Results for “Entropy minimization” — Page 4

NASA NTRS1990

Test images for the maximum entropy image restoration method

One of the major activities of any experimentalist is data analysis and reduction. In solar physics, remote observations are made of the sun in a variety of wavelengths and circumstances. In no case is the data collected free from the influence of the design and operation of the data gathering instrument as well as the ever present problem of noise. The presence of significant noise invalidates the simple inversion procedure regardless of the range of known correlation functions. The Maximum Entropy Method (MEM) attempts to perform this inversion by making minimal assumptions about the data. To provide a means of testing the MEM and characterizing its sensitivity to noise, choice of point spread function, type of data, etc., one would like to have test images of known characteristics that can represent the type of data being analyzed. A means of reconstructing these images is presented.

Mackey, James E.↗

NASA NTRS2016

Temperature-Staged Thermal Energy Storage Enabling Low Thermal Exergy Loss Reflux Boiling in Full Spectrum Solar Systems

Hybrid full spectrum solar systems (FSSS) designed to capture and convert the full solar wavelength spectrum use hybrid solar photovoltaic/thermodynamic cycles that require low thermal exergy loss systems capable of transferring high thermal energy rates and fluxes with very low temperature differentials and losses. One approach to achieving this capability are high-heat-flux reflux boiling systems that take advantage of high heat transfer boiling and condensation mechanisms. Advanced solar systems are also intermittent by their nature and their electrical generation is often out-of-phase with electric utility power demand, and their required power system cycling reduces efficiency, performance (dispatch ability), lifetime, and reliability. High temperature thermal energy storage (TES) at 300-600°C enables these reflux boiling systems to simultaneously store thermal energy internally to increase the energy dispatch ability of the associated solar system, as this can increase the power generation profile by several hours (up to 6-10 hours) per day. Many TES phase change materials (PCM’s) exist including KNO3, NaNO3, LiBr/KBr, MgCl2/NaCl/KCl, Zn/Mg, and CuCl/NaCl, which have various operating melting points and different latent heats of fusion. Common, cost effective TES PCM's are FeCl2/NaCl/KCl mixtures, whose phase change temperature can be varied and controlled by simple composition adjustments. This paper presents and discusses unique "temperature-staged" thermal energy storage configurations using these TES materials and analysis of such systems integrated into high-heat-flux reflux boiling systems. In this specific application, the TES materials are designed to operate at staged temperatures surrounding an operating design point near 350°C, while providing 18 kW of source heat transfer to operate a thermoacoustic power system during off-sun conditions (e.g., temporary cloud conditions, after sun-down). This work discusses relevant configurations, and critical thermal and entropy models of the TES configurations, which show the inherent minimization of thermal exergy during critical heat transfers within the configurations and systems envisioned.

Hendricks, Terry J.↗

NASA NTRS2001

Entropy Splitting for High Order Numerical Simulation of Vortex Sound at Low Mach Numbers

A method of minimizing numerical errors, and improving nonlinear stability and accuracy associated with low Mach number computational aeroacoustics (CAA) is proposed. The method consists of two levels. From the governing equation level, we condition the Euler equations in two steps. The first step is to split the inviscid flux derivatives into a conservative and a non-conservative portion that satisfies a so called generalized energy estimate. This involves the symmetrization of the Euler equations via a transformation of variables that are functions of the physical entropy. Owing to the large disparity of acoustic and stagnation quantities in low Mach number aeroacoustics, the second step is to reformulate the split Euler equations in perturbation form with the new unknowns as the small changes of the conservative variables with respect to their large stagnation values. From the numerical scheme level, a stable sixth-order central interior scheme with a third-order boundary schemes that satisfies the discrete analogue of the integration-by-parts procedure used in the continuous energy estimate (summation-by-parts property) is employed.

