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arXiv2013

Phase diagram and water-like anomalies in core-softened shoulder-dumbbells system

Using molecular dynamics we studied the role of the anisotropy on the phase boundary and on the anomalous behavior of 250 dimeric particles interacting by a core-softened potential. This study led us to an unexpected result: the introduction of a rather small anisotropy, quantified by the distance between the particles inside each dimer, leads to the increase of the size of the regions in the pressure-temperature phase diagram of anomalies when compared to the isotropic monomeric case. However, as the anisotropy increases beyond a threshold the anomalous regions shrinks. We found that this behavior can be understood by decoupling the translational and non-translational kinetic energy components into different translational and non-translational temperatures.

cond-mat.stat-mech↗

arXiv2013

Random Walk on Lattices: Graph Theoretic Approach to Modeling Epitaxially Grown Thin Film

Immense interests in thin-film fabrication for industrial applications have driven both theoretical and computational aspects of modeling its growth with an aim to design and control film's surface morphology. Oftentimes, smooth surface is desirable and is experimentally achievable via molecular-beam epitaxy (MBE) growth technique with exceptionally low deposition flux. Adatoms on the film grown with such a method tend to have large diffusion length which can be computationally very costly when certain statistical aspects are demanded. We present a graph theoretic approach to modeling MBE grown thin film with long atomic mean free path. Using Markovian assumption and given a local diffusion bias, we derive the transition probabilities for a random walker to traverse from one lattice site to the others after a large, possibly infinite, number of hopping steps. Only computation with linear-time complexity is required for the surface morphology calculation without other probabilistic measures. The formalism is applied to simulate thin film growth on a two-dimensional flat substrate and around a screw dislocation under the modified Wolf--Villain diffusion rule. A rectangular spiral ridge is observed in the latter case with a smooth front feature similar to that obtained from simulations using the well-known multiple registration technique. An algorithm to compute the inverse of a class of sub-stochastic matrices is derived as a corollary.

cond-mat.stat-mech↗

arXiv2013

Does an irreversible chemical cycle support equilibrium?

The impossibility of attaining equilibrium for cyclic chemical reaction networks with irreversible steps is apparently due to a divergent entropy production rate. A deeper reason seems to be the violation of the detailed balance condition. In this work, we discuss how the standard theoretical framework can be adapted to include irreversible cycles, avoiding the divergence. With properly redefined force terms, such systems are also seen to reach and sustain equilibria that are characterized by the vanishing of the entropy production rate, though detailed balance is not maintained. Equivalence of the present formulation with Onsager's original prescription is established for both reversible and irreversible cycles, with a few adjustments in the latter case. Further justification of the attainment of true equilibrium is provided with the help of the minimum entropy production principle. All the results are generalized for an irreversible cycle comprising of N number of species.

physics.chem-ph↗

arXiv2013

Extreme lattices: symmetries and decorrelations

We study statistical and structural properties of extreme lattices, which are the local minima in the density landscape of lattice sphere packings, in $d$-dimensional Euclidean space $\mathbb{R}^d$. Specifically, we ascertain the distributions of densities, kissing numbers and numbers of symmetries of the packings across a wide range of dimensions using the stochastic Voronoi algorithm. The degree to which the packings decorrelate as well as the correlations between the density maxima as the space dimension increases is also investigated. We find that the extreme lattices decorrelate with increasing dimension, the least symmetric lattices decorrelate faster. The extreme lattices in a fixed dimension of space $d$ ($d\geq 8$) are dominated by typical lattices that have similar packing properties, like packing densities and kissing numbers, while the best and the worst packers are in the long tails of the distribution of the extreme lattices.

cond-mat.stat-mech↗

arXiv2013

Thermostatistics of μ-deformed analog of Bose gas model

For the recently introduced μ-deformed analog of Bose gas model (μ-Bose gas model) we study some thermodynamical aspects. Namely, we calculate total number of particles and, from it, the deformed partition function, both involving dependence on the deformation parameter μ. Such dependence of thermodynamic functions on the μ-parameter is at the core of modification of Bose gas model and arises through the use of new techniques given by us, the μ-calculus, an alternative to the well-known q-calculus (Jackson derivative and integral). Necessary elements of μ-calculus are first presented. Then, for high temperatures we obtain virial expansion of the equation of state and find five first virial coefficients, as functions of μ. At the other end, for low temperatures the critical temperature of condensation T_c^(μ) depending on μis found and compared with the usual T_c, and with the T_c^(p,q) of earlier studied p,q-Bose gas model. The internal energy, specific heat and the entropy of μ-Bose gas are also given, both for high and low temperatures. Features peculiar for the μ-Bose gas model are emphasized.

