Aagesenalmeida7470

Hopefully, with further development, NNs can offer an alternative computational method for knot identification and facilitate knot research in mathematical and physical sciences.We study the clustering of a model cyanobacterium Synechocystis into microcolonies. The bacteria are allowed to diffuse onto surfaces of different hardness and interact with the others by aggregation and detachment. We find that soft surfaces give rise to more microcolonies than hard ones. This effect is related to the amount of heterogeneity of bacteria's dynamics as given by the proportion of motile cells. A kinetic model that emphasizes specific interactions between cells, complemented by extensive numerical simulations considering various amounts of motility, describes the experimental results adequately. The high proportion of motile cells enhances dispersion rather than aggregation.This corrects the article DOI 10.1103/PhysRevE.100.012702.Unraveling the mechanisms of packing of DNA inside viral capsids is of fundamental importance to understanding the spread of viruses. It could also help develop new applications to targeted drug delivery devices for a large range of therapies. In this article, we present a robust, predictive mathematical model and its numerical implementation to aid the study and design of bacteriophage viruses for application purposes. Exploiting the analogies between the columnar hexagonal chromonic phases of encapsidated viral DNA and chromonic aggregates formed by plank-shaped molecular compounds, we develop a first-principles effective mechanical model of DNA packing in a viral capsid. The proposed expression of the packing energy, which combines relevant aspects of the liquid crystal theory, is developed from the model of hexagonal columnar phases, together with that describing configurations of polymeric liquid crystals. The method also outlines a parameter selection strategy that uses available data for a collection of viruses, aimed at applications to viral design. The outcome of the work is a mathematical model and its numerical algorithm, based on the method of finite elements, and computer simulations to identify and label the ordered and disordered regions of the capsid and calculate the inner pressure. It also presents the tools for the local reconstruction of the DNA "scaffolding" and the center curve of the filament within the capsid.We introduce an integral model of a two-dimensional neural field that includes a third dimension representing space along a dendritic tree that can incorporate realistic patterns of axodendritic connectivity. For natural choices of this connectivity we show how to construct an equivalent brain-wave partial differential equation that allows for efficient numerical simulation of the model. This is used to highlight the effects that passive dendritic properties can have on the speed and shape of large scale traveling cortical waves.Cell-cell communication is often achieved by secreted signaling molecules that bind membrane-bound receptors. A common class of such receptors are G-protein coupled receptors, where extracellular binding induces changes on the membrane affinity near the receptor for certain cytosolic proteins, effectively altering their chemical potential. We analyze the minimum-dissipation schedules for dynamically changing chemical potential to induce steady-state changes in protein copy-number distributions, and illustrate with analytic solutions for linear chemical reaction networks. Protocols that change chemical potential on biologically relevant timescales are experimentally accessible using optogenetic manipulations, and our framework provides nontrivial predictions about functional dynamical cell-cell interactions.We adapt the concept of Lagrangian descriptors, which have been recently introduced as efficient indicators of phase space structures in chaotic systems, to unveil the key features of open maps. We apply them to the open tribaker map, a paradigmatic example not only in classical but also in quantum chaos. Our definition allows us to identify in a very simple way the inner structure of the chaotic repeller, which is the fundamental invariant set that governs the dynamics of this system. The homoclinic tangles of periodic orbits (POs) that belong to this set are clearly found. selleck This could also have important consequences for chaotic scattering and in the development of the semiclassical theory of short POs for open systems.High-resolution numerical simulations of cracks driven by an internal pressure in a heterogeneous and brittle granular medium produce fragment-size distributions with the same characteristics as experiments on blasted cylinders of mortar and rock in both the fine- and the intermediate-size-fragment regions. To mimic full-scale blasts used, e.g., within the mining industry, the cracks propagate in a medium that is under compression, neutral, or under tension. In a compressive environment, shear fracture produces a large volume of fines, whereas in a neutral or tensile environment, unstable crack branching is responsible for a much smaller volume of fines. The boundary between the fine- and the intermediate-size fragments scales as the average grain size of the material. The ultimate goal is to develop a blasting process that minimizes the fines, which, in mining, are both an environmental hazard and useless for further processing.Chemical reactions in multidimensional systems are often described by a rank-1 saddle, whose stable and unstable manifolds intersect in the normally hyperbolic invariant manifold (NHIM). Trajectories started on the NHIM in principle never leave this manifold when propagated forward or backward in time. However, the numerical investigation of the dynamics on the NHIM is difficult because of the instability of the motion. We apply a neural network to describe time-dependent NHIMs and use this network to stabilize the motion on the NHIM for a periodically driven model system with two degrees of freedom. The method allows us to analyze the dynamics on the NHIM via Poincaré surfaces of section (PSOS) and to determine the transition-state (TS) trajectory as a periodic orbit with the same periodicity as the driving saddle, viz. a fixed point of the PSOS surrounded by near-integrable tori. Based on transition state theory and a Floquet analysis of a periodic TS trajectory we compute the rate constant of the reaction with significantly reduced numerical effort compared to the propagation of a large trajectory ensemble.