Mueller, B.↗

DOE OSTI2024

Entropy-Driven Charge Separation: A Potential Explanation for the Low Energy Loss Found in OPVs with Non-fullerene Acceptors

The recent development of non-fullerene acceptors (NFA) has led to an abrupt increase in the organic photovoltaic (OPV) efficiency from ~12% to ~20%. NFA OPVs can generate photocurrent efficiently without much energy loss, which contrasts with the large energy loss often needed for generating free charges from excitons in fullerene OPVs. Here, we argue that entropy-driven charge separation, which allows excitons to spontaneously gain heat from the environment, is responsible for the exceptionally low energy loss found in NFA OPVs. The entropic driving force is maximized when the delocalized electron and hole wave functions in the CT exciton intersect each other via pointlike junctions. Furthermore, these pointlike junctions are abundant in the polymer/NFA bulk heterojunction which consists of intertwined, stringlike donor and acceptor domains in which electron delocalizes anisotropically. Such microstructure favors entropy-driven charge separation, which can enable charge separation with a minimal energy loss.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Experimental entropic uncertainty relations in dimensions three to five

We provide experimental validation of tight entropic uncertainty relations for the Shannon entropies of observables with mutually unbiased eigenstates in high dimensions. In particular, we address the cases of dimensions 𝑑 = 3, 4, and 5 and consider from 2 to 𝑑 + 1 mutually unbiased bases. The experiment is based on pulsed frequency bins measured with a multioutput quantum pulse gate, which can perform projective measurements on a complete high-dimensional basis in the time-frequency domain. Our results fit the theoretical predictions: the bound on the sum of the entropies is never violated and is saturated by the states that minimize the uncertainty relations.

Serino, Laura [Paderborn University (Germany)] (OR↗

NASA NTRS1989

A physical model for earthquakes. III - Thermodynamical approach and its relation to nonclassical theories

An earthquake theory based on fundamental thermodynamical considerations was developed using two principles. The first principle is that physical systems, including fault systems, tend toward a state of minimal Helmholtz free energy, which corresponds to static equilibrium. The second postulate is that, if the system is not at minimal free energy, thermodynamic forces arise which drive the system back toward a minimum. According to this theory, the propagation of a fracture, or the formation of a slip on a frictional surface, are manifestations of the physics which attempt to return the system to minimal free energy. It is shown that the process of return to minimal free energy by the system corresponds to the production of entropy, thereby rendering the process irreversible.

Rundle, John B.↗

NASA NTRS1997

Nonlinear Rescaling and Proximal-Like Methods in Convex Optimization

The nonlinear rescaling principle (NRP) consists of transforming the objective function and/or the constraints of a given constrained optimization problem into another problem which is equivalent to the original one in the sense that their optimal set of solutions coincides. A nonlinear transformation parameterized by a positive scalar parameter and based on a smooth scaling function is used to transform the constraints. The methods based on NRP consist of sequential unconstrained minimization of the classical Lagrangian for the equivalent problem, followed by an explicit formula updating the Lagrange multipliers. We first show that the NRP leads naturally to proximal methods with an entropy-like kernel, which is defined by the conjugate of the scaling function, and establish that the two methods are dually equivalent for convex constrained minimization problems. We then study the convergence properties of the nonlinear rescaling algorithm and the corresponding entropy-like proximal methods for convex constrained optimization problems. Special cases of the nonlinear resealing algorithm are presented. In particular a new class of exponential penalty-modified barrier functions methods is introduced.

Polyak, Roman↗

DOE OSTI2022

Theory, observations, and simulations of kinetic entropy in a magnetotail electron diffusion region

In this work, we examine velocity-space kinetic entropy, a spatially local measure of entropy for systems out of thermal equilibrium, during an encounter of an electron diffusion region at a magnetic reconnection site in Earth’s magnetotail by the Magnetospheric Multiscale (MMS) mission. We start by generalizing the theory of kinetic entropy to the case of non-uniform velocity space grids and transforming the equations into spheri- cal energy coordinates useful to experimental plasma detectors. The theory is then applied to MMS data and compared to particle-in-cell simulations of reconnection. We demonstrate that the entropy-based non-Maxwellianity measure from the MMS data is of sufficiently high precision to reliably identify non-Maxwellian distributions and therefore the measurements when kinetic effects are most significant. By comparing two different non-Maxwellian measures, we show that total entropy density suffers from “information loss” because it lacks a dependence on the velocity space grid, and so has lost information about how well a distribution function is resolved. Local velocity-space kinetic entropy density recovers this information. We quantify information loss and argue that the considerations needed to minimize it are crucial for instruments designed to measure distribution functions in situ.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1979

A dual method for maximum entropy restoration

A simple iterative dual algorithm for maximum entropy image restoration is presented. The dual algorithm involves fewer parameters than conventional minimization in the image space. Minicomputer test results for Fourier synthesis with inadequate phantom data are given.

