Arbitrary Distribution Function Research Articles

Complete quasilinear model for the acceleration-driven lower hybrid drift instability and a computational assessment of its validity.

A complete quasilinear model is derived for the electrostatic acceleration-driven lower hybrid drift instability in a uniform two-species low-beta plasma in which current is perpendicular to the background magnetic field. The model consists of coupled nonlinear velocity space diffusion equationsfor the volume-averaged ion and electron distribution functions. Each species' diffusion coefficient depends on a time-evolving spectral density of the electric-field energy per unit volume and a time-evolving dispersion relation. The dispersion relation is expressed analytically in integral form without the use of asymptotic limits and applies to arbitrary distribution functions, so long as they can be expressed as a function of one velocity coordinate, e.g., f(v_{y}) or f(v_{⊥}). The quasilinear model conserves energy and is complete in that it fully describes the evolution of the distribution functions, including resonant and nonresonant particle-wave interactions, while accounting for distribution-function-dependent mixed-complex frequencies. The quasilinear diffusion model is solved numerically and self-consistently using a Crank-Nicolson temporal discretization and a second-order finite-volume velocity-space discretization. Numerical solutions are compared to nonlinear fourth-order accurate continuum kinetic Vlasov-Poisson simulations. Evolution of electric-field energy, growth rates, distribution functions, and diffusion coefficients are shown to be in agreement with Vlasov simulations. The quasilinear model is shown to predict anomalous transport terms, like resistivity and heating, to within a factor of order unity. Discrepancies between the quasilinear model and Vlasov simulations are assessed and attributed primarily to lack of damping in the quasilinear description and to the use of unperturbed-orbit susceptibilities in the linear theory dispersion relation. The results illuminate the predictive accuracy of the quasilinear model, place approximate bounds on its validity, and provide much needed vetting of quasilinear theory's ability to predict the nonlinear state of a microturbulent plasma.

Dynamic linkages in agricultural and energy markets: A quantile impulse response approach

AbstractThis article investigates the dynamic linkages between agricultural and energy markets, with a focus on an econometric analysis of multivariate stochastic dynamics based on the joint distribution of state variables. The analysis relies on a quantile approach followed by the evaluation of a copula. Applied to nonlinear price dynamics, the approach is flexible and supports a general evaluation of impulse response functions representing how prices adjust over time and across markets in response to a given shock. The analysis allows for arbitrary distribution functions; it captures own‐price and cross‐price dynamics that can depend on the nature of shocks; and it also allows current changes to affect all moments of the future price distributions. The usefulness of the approach is illustrated in an econometric investigation of dynamic linkages in US corn, ethanol, and crude oil markets. We show how price adjustments can vary across quantiles, reflecting different speeds of adjustments depending on market conditions. We find evidence of nonlinear dynamics specific to the tails of the price distributions. We uncover evidence of positive contemporaneous codependence, especially tail dependence. We show how price shocks affect mean, variance, skewness as well as kurtosis of future price distributions. These results stress the importance of going beyond a standard mean‐variance analysis. They also shed new light on the deep linkages existing in the food‐fuel nexus.

PyCoSMoS: An advanced toolbox for simulating real-world hydroclimatic data

Simulation models are a fundamental tool for investigating hydrological processes and for water resource management. In this study, we introduce PyCoSMoS, a Python toolbox that enables researchers to simulate observed univariate time series mimicking hydroclimatic processes. This toolbox preserves arbitrary marginal distribution and autocorrelation functions, while significantly reducing computational burden. PyCoSMoS is built upon the mixed-Uniform CoSMoS method recently proposed by Papalexiou et al. (2023). The toolbox is designed to minimize the user’s input, requiring only observed time series, marginal distribution, correlation function, and the number of lags. The output provides both visual and quantitative comparisons between the observed and simulated time series. We evaluate the performance of the package using various synthetic case studies and the results demonstrate satisfactory accuracy. Furthermore, we apply the toolbox to three real case studies: precipitation, temperature, and relative humidity, for which the toolbox can successfully simulate the observed time series in each case.

