Learning algorithm reflecting universal scaling behavior near phase transitions
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Maskara, N. (ORCID:0000000157759542)↗
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Results for “Scaling behavior”
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Vertical Dependence of Horizontal Scaling Behavior of Orographic Wind and Moisture Fields in Atmospheric Models
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M. Eghdami↗
Scaling Behavior of a Turbulent Kinetic Energy Closure Scheme for the Stably Stratified Atmosphere: A Steady-State Analysis
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Michael MacDonald↗
Superfluid weight cross-over and critical temperature enhancement in singular flat bands
Nonanalytic Bloch eigenstates at isolated band degeneracy points exhibit singular behavior in the quantum metric. Here, a description of superfluid weight for zero-energy flat bands in proximity to other high-energy bands is presented, where they together form a singular band gap system. When the singular band gap closes, the geometric and conventional contributions to the superfluid weight as a function of the superconducting gap exhibit different cross-over behaviors. The scaling behavior of superfluid weight with the band gap is studied in detail, and the effect on the Berezinskii–Kosterlitz–Thouless transition temperature is explored. It is found that tuning the singular band gap provides a unique mechanism for enhancing the supercurrent and critical temperature of two-dimensional superconductors.
Science & Technology - Other Topics↗
Temperature-driven changes in the Fermi surface of graphite
Here we report on temperature-dependent size and anisotropy of the Fermi pockets in graphite revealed by magnetotransport measurements. The magnetoresistances (MRs) obtained in fields along the c axis obey an extended Kohler's rule, with the carrier density following the prediction of a temperature-dependent Fermi energy, indicating a change in the Fermi pocket size with temperature. The angle-dependent magnetoresistivities at a given temperature exhibit a scaling behavior. The scaling factor that reflects the anisotropy of the Fermi surface is also found to vary with temperature. Our results demonstrate that temperature-driven changes in Fermi surface can be ubiquitous and need to be considered in understanding the temperature-dependent carrier density and MR anisotropy in semimetals.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
On the regeneration of fish scales: structure and mechanical behavior
Fish scales serve as a dermal armor that provides protection from physical injury. Owing to a number of outstanding properties, fish scales are inspiring new concepts for layered engineered materials and next-generation flexible armors. Although past efforts have primarily focused on the structure and mechanical behavior of ontogenetic scales, the structure–property relationships of regenerated scales have received limited attention. In the present study, common carp ( Cyprinus carpio ) acquired from the wild were held live in an aquatic laboratory at 10°C and 20°C. Ontogenetic scales were extracted from the fish for analysis, as well as regenerated scales after approximately 1 year of development and growth. Their microstructure was characterized using microscopy and Raman spectroscopy, and the mechanical properties were evaluated in uniaxial tension to failure under hydrated conditions. We note the strength, strain to fracture and toughness of the regenerated scales were significantly lower than those of ontogenetic scales from the same fish, regardless of the water temperature. Scales that regenerated at 20°C exhibited significantly higher strength, strain to fracture and toughness than those regenerated at 10°C. The regenerated scales exhibited a highly mineralized outer layer, but no distinct limiting layer or external elasmodine; they also possessed a significantly lower number of plies in the basal layer than the ontogenetic scales. The results suggest that a mineralized layer develops preferentially during scale regeneration with the topology needed for protection, prior to the development of other qualities.
59 BASIC BIOLOGICAL SCIENCES↗
Probabilistic Simulation of Multi-Scale Composite Behavior
A methodology is developed to computationally assess the non-deterministic composite response at all composite scales (from micro to structural) due to the uncertainties in the constituent (fiber and matrix) properties, in the fabrication process and in structural variables (primitive variables). The methodology is computationally efficient for simulating the probability distributions of composite behavior, such as material properties, laminate and structural responses. Bi-products of the methodology are probabilistic sensitivities of the composite primitive variables. The methodology has been implemented into the computer codes PICAN (Probabilistic Integrated Composite ANalyzer) and IPACS (Integrated Probabilistic Assessment of Composite Structures). The accuracy and efficiency of this methodology are demonstrated by simulating the uncertainties in composite typical laminates and comparing the results with the Monte Carlo simulation method. Available experimental data of composite laminate behavior at all scales fall within the scatters predicted by PICAN. Multi-scaling is extended to simulate probabilistic thermo-mechanical fatigue and to simulate the probabilistic design of a composite redome in order to illustrate its versatility. Results show that probabilistic fatigue can be simulated for different temperature amplitudes and for different cyclic stress magnitudes. Results also show that laminate configurations can be selected to increase the redome reliability by several orders of magnitude without increasing the laminate thickness--a unique feature of structural composites. The old reference denotes that nothing fundamental has been done since that time.