Smith, C. B.↗

DOE OSTI2022

Inference, Prediction, & Entropy-Rate Estimation of Continuous-Time, Discrete-Event Processes

Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide new methods for inferring, predicting, and estimating them. The methods rely on an extension of Bayesian structural inference that takes advantage of neural network’s universal approximation power. Based on experiments with complex synthetic data, the methods are competitive with the state-of-the-art for prediction and entropy-rate estimation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Accurate and Data‐Efficient Micro X‐ray Diffraction Phase Identification Using Multitask Learning: Application to Hydrothermal Fluids

Traditional analysis of highly distorted micro X‐ray diffraction (μ‐XRD) patterns from hydrothermal fluid environments is a time‐consuming process, often requiring substantial data preprocessing and labeled experimental data. Herein, the potential of deep learning with a multitask learning (MTL) architecture to overcome these limitations is demonstrated. MTL models are trained to identify phase information in μ‐XRD patterns, minimizing the need for labeled experimental data and masking preprocessing steps. Notably, MTL models show superior accuracy compared to binary classification convolutional neural networks. Additionally, introducing a tailored cross‐entropy loss function improves MTL model performance. Most significantly, MTL models tuned to analyze raw and unmasked XRD patterns achieve close performance to models analyzing preprocessed data, with minimal accuracy differences. This work indicates that advanced deep learning architectures like MTL can automate arduous data handling tasks, streamline the analysis of distorted XRD patterns, and reduce the reliance on labor‐intensive experimental datasets.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Effects of electron beam irradiation on CrMnV and CrMnTiV high entropy alloys: Nano-mechanical, structural, and thermodynamic perspectives

Beam exit windows are crucial components of any particle accelerator as they provide an interface between the beamline vacuum and target material at atmospheric media. For high beam power machines, special materials and designs are required to withstand high radiation and mechanical loads, while minimizing energy loss during transition and maximizing window lifetime. This research investigates the impact of electron beam exposure to bulk CrMnV and CrMnTiV high entropy alloys (HEAs) with the primary goal of identifying suitable candidate materials for the design of robust and durable exit window settings. The selection criteria include intrinsic characteristics, power dissipation, and mechanical responses. According to the thermodynamic calculations, both equiatomic CrMnV and the addition of 7% of Ti with equiatomic CrMnV yield solid-solutions phases. The structural and mechanical properties of CrMnV and CrMnTiV samples were tested using field emission scanning electron microscopy, atomic force microscopy, scanning electron microcopy with energy dispersive x-ray spectroscopy, x-ray diffraction, and nanoindentation before and after exposure to a dose of ~66 kGy from a 10 MeV e-beam accelerator. Despite exhibiting beam transmission characteristics comparable to Cr and V, the indentation hardness of HEAs exceeded that of the Cr and V samples by five to six times. The examination of the CrMnTiV irradiated samples revealed organized deformation patterns depicting new features, which we suspect twinning and twin boundaries due to the addition of Ti to CrMnV. Ti, a hexagonal-close-packed crystal structure, is commonly known for deformation twinning behavior.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Magnetocaloric effect in Mn-rich Heusler-derived alloys for room temperature-based applications

