Understanding Nuclear Matter with Jet Physics and Statistics
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Atomic, Nuclear and Particle Physics↗
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Particle transport in Markov stochastic mixtures with spatial gradients
Markov geometries are a prototype class of stochastic media that are widely used to model complex disordered systems. In a series of recent works, we have shown that spatially homogeneous (but possibly non-isotropic) Poisson tessellations can be conveniently used in order to generate three-dimensional realizations of Markov media and thus characterize the features of particle transport e.g. in fragmented fuel elements following severe nuclear accidents or Rayleigh-Taylor turbulent mixing for inertial confinement fusion. In this paper we show that Poisson tessellations can be extended to take into account the presence of spatial gradients, which commonly occur in real-world applications due to material stratification. For this purpose, we will provide an explicit construction of spatially-non-homogeneous Poisson tessellations, fully characterize their statistical properties, and finally illustrate the behaviour of particle transport in such random media. (authors)
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
A variance deconvolution estimator for efficient uncertainty quantification in Monte Carlo radiation transport applications
Monte Carlo simulations are at the heart of many high-fidelity simulations and analyses for radiation transport systems. As is the case with any complex computational model, it is important to propagate sources of input uncertainty and characterize how they affect model output. Unfortunately, uncertainty quantification (UQ) is made difficult by the stochastic variability that Monte Carlo transport solvers introduce. The standard method to avoid corrupting the UQ statistics with the transport solver noise is to increase the number of particle histories, resulting in very high computational costs. In this contribution, we propose and analyze a sampling estimator based on the law of total variance to compute UQ variance even in the presence of residual noise from Monte Carlo transport calculations. Here, we rigorously derive the statistical properties of the new variance estimator, compare its performance to that of the standard method, and demonstrate its use on neutral particle transport model problems involving both attenuation and scattering physics. We illustrate, both analytically and numerically, the estimator’s statistical performance as a function of available computational budget and the distribution of that budget between UQ samples and particle histories. We show analytically and corroborate numerically that the new estimator is unbiased, unlike the standard approach, and is more accurate and precise than the standard estimator for the same computational budget.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Reconstruction of effective potential from statistical analysis of dynamic trajectories
The broad incorporation of microscopic methods is yielding a wealth of information on the atomic and mesoscale dynamics of individual atoms, molecules, and particles on surfaces and in open volumes. Analysis of such data necessitates statistical frameworks to convert observed dynamic behaviors to effective properties of materials. Here, we develop a method for the stochastic reconstruction of effective local potentials solely from observed structural data collected from molecular dynamics simulations (i.e., data analogous to those obtained via atomically resolved microscopies). Using the silicon vacancy defect in graphene as a model, we apply the statistical framework presented herein to reconstruct the free energy landscape from the calculated atomic displacements. Evidence of consistency between the reconstructed local potential and the trajectory data from which it was produced is presented, along with a quantitative assessment of the uncertainty in the inferred parameters.
74 ATOMIC AND MOLECULAR PHYSICS↗
Single electron in a storage ring: a probe into the fundamental properties of synchrotron radiation and a powerful diagnostic tool
An experimental study of undulator radiation generated by a single electron was carried out at the Integrable Optics Test Accelerator (IOTA) storage ring at Fermilab. Photons were detected with a single-photon avalanche diode (SPAD) at an average rate of 20 kHz, corresponding to one detection every few hundred revolutions. Events were continuously recorded by a picosecond event timer for as long as 5 minutes at a time. The collected data were used to directly test the predictions of classical Poisson photostatistics. The study was motivated in part by a previous observation of sub-Poissonian statistics in a similar experiment with synchrotron radiation. In addition, we show that the time series of recorded events can be used to study the synchrotron motion of a single electron, yielding dynamical parameters such as the phase jitter of the radiofrequency cavity and the dependence of the synchrotron period on amplitude. Research plans for further experiments are also discussed.