Chamis, Christos C.↗
Spatial Scaling of Snow Observations and Microwave Emission Modeling During CLPX and Appropriate Satellite Sensor Resolution
Accurate estimates of snow water equivalent and other properties play an important role in weather, natural hazard, and hydrological forecasting and climate modeling over a range of scales in space and time. Remote sensing-derived estimates have traditionally been of the "snapshot" type, but techniques involving models with assimilation are also being explored. In both cases, forward emission models are useful to understand the observed passive microwave signatures and developing retrieval algorithms. However, mismatches between passive microwave sensor resolutions and the scales of processes controlling subpixel heterogeneity can affect the accuracy of the estimates. Improving the spatial resolution of new passive microwave satellite sensors is a major desire in order to (literally) resolve such subpixel heterogeneity, but limited spacecraft and mission resources impose severe constraints and tradeoffs. In order to maximize science return while mitigating risk for a satellite concept, it is essential to understand the scaling behavior of snow in terms of what the sensor sees (brightness temperature) as well as in terms of the actual variability of snow. NASA's Cold Land Processes Experiment-1 (CLPX-1: Colorado, 2002 and 2003) was designed to provide data to measure these scaling behaviors for varying snow conditions in areas with forested, alpine, and meadow/pasture land cover. We will use observations from CLPX-1 ground, airborne, and satellite passive microwave sensors to examine and evaluate the scaling behavior of observed and modeled brightness temperatures and observed and retrieved snow parameters across scales from meters to 10's of kilometers. The conclusions will provide direct examples of the appropriate spatial sampling scales of new sensors for snow remote sensing. The analyses will also illustrate the effects and spatial scales of the underlying phenomena (e.g., land cover) that control subpixel heterogeneity.
Kim, Edward J.↗
Transport Upscaling under Flow Heterogeneity and Matrix-Diffusion in Three-Dimensional Discrete Fracture Networks
For this work, we investigate the combined effects of network scale flow variability and retention due to matrix-diffusion on the scaling behavior of transport through fractured media. Two of the principal mechanisms controlling the transport of solutes through fractured low-permeability media are broad distributions of flow velocities and retention times in the solid matrix. We study the relative impact of these two processes under different initial conditions using a set of three-dimensional discrete fracture network simulations. We use these simulations to develop and calibrate an upscaled continuous time random walk (CTRW) approach for advective transport based on an Ornstein-Uhlenbeck model for the particle velocities that accounts for the fracture-matrix coupling using a compound Poisson process. This CTRW model can be conditioned on the initial solute distribution and allows to observe late-time scaling behavior at distances beyond what is feasible to observe using high-fidelity direct numerical simulations. We determine that the initial distribution of particles leads to marked differences in the persistent long-term scale behavior in the solute travel time distributions, even those undergoing retention due to matrix diffusion through implementation and analysis of the model.
54 ENVIRONMENTAL SCIENCES↗
Probabilistic simulation of multi-scale composite behavior
A methodology is developed to computationally assess the probabilistic composite material properties at all composite scale levels due to the uncertainties in the constituent (fiber and matrix) properties and in the fabrication process variables. The methodology is computationally efficient for simulating the probability distributions of material properties. The sensitivity of the probabilistic composite material property to each random variable is determined. This information can be used to reduce undesirable uncertainties in material properties at the macro scale of the composite by reducing the uncertainties in the most influential random variables at the micro scale. This methodology was implemented into the computer code PICAN (Probabilistic Integrated Composite ANalyzer). The accuracy and efficiency of this methodology are demonstrated by simulating the uncertainties in the material properties of a typical laminate and comparing the results with the Monte Carlo simulation method. The experimental data of composite material properties at all scales fall within the scatters predicted by PICAN.