A new approach to the evaluation and solution of the relativistic kinetic dispersion relation and verification with continuum kinetic simulation

The present work describes a new approach to evaluation and root finding for the kinetic dispersion relation of Langmuir waves, which is central to the analytical understanding of collisionless damping in plasmas. The plasma dispersion function is solved to machine precision using direct integration in the complex plane in combination with an analytic evaluation of the residue to account for the deformation along the Landau contour. To efficiently attain machine precision, the contour is displaced in the complex plane prior to integration, and numerical subtleties related to the placement of the contour are discussed. The approach is generic in that it applies to arbitrary distribution functions, with the present manuscript focused on relativistic cases. Detailed verification of results via direct kinetic simulation in a variety of configuration space dimensions is also presented. Finally, the technique is applied to the challenging case of highly relativistic (i.e. extremely hot) plasmas. Here we show both qualitative agreement with prior work, as well as the disappearance of the Landau root which would have significant implication for real-life observation or experiment.

Modeling and braking analyses of longitudinal-vertical coupling towbarless aircraft taxiing system

The variation of tire vertical load has effects on the vehicle braking performance, which may lead to the misjudgment of braking distance and increasement of the accident risks. In order to evaluate the braking distance of the towbarless aircraft taxiing system (TLATS) accurately, a longitudinal-vertical coupling model of the TLATS is established, in which the effects of the vertical vibration on braking dynamics is considered. An 11-degrees of freedom (DOF) dynamic model of the TLATS, which consists of the system longitudinal motion, vertical vibration, and an advanced Lugre tire model, is proposed. The tire vertical dynamic loads are obtained by calculating system vibration differential equations as the input for the Lugre tire model, in which an arbitrary pressure distribution function over the contact patch and load related parameters are used. The Lugre tire model parameters are identified based on the virtual experiment results in ADAMS/Car software through a multi-objective optimization (MOO) method. The proposed tire model is more accurate by comparing with the models using other pressure distribution functions. The advanced Lugre model is integrated into the longitudinal-vertical coupling dynamic model of the TLATS, and the fuzzy PID control method is used to achieve the optimal slip rate during the braking procedure. The tire friction and TLATS’s braking performances in terms of the slip rate, braking speed and braking distance are compared between the coupling and uncoupling models under different traction velocities and the road excitations when a same fuzzy control method is used for the system braking. The results show that the proposed longitudinal-vertical coupling TLATS dynamic model could assess the braking behaviors of the TLATS more accurately than the simplified uncoupling model, which could decrease the potential safety risk of the aircraft towing operation on the airport apron.

On the analytical description of the nonlinear stage of the Weibel instability in collisionless anisotropic plasma

On the basis of the energy invariants for the Weibel instability in a collisionless non-relativistic plasma, an analytical relation is obtained between the instantaneous values of the space-averaged energy density of the magnetic field, its dominant wavenumber and the average plasma anisotropy parameter. The relation is valid for arbitrary particle velocity distribution functions, including ones that vary with time at the nonlinear stage of instability. It is obtained under the assumption that the plasma is homogeneous along a certain axis, determined, for example, by an external magnetic field, and taking into account only the modes with wavevectors orthogonal to this axis. We give an estimate of the maximum magnetic field energy achievable during the Weibel instability and show that its ratio to the initial longitudinal energy of particles, even for a large initial plasma anisotropy parameter, cannot exceed the value approximately equal to 0.2. The obtained analytical relation is verified using two-dimensional particle-in-cell simulations.

Partial EEDF analysis and electron diagnostics of atmospheric-pressure argon and argon–helium DBD plasma

Partial arbitrary electron energy distribution function (EEDF) results for cold atmospheric-pressure plasma are reported. The EEDF is obtained using the visible bremsstrahlung inversion (VBI) method. This machine learning method requires only optical emission spectroscopy (OES) measurement and a momentum transfer cross section to determine a partial EEDF. Numerical EEDF of a pure-argon dielectric barrier discharge dataset with changing peak-to-peak voltage and a helium–argon discharge with changing mixture ratio are reported. Resemblance between the numerical EEDF and a two-temperature Maxwell distribution is observed and a simplified three-point numerical EEDF is obtained. The electron temperature and relative electron number density for the bulk and high-energy electron populations are measured. The bulk electron temperature was consistently 0.3 eV. For pure argon, the high-energy electron temperature decreased exponentially from 3 to 2.2 eV with increasing peak-to-peak voltage from 3.6 to 6.3 kV. For the helium–argon dataset, the high-energy electron temperature decreased linearly from 4.2 to 2.2 eV with increasing argon fraction 25%–100%. From an OES measurement, the arbitrary EEDF can be observed by utilization of the VBI method. Based on this numerical EEDF, appropriate assumptions can be applied to simplify the quantification of electron diagnostics.

