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In support of the development of 3-dimensional transport codes, this paper derives the relevant relativistic particle kinematic theory. Formulas are given for invariant, spectral and angular distributions in both the lab (spacecraft) and center of momentum frames, for collisions involving 2, 3 and n - body final states.
Water vapor is one of the most important constituents of the earth's atmosphere. It has a major impact on both atmospheric dynamics and radiative transfer. From a dynamic standpoint, the distribution of water vapor with height determines convective stability which is the major indicator of destructive storm development. Also, water vapor stored in the planetary boundary layer acts as the fuel to intensify severe weather. In regards to radiative transfer, water vapor is the most active IR molecule in the atmosphere. It is more effective in absorbing and emitting IR radiation than either carbon dioxide or methane, and thus plays an important role in global change. The main objective of FIRE (First ISSCCP (International Satellite Cloud Climatology Project) Regional Experiment) was to study the development and radiative characteristics of cirrus clouds. The SPECTRE (Spectral Radiation Experiment) project was designed to acquire the necessary atmospheric observations to compare radiative measurements with radiative transfer theory, with special emphasis on understanding the water vapor spectral continuum. The FIRE/SPECTRE field campaign was conducted during Nov. - Dec. 1991 in Coffeyville, Kansas. A complete understanding of water vapor, its distribution with height, and its temporal variation was important for both experiments.
Wiener filtering theory for stationary ergodic inputs with known spectral densities and optimal control transfer functions of random-input nonlinear saturating systems with random unwanted disturbances
Hart (1979) showed that the truncated spectral equations obtained by Charney and Devore (1979) could be derived merely by assuming that the cross-stream scale of the topography was large compared to the downstream scale. Since actual topography does not have the large y scales postulated by Hart, his model was modified in the current investigation to obtain equations with arbitrary zonal variations of topography by projecting all variable functions onto the first topographic cross-stream mode. The topographic heights and streamfunctions are expanded as Fourier series in the cross-stream coordinate and the series are truncated after the first term. This accomplishes Hart's results but permits more realistic y variations in the topography. The present investigation is the first in a two-part series. The second part will deal with a two-layer baroclinic channel flow, again with arbitrary zonal variations of topography.
Radiative transfer theory was used to model upwelling radiance for an orbiting sensor viewing an estuarine environment. Radiance was calculated in Tm bands 3,4, and 5 and MSS bands 4 and 5 for an optically shallow estuary of either clear or turbid water, and of three bottom types: vegetation, sand, or mud. A portion of a TM image of Chesapeake Bay was enhanced to obtain a quick look at what submerged features could be detected. The enhancements were compared with low altitude color aerial photography. The TM bands 1,2, and 3 were found to contain water and submerged features information. Band 1 contained a significant amount of noise and low contrast. Band 2 appeared to contain the most amount of bottom information. Band 3, while having the least amount of noise and best constrast, contained a lesser amount of bottom information because of increase water absorption. Several water signatures were identified which correlated with submerged vegetation shown in the aerial photography.
We develop a method to obtain fermion spectral functions non-perturbatively in a non-Abelian gauge theory with high occupation numbers of gauge fields. After recovering the free field case, we extract the spectral function of fermions in a highly occupied non-Abelian plasma close to its non-thermal fixed point, i.e., in a self-similar regime of the non-equilibrium dynamics. We find good agreement with hard loop perturbation theory for medium-induced masses, dispersion relations and quasiparticle residues. We also extract the full momentum dependence of the damping rate of the collective excitations.
The standard understanding of topological protection from band theory is that a system's topology cannot change without first closing the bulk band gap. However, in Floquet systems, this typical definition of topological protection is one step removed from the experimentally accessible system parameters, as the relationship between the disorder in a system's instantaneous Hamiltonian and its Floquet Hamiltonian that defines its topology is not straightforward. Here, in this study, we demonstrate that the spectral localizer framework for classifying material topology can be applied to Floquet systems using solely the Floquet Hamiltonian and prove that its associated measure of topological protection can be understood in terms of the disorder across the system's instantaneous Hamiltonians. As such, we have derived a quantitative bound on a Floquet system's topological protection in terms of the instantaneous system. Moreover, we show the utility of these bounds in both ordinary and anomalous Floquet Chern insulators.
Relativistic shock models of gamma-ray bursts may be tested by comparing their predicted low-energy asymptotic spectral indices s to observations. Synchrotron radiation theory predicts that the instantaneous spectrum has s = 1/3, and the spectrum integrated over the radiative decay of the electrons' energies has s = 1/2 with other cases lying between these limits. We examine the spectra of 11 bursts obtained by the Large Area Detectors on BATSE. One agrees with the predicted instantaneous spectrum, as does the initial portion of a second, and three are close to the predicted integrated spectrum. All of the observed asymptotic spectral slopes lie in the predicted range. This evidence for relativistic shocks is independent of detailed models of bursts and of assumptions about their distances. Radiation observed with the predicted instantaneous spectrum has a comparatively smooth time dependence, consistent with the necessarily long radiation time, while radiation observed with the predicted integrated spectrum has a spiky time dependence, consistent with the necessarily short radiation time.
