Coexisting Ordering and Phase Separation in Binary Fcc Alloys

1982 ◽  
Vol 21 ◽  
Author(s):  
P.L. Rossiter ◽  
P.J. Lawrence
Keyword(s):  
Miscibility Gap ◽  
Nearest Neighbour ◽  
Many Body ◽  
Range Interaction ◽  
Slow Cooling ◽  
Pairwise Interactions ◽  
Fcc Alloys ◽  
Many Body Interactions ◽  
Comparable Magnitude

ABSTRACTConsideration of only nearest neighbour pairwise interactions Vij in a binary alloy leads to the classification of the system as ordering (unlike near neighbours) or clustering (like near neighbours), depending upon the sign of Vij However, this simple classification loses meaning when multi-atom correlations, many-body interactions or a longer range interaction are considered. For example, the first nearest neighbour interaction may favour ordering while the second, which may be of comparable magnitude, may favour clustering. By extending the Bragg-Williams model to include second near-neighbour interactions in fcc alloys, it is shown that a miscibility gap may form in the region of the orderdisorder solvus, leading to a complicated sequence of atomicrearrangement upon slow cooling. Despite the well-known failings of the point approximation when applied to fcc alloys, the results are shown to be consistent with the unusual behaviour exhibited by some systems.

scholarly journals Cliques Are Bricks for k-CT Graphs

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1160
Author(s):  
Václav Snášel ◽  
Pavla Dráždilová ◽  
Jan Platoš
Keyword(s):  
Complex Networks ◽  
Simplicial Complex ◽  
Dynamic Properties ◽  
Simplicial Complexes ◽  
Many Body ◽  
Chemistry Industry ◽  
The Past ◽  
Pairwise Interactions ◽  
The Many ◽  
Many Body Interactions

Many real networks in biology, chemistry, industry, ecological systems, or social networks have an inherent structure of simplicial complexes reflecting many-body interactions. Over the past few decades, a variety of complex systems have been successfully described as networks whose links connect interacting pairs of nodes. Simplicial complexes capture the many-body interactions between two or more nodes and generalized network structures to allow us to go beyond the framework of pairwise interactions. Therefore, to analyze the topological and dynamic properties of simplicial complex networks, the closed trail metric is proposed here. In this article, we focus on the evolution of simplicial complex networks from clicks and k-CT graphs. This approach is used to describe the evolution of real simplicial complex networks. We conclude with a summary of composition k-CT graphs (glued graphs); their closed trail distances are in a specified range.

Group Classification of Many-Body Interactions

1967 ◽  
Vol 163 (4) ◽  
pp. 1044-1050 ◽  
Author(s):  
C. M. Vincent
Keyword(s):  
Group Classification ◽  
Many Body ◽  
Many Body Interactions

scholarly journals Bond order redefinition needed to reduce inherent noise in molecular dynamics simulations

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ibnu Syuhada ◽  
Nikodemus Umbu Janga Hauwali ◽  
Ahmad Rosikhin ◽  
Euis Sustini ◽  
Fatimah Arofiati Noor ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Bond Order ◽  
Interatomic Potential ◽  
Interatomic Potentials ◽  
Many Body ◽  
Range Interaction ◽  
Dynamics Simulations ◽  
Interaction Approach ◽  
Many Body Interactions

AbstractIn this work, we present the bond order redefinition needed to reduce the inherent noise in order to enhance the accuracy of molecular dynamics simulations. We propose defining the bond order as a fraction of energy distribution. It happens due to the character of the material in nature, which tries to maintain its environment. To show the necessity, we developed a factory empirical interatomic potential (FEIP) for carbon that implements the redefinition with a short-range interaction approach. FEIP has been shown to enhance the accuracy of the calculation of lattice constants, cohesive energy, elastic properties, and phonons compared to experimental data, and can even be compared to other potentials with the long-range interaction approach. The enhancements due to FEIP can reduce the inherent noise, then provide a better prediction of the energy based on the behaviour of the atomic environment. FEIP can also transform simple two-body interactions into many-body interactions, which is useful for enhancing accuracy. Due to implementing the bond order redefinition, FEIP offers faster calculations than other complex interatomic potentials.

scholarly journals Stability of synchronization in simplicial complexes

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
L. V. Gambuzza ◽  
F. Di Patti ◽  
L. Gallo ◽  
S. Lepri ◽  
M. Romance ◽  
...  
Keyword(s):  
Social Sciences ◽  
Dynamical Systems ◽  
Invariant Solution ◽  
Stable State ◽  
Necessary Condition ◽  
Many Body ◽  
Complete Synchronization ◽  
Stability Function ◽  
Pairwise Interactions ◽  
Many Body Interactions

AbstractVarious systems in physics, biology, social sciences and engineering have been successfully modeled as networks of coupled dynamical systems, where the links describe pairwise interactions. This is, however, too strong a limitation, as recent studies have revealed that higher-order many-body interactions are present in social groups, ecosystems and in the human brain, and they actually affect the emergent dynamics of all these systems. Here, we introduce a general framework to study coupled dynamical systems accounting for the precise microscopic structure of their interactions at any possible order. We show that complete synchronization exists as an invariant solution, and give the necessary condition for it to be observed as a stable state. Moreover, in some relevant instances, such a necessary condition takes the form of a Master Stability Function. This generalizes the existing results valid for pairwise interactions to the case of complex systems with the most general possible architecture.

