Kinetic Theory

The Photon Matrix Model (PMM) predicts a dimensionless bifurcation constant k c ≈ 0.145898034, conjectured from PMM lattice symmetry and geometry to take the form k c = ϕ-4 , where ϕ = (1 + √ 5)/2. This constant marks the collapse threshold for the onset of structured field modes in coupled density-tension (ρ, τ) fields. The correlated region is scale-invariant within the PMM framework, with material-specific energy scales obtained via mapping from k c. For VO 2 , using a characteristic lattice spacing a ≈ 1.9 Å (V-O bond length) and an effective carrier mass m * ≈ 3m e from photoelectron spectroscopy measurements [13], E c ≈ ℏ 2 k 2 phys /(2m *) with k phys = √ k c /a gives E c ≈ 0.05 eV, within the scale of prior XAS anomalies. We propose time-resolved, coherent X-ray absorption experiments at the APS to resolve this threshold in VO 2 with ≤ 0.5 eV at the V K-edge (5465 eV) and ≤ 0.1 eV at the V L and O K edges (soft X-rays), applying Bayesian changepoint detection (p < 0.01) and high-SNR acquisition, including controls (TiO 2 ; W-doped VO 2). The aim is to achieve ≥ 5σ detection at effective SNR ≥ 200. This will be the first targeted, quantitative empirical test of the PMM's deterministic collapse geometry in a quantum material.

We show theoretically that nonlinear optical media characterized by a finite response time may support the existence of discrete spectral incoherent solitons. The structure of the soliton consists of three incoherent spectral bands that propagate in frequency space toward the low-frequency components in a discrete fashion and with a constant velocity. Discrete spectral incoherent solitons do not exhibit a confinement in the space-time domain, but exclusively in the frequency domain. The kinetic theory describes in detail all the essential properties of discrete spectral incoherent solitons: A quantitative agreement has been obtained between simulations of the kinetic equation and the nonlinear Schrödinger equation. Discrete spectral incoherent solitons may be supported in both the normal dispersion regime or the anomalous dispersion regime. These incoherent structures find their origin in the causality condition inherent to the nonlinear response function of the material. Considering the concrete example of the Raman effect, we show that discrete incoherent solitons may be spontaneously generated through the process of supercontinuum generation in photonic crystal fibers.

This study presents a comprehensive analysis of galaxy rotation curves from the SPARC database, aimed at uncovering systematic patterns in their shape and oscillations. We show that the observed oscillations are not random noise. Instead, they are statistically significant, reproducible features exhibiting clear spatial localization and correlation with morphological type. Three robust dynamical regimes—rising, flat, and declining—are identified. These regimes show weak correlation with internal galaxy parameters, suggesting a dominant role of the large-scale environment. Analysis of the radial acceleration profile $g_{\rm obs}(r)$ reveals systematic oscillations, especially in central regions. This challenges the interpretation of scatter in the Radial Acceleration Relation (RAR) as a purely baryonic effect. Our results establish an \textbf{empirical fact}: any complete theory of galactic dynamics must explain not only the average shape of the rotation curve but also its oscillatory structure. We propose that the shape of the rotation curve be viewed as a \textbf{dynamic imprint} of a galaxy’s position within the hierarchical structure of the Universe.

Velocity statistics of a uniformly heated granular fluid PEDRO M. REIS, MARK D. SHATTUCK , Benjamin Levich Institute, City College of New York, CUNY -We report results from an experimental investigation of a uniformly heated granular fluid. We vertically vibrate an ensemble of spheres (diameter D) confined by two horizontal glass plates. The top and bottom plates are separated by 1.6D which ensures a quasi-two dimensional configuration. We show that the use a rough, instead of flat, bottom plate has the considerable advantage of a more effective transfer of momentum from the vertical mode of the cell's vibration onto the motion of individual spheres in the horizontal plane. This allows a greater range of cell's filling fraction, ϕ, to be explored. We study the single particle velocity distributions, f (c), as a function of ϕ and vibration parameters; frequency and amplitude. In agreement with previous studies, we find a consistent overpopulation in the distribution's high energy tails, of the form log f ∼ -c 3/2 . Moreover, we calculate the deviations from a Mawellian, ∆(c) = f (c)/f M B (c) -1, where f M B ∼ exp(-c 2 ). We find ∆(c) to be well described by a 4th-order polynomial which, however, is not the Sonine polynomial commonly used in the solution of the Enskog-Boltzmann equation for inelastic hard spheres driven by a stochastic thermostat.

for an Invited Paper for the MAR08 Meeting of the American Physical Society "Free Energy" in Vibrated Granular Non-Equilibrium Steady-States. 1 MARK SHATTUCK, City College of New York Equilibrium statistical mechanics is generally not applicable to systems with energy input and dissipation present, and identifying relevant tools for understanding these far-from-equilibrium systems poses a serious challenge. Excited granular materials or granular fluids have become a canonical system to explore such ideas since they are inherently dissipative due to inter-particle frictional contacts and inelastic collisions. Granular materials also have far reaching practical importance in a number of industries, but accumulated ad-hoc knowledge is often the only design tool. An important feature of granular fluids is that the driving and dissipation mechanisms can be made to balance such that a Non-Equilibrium Steady-State (NESS) is achieved. We present strong experimental evidence for a NESS first-order phase transition in a vibrated twodimensional granular fluid. The phase transition between a gas and a crystal is characterized by a discontinuous change in both density and temperature and exhibits rate dependent hysteresis. We measure a "free energy"-like function for the system and compare and contrast this type of transition with an equilibrium first-order phase transition and a hysteretic backward bifurcation in a nonlinear pattern forming system.

