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A new technique for obtaining rigorous results concerning the global dynamics of nonlinear systems is described. The technique combines abstract existence results based on the Conley index theory with computer- assisted computations. As an…
Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were…
We discuss the relevance of studying ecology within the framework of Complexity Science from a statistical mechanics approach. Ecology is concerned with understanding how systems level properties emerge out of the multitude of interactions…
This paper studies the relations among system parameters, uniqueness, and stability of equilibria, for kinetic systems given in the form of polynomial ODEs. Such models are commonly used to describe the dynamics of nonnegative systems, with…
This work is concerned with ($N$-component) hyperbolic system of balance laws in arbitrary space dimensions. Under entropy dissipative assumption and the Shizuta-Kawashima algebraic condition, a general theory on the well-posedness of…
We present the bond-calculus, a process algebra for modelling biological and chemical systems featuring nonlinear dynamics, multiway interactions, and dynamic bonding of agents. Mathematical models based on differential equations have been…
This book deals with the theory of generalized algebraic transformations, which is elaborated with the aim to provide a relatively simple theoretical tool that enables an exact treatment of diverse more complex lattice-statistical models.…
The emergence of macroscopic coherence in a many-body quantum system is a ubiquitous phenomenon across different physical systems and scales. This Chapter reviews key concepts characterizing such systems (correlation functions,…
Motivated by the question of how biological systems maintain homeostasis in changing environments, Shinar and Feinberg introduced in 2010 the concept of absolute concentration robustness (ACR). A biochemical system exhibits ACR in some…
Stationary states of quantum many-body Hamiltonians are invariant under the Hamiltonian evolution. Besides ground and thermal states, this class includes microcanonical ensembles that are of fundamental importance in statistical physics. We…
For a quantum system to be captured by a stationary statistical ensemble, as is common in thermodynamics and statistical mechanics, it is necessary that it reaches some apparently stationary state in the first place. In this book chapter,…
We describe a computational method for constructing a coarse combinatorial model of some dynamical system in which the macroscopic states are given by elementary cycling motions of the system. Our method is in particular applicable to time…
The 14 moments model for dense gases, introduced in the last years by Arima, Taniguchi Ruggeri, Sugiyama, is here considered. They have found the closure of the balance equations up to second order with respect to equilibrium; here the…
We present an overview of our studies on the nonequilibrium dynamics of quantum systems that have many interacting particles. Our emphasis is on systems that show strong level repulsion, referred to as chaotic systems. We discuss how full…
We demonstrate the equilibration of isolated macroscopic quantum systems, prepared in non-equilibrium mixed states with significant population of many energy levels, and observed by instruments with a reasonably bound working range compared…
In recent years considerable portion of the computer science community has focused its attention on understanding living cell biochemistry and efforts to understand such complication reaction environment have spread over wide front, ranging…
The over-relaxation approach is an alternative to the Jin-Xin relaxation method (Jin and Xin [1]) in order to apply the equilibrium source term in a more precise way (Coulette et al. [2, 3]). This is also a key ingredient of the…
Homogenisation empowers the efficient macroscale system level prediction of physical scenarios with intricate microscale structures. Here we develop an innovative powerful, rigorous and flexible framework for asymptotic homogenisation of…
Complex biochemical pathways or regulatory enzyme kinetics can be reduced to chains of elementary reactions, which can be described in terms of chemical kinetics. This discipline provides a set of tools for quantifying and understanding the…
Central configurations have been of great interest over many years, with the earliest examples due to Euler and Lagrange. There are numerous results in the literature demonstrating the existence of central configurations with specific…