cond-mat.stat-mech↗

arXiv2013

Phase Transition in Dimer Liquids

We study the phase transition in a system composed of dimers interacting with each other via a nearest-neighbor (NN) exchange $J$ and competing interactions taken from a truncated dipolar coupling. Each dimer occupies a link between two nearest sites of a simple cubic lattice. We suppose that dimers are self-avoiding and can have only three orientations which coincide with the $x$, $y$ or $z$ direction. The interaction $J$ is attractive if the two dimers are parallel with each other at the NN distance, zero otherwise. The truncated dipolar interaction is characterized by two parameters: its amplitude $D$ and the cutoff distance $r_c$. Using the steepest-descent method, we determine the ground-state (GS) configuration as functions of $D$ and $r_c$. We then use Monte Carlo simulations to investigate the nature of the low-temperature phase and to determine characteristics of the phase transition from the ordered phase to the disordered phase at high temperatures at a given dimer concentration. We show that as the temperature increases, dimers remain in the compact state and the transition from the low-$T$ compact phase to the disordered phase where dimers occupy the whole space is of second order when $D$ is small, but it becomes of first order for large enough $D$, for both polarized and non polarized dimers. This transition has a resemblance with the unfolding polymer transition. The effect of $r_c$ is discussed.

cond-mat.stat-mech↗

arXiv2013

Alternative Derivation of the Partition Function for Generalized Ensembles

A pedagogical approach for deriving the statistical mechanical partition function, in a manner that emphasizes the key role of entropy in connecting the microscopic states to thermodynamics, is introduced. The connections between the combinatoric formula $S= k \ln W$ applied to the Gibbs construction, the Gibbs entropy, $S = -k \sum\limits_i p_i \ln p_i$, and the microcanonical entropy expression $S= k \ln Ω$ are clarified. The condition for microcanonical equilibrium, and the associated role of the entropy in the thermodynamic potential is shown to arise naturally from the postulate of equal {\itshape a priori} states. The derivation of the canonical partition function follows simply by invoking the Gibbs ensemble construction at constant temperature and using the first and second law of thermodynamics (\emph{via} the fundamental equation $dE = TdS - PdV + μdN$) that incorporate the conditions of conservation of energy and composition without the needs for explicit constraints; other ensemble follow easily. The central role of the entropy in establishing equilibrium for a given ensemble emerges naturally from the current approach. Connections to generalized ensemble theory also arise and are presented in this context.

cond-mat.stat-mech↗

arXiv2013

Anisotropic polarization, predicted as a result of the diffraction of blackbody radiation at a reflective phase grating with ideal conductivity

In the course of analyzing the axiomatic principles that form the basis of statistical physics, the validity of the postulate that all the isoenergetic microstates of a closed system are equally probable was checked. This article reports the results of numerically modelling the interaction of thermodynamically equilibrium blackbody radiation with a reflective phase diffraction grating that possesses ideal conductivity. Cases are found in which anisotropy of the polarization parameters is guaranteed to appear inside a closed volume of initially homogeneous blackbody radiation, resulting in a formal decrease of its Boltzmann entropy as a consequence of deviation from the microcanonical Gibbs distribution. This is apparently caused by the discontinuous character of the change of the phase trajectories of the photons during diffraction, which makes the physical system under consideration nonergodic.

physics.optics↗

arXiv2013

Nonlinear macroscopic transport equations in many-body systems from microscopic exclusion processes

