An Avoidance Model for Short-Range Order Induced by Soft Repulsions in Systems of Rigid Rods

1996 ◽  
Vol 463 ◽  
Author(s):  
Jining Han ◽  
Judith Herzfeld
Keyword(s):  
Short Range ◽  
Short Range Order ◽  
Mean Field ◽  
Axial Ratio ◽  
Field Approximation ◽  
Particle Systems ◽  
Range Order ◽  
Mean Field Approximation ◽  
Hard Particle ◽  
Rigid Rods

ABSTRACTThe effects of soft repulsions on hard particle systems are calculated using an avoidance model which improves upon the simple mean field approximation. The method not only yields a better free energy, but also gives an estimate for the short-range positional order induced by soft repulsions. The results indicate little short-range order for isotropically oriented rods. However, for parallel rods short-range order increases to significant levels as the particle axial ratio increases.

Short-range order in ND4Br studied by diffuse neutron scattering

1971 ◽  
Vol 27 (4) ◽  
pp. 348-353 ◽  
Author(s):  
R. S. Seymour
Keyword(s):  
Ising Model ◽  
Short Range ◽  
Short Range Order ◽  
Field Approximation ◽  
Range Order ◽  
Mean Field Approximation ◽  
Ammonium Ion ◽  
Ammonium Bromide ◽  
Hydrogen Atoms ◽  
Diffuse Intensity

Diffuse elastic scattering of neutrons has been observed from a single crystal of deuterated ammonium bromide and is interpreted as being due to short-range order among ammonium ion orientations. Both the temperature dependence of the diffuse intensity and its distribution in reciprocal space can be described in terms of a simple Ising model of the order-disorder transition. An expression for the diffuse intensity obtained from the mean-field approximation to the Ising model is least-squares fitted to the data. Interactions between first, second and third nearest neighbour ammonium ions have to be included in the model to give an adequate fit. The interaction energies so obtained are compared with calculations based on a simple electrostatic theory, For agreement, a charge of 0.358e on hydrogen atoms and a polarizability of 1.40 Å3 for Br− ions have to be assumed in the calculations and the significance of these unlikely values is discussed.

Molecular statistical theory of nematic liquid crystals

1971 ◽  
Vol 27 (4) ◽  
pp. 303-313 ◽  
Author(s):  
S. Chandrasekhar ◽  
N. V. Madhusudana
Keyword(s):  
Statistical Theory ◽  
Liquid Phase ◽  
Long Range ◽  
Short Range ◽  
Short Range Order ◽  
Orientational Order ◽  
Field Approximation ◽  
Quantitative Agreement ◽  
Range Order ◽  
Mean Field Approximation

Assuming a model based on permanent dipole-dipole, dispersion, induction and repulsion forces, the potential energy of a molecule in a nematic liquid crystal is derived as a function of its orientation. Analysis of the temperature variation of the degree of orientational order in p-azoxyanisole (PAA) and p-azoxyphenetole (PAP) indicates that the permanent dipole interactions are relatively unimportant. Making use of a mean field approximation, a statistical theory of long-range orientational order is developed and the thermodynamic properties of the ordered system are derived relative to those of the completely disordered one. Application of the theory to PAA and PAP shows conclusively that a certain degree of short-range orientational order is present in the liquid phase. Using just three parameters for each compound, viz. the two constants of the potential function and a numerical factor to allow for short range order, the following physical properties have been evaluated which are in quantitative agreement with the experimental data: the long-range orientational order parameter, specific heat and compressibility as functions of temperature in the liquid crystalline range, the latent heat and volume change at the nematic-isotropic transition point. The magnetic birefringence of the liquid phase affords an independent estimate of the short range order which supports the previous calculations.

scholarly journals Quadratic short-range order corrections to the mean-field free energy

1998 ◽  
Vol 10 (42) ◽  
pp. L683-L689 ◽  
Author(s):  
Igor Tsatskis
Keyword(s):  
Free Energy ◽  
Short Range ◽  
Short Range Order ◽  
Mean Field ◽  
Range Order ◽  
The Mean

scholarly journals Classical transverse Ising spin glass with short-range interactions beyond the mean-field approximation

1998 ◽  
Vol 31 (27) ◽  
pp. 5733-5739 ◽  
Author(s):  
K Walasek ◽  
K Lukierska-Walasek ◽  
L De Cesare ◽  
I Rabuffo
Keyword(s):  
Spin Glass ◽  
Short Range ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Ising Spin Glass ◽  
Ising Spin ◽  
The Mean

scholarly journals Controlling the Short-Range Order and Packing Densities of Many-Particle Systems

2002 ◽  
Vol 106 (43) ◽  
pp. 11406-11406 ◽  
Author(s):  
S. Torquato ◽  
F. H. Stillinger
Keyword(s):  
Short Range ◽  
Short Range Order ◽  
Particle Systems ◽  
Range Order ◽  
Packing Densities

Long-Range Order and Short-Range Order in Pd3V: Breakdown of the Mean Field Theory

1989 ◽  
pp. 107-111 ◽  
Author(s):  
F. Solal ◽  
R. Caudron ◽  
A. Finel
Keyword(s):  
Field Theory ◽  
Long Range ◽  
Short Range ◽  
Short Range Order ◽  
Mean Field Theory ◽  
Mean Field ◽  
Range Order ◽  
Long Range Order ◽  
The Mean

scholarly journals Small-scale spatial structure affects predator-prey dynamics and coexistence

2019 ◽  
Author(s):  
Anudeep Surendran ◽  
Michael Plank ◽  
Matthew Simpson
Keyword(s):  
Spatial Structure ◽  
Spatial Variability ◽  
Short Range ◽  
Community Dynamics ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Small Scale ◽  
Individual Based Model ◽  
Predator Prey

AbstractSmall-scale spatial variability can affect community dynamics in many ecological and biological processes, such as predator-prey dynamics and immune responses. Spatial variability includes short-range neighbour-dependent interactions and small-scale spatial structure, such as clustering where individuals aggregate together, and segregation where individuals are spaced apart from one another. Yet, a large class of mathematical models aimed at representing these processes ignores these factors by making a classical mean-field approximation, where interactions between individuals are assumed to occur in proportion to their average density. Such mean-field approximations amount to ignoring spatial structure. In this work, we consider an individual based model of a two-species community that is composed of consumers and resources. The model describes migration, predation, competition and dispersal of offspring, and explicitly gives rise to varying degrees of spatial structure. We compare simulation results from the individual based model with the solution of a classical mean-field approximation, and this comparison provides insight into how spatial structure can drive the system away from mean-field dynamics. Our analysis reveals that mechanisms leading to intraspecific clustering and interspecific segregation, such as short-range predation and short-range dispersal, tend to increase the size of the resource species relative to the mean-field prediction. We show that under certain parameter regimes these mechanisms lead to the extinction of consumers whereas the classical mean-field model predicts the coexistence of both species.

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