Detecting interfacial defects at magnetic/nonmagnetic junctions 1 NICHOLAS HARMON, MICHAEL FLATT É, University of Iowa -Recent three terminal (3T) measurements in Co/LaAlO3/SrTiO3 show that spin-dependent transport through an interfacial defect is occurring instead of Hanle dephasing [1]. We propose extending 3T measurements into a coherent regime where single defects are detected by their local fields. The setup involves defects being situated between biased non-magnetic (NM) and ferromagnetic (FM) contacts. Spin torque on the FM drives an AC magnetization. Due to the large exchange interaction, the ability for charge to enter the FM depends on its spin and FM's relative orientation. As the FM precesses, the spin is dynamically filtered and a precessing spin accumulation remains at the defect. Local fields also precess the defect spin and interfere with the dynamic spin filtering. If the AC and local field are resonant, the spin accumulation is locked anti-parallel to the FM and leads to a dip in current. By adjusting the AC frequency, information on the local field is ascertained which, for hyperfine local fields, tells which nuclei are present at the defect and aids in identifying the defect. In the DC limit, defect spin accumulation leads to modifications in Hanle signals.

We prove nonlinear stability of line soliton solutions of the KP-II equation with respect to transverse perturbations that are exponentially localized as x → ∞. We find that the amplitude of the line soliton converges to that of the line soliton at initial time whereas jumps of the local phase shift of the crest propagate in a finite speed toward y = ±∞. The local amplitude and the phase shift of the crest of the line solitons are described by a system of 1D wave equations with diffraction terms. 1. Introduction 2. The Miura transformation and resonant modes of the linearized operator 2.1. Resonant modes 2.2. Linearized Miura transformation 3. Semigroup estimates for the linearized KP-II equation 4. Preliminaries 5. Decomposition of the perturbed line soliton 6. Modulation equations 7. À priori estimates for c(t, y) and x y (t, y) 8. L 2 bound on v(t, z, y) 9. Low frequencies bound of v(t, x, y) in y 10. Virial estimates 11. Proof of Theorem 1.1 12. Proof of Theorem 1.2 13. Proof of Theorem 1.3 Appendix A. Proof of Lemma 6.1

We introduce the S M Nazmuz Sakib Causal-Diamond Isoperimetric Law and the associated Sakib constants as a concise packaging of known small-diamond geometry in general relativity. For a 4D spacetime and a timelike geodesic observer with 4-velocity u a , we study the isoperimetric observable S(τ) = A(τ) 2 /V (τ) A0(τ) 2 /V0(τ) for a causal diamond of duration τ ; here (A 0 , V 0) denote Minkowski benchmarks of the same τ. We show that, as τ → 0, the expansion S(τ) = 1 + τ 2 κ 1 R ab u a u b + κ 2 R + O(τ 3) is universal and independent of the Weyl tensor at order τ 2 , in agreement with the analytic framework of small causal diamonds [1, 2, 3, 4]. With the convention above, the Sakib constants take the values κ 1 =-1 72 and κ 2 =-1 18 , which we verify numerically via correctly constructed null-boundary diamonds in FRW (conformal time), Schwarzschild, and Kottler (Schwarzschild-de Sitter) spacetimes, extending and systematizing computational checks previously scattered in the literature. We also clarify how alternative normalizations (e.g. using different S or boundary constructions) map to different coefficient pairs, resolving common sign/magnitude confusions. The work frames a reproducible numerical protocol that can serve as a benchmark for codes dealing with null congruences and small-set geometry.

