Related papers: Poly: An abundant categorical setting for mode-dep…
It is shown how different globally coupled map systems can be analyzed under a common framework by focusing on the dynamics of their respective global coupling functions. We investigate how the functional form of the coupling determines the…
In the first part of this note, we review and compare various instances of the notion of twisted coefficient system, a.k.a. polynomial functor, appearing in the literature. This notion hinges on how one defines the degree of a functor from…
Collective actuation in active solids, the spontaneous condensation of the dynamics on a few elastic modes, takes place whenever the deformations of the structure reorient the forces exerted by the active units composing, or embedded in,…
The static and dynamic properties of ring polymers in concentrated solutions remains one of the last deep unsolved questions in Polymer Physics. At the same time, the nature of the glass transition in polymeric systems is also not well…
We propose a new driving scheme, when different parts of a system are driven with different, generally incommensurate, frequencies. Such driving provides a flexible handle to control various properties of the system and to obtain new types…
Field induced assembly of reconfigurable structures with complex hierarchical configurations has recently become an area of intense research with the promise for exciting applications in programmable self-assembly and nano/microstructure…
We give a mathematical framework to describe the evolution of an open quantum systems subjected to finitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems…
In this paper we adapt previous work on rewriting string diagrams using hypergraphs to the case where the underlying category has a traced comonoid structure, in which wires can be forked and the outputs of a morphism can be connected to…
It has been recently argued that near-integrable nonautonomous one-degree-of-freedom Hamiltonian systems are constrained by KAM theory even when the time-dependent (nonintegrable) part of the Hamiltonian is given in the form of a…
Lenses, optics and dependent lenses (or equivalently morphisms of containers, or equivalently natural transformations of polynomial functors) are all widely used in applied category theory as models of bidirectional processes. From the…
One can think of power series or polynomials in one variable, such as $P(x)=2x^3+x+5$, as functors from the category $\mathsf{Set}$ of sets to itself; these are known as polynomial functors. Denote by $\mathsf{Poly}_{\mathsf{Set}}$ the…
The well-defined but intricate course of time evolution exhibited by many naturally occurring phenomena suggests some source of dynamic order sustaining it. In spite of its obviousness as a problem, it has remained absent from the…
We develop layered monoidal theories -- a generalisation of monoidal theories combining formal descriptions of a system at different levels of abstraction. Via their representation as string diagrams, monoidal theories provide a graphical…
Most work on causality in machine learning assumes that causal relationships are driven by a constant underlying process. However, the flexibility of agents' actions or tipping points in the environmental process can change the qualitative…
In this article we examine the dynamics of a colloidal particle driven by a modulated force over a sinusoidal optical potential energy landscape. Coupling between the competing frequencies of the modulated drive and that of particle motion…
Starting from the notion of discriminantly separable polynomials of degree two in each of three variables, we construct a class of integrable dynamical systems. These systems can be integrated explicitly in genus two theta-functions in a…
Expansion of the categorical point of view on many areas of the mathematics and mathematical physics will cause to deeper understanding of genuine features of these problems. New applications of categorical methods are connected with new…
This short article is devoted to the dynamics of controlled (and, therefore, open) systems. The internal forces, which appear only in the presence of external free controls and depend explicitely on them, are considered. Such interactive…
The dynamics of a polymer ring enclosing a constant {\sl algebraic} area is studied. The constraint of a constant area is found to couple the dynamics of the two Cartesian components of the position vector of the polymer ring through the…
Our aim is to introduce a category-theoretic framework sufficiently general to describe a wide variety of open kinematic systems in classical mechanics while uniquely characterizing systems with specified simplest components. The framework…