Liaw, D. G.↗
Soft pions and transport near the chiral critical point
During the expansion of a heavy ion collision, the system passes close to the $\textit{O}$(4) critical point of QCD, and thus the fluctuations of the order parameter $(σ, \overrightarrow{π}$) are expected to be enhanced. In this work, our goal is to compute how these enhanced fluctuations modify the transport coefficients of QCD near the pseudocritical point. We also make a phenomenological estimate for how chiral fluctuations could effect the momentum spectrum of soft pions. We first formulate the appropriate stochastic hydrodynamic equations close to the $\textit{O}$(4) critical point. Then, working in mean field, we determine the correlation functions of the stress tensor and the currents which result from this stochastic real-time theory, and use these correlation functions to determine the scaling behavior of the transport coefficients. The hydrodynamic theory also describes the propagation of pion waves, fixing the scaling behavior of the dispersion curve of soft pions. We present scaling functions for the shear viscosity and the charge conductivities near the pseudocritical point and estimate the absolute magnitude of the critical fluctuations to these parameters and the bulk viscosity. Using the calculated pion dispersion curve, we estimate the expected critical enhancement of soft pion yields, and this estimate provides a plausible explanation for the excess seen in experiment relative to ordinary hydrodynamic computations. Our results motivate further phenomenological and numerical work on the implications of chiral symmetry on real-time properties of thermal QCD near the pseudocritical point.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Cloud Power Spectra-Dependence on Solar Zenith Angle and Wavelength, Implications for Cloud Optical Property Retrievals
Scale breaks (spatial scales at which power-law exponent changes occur) observed in Landsat radiances have proven to be useful indicators of radiative interactions, and have aided the development of improved techniques in the remote sensing of clouds. This work extends previous theoretical studies to absorbing wavelengths by using both Landsat Thematic Mapper (TM) observations and Monte Carlo (MC) simulations to infer the systematic dependencies of power spectral shape on cloud characteristics, illumination conditions, and wavelength. We show that MC simulations operating on a simple fractal model of horizontally inhomogeneous clouds produce power spectra that qualitatively resemble observed spectra. We also show that the decrease in the spectra power-law exponent seen at intermediate scales (referred to as "roughening") as the Sun becomes more oblique is more pronounced at absorbing wavelengths. An automated procedure designed to detect the small scale break location is unable to find systematic differences between TM Band 4 and Band 7, despite the fact that MC simulations point to systematic differences in horizontal fluxes. The effect of these qualitative characteristics of the spatial spectra on the retrieval of cloud optical properties is examined by comparing power spectra of nadir radiances with power spectra of optical properties retrieved using either traditional Independent Pixel Approximation approaches or modifications based on normalized radiance indices and the inverse Non-local Independent Pixel Approximation. Assuming that the actual cloud properties follow perfect scaling behavior at all scales, we show the improvement of the proposed retrieval modifications.
Oreopoulos, Lazaros↗
Effects of spatial variability and scale on areal -average evapotranspiration
This paper explores the effect of spatial variability and scale on areally-averaged evapotranspiration. A spatially-distributed water and energy balance model is employed to determine the effect of explicit patterns of model parameters and atmospheric forcing on modeled areally-averaged evapotranspiration over a range of increasing spatial scales. The analysis is performed from the local scale to the catchment scale. The study area is King's Creek catchment, an 11.7 sq km watershed located on the native tallgrass prairie of Kansas. The dominant controls on the scaling behavior of catchment-average evapotranspiration are investigated by simulation, as is the existence of a threshold scale for evapotranspiration modeling, with implications for explicit versus statistical representation of important process controls. It appears that some of our findings are fairly general, and will therefore provide a framework for understanding the scaling behavior of areally-averaged evapotranspiration at the catchment and larger scales.
Famiglietti, J. S.↗
Spectrum of Dirac eigenvalues across QCD chiral transition
Here, we show that the universal scaling properties of the chiral phase transition in quantum chromodynamics (QCD) at the macroscale are encoded in the microscopic energy levels of the quarks in the background of gluon fields, defined as eigenvalues of the Dirac operator. We introduce a novel relation between the cumulants of the chiral condensate, and the correlations among the energy levels of quarks, i.e., the eigenspectra of the massless QCD Dirac operator. This relation elucidates how the fluctuations of the chiral condensate arise from the correlations within the infrared part of the energy spectra of quarks, and naturally leads to a generalization of the Banks-Casher relation for the cumulants of the chiral condensate. Then, through (2+1)-flavor lattice QCD calculations using HISQ action with varying light quark masses around the chiral phase transition temperature, we demonstrate that the correlations among the infrared part of the Dirac eigenvalue spectra exhibit same universal scaling behaviors as expected of the cumulants of the chiral condensate. We find that these universal scaling behaviors extend up to the physical values of the up and down quark masses.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Effects of the Grazing Incidence Geometry on X-ray Photon Correlation Spectroscopy Measurements
X-ray photon correlation spectroscopy (XPCS) is a versatile tool to measure dynamics on the nanometer to micrometer scale in bulk samples. XPCS has also been applied in grazing incidence (GI) geometry to examine the dynamics of surface layers. However, considering GI scattering experiments more universally, the GI geometry leads to a superposition of signals due to reflection and refraction effects, also known from the distorted-wave Born approximation (DWBA). In this paper, the impact of these reflection and refraction effects on the correlation analysis is determined experimentally by measuring grazing incidence transmission XPCS (GT-XPCS) and grazing incidence XPCS (GI-XPCS) simultaneously for a thin film sample, showing non-equilibrium dynamics. Here the results of the GI and GT geometry comparisons are combined within the framework of the standardly applied, simplified DWBA. These calculations allow identifying the main contributions of the detected signal from the leading scattering terms along the out-of-plane direction q z , which dominate the measured intensity pattern on the detector. In combination with the calculation of the non-linear effect of refraction in GTSAXS and GISAXS, it is possible to identify experimental conditions that can be chosen to run experiments and data analysis as close as possible to transmission XPCS and to explain which limitations for data interpretations are observed. Consequently, the beam exposure can be significantly reduced by using GI geometry only. Calculations of experimental settings prior to experiments are detailed to determine suitable q z regions for a variety of material systems measured in bulk-sensitive GI-XPCS experiments, allowing us to determine the scaling behavior of typical decay times as a function of q that is comparable to the scaling behavior obtained in distortion-free GT-XPCS or transmission XPCS experiments.