According to the late A.B. Metzner , the phenomenon of polymer-induced drag reduction was independently discovered by two researchers, K.J. Mysels in May 1945, as reported by the discoverer at an AIChE symposium on drag reduction in 1970, and B.A. Toms in the summer of 1945, as reported by the discoverer at the IUTAM symposium on the structure of turbulence and drag reduction held in Washington, DC in 1976. The original fluids studied in these two first experimental investigations were micellar aluminum disoaps or rubber in gasoline (K.J. Mysels) and polymethyl methacrylate in monochlorobenzene (B.A. Toms). However, due to the war, the first records in an accessible publication were found later [2, 3] with journal contributions even much later . Since that time, the field has literally exploded with 500 papers until the seminal review by Virk [6] and 4900 papers by 1995 [1]. The first attribution of drag reduction to fluid viscoelasticity was by Dodge and Metzner [7], whereas the first description of drag reduction as Toms effect was by Fabula at the Fourth International Congress on Rheology, held in 1996 [8]. The first measurements of viscoelasticity of drag-reducing fluids were performed by Metzner and Park [9] and Hershey and Zakin [10]. The first articulations of a maximum drag reduction asymptote for dilute polymer solutions were reported by Castro and Squire [11], Giles and Pettit [12], and Virk et al. [13]. As far as the first proposed mechanisms of drag reduction due to fluid mechanical effects are concerned, Lumley attributed drag reduction to molecular stretching in the radial flow patterns in turbulent flows [14]. Simultaneously, Seyer and Metzner [15] clarified it even further, as due to high extensional deformation rates in radial flow patterns in turbulent flows and high resistance to stretching of viscoelastic fluids. More recently, Lumley and Blossey [16] elaborated further by arguing that polymer additives, by boosting the extensional viscosity of the fluid, affect especially the structure of the turbulent bursts; see also Ref. [17]. This same mechanism is also suspected to be operative when other additives are employed, such as micellar surfactant solutions

prevents the development of the tearing instability in plasma formations with strongly curved magnetic fields. However, this stability effect is largely diminished due to the phenomenon of deterministic chaos. This is due to the boundary between the regions of chaotic and regular motion that may work like the Cherenkov cone for the potential component of a tearing perturbation.

We construct a linear response theory of applying shear deformations from boundary walls in the film geometry in Kubo's theoretical scheme. Our method is applicable to any solids and fluids. For glasses, we assume quasi-equilibrium around a fixed inherent state. Then, we obtain linearresponse expressions for any variables including the stress and the particle displacements, even though the glass interior is elastically inhomogeneous. In particular, the shear modulus can be expressed in terms of the correlations between the interior stress and the forces from the walls. It can also be expressed in terms of the inter-particle correlations, as has been shown in the previous literature. Our stress relaxation function includes the effect of the boundary walls and can be used for inhomogeneous flow response. We show the presence of long-ranged, long-lived correlations among the fluctuations of the forces from the walls and the displacements of all the particles in the cell. We confirm these theoretical results numerically in a two-dimensional model glass. As an application, we describe propagation of transverse sounds after boundary wall motions using these time-correlation functions We also find resonant sound amplification when the frequency of an oscillatory shear approaches that of the first transverse sound mode.

Is the kinetic equation for turbulent gas-particle flows ill-posed? MICHAEL REEKS, DAVID SWAILES, Univ of Newcastle, ANDREW BRAGG, Duke University -We examine recent claims that the kinetic equation for dispersed gas-particle flows has the properties of a backward heat equation and as a consequence, its solutions will in the course of time exhibit finite-time singularities. We show that the analysis leading to this conclusion is fundamentally incorrect because it ignores the coupling between the phase space variables in the kinetic equation and the time and particle inertia dependence of the phase space diffusion tensor. This contributes an extra +ve diffusion that always outweighs the contribution from the -ve diffusion associated with the dispersion along one of the principal axes of the phase space diffusion tensor. This is confirmed by a numerical evaluation of analytic solutions of these +ve and -ve contributions to the particle diffusion coefficient along this principal axis. We also examine other erroneous claims and assumptions made in previous studies that demonstrate the apparent superiority of the GLM PDF approach over the kinetic approach. In so doing we give a more balanced appraisal of the benefits of both PDF approaches. Date submitted: 31 Jul 2017 Electronic form version 1.4

The acceleration of interstellar pick-up ions as well as solar wind species has been observed at a multitude of interplanetary (IP) shocks by different spacecraft. The efficiency of injection of the pick-up ion component differs from that of the solar wind, and is strongly enhanced at highly oblique and quasi-perpendicular shock events. This paper expands upon previous work modeling the phase space distributions of accelerated ions associated with the shock event encountered on day 292 of 1991 by the Ulysses mission at 4.5 AU. As in the prior work, a kinetic Monte Carlo simulation is employed here to model the diffusive acceleration process. This exposition presents recent developments pertaining to the incorporation into the simulation of the diffusive characteristics incurred by field line wandering (FLW), according to the work of Giacalone and Jokipii. Resulting ion distributions and upstream diffusion scales are presented and compared with Ulysses data. For a pure field-line wandering construct, it is determined that the upstream spatial ramp scales are too short to accommodate the HI-SCALE flux increases for 200 keV protons, and that the distribution function for H + somewhat underpopulates the combined SWICS/HI-SCALE spectra at the shock. This contrasts our earlier theory/data comparison where it was demonstrated that diffusive transport in highly turbulent fields according to kinetic theory can successfully account for both the proton distribution data near the shock, and the observation of energetic protons upstream of this interplanetary shock, using a single turbulence parameter. The principal conclusion here is that, in a FLW scenario, the transport of ions across the mean magnetic field is slightly less efficient than is required to effectively trap energetic ions within a few Larmor radii of the shock layer, and thereby sustain acceleration at levels that match the observed distributions. This highlights the contrast between ion transport in highly turbulent shock environs and remote, less-disturbed interplanetary regions.