47 OTHER INSTRUMENTATION↗
Mechanisms of energetic-particle transport in magnetically confined plasmas
Super-thermal ions and electrons occur in both space and fusion plasmas. Because these energetic particles (EP) have large velocities, EP orbits necessarily deviate substantially from magnetic surfaces. Orbits are described by conserved constants of motion that define topological boundaries for different orbit types. Electric and magnetic field perturbations produced by instabilities can disrupt particle orbits, causing the constants of motion to change. The statistics of the “kicks” associated with these perturbations determines the resulting cross field transport. A unifying theme of this tutorial is the importance of the perturbation’s phase at the particle’s position Θ = k • r – ωt, where k and ω are the wavevector and frequency of the perturbation, r is the EP position, and t is the time. A distinction is made between field perturbations that resonate with an aspect of the orbital motion and those that do not. Resonance occurs when the wave phase returns to its initial value in an integer multiple of an orbital period. Convective transport occurs when resonant particles experience an unvarying wave phase. Alternatively, multiple wave-particle resonances usually decorrelate the phase, resulting in diffusive transport. Large orbits increase the number of important resonances and can cause chaotic orbits even for relatively small amplitude waves. In contrast, in the case of non-resonant perturbations, orbital phase averaging reduces transport. Here, large field perturbations introduce additional effects, including nonlinear resonances at fractional values of the orbital motion. In summary, large orbits are a blessing and a curse: For non-resonant modes, orbit-averaging reduces transport but, for resonant transport, large orbits facilitate jumps across topological boundaries and enhance the number of important resonances.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Dynamic Rubies
Algorithmic art selected as a winner of the contest Pixel by Pixel: The Art of CHANCE, to be published in the April 2024 issue of CHANCE, the magazine of the American Statistical Association.
43 PARTICLE ACCELERATORS↗
Lagrangian and Eulerian drag models that are consistent between Euler-Lagrange and Euler-Euler (two-fluid) approaches for homogeneous systems
The undisturbed flow of a particle is of fundamental importance since it controls both the undisturbed flow force and the perturbation force (which includes quasisteady, added-mass, and history forces). Here we use the pairwise interaction extended point particle framework to evaluate the undisturbed flow of each particle through superposition of the perturbation flow induced by all its neighbors. This approach allows calculation of various statistics related to undisturbed fluid velocity under conditions of both stationary and nonstationary particles. In a random distribution of stationary particles, while the macroscale undisturbed flow is slowly varying, the microscale undisturbed flow that arises due to the perturbation flow of neighbors varies substantially from one particle to another and this in turn leads to large variation in the hydrodynamic force exerted on the particles. The effect of particle motion is generally to increase the particle-to-particle variation in the undisturbed fluid velocity of the particles. We observe that this increase is greater for the transverse component than for the streamwise component. As a result, with increasing random particle motion, the distribution of undisturbed fluid-velocity fluctuation becomes isotropic. Three different normalized forces are defined: $Φ^L$ is the Lagrangian normalized force on an individual particle suitable for application in a microscale-informed Euler-Lagrange simulation, $Φ^E$ is the Eulerian normalized average force suitable for application in an Euler-Euler simulation, and $Φ^{LE}$ is the Lagrangian normalized force on an individual particle suitable for application in the standard Euler-Lagrange simulation. In this work, we establish precise relations between these different definitions. The drag laws developed based on particle-resolved direct numerical simulation results and experiments are appropriate for application only as the Eulerian normalized average force. We introduce the force consistency relation and use it to obtain an expression for $Φ^L$, which when applied to each particle and averaged over all the particles equals $Φ^E$. The results are first obtained in the limit of stationary particles and then extended to the general case of nonstationary particles.
