Collaborative filtering based on multi-channel diffusion

In this paper, by applying a diffusion process, we propose a new index to quantify the similarity between two users in a user-object bipartite graph. To deal with the discrete ratings on objects, we use a multi-channel representation where each object is mapped to several channels with the number of channels being equal to the number of different ratings. Each channel represents a certain rating and a user having voted an object will be connected to the channel corresponding to the rating. Diffusion process taking place on such a user-channel bipartite graph gives a new similarity measure of user pairs, which is further demonstrated to be more accurate than the classical Pearson correlation coefficient under the standard collaborative filtering framework.     

Jarzynski equation for the expansion of a relativistic gas and black-body radiation

Generalizing the work of Lua and Grosberg [R.C. Lua, A.Y. Grosberg, J. Phys. Chem. B 109 (2005) 6805], we verify the validity of the Jarzynski equation for the non-equilibrium expansion of an ideal relativistic gas and black-body radiation, respectively. The upper limit for the speed of the particles allows one to choose the parameters of the problem such that no multiple collisions need to be taken into account. Although related, the two cases considered differ from each other due to the quantum nature of photons. We show that bunching of photons is crucial for the Jarzynski equation to hold.     

Quantum dynamics of atomic coherence in a spin-1 condensate: Mean-field versus many-body simulation

We analyse and numerically simulate the full many-body quantum dynamics of a spin-1 condensate in the single spatial mode approximation. Initially, the condensate is in a “ferromagnetic” state with all spins aligned along the y axis and the magnetic field pointing along the z axis. In the course of evolution the spinor condensate undergoes a characteristic change of symmetry, which in a real experiment could be a signature of spin-mixing many-body interactions. The results of our simulations are conveniently visualised within the picture of irreducible tensor operators.     

Thermal cycles, interface chemistry and optical performance of Mg/SiC multilayers

The interplay between optical performance and the thermally activated interface chemistry of periodic Mg/SiC multilayers designed for application at 30.4 nm are investigated by optical (hard X-ray, soft X-ray and ultraviolet ranges, i.e. from 0.154 to 30.4 nm) reflectivity and X-ray emission spectroscopy. The multilayers are prepared by magnetron sputtering and then annealed up to a temperature of 500 °C. Two clear changes take place in the multilayer upon annealing. At first, between 200 and 300 °C a strong decrease of the reflectivity is observed, due to the development of interfacial roughness following the crystallization of the Mg layers. No interfacial compound is detected. Then, between 350 and 400 °C there is formation of the Mg₂Si magnesium silicide at the interfaces following the reaction between the Mg and SiC layers. This also leads to the almost total loss of reflectivity of the multilayer. Thus, this kind of multilayer is thermally stable only for application requiring no heating above 200 °C.     

Statistical Interaction Term of One-Dimensional Anyon Models

A form of statistical interaction term of one-dimensional anyons is introduced, based on which one-dimensional anyon models are theoretically realized, and the statistical transmutation between bosons （or fermions） and anyons is established in quantum mechanics formalism. Two kinds of anyon models which are being studied are recovered and reexplained naturally in our formalism.     

Do bosons obey Bose-Einstein distribution: Two iterated limits of Gentile distribution

It is a common impression that by only setting the maximum occupation number to infinity, which is the demand of the indistinguishability of bosons, one can achieve the statistical distribution that bosons obey — the Bose-Einstein distribution. In this Letter, however, we show that only with an infinite maximum occupation number one cannot uniquely achieve the Bose-Einstein distribution, since in the derivation of the Bose-Einstein distribution, the problem of iterated limit is encountered. For achieving the Bose-Einstein distribution, one needs to take both the maximum occupation number and the total number of particles to infinities, and, then, the problem of the order of taking limits arises. Different orders of the limit operations will lead to different statistical distributions. For achieving the Bose-Einstein distribution, besides setting the maximum occupation number, we also need to state the order of the limit operations.     