Non-perturbative non-Gaussianity and primordial black holes

We present a non-perturbative method for calculating the abundance of primordial black holes given an arbitrary one-point probability distribution function for the primordial curvature perturbation, . A non-perturbative method is essential when considering non-Gaussianities that cannot be treated using a conventional perturbative expansion. To determine the full statistics of the density field, we relate ζ to a Gaussian field by equating the cumulative distribution functions. We consider two examples: a specific local-type non-Gaussian distribution arising from ultra slow roll models, and a general piecewise model for with an exponential tail. We demonstrate that the enhancement of primordial black hole formation is due to the intermediate regime, rather than the far tail. We also show that non-Gaussianity can have a significant impact on the shape of the primordial black hole mass distribution.

Random Cantor sets and mini-bands in local spectrum of quantum systems

In this paper we give a physically transparent picture of singular-continuous spectrum in disordered systems which possess a non-ergodic extended phase. We present a simple model of identically and independently distributed level spacing in the spectrum of local density of states and show how a fat tail appears in this distribution at the broad distribution of eigenfunction amplitudes. For the model with a power-law local spacing distribution we derive the correlation function K(ω) of the local density of states and show that depending on the relation between the eigenfunction fractal dimension D2 and the spectral fractal dimension Ds encoded in the power-law spacing distribution, a singular continuous spectrum of a random Cantor set or that of an isolated mini-band may appear. In the limit of an infinite number of degrees of freedom the function K(ω) in the non-ergodic extended phase is singular at ω=0 with the branch-cut singularity for the case of a random Cantor set and with the δ-function singularity for the case of an isolated mini-band. For an absolutely continuous spectrum K(ω) tends to a finite limit as ω→0. For an arbitrary local spacing distribution function we formulated a criterion of fractality of local spectrum and tested it on simple examples.

Statistical Analysis of Single-Order Diffraction Grating with Quasi-Random Structures

Single-order diffraction gratings with quasi-random structures are effective optical elements in suppressing harmonics contamination. However, background intensity fluctuations introduced by quasi-random structures may affect the measurement of the spectra and the fluctuations lack quantitative description. A unified theoretical method is provided to describe quasi-random diffraction structures with arbitrary distribution functions and an arbitrary number of microstructures. The effect of the number of microstructures and distribution functions on the level of background fluctuations is evaluated. This work provides important guidance for the design and optimization of single-order diffraction gratings, which are attractive for spectral analysis and monochromator applications in synchrotron beam lines.

LaSCA: A Visualization Analysis Tool for Microstructure of Complex Systems

Over the past few decades, plenty of visualization software for the structural analysis of disordered/complex systems has been developed, but the uniqueness and correctness of structural quantification for such systems are still challenging. This paper introduces a visualization analysis tool based on the largest standard cluster analysis (LaSCA), which satisfies the three essential requirements for general structural analysis: physical correctness, objective identification, and injective representation. The specific functionalities of LaSCA include the directed graph model of complex systems, novel structural parameters, topologically close-packed structures, arbitrary partial pair distribution functions, the identification of long-range ordered structures, the adaptive selection of graphical elements, the tracking display of atom ID, user-defined view angles, various options for atom selection, and so on. The program is efficiently based on OpenGL hardware acceleration, employing special algorithms to treat bonds as cylinders or lines and treat atoms as spheres, icosahedrons, tetrahedrons, or points. LaSCA can process more than 1.2 million atoms within 50 s on a PC with 1 GB memory and four cores (Intel Core i7-9700). It is robust and low-cost for surveying short-, medium-, and long-range ordered structures and tracking their evolutions.

