Related papers: Diagrammatic approach to response problems in comp…
Certifying feasibility in decision-making, critical in many industries, can be framed as a constraint satisfaction problem. This paper focuses on characterising a subset of parameter values from an a priori set that satisfy constraints on a…
A decomposition principle for nonlinear dynamic compartmental systems is introduced in the present paper. This theory is based on the mutually exclusive and exhaustive, analytical and dynamic, novel system and subsystem partitioning…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
When colloids flow in a narrow channel, the transport efficiency is controlled by the non-equilibrium interplay between colloid-wall interactions and hydrodynamics. In this paper, a general, unifying description of colloidal dispersion flow…
A mass transport directed from low to high density region in an inhomogeneous medium is modeled as a limiting case of a two-component lattice gas with excluded volume constraint and one of the components fixed. In the long-wavelength…
The linear response of an isolated, homogeneous granular fluid to small spatial perturbations is studied by methods of non-equilibrium statistical mechanics. The long wavelength linear hydrodynamic equations are obtained, with formally…
Complex systems thinking is applied to a wide variety of domains, from neuroscience to computer science and economics. The wide variety of implementations has resulted in two key challenges: the progenation of many domain-specific…
We show how the nonlinear interaction effects `volume filling' and `adhesion' can be incorporated into the fractional subdiffusive transport of cells and individual organisms. To this end, we use microscopic random walk models with…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
A hydrodynamic formulation of the evolution of large-scale structure in the Universe is presented. It relies on the spatially coarse-grained description of the dynamical evolution of a many-body gravitating system. Because of the assumed…
A unified set of hydrodynamic equations describing condensed phases of matter with broken continuous symmetries is derived using a generalization of the statistical-mechanical approach based on the local equilibrium distribution. The…
Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is…
Hydrodynamic transport coefficients may be evaluated from first principles in a weakly coupled scalar field theory at arbitrary temperature. In a theory with cubic and quartic interactions, the infinite class of diagrams which contribute to…
The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, combinatorics, and the analysis of nonlinear time-varying dynamical systems. There is a…
Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…
Delay-coupled networks are investigated with nonidentical delay times and the effects of such heterogeneity on the emergent dynamics of complex systems are characterized. A simple decomposition method is presented that decouples the…
Network systems consist of subsystems and their interconnections, and provide a powerful framework for analysis, modeling and control of complex systems. However, subsystems may have high-dimensional dynamics, and the amount and nature of…
Linear response theory is a fundamental framework studying the macroscopic response of a physical system to an external perturbation. This paper focuses on the rigorous mathematical justification of linear response theory for Langevin…
We study the adsorption-desorption of fluid molecules on a solid substrate by introducing a schematic model in which the adsorption/desorption transition probabilities are given by irreversible kinetic constraints with a tunable violation…
Thermal gradients lead to macroscopic fluid motion if a confining surface is present along the gradient. This fundamental nonequilibrium effect, known as thermo-osmosis, is held responsible for particle thermophoresis in colloidal…