Fractional exclusion statistics in general systems of interacting particles

I show that fractional exclusion statistics is manifested in general interacting systems and I calculate the exclusion statistics parameters. Most importantly, I prove that the mutual exclusion statistics parameters are proportional to the dimension of the Hilbert space on which they act [D.V. Anghel, J. Phys. A: Math. Theor. 40 (2007) F1013].     

From the conserved Kuramoto-Sivashinsky equation to a coalescing particles model

The conserved Kuramoto-Sivashinsky (CKS) equation, , has recently been derived in the context of crystal growth, and it is also strictly related to a similar equation appearing, e.g., in sand-ripple dynamics. We show that this equation can be mapped into the motion of a system of particles with attractive interactions, decaying as the inverse of their distance. Particles represent vanishing regions of diverging curvature, joined by arcs of a single parabola, and coalesce upon encounter. The coalescing particles model is easier to simulate than the original CKS equation. The growing interparticle distance ? represents coarsening of the system, and we are able to establish firmly the scaling . We obtain its probability distribution function, g(?), numerically, and study it analytically within the hypothesis of uncorrelated intervals, finding an overestimate at large distances. Finally, we introduce a method based on coalescence waves which might be useful to gain better analytical insights into the model.     

Green functions and Langevin equations for nonlinear diffusion equations: A comment on ‘Markov processes, Hurst exponents, and nonlinear diffusion equations’ by Bassler et al.

We discuss two central claims made in the study by Bassler et al. [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343]. Bassler et al. claimed that Green functions and Langevin equations cannot be defined for nonlinear diffusion equations. In addition, they claimed that nonlinear diffusion equations are linear partial differential equations disguised as nonlinear ones. We review bottom-up and top-down approaches that have been used in the literature to derive Green functions for nonlinear diffusion equations and, in doing so, show that the first claim needs to be revised. We show that the second claim as well needs to be revised. To this end, we point out similarities and differences between non-autonomous linear Fokker-Planck equations and autonomous nonlinear Fokker-Planck equations. In this context, we raise the question whether Bassler et al.’s approach to financial markets is physically plausible because it necessitates the introduction of external traders and causes. Such external entities can easily be eliminated when taking self-organization principles and concepts of nonextensive thermostatistics into account and modeling financial processes by means of nonlinear Fokker-Planck equations.     

Generalized statistical description of adsorption of polyatomics

Multisite-occupancy adsorption is described as a fractional statistic problem, based on Haldane’s statistics. Site exclusion is characterized by a statistical exclusion parameter, g, which relates to the molecular size and lattice geometry. A general adsorption isotherm is obtained and comparisons with experiments indicate that the spatial configuration of adsorbed molecules and lateral interactions may accurately be assessed from this theory. In addition, the theoretical framework developed in this paper allows to describe orientational transitions occurring in adlayers of polyatomics.     

Spectrum of the non-abelian phase in Kitaev’s honeycomb lattice model

The spectral properties of Kitaev’s honeycomb lattice model are investigated both analytically and numerically with the focus on the non-abelian phase of the model. After summarizing the fermionization technique which maps spins into free Majorana fermions, we evaluate the spectrum of sparse vortex configurations and derive the interaction between two vortices as a function of their separation. We consider the effect vortices can have on the fermionic spectrum as well as on the phase transition between the abelian and non-abelian phases. We explicitly demonstrate the 2ⁿ-fold ground state degeneracy in the presence of 2n well separated vortices and the lifting of the degeneracy due to their short-range interactions. The calculations are performed on an infinite lattice. In addition to the analytic treatment, a numerical study of finite size systems is performed which is in exact agreement with the theoretical considerations. The general spectral properties of the non-abelian phase are considered for various finite toroidal systems.     

A computationally efficient scheme for the non-linear diffusion equation

This Letter proposes a new numerical scheme for integrating the non-linear diffusion equation. It is shown that it is linearly stable. Some tests are presented comparing this scheme to a popular decentered version of the linearized Crank-Nicholson scheme, showing that, although this scheme is slightly less accurate in treating the highly resolved waves, (i) the new scheme better treats highly non-linear systems, (ii) better handles the short waves, (iii) for a given test bed turns out to be three to four times more computationally cheap, and (iv) is easier in implementation.     

