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At least 991 records · Page 55Linked to original sources
PubMed1999

Critical-point finite-size scaling in the microcanonical ensemble.

We develop a scaling theory for the finite-size critical behavior of the microcanonical entropy (density of states) of a system with a critically divergent heat capacity. The link between the microcanonical entropy and the canonical energy distribution is exploited to establish the former, and corroborate its predicted scaling form, in the case of the 3d Ising universality class. We show that the scaling behavior emerges clearly when one accounts for the effects of the negative background constant contribution to the canonical critical specific heat. We show that this same constant plays a significant role in determining the observed differences between the canonical and microcanonical specific heats of systems of finite size, in the critical region.

Journal Article↗
PubMed2001

Cluster synchronization modes in an ensemble of coupled chaotic oscillators.

Considering systems of diffusively coupled identical chaotic oscillators, an effective method to determine the possible states of cluster synchronization and ensure their stability is presented. The method, which may find applications in communication engineering and other fields of science and technology, is illustrated through concrete examples of coupled biological cell models.

Journal Article↗
PubMed2003

Phase transition in an ensemble of dissipative solitons of a Turing system.

Numerical study of a two-component reaction-diffusion system where Turing spatial structures are formed has revealed the existence of phase transition between condensed and rarefied phases of dissipative solitons. The effect is due to the dependence of soliton structure on control parameters. The transition manifests a hysteresis, which gives evidence for the possibility of phases to coexist.

Journal Article↗
PubMed2004

Discerning aggregation in homogeneous ensembles: a general description of photon counting spectroscopy in diffusing systems.

In order to discern aggregation in solution, we present a quantum mechanical analog of the photon statistics from fluorescent molecules diffusing through a focused beam. A generating functional is developed to fully describe the experimental physical system as well as the statistics. Histograms of the measured time delay between photon counts are fit by an analytical solution describing the static as well as diffusing regimes. To determine empirical fitting parameters, fluorescence correlation spectroscopy is used in parallel to the photon counting. For expedient analysis, we find that the distribution's deviation from a single Poisson shows a difference between two single fluor monomers or a double fluor aggregate of the same total intensities. Initial studies were performed on fixed-state aggregates limited to dimerization. However preliminary results on reactive species suggest that the method can be used to characterize any aggregating system.

Biophysics↗
PubMed2004

Granular contact force density of states and entropy in a modified Edwards ensemble.

A method has been found to analyze Edwards' granular contact force probability functional for a special case. As a result, the granular contact force probability density functions are obtained from first principles for this case. The results are in excellent agreement with the experimental and simulation data. The derivation assumes Edwards' flat measure--a density of states (DOS) that is uniform within the metastable regions of phase space. The enabling assumption, supported by physical arguments and empirical evidence, is that correlating information is not significantly recursive through loops in the packing. Maximizing a state-counting entropy results in a transport equation that can be solved numerically. For the present this has been done using the "mean-structure approximation," projecting the DOS across all angular coordinates to more clearly identify its predominant nonuniformities. These features are (1) the grain factor Psi related to grain stability and strong correlation between the contact forces on the same grain and (2) the structure factor Upsilon related to Newton's third law and strong correlation between neighboring grains.

Journal Article↗
PubMed2006

Quantum Monte Carlo simulation in the canonical ensemble at finite temperature.

A quantum Monte Carlo method with a nonlocal update scheme is presented. The method is based on a path-integral decomposition and a worm operator which is local in imaginary time. It generates states with a fixed number of particles and respects other exact symmetries. Observables like the equal-time Green's function can be evaluated in an efficient way. To demonstrate the versatility of the method, results for the one-dimensional Bose-Hubbard model and a nuclear pairing model are presented. Within the context of the Bose-Hubbard model the efficiency of the algorithm is discussed.

Journal Article↗