Unraveling the Role of Temperature and Rainfall on Active Fires in the Brazilian Amazon Using a Nonlinear Poisson Model
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Carlos H. R. Lima↗
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Three-Point Correlations in Poisson Media
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Shelley, Alec [Stanford University]↗
On finite-dimensional smoothed-particle Hamiltonian reductions of the Vlasov equation
The inclusion of spatial smoothing in finite-dimensional particle-based Hamiltonian reductions of the Vlasov equation and related models is considered. Here, this work investigates the underlying Hamiltonian structure of such smoothed particle-based methods for Hamiltonian systems and the small-scale regularization such methods implicitly make in approximating the continuum theory. In the context of the Vlasov–Poisson equation and other mean-field Lie–Poisson systems, of which Vlasov–Poisson is a special case, smoothing amounts to a convolutive regularization of the Hamiltonian. This regularization may be interpreted as a change of the inner product structure used to identify the dual space in the Lie–Poisson Hamiltonian formulation. In particular, the shape function used for spatial smoothing may be identified as the kernel function of a reproducing kernel Hilbert space whose inner product is used to define the Lie–Poisson Hamiltonian structure. It is likewise possible to introduce smoothing in the Vlasov–Maxwell system, but in this case the Poisson bracket must be modified rather than the Hamiltonian. The smoothing applied to the Vlasov–Maxwell system is incorporated by inserting smoothing in the map from canonical to kinematic coordinates. In the filtered system, the Lorentz force law and the current, the two terms coupling the Vlasov equation with Maxwell’s equations, are spatially smoothed.
Hamiltonian mechanics↗
Tensor decompositions for count data that leverage stochastic and deterministic optimization
There is growing interest to extend low-rank matrix decompositions to multi-way arrays, or tensors. One fundamental low-rank tensor decomposition is the canonical polyadic decomposition (CPD). The challenge of fitting a low-rank, nonnegative CPD model to Poisson-distributed count data is of particular interest. Several popular algorithms use local search methods to approximate the maximum likelihood estimator (MLE) of the Poisson CPD model. Here, this work presents two new algorithms that extend state-of-the-art local methods for Poisson CPD. Hybrid GCP-CPAPR combines Generalized Canonical Decomposition (GCP) with stochastic optimization and CP Alternating Poisson Regression (CPAPR), a deterministic algorithm, to increase the probability of converging to the MLE over either method used alone. Restarted CPAPR with SVDrop uses a heuristic based on the singular values of the CPD model unfoldings to identify convergence toward optimizers that are not the MLE and restarts within the feasible domain of the optimization problem, thus reducing overall computational cost when using a multi-start strategy. We provide empirical evidence that indicates our approaches outperform existing methods with respect to converging to the Poisson CPD MLE.
CPAPR↗
Bounds on galaxy stochasticity from halo occupation distribution modeling
The joint probability distribution of matter overdensity and galaxy counts in cells is a powerful probe of cosmology, and the extent to which variance in galaxy counts at fixed matter density deviates from Poisson shot noise is not fully understood. The lack of informed bounds on this stochasticity is currently the limiting factor in constraining cosmology with the galaxy–matter probability distribution function (PDF). We investigate stochasticity in the conditional distribution of galaxy counts along lines of sight with fixed matter density, and we present a halo occupation distribution (HOD)-based approach for obtaining plausible ranges for stochasticity parameters. To probe the high-dimensional space of possible galaxy–matter connections, we derive a set of HODs that conserve the galaxies’ linear bias and number density to produce RED M A G I C-like galaxy catalogs within the A BACUS S UMMIT suite of N -body simulations. We study the impact of individual HOD parameters and cosmology on stochasticity and perform a Monte Carlo search in HOD parameter space subject to the constraints on bias and density. In mock catalogs generated by the selected HODs, shot noise in galaxy counts spans both sub-Poisson and super-Poisson values, ranging from 80% to 133% of Poisson variance for cells with mean matter density. Nearly all of the derived HODs show a positive relationship between local matter density and stochasticity. For galaxy catalogs with higher stochasticity, modeling galaxy bias to second order is required for an accurate description of the conditional PDF of galaxy counts at fixed matter density. The presence of galaxy assembly bias also substantially extends the range of stochasticity in the super-Poisson direction. This HOD-based approach leverages degrees of freedom in the galaxy–halo connection to obtain informed bounds on nuisance model parameters and can be adapted to study other parametrizations of shot noise in galaxy counts, in particular to motivate prior ranges on stochasticity for cosmological analyses.