42 ENGINEERING↗
Kinetic theory of particle-in-cell simulation plasma and the ensemble averaging technique
Abstract We derive the kinetic theory of fluctuations in physically and numerically stable particle-in-cell (PIC) simulations of electrostatic plasmas. The starting point is the single-time correlation at the start of the simulation between the statistical fluctuations of the weighted densities of macroparticle centers in the plasma particle phase-space. The fluctuations are associated with different initial conditions, typically due to the random initial conditions (in velocity space) of the macroparticles/simulation plasma, assigned according to their initial distribution of probability. The single-time correlations at all time steps and in each spatial grid cell are then determined from the Laplace–Fourier transforms of the discretized Klimontovich-like equation for the macroparticles and Maxwell’s equations for the fields, as computed by modern PIC codes. We recover the expressions for the electrostatic field and the plasma particle density fluctuation autocorrelation spectra as well as the kinetic equations describing the average evolution of PIC-simulated plasma particles, first derived by Langdon (1970b Proc. 4th Conf. Numerical Simulation of Plasmas ) using a test macroparticle approach perturbing a discretized Vlasovian plasma and then averaging the obtained physical quantity over the initial macroparticle velocity distribution. We generalize and extend these results to the modern algorithms in PIC codes using arbitrary macroparticle weights. Analytical estimates of statistical fluctuation amplitudes are derived as a function of the plasma simulation parameters, using the central limit theorem in the limit of a large number of macroparticles per cell. The theory is then used to analyze the ensemble averaging technique of PIC simulations where statistical averages are performed over ensembles of PIC simulations, modeling the same plasma physics problem but using different statistical realizations of the initial distribution functions of the macroparticles. This method is illustrated by linear Landau damping uncovering (from noise, which is usually considered numerical) the physical fluctuations driven by a single small amplitude electrostatic wave perturbing a PIC simulation plasma in equilibrium.
fluctuations correlations↗
Charging Reactions Promoted by Geometrically Necessary Dislocations in Battery Materials Revealed by In Situ Single-Particle Synchrotron Measurements
Crystallographic defects exist in many redox active energy materials, e.g., battery and catalyst materials, which significantly alter their chemical properties for energy storage and conversion. However, there is lack of quantitative understanding of the interrelationship between crystallographic defects and redox reactions. Herein, crystallographic defects, such as geometrically necessary dislocations, are reported to influence the redox reactions in battery particles through single-particle, multimodal, and in situ synchrotron measurements. Through Laue X-ray microdiffraction, many crystallographic defects are spatially identified and statistically quantified from a large quantity of diffraction patterns in many layered oxide particles, including geometrically necessary dislocations, tilt boundaries, and mixed defects. The in situ and ex situ measurements, combining microdiffraction and X-ray spectroscopy imaging, reveal that LiCoO 2 particles with a higher concentration of geometrically necessary dislocations provide deeper charging reactions, indicating that dislocations may facilitate redox reactions in layered oxides during initial charging. The present study illustrates that a precise control of crystallographic defects and their distribution can potentially promote and homogenize redox reactions in battery materials.
25 ENERGY STORAGE↗
The 2025 Evaluation of Experimental Thermonuclear Reaction Rates (ETR25)
This work describes the formalism for estimating thermonuclear reaction rates for astrophysical applications, emphasizing modern statistical approaches such as Monte Carlo sampling and Bayesian models. We discuss related topics including the calculation of resonance energies from nuclear Q values, indirect estimates of particle partial widths, and matching of reaction rates at elevated temperatures to statistical model results. We have evaluated available experimental data on cross sections, resonance energies and strengths, partial widths, lifetimes, spin-parities, and spectroscopic factors. Based on these results, we have estimated numerical values of 78 experimental charged-particle thermonuclear reaction rates for target nuclei in the A = 2–40 mass region, for temperatures ranging from 1 MK to 10 GK. For each reaction, three rate values are provided: low, median, and high, corresponding to the 16th, 50th, and 84th percentiles, respectively, of the cumulative reaction rate probability density distribution. Additionally, we present the factor uncertainty of each rate at each temperature grid point. These results enable users to sample the reaction rate probability density in nucleosynthesis calculations, facilitating uncertainty estimates of nuclidic abundances. The rates presented here refer to their laboratory values. For use in stellar model simulations, these values need to be corrected for the effects of thermal excitations of the interacting nuclei. For each reaction, we include graphs that illustrate the fractional contributions to the overall reaction rate along with the associated uncertainty. These visuals are designed to assist both stellar modelers and nuclear experimentalists by identifying the primary sources of rate uncertain=^texttx);ty at specific stellar temperatures. A graphical comparison with earlier Monte Carlo rates is also provided.