The simplest gas and approaching the simplest properties of a true gas is an ideal gas. Ideal gases satisfy the ordinary gas equation, while real gases do not always satisfy the ideal gas equation. Gas laws such as Boyle's Law, Charles' Law, and Gay Lusaac's Law, show the relationships between macroscopic units of various processes and formulations.This research is a type of literature review research by looking for theoretical references that are relevant to the cases or problems found.The results of Boyle's experiments stated that if the temperature of a gas in a closed vessel is kept constant, the gas pressure will be inversely proportional to its volume. Gay-Lusaac's law states that the volume of gas in a closed vessel is maintained constant, the gas pressure will be proportional to its absolute temperature. Charles's law states that at constant pressure, the volume of an ideal gas of a certain mass is directly proportional to its temperature. An ideal gas is a concept in physics which assumes that a gas consists of very small particles with zero volume, do not interact with each other, and move randomly in a closed container. This concept also assumes that collisions between gas particles and the walls of the container are elastic, meaning that kinetic energy is maintained in each collision.

Brief Description: This work presents a fundamental alternative to the standard ΛCDM model that explains 85% of the presumed universe mass (dark matter) and cosmic acceleration (dark energy) through a single physical mechanism: primordial vortices in the timestream. The theory makes specific, testable predictions for pulsar timing arrays (100 ns anomalies), GPS clocks, and supernova observations. If confirmed, this would mean that the majority of assumed cosmic substances are geometric effects of spacetime itself-a paradigm shift of similar magnitude to relativity theory.

Turbulent transport dynamics and level are investigated with the 5D gyrokinetic global code GY-SELA, modelling the Ion Temperature Gradient instability with adiabatic electrons. The heat transport exhibits large scale events, propagating radially in both directions at velocities of the order of the diamagnetic velocity. The effective diffusivity is in agreement with that reported in other gyrokinetic codes such as ORB5. Transition from Bohm to gyroBohm scaling is observed on the turbulence correlation length and time, when the normalized gyroradius ρ * is decreased from 10 -2 to 5.10 -3 . The transition value could depend on the distance to the ITG threshold. Collisions are modelled by a reduced Lorentz-type operator. It allows one to recover theoretical neoclassical predictions in the banana and plateau regimes, namely the heat diffusivity and the mean poloidal flow. In the turbulent regime, preliminary results suggest the turbulent transport increases with collisionality close to the threshold, in agreement with previous publications. Finally, the mean poloidal flow can be increased by about 40% as compared to the neoclassical value.

We systematically derived hydrodynamic equations and transport coefficients for a class of multi-speed lattice Boltzmann models in D dimensions, using the multi-scale technique. The constitutive relation of physical fluid is recovered by a modified equilibrium distribution in Maxwell-Boltzmann type. With the use of the rest particles and the particle reservoir, we were able to add one degree of freedom into the sound speed of the modeled fluid. When the sound speed is tuned small enough, the compressible region of fluid flow can be reached. An example 2-D model is presented, together with the numerical verification for its transport coefficients.

We consider the axisymmetric formulation of the equilibrium problem for a hot plasma in a tokamak. We adopt a non-overlapping mortar element approach, that couples C 0 piece-wise linear Lagrange finite elements in a region that does not contain the plasma and C 1 piece-wise cubic reduced Hsieh-Clough-Tocher finite elements elsewhere, to approximate the magnetic flux field on a triangular mesh of the poloidal tokamak section. The inclusion of ferromagnetic parts is simplified by assuming that they fit within the axisymmetric modeling and a new formulation of the Newton algorithm for the problem solution is stated.

This work demonstrates that Maxwell's equations and the Navier-Stokes equations emerge as macroscopic limits of a single, unified discrete dynamics of the θ-network within the Tensor Model of Discrete Dynamics (TMDD). By employing an analogy-based method and a rigorous continuum limit, we establish ontological correspondences: electromagnetic fields arise from the network's informational modes, while hydrodynamic parameters emerge from its coherent and geometric modes. We show that the fundamental constants ϵ 0 , µ 0 , and the kinematic viscosity ν are emergent, being expressed in terms of the model parameters ϵ, ζ, and γ. An analysis of the "tail" terms of the action-those that vanish in the classical limit-suggests a unified ontological framework for explaining several observed cosmological anomalies, including the H 0 tension, CMB anisotropy, variations in the fine-structure constant, and galactic rotation curve anomalies. In this interpretation, "dark matter" manifests as the internal pressure and viscous forces of the informational network, while galaxy morphology is determined by a dimensionless R eM number, which balances coherence and smoothing effects. This work demonstrates that TMDD provides a coherent ontological foundation from which both classical physical laws and their observed deviations arise naturally.

