Related papers: Dynamical Systems On Generalised Klein Bottles
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
The general Ericksen-Leslie system for the flow of nematic liquid crystals is reconsidered in the non-isothermal case aiming for thermodynamically consistent models. The non-isothermal model is then investigated analytically. A fairly…
We present a universal approach to the investigation of the dynamics in generalized models. In these models the processes that are taken into account are not restricted to specific functional forms. Therefore a single generalized models can…
Resent works of Hawking and Susskind suggested that information is conserved in the universe. We extend this thesis and propose that dynamics of information - computations can conserve in Anti-de-Sitter cosmological model. Information…
A 2D numerical hydrodynamics approach is considered for modelling recent experimental results on the oscillation and collective behavior of convective flows. Our simulations consider the rising dynamics of heated fluid columns in a…
This paper is concerned with probabilistic techniques for forecasting dynamical systems described by partial differential equations (such as, for example, the Navier-Stokes equations). In particular, it is investigating and comparing…
We explore how to build a vector field from the various functions involved in a given mathematical program, and show that locally-stable equilibria of the underlying dynamical system are precisely the local solutions of the optimization…
We consider complex dynamical systems showing metastable behavior but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective…
Colloidal dispersions are commonly encountered in everyday life and represent an important class of complex fluid. Of particular significance for many commercial products and industrial processes is the ability to control and manipulate the…
Modeling and control of agent-based models is twice cursed by the dimensionality of the problem, as both the number of agents and their state space dimension can be large. Even though the computational barrier posed by a large ensemble of…
We introduce a new class of multiplications of distributions in one dimension merging together two different regularizations of distributions. Some of the features of these multiplications are discussed in a certain detail. We use our…
In this paper, We study the problem of learning a controllable representation for high-dimensional observations of dynamical systems. Specifically, we consider a situation where there are multiple sets of observations of dynamical systems…
Although real-world complex systems typically interact through sparse and heterogeneous networks, analytic solutions of their dynamics are limited to models with all-to-all interactions. Here, we solve the dynamics of a broad range of…
Boolean networks are a valuable class of discrete dynamical systems models, but they remain fundamentally limited by their inability to capture multi-way interactions in their components. To remedy this limitation, we propose a model of…
A discrete quantum spin system is presented in which several modern methods of canonical quantum gravity can be tested with promising results. In particular, features of interacting dynamics are analyzed with an emphasis on homogeneous…
A general system of particles (of one or several species) on a one dimensional lattice with boundaries is considered. Two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the…
Understanding the dissemination of diseases, information, and behavior stands as a paramount research challenge in contemporary network and complex systems science. The COVID-19 pandemic and the proliferation of misinformation are relevant…
The study of dynamic singularity formation in spacetime, focusing on scalar field collapse models, is analysed. We revisit key findings regarding open spatial topologies, concentrating on minimal conditions necessary for singularity and…
Inspired by the observation of intricate and beautifully dynamic patterns generated by food coloring on clean glass slides, we have investigated the behavior of propylene glycol and water droplets on high energy surfaces. In this fluid…
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…