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Computer simulations of coarse-grained molecular models for amphiphilic systems can provide insight into the the structure of amphiphiles at interfaces. They can help to identify the factors that determine the phase behavior, and they can…
A perturbative technique, the low-temperature expansion, is developed for matrix models of random surfaces. It can be applied to models with arbitrary target spaces, including ones with c>1. As a simple illustration, the series is worked…
Meanders form a set of combinatorial problems concerned with the enumeration of self-avoiding loops crossing a line through a given number of points, $n$. Meanders are considered distinct up to any smooth deformation leaving the line fixed.…
Membrane potential in a mathematical model of a cardiac myocyte can be formulated in different ways. Assuming a spatially homogeneous myocyte that is strictly charge-conservative and electroneutral as a whole, two methods will be compared:…
Single three dimensional polymers confined to a slab, i.e. to the region between two parallel plane walls, are studied by Monte Carlo simulations. They are described by $N$-step walks on a simple cubic lattice confined to the region $1 \le…
Membrane systems represent a computational model that operates in a distributed and parallel manner, inspired by the behavior of biological cells. These systems feature objects that transform within a nested membrane structure. This…
Membrane bending is an extensively studied problem from both modeling and experimental perspectives because of the wide implications of curvature generation in cell biology. Many of the curvature generating aspects in membranes can be…
We study normal functions capturing D-brane superpotentials on several one- and two-parameter Calabi-Yau hypersurfaces and complete intersections in weighted projective space. We calculate in the B-model and interpret the results using…
Two-dimensional simulations of Rayleigh-B\'enard convection at $Ra = 5\times10^{10}$ show that vertical logarithmic mean temperature profiles can be observed in regions of the boundary layer where thermal plumes are emitted. The profile is…
We examine the structure of winding toroidal and open cylindrical membranes, especially in cases where they are stretched between boundaries. Non-zero winding or stretching means that there are linear terms in the mode expansion of the…
We consider a model of bilayer lipid membrane with bola-lipids. The bola-lipid is modeled by linking tails of the hydrophobic chains in the opposite monolayers within bilayer as a first approximation. A number of thermodynamical…
Three themes of general topology: quotient spaces; absolute retracts; and inverse limits - are reapproached here in the setting of metrizable uniform spaces, with an eye to applications in geometric and algebraic topology. The results…
We consider a discrete-continuum model of a biomembrane with embedded particles. While the membrane is represented by a continuous surface, embedded particles are described by rigid discrete objects which are free to move and rotate in…
We present an area formula for continuous mappings between metric spaces, under minimal regularity assumptions. In particular, we do not require any notion of differentiability. This is a consequence of a measure theoretic notion of…
The generality of inflation in closed FRW Universe is studied for the models with a scalar field on a brane and with a complex scalar field. The results obtained are compared with the previously known results for the model with a scalar…
The liquid crystalline model biomembrane system consisting of a stack of interacting membranes is studied by the newly developed Fourier Monte Carlo simulation technique. In comparison to perturbation theory, substantial quantitative…
We present a simple, and physically motivated, coarse-grained model of a lipid bilayer, suited for micron scale computer simulations. Each ~25 nm^2 patch of bilayer is represented by a spherical particle. Mimicking forces of hydrophobic…
Maxwell equations are solved in a layer comprising a finite number of homogeneous isotropic dielectric regions ended by anisotropic perfectly matched layers (PMLs). The boundary-value problem is solved and the dispersion relation inside the…
In this paper, phase field models are developed for multi-component vesicle membranes with different lipid compositions and membranes with free boundary. These models are used to simulate the deformation of membranes under the elastic…
Lipid membranes constitute very particular materials: on the one hand, they break very easily under microscopical stretching; on the other hand, they are extremely flexible, presenting deformations even at small scales. Consequently, a…