Related papers: Input-to-state type Stability for Simplified Fluid…
Under certain conditions we prove the existence of a steady-state transport regime for interacting mesoscopic systems coupled to reservoirs (leads). The partitioning and partition-free scenarios are treated on an equal footing. Our…
The thermodynamic stability of the hard-sphere gas has been examined, using the formalism of scaled particle theory [SPT], and by applying explicitly the conditions of stability required by both the second and third laws of thermodynamics.…
The coupling-parameter method, whereby an extra particle is progressively coupled to the rest of the particles, is applied to the sticky-hard-sphere fluid to obtain its equation of state in the so-called chemical-potential route ($\mu$…
For large classes of infinite-dimensional time-varying control systems, the equivalence between integral input-to-state stability (iISS) and the combination of global uniform asymptotic stability under zero input (0-GUAS) and uniformly…
We prove a null controllability result for the Vlasov-Navier-Stokes system, which describes the interaction of a large cloud of particles immersed in a fluid. We show that one can modify both the distribution of particles and the velocity…
The goal of this paper is to analyze Long Short Term Memory (LSTM) neural networks from a dynamical system perspective. The classical recursive equations describing the evolution of LSTM can be recast in state space form, resulting in a…
This paper studies integral input-to-state stability (iISS) of nonlinear impulsive systems with time-delay in both the continuous dynamics and the impulses. Several iISS results are established by using the method of Lyapunov-Krasovskii…
Gradual advancement of control technology gives rise to the studies of the stability of linear systems. The stability of the linear multiagent system is motivated by increasing utilization of agent dynamics together with the number of…
We consider nonlinear control systems of the so-called generalized triangular form (GTF) with time-varying and periodic dynamics which linearly depends on some external disturbances. Our purpose is to construct a feedback controller which…
We investigate the instability and stability of specific steady-state solutions of the two-dimensional non-homogeneous, incompressible, and viscous Navier-Stokes equations under the influence of a general potential $f$. This potential is…
We investigate a paradigm example of cavity quantum electrodynamics with many body systems: an ultracold atomic gas inside a pumped optical resonator. In particular, we study the stability of atomic insulator-like states, confined by the…
Minimal models of self-propelled particles with short-range volume exclusion interactions have been shown to exhibit signatures of phase separation. Here I show that the observed interfacial stability and fluctuations in motility-induced…
In this work we present further characterizations of integral input-to-state stability (iISS) for hybrid systems. In particular, the equivalence between 0-input uniform global asymptotic stability (0-UGAS) plus uniform bounded energy…
For three-dimensional piecewise-smooth systems of ordinary differential equations, this paper characterises the stability of points that belong to a switching surface and are equilibria of exactly one of the two neighbouring pieces of the…
We study stationary states of a one-dimensional gas of granular point-like particles not subject to gravity between two walls at temperatures T- and T+, with T- < T+. Depending on the normalized temperature difference Delta = (T+ - T-)/(T+…
We characterise the steady states of a suspension of two-dimensional active brownian particles (ABPs). We calculate the steady-state probability distribution to lowest order in Peclet number. We show that macroscopic quantities can be…
In this paper, we prove the local in time well-posedness of thick spray equations in Sobolev spaces, for initial data satisfying a Penrose-type stability condition. This system is a coupling between particles described by a kinetic equation…
Generalized Navier-Stokes equations which were proposed recently to describe active turbulence in living fluids are analyzed rigorously. Results on wellposedness and stability in the $L^2(\mathbb{R}^n)$-setting are derived. Due to the…
In this work, we study the well-posedness of a system of partial differential equations that model the dynamics of a two-dimensional Stokes bubble immersed in two-dimensional ambient Stokes fluid of the same viscosity that extends to…
An extension of the relativistic density functional approach to the equation of state for strongly interacting matter is suggested which generalizes a recently developed modified excluded-volume mechanism to the case of temperature and…