A theory which gives statistical predictions for how often sonic booms propagating through the earth's turbulent boundary layer will encounter caustics, given the spectral properties of the atmospheric turbulence, is outlined. The theory is simple but approximately accounts for the variation of ray tube areas along ray paths. This theory predicts that the variation of ray tube areas is determined by the product of two similar area factors, psi (x) and phi (x), each satisfying a generic harmonic oscillator equation. If an area factor increases the peak acoustic pressure decreases, and if the factor decreases the peak acoustic pressure increases. Additionally, if an area factor decreases to zero and becomes negative, the ray has propagated through a caustic, which contributes a phase change of 90 degrees to the wave. Thus, it is clear that the number of times that a sonic boom wave passes through a caustic should be related to the distorted boom waveform received on the ground. Examples are given based on a characterization of atmospheric turbulence due to the structure function of Tatarski as modified by Crow.
By quantifying the distance between two collider events, one can triangulate a metric space and reframe collider data analysis as computational geometry. One popular geometric approach is to first represent events as an energy flow on an idealized celestial sphere and then define the metric in terms of optimal transport in two dimensions. In this paper, we advocate for representing events in terms of a spectral function that encodes pairwise particle angles and products of particle energies, which enables a metric distance defined in terms of one-dimensional optimal transport. This approach has the advantage of automatically incorporating obvious isometries of the data, like rotations about the colliding beam axis. It also facilitates first-principles calculations, since there are simple closed-form expressions for optimal transport in one dimension. Up to isometries and event sets of measure zero, the spectral representation is unique, so the metric on the space of spectral functions is a metric on the space of events. At lowest order in perturbation theory in electron-positron collisions, our metric is simply the summed squared invariant masses of the two event hemispheres. Going to higher orders, we present predictions for the distribution of metric distances between jets in fixed-order and resummed perturbation theory as well as in parton-shower generators. Finally, we speculate on whether the spectral approach could furnish a useful metric on the space of quantum field theories.
Each of the two Voyager spacecraft launched in 1977 has completed a reconnaissance of the Jovian and Saturnian systems. In connection with occultation experiments, strong scintillations were observed. Further theoretical work is required before these scintillations can be interpreted. The present study is, therefore, concerned with the derivation of a theory for strong scattering during atmospheric occultation experiments, taking into account as fundamental quantity of interest the spatial spectrum (or spectral density) of intensity fluctuations. Attention is given to a theory for intensity spectra, and numerical calculations. The new formula derived for Phi-i accounts for strong scattering of electromagnetic waves during atmospheric occultations.
The mesoscale spectrum describes the distribution of kinetic energy in the Earth's atmosphere between length scales of 10 and 400 km. Since the first observations, the origins of this spectrum have been controversial. At synoptic scales, the spectrum follows a –3 spectral slope, consistent with two-dimensional turbulence theory, but a shallower –5/3 slope was observed at the shorter mesoscales. The cause of the shallower slope remains obscure, illustrating our lack of understanding. Through a novel coarse-graining methodology, we are able to present a spatio-temporal climatology of the spectral slope. We find convection and orography have a shallowing effect and can quantify this using “conditioned spectra.” These are typical spectra for a meteorological condition, obtained by aggregating spectra where the condition holds. This allows the investigation of new relationships, such as that between energy flux and spectral slope. Potential future applications of our methodology include predictability research and model validation.
Confidence limit is a routine requirement for Fourier spectral analysis. But this confidence limit is established based on ergodic theory: For stationary process, temporal average equals the ensemble average. Therefore, one can divide the data into n-sections and treat each section as independent realization. Most natural processes in general, and climate data in particular, are not stationary; therefore, there is a need for the Hilbert Spectral analysis for such processes. Here ergodic theory is no longer applicable. We propose to use various adjustable parameters in the shifting processes of the Empirical Mode Decomposition (EMD) method to obtain an ensemble of Intrinsic Mode Function 0 sets. Based on such an ensemble, we introduce a statistical measure in. a form of confidence limits for the Intrinsic Mode Functions, and consequently, the Hilbert spectra. The criterion of selecting the various adjustable parameters is based on the orthogonality test of the resulting M F sets. Length-of-day data from 1962 to 2001 will be used to illustrate this new approach. Its implication in climate data analysis will also be discussed.