Magnetic refrigeration-based technologies rely on the magnetocaloric properties of materials and are crucial for improving energy efficiency and for supporting clean environments. However, materials possessing significant magnetocaloric properties that can be used for room temperature-based applications are still lacking. Heusler alloys (such as Mn–Ni–Ga) show giant magnetocaloric effects, which can be further improved by tuning their composition. Herein, we optimized the ratio of Ni to Ga to achieve an alloy with unique magnetocaloric properties. Here, the alloy demonstrated a substantial magnetocaloric effect, attributed to its narrow temperature range for structural and magnetic phase transitions (near room temperature with minimal hysteresis). Structural phase changes were also observed through high-resolution transmission electron microscopy. Optimum entropy changes, calculated from isothermal magnetization curves (4 Tesla magnetic field), were found to be 24.50 J kg −1 K −1 , which is higher than that of state-of-the-art alloys. Experimental demonstration of the magnetocaloric effect (refrigeration cycle) was also carried out using a thermal imaging camera. Furthermore, first-principles calculations were conducted to validate the experimental findings, specifically focusing on the compositional effects on the structural transitions and magnetic properties of the investigated MNG alloys.

36 MATERIALS SCIENCE↗

NASA NTRSDate not supplied

A New Approach for a Wider Class of Entropy Split Methods for Compressible Gas Dynamics and MHD

The high order entropy split methods of Sjögreen & Yee [1, 2] by entropy splitting of the compressible Euler (inviscid) flux derivatives for a thermally-perfect gas are based on Harten’s entropy function [3, 4, 5]. Their derivation takes advantage of the homogeneity property of Euler flux, symmetrizable Euler flux derivatives and energy-norm stability in conjunction with high order classical spatial central, DRP (dispersion relation-preserving) [6, 7, 8] or Padé (compact) spatial discretizations [9] with summation-by-parts (SBP) operators [10]. Our entropy split methods have been proven entropy conserving and stable [1, 11, 12]. Our proofs do not rely on a two-point numerical flux, but rather only a linear difference operator is required to derive these methods. To extend the entropy split method for the MHD, we used the Godunov symmetrizable non-conservative MHD form [12, 13, 14]. These high order entropy split methods not only preserve certain physical properties of the chosen governing equations but are also known to either improve numerical stability, and/or minimize aliasing errors in long time integration of turbulent flow computations without the aid of added numerical dissipation. In our previous published work, extensive error norm comparison with grid refinement was performed to show the high accuracy performance of these methods. These studies also showed how well the entropy split methods conserve the entropy, momentum and mass, and preserve the kinetic energy for long time integration of the various flows [1, 2, 12, 13, 14]. The objective of the present work is to use a new approach to obtain a wider class of entropy split methods consisting of a two-point numerical flux portion and a non-conservative portion in such a way that the homogeneity property of the compressible Euler flux is not required. For high order classical spatial central, DRP (dispersion relation-preserving) or Padé (compact) spatial discretizations, this new approach can be proven to be entropy conservative with conservative spatial dsicretizations while at the same time allowing a wider class of symmetrizable inviscid flux derivatives. We also use this generalization to derive an entropy split scheme that is entropy conserving for the equations of MHD without the homogeneity property using the Godunov symmetrizable ideal MHD formulation [15].

High Order Physical Preserving Methods↗

DOE OSTI2025

A Quantum Computational Determination of the Weak Mixing Angle in the Standard Model

The weak mixing angle $s_W$ is a fundamental constant in the Standard Model (SM) and measured at the $Z$ boson mass to be $\widehat{s}^2_W(m_Z) = 0.23129 \pm 0.00004$ in the $\overline{\rm MS}$ renormalization scheme, where $m_Z=91.2\ \text{GeV}$. On the other hand, non-stabilizerness - the magic - characterizes the computational advantage of a quantum system over classical computers. We consider the production of magic from stabilizer initial states, which carry zero magic, in the 2-to-2 scattering of charged leptons in the SM at the tree level, which is mediated by the photon and the $Z$ boson. Using the second order stabilizer Rényi entropy, and averaging over all 60 initial stabilizer states and the scattering angle, we compute and minimize the magic production as a function of $s^2_W$ in the Møller scattering $e^-e^-\to e^-e^-$, which is free of kinematic thresholds. At the centre-of-mass energy $\sqrt{s}=m_Z$, there is a unique minimum in magic production at $\mathbf{s}^{2}_W(m_Z)=0.2317$, which agrees with the measured $\widehat{s}^2_W(m_Z)$ at the sub-percent level. At higher energies, the magic-minimizing $\mathbf{s}^{2}_W$ continues to agree with the empirical value at the percent level or better, up to 10 TeV. The finding suggests the electroweak sector of the SM tends to generate minimal quantum resources from the computational viewpoint.

