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arXiv2013

Water Propagation in the Porous Media, Self-Organized Criticality and Ising Model

In this paper we propose the Ising model to study the propagation of water in 2 dimensional (2D) petroleum reservoir in which each bond between its pores has the probability $p$ of being activated. We analyze the water movement pattern in porous media described by Darcy equations by focusing on its geometrical objects. Using Schramm-Loewner evolution (SLE) technique we numerically show that at $p=p_c\simeq 0.59$, this model lies within the Ising universality class with the diffusivity parameter $κ=3$ and the fractal dimension $D_f=\frac{11}{8}$. We introduce a self-organized critical model in which the water movement is modeled by a chain of topplings taking place when the amount of water exceeds the critical value and numerically show that it coincides with the numerical reservoir simulation. For this model, the behaviors of distribution functions of the geometrical quantities and the Green function are investigated in terms of $p$. We show that percolation probability has a maximum around $p=0.68$, in contrast to common belief.

cond-mat.stat-mech↗

arXiv2013

The Role of Trends in Evolving Networks

Modeling complex networks has been the focus of much research for over a decade. Preferential attachment (PA) is considered a common explanation to the self organization of evolving networks, suggesting that new nodes prefer to attach to more popular nodes. The PA model results in broad degree distributions, found in many networks, but cannot explain other common properties such as: The growth of nodes arriving late and Clustering (community structure). Here we show that when the tendency of networks to adhere to trends is incorporated into the PA model, it can produce networks with such properties. Namely, in trending networks, newly arriving nodes may become central at random, forming new clusters. In particular, we show that when the network is young it is more susceptible to trends, but even older networks may have trendy new nodes that become central in their structure. Alternatively, networks can be seen as composed of two parts: static, governed by a power law degree distribution, and a dynamic part governed by trends, as we show on Wiki pages. Our results also show that the arrival of trending new nodes not only creates new clusters, but also has an effect on the relative importance and centrality of all other nodes in the network. This can explain a variety of real world networks in economics, social and online networks, and cultural networks. Products popularity, formed by the network of people's opinions, exhibit these properties. Some lines of products are increasingly susceptible to trends and hence to shifts in popularity, while others are less trendy and hence more stable. We believe that our findings have a big impact on our understanding of real networks.

physics.soc-ph↗

arXiv2013

Searching with and against the stream: Levy or Brown?

We study the efficiency of search processes based on Levy flights (LFs) with power-law distributed jump lengths in the presence of an external drift. While LFs turn out to be efficient search processes when relative to the starting point the target is upstream, in the downstream scenario regular Brownian motion turns out to be advantageous. This is caused by the occurrence of leapovers of LFs, due to which LFs typically overshoot a point in space. We establish criteria when the combination of the external stream and the initial distance between the starting point and the target favors LFs over regular Brownian search. Contrary to the common belief that LFs with a stable index alpha=1 are optimal, we find that the optimal alpha may range in the entire interval (1,2) and even include Brownian motion as the overall most efficient search strategy.

cond-mat.stat-mech↗

arXiv2013

Random close packing fractions of lognormal distributions of hard spheres

We apply a recent one-dimensional algorithm for predicting random close packing fractions of polydisperse hard spheres [Farr and Groot, J. Chem. Phys. 133, 244104 (2009)] to the case of lognormal distributions of sphere sizes and mixtures of such populations. We show that the results compare well to two much slower algorithms for directly simulating spheres in three dimensions, and show that the algorithm is fast enough to tackle inverse problems in particle packing: designing size distributions to meet required criteria. The one-dimensional method used in this paper is implemented as a computer code in the C programming language, available at http://sourceforge.net/projects/spherepack1d/ under the terms of the GNU general public licence (version 2).

cond-mat.mtrl-sci↗

arXiv2013

Spontaneous evolution of self-assembled phases from anisotropic colloidal dispersions

We investigate the spontaneous evolution of various self-assembled phase states from a homogeneous aqueous dispersion of high-aspect ratio Montmorillonite (Na Cloisite) nanoclay platelets grounded on the observations made over a period of 3.5 years. We have established the tw-c phase diagram for this system for the first time in salt-free suspensions under normal pH conditions using rheology experiments and have detected that these suspensions do undergo nontrivial phase evolution and aging dynamics. Distinctive phase separation, equilibrium fluid and equilibrium gels in the tw-c phase space are discovered. Cole-Cole plots derived from rheology measurements suggested the presence of inter connected network-like structures for c > cg, cg being the gelation concentration. All dispersions formed stable sols during the initial time, and with aging network-like structures were found to form via two routes: one for c < cg, by phase separation and another for c > cg, through equilibrium gelation. This has invoked and called for a revisit of the phase diagram of aging MMT dispersions.