The spatiotemporal characteristics of the flow of 125 m glass beads have been studied experimentally in a 2.9 mm diameter vertical glass pipe by means of a digital linear charge coupled device camera. The dynamics and propagation of granular density fluctuations have been analyzed in various flow regimes for different values of the granular mass-flow rate and of the degree of humidity H. At low flow rates, the granular flow has a high compactness and periodic intermittency effects occur at high H values: a pulsating bubble appears at the top of the flow channel and its time dependence is studied. At higher granular flow rates, a wave regime is observed with alternate low and high compactness regions: at low H values, the wave velocity is constant with time and can be measured precisely from the spatiotemporal diagrams. At higher humidity contents, periodic oscillations of the wave system are observed: at high amplitudes, transient blockages of the flow and a stick-slip displacement mode have been identified. ͓S1063-651X͑99͒06901-9͔

We consider the oscillation of a class of second order delay functional differential equations. This relatively difficult problem is completely solved by applying the Cheng-Lin envelope method to find the exact conditions for the absence of real roots of the associated characteristic function. Several specific examples are also included to illustrate these conditions.

In the fast ignitor scenario the MA current carried by the forward laser driven beam MeV electrons, beyond the Alfvén limit, can be transported only by the presence of a plasma return current. This system is subject to collisionless filamentation (Weibel) instability in the coronal region. The effects of collisions in inner regions of the fusion pellet change the features of the filamentation instability and have to be considered. Simulations performed with PIC code osiris 2.0, including binary collisions, are presented, analyzing the filament behavior due to the collisional filamentation instability. As the collision frequency increases, the instability occurs at larger typical wavelengths compared to the collisionless case. Hence, only larger filaments can form, eventually becoming comparable to the typical beam size, and whole beam instabilities can be driven. These features are theoretically recovered using relativistic kinetic theory, including space charge effects, warm species and collisions through the BGK model. Furthermore, it is shown that collisions lead to small but not negligible growth rates even at temperatures for which the collisionless instability is completely stabilized by thermal effects.

In the current study, our aim is to define new generalized extended beta and hypergeometric types of functions. Next, we methodically determine several integral representations, Mellin transforms, summation formulas, and recurrence relations. Moreover, we provide log-convexity, Turán type inequality for the generalized extended beta function and differentiation formulas, transformation formulas, differential and difference relations for the generalized extended hypergeometric type functions. Also, we additionally suggest a generating function. Further, we provide the generalized extended beta distribution by making use of the generalized extended beta function as an application to statistics and obtaining variance, coefficient of variation, moment generating function, characteristic function, cumulative distribution function, and cumulative distribution function’s complement.

This manuscript continues and extends in various directions the result in , which gave a full derivation of the wave kinetic equation (WKE) from the nonlinear Schrödinger (NLS) equation in dimensions d ≥ 3. The wave kinetic equation describes the effective dynamics of the second moments of the Fourier modes of the NLS solution at the kinetic timescale, and in the kinetic limit in which the size of the system diverges to infinity and the strength of the nonlinearity vanishes to zero, according to a specified scaling law. Here, we investigate the behavior of the joint distribution of these Fourier modes and derive their effective limit dynamics at the kinetic timescale. In particular, we prove propagation of chaos in the wave setting: initially independent Fourier modes retain this independence in the kinetic limit. Such statements are central to the formal derivations of all kinetic theories, dating back to the work of Boltzmann (Stosszahlansatz). We obtain this by deriving the asymptotics of the higher Fourier moments, which are given by solutions of the wave kinetic heirarchy (WKH) with factorized initial data. As a byproduct, we also provide a rigorous justification of this hierarchy for general (not necessarily factorized) initial data. We treat both Gaussian and non-Gaussian initial distributions. In the Gaussian setting, we prove propagation of Gaussianity as we show that the asymptotic distribution retains the Gaussianity of the initial data in the limit. In the non-Gaussian setting, we derive the limiting equations for the higher order moments, as well as for the density function (PDF) of the solution. Some of the results we prove were conjectured in the physics literature, others appear to be new. This gives a complete description of the statistics of the solutions in the kinetic limit.

We study the time behavior of the Fokker-Planck equation in Zwanzig's rule (the backward-Ito's rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation-dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker-Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution.

Fluidization velocity is one of the significant parameter to characterize the hydrodynamic studies of fluidized bed as it determines different flow regimes. Computational Fluid Dynamics simulations are carried for a cylindrical bubbling fluidized bed with a static bed height of 1m with 0.150m diameter of gasification chamber. The parameter investigated is fluidization velocity in range of 0.05m/s to 0.7m/s. Sand with density 2600kg/m 3 and with a constant particle diameter of sand 385µm is employed for all the simulations. Simulations are conducted utilizing with the commercial Computational Fluid Dynamics software, ANSYS-FLUENT. The bubbling flow regime is appeared above the air inlet velocity of 0.2m/s. Bubbling character is increased with increase in inlet air velocities indicated by asymmetrical fluctuations of volume fractions in radial directions at different bed heights

1.1 Three normal gravity n-Heptane impacts conducted at the different initial solid temperatures of 24 • C, 90 • C and 104 • C. 1.2 Three normal gravity n-Heptane impacts conducted at the different initial solid temperatures of 160 • C, 195 • C and 205 • C.

