scholarly journals Analysis of Two-Layered Random Interfaces for Two Dimensional Widom-Rowlinson's Model

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Jun Wang ◽  
Jiguang Shao ◽  
Bingtuan Wang
Keyword(s):  
Free Energy ◽  
Chemical Potential ◽  
Probability Distributions ◽  
Random Phase ◽  
Polymer Chains ◽  
Two Dimensional ◽  
Cluster Expansions ◽  
Coexisting Phases ◽  
Random Interfaces

The statistical behaviors of two-layered random-phase interfaces in two-dimensional Widom-Rowlinson's model are investigated. The phase interfaces separate two coexisting phases of the lattice Widom-Rowlinson model; when the chemical potentialμof the model is large enough, the convergence of the probability distributions which describe the fluctuations of the phase interfaces is studied. In this paper, the backbones of interfaces are introduced in the model, and the corresponding polymer chains and cluster expansions are developed and analyzed for the polymer weights. And the existence of the free energy for two-layered random-phase interfaces of the two-dimensional Widom-Rowlinson model is given.

Calculation of Equilibrium Island Morphologies for Strained Epitaxial Systems

1996 ◽  
Vol 436 ◽  
Author(s):  
R. V. Kukta ◽  
L. B. Freund
Keyword(s):  
Free Energy ◽  
Stress Distribution ◽  
Aspect Ratio ◽  
Misfit Dislocation ◽  
Chemical Potential ◽  
Equilibrium Shape ◽  
Two Dimensional ◽  
Surface Chemical ◽  
Thick Substrate ◽  
Lower Height

AbstractStrained islands grown coherently on a relatively thick substrate with similar elastic properties are considered within the framework of continuum mechanics. The condition of uniform surface chemical potential is imposed to calculate two-dimensional equilibrium island shapes. The stress distribution in the equilibrium islands is shown to be highly nonhomogeneous. The effects of introducing a single misfit dislocation at the island-substrate interface are considered. It is found that there is critical island volume above which a dislocation decreases the total free energy of the system. The dislocation alters the stress distribution in the island, causing the island to relax via mass transport to an equilibrium shape with a lower height-to-width aspect ratio and a smaller surface chemical potential than the island prior to the introduction of the dislocation.

scholarly journals A 4d $$ \mathcal{N} $$ = 1 Cardy Formula

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Joonho Kim ◽  
Seok Kim ◽  
Jaewon Song
Keyword(s):  
Black Holes ◽  
Free Energy ◽  
Asymptotic Behavior ◽  
High Temperature ◽  
Gauge Theory ◽  
Chemical Potential ◽  
Temperature Limit ◽  
Superconformal Index ◽  
High Temperature Limit ◽  
Cardy Formula

Abstract We study the asymptotic behavior of the (modified) superconformal index for 4d $$ \mathcal{N} $$ N = 1 gauge theory. By considering complexified chemical potential, we find that the ‘high-temperature limit’ of the index can be written in terms of the conformal anomalies 3c − 2a. We also find macroscopic entropy from our asymptotic free energy when the Hofman-Maldacena bound 1/2 < a/c < 3/2 for the interacting SCFT is satisfied. We study $$ \mathcal{N} $$ N = 1 theories that are dual to AdS5 × Yp,p and find that the Cardy limit of our index accounts for the Bekenstein-Hawking entropy of large black holes.

scholarly journals On the Kirchhoff-Love Hypothesis (Revised and Vindicated)

2021 ◽  
Author(s):  
Olivier Ozenda ◽  
Epifanio G. Virga
Keyword(s):  
Free Energy ◽  
Dimension Reduction ◽  
Three Dimensional ◽  
Energy Functional ◽  
The Other ◽  
Variational Model ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Kinematic Constraint ◽  
Free Energy Functional

