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Probability Distribution Functions of the Number of Scattering Collisions in Electron Slowing Down.
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Develop a Tolerance System for the CODE V Monte Carlo Tolerancing Module that Uses Manufacturing Data as Input for the Required Probability Distribution Functions
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Interpretation of Magnetospheric Cold Particle Distribution Functions Measured with Active Spacecraft Control
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Quarkonium semiclassical transport in quark-gluon plasma: factorization and quantum correction
We study quarkonium transport in the quark-gluon plasma by using the potential nonrelativistic QCD (pNRQCD) effective field theory and the framework of open quantum systems. We argue that the coupling between quarkonium and the thermal bath is weak using separation of scales, so the initial density matrix of the total system factorizes and the time evolution of the subsystem is Markovian. We derive the semiclassical Boltzmann equation for quarkonium by applying a Wigner transform to the Lindblad equation and carrying out a semiclassical expansion. We resum relevant interactions to all orders in the coupling constant at leading power of the nonrelativistic and multipole expansions. The derivation is valid for both weakly coupled and strongly coupled quark-gluon plasmas. We find reaction rates in the transport equation factorize into a quarkonium dipole transition function and a chromoelectric gluon distribution function. For the differential reaction rate, the definition of the momentum dependent chromoelectric gluon distribution function involves staple-shaped Wilson lines. For the inclusive reaction rate, the Wilson lines collapse into a straight line along the real time axis and the distribution becomes momentum independent. The relation between the two Wilson lines is analogous to the relation between the Wilson lines appearing in the gluon parton distribution function (PDF) and the gluon transverse momentum dependent parton distribution function (TMDPDF). The centrality dependence of the quarkonium nuclear modification factor measured by experiments probes the momentum independent distribution while the transverse momentum dependence and measurements of the azimuthal angular anisotropy may be able to probe the momentum dependent one. We discuss one way to indirectly constrain the quarkonium in-medium real potential by using the factorization formula and lattice calculations. The leading quantum correction to the semiclassical transport equation of quarkonium is also worked out. The study can be easily generalized to quarkonium transport in cold nuclear matter, which is relevant for quarkonium production in eA collisions in the future Electron-Ion Collider.
Molecular dynamics simulation of the effect of cooling rate on the structure and properties of lithium disilicate glass
The effects of cooling rate on the structure and properties of lithium disilicate (LS2) glass are investigated using molecular dynamics (MD) computer simulations. The evolution of structural features such as pair distribution function, bond angle distribution, and Li coordination distribution are determined, and correlated with dynamic and static properties to elucidate the effects of cooling rate. The density, elastic moduli, and diffusion coefficient are found to be highly sensitive to cooling rate, whereas the Si pair distribution function and bond angle distribution are weakly affected by the cooling rate. Additionally, the changes of Si-O-Si bond angle and Li coordination number suggest the formation of Li cluster at lower cooling rates. Furthermore, by comparing results from other simulations and reported experiments, we confirm that the increase of cooling rate leads to an increase of conductivity and a decrease of density. Finally, at very high cooling rates, we find that all the atoms in LS2-glass do not relax simultaneously, but do so in two distinct configurations.
Evidence Theory Representations for Properties Associated With Weak Link/Strong Link Systems, Part 2: Failure Time and Failure Temperature
The use of evidence theory and associated cumulative plausibility functions (CPFs), cumulative belief functions (CBFs), cumulative distribution functions (CDFs), complementary cumulative plausibility functions (CCPFs), complementary cumulative belief functions (CCBFs), and complementary cumulative distribution functions (CCDFs) in the analysis of loss of assured safety (LOAS) for weak link (WL)/strong link (SL) systems is introduced and illustrated. Article content includes cumulative and complementary cumulative belief, plausibility, and probability for (i) time at which LOAS occurs for a one WL/two SL system, (ii) time at which a two-link system fails, (iii) temperature at which a two-link system fails, and (iv) temperature at which LOAS occurs for a one WL/two SL system. The presented results can be generalized to systems with more than one WL and two SLs.