Aiming at the energy efficient use and valorization of carbon dioxide in the framework of decarbonization studies and hydrogen research, a novel dielectric barrier discharge (DBD) reactor has been designed, constructed and developed. This test rig with water cooled electrodes is capable of a plasma power tunable in a wide range from 20W to 2 kW per unit. The reactor was designed to be ready for catalysts and membrane integration aiming at a broad range plasma conditions and processes, including low to moderate high pressures (0.05–2 bar). In this paper, preliminary studies on the highly endothermic dissociation of CO2, into O2 and CO, in a pure, inert, and noble gas mixture flow are presented. These initial experiments were performed in a geometry with a 3 mm plasma gap in a chamber volume of 40cm3, where the process pressure was varied from few 200 mbar to 1 bar, using pure CO2, and diluted in N2. Initial results confirmed the well-known trade-off between conversion rate (up to 60%...

We present a deep learning approximation, stochastic optimization based, method for wave kinetic equations. To build confidence in our approach, we apply the method to a Smoluchowski coagulation equation with multiplicative kernel for which an analytic solution exists. Our deep learning approach is then used to approximate the non-stationary solution to a 3-wave kinetic equation corresponding to acoustic wave systems. To validate the neural network approximation, we compare the decay rate of the total energy with previously obtained theoretical results. A finite volume solution is presented and compared with the present method.

Electrostatic streaming instabilities have been proposed as the generation mechanism for the electrostatic solitary waves observed in various space plasma environments. Past studies on the subject have been mostly based on the kinetic theory and particle simulations. In this paper, we extend our recent study based on one-dimensional fluid theory and particle simulations to two-dimensional regimes for both bi-streaming and bump-on-tail streaming instabilities in electron-ion plasmas. Both linear fluid theory and kinetic simulations show that for bi-streaming instability, the oblique unstable modes tend to be suppressed by the increasing background magnetic field, while for bump-on-tail instability, the growth rates of unstable oblique modes are increased with increasing background magnetic field. For both instabilities, the fluid theory gives rise to the linear growth rates and the wavelengths of unstable modes in good agreement with those obtained from the kinetic simulations. For u...

We give an update of results from two-colour, two-flavour QCD. Using a Wilson fermion action we calculate thermodynamic quantities as a function of chemical potential µ. Calculating the Karsch Coefficients non-perturbatively gives us access to the derivative method. Compared to our previously published results, we have improved our analysis leading to revised and more accurate estimates for the renormalised energy density, pressure and the trace anomaly.

Items with a reviewer byline (coded R) are by AMR's corps of dedicated outside volunteer reviewers. AMR will attempt to get critical reviews of all relevant textbooks, reference works, and monographs. Items without a reviewer byline (coded N) are prepared by AMR in-house staff and are largely based on material such as a book's table of contents and editor's preface or foreword. In the interest of timeliness, most conference proceedings and multi-author contributed volumes will receive descriptive notes in this fashion. Books deemed to be somewhat peripheral to AMR's basic scope may simply be listed by title. Also listed by title when first received are books under review.

ABSTRACT：A Cumulant based method has been introduced to extract quantum corrections in distribution function with the equilibrium Wigner-Boltzmann equation. It is shown that unlike the moment expansion used in hydrodynamic model, cumulant expansion converges much faster when distribution function is closed to Maxwellian with only first three cumulants are non-zero. In this case, quantum corrections higher than first order can be extracted mainly by lowest three cumulants and odd number derivatives of potential function. This method also provides a new way to determine the distribution function with Maxwellian form and study the role of potential function in quantum correction field.

A new dataset of uniform and steady sheet-flow experiments is presented in this paper. An acoustic concentration and velocity profiler (ACVP) is used to measure time-resolved profiles of collocated 2C velocity ($u,w$) and sediment concentration and to measure the time evolution of the bed interface position. Ensemble averaging over 11 similar experiment realisations is done to evaluate the mean profiles of streamwise velocity, concentration, sediment flux and Reynolds shear stress. The repeatability, stationarity and uniformity of the flow are carefully checked for a Shields number${\it\theta}\approx 0.5$and a suspension number of$S=1.1$. The mean profile analysis allows to separate the flow into two distinct layers: a suspension layer dominated by turbulence and a bed layer dominated by granular interactions. The bed layer can be further subdivided into a frictional layer capped by a collisional layer. In the suspension layer, the mixing length profile is linear with a strongly red...

In this paper, a gas-kinetic Bhatnagar-Gross-Krook ͑BGK͒ model is constructed for the Rayleigh-Be ´nard thermal convection in the incompressible flow limit, where the flow field and temperature field are described by two coupled BGK models. Since the collision times in the corresponding BGK models can be different, the Prandtl number can be changed to any value instead of a fixed Prϭ1 in the original BGK model ͓P. L. Bhatnagar, E. P. Gross, and M. Krook, Phys. Rev. 94, 511 ͑1954͔͒. The two-dimensional Rayleigh-Be ´nard thermal convection is studied and numerical results are compared with theoretical ones as well as other simulation results. ͓S1063-651X͑99͒00205-6͔

This paper shows finite time singularity formation for the Muskat problem in a stable regime. The framework we exhibit is with a dry region, where the density and the viscosity are set equal to 0 (the gradient of the pressure is equal to (0, 0)) in the complement of the fluid domain. The singularity is a splash-type: a smooth fluid boundary collapses due to two different particles evolve to collide at a single point. This is the first example of a splash singularity for a parabolic problem.

