A new method to locate saddle points for reactions in solution by using the free-energy gradient method and the mean field approximation

2004 ◽  
Vol 25 (10) ◽  
pp. 1227-1233 ◽  
Author(s):  
I. Fdez. Galván ◽  
M. E. Martín ◽  
M. A. Aguilar
Keyword(s):  
Free Energy ◽  
Gradient Method ◽  
Saddle Points ◽  
Mean Field ◽  
Field Approximation ◽  
New Method ◽  
Mean Field Approximation ◽  
Energy Gradient ◽  
The Mean

Geometry optimization of molecules in solution: Joint use of the mean field approximation and the free-energy gradient method

2003 ◽  
Vol 118 (1) ◽  
pp. 255-263 ◽  
Author(s):  
I. Fdez. Galván ◽  
M. L. Sánchez ◽  
M. E. Martín ◽  
F. J. Olivares del Valle ◽  
M. A. Aguilar
Keyword(s):  
Free Energy ◽  
Gradient Method ◽  
Mean Field ◽  
Geometry Optimization ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Energy Gradient ◽  
The Mean

New Method for Latticeal Mean Field Models

1997 ◽  
Vol 11 (08) ◽  
pp. 339-345 ◽  
Author(s):  
Raluca S. Bundaru
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Free Energy ◽  
Mean Field ◽  
Field Approximation ◽  
New Method ◽  
Mean Field Approximation ◽  
Mean Field Models ◽  
The Mean

We develop a new method to find the free-energy for latticealsystems of classical spins in the mean-field approximation. The simplerecurrence relation which the Hamiltonian satisfies in this case, allows us to obtain the free-energy by solving an ordinary differential equation.

scholarly journals The Possibility of Many Compensation Points in a Mixed-Spin Ising Ferrimagnetic System

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Hadey K. Mohamad
Keyword(s):  
Free Energy ◽  
Mean Field ◽  
Field Approximation ◽  
Spin Model ◽  
Mean Field Approximation ◽  
Zero Field ◽  
Mixed Spin ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
The Mean

The magnetic properties of a ferrimagnetic mixed spin-3/2 and spin-5/2 Ising model with different anisotropies are investigated by using the mean-field approximation (MFA). In particular, the effect of magnetic anisotropies on the compensation phenomenon, acting on A-atoms and B-ones for the mixed-spin model, has been considered in a zero field. The free energy of a mixed-spin Ising ferrimagnetic system from MFA of the Hamiltonian is calculated. By minimizing the free energy, we obtain the equilibrium magnetizations and the compensation points. The phase diagram of the system in the anisotropy dependence of transition temperature has been discussed as well. Our results of this model predict the existence of many (two or three) compensation points in the ordered system on a simple cubic lattice.

Active Inference, Belief Propagation, and the Bethe Approximation

2018 ◽  
Vol 30 (9) ◽  
pp. 2530-2567 ◽  
Author(s):  
Sarah Schwöbel ◽  
Stefan Kiebel ◽  
Dimitrije Marković
Keyword(s):  
Free Energy ◽  
Belief Propagation ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Active Inference ◽  
Inference Process ◽  
Bethe Approximation ◽  
Variational Free Energy ◽  
The Mean

When modeling goal-directed behavior in the presence of various sources of uncertainty, planning can be described as an inference process. A solution to the problem of planning as inference was previously proposed in the active inference framework in the form of an approximate inference scheme based on variational free energy. However, this approximate scheme was based on the mean-field approximation, which assumes statistical independence of hidden variables and is known to show overconfidence and may converge to local minima of the free energy. To better capture the spatiotemporal properties of an environment, we reformulated the approximate inference process using the so-called Bethe approximation. Importantly, the Bethe approximation allows for representation of pairwise statistical dependencies. Under these assumptions, the minimizer of the variational free energy corresponds to the belief propagation algorithm, commonly used in machine learning. To illustrate the differences between the mean-field approximation and the Bethe approximation, we have simulated agent behavior in a simple goal-reaching task with different types of uncertainties. Overall, the Bethe agent achieves higher success rates in reaching goal states. We relate the better performance of the Bethe agent to more accurate predictions about the consequences of its own actions. Consequently, active inference based on the Bethe approximation extends the application range of active inference to more complex behavioral tasks.

Simulation of Segregation to Interfaces in Metal-Oxides

1994 ◽  
Vol 357 ◽  
Author(s):  
C. Battaile ◽  
R. Najafabadi ◽  
D.J. Srolovitz
Keyword(s):  
Free Energy ◽  
Mean Field ◽  
Misfit Strain ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Free Energy Surface ◽  
Field Representation ◽  
Free Surfaces ◽  
Equilibrium Distributions ◽  
The Mean

AbstractSegregation of isovalent cation impurities to (001) and (011) free surfaces in (Co0.3Ni0.7)O and (Fe0.12Mn0.88)O was investigated using atomistic computer simulations. Impurity concentrations were represented by a mean-field approximation, and equilibrium distributions of impurities were calculated by minimization of the free energy. Surface energy effects were found to dominate segregation behavior, even when in competition with misfit strain energy effects. These Free Energy method predictions compared well with more accurate Monte Carlo simulations, suggesting that the mean-field representation of impurity concentration is satisfactory for this application.

scholarly journals On the free energy within the mean-field approximation

2006 ◽  
Vol 27 (2) ◽  
pp. 407-412 ◽  
Author(s):  
Rafael Agra ◽  
Frédéric van Wijland ◽  
Emmanuel Trizac
Keyword(s):  
Free Energy ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
The Mean

scholarly journals Merging Belief Propagation and the Mean Field Approximation: A Free Energy Approach

2013 ◽  
Vol 59 (1) ◽  
pp. 588-602 ◽  
Author(s):  
Erwin Riegler ◽  
Gunvor Elisabeth Kirkelund ◽  
Carles Navarro Manchon ◽  
Mihai-Alin Badiu ◽  
Bernard Henri Fleury
Keyword(s):  
Free Energy ◽  
Belief Propagation ◽  
Mean Field ◽  
Field Approximation ◽  
Energy Approach ◽  
Mean Field Approximation ◽  
The Mean

scholarly journals Ferrimagnetism in the Mean-Field Approximation of the Mixed Spin-3/2 and Spin-5/2 Ising System

2015 ◽  
Vol 57 ◽  
pp. 114-121 ◽  
Author(s):  
Hadey K. Mohamad
Keyword(s):  
Free Energy ◽  
Mean Field Theory ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Mixed Spin ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Bogoliubov Inequality ◽  
The Mean

Using the Mean-field theory based on Bogoliubov inequality for the free energy, a ferrimagnetic mixed spin-3/2 and spin-5/2 Ising model with different anisotropies is investigated. The free energy of a mixed spin Ising ferrimagnetic system from MF approximation of the Hamiltonian is calculated. By minimizing the free energy, we obtain the equilibrium magnetizations and compensation points. In particular, we investigate the effect of a single-ion anisotropy on the magnetic properties including the compensation phenomenon, in order to clarify the characteristic behaviours in a series of molecular-based magnets . The phase diagram of the system is also discussed in the anisotropy dependence of transition temperature. Our results of this model predict the existence of many (two or three) compensation points in the ordered system on a simple cubic lattice.

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