Related papers: A Topological and Operator Algebraic Framework for…
We introduce a framework for analyzing topological tipping in time-evolutionary point clouds by extending the recently proposed Topological Optimal Transport (TpOT) distance. While TpOT unifies geometric, homological, and higher-order…
Synchrony patterns describe network states in which nodes of a coupled dynamical system are grouped into clusters based on synchronization between nodes. Beyond simple synchrony, synchronized clusters may also exhibit active or inactive…
Recent progress of symbolic dynamics of one- and especially two-dimensional maps has enabled us to construct symbolic dynamics for systems of ordinary differential equations (ODEs). Numerical study under the guidance of symbolic dynamics is…
We study nonequilibrium dynamics of SU(2) lattice gauge theory in Minkowski space-time in a classical-statistical regime, where characteristic gluon occupancies are much larger than unity. In this strongly correlated system far from…
This text, based on the author's Bachelor's thesis, introduces the theory of Algebraic Operads, a mathematical formalism that provides a unifying framework for modern algebra. We demonstrate how the fundamental theories of associative,…
We investigate the topological properties of dynamical states evolving on periodic oriented graphs. This evolution, that encodes the scattering processes occurring at the nodes of the graph, is described by a single-step global operator, in…
Symmetries are known to dictate important physical properties and can be used as a design principle in particular in wave physics, including wave structures and the resulting propagation dynamics. Local symmetries, in the sense of a…
We study the uniform ergodicity property for non-invertible topological and measure-preserving dynamical systems. It is shown that for topological dynamical systems uniform ergodicity is equivalent to eventually periodicity and that for…
All interesting and fascinating collective properties of a complex system arise from the intricate way in which its components interact. Various systems in physics, biology, social sciences and engineering have been successfully modelled as…
Persistent homology analysis, a recently developed computational method in algebraic topology, is applied to the study of the phase transitions undergone by the so-called XY-mean field model and by the phi^4 lattice model, respectively. For…
A unifying description of lattice potentials generated by aperiodic one-dimensional sequences is proposed in terms of their local reflection or parity symmetry properties. We demonstrate that the ranges and axes of local reflection symmetry…
We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By studying the intrinsic dynamics of each member of the population and their mutual interactions we observe the emergence of either spatio-temporal…
We propose an adaptive control strategy for the simultaneous estimation of topology and synchronization in complex dynamical networks with unknown, time-varying topology. Our approach transforms the problem of time-varying topology…
This study proposes the topology optimization method for moving rigid bodies subjected to forces from fluid flow, such as sails and turbines, with an unsteady time-dependent formulation. Unlike existing topology optimization frameworks in…
The Adler equation is a well-known one-dimensional model describing phase locking and synchronization. Motivated by recent experiments using optomechanical oscillators, we extend the model to include overtone-synthesized sinusoidal coupling…
The interplay between topology, dissipation and nonlinearities can give rise to a wealth of new phenomena and pave the way for novel topological lasers, sensors and other quantum devices. Along these lines, we propose here an optomechanical…
Topologically engineered optical materials support robust light transport. Herein, the investigated non-Hermitian lattice is trimerized and inhomogeneously coupled using uniform intracell coupling. The topological properties of the coupled…
We examine "dynamical similarities" in the Lagrangian framework. These are symmetries of an intrinsically determined physical system under which observables remain unaffected, but the extraneous information is changed. We establish three…
Understanding the realization of thermal equilibrium through the thermalization process in a many-body system is a fundamental and complex scientific question, bridging thermodynamics and classical dynamics and connecting to a host of…
Fish schools and bird flocks exhibit complex collective dynamics whose self-organization principles are largely unknown. The influence of hydrodynamics on such collectives has been relatively unexplored theoretically, in part due to the…