We have explored a simple microscopic model to simulate a thermally activated rate process where the associated bath which comprises a set of relaxing modes is not in an equilibrium state. The model captures some of the essential features of non-Markovian Langevin dynamics with a fluctuating barrier. Making use of the Fokker-Planck description, we calculate the barrier dynamics in the steady-state and nonstationary regimes. The Kramers-Grote-Hynes reactive frequency has been computed in closed form in the steady state to illustrate the strong dependence of the dynamic coupling of the system with the relaxing modes. The influence of nonequilibrium excitation of the bath modes and its relaxation on the kinetics of activation of the system mode are demonstrated. We derive the dressed time-dependent Kramers rate in the nonstationary regime in closed analytical form which exhibits strong nonexponential kinetics of the reaction coordinate. The feature can be identified as a typical non-Ma...

We investigate the scale-locality of cascades of conserved invariants at high kinetic and magnetic Reynolds numbers in the "inertial-inductive range" of magnetohydrodynamic (MHD) turbulence, where velocity and magnetic field increments exhibit suitable power-law scaling. We prove that fluxes of total energy and cross-helicity-or, equivalently, fluxes of Elsasser energies-are dominated by the contributions of local triads. Corresponding spectral transfers are also scale-local when defined using octave wavenumber bands. Flux and transfer of magnetic helicity may be dominated by nonlocal triads. The magnetic stretching term also may be dominated by non-local triads but we prove that it can convert energy only between velocity and magnetic modes at comparable scales. We explain the disagreement with numerical studies that have claimed conversion non locally between disparate scales. We present supporting data from a 1024 3 simulation of forced MHD turbulence.

A rigorous and most general covariant kinetic formalism is developed to study the nonlinear waves interaction in relativistic Vlasov plasmas. The typical nonlinear plasma reaction is a nonlinear current measured by the nonlinear plasma conductivity, and these quantities are derived here on the basis of relativistic Vlasov-Maxwell equations. Knowing the nonlinear plasma conductivity allows us to determine all plasma modes nonlinearly excited in plasma. The general covariant form of nonlinear conductivity is provided first for any value of plasma temperature and for the whole complex frequency plane by a correct analytical continuation. The further analysis is restricted to a correct relativistic particle distribution which is vanishing for particle speeds greater than speed of light. In the limit of nonrelativistic plasma temperatures the covariant nonlinear conductivity is significantly different from the standard noncovariant nonrelativistic results which are reached only in the formal limit of an infinitely large speed of light c → ∞.

The authors have evaluated the coefficients of the first nonanalytic logarithmic term in the density expansion for the transport properties of a gas of hard spheres, which is due to long-range dynamical correlations between molecules. Their results resolve present uncertainties about the magnitude of the effect, appear to be consistent with available information from molecular-dynamics calculations, and satisfy bounds for the logarithmic contribution deduced from experimental viscosity data for real gases.

Direct simulation Monte Carlo (DSMC) method was applied to numerical study of detonation in an H 2 /O 2 mixture with detailed chemical kinetics on the basis of effective DSMC molecular chemistry models. The results of the DSMC modeling of an unsteady detonation wave initiated by breakdown of a diaphragm between two channels with different pressures yield the velocity of detonation, which coincides with the Chapman-Jouguet velocity. The internal structure of the detonation wave obtained in DSMC simulations is in good qualitative agreement with the detonation-wave structure calculated on the basis of the Zeldovich -von Neumann -Doering (ZND) theory.

A hypersonic flow about a cylindrically blunted thick plate at a zero angle of attack is numerically studied with the kinetic (DSMC) and continuum (Navier-Stokes equations) approaches. The Navier-Stokes equations with velocity slip and temperature jump boundary conditions correctly predict the flow fields and surface parameters for values of the Knudsen number (based on the radius of leading edge curvature) smaller than 0.1. The results of computations demonstrate significant effects of the entropy layer on the boundary layer characteristics.

The submicroscopic track kinetic theory (STKT) is able to deal with a broad range of cases. We derive here its behaviour for very short etching times (new born tracks) and also for long etching times, where the classical track kinetic theory is a particular case of the STKT. Experimental data obtained previously by Bean et al. using the electroconductivity method are then analyzed by the STKT method. We show that good agreement is obtained between Bean and STKT theoretical results for the track diameter evolution.

time in Makrofol E is evaluated applying the nuclear track replica method and electron microscopy with 10 A resolution. The induction time is observed in foils with and without pre-etching. The track diameter vs etching time curves do not follow a linear relation for small track diameters.