Britt, Dylan (ORCID:000000019905601X)↗
Krylov complexity in mixed phase space
We investigate the Krylov complexity of thermofield double states in systems with mixed phase space, uncovering a direct correlation with the Brody distribution, which interpolates between Poisson and Wigner statistics. Our analysis spans two-dimensional random matrix models featuring (I) GOE-Poisson and (II) GUE-Poisson transitions and extends to higher-dimensional cases, including a stringy matrix model (GOE-Poisson) and the mass-deformed SYK model (GUE-Poisson). Krylov complexity consistently emerges as a reliable marker of quantum chaos, displaying a characteristic peak in the chaotic regime that gradually diminishes as the Brody parameter approaches zero, signaling a shift toward integrability. These results establish Krylov complexity as a powerful diagnostic of quantum chaos and highlight its interplay with eigenvalue statistics in mixed phase systems.
chaos & nonlinear dynamics↗
Two transitions in complex eigenvalue statistics: Hermiticity and integrability breaking
Open quantum systems have complex energy eigenvalues which are expected to follow non-Hermitian random matrix statistics, when chaotic, or two-dimensional (2d) Poisson statistics, when integrable. We investigate the spectral properties of a many-body quantum spin chain, i.e., the Hermitian Heisenberg model with imaginary disorder. Its rich complex eigenvalue statistics is found to separately break both Hermiticity and integrability at different scales of the disorder strength. With no disorder, the system is integrable and Hermitian, with spectral statistics corresponding to the 1d Poisson point process. At very small disorder, we find a transition from 1d Poisson statistics to an effective D -dimensional Poisson point process, showing Hermiticity breaking. At intermediate disorder, we find integrability breaking, as inferred from the statistics matching that of non-Hermitian complex symmetric random matrices in class AI † . For large disorder, as the spins align, we recover the expected integrability (now in the non-Hermitian setup), indicated by 2d Poisson statistics. These conclusions are based on fitting the spin-chain data of numerically generated nearest- and next-to-nearest-neighbor spacing distributions to an effective 2d Coulomb gas description at inverse temperature β . We confirm that such an effective description of random matrices also applies in classes AI † and AII † up to next-to-nearest-neighbor spacings. Published by the American Physical Society 2025
Akemann, Gernot (ORCID:0000000217104258)↗
The Use of Crow-AMSAA Plots to Assess Mishap Trends
Crow-AMSAA (CA) plots are used to model reliability growth. Use of CA plots has expanded into other areas, such as tracking events of interest to management, maintenance problems, and safety mishaps. Safety mishaps can often be successfully modeled using a Poisson probability distribution. CA plots show a Poisson process in log-log space. If the safety mishaps are a stable homogenous Poisson process, a linear fit to the points in a CA plot will have a slope of one. Slopes of greater than one indicate a nonhomogenous Poisson process, with increasing occurrence. Slopes of less than one indicate a nonhomogenous Poisson process, with decreasing occurrence. Changes in slope, known as "cusps," indicate a change in process, which could be an improvement or a degradation. After presenting the CA conceptual framework, examples are given of trending slips, trips and falls, and ergonomic incidents at NASA (from Agency-level data). Crow-AMSAA plotting is a robust tool for trending safety mishaps that can provide insight into safety performance over time.
Dawson, Jeffrey W.↗
Exploration of Failure and Potential Damage Markers in Ti-6Al-4V
To improve prognostics for predicting component life, coupon tests were conducted on Ti-6Al-4V to investigate the development of damage. Various test types were employed (tension, creep, stress relaxation, and fatigue) under a wide range of temperatures and loading rates to engage various amounts of time-dependent and damage behavior. Both stiffness degradation and Poisson’s ratio were monitored to see if they were useful in indicating the initiation and accumulation of damage and subsequently the onset of failure. Stiffness exhibited large decreases with increasing strain when calculated using engineering stress and strain. However, minimal stiffness change was observed when using the true-stress and true- strain values. Detailed microscopy and image analysis were performed to document the actual physical damage that occurred within the various specimens. Two types of damage were observed: shallow surface cracks and internal pores. The severity of damage was greater in the region of localized necking and diminished further away from the neck. The area fraction of pores was higher in the necked region, yet even there it did not exceed more than a few percent and, in most cases, was significantly lower. It was observed that conditions that induced more time-dependent deformation (e.g., slower strain rate testing) resulted in a larger number of pores and larger pore sizes. The pores were always found to occur in the softer β-phase. The severity of observed damage was inconsistent with the large drop in engineering stiffness, but was more aligned with stiffness changes from the true-stress and -strain values. Poisson’s ratio was monitored on every test and showed promise as a damage indicator. It was found to be more sensitive than either the ultimate tensile strength or the inception of tertiary creep. However, calculation of Poisson’s ratio was found to be more involved than expected because of anisotropy and the presence of strain gradients along the specimen at large applied strains. First, the material had a moderate texture and resulted in anisotropy of the strains. Second, the evolution of Poisson’s ratio as a function of axial strain showed strange and unexpected behaviors, which necessitated more extensive analyses of its development. This led to an investigation on the use of small versus large strain approaches and the importance of making consistent measurements; that is, axial and transverse strain measurements over the same volume of material. Additionally, finite element analysis of a tensile sample indicated that non- uniform strain occurred in the sample prior to attaining the maximum strength. This, along with the location at which transverse strain was measured, had a significant influence on the resulting values of Poisson’s ratio. Based on this, lessons learned are offered for future testing.
