scholarly journals A multifractal analysis for cuspidal windings on hyperbolic surfaces

2021 ◽  
pp. 2140007
Author(s):  
Johannes Jaerisch ◽  
Marc Kesseböhmer ◽  
Sara Munday
Keyword(s):  
Free Energy ◽  
Energy Function ◽  
Multifractal Spectrum ◽  
Iterated Function Systems ◽  
Legendre Transform ◽  
Scaling Exponent ◽  
Free Energy Function ◽  
Winding Number ◽  
Iterated Function ◽  
The Mean

In this paper, we investigate the multifractal decomposition of the limit set of a finitely generated, free Fuchsian group with respect to the mean cusp-winding number. We completely determine its multifractal spectrum by means of a certain free energy function and show that the Hausdorff dimension of sets consisting of limit points with the same scaling exponent coincides with the Legendre transform of this free energy function. As a by-product we generalize previously obtained results on the multifractal formalism for infinite iterated function systems to the setting of infinite graph directed Markov systems.

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.

scholarly journals Run-and-Tumble Motion: The Role of Reversibility

2021 ◽  
Vol 183 (3) ◽  
Author(s):  
Bart van Ginkel ◽  
Bart van Gisbergen ◽  
Frank Redig
Keyword(s):  
Free Energy ◽  
Diffusion Coefficient ◽  
Large Deviations ◽  
Energy Function ◽  
Internal State ◽  
Rate Function ◽  
Free Energy Function ◽  
Large Deviations Principle ◽  
Preferred Direction ◽  
State Process

AbstractWe study a model of active particles that perform a simple random walk and on top of that have a preferred direction determined by an internal state which is modelled by a stationary Markov process. First we calculate the limiting diffusion coefficient. Then we show that the ‘active part’ of the diffusion coefficient is in some sense maximal for reversible state processes. Further, we obtain a large deviations principle for the active particle in terms of the large deviations rate function of the empirical process corresponding to the state process. Again we show that the rate function and free energy function are (pointwise) optimal for reversible state processes. Finally, we show that in the case with two states, the Fourier–Laplace transform of the distribution, the moment generating function and the free energy function can be computed explicitly. Along the way we provide several examples.

Modeling and Simulation of Damage Processes based on a Gradient-Enhanced Free Energy Function

PAMM ◽  
2014 ◽  
Vol 14 (1) ◽  
pp. 151-152
Author(s):  
Stephan Schwarz ◽  
Philipp Junker ◽  
Klaus Hackl
Keyword(s):  
Free Energy ◽  
Modeling And Simulation ◽  
Energy Function ◽  
Free Energy Function ◽  
Damage Processes

scholarly journals Automated docking using a Lamarckian genetic algorithm and an empirical binding free energy function

1998 ◽  
Vol 19 (14) ◽  
pp. 1639-1662 ◽  
Author(s):  
Garrett M. Morris ◽  
David S. Goodsell ◽  
Robert S. Halliday ◽  
Ruth Huey ◽  
William E. Hart ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Free Energy ◽  
Energy Function ◽  
Binding Free Energy ◽  
Free Energy Function ◽  
Lamarckian Genetic Algorithm ◽  
Automated Docking
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