Evidence Theory Representations for Properties Associated With Weak Link/Strong Link Systems, Part 3: Margins for Failure Time and Failure Temperature
The use of evidence theory and associated cumulative plausibility functions (CPFs), cumulative belief functions (CBFs), cumulative distribution functions (CDFs), complementary cumulative plausibility functions (CCPFs), complementary cumulative belief functions (CCBFs), and complementary cumulative distribution functions (CCDFs) in the analysis of time and temperature margins associated with loss of assured safety (LOAS) for one weak link (WL)/two strong link (SL) systems is illustrated. Article content includes cumulative and complementary cumulative belief, plausibility, and probability for (i) SL/WL failure time margins defined by (time at which SL failure potentially causes LOAS) – (time at which WL failure potentially prevents LOAS), (ii) SL/WL failure temperature margins defined by (the temperature at which SL failure potentially causes LOAS) – (the temperature at which WL failure potentially prevents LOAS), and (iii) SL/SL failure temperature margins defined by (the temperature at which SL failure potentially causes LOAS) – (the temperature of SL whose failure potentially causes LOAS at the time at which WL failure potentially prevents LOAS).
Renormalization and matching for the Collins-Soper kernel from lattice QCD
The Collins-Soper kernel, which governs the energy evolution of transverse- momentum dependent parton distribution functions (TMDPDFs), is required to accurately predict Drell-Yan like processes at small transverse momentum, and is a key ingredient for extracting TMDPDFs from experiment. Earlier we proposed a method to calculate this kernel from ratios of the so-called quasi-TMDPDFs determined with lattice QCD, which are defined as hadronic matrix elements of staple-shaped Euclidean Wilson line operators. Here we provide the one-loop renormalization of these operators in a regularization-independent momentum subtraction (RI'/MOM) scheme, as well as the conversion factor from the RI'/MOM-renormalized quasi-TMDPDF to the \( \overline{\mathrm{MS}} \) scheme. We also propose a procedure for calculating the Collins-Soper kernel directly from position space correlators, which simplifies the lattice determination.
Spatial coupling of gyrokinetic simulations, a generalized scheme based on first-principles
In this paper, we present a scheme that spatially couples two gyrokinetic codes using first-principles. Coupled equations are presented and a necessary and sufficient condition for ensuring accuracy is derived. This new scheme couples both the field and the particle distribution function. The coupling of the distribution function is only performed once every few time-steps, using a five-dimensional (5D) grid to communicate the distribution function between the two codes. This 5D grid interface enables the coupling of different types of codes and models, such as particle and continuum codes, or delta-f and total-f models. Transferring information from the 5D grid to the marker particle weights is achieved using a new resampling technique. Demonstration of the coupling scheme is shown using two XGC gyrokinetic simulations for both the core and edge. We also apply the coupling scheme to two continuum simulations for a one-dimensional advection–diffusion problem.
Stochastic Averaging of Radiative Transfer Coefficients for Relativistic Electrons
Abstract Synchrotron emissivities, absorptivities, and Faraday rotation and conversion coefficients are needed in modeling a variety of astrophysical sources, including Event Horizon Telescope (EHT) sources. We develop a method for estimating transfer coefficients that exploits their linear dependence on the electron distribution function, decomposing the distribution function into a sum of parts each of whose emissivity can be calculated easily. We refer to this procedure as stochastic averaging and apply it in two contexts. First, we use it to estimate the emissivity of an isotropicκdistribution function with a high-energy cutoff. The resulting coefficients can be evaluated efficiently enough to be used directly in ray-tracing calculations, and we provide an example calculation. Second, we use stochastic averaging to assess the effect of subgrid turbulence on the volume-averaged emissivity and along the way provide a prescription for a turbulent emissivity. We find that for parameters appropriate to EHT sources turbulence reduces the emissivity slightly. In the infrared, turbulence can dramatically increase the emissivity.
