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Results for “maximum entropy”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Restored pictures of Ganymede, moon of Jupiter

The paper discusses results of an attempt to restore two blurred pictures of Ganymede taken by Pioneer 10 through a blue filter and a red filter. The mathematical formulation of the restoration problem is outlined, it is noted that both conventional linear filtering and the maximum-entropy algorithm were employed as restoration techniques, and the two methods are described. The original blurred pictures are reproduced along with the two restorations of each image. The restored images are found to exhibit some mare-like features as well as a few large bright rings, possibly ice ridges. The results obtained with the two restoration techniques are compared, and it is concluded that the maximum-entropy method is more advantageous than linear methods in applications to moderately extended images.

Frieden, B. R.↗
NASA NTRS1989

Power spectral estimation algorithms

Algorithms to estimate the power spectrum using Maximum Entropy Methods were developed. These algorithms were coded in FORTRAN 77 and were implemented on the VAX 780. The important considerations in this analysis are: (1) resolution, i.e., how close in frequency two spectral components can be spaced and still be identified; (2) dynamic range, i.e., how small a spectral peak can be, relative to the largest, and still be observed in the spectra; and (3) variance, i.e., how accurate the estimate of the spectra is to the actual spectra. The application of the algorithms based on Maximum Entropy Methods to a variety of data shows that these criteria are met quite well. Additional work in this direction would help confirm the findings. All of the software developed was turned over to the technical monitor. A copy of a typical program is included. Some of the actual data and graphs used on this data are also included.

Bhatia, Manjit S.↗
DOE OSTI2014

Statistical mechanics of collisionless orbits. IV. Distribution of angular momentum

It has been shown in previous work that DARKexp, which is a theoretically derived, maximum entropy, one shape parameter model for isotropic collisionless systems, provides very good fits to simulated and observed dark matter halos. Specifically, it fits the energy distribution, N(E), and the density profiles, including the central cusp. Here, we extend DARKexp N(E) to include the distribution in angular momentum, L {sup 2}, for spherically symmetric systems. First, we argue, based on theoretical, semi-analytical, and simulation results, that while dark matter halos are relaxed in energy, they are not nearly as relaxed in angular momentum, which precludes using maximum entropy to uniquely derive N(E, L {sup 2}). Instead, we require that when integrating N(E, L {sup 2}) over squared angular momenta one retrieves the DARKexp N(E). Starting with a general expression for N(E, L {sup 2}) we show how the distribution of particles in L {sup 2} is related to the shape of the velocity distribution function, VDF, and velocity anisotropy profile, β(r). We then demonstrate that astrophysically realistic halos, as judged by the VDF shape and β(r), must have linear or convex distributions in L {sup 2}, for each separate energy bin. The distribution in energy of the most bound particles must be nearly flat, and become more tilted in favor of radial orbits for less bound particles. These results are consistent with numerical simulations and represent an important step toward deriving the full distribution function for spherically symmetric dark matter halos.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Modeling of dissociation and energy transfer in shock-heated nitrogen flows

This work addresses the modeling of dissociation and energy transfer processes in shock heated nitrogen flows by means of the maximum entropy linear model and a newly proposed hybrid bin vibrational collisional model. Both models aim at overcoming two of the main limitations of the state of the art non-equilibrium models: (i) the assumption of equilibrium between rotational and translational energy modes of the molecules and (ii) the reliance on the quasi-steady-state distribution for the description of the population of the internal levels. The formulation of the coarse-grained models is based on grouping the energy levels into bins, where the population is assumed to follow a Maxwell-Boltzmann distribution at its own temperature. Different grouping strategies are investigated. Following the maximum entropy principle, the governing equations are obtained by taking the zeroth and first-order moments of the rovibrational master equations. The accuracy of the proposed models is tested against the rovibrational master equation solution for both flow quantities and population distributions. Calculations performed for free-stream velocities ranging from 5 km/s to 10 km/s demonstrate that dissociation can be accurately predicted by using only 2-3 bins. It is also shown that a multi-temperature approach leads to an under-prediction of dissociation, due to the inability of the former to account for the faster excitation of high-lying vibrational states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

General multi-group macroscopic modeling for thermo-chemical non-equilibrium gas mixtures

