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In this paper we propose local and global existence results for the solution of systems characterized by the coupling of ODEs and PDEs. The coexistence of distinct mathematical formalisms represents the main feature of hybrid approaches, in…
Bulk-surface systems on evolving domains are studied. Such problems appear typically from modelling receptor-ligand dynamics in biological cells. Our first main result is the global existence and boundedness of solutions in all dimensions.…
The prevailing models for advancing dynamic contact angle are under intensive debates, and the fitting performances are far from satisfying in practice. The present study proposes a model based on the recent understanding of the multi-scale…
This article deals with invariant manifolds for infinite dimensional random dynamical systems with different time scales. Such a random system is generated by a coupled system of fast-slow stochastic evolutionary equations. Under suitable…
The aim of this paper is to analyze a class of consensus algorithms with finite-time or fixed-time convergence for dynamic networks formed by agents with first-order dynamics. In particular, in the analyzed class a single evaluation of a…
Interfacial instability is highly relevant to many important biological processes. A key example arises in wound healing experiments, which observe that an epithelial layer with an initially straight edge does not heal uniformly. We…
The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been…
Using scalar-vector-tensor Brans Dicke (VBD) gravity [3] in presence of self interaction BD potential $V(\phi)$ and perfect fluid matter field action we solve corresponding field equations via dynamical system approach for flat Friedmann…
This chapter is an up-to-date account of results on globally hyperbolic spacetimes, and serves several purposes. We begin with the exposition of results from a foundational level, where the main tools are order theory and general topology,…
In this paper, we introduce a fictitious dynamics for describing the only fast relaxation of a stiff ordinary differential equation (ODE) system towards a stable low-dimensional invariant manifold in the phase-space (slow invariant manifold…
We study the problem of solving fixed-point equations for seminorm-contractive operators and establish foundational results on the non-asymptotic behavior of iterative algorithms in both deterministic and stochastic settings. Specifically,…
Track systems effectively distribute loads, augmenting traction and maneuverability on unstable terrains, leveraging their expansive contact areas. This tracked locomotion capability also aids in hand manipulation of not only regular…
We propose an efficient numerical method for the simulation of multi-phase flows with moving contact lines in three dimensions. The mathematical model consists of the incompressible Navier-Stokes equations for the two immiscible fluids with…
This paper is devoted to derive some necessary and suficient conditions for the existence of positive solutions to a singular second order system of dynamic equations with Dirichlet boundary conditions. The results are obtained by employing…
The concurrent optimization of topology and fibre orientation is a promising approach to pursue higher strength and lighter weight of variable-stiffness structure. This study proposes a novel discrete-continuous scheme for the concurrent…
In the present work we explore the potential of models of the discrete nonlinear Schr\"odinger (DNLS) type to support spatially localized and temporally quasiperiodic solutions on top of a finite background. Such solutions are rigorously…
Like many other biological processes, calcium dynamics in neurons containing an endoplasmic reticulum are governed by diffusion-reaction equations on interface-separated domains. Interface conditions are typically described by systems of…
Dynamical similarities are non-standard symmetries found in a wide range of physical systems that identify solutions related by a change of scale. In this paper we will show through a series of examples how this symmetry extends to the…
We experimentally demonstrate a dynamical classification approach for investigation of topological quantum phases using a solid-state spin system through nitrogen-vacancy (NV) center in diamond. Similar to the bulkboundary correspondence in…
This paper proposes a computational technique based on "deep unfolding" to solving the finite-time maximum hands-off control problem for discrete-time nonlinear stochastic systems. In particular, we seek a sparse control input sequence that…