cond-mat.soft↗

arXiv2013

B2O3 glass former as a molecular matter revealed by heat capacity

Heat capacity of B2O3 glass former in a wide temperature region is described well with the intrinsic motions for non-spherical B2O3 molecules, revealing that rather than a conventional network glass former, B2O3 is a typical molecular matter in which the transition from liquid to glass in the system corresponds to the frozen of translational motions for molecules. The finding might provide an opportunity to understand the mysterious glass transition, as well as the intrinsic difference between solids and liquids.

cond-mat.mtrl-sci↗

arXiv2013

Conditional statistical physical properties in two-joint complex systems having long-range interactions

We propose the sum and the difference of the normalized velocity of two-joint systems to describe its long-range interaction. It is found that the conditional probability distribution function (CPDF) of the normalized velocity between two-joint systems can be derived. The analytical CPDF needs only six parameters for arbitrary two-joint systems. Two typical currency exchange databases, i.e., EUR/USD and GBP/USD, which collect the minutely opening exchange prices from 1 January 1999 to 31 December 2011, are adopted as example. By calculating the CPDF in the currency exchange databases, it is shown that all of the results are well described by our theory. We also use the analytical CPDF to calculate the entropy of two-joint systems, it is found that the entropy of two-joint systems is less than the sum of entropy of each system in the two currency exchange databases. It means that some information of two-joint systems may overlap. We must important to note that the results presented here do not need to know the form of interaction of two-joint systems, and the analytical CPDF is a general expression. It is valid not only for current exchange systems, but also helpful for investigate other conditional statistical properties in any two-joint long-range interactions complex systems.

cond-mat.stat-mech↗

arXiv2013

Rigidity of thermalized soft repulsive spheres around the jamming point

We study the effect of thermalization on the rigidity of a randomly packed soft repulsive sphere system around the jamming point by analyzing the shear-modulus using the cloned liquid theory with the 1 step replica symmetry breaking ansatz and molecular dynamics simulations. Contrarily to the usual harmonic picture for solids, we found that the thermalized jamming system is anomalously softer than at zero temperature such that the shear-modulus becomes as small as the pressure down to vanishingly low temperatures.

cond-mat.soft↗

arXiv2013

First Passage in Conical Geometry and Ordering of Brownian Particles

We survey recent results on first-passage processes in unbounded cones and their applications to ordering of particles undergoing Brownian motion in one dimension. We first discuss the survival probability S(t) that a diffusing particle, in arbitrary spatial dimension, remains inside a conical domain up to time t. In general, this quantity decays algebraically S ~ t^{-beta} in the long-time limit. The exponent beta depends on the opening angle of the cone and the spatial dimension, and it is root of a transcendental equation involving the associated Legendre functions. The exponent becomes a function of a single scaling variable in the limit of large spatial dimension. We then describe two first-passage problems involving the order of N independent Brownian particles in one dimension where survival probabilities decay algebraically as well. To analyze these problems, we identify the trajectories of the N particles with the trajectory of one particle in N dimensions, confined to within a certain boundary, and we use a circular cone with matching solid angle as a replacement for the confining boundary. For N=3, the confining boundary is a wedge and the approach is exact. In general, this "cone approximation" gives strict lower bounds as well as useful estimates or the first-passage exponents. Interestingly, the cone approximation becomes asymptotically exact when N-->infinity as it predicts the exact scaling function that governs the spectrum of first-passage exponents.

cond-mat.stat-mech↗

arXiv2013

Universal current fluctuations in the symmetric exclusion process and other diffusive systems

We show, using the macroscopic fluctuation theory of Bertini, De Sole, Gabrielli, Jona-Lasinio, and Landim, that the statistics of the current of the symmetric simple exclusion process (SSEP) connected to two reservoirs are the same on an arbitrary large finite domain in dimension $d$ as in the one dimensional case. Numerical results on squares support this claim while results on cubes exhibit some discrepancy. We argue that the results of the macroscopic fluctuation theory should be recovered by increasing the size of the contacts. The generalization to other diffusive systems is straightforward.

cond-mat.stat-mech↗

arXiv2013

Universality of rotons in liquids, generalized superfluidity criterion and helons in helium II