A continuum model of many-body interactions in a perfect crystal

1979 ◽  
Vol 85 (2) ◽  
pp. 379-385 ◽  
Author(s):  
G. P. Parry
Keyword(s):  
Continuum Model ◽  
Perfect Crystal ◽  
Many Body ◽  
Energy Functions ◽  
Pairwise Interactions ◽  
Green Strain ◽  
Strain Energy Functions ◽  
Many Body Interactions ◽  
Cauchy Relations ◽  
Green Measure

AbstractTheoretical and numerical calculations of the mechanical properties of single crystals usually presuppose pairwise interactions between the atoms of the lattice. It follows from this assumption that the Cauchy relations hold in respect of the Green measure of strain. Here we account for many-body interactions between the atoms of the lattice. The main result is that a continuum model of n-body interactions must possess completely symmetric (n − 1)th order Green strain moduli. Existing strain energy functions, used to model crystal elasticity, are thereby given some physical significance.

scholarly journals Entropy and Entropic Forces to Model Biological Fluids

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1166
Author(s):  
Rafael M. Gutierrez ◽  
George T. Shubeita ◽  
Chandrashekhar U. Murade ◽  
Jianfeng Guo
Keyword(s):  
Complex Systems ◽  
Biological Fluids ◽  
Living Cells ◽  
Biological Information ◽  
Many Body ◽  
Range Interaction ◽  
Significant Information ◽  
Microscopic Interactions ◽  
Physical Phenomena ◽  
Many Body Interactions

Living cells are complex systems characterized by fluids crowded by hundreds of different elements, including, in particular, a high density of polymers. They are an excellent and challenging laboratory to study exotic emerging physical phenomena, where entropic forces emerge from the organization processes of many-body interactions. The competition between microscopic and entropic forces may generate complex behaviors, such as phase transitions, which living cells may use to accomplish their functions. In the era of big data, where biological information abounds, but general principles and precise understanding of the microscopic interactions is scarce, entropy methods may offer significant information. In this work, we developed a model where a complex thermodynamic equilibrium resulted from the competition between an effective electrostatic short-range interaction and the entropic forces emerging in a fluid crowded by different sized polymers. The target audience for this article are interdisciplinary researchers in complex systems, particularly in thermodynamics and biophysics modeling.

Thermodynamics of (Zn,Fe)S sphalerite. A CVM approach with large basis clusters

2000 ◽  
Vol 64 (5) ◽  
pp. 923-943 ◽  
Author(s):  
A. I. Balabin ◽  
R. O. Sack
Keyword(s):  
Long Range ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Nearest Neighbour ◽  
Many Body ◽  
Mean Values ◽  
Equilateral Triangles ◽  
Cluster Variation ◽  
Long Range Ordering ◽  
Many Body Interactions

AbstractWe have developed a cluster variation method (CVM) model based on cuboctahedral and octahedral basis clusters containing 13 and 6 atoms, respectively, and applied it to the analysis of the thermodynamic mixing properties of (Zn,Fe)S solid solutions. The model, in which the internal energy of the lattice is approximated by next to nearest neighbour (nnn) pair interactions and many-body interactions associated with nearest neighbour (nn) equilateral triangles, describes the FeS contents of sphalerites equilibrated with pyrrhotite and pyrite, and with pyrrhotite and iron metal within experimental uncertainties. The model predicts moderate deviations from ideality; the mean values of the Lewis and Randall activity coefficient of FeS and ZnS are, 1.48 and 1.03, respectively. Predictions of the model are in qualitative agreement with cell-edge data. The model also predicts that sphalerites undergo long-range ordering to lower-symmetry structures at temperatures only slightly below those investigated experimentally, a result in agreement with inferences from an existing Mössbauer investigation of synthetic sphalerites.More realistic models in which interactions are ascribed to larger species (nn triangular and centred square species) predict that such long-range ordering occurs at even higher temperatures and underscore the need for better characterization of the structures of (Zn,Fe)S minerals.

Data-Driven Many-Body Models with Chemical Accuracy for CH4/H2O Mixtures

2020 ◽  
Author(s):  
Marc Riera ◽  
Alan Hirales ◽  
Raja Ghosh ◽  
Francesco Paesani
Keyword(s):  
Liquid Phase ◽  
Quantitative Description ◽  
Liquid Mixtures ◽  
Many Body ◽  
Energy Functions ◽  
Potential Energy Functions ◽  
Dynamics Simulations ◽  
Body Potential ◽  
Small Clusters ◽  
Many Body Interactions

<div> <div> <div> <p>Many-body potential energy functions (PEFs) based on the TTM-nrg and MB-nrg theoretical/computational frameworks are developed from coupled cluster reference data for neat methane and mixed methane/water systems. It is shown that that the MB-nrg PEFs achieve subchemical accuracy in the representation of individual many-body effects in small clusters and enables predictive simulations from the gas to the liquid phase. Analysis of structural properties calculated from molecular dynamics simulations of liquid methane and methane/water mixtures using both TTM-nrg and MB-nrg PEFs indicates that, while accounting for polarization effects is important for a correct description of many-body interactions in the liquid phase, an accurate representation of short-range interactions, as provided by the MB-nrg PEFs, is necessary for a quantitative description of the local solvation structure in liquid mixtures. </p> </div> </div> </div>

Sign in / Sign up

Export Citation Format

Share Document