Quoting from: the Britannica 2009 DVD "Relativistic cosmologies To derive his 1917 cosmological model, Einstein made three assumptions that lay outside the scope of his equations. The first was to suppose that the universe is homogeneous and isotropic in the large (i.e., the same everywhere on average at any instant in time), an assumption that the English astrophysicist Edward A. Milne later elevated to an entire philosophical outlook by naming it the cosmological principle. Given the success of the Copernican revolution, this outlook is a natural one. Newton himself had it implicitly in mind in his letter to Bentley (see above) when he took the initial state of the Cosmos to be everywhere the same before it developed "ye Sun and Fixt stars."

In this work, we consider a dilute reactive mixture of four constituents undergoing the reversible reaction A + B C + D. The mixture is described using the Boltzmann equation (BE) to chemically reactive systems which treats both elastic and reactive collisions as hard spheres type. We use the Chapman-Enskog method, at the first-order level of the Enskog expansion, to determine the non-equilibrium solution to the system in a chemical regime for which both elastic and reactive collisions occur with comparable characteristic times. In this case, the chemical reaction can be considered in its final stage, close to chemical equilibrium (fast process). We then determine the transport coefficients and focus our analysis on the evaluation of the coefficient associated with the shear viscosity and investigate how the reaction heat and the activation energy changes this coefficient. .

In this work, we consider a dilute reactive mixture of four constituents undergoing the reversible reaction A + B C + D. The mixture is described using the Boltzmann equation (BE) to chemically reactive systems which treats both elastic and reactive collisions as hard spheres type. We use the Chapman-Enskog method, at the first-order level of the Enskog expansion, to determine the non-equilibrium solution to the system in a chemical regime for which both elastic and reactive collisions occur with comparable characteristic times. In this case, the chemical reaction can be considered in its final stage, close to chemical equilibrium (fast process). We then determine the transport coefficients and focus our analysis on the evaluation of the coefficient associated with the shear viscosity and investigate how the reaction heat and the activation energy changes this coefficient. .

The quadrature-based method of moments (QMOM) offers a promising class of approximation techniques for reducing kinetic equations to fluid equations that are valid beyond thermodynamic equilibrium. In this work, we study a particular five-moment variant of QMOM known as HyQMOM and establish that this system is moment-invertible over a convex region in solution space. We then develop a highorder discontinuous Galerkin (DG) scheme for solving the resulting fluid system. The scheme is based on a predictor-corrector approach, where the prediction is a localized space-time DG scheme. The nonlinear algebraic system in this prediction is solved using a Picard iteration. The correction is a straightforward explicit update based on the time-integral of the evolution equation, where the space-time prediction replaces all instances of the exact solution. In the absence of limiters, the high-order scheme does not guarantee that solutions remain in the convex set over which HyQMOM is moment-realizable. To overcome this, we introduce novel limiters that rigorously guarantee that the computed solution does not leave the convex set of realizable solutions, thus guaranteeing the hyperbolicity of the system. We develop positivitypreserving limiters in both the prediction and correction steps and an oscillation limiter that damps unphysical oscillations near shocks. We also develop a novel ★ Corresponding author This research was partially funded by NSF Grants DMS-1620128 and DMS-2012699.

The quadrature-based method of moments (QMOM) offers a promising class of approximation techniques for reducing kinetic equations to fluid equations that are valid beyond thermodynamic equilibrium. In this work, we study a particular five-moment variant of QMOM known as HyQMOM and establish that this system is moment-invertible over a convex region in solution space. We then develop a highorder discontinuous Galerkin (DG) scheme for solving the resulting fluid system. The scheme is based on a predictor-corrector approach, where the prediction is a localized space-time DG scheme. The nonlinear algebraic system in this prediction is solved using a Picard iteration. The correction is a straightforward explicit update based on the time-integral of the evolution equation, where the space-time prediction replaces all instances of the exact solution. In the absence of limiters, the high-order scheme does not guarantee that solutions remain in the convex set over which HyQMOM is moment-realizable. To overcome this, we introduce novel limiters that rigorously guarantee that the computed solution does not leave the convex set of realizable solutions, thus guaranteeing the hyperbolicity of the system. We develop positivitypreserving limiters in both the prediction and correction steps and an oscillation limiter that damps unphysical oscillations near shocks. We also develop a novel ★ Corresponding author This research was partially funded by NSF Grants DMS-1620128 and DMS-2012699.

Hemiwicking has been introduced to describe the wetting state in which a liquid film surrounds a drop. To fully understand this special wetting state, we performed energy analysis and systematic lattice Boltzmann (LB) simulations on the wetting state through spreading liquid droplets on pillared hydrophilic substrates. Although the energy analysis shows that the hemiwicking is energetically unfavorable, droplets in stable hemiwicking are indeed observed in our LB simulations. This observation led us to conclude that we have obtained a result that is the same as the result obtained in the published experiment and theory: hemiwicking is dynamically trapped by the pinning of the imbibition front during invasion of the substrate texture by the liquid film. Our simulations show that the special wetting state is always found to emerge near the phase boundary between the liquid film and the Wenzel state. For the morphology of the droplet, strong deviation of the apparent contact angle from...