An analysis of experimental data shows that, in addition to phonon--roton excitations in superfluid helium, there necessarily exist at least one branch of elementary excitations whose energy spectrum strongly depends on temperature. On this basis, the Landau superfluidity criterion is generalized for several branches of elementary excitations, taking into account that the critical velocity should vanish during the phase transition of liquid helium from the superfluid state to the normal state. We suppose that a new spectrum of excitations with a gap, depending on interparticle interaction, corresponds to the transition of helium to superfluid state. This gap exists only in superfluid state and disappears at the transition temperature to normal state. The phonon-roton branch of excitations has no crucial influence on superfluidity. Rotons, as well as phonons, are not the specific excitations for the superfluid helium, but exist as universal excitations in liquid state, and form the continuous branch of excitations in different liquids. This point of view is confirmed experimentally and numerically.

cond-mat.stat-mech↗

arXiv2013

A Continuum Generalization of the Ising Model

The Lenz-Ising model has served for almost a century as a basis for understanding ferromagnetism, and has become a paradigmatic model for phase transitions in statistical mechanics. While retaining the Ising energy arguments, we use techniques previously applied to sociophysics to propose a continuum model. Our formulation results in an integro-differential equation that has several advantages over the traditional version: it allows for asymptotic analysis of phase transitions, material properties, and the dynamics of the formation of magnetic domains.

cond-mat.stat-mech↗

arXiv2013

Recurrence Theorems: a unified account

I discuss classical and quantum recurrence theorems in a unified manner, treating both as generalisations of the fact that a system with a finite state space only has so many places to go. Along the way I prove versions of the recurrence theorem applicable to dynamics on linear and metric spaces, and make some comments about applications of the classical recurrence theorem in the foundations of statistical mechanics.

quant-ph↗

arXiv2013

Quantum generalized fluctuation-dissipation relations in terms of time-distributed observations

New formulations of quantum generalized fluctuation-dissipation relations in terms of characteristic and probabilistic functionals of continuous observations are suggested and discussed. It is shown that control of entropy production in quantum system turns any measurement in it to a source of its extra perturbations, and because of this effect relations between probabilities of mutually time-reversed processes become definitely non-local in their functional space

cond-mat.stat-mech↗

arXiv2013

alpha-Kuramoto partitions: graph partitions from the frustrated Kuramoto model generalise equitable partitions

The Kuramoto model describes the collective dynamics of a system of coupled oscillators. An alpha-Kuramoto partition is a graph partition induced by the Kuramoto model, when the oscillators include a phase frustration parameter. We prove that every equitable partition is an alpha-Kuramoto partition, but that the converse does necessarily not hold. We give an exact characterisation of alpha-Kuramoto bipartitions.

math.CO↗

arXiv2013

Separation of spin and charge in the continuum Schrödinger equation

I describe here the attempt to introduce spin-charge separation in Schrodinger equation. The construction we present here gives a decomposed Schrodinger spinor that has one problem: Its absolute value can only have value between 0 and ${1}{2}$. The problem we solve is to expand and generalize this construction so that one can have a Schrodinger spinor with absolute value that are arbitrary non-negative numbers. It may be that one has to introduce a set of different decompositions to cover all nonnegative values, that is to introduce patches over $\mathbb{R}_{+}^{3}$ so that in each patch one has a different representation. It seems that the decomposition has a direct relation to so called entangled states that have been discussed very much in connection of e.g. quantum computing, and we would like to find this relation and discuss it in detail.

cond-mat.stat-mech↗

arXiv2013

Stratified Sampling for the Ising Model: A Graph-Theoretic Approach

We present a new approach to a classical problem in statistical physics: estimating the partition function and other thermodynamic quantities of the ferromagnetic Ising model. Markov chain Monte Carlo methods for this problem have been well-studied, although an algorithm that is truly practical remains elusive. Our approach takes advantage of the fact that, for a fixed bond strength, studying the ferromagnetic Ising model is a question of counting particular subgraphs of a given graph. We combine graph theory and heuristic sampling to determine coefficients that are independent of temperature and that, once obtained, can be used to determine the partition function and to compute physical quantities such as mean energy, mean magnetic moment, specific heat, and magnetic susceptibility.

cond-mat.stat-mech↗

arXiv2013

Inferential vs. Dynamical Conceptions of Physics

I contrast two possible attitudes towards a given branch of physics: as inferential (i.e., as concerned with an agent's ability to make predictions given finite information), and as dynamical (i.e., as concerned with the dynamical equations governing particular degrees of freedom). I contrast these attitudes in classical statistical mechanics, in quantum mechanics, and in quantum statistical mechanics; in this last case, I argue that the quantum-mechanical and statistical-mechanical aspects of the question become inseparable. Along the way various foundational issues in statistical and quantum physics are (hopefully!) illuminated.

quant-ph↗