相关论文: Predicting reaction coordinates in energy landscap…
Protein-protein interactions comprise both transport and reaction steps. During the transport step, anisotropy of proteins and their complexes is important both for hydrodynamic diffusion and accessibility of the binding site. Using a…
Diffusion-limited reaction A+A->inert with anisotropic hopping on the d=1 lattice, is solved exactly for a simultaneous updating, discrete time-step dynamics. Diffusion-dominated processes slow down as the anisotropy increases. For large…
Reaction-diffusion systems offer a powerful framework for understanding self-organized patterns in biological systems, yet controlling these patterns remains a significant challenge. As a consequence, we present a rigorous framework of…
A residual error estimator is proposed for the energy norm of the error for a scalar reaction-diffusion problem and for the monodomain model used in cardiac electrophysiology. The problem is discretized using $P_1$ finite elements in space,…
The dominant reaction pathway (DRP) is a rigorous framework to microscopically compute the most probable trajectories, in non-equilibrium transitions. In the low-temperature regime, such dominant pathways encode the information about the…
A general method to describe stochastic dynamics of Markov processes is suggested. The method aims to solve three related problems. The determination of an optimal coordinate for the description of stochastic dynamics. The reconstruction of…
We propose a cross-entropy minimization method for finding the reaction coordinate from a large number of collective variables in complex molecular systems. This method is an extension of the likelihood maximization approach describing the…
Numerical simulations of two dimensional pattern formation in an anisotropic bistable reaction-diffusion medium reveal a new dynamical state, stratified spatiotemporal chaos, characterized by strong correlations along one of the principal…
In this paper we present a method to approximate optimal feedback controls for stochastic reaction-diffusion equations. We derive two approximation results providing the theoretical foundation of our approach and allowing for explicit error…
We study the effect of anisotropic diffusion on the one-dimensional annihilation reaction kA->inert with partial reaction probabilities when hard-core particles meet in groups of k nearest neighbors. Based on scaling arguments, mean field…
Cooperative driving is a safety- and efficiency-critical task that requires the coordination of diverse, interaction-realistic multi-agent trajectories. Although existing diffusion-based methods can capture multimodal behaviors from…
Reaction coordinates (RCs) are low-dimensional representations of complex dynamical systems that capture their long-term dynamics. In this work, we focus on the criteria of lumpability and decomposability, previously established for…
We find in a model system of thermotropic liquid crystals that the translational diffusion coefficient parallel to the director $D_{\parallel}$ first increases and then decreases as temperature drops through the nematic phase, and this…
We consider complex dynamical systems showing metastable behavior but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective…
Understanding the complex patterns in space-time exhibited by active systems has been the subject of much interest in recent times. Complementing this forward problem is the inverse problem of controlling active matter. Here we use optimal…
A key problem of robotic environmental sensing and monitoring is that of active sensing: How can a team of robots plan the most informative observation paths to minimize the uncertainty in modeling and predicting an environmental…
Viscous hydrodynamics is commonly used to model the evolution of the matter created in an ultra-relativistic heavy-ion collision. It provides a good description of transverse momentum spectra and anisotropic flow. These observables,…
The enormous technological potential accumulated over the past two decades would make it possible to change the operating principles of power systems entirely. The consequent technological evolution is not only affecting the structure of…
The existing methods for trajectory prediction are difficult to describe trajectory of moving objects in complex and uncertain environment accurately. In order to solve this problem, this paper proposes an adaptive trajectory prediction…
We explore the effects of mesh skewness on the accuracy of standard Hybrid High-Order (HHO) schemes for anisotropic diffusion equations. After defining a notion of regular skewed mesh sequences, which allows, e.g., for elements that become…