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At least 1,513 records · Page 84

Statistical properties of three-dimensional two-fluid plasma model

The nonlinear dynamics of incompressible non-dissipative two-fluid plasma model is investigated through classical Gibbs ensemble methods. Liouville's theorem of phase space for each wave number is proved, and the absolute equilibrium spectra for Galerkin truncated two-fluid model are calculated. In two-fluid theory, the equilibrium is built on the conservation of three quadratic invariants: the total energy and the self-helicities for ions and electrons fluid, respectively. The implications of statistic equilibrium spectra with arbitrary ratios of conserved invariants are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Resistive switching phenomena: A review of statistical physics approaches

Here we report that resistive switching (RS) phenomena are reversible changes in the metastable resistance state induced by external electric fields. After discovery ~50 years ago, RS phenomena have attracted great attention due to their potential application in next-generation electrical devices. Considerable research has been performed to understand the physical mechanisms of RS and explore the feasibility and limits of such devices. There have also been several reviews on RS that attempt to explain the microscopic origins of how regions that were originally insulators can change into conductors. However, little attention has been paid to the most important factor in determining resistance: how conducting local regions are interconnected. Here, we provide an overview of the underlying physics behind connectivity changes in highly conductive regions under an electric field. We first classify RS phenomena according to their characteristic current–voltage curves: unipolar, bipolar, and threshold switchings. Second, we outline the microscopic origins of RS in oxides, focusing on the roles of oxygen vacancies: the effect of concentration, the mechanisms of channel formation and rupture, and the driving forces of oxygen vacancies. Third, we review RS studies from the perspective of statistical physics to understand connectivity change in RS phenomena. We discuss percolation model approaches and the theory for the scaling behaviors of numerous transport properties observed in RS. Fourth, we review various switching-type conversion phenomena in RS: bipolar-unipolar, memory-threshold, figure-of-eight, and counter-figure-of-eight conversions. Finally, we review several related technological issues, such as improvement in high resistance fluctuations, sneak-path problems, and multilevel switching problems.

36 MATERIALS SCIENCE↗

Statistical characteristic in time-domain of direct current corona-generated audible noise from conductor in corona cage

The corona-generated audible noise (AN) has become one of decisive factors in the design of high voltage direct current (HVDC) transmission lines. The AN from transmission lines can be attributed to sound pressure pulses which are generated by the multiple corona sources formed on the conductor, i.e., transmission lines. In this paper, a detailed time-domain characteristics of the sound pressure pulses, which are generated by the DC corona discharges formed over the surfaces of a stranded conductors, are investigated systematically in a laboratory settings using a corona cage structure. The amplitude of sound pressure pulse and its time intervals are extracted by observing a direct correlation between corona current pulses and corona-generated sound pressure pulses. Based on the statistical characteristics, a stochastic model is presented for simulating the sound pressure pulses due to DC corona discharges occurring on conductors. The proposed stochastic model is validated by comparing the calculated and measured A-weighted sound pressure level (SPL). The proposed model is then used to analyze the influence of the pulse amplitudes and pulse rate on the SPL. Furthermore, a mathematical relationship is found between the SPL and conductor diameter, electric field, and radial distance.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Statistical effects related to low numbers of reacting molecules analyzed for a reversible association reaction A + B = C in ideally dispersed systems: An apparent violation of the law of mass action

