Search results for "Statistical"
showing 10 items of 4960 documents
Genome-wide association scan of attention deficit hyperactivity disorder
2008
Contains fulltext : 70191.pdf (Publisher’s version ) (Closed access) Results of behavioral genetic and molecular genetic studies have converged to suggest that genes substantially contribute to the development of attention deficit/hyperactivity disorder (ADHD), a common disorder with an onset in childhood. Yet, despite numerous linkage and candidate gene studies, strongly consistent and replicable association has eluded detection. To search for ADHD susceptibility genes, we genotyped approximately 600,000 SNPs in 958 ADHD affected family trios. After cleaning the data, we analyzed 438,784 SNPs in 2,803 individuals comprising 909 complete trios using ADHD diagnosis as phenotype. We present t…
A note on the uniqueness result for the inverse Henderson problem
2019
The inverse Henderson problem of statistical mechanics is the theoretical foundation for many bottom-up coarse-graining techniques for the numerical simulation of complex soft matter physics. This inverse problem concerns classical particles in continuous space which interact according to a pair potential depending on the distance of the particles. Roughly stated, it asks for the interaction potential given the equilibrium pair correlation function of the system. In 1974, Henderson proved that this potential is uniquely determined in a canonical ensemble and he claimed the same result for the thermodynamical limit of the physical system. Here, we provide a rigorous proof of a slightly more …
Canonical versus microcanonical analysis of first-order phase transitions
1998
Abstract I discuss the relation between canonical and microcanonical analyses of first-order phase transitions. In particular it is shown that the microcanonical Maxwell construction is equivalent to the equal-peak-height criterion often employed in canonical simulations. As a consequence the microcanonical finite-size estimators for the transition point, latent heat and interface tension are identical to standard estimators in the canonical ensemble. Special emphasis is placed on various ways for estimating interface tensions. The theoretical considerations are illustrated with numerical data for the two-dimensional 10-state Potts model.
Monte Carlo Simulation of Alloy Phase Diagrams and Short-Range Order
1986
As a prototype model for order-disorder phenomena in binary alloys, a face-centered cubic lattice is considered,the sites of which can be taken by either A-atoms or B-atoms, assuming pair-wise interactions between nearest (J) and next nearest neighbours (J). The phase diagram is constructed from Monte Carlo calculations. Some technical aspects essential for the success of such calculations are briefly mentioned (use of grand-canonical rather than canonical ensemble, how to obtain the free energy needed to locate first-order phase transitions, etc.). It is shown that the topology of the phase diagram changes when the ratio R = Jnnn/Jnn is varied, and this behaviour is discussed in the contex…
Simulation studies of gas-liquid transitions in two dimensions via a subsystem-block-density distribution analysis
1993
The finite-size scaling analysis of the density distribution function of subsystems of a system studied at constant total density is studied by a comparative investigation of two models: (i) the nearest-neighbor lattice gas model on the square lattice, choosing a total lattice size of 64×64 sites. (ii) The two-dimensional off-lattice Lennard-Jones system (truncated at a distance of 2.5 σ, σ being the range parameter of the interaction) withN=4096 particles, applying the NVT ensemble. In both models, the density distribution functionPL(ρ) is obtained forL×L subsystems for a wide range of temperaturesT, subblock linear dimensionsL and average densities . Particular attention is paid to the qu…
Replica-exchange molecular dynamics simulation for supercooled liquids
2000
We investigate to what extend the replica-exchange Monte Carlo method is able to equilibrate a simple liquid in its supercooled state. We find that this method does indeed allow to generate accurately the canonical distribution function even at low temperatures and that its efficiency is about 10-100 times higher than the usual canonical molecular dynamics simulation.
CLASSIFICATION THEORY FOR PHASE TRANSITIONS
1993
A refined classification theory for phase transitions in thermodynamics and statistical mechanics in terms of their orders is introduced and analyzed. The refined thermodynamic classification is based on two independent generalizations of Ehrenfests traditional classification scheme. The statistical mechanical classification theory is based on generalized limit theorems for sums of random variables from probability theory and the newly defined block ensemble limit. The block ensemble limit combines thermodynamic and scaling limits and is similar to the finite size scaling limit. The statistical classification scheme allows for the first time a derivation of finite size scaling without reno…
Driven Brownian particle as a paradigm for a nonequilibrium heat bath: Effective temperature and cyclic work extraction
2017
We apply the concept of a frequency-dependent effective temperature based on the fluctuation-dissipation ratio to a driven Brownian particle in a nonequilibrium steady state. Using this system as a thermostat for a weakly coupled harmonic oscillator, the oscillator thermalizes according to a canonical distribution at the respective effective temperature across the entire frequency spectrum. By turning the oscillator from a passive "thermometer" into a heat engine, we realize the cyclic extraction of work from a single thermal reservoir, which is feasible only due to its nonequilibrium nature.
Finite-size scaling in a microcanonical ensemble
1988
The finite-size scaling technique is extended to a microcanonical ensemble. As an application, equilibrium magnetic properties of anL×L square lattice Ising model are computed using the microcanonical ensemble simulation technique of Creutz, and the results are analyzed using the microcanonical ensemble finite-size scaling. The computations were done on the multitransputer system of the Condensed Matter Theory Group at the University of Mainz.
Classical and Quantum Two-Dimensional Fluids in the Gibbs Ensemble
1994
We study the properties of model fluids in two spatial dimensions with Gibbs ensemble Monte Carlo (GEMC) techniques. In particular in the first part of the paper we study the entropy driven phase separation in case of a nonadditive symmetric hard disc fluid and locate by a combination of GEMC with finite size scaling techniques the critical line of nonadditivities as a function of the system density, which separates the mixing/demixing regions, we compare with a simple approximation. In the second part we successfully combine path integral Monte Carlo (PIMC) and GEMC techniques in order to locate the gas-liquid coexistence densities for a fluid with classical degrees of freedom and internal…