Effect of temperature anisotropy on the dynamics of geodesic acoustic modes

In this work, we revisit the linear gyro-kinetic theory of geodesic acoustic modes (GAMs) and derive a general dispersion relation for an arbitrary equilibrium distribution function of ions. A bi-Maxwellian distribution of ions is then used to study the effects of ion temperature anisotropy on GAM frequency and growth rate. We find that ion temperature anisotropy yields sensible modifications to both the GAM frequency and growth rate as both tend to increase with anisotropy and these results are strongly affected by the electron to ion temperature ratio.

ANALYSIS OF THE USE OF ALGORITHMS TO FILTER INFORMATION AND FILL GAPS

The analysis shows that the real information flows are characterized by: arbitrary distribution function; the presence of both quantitative and qualitative indicators; the absence of part of the meaningful data fragments; unreliability of data associated with errors in registration and their entry; parametric redundancy.
 Not all of the existing tools included in most of the instrumental systems, make it possible to solve a number of these problems. The article deals with the problem related to information filtering. The illustration of an algorithm scheme, which allows to conduct information filtering, is presented. The stages used in the construction of the algorithm are specified in detail. The geometric approach is applied. It gives an opportunity to lead consideration of information messages in the form of “constellations” which are connected with the i-dimensional feature hyperspace. An algorithm that allows to implement gap filling is proposed. The results presented in the paper can be useful when considering different information flows in modern information systems.

Homogeneous generalized master equation for an arbitrary initial state of a many-particle classical system

A special projection operator is introduced, which exactly transforms the Nakajima–Zwanzig inhomogeneous Generalized Master Equation (GME) with an irrelevant initial condition term (a source) into a completely closed homogeneous GME (with no initial correlations term) for the relevant part of an N-particle distribution function FN(t) for an arbitrary initial distribution function FN(0) of a system of classical particles. It resolves the problem of the derivation of a closed linear evolution equation from the Liouville equation with no “molecular chaos” type approximation. The obtained equation is equivalent to the completely closed equation for s-particle (s≤N) distribution function Fs(t). The initial correlations are accounted for in this equation in the modified by the introduced projection operator kernel governing the evolution of Fs(t). This equation is further simplified by presenting its kernel in the linear in the particles’ density n approximation. In this approximation the equations for one-particle F1(t) and two-particle F2(t) distribution functions are derived. Special attention is given to analyzing the equation for F1(t) and showed that this equation in the Markov approximation can be written as the linear Boltzmann or Landau (for a small interparticle interaction) equations but with additional terms caused by initial correlations.

Characterization of an atmospheric pressure plasma jet producing the auroral transition O(1S) to O(1D)

We present a detailed characterization of an atmospheric pressure plasma jet that produces the metastable oxygen states O(1S) and OD) with emission of the ‘auroral’ green line. The device used 99.999 pure argon as a working gas for the plasma generation. Optical emission spectroscopy was used to understand the active species present in the plasma jet and to infer the mechanism of O(1S) creation and destruction. The continuum spectrum was used in conjunction with a method based on machine learning for determining the arbitrary electron probability distribution function. Discharge and plasma properties were estimated from Lissajous plots and using calculations with the BOLSIG+ software. The metastable oxygen forms for all operating parameters of the plasma jet system in a linear electrode configuration. The camera images provided information of the overall plasma jet behavior as parameters were altered. While the metastable oxygen was produced for every iteration, the plasma jet behavior changed considerably when the powered and grounded electrodes are switched. Small admixtures of oxygen and nitrogen were introduced in the plasma jet to understand the kinetic processes of metastable oxygen destruction and the 557.7 nm auroral line. This behavior has implications for plasma reactive chemistry in fundamental areas such as auroral physics as well as technological applications of plasmas.

