Related papers: On Mathematics of Bubbles in Dynamical Systems

Bubbles in complex fluids are often desirable, and sometimes simply inevitable, in the processing of formulated products. Bubbles can rise by buoyancy, grow or dissolve by mass transfer, and readily respond to changes in pressure, thereby…

Hydrodynamic turbulence is studied as a constrained system from the point of view of metafluid dynamics. We present a Lagrangian description for this new theory of turbulence inspired from the analogy with electromagnetism. Consequently it…

Incompressible, inviscid, irrotational, and unsteady flows with circulation $\Gamma$ around a distorted toroidal bubble are considered. A general variational principle that determines the evolution of the bubble shape is formulated. For a…

Nonequilibrium steady states in driven diffusive systems exhibit many features which are surprising or counterintuitive, given our experience with equilibrium systems. We introduce the prototype model and review its unusual behavior in…

We consider the basic features of complex dynamic and control systems, including systems having hierarchical structure. Special attention is paid to the problems of design and synthesis of complex systems and control models, and to the…

We consider binary mixtures of fluids with components having different temperatures. A new dynamical pressure term is associated with the difference of temperatures between components even if fluid viscosities are null. The non-equilibrium…

The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this…

A new self-learning algorithm for accelerated dynamics, reconnaissance metadynamics, is proposed that is able to work with a very large number of collective coordinates. Acceleration of the dynamics is achieved by constructing a bias…

A novel formulation of fluid dynamics as a kinetic theory with tailored, on-demand constructed particles removes any restrictions on Mach number and temperature as compared to its predecessors, the lattice Boltzmann methods and their…

Dynamical systems are a broad class of mathematical tools used to describe the evolution of physical and computational processes. Traditionally these processes model changing entities in a static world. Picture a ball rolling on an empty…

We propose a multiscale approach for predicting quantities in dynamical systems which is explicitly structured to extract information in both fine-to-coarse and coarse-to-fine directions. We envision this method being generally applicable…

We introduce the notion of a quasistatic dynamical system, which generalizes that of an ordinary dynamical system. Quasistatic dynamical systems are inspired by the namesake processes in thermodynamics, which are idealized processes where…

We present a new approach to studies of bubble dynamics in fluids. Relying on particle-based simulations, this method is general and suitable for cases where the commonly used perfect fluid description fails. We study expanding true vacuum…

The spherical dynamics of a bubble in a compressible liquid has been studied extensively since the early work of Gilmore. Numerical codes to study the behavior, including when large non-spherical deformations are involved, have since been…

We briefly review the foundations of a new relativistic fluid dynamics framework for polarized systems of particles with spin one half. Using this approach we numerically study the dynamics of the spin polarization of a rotating medium…

A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriate assumptions, the…

We review some recent developments which make use of the concept of `superstatistics', an effective description for nonequilibrium systems with a varying intensive parameter such as the inverse temperature. We describe how the asymptotic…

A series of stationary principles are developed for dynamical systems by formulating the concept of mixed convolved action, which is written in terms of mixed variables, using temporal convolutions and fractional derivatives. Dynamical…

This paper develops a dynamic equilibrium model where agents exhibit a strong form of belief heterogeneity: they disagree about zero probability events. It is shown that, somewhat surprisingly, equilibrium exists in this setting, and that…

Using the combinatorial properties of subsets of integers, a classification of metric dynamical systems was given in [V. Bergelson and T. Downarowicz, Large sets of integers and hierarchy of mixing properties of measure-preserving systems,…