1,721,001 research outputs found
Probabilistic Cellular Automata Monte Carlo for the Maximum Clique Problem
No full textWe consider the problem of finding the largest clique of a graph. This is an NP-hard problem and no exact algorithm to solve it exactly in polynomial time is known to exist. Several heuristic approaches have been proposed to find approximate solutions. Markov Chain Monte Carlo is one of these. In the context of Markov Chain Monte Carlo, we present a class of “parallel dynamics”, known as Probabilistic Cellular Automata, which can be used in place of the more standard choice of sequential “single spin flip” to sample from a probability distribution concentrated on the largest cliques of the graph. We perform a numerical comparison between the two classes of chains both in terms of the quality of the solution and in terms of computational time. We show that the parallel dynamics are considerably faster than the sequential ones while providing solutions of comparable quality
Ionization of carbonyl sulphide/disulphur monoxide mixtures in atmospheric gases: A theoretical study of the formation of S3O+ ions
No full textA theoretical study performed at B3LYP and CCSD(T) level of theory of the reaction of formation Of S3O+ in ionized carbonyl sulphide/disulpbur monoxide mixtures is reported here. The interaction of carbonyl sulphide with disulphur monoxide cation leads to three different [CS3O2](+) isomers, essentially formed by a S3O+ cation solvated by a CO molecule. The S3O+ cation is present in the three structures cis, trans and ring, showed also by the isolated S3O+ species. The complex with the ring S3O+ unit is the most stable, but a direct ath to its formation starting from OCS and S2O+ has not been found in the potential energy surface Of [CS3O2]+. This species can be obtained from the isomerization of the complexes containing the cis or trans S3O+ unit, overcoming relatively low barrier heights
Lonely Planets and Lightweight Asteroids: A Statistical Mechanics Model for the Planetary Problem
Full text linkIn this paper we propose a notion of stability, which we call ε- N-stability, for systems of particles interacting via Newton’s gravitational potential, and orbiting a much bigger object. For these systems the usual thermodynamical stability condition, ensuring the possibility to perform the thermodynamical limit, fails, but one can use as relevant parameter the maximum number of particles N that guarantees the ε- N-stability. With some judicious but not particularly optimized estimates, borrowed from the classical theory of equilibrium statistical mechanics, we show that our model has a good fit with the data observed in the Solar System, and it gives a reasonable interpretation of some of its global properties
Theoretical investigations of atmospheric species relevant for the search of high-energy density materials
No full textOn some features of quadratic unconstrained binary optimization with random coefficients
No full textQuadratic Unconstrained Binary Optimization (QUBO or UBQP) is concerned with maximizing/minimizing the quadratic form H(J,eta)=W & sum;(i,j)J(i,j)eta(i)eta(j )with J a matrix of coefficients, eta is an element of {0,1}(N) and W a normalizing constant. In the statistical mechanics literature, QUBO is a lattice gas counterpart to the (generalized) Sherrington-Kirkpatrick spin glass model. Finding the optima of H is an NP-hard problem. Several problems in combinatorial optimization and data analysis can be mapped to QUBO in a straightforward manner. In the combinatorial optimization literature, random instances of QUBO are often used to test the effectiveness of heuristic algorithms. Here we consider QUBO with random independent coefficients and show that if the J(i,j)'s have zero mean and finite variance then, after proper normalization, the minimum and maximum per particle of H do not depend on the details of the distribution of the couplings and are concentrated around their expected values. Further, with the help of numerical simulations, we study the minimum and maximum of the objective function and provide some insight into the structure of the minimizer and the maximizer of H. We argue that also this structure is rather robust. Our findings hold also in the diluted case where each of the J(i,j)'s is allowed to be zero with probability going to 1 as N ->infinity in a suitable way
Parallel Simulation of Two-Dimensional Ising Models Using Probabilistic Cellular Automata
Full text linkWe study the numerical simulation of the shaken dynamics, a parallel Markovian dynamics for spin systems with local interaction and transition probabilities depending on the two parameters q and J that “tune” the geometry of the underlying lattice. The analysis of the mixing time of the Markov chain and the evaluation of the spin-spin correlations as functions of q and J, make it possible to determine in the (q, J) plane a phase transition curve separating the disordered phase from the ordered one. The relation between the equilibrium measure of the shaken dynamics and the Gibbs measure for the Ising model is also investigated. Finally two different coding approaches are considered for the implementation of the dynamics: a multicore CPU approach, coded in Julia, and a GPU approach coded with CUDA
Kawasaki Dynamics with Two Types of Particles: Stable/Metastable Configurations and Communication Heights
Full text linkThis is the second in a series of three papers in which we study a two-dimensional lattice gas consisting of two types of particles subject to Kawasaki dynamics at low temperature in a large finite box with an open boundary. Each pair of particles occupying neighboring sites has a negative binding energy provided their types are different, while each particle has a positive activation energy that depends on its type. There is no binding energy between particles of the same type. At the boundary of the box particles are created and annihilated in a way that represents the presence of an infinite gas reservoir. We start the dynamics from the empty box and are interested in the transition time to the full box. This transition is triggered by a critical droplet appearing somewhere in the box. In the first paper we identified the parameter range for which the system is metastable, showed that the first entrance distribution on the set of critical droplets is uniform, computed the expected transition time up to and including a multiplicative factor of order one, and proved that the nucleation time divided by its expectation is exponentially distributed, all in the limit of low temperature. These results were proved under three hypotheses, and involve three model-dependent quantities: the energy, the shape and the number of critical droplets. In the second paper we prove the first and the second hypothesis and identify the energy of critical droplets. In the third paper we settle the rest. Both the second and the third paper deal with understanding the geometric properties of subcritical, critical and supercritical droplets, which are crucial in determining the metastable behavior of the system, as explained in the first paper. The geometry turns out to be considerably more complex than for Kawasaki dynamics with one type of particle, for which an extensive literature exists. The main motivation behind our work is to understand metastability of multi-type particle systems. © 2011 The Author(s)
Direct Experimental Observation of CS2OH
No full textThe first experimental detection of CS2OH is reported. CS2OH was observed for about one microsecond after its formation, as an intact isolated species in the gas phase. It was generated by electron transfer to the CS2OH+ ion, prepared in the source of a multisector mass spectrometer by suitable ion-molecule reactions. The vertical formation process allowed characterization of CS2OH by structural analysis of CS2OH+. Theoretical calculations were performed at the B3LYP/6-311 + G(2dp) and CCSD(T)/aug-cc-pVTZ//B3LYP/6-311 + G(2d,p) levels of theory. The computed structure and stability of CS2OH and CS2OH+ as well as the energetics of the involved processes satisfactorily fit with the experimental results
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