A decomposed equation for local entropy and entropy production in volume-preserving coarse-grained systems

In this study an equation for the local entropy is derived based on the formulation of a master equation and is applied to volume-preserving maps. The equation consists of the following terms: unsteady, convection, diffusion, probability-weighted phase space volume expansion rate, nonnegative entropy production, and residuals. The decomposition makes it possible to evaluate entropy production in terms of microscopic dynamics and is expected to be applicable to many coarse-grained systems on the phase space. When it is applied to two volume-preserving multibaker chain systems it is confirmed that the summation of the nonnegative entropy production on each site numerically coincides with the entropy production introduced by Gilbert et al. [T. Gilbert, J.R. Dorfman, P. Gaspard, Entropy production, fractals, and relaxation to equilibrium, Phys. Rev. Lett. 85 (2000) 1606-1609] and the phenomenological expression both in nonequilibrium steady and unsteady states. The coincidence is brought about by the fact that the residual terms vanish in the thermodynamic limit when they are integrated on each site. It follows that the entropy production is dominated by the nonnegative entropy production term and becomes positive in nonequilibrium states.     

Non-equilibrium effects in spinodal decomposition of a binary system

A model for diffusion and phase separation which takes into account relaxation of the solute diffusion flux is developed. It is shown that the model predicts non-linearity in the amplification rate of decomposition, which is governed by the ratio between diffusion and correlation lengths. The predicted amplification rate is tested against experimental data on a binary phase-separated glass.     

New implementation of composite fermions in terms of subgroups of a braid group

The new implementation of composite fermions and more generally — of composite anyons is formulated, exploiting one-dimensional unitary representations of appropriately constructed subgroups of the full braid group. The nature of hypothetical fluxes attached to the Jain's composite fermions is explained via additional cyclotron trajectory loops consistently with the braid subgroup structure. It is demonstrated that composite fermions are proper 2D particles (not an auxiliary construction), but associated with braid subgroups instead of the full braid group.     

Representation of orthofermion spin operators

The algebraic expressions for the total spin operators expressed in terms of orthofermion creation and annihilation operators are combined into a single equation. The terms in this expressions are rearranged to provide representations of local spin operators. This task is essential for modelling a system of orthofermions in the presence of a magnetic field. By factorizing the orthofermion annihilation (creation) operators into charge and spin dependent parts, it is shown that the latter part suffices to represent spin number, raising and lowering operators. Finally a connection is provided between the spin systems and Greenberg’s infinite statistics.     

Analytical results on the magnetization of the Hamiltonian Mean-Field model

The violent relaxation and the metastable states of the Hamiltonian Mean-Field model, a paradigmatic system of long-range interactions, is studied using a Hamiltonian formalism. Rigorous results are derived algebraically for the time evolution of selected macroscopic observables, e.g., the global magnetization. The high- and low-energy limits are investigated and the analytical predictions are compared with direct N-body simulations. The method we use enables us to re-interpret the out-of-equilibrium phase transition separating magnetized and (almost) unmagnetized regimes.     

Performance analysis of a thermosize micro/nano heat engine

In a recent paper [A. Sisman, I. Muller, Phys. Lett. A 320 (2004) 360] the thermodynamic properties of ideal gases confined in a narrow box were examined theoretically. The so-called “thermosize effects” similar to thermoelectric effects, such as Seebeck-like thermosize effect, Peltier-like thermosize effect and Thomson-like thermosize effect, were analyzed. Like the thermoelectric generator, based on the thermosize effects we have established a model of micro/nano scaled ideal gas heat engine cycle which includes two isothermal and two isobaric processes. The expressions of power output and efficiency of this cycle in the two cases of reversible and irreversible heat exchange are derived and the optimal performance characteristics of the heat engine is discussed by some numerical example. The results obtained here will provide theoretical guidance for the design of micro/nano scaled device.