N^2\times N^2$ braid matrices: Explicit eigenvalues of transfer matrices ${\bf T}^{(r)}$, spin chains, factorizable scatterings for all $N$

For a class of multiparameter statistical models based on $N^2\times N^2$ braid matrices the eigenvalues of the transfer matrix ${\bf T}^{(r)}$ are obtained explicitly for all $(r,N)$. Our formalism yields them as solutions of sets of linear equations with simple constant coefficients. The role of zero-sum multiplets constituted in terms of roots of unity is pointed out and their origin is traced to circular permutations of the indices in the tensor products of basis states induced by our class of ${\bf T}^{(r)}$ matrices. The role of free parameters, increasing as $N^2$ with $N$, is emphasized throughout. Spin chain Hamiltonians are constructed and studied for all $N$. Inverse Cayley transforms of Yang-Baxter matrices corresponding to our braid matrices are obtained for all $N$. They provide potentials for factorizable $S$-matrices. Main results are summarized and perspectives are indicated in the concluding remarks.

math.QA↗
arXiv2008

Solid liquid phase changes with different densities

In this paper we present a new thermodynamically consistent phase transition model describing the evolution of a liquid substance, e.g., water, in a rigid container $Ω$ when we freeze the container. Since the density $\varrho_{2}$ of ice with volume fraction $β_{2}$, is lower than the density $\varrho_{1}$ of water with volume fraction $β_{1}$, experiments - for instance the freezing of a glass bottle filled with water - show that the water pressure increases up to the rupture of the bottle. When the container is not impermeable, freezing may produce a non-homogeneous material, for instance water ice or sorbet. Here we describe a general class of phase transition processes including this example as particular case. Moreover, we study the resulting nonlinear and singular PDE system from the analytical viewpoint recovering existence of a global (in time) weak solution and also uniqueness for some particular choices of the nonlinear functions involved.

math.AP↗
arXiv2008

Soft Elasticity in Nematic Liquid-Crystal Networks

Liquid-crystal networks consist of weakly crosslinked polymers that are coupled to liquid-crystal molecules. The resultant hybrid system has rich elastic properties. We develop a phase field model to describe mechanical properties of a hexagonal liquid-crystal network. The hexagonal liquid-crystal network is found to have soft shear deformations. The elastic properties are predicted analytically and confirmed with numerical simulations. In addition the model incorporates non-linear elasticity and dislocations or disclinations.

cond-mat.soft↗
arXiv2009

Link invariants, the chromatic polynomial and the Potts model

We study the connections between link invariants, the chromatic polynomial, geometric representations of models of statistical mechanics, and their common underlying algebraic structure. We establish a relation between several algebras and their associated combinatorial and topological quantities. In particular, we define the chromatic algebra, whose Markov trace is the chromatic polynomial χ_Q of an associated graph, and we give applications of this new algebraic approach to the combinatorial properties of the chromatic polynomial. In statistical mechanics, this algebra occurs in the low temperature expansion of the Q-state Potts model. We establish a relationship between the chromatic algebra and the SO(3) Birman-Murakami-Wenzl algebra, which is an algebra-level analogue of the correspondence between the SO(3) Kauffman polynomial and the chromatic polynomial.

math.CO↗
arXiv2008

Insulator to superfluid transition in coupled photonic cavities in two dimensions

A system of coupled photonic cavities on a two-dimensional square lattice is systematically investigated using the stochastic series expansion quantum Monte Carlo method. The ground state phase diagram contains insulating phases with integer polariton densities surrounded by a superfluid phase. The finite-size scaling of the superfluid density is used to determine the phase boundaries accurately. We find that the critical behavior is that of the generic, density-driven Mott-superfluid transition with dynamic exponent $z=2$, with no special multicritical points with $z=1$ at the tips of the insulating-phase lobes (as exist in the case of the Bose-Hubbard model). This demonstrates a limitation of the description of polaritons as structureless bosons.

cond-mat.other↗
arXiv2009

Counterion correlations near charged surfaces: from the weak to the strong coupling regime

A simple field theory approach is developed to model the properties of charged, dielectric bodies and their associated counterions. This predictive theory is able to accurately describe the properties of systems (as compared to computer simulation data) from the weak coupling limit, where the Poisson-Boltzmann theory works well, through to the strong coupling limit. In particular, it is able to quantitatively describe the attraction between like-charged plates and the influence of image charge interactions.

cond-mat.soft↗
arXiv2008

Statistical Physics of Hard Optimization Problems

Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a cost function depending on these variables. Optimization problems in the NP-complete class are particularly difficult, it is believed that the number of operations required to minimize the cost function is in the most difficult cases exponential in the system size. However, even in an NP-complete problem the practically arising instances might, in fact, be easy to solve. The principal question we address in this thesis is: How to recognize if an NP-complete constraint satisfaction problem is typically hard and what are the main reasons for this? We adopt approaches from the statistical physics of disordered systems, in particular the cavity method developed originally to describe glassy systems. We describe new properties of the space of solutions in two of the most studied constraint satisfaction problems - random satisfiability and random graph coloring. We suggest a relation between the existence of the so-called frozen variables and the algorithmic hardness of a problem. Based on these insights, we introduce a new class of problems which we named "locked" constraint satisfaction, where the statistical description is easily solvable, but from the algorithmic point of view they are even more challenging than the canonical satisfiability.

