Related papers: Polymers with spatial or topological constraints: …
Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space,…
In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…
We use the implicitization procedure to generate polynomial equality constraints on the set of distributions induced by local interventions on variables governed by a causal Bayesian network with hidden variables. We show how we may reduce…
A selection of open problems in the theory of composites is presented. Particular attention is drawn to the question of whether two-dimensional, two-phase, composites with general geometries have the same set of possible effective tensors…
In this paper, ideas of open ball, closed ball, compact set are introduced and some related basic properties are studied. Some topological properties and some other well known results of metric spaces including Cantor intersection theorem…
We present a unified theory for the longitudinal dynamic response of a stiff polymer in solution to various external perturbations (mechanical excitations, hydrodynamic flows, electrical fields, temperature quenches ...) that can be…
The formation of (bio)molecular condensates via liquid-liquid phase separation in cells has received increasing attention, as these coacervates play important functional and regulatory roles within biological systems. However, the majority…
This article is meant as a gentle introduction to the "topological terms" that often play a decisive role in effective theories describing topological quantum effects in condensed matter systems. We first take up several prominent examples,…
The cavitation flow of linear-polymer solutions around a cylinder is studied by performing a large-scale molecular dynamics simulation. The addition of polymer chains remarkably suppresses the cavitation. The polymers are stretched into a…
This is a survey on tropical polytopes from the combinatorial point of view and with a focus on algorithms. Tropical convexity is interesting because it relates a number of combinatorial concepts including ordinary convexity, monomial…
During the life cycle of bacterial cells the non-mixing of the two ring-shaped daughter genomes is an important prerequisite for the cell division process. Mimicking the environments inside highly crowded biological cells, we study the…
We review a recently proposed theory of random packings. We describe the volume fluctuations in jammed matter through a volume function, amenable to analytical and numerical calculations. We combine an extended statistical mechanics…
Under high cylindrical confinement, segments of ring polymers can be localized along the long axis of the cylinder by introducing internal loops within the ring polymer. The emergent organization of the polymer segments occurs because of…
We study the static properties of a semiflexible polymer exposed to a quenched random environment by means of computer simulations. The polymer is modeled as two-dimensional Heisenberg chain. For the random environment we consider hard…
A simple application of classical density functional theory is derived and applied to a system of polymers grafted to a plane. The system is assumed to have symmetry in directions parallel to the grafting plane hence it being a…
We numerically study Turing patterns (TPs) on two-dimensional surfaces with a square boundary in ${\bf R}^3$ using a surface model for polymerized membranes. The variables used to describe the membranes correspond to two distinct degrees of…
We report molecular dynamics simulation results on the equilibrium properties of polymer thin films adsorbed onto flat and curved substrates. We first systematically determine the contact angle of polymer droplets on flat substrates as a…
Smectic materials represent a unique state between fluids and solids, characterized by orientational and partial positional order, making them notoriously difficult to model, particularly in confining geometries. We propose a complex order…
Systems under external confinement and constraints often show interesting properties. In this thesis, we study some systems under external confinement. We begin by finding out the probability distribution of end-to-end separation of a Worm…
In this paper, we construct an effective model for the dynamics of an excluded-volume chain under confinement, by extending the formalism of Rouse modes. We make specific predictions about the behavior of the modes for a single polymer…