Describing particle transport at the macroscopic or mesoscopic level in non-ideal environments poses fundamental theoretical challenges in domains ranging from inter and intra-cellular transport in biology to diffusion in porous media. Yet, often the nature of the constraints coming from many-body interactions or reflecting a complex and confining environment are better understood and modeled at the microscopic level. In this paper we investigate the subtle link between microscopic exclusion processes and the mean-field equations that ensue from them in the continuum limit. We derive a generalized nonlinear advection diffusion equation suitable for describing transport in a inhomogeneous medium in the presence of an external field. Furthermore, taking inspiration from a recently introduced exclusion process involving agents with non-zero size, we introduce a modified diffusion equation appropriate for describing transport in a non-ideal fluid of $d$-dimensional hard spheres. We consider applications of our equations to the problem of diffusion to an absorbing sphere in a non-ideal self-crowded fluid and to the problem of gravitational sedimentation. We show that our formalism allows one to recover known results. Moreover, we introduce the notions of point-like and extended crowding, which specify distinct routes for obtaining macroscopic transport equations from microscopic exclusion processes.

cond-mat.stat-mech↗

arXiv2013

Phase behavior of binary mixtures of hard convex polyehdra

Shape anisotropy of colloidal nanoparticles has emerged as an important design variable for engineering assemblies with targeted structure and properties. In particular, a number of polyhedral nanoparticles have been shown to exhibit a rich phase behavior [Agarwal et al., Nature Materials, 2011, 10, 230]. Since real synthesized particles have polydispersity not only in size but also in shape, we explore here the phase behavior of binary mixtures of hard convex polyhedra having similar sizes but different shapes. Choosing representative particle shapes from those readily synthesizable, we study in particular four mixtures: (i) cubes and spheres (with spheres providing a non-polyhedral reference case), (ii) cubes and truncated octahedra, (iii) cubes and cuboctahedra, and (iv) cuboctahedra and truncated octahedra. The phase behavior of such mixtures is dependent on the interplay of mixing and packing entropy, which can give rise to miscible or phase-separated states. The extent of mixing of two such particle types is expected to depend on the degree of shape similarity, relative sizes, composition, and compatibility of the crystal structures formed by the pure components. While expectedly the binary systems studied exhibit phase separation at high pressures due to the incompatible pure-component crystal structures, our study shows that the essential qualitative trends in miscibility and phase separation can be correlated to properties of the pure components, such as the relative values of the order-disorder transition pressure (ODP) of each component. Specifically, if for a mixture A+B we have that ODP_B <ODP_A and ΔODP = ODP_A - ODP_B, then at any particular pressure where phase separation occurs, the larger the ΔODP the lower the solubility of A in the B-rich ordered phase and the higher the solubility of B in the A-rich ordered phase.

cond-mat.soft↗

arXiv2013

Phase controlling current reversals in a chaotic ratchet transport

We consider a deterministic chaotic ratchet model for which the driving force is designed to allow the rectification of current as well as the control of chaos of the system. Besides the amplitude of the symmetric driving force which is often used in this framework as control parameter, a phase has been newly included here. Exploring this phase, responsible of the asymmetry of the driven force, a number of interesting departures have been revealed. Remarkably, it becomes possible to drive the system into one of the following regime: the state of zero transport, the state of directed transport and most importantly the state of reverse transport (current reversal). To have a full control of the system, a current reversal diagram has been computed thereby clearly showing the entire transport spectrum which is expected to be of interest for possible experiments in this model.

nlin.CD↗

arXiv2013

Exact Complexity: The Spectral Decomposition of Intrinsic Computation

We give exact formulae for a wide family of complexity measures that capture the organization of hidden nonlinear processes. The spectral decomposition of operator-valued functions leads to closed-form expressions involving the full eigenvalue spectrum of the mixed-state presentation of a process's epsilon-machine causal-state dynamic. Measures include correlation functions, power spectra, past-future mutual information, transient and synchronization informations, and many others. As a result, a direct and complete analysis of intrinsic computation is now available for the temporal organization of finitary hidden Markov models and nonlinear dynamical systems with generating partitions and for the spatial organization in one-dimensional systems, including spin systems, cellular automata, and complex materials via chaotic crystallography.