Liu, Qiaofeng [Northwestern U.]↗

DOE OSTI2025

A Quantum Computational Determination of the Weak Mixing Angle in the Standard Model

The weak mixing angle $s_W$ is a fundamental constant in the Standard Model (SM) and measured at the $Z$ boson mass to be $\widehat{s}^2_W(m_Z) = 0.23129 \pm 0.00004$ in the $\overline{\rm MS}$ renormalization scheme, where $m_Z=91.2\ \text{GeV}$. On the other hand, non-stabilizerness - the magic - characterizes the computational advantage of a quantum system over classical computers. We consider the production of magic from stabilizer initial states, which carry zero magic, in the 2-to-2 scattering of charged leptons in the SM at the tree level, which is mediated by the photon and the $Z$ boson. Using the second order stabilizer Rényi entropy, and averaging over all 60 initial stabilizer states and the scattering angle, we compute and minimize the magic production as a function of $s^2_W$ in the Møller scattering $e^-e^-\to e^-e^-$, which is free of kinematic thresholds. At the centre-of-mass energy $\sqrt{s}=m_Z$, there is a unique minimum in magic production at $\mathbf{s}^{2}_W(m_Z)=0.2317$, which agrees with the measured $\widehat{s}^2_W(m_Z)$ at the sub-percent level. At higher energies, the magic-minimizing $\mathbf{s}^{2}_W$ continues to agree with the empirical value at the percent level or better, up to 10 TeV. The finding suggests the electroweak sector of the SM tends to generate minimal quantum resources from the computational viewpoint.

Liu, Qiaofeng [Northwestern U.]↗

DOE OSTI2025

A Quantum Computational Determination of the Weak Mixing Angle in the Standard Model

The weak mixing angle $s_W$ is a fundamental constant in the Standard Model (SM) and measured at the $Z$ boson mass to be $\widehat{s}^2_W(m_Z) = 0.23129 \pm 0.00004$ in the $\overline{\rm MS}$ renormalization scheme, where $m_Z=91.2\ \text{GeV}$. On the other hand, non-stabilizerness - the magic - characterizes the computational advantage of a quantum system over classical computers. We consider the production of magic from stabilizer initial states, which carry zero magic, in the 2-to-2 scattering of charged leptons in the SM at the tree level, which is mediated by the photon and the $Z$ boson. Using the second order stabilizer Rényi entropy, and averaging over all 60 initial stabilizer states and the scattering angle, we compute and minimize the magic production as a function of $s^2_W$ in the Møller scattering $e^-e^-\to e^-e^-$, which is free of kinematic thresholds. At the centre-of-mass energy $\sqrt{s}=m_Z$, there is a unique minimum in magic production at $\mathbf{s}^{2}_W(m_Z)=0.2317$, which agrees with the measured $\widehat{s}^2_W(m_Z)$ at the sub-percent level. At higher energies, the magic-minimizing $\mathbf{s}^{2}_W$ continues to agree with the empirical value at the percent level or better, up to 10 TeV. The finding suggests the electroweak sector of the SM tends to generate minimal quantum resources from the computational viewpoint.

Liu, Qiaofeng [Northwestern U.]↗

NASA NTRS1983

Crop identification of SAR data using digital textural analysis

After preprocessing SEASAT SAR data which included slant to ground range transformation, registration to LANDSAT MSS data and appropriate filtering of the raw SAR data to minimize coherent speckle, textural features were developed based upon the spatial gray level dependence method (SGLDM) to compute entropy and inertia as textural measures. It is indicated that the consideration of texture features are very important in SAR data analysis. The SEASAT SAR data are useful for the improvement of field boundary definitions and for an earlier season estimate of corn and soybean area location than is supported by LANDSAT alone.

Nuesch, D. R.↗