Nuclear astrophysics↗
Overview of Algorithms for Using Particle Morphology in Pre-Detonation Nuclear Forensics
A major goal in pre-detonation nuclear forensics is to infer the processing conditions and/or facility type that produced radiological material. This review paper focuses on analyses of particle size, shape, texture (“morphology”) signatures that could provide information on the provenance of interdicted materials. For example, uranium ore concentrates (UOC or yellowcake) include ammonium diuranate (ADU), ammonium uranyl carbonate (AUC), sodium diuranate (SDU), magnesium diuranate (MDU), and others, each prepared using different salts to precipitate U from solution. Once precipitated, UOCs are often dried and calcined to remove adsorbed water. The products can be allowed to react further, forming uranium oxides UO3, U3O8, or UO2 powders, whose surface morphology can be indicative of precipitation and/or calcination conditions used in their production. This review paper describes statistical issues and approaches in using quantitative analyses of measurements such as particle size and shape to infer production conditions. Statistical topics include multivariate t tests (Hotelling’s T 2 ), design of experiments, and several machine learning (ML) options including decision trees, learning vector quantization neural networks, mixture discriminant analysis, and approximate Bayesian computation (ABC). ABC is emphasized as an attractive option to include the effects of model uncertainty in the selected and fitted forward model used for inferring processing conditions.
98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
Searching for TeV Dark Matter in Irregular Dwarf Galaxies with HAWC Observatory
We present the results of dark matter (DM) searches in a sample of 31 dwarf irregular (dIrr) galaxies within the field of view of the HAWC Observatory. dIrr galaxies are DM-dominated objects in which astrophysical gamma-ray emission is estimated to be negligible with respect to the secondary gamma-ray flux expected by annihilation or decay of weakly interacting massive particles (WIMPs). While we do not see any statistically significant DM signal in dIrr galaxies, we present the exclusion limits (95% C.L.) for annihilation cross section and decay lifetime for WIMP candidates with masses between 1 and 100 TeV. Exclusion limits from dIrr galaxies are relevant and complementary to benchmark dwarf Spheroidal (dSph) galaxies. In fact, dIrr galaxies are targets kinematically different from benchmark dSph, preserving the footprints of different evolution histories. We compare the limits from dIrr galaxies to those from ultrafaint and classical dSph galaxies previously observed with HAWC. We find that the constraints are comparable to the limits from classical dSph galaxies and ~2 orders of magnitude weaker than the ultrafaint dSph limits.
