Related papers: On Mathematics of Bubbles in Dynamical Systems
Recent work in dynamical systems theory has shown that many properties that are associated with irreversible processes in fluids can be understood in terms of the dynamical properties of reversible, Hamiltonian systems. That is,…
This short note is devoted to the representative dynamics, which realizes a link between the theory of controlled systems and representation theory. Dynamical inverse problem of representation theory for controlled systems is considered: to…
We analyse collective motion that occurs during rare (large deviation) events in systems of active particles, both numerically and analytically. We discuss the associated dynamical phase transition to collective motion, which occurs when…
A stochastic dynamics framework for the study of complex systems is presented.
Fluid turbulence is commonly associated with stronger drag, greater heat transfer, and more efficient mixing than in laminar flows. In many natural and industrial settings, turbulent liquid flows contain suspensions of dispersed bubbles and…
By using concrete scenarios, we present and discuss a new concept of probabilistic Self-Stabilization in Distributed Systems.
The dynamics of rapidly collapsing bubbles are of great interest due to the high degree of energy focusing that occurs withing the bubble. Molecular dynamics provides a way to model the interior of the bubble and couple the gas dynamics…
Dissipativity is an essential concept of systems theory. The paper provides an extension of dissipativity, named differential dissipativity, by lifting storage functions and supply rates to the tangent bundle. Differential dissipativity is…
A novel theoretical model for bubble dynamics is established that simultaneously accounts for the liquid compressibility, phase transition, oscillation, migration, ambient flow field, etc. The bubble dynamics equations are presented in a…
This paper exposes a novel exploratory formalism, which end goal is the numerical simulation of the dynamics of a cloud of particles weakly or strongly coupled with a turbulent fluid. Giventhe large panel of expertise of the list of…
Different mechanisms believed to be responsible for the generation of bursts in hydrodynamical systems are reviewed and a new mechanism capable of generating regular or irregular bursts of large dynamic range near threshold is described.…
Drag reduction in stationary turbulent flows by bubbles is sensitive to the dynamics of bubble oscillations. Without this dynamical effect the bubbles only renormalize the fluid density and viscosity, an effect that by itself can only lead…
We present a graphical analysis of the mechanisms underlying the occurrences of bubbling sequences and bistability regions in the bifurcation scenario of a special class of one dimensional two parameter maps. The main result of the analysis…
This article is an invitation. It is, first, an invitation to consider as a subject worthy of attention the wide range of situations where small discrete elements, either bubbles, droplets or solid particles, are embedded in turbulent…
Dissipative particle dynamics (DPD) belongs to a class of models and computational algorithms developed to address mesoscale problems in complex fluids and soft matter in general. It is based on the notion of particles that represent…
We introduce behavioral inequalities as a way to model dynamical systems defined by inequalities among their variables of interest. We claim that such a formulation enables the representation of safety-aware dynamical systems, systems with…
Discovery of causal relations is fundamental for understanding the dynamics of complex systems. While causal interactions are well defined for acyclic systems that can be separated into causally effective subsystems, a mathematical…
Equations of radial motion of a gas bubble in a compressible viscous liquid have been modified to account for compressibility at the bubble boundary. A new bubble boundary equation has been derived, including a new term resulted from liquid…
This paper introduces a new approach for bubble detection based on mixed causal and noncausal autoregressive processes and their tail process representation during an explosive episode. Departing from traditional definitions of bubbles as…
A dynamic sieve method is designed according to the basic sieve method. It mainly refers to the symbolic dynamics theory. By this method, we could connect the prime system with familiar 'Logistic Mapping'. An interesting discovery is that…