Theoretical analysis and computer simulations (Monte Carlo and numerical integration of differential equations) show that the statistical effect of a small number of reacting molecules depends on a way the molecules are distributed among the small volume nano-reactors (droplets in this study). A simple reversible association A + B = C was chosen as a model reaction, enabling to observe both thermodynamic (apparent equilibrium constant) and kinetic effects of a small number of reactant molecules. When substrates are distributed uniformly among droplets, all containing the same equal number of substrate molecules, the apparent equilibrium constant of the association is higher than the chemical one (observed in a macroscopic—large volume system). The average rate of the association, being initially independent of the numbers of molecules, becomes (at higher conversions) higher than that in a macroscopic system: the lower the number of substrate molecules in a droplet, the higher is the rate. This results in the correspondingly higher apparent equilibrium constant. A quite opposite behavior is observed when reactant molecules are distributed randomly among droplets: the apparent association rate and equilibrium constants are lower than those observed in large volume systems, being the lower, the lower is the average number of reacting molecules in a droplet. The random distribution of reactant molecules corresponds to ideal (equal sizes of droplets) dispersing of a reaction mixture. Our simulations have shown that when the equilibrated large volume system is dispersed, the resulting droplet system is already at equilibrium and no changes of proportions of droplets differing in reactant compositions can be observed upon prolongation of the reaction time.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Study on statistical breakdown delay time in argon gas using a W-band millimeter-wave gyrotron

In this study, we investigated plasma initiation delay times for argon volume breakdown at the W-band frequency regime. The threshold electric field is defined as the minimum electric field amplitude needed for plasma breakdown at various pressures. The measured statistical delay time showed an excellent agreement with the theoretical Gaussian distribution and the theoretically estimated formative delay time. Also, we demonstrated that the normalized effective electric field as a function of the product of pressure and formative time shows an outstanding agreement to that of 1D particle-in-cell simulation coupled with a Monte Carlo collision model [H. C. Kim and J. P. Verboncoeur, Phys. Plasmas 13, 123506 (2006)].

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A statistical study of gyro-averaging effects in a reduced model of drift-wave transport

Here, a statistical study of finite Larmor radius (FLR) effects on transport driven by electrostatic driftwaves is presented. The study is based on a reduced discrete Hamiltonian dynamical system known as the gyro-averaged standard map (GSM). In this system, FLR effects are incorporated through the gyro-averaging of a simplified weak-turbulence model of electrostatic fluctuations. Formally, the GSM is a modified version of the standard map in which the perturbation amplitude, K 0 , becomes K 0 J 0 ($\hat{p}$), where J 0 is the zeroth-order Bessel function and $\hat{p}$ s the Larmor radius. Assuming a Maxwellian probability density function (pdf) for $\hat{p}$ , we compute analytically and numerically the pdf and the cumulative distribution function of the effective drift-wave perturba- tion amplitude K 0 J 0 ($\hat{p}$). Using these results, we compute the probability of loss of confinement (i.e., global chaos), P c provides an upper bound for the escape rate, and that P t rovides a good estimate of the particle trapping rate. Lastly. the analytical results are compared with direct numerical Monte-Carlo simulations of particle transport.

42 ENGINEERING↗

Examining the role of fluctuations in the early stages of homogenous polymer crystallization with simulation and statistical learning

Here, we propose a relationship between the dynamics in the amorphous and crystalline domains during polymer crystallization: the fluctuations of ordering-rate about a material-specific value in the amorphous phase drive those fluctuations associated with the increase in percent crystallinity. This suggests a differential equation that satisfies the three experimentally observed time regimes for the rate of crystal growth. To test this postulated expression, we applied a suite of statistical learning tools to molecular dynamics simulations to extract the relevant phenomenology. This study shows that the proposed relationship holds in the early time regime. It illustrates the effectiveness of soft computing tools in the analysis of coarse-grained simulations in which patterns exist, but may not easily yield to strict quantitative evaluation. This ability assists us in characterizing the critical early time molecular arrangement during the primary nucleation phase of polymer melt crystallization. In addition to supporting the validity of the proposed kinetics expression, the simulations show that (i) the classical nucleation and growth mechanism is active in the early stages of ordering; (ii) the number of nuclei and their masses grow linearly during this early time regime; and (iii) a fixed inter-nuclei distance is established.