Ti-6Al-4V↗
Accelerating high-order continuum kinetic plasma simulations using multiple GPUs
Kinetic plasma simulations solve the Vlasov-Poisson or Vlasov-Maxwell equations to evolve scalar-variable distribution functions in position-velocity phase space and vector-variable electromagnetic fields in configuration space. The immense computational cost of evolving high-dimensional variables, and their large number of degrees of freedom, often limits the utility of continuum kinetic simulations and presents a challenge when it comes to accurately simulating real-world physical phenomena. To address this challenge, we present techniques that accelerate and minimize the computational work required for a scalable Vlasov-Poisson solver. We show theoretical hardware compute and communication bounds for solving a fourth-order finite-volume Vlasov-Poisson system. These bounds are then used to inform and evaluate the design of performance portable algorithms for a multiple graphics processing unit (GPU) accelerated version of the Vlasov-Poisson solver VCK-CPU [1]. We demonstrate that the multi-GPU Vlasov solver implementation, VCK-GPU, simultaneously minimizes required inter-process data transfer while also being bounded by the machine network performance limits. This results in an overall strong scaling speedup per timestep of up to 40x in three-dimensional phase space (one position, two velocity coordinates) and 54x in four dimensional phase space (two position, two velocity coordinates) and a 341x increase in simulation throughput of the GPU accelerated code over the existing CPU code. The GPU code is also able to weak scale up to 256 compute nodes and 1024 GPUs. In conclusion, we demonstrate that the improved compute performance enables exploring configurations which were previously computationally infeasible, including resolving fine-scale distribution function filamentation and multi-species dynamics with realistic electron-proton mass ratios.
Continuum kinetics↗
Bayesian Estimation of Earth’s Undiscovered Mineralogical Diversity Using Noninformative Priors
Recently, statistical distributions have been explored to provide estimates of the mineralogical diversity of Earth, and Earth-like planets. In this paper, a Bayesian approach is introduced to estimate Earth’s undiscovered mineralogical diversity. Samples are generated from a posterior distribution of the model parameters using Markov chain Monte Carlo simulations such that estimates and inference are directly obtained. It was previously shown that the mineral species frequency distribution conforms to a generalized inverse Gauss–Poisson (GIGP) large number of rare events model. Even though the model fit was good, the population size estimate obtained by using this model was found to be unreasonably low by mineralogists. In this paper, several zero-truncated, mixed Poisson distributions are fitted and compared, where the Poisson-lognormal distribution is found to provide the best fit. Subsequently, the population size estimates obtained by Bayesian methods are compared to the empirical Bayes estimates. Species accumulation curves are constructed and employed to estimate the population size as a function of sampling size. Finally, the relative abundances, and hence the occurrence probabilities of species in a random sample, are calculated numerically for all mineral species in Earth’s crust using the Poisson-lognormal distribution. These calculations are connected and compared to the calculations obtained in a previous paper using the GIGP model for which mineralogical criteria of an Earth-like planet were given.
Bayesian statistics↗
Cost performance satellite design using queueing theory
A modified Poisson arrival, infinite server queuing model is used to determine the effects of limiting the number of broadcast channels (C) of a direct broadcast satellite used for public service purposes (remote health care, education, etc.). The model is based on the reproductive property of the Poisson distribution. A difference equation has been developed to describe the change in the Poisson parameter. When all initially delayed arrivals reenter the system a (C plus 1) order polynomial must be solved to determine the effective value of the Poisson parameter. When less than 100% of the arrivals reenter the system the effective value must be determined by solving a transcendental equation. The model was used to determine the minimum number of channels required for a disaster warning satellite without degradation in performance. Results predicted by the queuing model were compared with the results of digital simulation.
Hein, G. F.↗
Generic Karman-Rostovstev plate equations in an affine space
The Karman-Rostovstev plate equations are affinely transformed into equations that depend on the generic plate constants generalized rigidity, generalized extensional rigidity, and generalized Poisson ratio associated with the well-known linearized orthotropic plate/slab equations. Furthermore, since the generalized extensional rigidity is a function of generalized rigidity and generalized Poisson ratio only, with generalized Poisson ratio being a weak parameter, the only fundamental constant is generalized rigidity. This means that regardless of what analysis technique is used, the results can be cast in terms of only one strong material parameter (whose range is from zero to one). The affine stretching is performed on the dependent variables as well as the independent variables, so that the dependence of all quantities of interest on generalized rigidity and generalized Poisson ratio are easily calculated (e.g., even auxiliary quantities such as stress, strain, all weighted stress resultants, etc.). Some typical results (static side load response, collapse load limited by rib buckling) are presented by modifying an approximate technique due to Donnell (1976).