This paper opens a new door to macroscopic modeling for thermal and chemical non-equilibrium. In a game-changing approach, we discard conventional theories and practices stemming from the separation of internal energy modes and the Landau-Teller relaxation equation. Instead, we solve the fundamental microscopic equations in their moment forms but seek only optimum representations for the microscopic state distribution function that provides converged and time accurate solutions for certain macroscopic quantities at all times. The modeling makes no ad hoc assumptions or simplifications at the microscopic level and includes all possible collisional and radiative processes; it therefore retains all non-equilibrium fluid physics. We formulate the thermal and chemical non-equilibrium macroscopic equations and rate coefficients in a coupled and unified fashion for gases undergoing completely general transitions. All collisional partners can have internal structures and can change their internal energy states after transitions. The model is based on the reconstruction of the state distribution function. The internal energy space is subdivided into multiple groups in order to better describe non-equilibrium state distributions. The logarithm of the distribution function in each group is expressed as a power series in internal energy based on the maximum entropy principle. The method of weighted residuals is applied to the microscopic equations to obtain macroscopic moment equations and rate coefficients succinctly to any order. The model’s accuracy depends only on the assumed expression of the state distribution function and the number of groups used and can be self-checked for accuracy and convergence. We show that the macroscopic internal energy transfer, similar to mass and momentum transfers, occurs through nonlinear collisional processes and is not a simple relaxation process described by, e.g., the Landau-Teller equation. Unlike the classical vibrational energy relaxation model, which can only be applied to molecules, the new model is applicable to atoms, molecules, ions, and their mixtures. Numerical examples and model validations are carried out with two gas mixtures using the maximum entropy linear model: one mixture consists of nitrogen molecules undergoing internal excitation and dissociation and the other consists of nitrogen atoms undergoing internal excitation and ionization. Results show that the original hundreds to thousands of microscopic equations can be reduced to two macroscopic equations with almost perfect agreement for the total number density and total internal energy using only one or two groups. We also obtain good prediction of the microscopic state populations using 5-10 groups in the macroscopic equations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Sodium Ion Transport Mechanisms in Antiperovskite Electrolytes Na 3 OBr and Na 4 OI 2 : An in Situ Neutron Diffraction Study

Na-rich antiperovskites are recently developed solid electrolytes with enhanced sodium ionic conductivity and show promising functionality as a novel solid electrolyte in an all solid-state battery. In this work, the sodium ionic transport pathways of the parent compound Na3OBr, as well as the modified layered antiperovskite Na4OI2, were studied and compared through temperature dependent neutron diffraction combined with the maximum entropy method. In the cubic Na3OBr antiperovskite, the nuclear density distribution maps at 500 K indicate that sodium ions hop within and among oxygen octahedra, and Br- ions are not involved. In the tetragonal Na4OI2 antiperovskite, Na ions, which connect octahedra in the ab plane, have the lowest activation energy barrier. The transport of sodium ions along the c axis is assisted by I- ions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Small-angle scattering of polychromatic X-rays: effects of bandwidth, spectral shape and high harmonics

Polychromatic X-ray sources can be useful for photon-starved small-angle X-ray scattering given their high spectral fluxes. Their bandwidths, however, are 10–100 times larger than those using monochromators. To explore the feasibility, ideal scattering curves of homogeneous spherical particles for polychromatic X-rays are calculated and analyzed using the Guinier approach, maximum entropy and regularization methods. Monodisperse and polydisperse systems are explored. The influence of bandwidth and asymmetric spectra shape are explored via Gaussian and half-Gaussian spectra. Synchrotron undulator spectra represented by two undulator sources of the Advanced Photon Source are examined as an example, as regards the influence of asymmetric harmonic shape, fundamental harmonic bandwidth and high harmonics. The effects of bandwidth, spectral shape and high harmonics on particle size determination are evaluated quantitatively.