36 MATERIALS SCIENCE↗

Exploring the statistics of magnetic reconnection X-points in kinetic particle-in-cell turbulence

Magnetic reconnection is a ubiquitous phenomenon in turbulent plasmas. It is an important part of the turbulent dynamics and heating of space and astrophysical plasmas. We examine the statistics of magnetic reconnection using a quantitative local analysis of the magnetic vector potential, previously used in magnetohydrodynamics simulations, and now employed to fully kinetic particle-in-cell (PIC) simulations. Different ways of reducing the particle noise for analysis purposes, including multiple smoothing techniques, are explored. We find that a Fourier filter applied at the Debye scale is an optimal choice for analyzing PIC data. Lastly, we find a broader distribution of normalized reconnection rates compared to the MHD limit with rates as large as 0.5 but with an average of approximately 0.1.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Applying neutron transmission physics and 3D statistical full-field model to understand 2D Bragg-edge imaging

Bragg-edge imaging, which is also known as neutron radiography, has recently emerged as a novel crystalline characterization technique. Modelling of this novel technique by incorporating various features of the underlying microstructure (including the crystallographic texture, the morphological texture, and the grain size) of the material remains a subject of considerable research and development. In this paper, Inconel 718 samples made by additive manufacturing were investigated by neutron diffraction and neutron radiography techniques. The specimen features strong morphological and crystallographic textures and a highly heterogeneous microstructure. A 3D statistical full-field model is introduced by taking details of the microstructure into account to understand the experimental neutron radiography results. The Bragg-edge imaging and the total cross section were calculated based on the neutron transmission physics. A good match was obtained between the model predictions and experimental results at different incident beam angles with respect to the sample build direction. The current theoretical approach has the ability to incorporate 3D spatially resolved microstructural heterogeneity information and shows promise in understanding the 2D neutron radiography of bulk samples. With further development to incorporate the heterogeneity in lattice strain in the model, it can be used as a powerful tool in the future to better understand the neutron radiography data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

The ratio of the number of states in asymmetric and symmetric ozone molecules deviates from the statistical value of 2

Accurate calculations of vibrational states in singly and doubly substituted ozone molecules are carried out, up to dissociation threshold. Analysis of these spectra reveals noticeable deviations from the statistical factor of 2 for the ratio between the number of states in asymmetric and symmetric ozone molecules. It is found that, for the lower energy parts of spectra, the ratio is less than 2 in the singly substituted ozone molecules, but it is more than 2 in the doubly substituted ozone molecules. However, the upper parts of spectra, just below dissociation thresholds, exhibit a different behavior. In this energy range, the singly and doubly substituted ozone molecules behave similar, with the ratio of states in asymmetric and symmetric ozone molecules being more than 2 in both cases. Here, this property may contribute to an explanation of the mysterious η-effect in the ozone forming reaction that favors the formation of the asymmetric ozone molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Accelerating quantum optics experiments with statistical learning

Quantum optics experiments, involving the measurement of low-probability photon events, are known to be extremely time-consuming. We present a methodology for accelerating such experiments using physically motivated ansatzes together with simple statistical learning techniques such as Bayesian maximum a posteriori estimation based on few-shot data. We show that it is possible to reconstruct time-dependent data using a small number of detected photons, allowing for fast estimates in under a minute and providing a one-to-two order of magnitude speed-up in data acquisition time. We test our approach using real experimental data to retrieve the second order intensity correlation function, G (2) ($τ$), as a function of time delay τ between detector counts, for thermal light as well as anti-bunched light emitted by a quantum dot driven by periodic laser pulses. The proposed methodology has a wide range of applicability and has the potential to impact the scientific discovery process across a multitude of domains.

36 MATERIALS SCIENCE↗

Hall conductance and the statistics of flux insertions in gapped interacting lattice systems

We study charge transport for zero-temperature infinite-volume gapped lattice systems in two dimensions with short-range interactions. We show that the Hall conductance is locally computable and is the same for all systems that are in the same gapped phase. Here, we provide a rigorous version of Laughlin’s flux-insertion argument, which shows that for short-range entangled systems, the Hall conductance is an integer multiple of e 2 / h . We show that the Hall conductance determines the statistics of flux insertions. For bosonic short-range entangled systems, this implies that the Hall conductance is an even multiple of e 2 / h . Finally, we adapt a proof of quantization of the Thouless charge pump to the case of infinite-volume gapped lattice systems in one dimension.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Interface learning in fluid dynamics: Statistical inference of closures within micro–macro-coupling models

