This paper considers the problem of stabilizing (bio)chemical reaction networks that can be represented as cyclic interconnections. The objective of the paper is to present a constructive way to compute a dissipative potential function for the system. This potential is then used for constructing a smooth feedback stabilizing controller. We obtain a characteristic one-form for the system by taki...

We present a convergence analysis for the implicit-explicit (IMEX) Euler discretization of nonlinear evolution equations. The governing vector field of such an equation is assumed to be the sum of an unbounded dissipative operator and a Lipschitz continuous perturbation. By employing the theory of dissipative operators on Banach spaces, we prove that the IMEX Euler and the implicit Euler scheme...

We introduce a method for determining the functional form of the stochastic and dissipative interactions in a dissipative particle dynamics (DPD) model from projected phase space trajectories. The DPD model is viewed as a coarse graining of a detailed dynamics that displays a clear timescale separation. Based on the Mori-Zwanzig projection operator method we derive a consistency equation for th...

The Peaceman–Rachford scheme is a commonly used splitting method for discretizing semilinear evolution equations, where the vector fields are given by the sum of one linear and one nonlinear dissipative operator. Typical examples of such equations are reaction-diffusion systems and the damped wave equation. In this paper we conduct a convergence analysis for the Peaceman– Rachford scheme in the...

The perturbation Γ may be either random or deterministic. We will focus on two complementary situations. The first regime is when L is very mixing but non-dissipative, while Γ is dissipative. Their interaction leads to a dramatically increased dissipation, that can not be achieved by either of them alone. This phenomenon is known as relaxation enhancement. The second set of problems involves ra...

We study a reaction-diffusion evolution equation perturbed by a Gaussian noise. Here the leading operator is the infinitesimal generator of a C0-semigroup of strictly negative type, the nonlinear term has at most polynomial growth and is such that the whole system is dissipative. The corresponding Itô stochastic equation describes a process on a Hilbert space with dissipative nonlinear drift an...

Special thanks also goes my colleagues in the Intelligent Machine Dynamics Laboratory and surrounding labs for the contributions they made to this research. They include, but are not limited to, L. Acknowledgment must also be made to John Graham and Donald Long in the machine shop for their cooperation in the fabrication process. SUMMARY This project focuses on the design and modeling of a two ...

Careful monitoring of harmonically bound (or as a limiting case, free) masses is the basis of current and future gravitational wave detectors, and of nanomechanical devices designed to access the quantum regime. We analyze the effects of stochastic localization models for state vector reduction, and of related models for environmental decoherence, on such systems, focusing our analysis on the n...