Chen, Sen↗
DOE OSTI2014

Electron density distribution and disordered crystal structure of 8H-SiAlON, Si{sub 3−x}Al{sub 1+x}O{sub x}N{sub 5−x} (x∼2.2)

The 8H-SiAlON crystal with general formula Si{sub 3−x}Al{sub 1+x}O{sub x}N{sub 5−x} was characterized using laboratory X-ray powder diffraction (CuKα{sub 1}), transmission electron microscopy and energy dispersive X-ray spectroscopy. The [Si: Al] molar ratios were determined to be [0.21(1): 0.79(1)], corresponding to x=2.2(1). The Si{sub 0.8(1)}Al{sub 3.2(1)}O{sub 2.2(1)}N{sub 2.8(1)} compound is hexagonal with space group P6{sub 3}/mmc (Z=2). The unit-cell dimensions are a=0.298877(8) nm, c=2.30872(5) nm and V=0.178602(8) nm{sup 3}. The initial structural model was successfully derived by the charge-flipping method and further refined by the Rietveld method. The final structural model showed the positional disordering of two of the three (Si,Al) sites. The maximum-entropy method-based pattern fitting (MPF) method was used to confirm the validity of the split-atom model, in which conventional structure bias caused by assuming intensity partitioning was minimized. The reliability indices calculated from the MPF were R{sub wp}=4.74%, S (=R{sub wp}/R{sub e})=1.30, R{sub p}=3.40%, R{sub B}=1.04% and R{sub F}=0.74%. The disordered crystal structure was successfully described by overlapping four types of domains with ordered atom arrangements. The distribution of atomic positions in each of the domains can be achieved in the space group P6{sub 3}mc. Two of the four types of domains are related by a pseudo-symmetry inversion, and the two remaining domains also have each other the inversion pseudo-symmetry. - Graphical abstract: Bird's eye view of electron densities up to 49.3% (0.071 nm{sup −3}) of the maximum on the plane parallel to (110) with the corresponding atomic arrangements of Si{sub 0.8}Al{sub 3.2}O{sub 2.2}N{sub 2.8}. - Highlights: • Crystal structure of Si{sub 0.8}Al{sub 3.2}O{sub 2.2}N{sub 2.8} is determined by laboratory X-ray powder diffraction. • The atom arrangements are represented by the split-atom model. • The maximum-entropy method-based pattern fitting method is used to confirm the validity of the model. • The disordered structure is described by overlapping four types of domains with ordered atom arrangements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Electron density distribution and disordered crystal structure of 15R-SiAlON, SiAl{sub 4}O{sub 2}N{sub 4}

The crystal structure of SiAl{sub 4}O{sub 2}N{sub 4} was characterized by laboratory X-ray powder diffraction (CuKα{sub 1}). The title compound is trigonal with space group R3-bar m. The hexagonal unit-cell dimensions (Z=3) are a=0.301332(3) nm, c=4.18616(4) nm and V=0.3291825(5) nm{sup 3}. The initial structural model was successfully derived by the charge-flipping method and further refined by the Rietveld method. The final structural model showed the positional disordering of one of the three (Si,Al) sites. The maximum-entropy method-based pattern fitting (MPF) method was used to confirm the validity of the split-atom model, in which conventional structure bias caused by assuming intensity partitioning was minimized. The reliability indices calculated from the MPF were R{sub wp}=5.05%, S (=R{sub wp}/R{sub e})=1.21, R{sub p}=3.77%, R{sub B}=1.29% and R{sub F}=1.01%. The disordered crystal structure was successfully described by overlapping three types of domains with ordered atom arrangements. The distribution of atomic positions in one of the three types of domains can be achieved in the space group R3-bar m. The atom arrangements in the other two types of domains are noncentrosymmetrical with the space group R3m. These two structural configurations are related by the pseudo-symmetry inversion. -- Graphical abstract: A bird's eye view of electron densities up to 75.3% (0.133 nm{sup −3}) of the maximum on the plane parallel to (110) with the corresponding atomic arrangements of SiAl{sub 4}O{sub 2}N{sub 4}. Highlights: • Crystal structure of SiAl{sub 4}O{sub 2}N{sub 4} is determined by laboratory X-ray powder diffraction. • The atom arrangements are represented by the split-atom model. • The maximum-entropy method-based pattern fitting method is used to confirm the validity of the model. • The disordered structure is described by overlapping three types of domains with ordered atom arrangements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2013

Electron density distribution and crystal structure of 27R-AlON, Al{sub 9}O{sub 3}N{sub 7}