cond-mat.stat-mech↗

arXiv2013

General Clique Percolation in Network Evolution

We introduce a general $(k,l)$ clique community, which consists of adjacent $k$-cliques sharing at least $l$ vertices with $k-1 \ge l \ge 1$. The emergence of a giant $(k,l)$ clique community indicates a $(k,l)$ clique percolation, which is studied by the largest size gap $Δ$ of the largest clique community during network evolution and the corresponding evolution step $T_c$. For a clique percolation, the averages of $Δ$ and $T_c$ and the root-mean-squares of their fluctuations have power law finite-size effects whose exponents are related to the critical exponents. The fluctuation distribution functions of $Δ$ and $T_c$ follow a finite-size scaling form. In the evolution of the Erdős-Rényi network, there are a series of $(k,l)$ clique percolation with $(k,l)=(2,1),(3,1),(3,2),(4,1),(4,2),(5,1),(4,3)$, and so on. The critical exponents of clique percolation depend on $l$, but are independent of $k$. The universality class of a $(k,l)$ clique percolation is characterized alone by $l$.

cond-mat.stat-mech↗

arXiv2013

Effects of Nonlinear Coupling on Spatiotemporal Regularity

In this work we investigate the spatiotemporal behaviour of lattices of coupled chaotic logistic maps, where the coupling between sites has a nonlinear form. We show that the stable range of the spatiotemporal fixed point state is significantly enhanced for increasingly nonlinear coupling. We demonstrate this through numerical simulations and linear stability analysis of the synchronized fixed point. Lastly, we show that these results also hold in coupled map lattices where the nodal dynamics is given by the Gauss Map, Sine Circle Map and the Tent Map.

nlin.CD↗

arXiv2013

On Metropolis Integrators for Molecular Dynamics

This paper invites the reader to experiment with an easy-to-use MATLAB implementation of Metropolis integrators for Molecular Dynamics (MD) simulation. These integrators are analysis-based, in the sense that they can rigorously simulate dynamics along an infinitely long MD trajectory. Among explicit integrators for MD, they seem to be the only ones that satisfy the fundamental requirement of stability. The schemes can handle stiff or hard-core potentials, and are straightforward to set up, apply and extend to new situations. Potential pitfalls in high dimension are discussed, and tricks for mitigation are given.

physics.comp-ph↗

arXiv2013

Ground state of the competing spin chain Cs2Cu2Mo3O12

The high-field ground state of the competing-spin-chain compound Cs2Cu2Mo3O12 with the ferromagnetic first-nearest-neighbor J1=-93 K and the antiferromagnetic second-nearest-neighbor J2 = +33 K was investigated by 133Cs-NMR. A divergence of T1-1 and a peak-splitting in spectra were observed at TN = 1.85 K, indicating the existence of a field-induced long range magnetic order. In the paramagnetic region above 4 K, T1-1 showed a power-law temperature dependence T2K-1. The exponent K was strongly field-dependent, suggesting the possibility of the spin-nematic Tomonaga Luttinger Liquid state.

cond-mat.stat-mech↗

arXiv2013

Comment on "Is there a breakdown of the Stokes-Einstein relation in Kinetically Constrained Models at low temperature?" by O. Blondel and C. Toninelli, arXiv:1307.1651

We consider the diffusion constant, D, of a probe particle coupled to the East model, extending previous numerical results for this model to encompass a total of twelve orders of magnitude in relaxation time, τ. Our considerations thus cover the full range of relaxation times relevant to experimental studies of reversible glass formers. Throughout this range, we show that the results of the model are consistent with a fractional Stokes-Einstein law, D \propto τ^{-ξ} with ξ \approx 0.77. The same data can also be fit by relating Dτ to the East model excitation concentration q, specifically, Dτ \sim 1/q^α with α \approx 1.6. In either case, breakdown of the Stokes-Einstein relation in this kinetically constrained model is unquestionable and large.

cond-mat.stat-mech↗

arXiv2013

O(N) Models with Topological Lattice Actions

A variety of lattice discretisations of continuum actions has been considered, usually requiring the correct classical continuum limit. Here we discuss "weird" lattice formulations without that property, namely lattice actions that are invariant under most continuous deformations of the field configuration, in one version even without any coupling constants. It turns out that universality is powerful enough to still provide the correct quantum continuum limit, despite the absence of a classical limit, or a perturbative expansion. We demonstrate this for a set of O(N) models (or non-linear $σ$-models). Amazingly, such "weird" lattice actions are not only in the right universality class, but some of them even have practical benefits, in particular an excellent scaling behaviour.

hep-lat↗