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Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial…
Gyrokinetics is a rich and rewarding playground to study some of the mysteries of modern physics. In this thesis I present work, motivated by the quest for fusion energy, which seeks to uncover some of the inner workings of turbulence in…
The utilization of statistical methods an their applications within the new field of study known as Topological Data Analysis has has tremendous potential for broadening our exploration and understanding of complex, high-dimensional data…
Plasma turbulence occurs ubiquitously in space and astrophysical plasmas, mediating the nonlinear transfer of energy from large-scale electromagnetic fields and plasma flows to small scales at which the energy may be ultimately converted to…
In traditional thermodynamical and statistical-mechanical approaches one has (some) detailed knowledge of the principles governing the microdynamics of a system. However in many instances we may not have a Hamiltonian or good information…
It is shown, that at weakly nonlinear interaction of waves are possible as modes with chaotic dynamics, and with increasing degree of coherence. Conditions are found at which they arise. One of the types of such interaction is decays. The…
The space-filter approach has proved a fundamental tool in studying turbulence in neutral fluids, providing the ability to analyze scale-to-scale energy transfer in configuration space. It is well known that turbulence in plasma presents…
The application of linear kinetic treatments to plasma waves, damping, and instability requires favorable inequalities between the associated linear timescales and timescales for nonlinear (e.g., turbulence) evolution. In the solar wind…
Laboratory experiments provide a valuable complement to explore the fundamental physics of space plasmas without the limitations inherent to spacecraft measurements. Specifically, experiments overcome the restriction that spacecraft…
The nonlinear interaction of waves in a driven medium may lead to wave turbulence, a state such that energy is transferred from large to small lengthscales. Here, wave turbulence is observed in experiments on a vibrating plate. The…
The goal of this paper is the identification of the physical processes at the origin of the nonlinear behavior of a plasma conductor when an external constraint gradually departs the system from thermal equilibrium. This reveals the…
This brief overview stresses the importance of laboratory data and theory in analyzing astronomical observations and understanding the physical and chemical processes that drive the astrophysical phenomena in our Universe. This includes…
Astrophysical fluids are turbulent, magnetized and frequently partially ionized. As an example of astrophysical turbulence, the interstellar turbulence extends over a remarkably large range of spatial scales and participates in key…
In 1980 and 1981, two pioneering papers laid the foundation for what became known as nonlinear time-series analysis: the analysis of observed data---typically univariate---via dynamical systems theory. Based on the concept of state-space…
We describe main ideas of method of many-particle quantum hydrodynamics allows to derive equations for description of quantum plasma evolution. We also present definitions of collective quantum variables suitable for quantum plasmas. We…
Thermophoresis is a tool often applied in complex plasma experiments. One of the usual stated benefits over other experimental tools is that changes induced by thermophoresis neither directly depend on, nor directly influence, the plasma…
The advancement of millimeter wave and terahertz technologies have revolutionized high speed wireless networks and precise tracking systems. These technologies offer unique penetration capabilities in specific scenarios, significantly…
A consistent statistical description of kinetics and hydrodynamics of dusty plasma is proposed based on the Zubarev nonequilibrium statistical operator method. For the case of partial dynamics the nonequilibrium statistical operator and the…
Quantum computing is gaining increased attention as a potential way to speed up simulations of physical systems, and it is also of interest to apply it to simulations of classical plasmas. However, quantum information science is…
We focus our attention on some relevant aspects of the beam-plasma instability in order to refine some features of the linear and non-linear dynamics. After a re-analysis of the Poisson equation and of the assumption dealing with the…