Brunelle, E. J.↗
Estimating Random Errors Due to Shot Noise in Backscatter Lidar Observations
In this paper, we discuss the estimation of random errors due to shot noise in backscatter lidar observations that use either photomultiplier tube (PMT) or avalanche photodiode (APD) detectors. The statistical characteristics of photodetection are reviewed, and photon count distributions of solar background signals and laser backscatter signals are examined using airborne lidar observations at 532 nm using a photon-counting mode APD. Both distributions appear to be Poisson, indicating that the arrival at the photodetector of photons for these signals is a Poisson stochastic process. For Poisson-distributed signals, a proportional, one-to-one relationship is known to exist between the mean of a distribution and its variance. Although the multiplied photocurrent no longer follows a strict Poisson distribution in analog-mode APD and PMT detectors, the proportionality still exists between the mean and the variance of the multiplied photocurrent. We make use of this relationship by introducing the noise scale factor (NSF), which quantifies the constant of proportionality that exists between the root-mean-square of the random noise in a measurement and the square root of the mean signal. Using the NSF to estimate random errors in lidar measurements due to shot noise provides a significant advantage over the conventional error estimation techniques, in that with the NSF uncertainties can be reliably calculated from/for a single data sample. Methods for evaluating the NSF are presented. Algorithms to compute the NSF are developed for the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) lidar and tested using data from the Lidar In-space Technology Experiment (LITE). OCIS Codes:
Liu, Zhaoyan↗
Applying Flammability Limit Probabilities and the Normoxic Upward Limiting Pressure Concept to NASA STD-6001 Test 1
Repeated Test 1 extinction tests near the upward flammability limit are expected to follow a Poisson process trend. This Poisson process trend suggests that rather than define a ULOI and MOC (which requires two limits to be determined), it might be better to define a single upward limit as being where 1/e (where e (approx. equal to 2.7183) is the characteristic time of the normalized Poisson process) of the materials burn, or, rounding, where approximately 1/3 of the samples fail the test (and burn). Recognizing that spacecraft atmospheres will not bound the entire oxygen-pressure parameter space, but actually lie along the normoxic atmosphere control band, we can focus the materials flammability testing along this normoxic band. A Normoxic Upward Limiting Pressure (NULP) is defined that determines the minimum safe total pressure for a material within the constant partial pressure control band. Then, increasing this pressure limit by a factor of safety, we can define the material as being safe to use at the NULP + SF (where SF is on the order of 10 kilopascal, based on existing flammability data). It is recommended that the thickest material to be tested with the current Test 1 igniter should be 3 mm thick (1/8 inches) to avoid the problem of differentiating between an ignition limit and a true flammability limit.
flammability↗
An application of queueing theory to the design of channel requirements for special purpose communications satellites
Special purpose satellites are very cost sensitive to the number of broadcast channels, usually will have Poisson arrivals, fairly low utilization (less than 35%), and a very high availability requirement. To solve the problem of determining the effects of limiting C the number of channels, the Poisson arrival, infinite server queueing model will be modified to describe the many server case. The model is predicated on the reproductive property of the Poisson distribution.
Hein, G. F.↗
A well posed boundary value problem in transonic gas dynamics
A new approach considered by Garabedian and Korn (1976) to solve a problem of airfoil design has led to a transonic boundary value problem. It remains to be shown that this problem is well posed. A description is presented of an investigation in which it is shown that a corresponding problem for the Tricomi equation is well posed. The solution to the boundary value problem is characterized, in a unique way, as a sum of two particular solutions. The Poisson formulas for the unit semicircle for the Euler-Poisson-Darboux equation are considered and reflection laws for solutions of the general Euler-Poisson-Darboux equation are established. It is proved that the considered boundary value problem for the case in which the involved function is periodic and continuous is well posed within the specified class of solutions.
Sanz, J. M.↗
The scaling of oblique plasma double layers
Strong oblique plasma double layers are investigated using three methods, i.e., electrostatic particle-in-cell simulations, numerical solutions to the Poisson-Vlasov equations, and analytical approximations to the Poisson-Vlasov equations. The solutions to the Poisson-Vlasov equations and numerical simulations show that strong oblique double layers scale in terms of Debye lengths. For very large potential jumps, theory and numerical solutions indicate that all effects of the magnetic field vanish and the oblique double layers follow the same scaling relation as the field-aligned double layers.
Borovsky, J. E.↗