Related papers: Some relations in topological dynamics

We derive reciprocal integral relations between phases and amplitude moduli for a class of wave functions that are cyclically varying in time. The relations imply that changes of a certain kind (e.g. not arising from the dynamic phase)…

Topological groupoids admit various types of morphisms. We push these notions to the level of continuous groupoid actions to obtain various types of groupoid action morphisms. Some dynamical properties and their relation to these morphisms…

The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…

In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction…

Characterization of real-world complex systems increasingly involves the study of their topological structure using graph theory. Among global network properties, small-world property, consisting in existence of relatively short paths…

In this paper, we develop several structure theorems concerning commuting transformations and minimal $\mathbb{R}$-flows. Specifically, we show that if $(X,S)$, $(X,T)$ are minimal systems with $S$ and $T$ being commutative, then they…

We analyze the role played by local translational symmetry in the context of gauge theories of fundamental interactions. Translational connections and fields are introduced, with special attention being paid to their universal coupling to…

We give a survey of recent results on weak-strong uniqueness for compressible and incompressible Euler and Navier-Stokes equations, and also make some new observations. The importance of the weak-strong uniqueness principle stems, on the…

Hydrodynamic interactions are important for diverse fluids especially those with low Reynold's number such as microbial and particle-laden suspensions, and proteins diffusing in membranes. Unfortunately, while far-field (asymptotic)…

There are interesting parallels between the physics of heavy ion collisions and cosmology. Both systems are out-of-equilibrium and relativistic fluid dynamics plays an important role for their theoretical description. From a comparison one…

For the dynamics of a discontinuous map on a compact metric space, we describe an approach using suitable closed relations and connect it with the continuous dynamics on an invariant G-delta subset and with the continuous dynamics on the…

In this article we revisit the significance of the often debated structural similarity between the equations of electromagnetism and fluid dynamics. Although the matching of the two sets of equations has successfully been done for…

We derive exact scaling relations for two-dimensional relativistic hydrodynamic turbulence in the inertial range of scales. We consider both the energy cascade towards large scales and the enstrophy cascade towards small scales. We…

To better understand the collisionless dark matter flow on different scales, statistical theory involving kinematic and dynamic relations must be developed for different types of flow, e.g. incompressible, constant divergence, and…

This article is devoted to questions concerning the existence of solutions for partial differential equation problems modeling granular flows. The models studied take into account the complex threshold rheology of these flows, as well as…

Periodic orbits and cycles, respectively, play a significant role in discrete- and continuous-time dynamical systems (i.e. maps and flows). To succinctly describe their shifts when the system is applied perturbation, the notions of…

The existence and dynamical role of particular unstable Navier-Stokes solutions (exact coherent structures) is revealed in laboratory studies of weak turbulence in a thin, electromagnetically-driven fluid layer. We find that the dynamics…

Thermodynamics and dynamics of a classical two-dimensional system with dipole-like isotropic repulsive interactions are studied systematically using extensive molecular dynamics (MD) simulations supplemented by appropriate theoretical…

We review the dynamical behavior of giant fluid vesicles in various types of external hydrodynamic flow. The interplay between stresses arising from membrane elasticity, hydrodynamic flows, and the ever present thermal fluctuations leads to…

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…