Related papers: Modeling Fibril Fragmentation in Real-Time
In the study of amyloid fiber formation, the fiber length distribution plays a central role. From this microscopic distribution, all macroscopic statistical quantities, like the fiber number concentration P(t) and mass concentration M(t),…
This paper presents an efficient approach to image segmentation that approximates the piecewise-smooth (PS) functional in [12] with explicit solutions. By rendering some rational constraints on the initial conditions and the final solutions…
We introduce three models of fragmentation in which the largest fragment in the system can be broken at each time step with a fixed probability, p. We solve these models exactly in the long time limit to reveal stable time invariant…
The fragmentation of filaments in molecular clouds has attracted a lot of attention as there seems to be a relation between the evolution of filaments and star formation. The study of the fragmentation process has been motivated by simple…
We present a series of simulations of the fragmentation of a molecular cloud, leading to the formation of a cluster of protostellar cores. The purpose of these simulations is to address a specific numerical problem called artificial…
Proteinaceous aggregation occurs through self-assembly-- a process not entirely understood. In a recent article [1], an analytical theory for amyloid fibril growth via secondary rather than primary nucleation was presented. Remarkably, with…
The growth-fragmentation equation arises in many different contexts, ranging from cell division, protein polymerization, biopolymers, neurosciences etc. Direct observation of temporal dynamics being often difficult, it is of main interest…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
We propose an exactly solvable simplified statistical mechanical model for the thermodynamics of beta-amyloid aggregation, generalizing a well-studied model for protein folding. The monomer concentration is explicitly taken into account as…
We consider nucleation of amyloid fibrils in the case when the process occurs by the mechanism of direct polymerization of practically fully extended protein segments, i.e. beta-strands, into beta-sheets. Applying the classical nucleation…
We present a novel platform for the large-scale simulation of fibrous structures immersed in a Stokesian fluid and evolving under confinement or in free-space. One of the main motivations for this work is to study the dynamics of fiber…
The fragmentation of small, brittle, flexible, inextensible fibers is investigated in a fully-developed, homogeneous, isotropic turbulent flow. Such small fibers spend most of their time fully stretched and their dynamics follows that of…
We present and study a minimal structure-based model for the self-assembly of peptides into ordered beta-sheet-rich fibrils. The peptides are represented by unit-length sticks on a cubic lattice and interact by hydrogen bonding and…
The gravitational instability of expanding shells is discussed. Linear and nonlinear terms are included in an analytical solution in the static and homogeneous medium. We discuss the interaction of modes and give the time needed for…
An efficient numerical algorithm is presented for massively parallel simulations of dispersion-managed wavelength-division-multiplexed optical fiber systems. The algorithm is based on a weak nonlinearity approximation and independent…
Above a critical concentration a wide variety of peptides and proteins self-assemble into amyloid fibrils which entangle to form percolating networks called hydrogels. Such hydrogels have important applications as biomaterials and in…
As an alternative to the paradigmatic fragmentation problem of a single object crushed into a great number of pieces, we survey a large collection of identical bodies, each one randomly split into two fragments only. While some key features…
Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical…
In the paper (Goloveshkin and Myagkov 2014) we proposed a two-dimensional energy-based model of fragmentation of rapidly expanding cylinder under plane strain conditions. The model allowed one to estimate the average fragment length and the…
Many different proteins self-aggregate into insoluble fibrils growing apically by reversible addition of elementary building blocks. But beyond this common principle, the modalities of fibril formation are very disparate, with various…