The concept of rotationally sampled wind speed is described. The unusual wind characteristics that result from rotationally sampling the wind are shown first for early measurements made using an 8-point ring of anemometers on a vertical plane array of meteorological towers. Quantitative characterization of the rotationally sampled wind is made in terms of the power spectral density function of the wind speed. Verification of the importance of the new concept is demonstrated with spectral analyses of the response of the MOD-OA blade flapwise root bending moment and the corresponding rotational analysis of the wind measured immediately upwind of the MOD-OA using a 12-point ring of anemometers on a 7-tower vertical plane array. The Pacific Northwest Laboratory (PNL) theory of the rotationally sampled wind speed power spectral density function is tested successfully against the wind spectrum measured at the MOD-OA vertical plane array. A single-tower empirical model of the rotationally sampled wind speed is also successfully tested against the measurements from the full vertical plane array. Rotational measurements of the wind velocity with hotfilm anemometers attached to rotating blades are shown to be accurate and practical for research on winds at the blades of wind turbines. Some measurements at the rotor blade of a MOD-2 turbine using the hotfilm technique in a pilot research program are shown. They are compared and contrasted to the expectations based upon application of the PNL theory of rotationally sampled wind to the MOD-2 size and rotation rate but without teeter, blade bending, or rotor induction accounted for. Finally, the importance of temperature layering and of wind modifications due to flow over complex terrain is demonstrated by the use of hotfilm anemometer data, and meteorological tower and acoustic doppler sounder data from the MOD-2 site at Goodnoe Hills, Washington.
We develop a nonperturbative definition of RMT 2 : a generalization of random matrix theory that is compatible with the symmetries of two-dimensional conformal field theory. Given any random matrix ensemble, its 𝑛-point spectral correlations admit a prescribed modular-invariant lift to RMT 2 , which moreover reduce to the original random matrix correlators in a near-extremal limit. Central to the prescription is a presentation of random matrix theory in Mellin space, which lifts to two dimensions via the SL(2,ℤ) spectral decomposition employed in previous work. As a demonstration we perform the explicit RMT 2 lift of two-point correlations of the GUE Airy model. We propose that in AdS 3 pure gravity, semiclassical amplitudes for off-shell 𝑛-boundary torus wormholes with topology Σ 0,𝑛 × 𝑆 1 are given by the RMT 2 lift of JT gravity wormhole amplitudes. For the three-boundary case, we identify a gravity calculation which matches the RMT 2 result.
The first results of observations of ion cyclotron waves by the elliptically orbiting ISEE 1 and 2 pair of spacecraft are reported. The most intense waves (8 nT) were observed in the outer plasmasphere where convection drift velocities were largest and the Alfven velocity was a minimum. Wave polarization is predominantly left-handed with propagation almost parallel to the ambient magnetic field, and the spectral slot and polarization reversal predicted by cold plasma propagation theory are identified in the wave data. Computations of the experimental wave spectra during the passage through the plasmapause show that the spectral slots relate to the local plasma parameters, possibly suggesting an ion cyclotron wave growth source near the spacecraft. A regular wave packet structure seen over the first 30 min of the event is attributed to the modulation of this energy source by the Pc 5 waves seen at the same time.
In this paper, we introduce a new family of spatially co-located field solvers for particle-in-cell applications which evolve the potential formulation of Maxwell’s equations under the Lorenz gauge. Our recent work [2] introduced the concept of time-consistency, which connects charge conservation to the preservation of the gauge at the semi-discrete level. It will be shown that there exists a large family of time discretizations which satisfy this property. Additionally, it will be further shown that for large classes of time marching methods, the satisfaction of the gauge condition automatically implies the satisfaction of Gauss’s law for electricity, with the potential formulation ensuring that that Gauss’s law for magnetism is satisfied by definition. We focus on popular time marching methods including centered differences, backward differences, and diagonally-implicit Runge-Kutta methods, which are coupled to a spectral discretization in space. We demonstrate the theory by testing the methods on a relativistic Weibel instability and a drifting cloud of electrons.
Abstract The Eliashberg theory of superconductivity accounts for the fundamental physics of conventional superconductors, including the retardation of the interaction and the Coulomb pseudopotential, to predict the critical temperature T c . McMillan, Allen, and Dynes derived approximate closed-form expressions for the critical temperature within this theory, which depends on the electron–phonon spectral function α 2 F ( ω ). Here we show that modern machine-learning techniques can substantially improve these formulae, accounting for more general shapes of the α 2 F function. Using symbolic regression and the SISSO framework, together with a database of artificially generated α 2 F functions and numerical solutions of the Eliashberg equations, we derive a formula for T c that performs as well as Allen–Dynes for low- T c superconductors and substantially better for higher- T c ones. This corrects the systematic underestimation of T c while reproducing the physical constraints originally outlined by Allen and Dynes. This equation should replace the Allen–Dynes formula for the prediction of higher-temperature superconductors.