Related papers: Mathematical Analysis for a Class of Stochastic Co…
Kinetic modeling of microbial growth is essential for the design, optimization, and scale-up of industrial bioprocesses. Classical empirical models often lack biologically interpretable parameters or fail to capture complex multiphasic…
We study statistical properties of a one dimensional infinite system of coalescing particles. Each particle moves with constant velocity $\pm v$ towards its closest neighbor and merges with it upon collision. We propose a mean-field theory…
Emergence and maintenance of polymers with complex sequences is a major question in the study of origins of life. To answer this, we studied a model polymerization reaction, where polymers are synthesized by stepwise ligation from two types…
The article provides a brief general introduction into the concepts of scaling, universality, and crossover scaling, plus the blob concept that provides an intuitive picture of crossover phenomena. We present the most important static and…
We discuss various aspects of the randomly interacting directed polymers with emphasis on the phases and phase transition. We also discuss the behaviour of overlaps of directed paths in a random medium.
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…
Constitutive equations are developed for a polymer fluid, which is treated as a permanent network of strands bridged by junctions. The junctions are assumed to slide with respect to their reference positions under loading. Governing…
The dynamical properties of entangled polymers originate from the dynamic constraints due to the uncrossability between polymer chains. We propose a highly coarse-grained simulation model with transient bonds for such dynamically…
Polynomial dynamical systems are widely used to model and study real phenomena. In biochemistry, they are the preferred choice for modelling the concentration of chemical species in reaction networks with mass-action kinetics. These systems…
Polymerization and formation of crosslinked polymer networks are important processes in manufacturing, materials fabrication, and in the case of hydrated polymer networks, synthesis of biomedical materials, drug delivery, and tissue…
This work is devoted to the derivation and the matematical study of a new model for water-soluble polymers and metal ions interactions, which are used in chemistry for their wide range of applications. First, we motivate and derive a model…
We present computer simulations of a simple bead-spring model for polymer melts with intramolecular barriers. By systematically tuning the strength of the barriers, we investigate their role on the glass transition. Dynamic observables are…
In classical stochastic theory, the joint probability distributions of a stochastic process obey by definition the Kolmogorov consistency conditions. Interpreting such a process as a sequence of physical measurements with probabilistic…
The recent experimental progresses in handling microscopic systems have allowed to probe them at levels where fluctuations are prominent, calling for stochastic modeling in a large number of physical, chemical and biological phenomena. This…
We present a model of polymer growth and diffusion with frustration mechanisms for density increase and with diffusion rates of Arrhenius form with mass-dependent energy barriers Gamma(m) ~ (m-1)^gamma. It shows non-universal logarithmic…
Here, we study the coalescence of two droplets that are moving in the same direction on a soft surface; the motion of the droplets is caused by a gradient in the surface stiffness. As reference, stationary coalescence of the same droplets…
The predictive ability of stochastic chemical reactions is currently limited by the lack of closed form solutions to the governing chemical master equation. To overcome this limitation, this paper proposes a computational method capable of…
The new method of the mean-field approximation is extended. An approach which enables to estimate some parameters of the transition from the isotropic state of hard sticks to the nematic ordering phase is suggested. An technique of the…
The presence of phenomena analogous to phase transition in Statistical Mechanics, has been suggested in the evolution of a polygenic trait under stabilizing selection, mutation and genetic drift. By using numerical simulations of a model…
Polymer dynamics is analyzed through the lens of linear dimensionality reduction methods, in particular principal (PCA) and time-lagged independent component analysis (tICA). For a polymer undergoing ideal Rouse dynamics, the slow modes…