36 MATERIALS SCIENCE↗
Microscopic origin of criticality at macroscale in QCD chiral phase transition
We reveal that the criticality of the chiral phase transition in QCD at the macroscale arises from the microscopic energy levels of its fundamental constituents, the quarks. We establish a novel relation between cumulants of the chiral order parameter (i.e., chiral condensate) and correlations among the energy levels of quarks (i.e., eigenspectra of the massless Dirac operator), which naturally leads to a generalization of the Banks-Casher relation. Based on this novel relation and through (2+1)-flavor lattice QCD calculations using the HISQ action with varying light quark masses in the vicinity of the chiral phase transition, we demonstrate that the correlations among the infrared part of the Dirac eigenspectra exhibit same universal scaling behaviors as expected of the cumulants of the chiral condensate. We find that these universal scaling behaviors extend up to the physical values of the up and down quark masses.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Multiplicity scaling of light nuclei production in relativistic heavy-ion collisions
Using the nucleon coalescence model based on kinetic freeze-out nucleons from the 3D MUSIC+UrQMD and the 2D VISHNU hybrid model with a crossover equation of state, we study the multiplicity dependence of deuteron ( d ) and triton ( t ) production from central to peripheral Au+Au collisions at s NN = 7.7, 14.5, 19.6, 27, 39, 62.4 and 200 GeV and Pb+Pb at s NN = 2.76 TeV, respectively. It is found that the ratio N t N p / N d 2 of the proton yield N p , deuteron yield N d and triton yield N t exhibits a scaling behavior in its multiplicity dependence, i.e., decreasing monotonically with increasing charged-particle multiplicity. A similar multiplicity scaling of this ratio is also found in the nucleon coalescence calculation based on kinetic freeze-out nucleons from a multiphase transport (AMPT) model. The scaling behavior of N t N p / N d 2 can be naturally explained by the interplay between the sizes of light nuclei and the nucleon emission source. We further argue that the multiplicity scaling of N t N p / N d 2 can be used to validate the production mechanism of light nuclei, and the collision energy dependence of this yield ratio can further serve as a baseline in the search for the QCD critical point in relativistic heavy-ion collisions.
79 ASTRONOMY AND ASTROPHYSICS↗
Inclusive studies of two- and three-nucleon short-range correlations in 3 H and 3 He
Inclusive electron scattering at carefully chosen kinematics can isolate scattering from the high-momentum nucleons in short-range correlations (SRCs). SRCs are produced by the hard, short-distance interactions of nucleons in the nucleus, and because the two-nucleon (2N) SRCs arise from the same N-N interaction in all nuclei, the cross section in the SRC-dominated regime is identical up to an overall scaling factor. This scaling behavior has been used to identify SRC dominance and to measure the contribution of SRCs in a wide range of nuclei. We examine this scaling behavior over a range of momentum transfers using new data on 2 H, 3 H, and 3 He, and find an expanded scaling region compared to heavy nuclei. Motivated by this improved scaling, we examine the 3 H and 3 He data in kinematics where three-nucleon SRCs may play an important role. The data for the largest struck nucleon momenta are consistent with isolation of scattering from three-nucleon SRCs, and suggest that the very highest momentum nucleons in 3 He have a nearly isospin-independent momentum configuration.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