相关论文: Modelling Meso-Scale Diffusion Processes in Stocha…
Numerous processes across both the physical and biological sciences are driven by diffusion. Partial differential equations (PDEs) are a popular tool for modelling such phenomena deterministically, but it is often necessary to use…
We model chaotic diffusion, in a symplectic 4D map by using the result of a theorem that was developed for stochastically perturbed integrable Hamiltonian systems. We explicitly consider a map defined by a free rotator (FR) coupled to a…
We study the stress distribution profiles and the height and thickness fluctuations of lipid membranes in the tilted gel state by Monte Carlo simulations of a generic coarse-grained model for lipid membranes, which reproduces many known…
Diffusion is the macroscopic manifestation of disordered molecular motion. Mathematically, diffusion equations are partial differential equations describing the fluid-like large-scale dynamics of parcels of molecules. Spatially…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
We investigate proteins within heterogeneous cell membranes where non-equilibrium phenomena arises from spatial variations in concentration and temperature. We develop simulation methods building on non-equilibrium statistical mechanics to…
Most classical work on the hydrodynamics of low-Reynolds-number swimming addresses deterministic locomotion in quiescent environments. Thermal fluctuations in fluids are known to lead to a Brownian loss of the swimming direction. As most…
Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…
Receptor-mediated endocytosis requires that the energy of adhesion overcomes the deformation energy of the plasma membrane. The resulting driving force is balanced by dissipative forces, leading to deterministic dynamical equations. While…
Subdiffusion has been proposed as an explanation of various kinetic phenomena inside living cells. In order to fascilitate large-scale computational studies of subdiffusive chemical processes, we extend a recently suggested mesoscopic model…
The immersed boundary method is a mathematical formulation and numerical method for solving fluid-structure interaction problems. For many biological problems, such as models that include the cell membrane, the immersed structure is a…
Image acquisition techniques such as micro-computed tomography are nowadays widely available. Quantitative analysis of the resulting 3D image data enables geometric characterization of the micro-structure of materials. Stochastic geometry…
The hydrodynamic theory of heterogeneous fluid membranes is extended to the case of a membrane adjacent to a solid substrate. We derive the coupling diffusion coefficients of pairs of membrane inclusions in the limit of large separation…
The stochastic dynamics of small elastic objects in fluid are central to many important and emerging technologies. It is now possible to measure and use the higher modes of motion of elastic structures when driven by Brownian motion alone.…
Lateral diffusion of molecules on surfaces plays a very important role in various biological processes, including lipid transport across the cell membrane, synaptic transmission and other phenomena such as exo- and endocytosis, signal…
A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and…
In this paper homogenization of a mathematical model for biomechanics of a plant tissue with randomly distributed cells is considered. Mechanical properties of a plant tissue are modelled by a strongly coupled system of…
Non-particulate continuum descriptions allow for computationally efficient modeling of suspension flows at scales that are inaccessible to more detailed particulate approaches. It is well known that the presence of particles influences the…
A possibility to use an integral operator for establishing the link between physical and structural levels of materials in modeling diffusion processes is considered. We show how to perform the transition from the stochastic description of…
Spatial profiling technologies in biology, such as imaging mass cytometry (IMC) and spatial transcriptomics (ST), generate high-dimensional, multi-channel data with strong spatial alignment and complex inter-channel relationships.…