36 research outputs found
Wetting on a spherical-shell substrate
No full textA density-functional theory for the wetting of an inert spherical-shell substrate by a single-component bulk vapor is developed, on the basis of the usual assumption that the pairwise intermolecular interaction is divided into a repulsive hard sphere and a weak attractive part. The substrate vapor-molecule pairwise interaction is also divided into a hard-wall repulsive interaction and a weak attractive tail. Choosing the attractive interactions properly, a second-order nonlinear functional differential equation results, which is solved numerically with appropriate boundary conditions. It is shown that the wetting layer, formed on the adsorbent, is either a thin or a thick film of finite thickness. Furthermore, in some cases the substrate is not at all wet. The wall-vapor and other interfacial tensions, the associated radii, and the principal tensors (the transverse pT(r) and normal pN(r)) are also calculated. The wall-vapor interface is mainly under tension (pN(r) > pT(r))
The random field Ising model with an asymmetric and anisotropic trimodal probability distribution
No full textThe Ising model in the presence of a random field, drawn from the asymmetric and anisotropic trimodal probability distribution P( hi)=pδ(hi-h0)+qδ( hi+λ*h0)+rδ(hi), is investigated. The partial probabilities p,q,r take on values within the interval [0,1] consistent with the constraint p+q+r=1; asymmetric distribution, hi is the random field variable with basic absolute value h0 (strength); λ is the competition parameter, which is the ratio between the respective strength of the random magnetic field in the two principal directions (+z) and (-z) and is positive so that the random fields are competing, anisotropic distribution. This probability distribution is an extension of the bimodal one allowing for the existence in the lattice of non magnetic particles or vacant sites. The current random field Ising system displays mainly second order phase transitions, which, for some values of p,q and h0, are followed by first order phase transitions joined smoothly by a tricritical point; occasionally, two tricritical points appear implying another second order phase transition. In addition to these points, re-entrant phenomena can be seen for appropriate ranges of the temperature and random field for specific values of λ, p and q. Using the variational principle, we write down the equilibrium equation for the magnetization and solve it for both phase transitions and at the tricritical point in order to determine the magnetization profile with respect to h0, considered as an independent variable in addition to the temperature. © 2012 Elsevier B.V. All rights reserved
Monte Carlo analysis of the critical properties of the two-dimensional randomly bond-diluted Ising model via Wang-Landau algorithm
No full textThe influence of random bond-dilution on the critical properties of the two-dimensional Ising model on a square lattice with periodic boundary conditions is presented using the Monte Carlo process with WangLandau sampling. The lattice linear size is L=20140 and the concentration of the diluted bonds spans a wide range from weak to strong dilution, namely, q=0.05,0.1,0.2,0.3,0.4; the respective percolation limit for the square lattice is qcPERC=0.5. Its pure version (q=0) has a second-order phase transition with vanishing specific heat critical exponent, an example of inapplicability of the Harris criterion. The main effort is focused on the temperature dependence of the specific heat and magnetic susceptibility to estimate the respective maximum values and subsequent pseudocritical temperatures for extracting the relative critical exponents. We have also looked at the probability distribution of the susceptibility, pseudocritical temperature and specific heat for assessing self-averaging. The study is carried out in the appropriately restricted but dominant energy subspaces. By applying the finite-size scaling analysis, the critical exponents are estimated; the specific heat exponent vanishes, the correlation-length exponent ν is equal to one and the critical exponents' ratio (γν) retains its pure-Ising-model value, thus supporting the strong universality hypothesis. © 2010 Elsevier B.V. All rights reserved
Polydispersity effect on the spectrum of light scattered by polymers with nearest- and next-nearest-neighbour interactions
No full textThe effect of polydispersity on the total integrated intensity and spectral density of light scattered by linear polymers in dilute solution is studied. Use is made of the chain model with nearest- and next-nearest-neighbour linear interactions. The length distribution is chosen to be that of Schulz. The analysis proceeds via normal mode decomposition, and the centre of mass contribution to the spectral density—as well as that of the normal modes, with and without mixing—becomes visible. The influence of polydispersity and elastic constants is significantly manifested in the normal mode contributions, and the spectral density curves of the polydisperse system are narrower than those of the monodisperse case. © 1982 Taylor & Francis Ltd
The random field Ising model with an asymmetric trimodal probability distribution
No full textThe Ising model in the presence of a random field is investigated within the mean field approximation based on Landau expansion. The random field is drawn from the trimodal probability distribution P(hi)= pδ(hi-h0)+qδ(hi+h 0)+rδ(hi), where the probabilities p,q,r take on values within the interval [0,1] consistent with the constraint p+q+r=1 (asymmetric distribution), hi is the random field variable and h 0 the respective strength. This probability distribution is an extension of the bimodal one allowing for the existence in the lattice of non magnetic particles or vacant sites. The current random field Ising system displays second order phase transitions, which, for some values of p,q and h0, are followed by first order phase transitions, thus confirming the existence of a tricritical point and in some cases two tricritical points. Also, reentrance can be seen for appropriate ranges of the aforementioned variables. Using the variational principle, we determine the equilibrium equation for magnetization, solve it for both transitions and at the tricritical point in order to determine the magnetization profile with respect to h 0. © 2011 Elsevier B.V. All rights reserved
The Sherrington-Kirkpatrick spin glass model in the presence of a random field with a joint Gaussian probability density function for the exchange interactions and random fields
No full textThe magnetic systems with disorder form an important class of systems, which are under intensive studies, since they reflect real systems. Such a class of systems is the spin glass one, which combines randomness and frustration. The Sherrington-Kirkpatrick Ising spin glass with random couplings in the presence of a random magnetic field is investigated in detail within the framework of the replica method. The two random variables (exchange integral interaction and random magnetic field) are drawn from a joint Gaussian probability density function characterized by a correlation coefficient ρ. The thermodynamic properties and phase diagrams are studied with respect to the natural parameters of both random components of the system contained in the probability density. The de Almeida-Thouless line is explored as a function of temperature, ρ and other system parameters. The entropy for zero temperature as well as for non zero temperatures is partly negative or positive, acquiring positive branches as h0 increases. © 2013 Elsevier B.V. All rights reserved
Wetting and structure of a fluid in a spherical cavity
No full textThe equilibrium local densities, structure, and wetting of a one-component fluid in a spherical cavity, of variable radius R, are determined, using density-functional theory, as functions of two parameters characterizing the system: the radius R and the cavity/fluid potential parameter [formula presented] The cavity acts as an external potential [formula presented] on the molecules of the confined fluid, the particles of which are of constant diameter d. The equilibrium density profile, as a result of strong confinement, develops peaks in the center of the cavity and/or close to the pore wall and, in certain situations, in other intermediate points; the cavity can also be liquid full, capillary condensation. © 2002 The American Physical Society
The random-field Ising model with asymmetric bimodal probability distribution
No full textThe Ising model, in the presence of a random field, is investigated within the mean-field approximation based on Landau expansion. The random field is drawn from the bimodal probability distribution P(h)=pδ(h-h0)+(1-p) δ(h+h0), where the probability p assumes any value within the interval [0,1], asymmetric distribution. The prevailing transitions are of second-order but, for some values of p and h0, first-order phase transitions take place for smaller temperatures and higher h0, thus confirming the existence of a tricritical point. Also, the possible reentrant phenomena in the phase diagram (T-h0 plane) occur for appropriate values of p and h0. Using the variational principle, we determine the equilibrium equation for magnetization and solve it for both transitions and at the tricritical point in order to determine the magnetization profile with respect to h0. © 2010 Elsevier B.V. All rights reserved