cond-mat.stat-mech↗
arXiv2008

Molecular dynamics simulations of ultrathin water film confined between flat diamond plates

Molecular dynamics simulations of ultrathin water film confined between atomically flat rigid diamond plates are described. Films with thickness of one and two molecular diameters are concerned and TIP4P model is used for water molecules. Dynamical and equilibrium characteristics of the system for different values of the external load and shear force are investigated. An increase of the external load causes the transition of the film to a solidlike state. This is manifested in the decreasing of the diffusion constant and in the ordering of the liquid molecules into quasidiscrete layers. For two-layer film under high loads molecules also become ordered parallel to the surfaces. Time dependencies of the friction force and the changes of its average value with the load are obtained. In general, the behaviour of the studied model is consistent with the experimental results obtained for simple liquids with spherical molecules.

cond-mat.stat-mech↗
arXiv2008

Rigidity-based approach to the boson peak in amorphous solids: from sphere packing to amorphous silica

Glasses have a large excess of low-frequency vibrational modes in comparison with continuous elastic body, the so-called Boson Peak, which appears to correlate with several crucial properties of glasses, such as transport or fragility. I review recent results showing that the Boson Peak is a necessary consequence of the weak connectivity of the solid. I explain why in assemblies repulsive spheres the boson peak shifts up to zero frequency as the pressure is lowered toward the jamming threshold, and derive the corresponding exponent. I show how these ideas capture the main low-frequency features of the vibrational spectrum of amorphous silica. These results extend arguments of Phillips on the presence of floppy modes in under-constrained covalent networks to glasses where the covalent network is rigid, or when interactions are purely radial.

cond-mat.mtrl-sci↗
arXiv2008

Diffusional Nucleation of Nanocrystals and Their Self-Assembly into Uniform Colloids

We review theoretical explanation of mechanisms of control of uniformity in growth of nanosize particles and colloids. The nanoparticles are synthesized as nanocrystals, by burst nucleation from solution. The colloids are self-assembled by aggregation of these nanocrystals. The two kinetic processes are coupled, and both are driven by diffusional transport. The interrelation of the two processes allows for formation of narrow-size-distribution colloid dispersions which are of importance in many applications. We review a mathematical model of cluster growth by capture of diffusing "singlets." Burst nucleation of nanoparticles in solution is then analyzed. Finally, we couple it to the secondary process of aggregation of nanoparticles to form colloids. We address aspects of modeling of particle size distribution, as well as other properties.

cond-mat.stat-mech↗
arXiv2008

Sampling constraints in average: The example of Hugoniot curves

We present a method for sampling microscopic configurations of a physical system distributed according to a canonical (Boltzmann-Gibbs) measure, with a constraint holding in average. Assuming that the constraint can be controlled by the volume and/or the temperature of the system, and considering the control parameter as a dynamical variable, a sampling strategy based on a nonlinear stochastic process is proposed. Convergence results for this dynamics are proved using entropy estimates.As an application, we consider the computation of points along the Hugoniot curve, which are equilibrium states obtained after equilibration of a material heated and compressed by a shock wave.

cond-mat.stat-mech↗
arXiv2008

The exponentially truncated q-distribution: A generalized distribution for real complex systems

To know the statistical distribution of a variable is an important problem in management of resources. Distributions of the power law type are observed in many real systems. However power law distributions have an infinite variance and thus can not be used as a standard distribution. Normally professionals in the area use normal distribution with variable parameters or some other approximate distribution like Gumbel, Wakeby, or Pareto, which has limited validity. Tsallis presented a microscopic theory of power law in the framework of non-extensive thermodynamics considering long-range interactions or long memory. In the present work, we consider softing of long-range interactions or memory and presented a generalized distribution which have finite variance and can be used as a standard distribution for all real complex systems with power law behaviour. We applied this distribution for a financial system, rain precipitation and some geophysical and social systems. We found a good agreement for entire range in all cases for the probability density function (pdf) as well as the accumulated probability. This distribution shows universal nature of the size limiting in real systems.

cond-mat.stat-mech↗
arXiv2008

Entropy, Probability and Dynamics

Boltzmann's struggle with a derivation of the Second Law of Thermodynamics is sketched. So is his first derivation of the connection between entropy and probability in 1877. Planck's derivation and quantum mechanical modifications of Boltzmann's connection between entropy probability are given next. Then Einstein's objections to a purely probabilistic rather than a dynamical interpretation of entropy are discussed. Finally, the dynamical basis of the Sinai-Ruelle-Bowen distribution for very chaotic systems is sketched and appears to be an example of Einstein's dynamical interpretation of entropy.

physics.hist-ph↗