AbstractThe Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This hypothesis has a long history checkered with the vicissitudes of life: even its paternity has been questioned, and recent rigorous dimension-reduction tools (based on standard $\varGamma $ Γ -convergence) have proven to be incompatible with it. We find that an appropriately revised version of the Kirchhoff-Love hypothesis is a valuable means to derive a two-dimensional variational model for elastic plates from a three-dimensional nonlinear free-energy functional. The bending energies thus obtained for a number of materials also show to contain measures of stretching of the plate’s mid surface (alongside the expected measures of bending). The incompatibility with standard $\varGamma $ Γ -convergence also appears to be removed in the cases where contact with that method and ours can be made.

scholarly journals The adsorption of vapours on mercury. I. Non-polar substances

1946 ◽  
Vol 187 (1008) ◽  
pp. 53-73 ◽  
Keyword(s):  
Free Energy ◽  
Total Energy ◽  
Langmuir Equation ◽  
Phase Changes ◽  
Two Dimensional ◽  
Surface Phase ◽  
Standard State ◽  
Spreading Pressure ◽  
Benzene Toluene ◽  
Entropy Of Adsorption

Reversible results for the adsorption of benzene, toluene and n -heptane vapours on mercury have been obtained. The films were found to be gaseous and obeyed the Volmer eqution F ( A - b ) = kT , where F = spreading pressure, A =area per molecule and b = co-area. The possibility that the films might be immobile was considered and the Langmuir equation was applied but found unsatisfactory. A standard state for the surface phase was defined and the free energy, total energy and entropy of adsorption evaluated. The heat of adsorption was shown to increase with the amount on the surface. A number of phase changes were found to occur after the completion of monolayer adsorp­tion, the most striking being interpreted as the change over from ‘flat’ to ‘vertical’ adsorp­tion of the toluene molecules. Others were thought to be either two-dimensional condensation or adsorption of a second layer.

The Free Energy Simulation Approach to Grain Boundary Segregation In Cu-Ni

1990 ◽  
Vol 209 ◽  
Author(s):  
H. Y. Wang ◽  
R. Najafabadi ◽  
D. J. Srolovitz ◽  
R. Lesar
Keyword(s):  
Monte Carlo ◽  
Free Energy ◽  
Grain Boundary ◽  
Chemical Potential ◽  
Boundary Segregation ◽  
Configurational Entropy ◽  
Accurate Method ◽  
Increasing Temperature ◽  
Atomic Coordinates ◽  
Good Agreement

ABSTRACTA new, accurate method for determining equilibrium segregation to defects in solids is employed to examine the segregation of Cu to grain boundaries in Cu-Ni alloys. The results are in very good agreement with the ones given by Monte Carlo. This method is based upon a point approximation for the configurational entropy, an Einstein model for vibrational contributions to the free energy. To achieve the equilibrium state of a defect in an alloy the free energy is minimized with respect to atomic coordinates and composition of each site at constant chemical potential. One of the main advantages this new method enjoys over other methods such as Monte Carlo, is the efficiency with which the atomic structure of a defect, segregation and thermodynamic properties can be determined. The grain boundary free energy can either increase or decrease with increasing temperature due to the competition between energetic and configurational entropy terms. In general, the grain boundary free energy increases with temperature when the segregation is strongest.

The effect of excluded volume on polymer dispersant action

1975 ◽  
Vol 343 (1635) ◽  
pp. 427-442 ◽  
Keyword(s):  
Free Energy ◽  
High Surface ◽  
Volume Effect ◽  
Polymer Chains ◽  
Excluded Volume ◽  
Density Distributions ◽  
Excluded Volume Effects ◽  
Adsorbed Polymer ◽  
Polymer Distribution ◽  
Dimensional Equation

Polymer-stabilized colloid particles are modelled theoretically by plane surfaces on to which polymer chains are adsorbed by one end only. Interactions between segments of the polymer are treated as an excluded volume effect. It is shown that for high surface densities the polymer distribution function exactly satisfies a one dimensional equation which is solved numerically for two values of excluded volume to give the polymer segment density distributions and the free energy of interaction for various separations of the plane surfaces. It is found that a positive value of excluded volume greatly increases the repulsive free energy compared with that for chains with zero excluded volume, particularly at large separation distances of the surfaces. Excluded volume effects must therefore play an important part in the stabilization of colloids by adsorbed polymer.

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