Session R18: Frontiers in Theory of Physical Systems

Heterodimensional Plasmonic Stubs Enabling THz Electronics

Emerging TeraFET technology has yielded sensitive tunable detectors of terahertz (THz) radiation. Using plasmonic crystals incorporating TeraFETs to achieve the instability of the plasma waves enabling electronic THz sources could revolutionize the THz electronics. But this approach faces challenges related to matching the boundary conditions between dissimilar plasmonic regions. We report on using “plasmonic stubs” – the narrow regions of an increased width to match the conditions at the interfaces between different devices regions. The physics of the problem (explored using the hydrodynamic model) is similar to that of the water flow in a river of a variable width. The mathematics of the problem is based on the transmission line model. Our analysis shows how to achieve tunable plasmonic instability (supporting THz emission) using plasmonic stubs.   

Measurement and Analysis of Uncertainty in Mechanical Quality Factor and Implications for LIGO Thermal-Noise Estimation

With the continued push for more-sensitive gravitational wave interferometers, reducing coating Brownian thermal noise becomes increasingly essential. We report on the uncertainty in quality factor experiments, which are key measurements for predicting the thermal noise of the optics in gravitational wave detectors. Through repeated measurements, we investigate the distribution associated with quality factor measurements. We estimate these uncertainties in mechanical loss measurements and discuss their possible causes. Finally, we comment on the implications of our results for the Laser Interferometer Gravitational-Wave Observatory, LIGO.   

Diffusion of Multi-Speed Gear-Shifting Brownian Swimmers.

We introduce a model for dispersion of independent swimmers jumping randomly between multiple translational velocities in arbitrary dimensions. Stochastic differential equations are introduced and used to produce simulations for comparison with theory. The associated Fokker-Planck equations are derived from the Langevin dynamics, giving an analytical prediction for the effective diffusion constant. This prediction is shown to be in good agreement with simulations, and is in a relatively simple form yielding a quick tool for experimentalists to obtain an accurate estimate of diffusion coefficient. A full analysis of the model is presented for the case with two velocities, and some extreme cases are discussed in the general model. We show adaptability of the model by fitting to three previous models of swimmers having two or three preferred velocities. These comparisons explore how stochastic vs. deterministic velocity changes and restricting certain velocity jumps result in different rates of dispersion.   

Unification of Gas Breakdown and Electron Emission

The miniaturization of technologies requires a deeper understanding of gas breakdown and electron emission at micro- and nanoscales. Previous work [A. M. Loveless and A. L. Garner, Phys. Plasmas, 24, 113522 (2017).] analytically unified Paschen’s law (PL) for Townsend avalanche with field emission (FE) to show continuous reduction in breakdown voltage with decreasing gap size. Another study [G. Meng, et al., Phys. Plasmas, 25, 082116 (2018).] demonstrated this behavior experimentally and derived an analytic solution with a linear relationship between breakdown voltage and gap size in the field emission-Townsend regime. Further reductions in gap size result in the transitions to space-charge limited emission (SCLE). This paper assesses the transitions between FE and the Mott-Gurney (MG) law for collisional SCLE, MG to the Child-Langmuir (CL) law for vacuum SCLE, and CL to quantum scales with Schrödinger’s equation. These derivations yield a triple point, where FE, MG, and CL predict a common breakdown voltage at a specific gap size and pressure. The implications of these transitions will be discussed.   

Nonlinear Evolution of Tearing Modes with Resistivity and Hyper-Resistivity

The nonlinear resistive tearing modes with hyper-resistivity has been analytically investigated. In contrast to the flux average method used by previous works, in the present work the quasilinear method has been extended to obtain the time evolution equation for nonlinear tearing modes. This equation can describe the general evolution of nonlinear tearing modes with both plasma resistivity and hyper-resistivity effects, especially the transition between these two situations. It is difficult to obtain its analytical solution directly. One special solution has been obtained. It is found that the magnetic flux grows with time to the one third power. Some discussions about two limiting cases for resistivity or hyper-resistivity dominant will be presented.   

