Related papers: Universality in computable dynamical systems: Old …
Using tools from computable analysis we develop a notion of effectiveness for general dynamical systems as those group actions on arbitrary spaces that contain a computable representative in their topological conjugacy class. Most natural…
Computational fluid dynamics lies at the heart of many issues in science and engineering, but solving the associated partial differential equations remains computationally demanding. With the rise of quantum computing, new approaches have…
Physical understanding of how the interplay between symmetries and nonlinear effects can control the scaling and multiscaling properties in a coupled driven system, such as magnetohydrodynamic turbulence or turbulent binary fluid mixtures,…
We introduce a fundamental theory for the kinetics of systems of classical particles. The theory represents a unification of kinetic theory, Brownian motion and field theory. It is self-consistent and is the dynamic generalization of the…
The study of fluids has been a topic of intense research for several hundred years. Over the years, this has further increased due to improved computational facility, which makes it easy to numerically simulate the fluid dynamics, which was…
This review article offers a survey of the research program focused on a systematic computational search for extreme and potentially singular behavior in hydrodynamic models motivated by open questions concerning the possibility of a…
Fluid turbulence is characterized by strong coupling across a broad range of scales. Furthermore, besides the usual local cascades, such coupling may extend to interactions that are non-local in scale-space. As such the computational…
The applications and impact of high fidelity simulation of fluid flows are far-reaching. They include settling some long-standing and fundamental questions in turbulence. However, the computational resources required for such efforts are…
We present TURB-Rot, a new open database of 3d and 2d snapshots of turbulent velocity fields, obtained by Direct Numerical Simulations (DNS) of the original Navier-Stokes equations in the presence of rotation. The aim is to provide the…
The notion of programming paradigms, with associated programming languages and methodologies, is a well established tenet of Computer Science pedagogy, enshrined in international curricula. However, this notion sits ill with Kuhn's classic…
The grand potential for open systems describes thermodynamics of fluid flows at low Mach numbers. A new system of reduced equations for the grand potential and the fluid momentum is derived from the compressible Navier-Stokes equations. The…
Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…
Advanced measurement techniques and high performance computing have made large data sets available for a wide range of turbulent flows that arise in engineering applications. Drawing on this abundance of data, dynamical models can be…
One of the fundamental results in computability is the existence of well-defined functions that cannot be computed. In this paper we study the effects of data representation on computability; we show that, while for each possible way of…
We explore the relationship between Turing completeness and topological entropy of dynamical systems. We first prove that a natural class of Turing machines that we call "branching Turing machines" (which includes most of the known examples…
The hydrodynamics of Newtonian fluids has been the subject of a tremendous amount of work over the past eighty years, both in physics and mathematics. Sadly, however, a mutual feeling of incomprehension has often hindered scientific…
Strand displacement and tile assembly systems are designed to follow prescribed kinetic rules (i.e., exhibit a specific time-evolution). However, the expected behavior in the limit of infinite time--known as thermodynamic equilibrium--is…
Numerical simulations of turbulent flows are well known to pose extreme computational challenges due to the huge number of dynamical degrees of freedom required to correctly describe the complex multi-scale statistical correlations of the…
Motivated by the phenomenologies of dynamic roughening of strings in random media and magnetohydrodynamics, we examine the universal properties of driven diffusive system with coupled fields. We demonstrate that cross-correlations between…
A model of fully developed turbulence of a compressible fluid is briefly reviewed. It is assumed that fluid dynamics is governed by a stochastic version of Navier-Stokes equation. We show how corresponding field theoretic-model can be…