The effect of internal and global modes on the radial distribution function of confined semiflexible polymers

The constraints imposed by nano- and microscale confinement on the conformational degrees of freedom of thermally fluctuating biopolymers are utilized in contemporary nano-devices to specifically elongate and manipulate single chains. A thorough theoretical understanding and quantification of the statistical conformations of confined polymer chains is thus a central concern in polymer physics. We present an analytical calculation of the radial distribution function of harmonically confined semiflexible polymers in the weakly bending limit. Special emphasis has been put on a proper treatment of global modes, i.e. the possibility of the chain to perform global movements within the channel. We show that the effect of these global modes significantly impacts the chain statistics in cases of weak and intermediate confinement. Comparing our analytical model to numerical data from Monte Carlo simulations we find excellent agreement over a broad range of parameters.Comment: 6 pages, 3 figures typo corrected, slightly revised line of reasoning, results unchange

A Critical Assessment of the Boltzmann Approach for Active Systems

Generic models of propelled particle systems posit that the emergence of polar order is driven by the competition between local alignment and noise. Although this notion has been confirmed employing the Boltzmann equation, the range of applicability of this equation remains elusive. We introduce a broad class of mesoscopic collision rules and analyze the prerequisites for the emergence of polar order in the framework of kinetic theory. Our findings suggest that a Boltzmann approach is appropriate for weakly aligning systems but is incompatible with experiments on cluster forming systems.Comment: 11 pages, 3 figure

Role of particle conservation in self-propelled particle systems

Actively propelled particles undergoing dissipative collisions are known to develop a state of spatially distributed coherently moving clusters. For densities larger than a characteristic value, clusters grow in time and form a stationary well-ordered state of coherent macroscopic motion. In this work we address two questions. (i) What is the role of the particles’ aspect ratio in the context of cluster formation, and does the particle shape affect the system’s behavior on hydrodynamic scales? (ii) To what extent does particle conservation influence pattern formation? To answer these questions we suggest a simple kinetic model permitting us to depict some of the interaction properties between freely moving particles and particles integrated in clusters. To this end, we introduce two particle species: single and cluster particles. Specifically, we account for coalescence of clusters from single particles, assembly of single particles on existing clusters, collisions between clusters and cluster disassembly. Coarse graining our kinetic model, (i) we demonstrate that particle shape (i.e. aspect ratio) shifts the scale of the transition density, but does not impact the instabilities at the ordering threshold and (ii) we show that the validity of particle conservation determines the existence of a longitudinal instability, which tends to amplify density heterogeneities locally, and in turn triggers a wave pattern with wave vectors parallel to the axis of macroscopic order. If the system is in contact with a particle reservoir, this instability vanishes due to a compensation of density heterogeneities

Treatment of renal stones by extracorporeal shockwave lithotripsy - An update

Aim: Despite the extensive experience with minimal invasive stone therapy, there are still different views on the ideal management of renal stones. Materials and Methods: Analysis of the literature includes more than 14,000 patients. We have compared these data with long-term results of two major stone centers in Germany. The results have been compared concerning the anatomical kidney situation, stone size, stone localization and observation time. Results: According to the importance of residual fragments following extracorporeal shock wave lithotripsy (ESWL), we have to distinguish between clinically insignificant residual fragments and clinically significant residual fragments (CIRF). 24 months following ESWL stone passage occurs as a continous process, and if there are no clinical symptoms, any endoscopic procedure should be considered as overtreatment. According to these results, stone-free rates of patients increase in longer follow-up periods. Newer ESWL technology has increased the percentage of CIRF. Conclusion: We consider ESWL in most patients with renal calculi as first-line treatment, except in patients with renal calculi bigger than 30 mm in diameter. Copyright (C) 2001 S. Karger AG, Basel

Longitudinal Response of Confined Semiflexible Polymers

The longitudinal response of single semiflexible polymers to sudden changes in externally applied forces is known to be controlled by the propagation and relaxation of backbone tension. Under many experimental circumstances, realized, e.g., in nano-fluidic devices or in polymeric networks or solutions, these polymers are effectively confined in a channel- or tube-like geometry. By means of heuristic scaling laws and rigorous analytical theory, we analyze the tension dynamics of confined semiflexible polymers for various generic experimental setups. It turns out that in contrast to the well-known linear response, the influence of confinement on the non-linear dynamics can largely be described as that of an effective prestress. We also study the free relaxation of an initially confined chain, finding a surprising superlinear t^(9/8) growth law for the change in end-to-end distance at short times.Comment: 18 pages, 1 figur

Bridging the gap between single-cell migration and collective dynamics

Motivated by the wealth of experimental data recently available, we present a cellularautomaton-based modeling framework focussing on high-level cell functions and their concerted effect on cellular migration patterns. Specifically, we formulate a coarse-grained description of cell polarity through self-regulated actin organization and its response to mechanical cues. Furthermore, we address the impact of cell adhesion on collective migration in cell cohorts. The model faithfully reproduces typical cell shapes and movements down to the level of single cells, yet allows for the efficient simulation of confluent tissues. In confined circular geometries, we find that specific properties of individual cells (polarizability;contractility) influence the emerging collective motion of small cell cohorts. Finally, we study the properties of expanding cellular monolayers (front morphology;stress and velocity distributions) at the level of extended tissues

Harmonically confined, semiflexible polymer in a channel: response to a stretching force and spatial distribution of the endpoints

We consider an inextensible, semiflexible polymer or worm-like chain which is confined in the transverse direction by a parabolic potential and subject to a longitudinal force at the ends, so that the polymer is stretched out and backfolding is negligible. Simple analytic expressions for the partition function, valid in this regime, are obtained for chains of arbitrary length with a variety of boundary conditions at the ends. The spatial distribution of the end points or radial distribution function is also analyzed.Comment: 14 pages including figure