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Dynamical two-particle susceptibilites are important for a wide range of different experiments in condensed-matter physics and beyond. Nevertheless, most textbooks avoid describing how to derive such response functions, perhaps because they…
The irreducible decomposition of a unitary representation often contains continuous spectrum when restricted to a non-compact subgroup. The author singles out a nice class of branching problems where each irreducible summand occurs…
We consider the reduction of parametric families of linear dynamical systems having an affine parameter dependence that differ from one another by a low-rank variation in the state matrix. Usual approaches for parametric model reduction…
The problem of incompressible fluid mixing arises in numerous engineering applications and has been well-studied over the years, yet many open questions remain. This paper aims to address the question "what do efficient flow fields for…
We analyse large deviations of the dynamical activity in one-dimensional systems of diffusing hard particles. Using an optimal-control representation of the large-deviation problem, we analyse effective interaction forces which can be added…
When the complete understanding of a complex system is not available, as, e.g., for systems considered in the real-world, we need a top-down approach to complexity. In this approach one may start with the desire to understand general…
A fundamental theory is presented for the mechanical response of polymer networks undergoing large deformation which seamlessly integrates statistical mechanical principles with macroscopic thermodynamic constitutive theory. Our formulation…
We investigate the chemical dissolution of porous media using a network model in which the system is represented as a series of interconnected pipes with the diameter of each segment increasing in proportion to the local reactant…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
Dynamics of systems of structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The…
Nonlinear dynamical systems are complex and typically only simple systems can be analytically studied. In applications, these systems are usually defined with a set of tunable parameters and as the parameters are varied the system response…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
Interacting systems are ubiquitous in nature and engineering, ranging from particle dynamics in physics to functionally connected brain regions. These interacting systems can be modeled by graphs where edges correspond to the interactions…
A recent experiment driving colloids electromagnetically, by B\'erut et al. [2014 Europhys. Lett. 107, 60004], is an ideal paradigm for illustrating a linear response theory for nonequilibrium overdamped systems including hydrodynamic…
We consider linear dynamical systems with a structure of a multigraph. The vertices are associated to linear spaces and the edges correspond to linear maps between those spaces. We analyse the asymptotic growth of trajectories (associated…
We study a reaction-diffusion model posed on two distinct spatial scales that accounts for diffusion, aggregation, fragmentation, and deposition of populations of colloidal particles within a porous material. In this model, the macroscopic…
Coarse-grained models that preserve hydrodynamics provide a natural approach to study collective properties of soft-matter systems. Here, we demonstrate that commonly used integration schemes in dissipative particle dynamics give rise to…
The long-term average response of observables of chaotic systems to dynamical perturbations can often be predicted using linear response theory, but not all chaotic systems possess a linear response. Macroscopic observables of complex…
Traditional methods in educational research often fail to capture the complex and evolving nature of learning processes. This chapter examines the use of complex systems theory in education to address these limitations. The chapter covers…
In the paper the flow in a thin tubular structure is considered. The velocity of the flow stands for a coefficient in the diffusion-convection equation set in the thin structure. An asymptotic expansion of solution is constructed. This…