Related papers: Pattern control via Diffussion interaction
In many biological situations, a species arriving from a remote source diffuses in a domain confined between two parallel surfaces until it finds a binding partner. Since such a geometric shape falls in between two- and three-dimensional…
We provide an overview on how to use the measurable selection techniques to derive the dynamic programming principle for a general stochastic optimal control/stopping problem. By considering its martingale problem formulation on the…
Stochasticity is a defining feature of the pairwise forces governing interactions in biological systems-from molecular motors to cell-cell adhesion-yet its consequences on large-scale dynamics remain poorly understood. Here, we show that…
Diffusion models have become popular for policy learning in robotics due to their ability to capture high-dimensional and multimodal distributions. However, diffusion policies are stochastic and typically trained offline, limiting their…
This paper introduces a continuous-time constrained nonlinear control scheme which implements a model predictive control strategy as a continuous-time dynamic system. The approach is based on the idea that the solution of the optimal…
Stochastic chemical systems with diffusion are modeled with a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic…
Originating from the pioneering study of Alan Turing, the bifurcation analysis predicting spatial pattern formation from a spatially uniform state for diffusing morphogens or chemical species that interact through nonlinear reactions is a…
In this article we present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model many different phenomena in areas such as developmental and…
The theory of patterns formation for a reaction-diffusion system defined on a multiplex is developed by means of a perturbative approach. The intra-layer diffusion constants act as small parameter in the expansion and the unperturbed state…
The description of surface-diffusion controlled dynamics via the phase-field method is less trivial than it appears at first sight. A seemingly straightforward approach from the literature is shown to fail to produce the correct…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
Biomolecular condensates are small droplets forming spontaneously in biological cells via phase separation. They play a role in many cellular processes, but it is unclear how cells control them. Cellular regulation often relies on…
Yet often neglected, dynamical interdependencies between concomitant contagion processes can alter their intrinsic equilibria and bifurcations. A particular case of interest for disease control is the emergence of explosive transitions in…
This paper formulates a framework for the analysis and distributed control of interconnected systems from the behavioural perspective. The discussions are carried out from the viewpoint of set theory and the results are completely…
We explain the principles of gene expression pattern stabilization in systems of interacting, diffusible morphogens, with dynamically established source regions. Using a reaction-diffusion model with step-function production term, we…
This paper investigates pattern formation in reaction--diffusion systems with both diffusive and nondiffusive components, providing necessary and sufficient conditions for diffusion-driven instability (DDI) and establishing the existence of…
Large time dynamics of reaction-diffusion systems modeling some irreversible reaction networks are investigated. Depending on initial masses, these networks possibly possess boundary equilibria, where some of the chemical concentrations are…
Reaction-diffusion processes across layered media arise in several scientific domains such as pattern-forming E. coli on agar substrates, epidermal-mesenchymal coupling in development, and symmetry-breaking in cell polarisation. We develop…
While imitation learning provides a simple and effective framework for policy learning, acquiring consistent actions during robot execution remains a challenging task. Existing approaches primarily focus on either modifying the action…
The coherent control of scattering processes is considered, with electron impact dissociation of H$_2^+$ used as an example. The physical mechanism underlying coherently controlled stationary state scattering is exposed by analyzing a…