Speed Selection Mechanism for Propagating Fronts in Reaction-Diffusion Systems with Multiple Fields

We introduce a speed selection mechanism for front propagation in reaction-diffusion systems with multiple fields. This mechanism applies to pulled and pushed fronts alike, and operates by restricting the fields to large "finite" intervals in the comoving frames of reference. The unique velocity for which the center of a monotonic solution for a particular field is insensitive to the location of the ends of the finite interval is the velocity that is physically selected for that field, making thus the solution approximately translation invariant. The fronts for the various fields may propagate at different speeds, all of them being determined through this mechanism. We present analytic results for the case of piecewise parabolic potentials, and numerical results for other cases.Comment: TeX file, 18 pages and 5 postscript figures, to appear in Physical Review

Formation, dissolution and properties of surface nanobubbles

Surface nanobubbles are stable gaseous phases in liquids that form on solid substrates. While their existence has been confirmed, there are many open questions related to their formation and dissolution processes along with their structures and properties, which are difficult to investigate experimentally. To address these issues, we carried out molecular dynamics simulations based on atomistic force fields for systems comprised of water, air (N2 and O2), and a Highly Oriented Pyrolytic Graphite (HOPG) substrate. Our results provide insights into the formation/dissolution mechanisms of nanobubbles and estimates for their density, contact angle, and surface tension. We found that the formation of nanobubbles is driven by an initial nucleation process of air molecules and the subsequent coalescence of the formed air clusters. The clusters form favorably on the substrate, which provides an enhanced stability to the clusters. In contrast, nanobubbles formed in the bulk either move randomly to the substrate and spread or move to the water--air surface and pop immediately. Moreover, nanobubbles consist of a condensed gaseous phase with a surface tension smaller than that of an equivalent system under atmospheric conditions, and contact angles larger than those in the equivalent nanodroplet case. We anticipate that this study will provide useful insights into the physics of nanobubbles and will stimulate further research in the field by using all-atom simulations

A study for the static properties of symmetric linear multiblock copolymers under poor solvent conditions

We use a standard bead-spring model and molecular dynamics simulations to study the static properties of symmetric linear multiblock copolymer chains and their blocks under poor solvent conditions in a dilute solution from the regime close to theta conditions, where the chains adopt a coil-like formation, to the poorer solvent regime where the chains collapse obtaining a globular formation and phase separation between the blocks occurs. We choose interaction parameters as is done for a standard model, i.e., the Lennard-Jones fluid and we consider symmetric chains, i.e., the multiblock copolymer consists of an even number $n$ of alternating chemically different A and B blocks of the same length $N_{A}=N_{B}=N$. We show how usual static properties of the individual blocks and the whole multiblock chain can reflect the phase behavior of such macromolecules. Also, how parameters, such as the number of blocks $n$ can affect properties of the individual blocks, when chains are in a poor solvent for a certain range of $n$. A detailed discussion of the static properties of these symmetric multiblock copolymers is also given. Our results in combination with recent simulation results on the behavior of multiblock copolymer chains provide a complete picture for the behavior of these macromolecules under poor solvent conditions, at least for this most symmetrical case. Due to the standard choice of our parameters, our system can be used as a benchmark for related models, which aim at capturing the basic aspects of the behavior of various biological systems.Comment: 13 pages, 11 figure

Emergence of Approximate Translation Invariance in Finite Intervals as a Speed Selection Mechanism for Propagating Fronts

We introduce a new velocity selection criterion for fronts propagating into unstable and metastable states. We restrict these fronts to large finite intervals in the comoving frame of reference and require their centers be insensitive to the locations of the ends of the finite intervals, exhibiting thus effectively an approximate translation invariance. Only one monotonic front has this behavior and its velocity is the one that is physically selected. We present analytic results in the case of piecewise parabolic potentials, and numerical results in other cases.Comment: 11 pages LaTex with 3 Postscipt Figures. To appear in Physical Review

Structure of bottle-brush brushes under good solvent conditions. A molecular dynamics study

We report a simulation study for bottle-brush polymers grafted on a rigid backbone. Using a standard coarse-grained bead-spring model extensive molecular dynamics simulations for such macromolecules under good solvent conditions are performed. We consider a broad range of parameters and present numerical results for the monomer density profile, density of the untethered ends of the grafted flexible backbones and the correlation function describing the range that neighboring grafted bottle-brushes are affected by the presence of the others due to the excluded volume interactions. The end beads of the flexible backbones of the grafted bottle-brushes do not access the region close to the rigid backbone due to the presence of the side chains of the grafted bottle-brush polymers, which stretch further the chains in the radial directions. Although a number of different correlation lengths exist as a result of the complex structure of these macromolecules, their properties can be tuned with high accuracy in good solvents. Moreover, qualitative differences with "typical" bottle-brushes are discussed. Our results provide a first approach to characterizing such complex macromolecules with a standard bead spring model.Comment: To appear in Journal of Physics Condensed Matter (2011