A Coarse-Graining Procedure for Differential Equation Models

The Renormalization Group framework gives a prescription to determine which macroscopic variables are relevant in a system and sufficient to describe large scale dynamics. Can we develop an analogous methodology to extract important parameters of dynamical systems in general? The Fisher Information Matrix (FIM) formalism measures the response sensitivity of a system to perturbations in its control parameters and has emerged as one way of extracting a hierarchy of relevant variables, even when renormalization isn’t straightforward. The relevant parameter directions are given by eigenvectors of FIM: the hierarchy of relevance is induced by the magnitude of their eigenvalues. This procedure has been done previously for discrete diffusion coarse-grained in time and for the lattice Ising model coarse-grained spatially (Machta et al 2013). Relevant parameters had Fisher information eigenvalues that remained large after microscopic data was discarded. We now extend this analysis to systems of stochastic differential equations utilizing a temporal coarse-graining scheme inspired from Compatible Monte Carlo: specific points in the system are held fixed while the rest of the system is free. Coarse-graining then corresponds to increasing the temporal separation between these fixed points.   

Wiener-Khinchin theorem for Fourier-Laplace transformation; new derivation, and application to molecular simulations

The Wiener-Khinchin theorem for Fourier-Laplace transformation (WKT-FLT) provides a general purpose method to calculate numerically the one-sided Fourier transformation of an arbitrary autocorrelation function (ACF) from molecular simulations. However, the existing derivation of the WKT-FLT equation includes some ambiguities. Moreover, the equation obtained always yields 2 artifacts in the data computed. In this work, we present a new derivation that eliminates these ambiguities and artifacts.
We define an ACF as a natural extension of the known ACF, and write its Fourier-Laplace transformation as the Fourier transformation of the product of the Heaviside unit step function and the ACF. As the result, we successfully obtain an equation for the WKT-FLT. Then, we discretized the WKT-FLT equation to compute the frequency-domain correlation function (FDCF) from numerical simulations. It is found that a correction term is needed in order to avoid over-counting and to satisfy the sum rule. With the correction term, an artifact previously observed in the real part of the FDCF disappears. On the other hand, another artifact still remains in the imaginary part of the FDCF. We will discuss the cause of this artifact.   

Radiofrequency Bremsstrahlung of Electrons and Nanoparticles of Heterogeneous Plasma with a Condensed Dispersed Phase

The mechanism of braking radiation generation in the bulk of heterogeneous plasma formations has been studied in the framework of the statistical “cell” approach to the description of the ionization in heterogeneous plasma (HP). In our description of the effective interaction between microfields and charges in plasma, the stochastic motion of charged particles in HP is considered as an evolution of anharmonic oscillations executed by separate charges in an instant field of electric forces in the electroneutral cell. Effective values of frequency and the specific integral power of the braking radiation from HP in the radiofrequency spectral range are calculated by averaging over the ensemble of cells. The amplitude-frequency function and relative contributions of separate oscillation modes of plasma charges to the emitted radiation intensity are determined in the random phase approximation. A comparative analysis of the modeling data and the experimental data obtained for plasma with aluminum oxide nanoparticles was carried out in the space of key HP parameters. A good agreement between numerical results and experimental data was obtained at both qualitative and quantitative levels. Possible applications for telediagnostics of heterogeneous plasma formations were discussed.   

Supernova, fluid instabilities, and interfacial mixing

Supernovae and their remnants are a central problem in astrophysics due to their role in the stellar evolution and nuclear synthesis. A supernova’s explosion is driven by a blast wave causing the development of Rayleigh–Taylor and Richtmyer–Meshkov instabilities and leading to intensive interfacial mixing of materials of a progenitor star. Rayleigh–Taylor and Richtmyer–Meshkov mixing breaks spherical symmetry of a star and provides conditions for synthesis of heavy mass elements in addition to light mass elements synthesized in the star before its explosion. By focusing on hydrodynamic aspects of the problem, we identify the properties of Rayleigh–Taylor and Richtmyer–Meshkov dynamics with variable acceleration, discover subdiffusive character of the blast wave-induced interfacial mixing, and reveal the new mechanism of energy accumulation and transport at small scales in supernovae.   

Validation of classical mixing rule coupled with van der Waals type equation of state for sound speed of non-ideal gas mixture

In the CFD analyses for the combustion chamber of liquid rocket engine, classical mixing rule (CMR) has been often applied to van der Waals (vdW) type equation of state (EOS) such as Soave-Redlich-Kwong (SRK) EOS for prediction of the thermodynamic properties of non-ideal gas mixture. However, the CMR has hardly been validated because of the lack of experimental data. In the present study, for validation of the CMR coupled with SRK EOS for sound speed, which is important to compute the flow field in the combustion chamber, we applied molecular dynamics (MD) method to a Lennard-Jones fluid with modified Lorentz-Berthelot rules that simulates oxygen-hydrogen gas mixture. For the computation of sound speed, NVEPG ensemble proposed by Meier and Kabelac (Meier, K. and Kabelac, S., J. Chem. Phys., 2006.) was employed. As a result, the sound speed from the CMR coupled with SRK EOS agreed with that from MD simulation: it was suggested that the CMR can be applied to sound speed of oxygen-hydrogen mixture system in supercritical condition corresponding to the inlet region of combustion chamber.   

