scholarly journals Geometric integrator for simulations in the canonical ensemble

2016 ◽  
Vol 145 (8) ◽  
pp. 084113 ◽  
Author(s):  
Diego Tapias ◽  
David P. Sanders ◽  
Alessandro Bravetti
Keyword(s):  
Canonical Ensemble ◽  
Geometric Integrator

A canonical ensemble derivation of the McMillan-Mayer solution theory

1983 ◽  
Vol 48 (10) ◽  
pp. 2888-2892 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Energy Function ◽  
Special Function ◽  
Helmholtz Free Energy ◽  
Canonical Ensemble ◽  
Free Energy Function ◽  
Solution Theory ◽  
Pure Solvent ◽  
The Common

A special free energy function is defined for a solution in the osmotic equilibrium with pure solvent. The partition function of the solution is derived at the McMillan-Mayer level and it is related to this special function in the same manner as the common partition function of the system to its Helmholtz free energy.

The Fast Multipole Method in Canonical Ensemble Dynamics on Massively Parallel Computers

1992 ◽  
Vol 278 ◽  
Author(s):  
Steven R. Lustig ◽  
J.J. Cristy ◽  
D.A. Pensak
Keyword(s):  
Canonical Ensemble ◽  
Yukawa Potential ◽  
Direct Method ◽  
Fast Multipole Method ◽  
Parallel Computers ◽  
Massively Parallel ◽  
Fast Multipole ◽  
Massively Parallel Computers ◽  
Multipole Method ◽  
Execution Times

AbstractThe fast multipole method (FMM) is implemented in canonical ensemble particle simulations to compute non-bonded interactions efficiently with explicit error control. Multipole and local expansions have been derived to implement the FMM efficiently in Cartesian coordinates for soft-sphere (inverse power law), Lennard- Jones, Morse and Yukawa potential functions. Significant reductions in execution times have been achieved with respect to the direct method. For a given number, N, of particles the execution times of the direct method scale asO(N2). The FMM execution times scale asO(N) on sequential workstations and vector processors and asymptotically0(logN) on massively parallel computers. Connection Machine CM-2 and WAVETRACER-DTC parallel FMM implementations execute faster than the Cray-YMP vectorized FMM for ensemble sizes larger than 28k and 35k, respectively. For 256k particle ensembles the CM-2 parallel FMM is 12 times faster than the Cray-YMP vectorized direct method and 2.2 times faster than the vectorized FMM. For 256k particle ensembles the WAVETRACER-DTC parallel FMM is 33 times faster than the Cray-YMP vectorized direct method.

On Bose-Einstein Condensation

1954 ◽  
Vol 50 (1) ◽  
pp. 65-76 ◽  
Author(s):  
P. T. Landsberg
Keyword(s):  
Closed System ◽  
Canonical Ensemble ◽  
Energy Levels ◽  
Volume Density ◽  
Einstein Condensation ◽  
Bose Einstein Condensation ◽  
Quantum Numbers ◽  
Finite Integer ◽  
Bose Einstein ◽  
Grand Canonical

ABSTRACTThis paper contains a proof that the description of the phenomenon of Bose-Einstein condensation is the same whether (1) an open system is contemplated and treated on the basis of the grand canonical ensemble, or (2) a closed system is contemplated and treated on the basis of the canonical ensemble without recourse to the method of steepest descents, or (3) a closed system is contemplated and treated on the basis of the canonical ensemble using the method of steepest descents. Contrary to what is usually believed, it is shown that the crucial factor governing the incidence of the condensation phenomenon of a system (open or closed) having an infinity of energy levels is the density of states N(E) ∝ En for high quantum numbers, a condition for condensation being n > 0. These results are obtained on the basis of the following assumptions: (i) For large volumes V (a) all energy levels behave like V−θ, and (b) there exists a finite integer M such that it is justifiable to put for the jth energy level Ej= c V−θand to use the continuous spectrum approximation, whenever j ≥ M c θ τ are positive constants, (ii) All results are evaluated in the limit in which the volume of the gas is allowed to tend to infinity, keeping the volume density of particles a finite and non-zero constant. The present paper also serves to coordinate much of previously published work, and corrects a current misconception regarding the method of steepest descents.

scholarly journals Phase diagram of brittle fracture in the semi-grand-canonical ensemble

2021 ◽  
Vol 103 (1) ◽  
Author(s):  
T. Mulla ◽  
S. Moeini ◽  
K. Ioannidou ◽  
R. J.-M. Pellenq ◽  
F.-J. Ulm
Keyword(s):  
Phase Diagram ◽  
Brittle Fracture ◽  
Canonical Ensemble ◽  
Grand Canonical Ensemble ◽  
Grand Canonical

scholarly journals FIELD THEORY OF N ENTANGLED POLYMERS

2000 ◽  
Vol 14 (32) ◽  
pp. 3881-3895 ◽  
Author(s):  
FRANCO FERRARI ◽  
HAGEN KLEINERT ◽  
IGNAZIO LAZZIZZERA
Keyword(s):  
Field Theory ◽  
Canonical Ensemble ◽  
Feynman Diagrams ◽  
Linking Number ◽  
Entangled Polymers

We formulate a field theory capable of describing a canonical ensemble of N polymers subjected to linking number constraints in terms of Feynman diagrams.

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