Mapping variations of redshift distributions with probability integral transforms
We present a method for mapping variations between probability distribution functions and apply this method within the context of measuring galaxy redshift distributions from imaging survey data. This method, which we name PITPZ for the probability integral transformations it relies on, uses a difference in curves between distribution functions in an ensemble as a transformation to apply to another distribution function, thus transferring the variation in the ensemble to the latter distribution function. This procedure is broadly applicable to the problem of uncertainty propagation. In the context of redshift distributions, for example, the uncertainty contribution due to certain effects can be studied effectively only in simulations, thus necessitating a transfer of variation measured in simulations to the redshift distributions measured from data. We illustrate the use of PITPZ by using the method to propagate photometric calibration uncertainty to redshift distributions of the Dark Energy Survey Year 3 weak lensing source galaxies. For this test case, we find that PITPZ yields a lensing amplitude uncertainty estimate due to photometric calibration error within 1 per cent of the truth, compared to as much as a 30 per cent underestimate when using traditional methods.
Kinetic stability of Chapman–Enskog plasmas
In this paper, we investigate the kinetic stability of classical, collisional plasma – that is, plasma in which the mean-free-path $\lambda$ of constituent particles is short compared with the length scale $L$ over which fields and bulk motions in the plasma vary macroscopically, and the collision time is short compared with the evolution time. Fluid equations are typically used to describe such plasmas, since their distribution functions are close to being Maxwellian. The small deviations from the Maxwellian distribution are calculated via the Chapman–Enskog (CE) expansion in $\lambda /L \ll 1$ , and determine macroscopic momentum and heat fluxes in the plasma. Such a calculation is only valid if the underlying CE distribution function is stable at collisionless length scales and/or time scales. We find that at sufficiently high plasma $\beta$ , the CE distribution function can be subject to numerous microinstabilities across a wide range of scales. For a particular form of the CE distribution function arising in strongly magnetised plasma ( viz. plasma in which the Larmor periods of particles are much smaller than collision times), we provide a detailed analytic characterisation of all significant microinstabilities, including peak growth rates and their associated wavenumbers. Of specific note is the discovery of several new microinstabilities, including one at sub-electron-Larmor scales (the ‘whisper instability’) whose growth rate in certain parameter regimes is large compared with other instabilities. Our approach enables us to construct the kinetic stability maps of classical, two-species collisional plasma in terms of $\lambda$ , the electron inertial scale $d_e$ and the plasma $\beta$ . This work is of general consequence in emphasising the fact that high- $\beta$ collisional plasmas can be kinetically unstable; for strongly magnetised CE plasmas, the condition for instability is $\beta \gtrsim L/\lambda$ . In this situation, the determination of transport coefficients via the standard CE approach is not valid.
ReaxFF molecular dynamics simulations of electrolyte–water systems at supercritical temperature
We have performed ReaxFF molecular dynamics simulations of alkali metal–chlorine pairs in different water densities at supercritical temperature (700 K) to elucidate the structural and dynamical properties of the system. The radial distribution function and the angular distribution function explain the inter-ionic structural and orientational arrangements of atoms during the simulation. The coordination number of water molecules in the solvation shell of ions increases with an increase in the radius of ions. We find that the self-diffusion coefficient of metal ions increases with a decrease in density under supercritical conditions due to the formation of voids within the system. The hydrogen bond dynamics has been interpreted by the residence time distribution of various ions, which shows Li+ having the highest water retaining capability. The void distribution within the system has been analyzed by using the Voronoi polyhedra algorithm providing an estimation of void formation within the system at high temperatures. We observe the formation of salt clusters of Na+ and K+ at low densities due to the loss of dielectric constants of ions. The diffusion of ions gets altered dramatically due to the formation of voids and nucleation of ions in the system.