Nucleation of Quantized Vortices within a Quantum-Mechanical Compton Generator

In 1913, Arthur Compton invented a simple way to measure the rotation rate of the Earth with a tabletop-sized experiment. The experiment consisted of a large diameter circular ring of thin glass tubing filled with water and oil droplets. After placing the ring in a plane perpendicular to the surface of the Earth and allowing the fluid mixture to come to rest, he then abruptly rotated the ring, flipping it 180 degrees about an axis passing through its own plane. The result was that the fluid acquired a measurable drift velocity due to the Coriolis effect of the Earth. Compton measured this induced drift velocity by observing the motion of the oil droplets in the water with a microscope. This device, which is now named after him, is known as a Compton generator. The fundamental research objective of this project is to explore the dynamics of a quantum-mechanical analogue to the classical Compton generator experiment through the use of numerical simulations. Here, we present the first definitive results on the nucleation of quantized vortices within a quantum Compton generator and discuss future directions of the project.   

Using Monte Carlo and self-consistency to solve Newton's 2nd Law

In working with Newton's 2nd law, given a force, one seeks to solve for the position, x(t), and the velocity, v(t), as a function of time, t. Obtaining an analytic solution is, of course, of great value, when the problem is solvable. However, a numerical solution is a common route to difficult problems and methods to effect them exist. Two different numerical approaches of interest here are a Monte Carlo (MC) approach [1] and a self-consistent (SC) method. The idea, in the MC case, is to make a random guess for the acceleration, a(t), and to use the trapezoid method to get the velocity versus time, v(t). The time dependent position, x(t), follows by standard numerical integration of v(t). Depending on the situation, sometimes this method is not very efficient. In the SC method, one starts by making an initial numerical guess for a(x(t)) to obtain a v(t), which is used to obtain an x(t), which results in a new a(x(t)), etc. The process is repeated until there is no change in x(t). Here both methods are applied to simple systems and compared to the known analytic solutions for comparison and assessment purposes.
[1] "Solving initial value ordinary differential equations by Monte Carlo Method," M. N. Akhtar, M. H. Drad, and A. Ahmed, Proceeding of IAM, V.4, N.2 (2015), pp 149-174.   

Dispersion dynamics applications

One starting point is the Klein Gordon equation and the stable wave packet [1]. Simpler is relativity: insert Planck’s law and the de Broglie hypothesis. In simple units, angular frequency = +(k²+m_o²)^1/2, with m_o the rest mass. Now differentiate with respect to wave vector k. Three related velocities are the phase velocity, the group velocity and the speed of light. Dispersion dynamics requires consistently, negative mass in the antiparticle, with negative kinetic energy, negative momentum and negative angular velocity. These properties have widespread application in: the Hall effect; superconductivity; the switching principle; galactic rotational velocities; event horizons, uncertainty, intrinsic spin, etc.
[1] Dispersion dynamics in the Hall effect and pair bonds in HiTc, Bourdillon AJ, Nova Science, 1917, ISBN 978-1-53612-568-9
  

A Computational Study of the Energy Levels of Black Holes

In Cosmology, both de Sitter space and Anti-de Stter ( AdS_n) space are both named after the astrophysicist de Sitter. In Einstein's General Theory of Relativity (GR), space and time are on an equal footing, and we have a unified geometry of space-time, instead of a separate space and a separate time. This yields three cases of constantly curved space-time: de Sitter space with positive curvature; Minkowski space with zero curvature; and anti-de Sitter space with negative curvature. Very conveniently, the Anti-de Sitter space can be extended to any number of dimensions, with n representing the number of dimensions. A combination of classical General Relativity (GR) and Quantum Field Theory (QFT) provides an interesting thermodynamic description of black holes. We us an algorithm proposed by Nemati et al. (2013). In this formalism, we start with a hypercube with each of its vertices labeled with black hole binaries. The back holes are associated with probability functions, and the black holes move based on the probabilities. Our research has applications both Quantum Gravity (QG) and in Black Hole Physics (BHP).