79 ASTRONOMY AND ASTROPHYSICS↗
$K^0_S$ and $Λ(\overline{Λ})$ two-particle femtoscopic correlations in PbPb collisions at $\sqrt{s_{NN}}$ = 5.02TeV
Two-particle correlations are presented for $K^0_S$, $Λ$, and $\overline{Λ}$ strange hadrons as a function of relative momentum in lead-lead collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV. The dataset corresponds to an integrated luminosity of 0.607 nb -1 and was collected using the CMS detector at the CERN LHC. These correlations are sensitive to quantum statistics and to final-state interactions between the particles. The source size extracted from the $K^0_S$$K^0_S$ correlations is found to decrease from 4.6 to 1.6 fm in going from central to peripheral collisions. Strong interaction scattering parameters (i.e., scattering length and effective range) are determined from the $ΛK^0_S$ and $ΛΛ$ (including their charge conjugates) correlations using the Lednický–Lyuboshitz model and are compared to theoretical and other experimental results.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Learning to simulate high energy particle collisions from unlabeled data
In many scientific fields which rely on statistical inference, simulations are often used to map from theoretical models to experimental data, allowing scientists to test model predictions against experimental results. Experimental data is often reconstructed from indirect measurements causing the aggregate transformation from theoretical models to experimental data to be poorly-described analytically. Instead, numerical simulations are used at great computational cost. We introduce Optimal-Transport-based Unfolding and Simulation (OTUS), a fast simulator based on unsupervised machine-learning that is capable of predicting experimental data from theoretical models. Without the aid of current simulation information, OTUS trains a probabilistic autoencoder to transform directly between theoretical models and experimental data. Identifying the probabilistic autoencoder’s latent space with the space of theoretical models causes the decoder network to become a fast, predictive simulator with the potential to replace current, computationally-costly simulators. Here, we provide proof-of-principle results on two particle physics examples, Z-boson and top-quark decays, but stress that OTUS can be widely applied to other fields.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
A modified Villain formulation of fractons and other exotic theories
We reformulate known exotic theories (including theories of fractons) on a Euclidean spacetime lattice. We write them using the Villain approach and then we modify them to a convenient range of parameters. The new lattice models are closer to the continuum limit than the original lattice versions. In particular, they exhibit many of the recently found properties of the continuum theories including emergent global symmetries and surprising dualities. Also, these new models provide a clear and rigorous formulation to the continuum models and their singularities. In appendices, we use this approach to review well-studied lattice models and their continuum limits. These include the XY-model, the $\mathbb{Z}_N$ clock-model, and various gauge theories in diverse dimensions. Here, this presentation clarifies the relation between the condensed-matter and the high-energy views of these systems. It emphasizes the role of symmetries associated with the topology of field space, duality, and various anomalies.
97 MATHEMATICS AND COMPUTING↗
Discovering invariant spatial features in electron energy loss spectroscopy images on the mesoscopic and atomic levels
Over the last two decades, Electron Energy Loss Spectroscopy (EELS) imaging with a scanning transmission electron microscope has emerged as a technique of choice for visualizing complex chemical, electronic, plasmonic, and phononic phenomena in complex materials and structures. The availability of the EELS data necessitates the development of methods to analyze multidimensional data sets with complex spatial and energy structures. Traditionally, the analysis of these data sets has been based on analysis of individual spectra, one at a time, whereas the spatial structure and correlations between individual spatial pixels containing the relevant information of the physics of underpinning processes have generally been ignored and analyzed only via the visualization as 2D maps. Here, we develop a machine learning-based approach and workflows for the analysis of spatial structures in 3D EELS data sets using a combination of dimensionality reduction and multichannel rotationally invariant variational autoencoders. This approach is illustrated for the analysis of both the plasmonic phenomena in a system of nanowires and in the core excitations in functional oxides using low loss and core-loss EELS, respectively. The code developed in this manuscript is open sourced and freely available and provided as a Jupyter notebook for the interested reader.
36 MATERIALS SCIENCE↗
Shock generated vorticity in spark discharges
Spark discharges induce a complex flow field consisting of a shock wave at early times (~ 1 μs), a pair of vortex rings, and a hot gas kernel. The vortex rings entrain ambient gas into the hot gas kernel and control its cooling and expansion. In this work, we investigate the shock wave's contribution in producing the vortex ring vorticity. We analyze high-speed (700 kHz) schlieren images of the shock wave for a range of electrical energies to measure the shock properties and estimate shock velocity and curvature. These measurements are combined with a model to calculate the vorticity generated. The measurements show that the highest vorticity is generated near the peak shock curvature location, and the shock curvature and strength increase with electrical energy deposited. A comparison of the vorticity estimated from the model to vorticity measurements from stereoscopic particle image velocimetry shows the results to be statistically equivalent. Furthermore, this suggests that the shock curvature and velocity contribute to the vortex rings induced by spark discharges.
42 ENGINEERING↗