The crystal structure of Al{sub 9}O{sub 3}N{sub 7} was characterized by laboratory X-ray powder diffraction (CuKα{sub 1}). The title compound is trigonal with space group R3-bar m (centrosymmetric). The hexagonal unit-cell dimensions (Z=3) are a=0.30656(2) nm, c=7.2008(3) nm and V=0.58605(5) nm{sup 3}. The initial structural model was derived by the powder charge-flipping method and subsequently refined by the Rietveld method. The final structural model showed the positional disordering of two of the five types of Al sites. The maximum-entropy method-based pattern fitting method was used to confirm the validity of the split-atom model, in which conventional structure bias caused by assuming intensity partitioning was minimized. The disordered crystal structure was successfully described by overlapping five types of domains with ordered atom arrangements. The distribution of atomic positions in one of the five types of domains can be achieved in the space group R3{sup ¯}m. The atom arrangements in the four other domains are noncentrosymmetric with the space group R3m. Two of the four types of domains are related by a pseudo-symmetry inversion, and the two remaining domains also have each other the inversion pseudo-symmetry. The very similar domain structure has been also reported for 21R-AlON (Al{sub 7}O{sub 3}N{sub 5}) in our previous study. - Graphical abstract: A bird’s eye view of electron densities up to 50% (0.074 nm{sup −3}) of the maximum on the plane parallel to (110) with the corresponding atomic arrangements of Al{sub 9}O{sub 3}N{sub 7}. Highlights: • Crystal structure of Al{sub 9}O{sub 3}N{sub 7} is determined by laboratory X-ray powder diffraction. • The atom arrangements are represented by the split-atom model. • The maximum-entropy method-based pattern fitting method is used to confirm the validity of the model. • The disordered structure is described by overlapping five types of domains with ordered atom arrangements.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Principle of Maximum Entanglement Entropy and Local Physics of Strongly Correlated Materials

We argue that, because of quantum entanglement, the local physics of strongly correlated materials at zero temperature is described in a very good approximation by a simple generalized Gibbs distribution, which depends on a relatively small number of local quantum thermodynamical potentials. We demonstrate that our statement is exact in certain limits and present numerical calculations of the iron compounds FeSe and FeTe and of the elemental cerium by employing the Gutzwiller approximation that strongly support our theory in general.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Deviations from maximal entanglement for eigenstates of the Sachdev-Ye-Kitaev model

We consider mid-spectrum eigenstates of the Sachdev-Ye-Kiteav (SYK) model. We prove that for subsystems whose size is a constant fraction of the system size, the entanglement entropy deviates from the maximum entropy by at least a positive constant. This result highlights the difference between the entanglement entropy of mid-spectrum eigenstates of the SYK model and that of random states.

Disordered Systems and Neural Networks (cond-mat.d↗
DOE OSTI2024

Lattice engineering of high-entropy olivine-type lithium metal phosphate as high-voltage cathodes

Engineering of high-entropy cathode materials for lithium-ion batteries has been actively pursued owing to the outstanding conductivity of high-entropy materials benefited from the maximum entropy and unique antisite disordering structure. Olivine lithium metal phosphates such as LiMnPO 4 and LiNiPO 4 feature high working voltages but low capacities due to their insulation nature. Here in this work, the synthesis of the high-entropy lithium metal phosphate materials (HELMPs) is realized by combining mechanochemistry with a calcination method. By regulating lattice of HELMPs, the high-entropy Li(Mn 0.35 Fe 0.35 Co0.1Mg 0.1 Ca 0.1 )PO 4 reveals three typical high-voltage plateaus in charge–discharge curves corresponding to the redox of Fe, Mn, and Co in the voltage range of 2.0–4.9 V vs Li + /Li, and a much higher initial capacity than LiMnPO 4 (104 vs 15 mAh g -1 ).

25 ENERGY STORAGE↗
DOE OSTI2022

Interfacial water asymmetry at ideal electrochemical interfaces

Controlling electrochemical reactivity requires a detailed understanding of the charging behavior and thermodynamics of the electrochemical interface. Experiments can independently probe the overall charge response of the electrochemical double layer by capacitance measurements and the thermodynamics of the inner layer with potential of maximum entropy measurements. Relating these properties by computational modeling of the electrochemical interface has so far been challenging due to the low accuracy of classical molecular dynamics (MD) for capacitance and the limited time and length scales of ab initio MD. Here, we combine large ensembles of long-time-scale classical MD simulations with charge response from electronic density functional theory to predict the potential-dependent capacitance of a family of ideal aqueous electrochemical interfaces with different peak capacitances. We show that while the potential of maximum capacitance varies, this entire family exhibits an electrode charge of maximum capacitance (CMC) between -2.9 and -2.2 μC/cm 2 , regardless of the details in the electronic response. Simulated heating of the same interfaces reveals that the entropy peaks at a charge of maximum entropy (CME) of -5.1 ± 0.6 μC/cm 2 , in agreement with experimental findings for metallic electrodes. The CME and CMC both indicate asymmetric response of interfacial water that is stronger for negatively charged electrodes, while the difference between CME and CMC illustrates the richness in behavior of even the ideal electrochemical interface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1992

