Delayed blow-up and enhanced diffusion by transport noise for systems of reaction–diffusion equations

This paper is concerned with the problem of regularization by noise of systems of reaction–diffusion equations with mass control. It is known that strong solutions to such systems of PDEs may blow-up in finite time. Moreover, for many systems of practical interest, establishing whether the blow-up occurs or not is an open question. Here we...

Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity

In this paper we consider a class of stochastic reaction-diffusion equations. We provide local well-posedness, regularity, blow-up criteria and positivity of solutions. The key novelties of this work are related to the use transport noise, critical spaces and the proof of higher order regularity of solutions – even in case of non-smooth...

Dynamic Growth of Macroscopically Structured Supramolecular Hydrogels through Orchestrated Reaction-Diffusion

Living organisms are capable of dynamically changing their structures for adaptive functions through sophisticated reaction-diffusion processes. Here we show how active supramolecular hydrogels with programmable lifetimes and macroscopic structures can be created by relying on a simple reaction-diffusion strategy. Two hydrogel precursors ...

Bridging scales in a multiscale pattern-forming system

Self-organized pattern formation is vital for many biological processes. Reaction-diffusion models have advanced our understanding of how biological systems develop spatial structures, starting from homogeneity. However, biological processes inherently involve multiple spatial and temporal scales and transition from one pattern to another...

In Situ Characterization of the Reaction-Diffusion Behavior during the Gradient Interphase Formation of Polyetherimide with a High-Temperature Epoxy System

This study presents two novel methods for in situ characterization of the reaction-diffusion process during the co-curing of a polyetherimide thermoplastic interlayer with an epoxy-amine thermoset. The first method was based on hot stage experiments using a computer vision point tracker algorithm to detect and trace diffusion fronts, and the...

Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence

In this paper we develop a new approach to nonlinear stochastic partial differential equations with Gaussian noise. Our aim is to provide an abstract framework which is applicable to a large class of SPDEs and includes many important cases of nonlinear parabolic problems which are of quasi- or semilinear type. This first part is on local...

Multiscale analysis for traveling-pulse solutions to the stochastic fitzhugh–nagumo equations

We investigate the stability of traveling-pulse solutions to the stochastic FitzHugh–Nagumo equations with additive noise. Special attention is given to the effect of small noise on the classical deterministically stable fast traveling pulse. Our method is based on adapting the velocity of the traveling wave by solving a scalar stochastic...

Cellular Dialogues: Cell-Cell Communication through Diffusible Molecules Yields Dynamic Spatial Patterns

Cells form spatial patterns by coordinating their gene expressions. How a group of mesoscopic numbers (hundreds to thousands) of cells, without pre-existing morphogen gradients and spatial organization, self-organizes spatial patterns remains poorly understood. Of particular importance are dynamic spatial patterns such as spiral waves that...

A compact matrix model for atrial electrograms for tissue conductivity estimation

Finding the hidden parameters of the cardiac electrophysiological model would help to gain more insight on the mechanisms underlying atrial fibrillation, and subsequently, facilitate the diagnosis and treatment of the disease in later stages. In this work, we aim to estimate tissue conductivity from recorded electrograms as an indication of...

Multistability and dynamic transitions of intracellular Min protein patterns

Cells owe their internal organization to self-organized protein patterns, which originate and adapt to growth and external stimuli via a process that is as complex as it is little understood. Here, we study the emergence, stability, and state transitions of multistable Min protein oscillation patterns in live Escherichia coli bacteria during...

Concentration fluctuations in non-isothermal reaction-diffusion systems. II. The nonlinear case

In this paper, we consider a simple reaction-diffusion system, namely, a binary fluid mixture with an association-dissociation reaction between two species. We study fluctuations at hydrodynamic spatiotemporal scales when this mixture is driven out of equilibrium by the presence of a temperature gradient, while still being far away from any...

Reaction-diffusion analysis for one-step plasma etching and bonding of microfluidic devices

A self-similar reaction front develops in reactive ion etching when the ions penetrate channels of shallow height h. This relates to the patterning of microchannels using a single-step etching and bonding, as described by Rhee et al. [Lab Chip 5, 102 (2005)] . Experimentally, we report that the front location scales as xf ? ht1/2 and the width...