Search results for "NODAL"
showing 10 items of 264 documents
Concurrent molecular dynamics simulation of spinodal phase transition on transputer arrays
1990
Abstract We describe a concurrent implementation on cost-effective transputer arrays of a molecular dynamics program to efficiently simulate physical systems consisting of thousands of mobile particles with an interaction range much shorter than the system dimensions. This program, which uses a geometric decomposition strategy and includes a distributed dynamic load balancer, has been extensively tested by simulating the two-dimensional spinodal phase separation of a large Lennard-Jones system.
Double-well thermodynamic potentials and spinodal curves: how real are they?
2007
The concept of double-well thermodynamic potentials, ubiquitous since the van der Waals description of the vapour-to-liquid transition and the Landau theory of phase transitions, is critically re-examined. Particular emphasis is put on the extent to which spinodal curves (separating ‘metastable’ from ‘unstable’ states) are meaningful. It is argued that in full thermodynamic equilibrium spinodals are well-defined when one either considers finite subsystems of an infinitely large system, or systems with all linear dimensions finite. Evidence is given that in a finite (cubic) d-dimensional box the spinodals correspond (in a fluid) to the rounded ‘droplet evaporation’ or ‘bubble condensation’ t…
Time scale of protein aggregation dictated by liquid-liquid demixing
2003
The growing impact of protein aggregation pathologies, together with the current high need for extensive information on protein structures are focusing much interest on the physics underlying the nucleation and growth of protein aggregates and crystals. Sickle Cell Hemoglobin (HbS), a point-mutant form of normal human Hemoglobin (HbA), is the first recognized and best-studied case of pathologically aggregating protein. Here we reanalyze kinetic data on nucleation of deoxy-HbS aggregates by referring them to the (concentration-dependent) temperature Ts characterizing the occurrence of the phase transition of liquid-liquid demixing (LLD) of the solution. In this way, and by appropriate scalin…
Copolymer Melts in Disordered Media
1996
The symmetric AB block copolymer melt in a gel matrix with preferential adsorption of A monomers on the gel gives an example of a random-field system, which is described near the point of the microphase separation transition by the random field Landau-Brazovskii Hamiltonian. By using the technique of the 2-nd Legendre transform, the phase diagram of the system is calculated. We found that the preferential adsorption of the copolymer on the gel results in two effects: a) It decreases the temperature of the first order phase transition between disordered and ordered phase. b) There exists a region on the phase diagram at some small but finite value of the adsorption energy in which the replic…
Symmetry Breaking and Establishment of Dorsal/Ventral Polarity in the Early Sea Urchin Embryo
2015
The mechanisms imposing the Dorsal/Ventral (DV) polarity of the early sea urchin embryo consist of a combination of inherited maternal information and inductive interactions among blastomeres. Old and recent studies suggest that a key molecular landmark of DV polarization is the expression of nodal on the future ventral side, in apparent contrast with other metazoan embryos, where nodal is expressed dorsally. A subtle maternally-inherited redox anisotropy, plus some maternal factors such as SoxB1, Univin, and p38-MAPK have been identified as inputs driving the spatially asymmetric transcription of nodal. However, all the mentioned factors are broadly distributed in the embryo as early as no…
A nonlinear eigenvalue problem for the periodic scalar p-Laplacian
2014
We study a parametric nonlinear periodic problem driven by the scalar $p$-Laplacian. We show that if $\hat \lambda_1 >0$ is the first eigenvalue of the periodic scalar $p$-Laplacian and $\lambda> \hat \lambda_1$, then the problem has at least three nontrivial solutions one positive, one negative and the third nodal. Our approach is variational together with suitable truncation, perturbation and comparison techniques.
Phase diagram and structure of colloid-polymer mixtures confined between walls
2006
The influence of confinement, due to flat parallel structureless walls, on phase separation in colloid-polymer mixtures, is investigated by means of grand-canonical Monte Carlo simulations. Ultra-thin films, with thicknesses between $D=3-10$ colloid diameters, are studied. The Asakura-Oosawa model [J. Chem. Phys. 22, 1255 (1954)] is used to describe the particle interactions. To simulate efficiently, a ``cluster move'' [J. Chem. Phys. 121, 3253 (2004)] is used in conjunction with successive umbrella sampling [J. Chem. Phys. 120, 10925 (2004)]. These techniques, when combined with finite size scaling, enable an accurate determination of the unmixing binodal. Our results show that the critica…
Applications of Finite-Size-Scaling Techniques to the Simulation of Critical Fluids
1995
A finite-size scaling theory is described that takes account of the lack of symmetry between the coexisting phases of fluids. This broken symmetry is manifest in the so-called ‘field mixing’ phenomenon which is a central feature of the non-universal critical behaviour of fluids. It is shown that the presence of field mixing leads to an alteration to the limiting form of the critical energy distribution and to a finite-size correction to the critical order parameter (particle density) distribution. As a result, finite-size shifts occur in the critical particle and energy densities. The theoretical predictions are tested with an extensive Monte-Carlo study of the critical density and energy f…
Coexistence Curve Singularities at Critical End Points
1997
We report an extensive Monte Carlo study of critical end point behaviour in a symmetrical binary fluid mixture. On the basis of general scaling arguments, singular behaviour is predicted in the diameter of the liquid-gas coexistence curve as the critical end point is approached. The simulation results show clear evidence for this singularity, as well as confirming a previously predicted singularity in the coexistence chemical potential. Both singularities should be detectable experimentally.
Curvature dependence of surface free energy of liquid drops and bubbles: A simulation study.
2010
We study the excess free energy due to phase coexistence of fluids by Monte Carlo simulations using successive umbrella sampling in finite LxLxL boxes with periodic boundary conditions. Both the vapor-liquid phase coexistence of a simple Lennard-Jones fluid and the coexistence between A-rich and B-rich phases of a symmetric binary (AB) Lennard-Jones mixture are studied, varying the density rho in the simple fluid or the relative concentration x_A of A in the binary mixture, respectively. The character of phase coexistence changes from a spherical droplet (or bubble) of the minority phase (near the coexistence curve) to a cylindrical droplet (or bubble) and finally (in the center of the misc…