Many complex multiphysics systems in fluid dynamics involve using solvers with varied levels of approximations in different regions of the computational domain to resolve multiple spatiotemporal scales present in the flow. The accuracy of the solution is governed by how the information is exchanged between these solvers at the interface and several methods have been devised for such coupling problems. In this article, we construct a data-driven model by spatially coupling a microscale lattice Boltzmann method (LBM) solver and macroscale finite difference method (FDM) solver for reaction-diffusion systems. The coupling between the micro-macro solvers has one to many mapping at the interface leading to the interface closure problem, and we propose a statistical inference method based on neural networks to learn this closure relation. The performance of the proposed framework in a bifidelity setting partitioned between the FDM and LBM domain shows its promise for complex systems where analytical relations between micro-macro solvers are not available.

42 ENGINEERING↗

Detection of photon statistics and multimode field correlations by Raman processes

Glauber’s g (2) -function provides a common measure of quantum field statistics through two-photon coincidence counting in Hanbury Brown–Twiss measurements. Here, we propose to use nonlinear optical signals as a tool for the characterization of quantum light. In particular, we show that Raman measurements provide an alternative direct probe for a different component of the four-point correlation function underlying the g (2) -function. We illustrate this capacity for a specific quantum state obtained from a frequency conversion process. Our work points out how the analysis of controlled optical nonlinear processes can provide an alternative window toward the analysis of quantum light sources.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A statistical study of three-second foreshock ULF waves observed by the Magnetospheric Multiscale mission

We perform a statistical study of 3-s ultra-low frequency (ULF) waves using Magnetospheric Multiscale observations in the Earth's foreshock region. The average phase velocity in the plasma rest frame is determined to be anti-sunward, and the intrinsic polarization is right-handed. We further examine the linear instability conditions based on the drift-bi-Maxwellian distribution functions according to the observed plasma conditions. The resulting instability is a solution to the common dispersion equation of the ion/ion right-hand non-resonant and left-hand resonant instabilities. The predicted wave propagation is also predominantly anti-sunward. The cyclotron resonant conditions of the solar wind and backstreaming beam ions are evaluated, and we find that, in some cases, the anti-sunward propagating waves can be resonant with beam ions, which was overlooked in previous studies. The study suggests that the dispersion equation provides the 3-s ULF waves a fundamental explanation that unifies a rich variety of resonant conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Thermal-fluctuation effects on small-scale statistics in turbulent gas flow

Kolmogorov's theory of turbulence assumes that the small-scale turbulent structures in the energy cascade are universal and are determined by the energy dissipation rate and the kinematic viscosity alone. However, thermal fluctuations, absent from the continuum description, terminate the energy cascade near the Kolmogorov length scale. Here, we propose a simple superposition model to account for the effects of thermal fluctuations on small-scale turbulence statistics. Furthermore, for compressible Taylor–Green vortex flow, we demonstrate that the superposition model in conjunction with data from direct numerical simulation of the Navier–Stokes equations yields spectra and structure functions that agree with the corresponding quantities computed from the direct simulation Monte Carlo method of molecular gas dynamics, verifying the importance of thermal fluctuations in the dissipation range.

42 ENGINEERING↗

Statistical analysis of displacement damage in small devices from neutron and ion irradiation

Modern semiconductor devices, such as gate-all-around nanosheet field-effect transistors (GAA NS FETs), are smaller than displacement damage cascades from fission neutrons. In this regime, device failure may occur through low-probability single events, rather than by parametric degradation previously seen in larger devices. Here, we present a statistical model that predicts the probability of a damage event in a small device and the probability distribution of the magnitude, i.e., number of displacements within the device, from each event. The model is developed first for neutron irradiation and then for energetic ion irradiation. The model is consistent with results from recent experiments in which lithium-ion irradiation produced stepwise increases in subthreshold current in GAA NS FETs.

Wampler, W. R.↗