arXiv subjects

Giovanni Russo

Publications and source records attributed to Giovanni Russo.

132 records · Page 8Linked to original sources

arXiv2011

Symmetries, Stability, and Control in Nonlinear Systems and Networks

This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence analysis tools based on nonlinear contraction theory and virtual dynamical systems. This synergy between structural properties (symmetries) and convergence properties (contraction) is illustrated in the contexts of network motifs arising e.g. in genetic networks, of invariance to environmental symmetries, and of imposing different patterns of synchrony in a network.

math.DS↗

arXiv2011

A New Class of Conservative Large Time Step Methods for the BGK Models of the Boltzmann Equation

This work is aimed to develop a new class of methods for the BGK model of the Boltzmann equation. This technique allows to get high order of accuracy both in space and time, theoretically without CFL stability limitation. It's based on a Lagrangian formulation of the problem: information is stored on a fixed grid in space and velocity, and the equation is integrated along the characteristics. The source term is treated implicitly by using a DIRK (Diagonally Implicit Runge Kutta) scheme in order to avoid the time step restriction due to the stiff relaxation. In particular some L-stable schemes are tested by smooth and Riemann problems, both in rarefied and fully fluid regimes. Numerical results show good accuracy and efficiency of the method.

math.NA↗

arXiv2010

Convergence of a Semi-Lagrangian Scheme for the BGK Model of the Boltzmann Equation

Recently, a new class of semi-Lagrangian methods for the BGK model of the Boltzmann equation has been introduced [8, 17, 18]. These methods work in a satisfactory way either in rarefied or fluid regime. Moreover, because of the semi-Lagrangian feature, the stability property is not restricted by the CFL condition. These aspects make them very attractive for practical applications. In this paper, we investigate the convergence properties of the method and prove that the discrete solution of the scheme converges in a weighted L1 norm to the unique smooth solution by deriving an explicit error estimate.

math.AP↗

arXiv2010

Global convergence of quorum-sensing networks

In many natural synchronization phenomena, communication between individual elements occurs not directly, but rather through the environment. One of these instances is bacterial quorum sensing, where bacteria release signaling molecules in the environment which in turn are sensed and used for population coordination. Extending this motivation to a general non- linear dynamical system context, this paper analyzes synchronization phenomena in networks where communication and coupling between nodes are mediated by shared dynamical quan- tities, typically provided by the nodes' environment. Our model includes the case when the dynamics of the shared variables themselves cannot be neglected or indeed play a central part. Applications to examples from systems biology illustrate the approach.

math.DS↗

arXiv2009

Global entrainment of transcriptional systems to periodic inputs

This paper addresses the problem of giving conditions for transcriptional systems to be globally entrained to external periodic inputs. By using contraction theory, a powerful tool from dynamical systems theory, it is shown that certain systems driven by external periodic signals have the property that all solutions converge to a fixed limit cycle. General results are proved, and the properties are verified in the specific case of some models of transcriptional systems. The basic mathematical results needed from contraction theory are proved in the paper, making it self-contained.

q-bio.QM↗

arXiv2005

Computation of Strained Epitaxial Growth in Three Dimensions by Kinetic Monte Carlo

A numerical method for computation of heteroepitaxial growth in the presence of strain is presented. The model used is based on a solid-on-solid model with a cubic lattice. Elastic effects are incorporated using a ball and spring type model. The growing film is evolved using Kinetic Monte Carlo (KMC) and it is assumed that the film is in mechanical equilibrium. The strain field in the substrate is computed by an exact solution which is efficiently evaluated using the fast Fourier transform. The strain field in the growing film is computed directly. The resulting coupled system is solved iteratively using the conjugate gradient method. Finally we introduce various approximations in the implementation of KMC to improve the computation speed. Numerical results show that layer-by-layer growth is unstable if the misfit is large enough resulting in the formation of three dimensional islands.

cond-mat.mtrl-sci↗