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 equations for 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(vy) 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. Further, 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.
Polymorphous nature of cubic halide perovskites
Many common crystal structures can be described by a single (or very few) repeated structural motif (“monomorphous structures”) such as octahedron in cubic halide perovskites. Interestingly, recent accumulated evidence suggests that electronic structure calculations based on such macroscopically averaged monomorphous cubic ($\textit{Pm} – 3m$) halide perovskites obtained from x-ray diffraction, show intriguing deviations from experiment. These include systematically too small band gaps, dielectric constants dominated by the electronic, negative mixing enthalpy of alloys, and significant deviations from the measured pair distribution function. We show here that a minimization of the systems $\textit{T}$ = 0 internal energy via density functional theory reveals a distribution of different low-symmetry local motifs, including tilting, rotations, and B-atom displacements (“polymorphous networks”). This is found only if one allows for larger-than-minimal cell size that does not geometrically exclude low symmetry motifs. As the (super) cell size increases, the energy is lowered relative to the monomorphous cell, and stabilizes after ~32 formula units (≥160 atoms) are included. Being a result of nonthermal energy minimization in the internal energy without entropy, this correlated set of displacements must represent the intrinsic geometry preferred by the underlying chemical bonding (lone pair bonding), and as such has a different origin than the normal, dynamic thermal disorder modeled by molecular dynamics. Indeed, the polymorphous network, not the monomorphous ansatz, is the kernel structure from which high temperature thermal agitation develops. The emerging physical picture is that the polymorphous network has an average structure with high symmetry, yet the local structural motifs have low symmetries. In this work we find that, compared with monomorphous counterparts, the polymorphous networks have significantly lower predicted total energies, larger band gaps, and ionic dominated dielectric constants, and agree much more closely with the observed pair distribution functions. An analogous polymorphous situation is found in the paraelectric phase of a few cubic oxide perovskites where local polarization takes the role of local displacements in halide perovskites, and in the paramagnetic phases of a few 3 d oxides where the local spin configuration takes that role.
Propagation Pattern for Moment Representation of the Lattice Boltzmann Method
A propagation pattern for the moment representation of the regularized lattice Boltzmann method (LBM) in three dimensions is presented. Using effectively lossless compression, the simulation state is stored as a set of moments of the lattice Boltzmann distribution function, instead of the distribution function itself. An efficient cache-aware propagation pattern for this moment representation has the effect of substantially reducing both the storage and memory bandwidth required for LBM simulations. This article extends recent work with the moment representation by expanding the performance analysis on central processing unit (CPU) architectures, considering how boundary conditions are implemented, and demonstrating the effectiveness of the moment representation on a graphics processing unit (GPU) architecture.
Parton distributions and lattice-QCD calculations: Toward 3D structure
The strong force which binds hadrons is described by the theory of quantum chromodynamics (QCD). Determining the character and manifestations of QCD is one of the most important and challenging outstanding issues necessary for a comprehensive understanding of the structure of hadrons. Within the context of the QCD parton picture, the parton distribution functions (PDFs) have been remarkably successful in describing a wide variety of processes. However, these PDFs have generally been confined to the description of collinear partons within the hadron. New experiments and facilities provide the opportunity to additionally explore the transverse structure of hadrons which is described by generalized parton distributions (GPDs) and transverse-momentum-dependent parton distribution functions (TMD PDFs). In our previous report Lin et al. (2018), we compared and contrasted the two main approaches used to determine the collinear PDFs: the first based on perturbative QCD factorization theorems, and the second based on lattice-QCD calculations. In the present report, we provide an update of recent progress on the collinear PDFs, and also expand the scope to encompass the generalized PDFs (GPDs and TMD PDFs). We review the current state of the various calculations, and consider what new data might be available in the near future. We also examine how a shared effort can foster dialog between the PDF and lattice-QCD communities, and yield improvements for these generalized PDFs.