Development of a model for stochastic analysis of vehicle–track interaction considering spatial variability of track parameters

In this work, a model for achieving stochastic analysis of vehicle–track interaction systems is proposed based on random field realization of track parameters and the finite element coupling of rigid-elastic bodies. Aiming at the clarification of the spatial variability and correlation of track parameters on the influence of vehicle–track dynamic performance, a general scheme based on Karhunen–Loève Expansion and cyclic calculation method is developed to realize a multi-dimensional random field that holds an arbitrary marginal distribution function and correlation structure, and to consider the inhomogeneity of system parameters along the longitudinal direction efficiently. Furthermore, the validation of the random field expansion against the vehicle–track system is implemented, and the dynamic effects of random track parameters are investigated through two special issues. Numerical results show that the spatial correlation of fastener stiffness affects the extreme response, especially the low-frequency component of rail displacement. The spatial dependence of the filling layer has little influence on the dynamic behavior of the vehicle subsystem, but it obviously changes the extreme stress and strain of the filling layer. Ignoring the spatial correlation of random variables might underestimate the performance of the track system.

Statistical Inference for Multi State Systems under the Generalized Modified Weibull Class

Multi state systems can be seen as semi-Markov processes by considering an arbitrary distribution function for sojourn times. Especially, in this work, the Modified Weibull distribution is employed to be the distribution of sojourn times with a shape parameter λ such that is member of a distributions family that is closed under minima. Parameters estimators are provided and the proposed methodology is evaluated using a detailed simulation procedure.

Practical considerations of the visible bremsstrahlung inversion (VBI) method for arbitrary EEDF determination in cold atmospheric-pressure plasma

The arbitrary electron energy distribution function (EEDF) of cold atmospheric-pressure plasma is determined from optical emission spectroscopy measurement. Using the electron-neutral bremsstrahlung-dominated continuum spectrum and relevant cross-section data, a partial arbitrary EEDF can be reconstructed through the reinforcement learning-based visible bremsstrahlung inversion method. From an atmospheric-pressure argon dielectric barrier discharge plasma emission spectrum (440–900 nm), a partial arbitrary EEDF can be determined with a resolution of 0.2 eV. The resemblance between the obtained arbitrary EEDF and a two-temperature Maxwellian was found with = 0.26 and 2.2 eV. The EEDF range is mostly constrained by the spectrum wavelength range.

A New Wavelet-Based Privatization Mechanism for Probability Distributions.

In this paper, we propose a new privatization mechanism based on a naive theory of a perturbation on a probability using wavelets, such as a noise perturbs the signal of a digital image sensor. Wavelets are employed to extract information from a wide range of types of data, including audio signals and images often related to sensors, as unstructured data. Specifically, the cumulative wavelet integral function is defined to build the perturbation on a probability with the help of this function. We show that an arbitrary distribution function additively perturbed is still a distribution function, which can be seen as a privatized distribution, with the privatization mechanism being a wavelet function. Thus, we offer a mathematical method for choosing a suitable probability distribution for data by starting from some guessed initial distribution. Examples of the proposed method are discussed. Computational experiments were carried out using a database-sensor and two related algorithms. Several knowledge areas can benefit from the new approach proposed in this investigation. The areas of artificial intelligence, machine learning, and deep learning constantly need techniques for data fitting, whose areas are closely related to sensors. Therefore, we believe that the proposed privatization mechanism is an important contribution to increasing the spectrum of existing techniques.

Characterizing stochastic cell-cycle dynamics in exponential growth.

Two powerful and complementary experimental approaches are commonly used to study the cell cycle and cell biology: One class of experiments characterizes the statistics (or demographics) of an unsynchronized exponentially growing population, while the other captures cell-cycle dynamics, either by time-lapse imaging of full cell cycles or in bulk experiments on synchronized populations. In this paper, we study the subtle relationship between observations in these two distinct experimental approaches. We begin with an existing model: A single-cell deterministic description of cell-cycle dynamics where cell states (i.e., periods or phases) have precise lifetimes. We then generalize this description to a stochastic model in which the states have stochastic lifetimes, as described by arbitrary probability distribution functions. Our analyses of the demographics of an exponential culture reveal a simple and exact correspondence between the deterministic and stochastic models: The corresponding state ages in the deterministic model are equal to the exponential mean of the age in the stochastic model. An important implication is therefore that the demographics of an exponential culture will be well fit by a deterministic model even if the state timing is stochastic. Although we explore the implications of the models in the context of the Escherichia coli cell cycle, we expect both the models as well as the significance of the exponential-mean lifetimes to find many applications in the quantitative analysis of cell-cycle dynamics in other biological systems.