Hydrodynamic Model for the System of Self Propelling Particles with Conservative Kinematic Constraints; Two dimensional stationary solutions

We consider a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities. The model aims to be analogous to a discrete algorithm used in works by T. Vicsek et al. In this paper we prove that the only types of the stationary planar solutions in the model are either of translational or axial symmetry of the flow. Within the proposed model we differentiate between finite and infinite flocking behavior by the finiteness of the kinetic energy functional.Comment: 12 pages, 1 figur

Cell dynamics simulations of sphere-forming diblock copolymers in thin films on chemically patterned substrates

The morphology of sphere-forming block copolymers assembled in thin films on patterned surfaces is theoretically analyzed. The patterns on the lower surface are alternating bands of a given width distinctively attracting or repelling a given block. We find that long- range order can be achieved, and it depends on the commensurability of the characteristic length of the block domains with both band periodicity and slit thickness. The comparison of the simulation results with experimental data shows a very good agreement. Furthermore, we show that the proper selection of the band periodicity and, consequently, of the film thickness permits the system to switch from hexagonal packing to body-centered orthohedra. Therefore, we show that it exists a way to control the formation of long-range ordered structures of different types in this kind of system

Stability properties of the collective stationary motion of self-propelling particles with conservative kinematic constraints

In our previous papers we proposed a continuum model for the dynamics of the systems of self-propelling particles with conservative kinematic constraints on the velocities. We have determined a class of stationary solutions of this hydrodynamic model and have shown that two types of stationary flow, linear and radially symmetric (vortical) flow, are possible. In this paper we consider the stability properties of these stationary flows. We show, using a linear stability analysis, that the linear solutions are neutrally stable with respect to the imposed velocity and density perturbations. A similar analysis of the stability of the vortical solution is found to be not conclusive.Comment: 13 pages, 3 figure

Block copolymers confined in a nanopore: Pathfinding in a curving and frustrating flatland

We have studied structure formation in a confined block copolymer melt by means of dynamic density functional theory (DDFT). The confinement is two-dimensional, and the confined geometry is that of a cylindrical nanopore. Although the results of this study are general, our coarse-grained molecular model is inspired by an experimental lamellae-forming PS-PBD diblock copolymer system (Shin et al, Science, 306, 76 (2004)), in which an exotic toroidal structure was observed upon confinement in alumina nanopores. Our computational study shows that a zoo of exotic structures can be formed, although the majority, including the catenoid, helix and double helix that were also found in Monte Carlo (MC) nanopore studies, are metastable states. We introduce a general classification scheme and consider the role of kinetics and elongational pressure on stability and formation pathway of both equilibrium and metastable structures in detail. We find that helicity and three-fold connections mediate structural transitions on a larger scale. Moreover, by matching the remaining parameter in our mesoscopic method, the Flory-Huggins parameter, to the experimental system, we obtain a structure that resembles the experimental toroidal structure in great detail. Here, the most important factor seems to be the roughness of the pore, i.e. small variations of the pore radius on a scale that is larger than the characteristic size in the system.Comment: The following article has been accepted by JCP. After it is published, it will be found at http://jcp.aip.org

Structure, dynamics, and function of the monooxygenase P450 BM-3: insights from computer simulations studies

The monooxygenase P450 BM-3 is a NADPH-dependent fatty acid hydroxylase enzyme isolated from soil bacterium Bacillus megaterium. As a pivotal member of cytochrome P450 superfamily, it has been intensely studied for the comprehension of structure-dynamics-function relationships in this class of enzymes. In addition, due to its peculiar properties, it is also a promising enzyme for biochemical and biomedical applications. However, despite the efforts, the full understanding of the enzyme structure and dynamics is not yet achieved. Computational studies, particularly molecular dynamics (MD) simulations, have importantly contributed to this endeavor by providing new insights at an atomic level regarding the correlations between structure, dynamics, and function of the protein. This topical review summarizes computational studies based on MD simulations of the cytochrome P450 BM-3 and gives an outlook on future directions

Orientational phase transitions in the hexagonal phase of a diblock copolymer melt under shear flow

We generalize the earlier theory by Fredrickson [J. Rheol. v.38, 1045 (1994)] to study the orientational behaviour of the hexagonal phase of diblock copolymer melt subjected to steady shear flow. We use symmetry arguments to show that the orientational ordering in the hexagonal phase is a much weaker effect than in the lamellae. We predict the parallel orientation to be stable at low and the perpendicular orientation at high shear rates. Our analysis reproduces the experimental results by Tepe et al. [Macromolecules v.28, 3008 (1995)] and explains the difficulties in experimental observation of the different orientations in the hexagonal phase.Comment: 21 pages, 6 eps figures, submitted to Physical Review

Influence of confinement on the orientational phase transitions in the lamellar phase of a block copolymer melt under shear flow

In this work we incorporate some real-system effects into the theory of orientational phase transitions under shear flow (M. E. Cates and S. T. Milner, Phys. Rev. Lett. v.62, p.1856 (1989) and G. H. Fredrickson, J. Rheol. v.38, p.1045 (1994)). In particular, we study the influence of the shear-cell boundaries on the orientation of the lamellar phase. We predict that at low shear rates the parallel orientation appears to be stable. We show that there is a critical value of the shear rate at which the parallel orientation loses its stability and the perpendicular one appears immediately below the spinodal. We associate this transition with a crossover from the fluctuation to the mean-field behaviour. At lower temperatures the stability of the parallel orientation is restored. We find that the region of stability of the perpendicular orientation rapidly decreases as shear rate increases. This behaviour might be misinterpreted as an additional perpendicular to parallel transition recently discussed in literature.Comment: 25 pages, 4 figures, submitted to Phys. Rev.