Far-infrared emission, gas, and ultraluminous HII regions in M101

We have made deconvolved maps of M101 in each of the 4 IRAS bands using a new maximum-entropy based model for reconstructing distributions with correlated structure on multiple scales. This new deconvolution procedure, developed by Weir (1992, J.Opt.Soc.Am., submitted), is superior to other maximum entropy-based techniques for several reasons. For our purposes, an important advantage is that it has less artifacts and greatly reduced systematic biases compared with the 'HiRes' maps of M101 produced by Aumann, Fowler, and Melnyk (1990, AJ, 99, 1674), thus it is accurate enough to perform aperture photometry. The deconvolved maps have a maximum resolution of approximately 30 sec, sufficient to resolve the brightest HII complexes and much of the spiral structure. The new maps and our comparison of the far-infrared, gas, and optical distributions are being written up in Kenney, Weir & Scoville (1992, in preparation). The quality of the reconstructed far-infrared maps is good enough for us to carry out most of the analyses outlined in the original proposal. From a ratio of the 60 micron and 100 micron maps, we have found that the ultraluminous HII complexes in the outer galaxy have the hottest dust temperatures with T approximately 50-60 K, which is twice as hot as most of the disk. Their extraordinary luminosity in the far-infrared is due to a relatively small amount of dust being heated to high temperatures, rather than a large concentration of dust and gas. A map of the dust opacity at 60 microns shows good overall agreement with a map of cold gas (HI+H2), indicating that throughout most of the galaxy only approximately 20 percent of the dust is warm enough to be detected by IRAS. The ultraluminous HII complexes have a high luminosity-to-gas mass ratio, independent of whether the far-infrared or the H-alpha emission line is used to measure the luminosity, which implies that gas is being converted into high mass stars more rapidly in these complexes compared to other locations in the disk.

Kenney, J. D. P.↗
DOE OSTI2018

Statistical Theory on the Functional Form of Cloud Particle Size Distributions

Abstract Several functional forms of cloud particle size distributions (PSDs) have been used in numerical modeling and remote sensing retrieval studies of clouds and precipitation, including exponential, gamma, lognormal, and Weibull distributions. However, there is no satisfying theoretical explanation as to why certain distribution forms preferentially occur instead of others. Intuitively, the analytical form of a PSD can be derived by directly solving the general dynamic equation, but no analytical solutions have been found yet. Instead of a process-level approach, the use of the principle of maximum entropy (MaxEnt) for determining the theoretical form of PSDs from the perspective of system is examined here. MaxEnt theory states that the probability density function with the largest information entropy among a group satisfying the given properties of the variable should be chosen. Here, the issue of variability under coordinate transformations that arises using the Gibbs–Shannon definition of entropy is identified, and the use of the concept of relative entropy to avoid these problems is discussed. Focusing on cloud physics, the four-parameter generalized gamma distribution is proposed as the analytical form of a PSD using the principle of maximum (relative) entropy with assumptions on power-law relations among state variables, scale invariance, and a further constraint on the expectation of one state variable (e.g., bulk water mass). The four-parameter generalized gamma distribution is very flexible to accommodate various type of constraints that could be assumed for cloud PSDs.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

ENTROPY PRODUCTION IN COLLISIONLESS SYSTEMS. III. RESULTS FROM SIMULATIONS

The equilibria formed by the self-gravitating, collisionless collapse of simple initial conditions have been investigated for decades. We present the results of our attempts to describe the equilibria formed in N-body simulations using thermodynamically motivated models. Previous work has suggested that it is possible to define distribution functions for such systems that describe maximum entropy states. These distribution functions are used to create radial density and velocity distributions for comparison to those from simulations. A wide variety of N-body code conditions are used to reduce the chance that results are biased by numerical issues. We find that a subset of initial conditions studied lead to equilibria that can be accurately described by these models, and that direct calculation of the entropy shows maximum values being achieved.

79 ASTRONOMY AND ASTROPHYSICS↗