Effect of spacewise variations in a random load field on the response of a linear system
Effect of spacewise variations in random load field on response of linear system - statistical mechanics
LINEAR SYSTEM↗
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Distributed system response characteristics in random pressure fields
Response characteristics of distributed structural systems to random excitation by acoustic pressure fields
Barnoski, R. L.↗
Effect of spacewise variations in a random load field on the response of a linear system.
Statistical properties of dynamic response of structure to random load field, examining simple deterministic loadings
APPROXIMATION METHOD↗
Random magnetic field and the Dirac Fermi surface
In this paper, we study a single two-dimensional Dirac fermion at finite density, subject to a quenched random magnetic field. At low energies and sufficiently weak disorder, the theory maps onto an infinite collection of 1D chiral fermions (associated to each point on the Fermi surface) coupled by a random vector potential. This low-energy theory exhibits an exactly solvable random fixed line, along which we directly compute various disorder-averaged observables without the need for the usual replica, supersymmetry, or Keldysh techniques. We find the longitudinal dc conductivity in the collisionless $\hbar$ω/k B T→∞ limit to be nonuniversal and to vary continuously along the fixed line.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
The diffusive idealization of charged-particle transport in random magnetic fields
The uniqueness and accuracy of the equations which describe the transport of charged particles diffusing in a random magnetic field parallel to a relatively large guiding field is examined. With regard to uniqueness, it is found that the same coefficient of diffusion is obtained by three methods that have apparently led to discrepancies in previous work. With regard to accuracy, it is found that two corrections must be added to Fick's law in which the diffusive flux is proportional to the gradient of the density. Explicit expressions are given for a characteristic time and a characteristic length which describe the corrections.
Earl, J. A.↗
New description of charged particle propagation in random magnetic fields
When charged particles spiral along a large constant magnetic field, their trajectories are scattered by random components that are superposed on the guiding field. In the simplest analysis of this situation, scattering causes the particles to diffuse parallel to the guiding field. At the next level of approximation, moving pulses that correspond to a coherent mode of propagation are present, but they are represented by delta-functions whose infinitely narrow width makes no sense physically and is inconsistent with the finite duration of coherent pulses observed in solar energetic particle events. To derive a more realistic description, the transport problem is formulated in terms of 4 x 4 matrices, which derive from a representation of the particle distribution function in terms of eigenfunctions of the scattering operator, and which lead to useful approximations that give explicit predictions of the detailed evolution not only of the coherent pulses, but also of the diffusive wake. More specifically, the new description embodies a simple convolution of a narrow Gaussian with the solutions above that involve delta-functions, but with a slightly reduced coherent velocity. The validity of these approximations, which can easily be calculated on a desktop computer, has been exhaustively confirmed by comparison with results of Monte Carlo simulations which kept track of 50 million particles and which were carried out on the Maspar computer at Goddard Space Flight Center.
Earl, James A.↗
Cosmic rays in a random magnetic field: Breakdown of the quasilinear derivation of the kinetic equation
The problem of deriving a kinetic equation for the cosmic ray distribution function in a random magnetic field is considered. A model is adopted which is mathematically simple but which contains the essential physics. The perturbation expansion upon which the quasi-linear treatment is based is investigated. The existence of resonant particles causes the breakdown of the adiabatic approximation frequently used in this theory. Resonant particles cause a general secular growth of higher order terms in the expansion which invalidates the entire perturbative approach.
Kaiser, T. B.↗
Coherent propagation of charged particle bunches in random magnetic fields
When the distribution function for energetic particles moving in interplanetary space is expressed in terms of eigenfunctions of an operator which describes pitch angle scattering by random magnetic fields, the familiar phenomenon of diffusion is the dominant solution of the transport equations provided that the spectrum of magnetic fluctuations is not too steep. The present paper describes a novel mode of particle transport when the latter condition is not satisfied (i.e., when the exponent for the spectrum of magnetic fluctuations is greater than 2). In this mode, the density inhomogeneities propagate coherently, in wavelike fashion, and with very little dispersion along the guiding field at a characteristic velocity equal to half the particle speed. The most striking manifestation of this phenomenon is the observed scatter-free propagation of solar flare electrons below 1 MeV.-
Earl, J. A.↗
Frequency of encounter of aircraft in a random horizontal field
Calculations were made of the frequency of encounter as a function of azimuth of encounter of a passing aircraft with the aircraft in a random planar horizontal field. All the field aircraft moved at a constant speed but in random directions. These calculations included the total frequency of encounter with the aircraft of the field and the frequency of encounter with those aircraft of the field which were encountered in the fore quadrant, in the lateral quadrants, and in the rear quadrant; the calculations were made for various speed ratios of the field aircraft and the passing aircraft.
Bird, J. D.↗
Probabilistic finite elements for transient analysis in nonlinear continua
The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.
Liu, W. K.↗
Pitch-angle scattering of charged particles in a random magnetic field
A calculation is presented in terms of the pitch angle that determines the conditions under which a Fokker-Planck equation gives a reasonable approximation of the pitch-angle scattering of low rigidity particles to first order in a random magnetic field. The formulation shows that the correlation scale of the fluctuation of the magnetic field about its mean does not enter directly into the approximation. The calculation is carried out for transverse magnetic fluctuations for which the magnetic field magnitude is constant to the order considered.
Jokipii, J. R.↗
Map-based cosmology inference with lognormal cosmic shear maps
ABSTRACT Most cosmic shear analyses to date have relied on summary statistics (e.g. ξ+ and ξ−). These types of analyses are necessarily suboptimal, as the use of summary statistics is lossy. In this paper, we forward-model the convergence field of the Universe as a lognormal random field conditioned on the observed shear data. This new map-based inference framework enables us to recover the joint posterior of the cosmological parameters and the convergence field of the Universe. Our analysis properly accounts for the covariance in the mass maps across tomographic bins, which significantly improves the fidelity of the maps relative to single-bin reconstructions. We verify that applying our inference pipeline to Gaussian random fields recovers posteriors that are in excellent agreement with their analytical counterparts. At the resolution of our maps – and to the extent that the convergence field can be described by the lognormal model – our map posteriors allow us to reconstruct all summary statistics (including non-Gaussian statistics). We forecast that a map-based inference analysis of LSST-Y10 data can improve cosmological constraints in the σ8–Ωm plane by $\approx\!{30}{{\ \rm per\ cent}}$ relative to the currently standard cosmic shear analysis. This improvement happens almost entirely along the $S_8=\sigma _8\Omega _{\rm m}^{1/2}$ directions, meaning map-based inference fails to significantly improve constraints on S8.
79 ASTRONOMY AND ASTROPHYSICS↗
Random strain induced correlations in materials with intertwined nematic and magnetic orders
Electronic nematicity is rarely observed as an isolated instability of a correlated electron system. Instead, in iron pnictides and in certain cuprates and heavy-fermion materials, nematicity is intertwined with an underlying spin-stripe or charge-stripe state. As a result, random strain, ubiquitous in any real crystal, creates both random-field disorder for the nematic degrees of freedom and random-bond disorder for the spin or charge ones. Here, we put forward an Ashkin-Teller model with random Baxter fields to capture the dual role of random strain in nematic systems for which nematicity is a composite order arising from a stripe state. Using Monte Carlo to simulate this random Baxter-field model, we find not only the expected break-up of the system into nematic domains, but also the emergence of nontrivial disorder-promoted magnetic correlations. Such correlations enhance and tie up the fluctuations associated with the two degenerate magnetic stripe states from which nematicity arises, leaving characteristic signatures in the spatial profile of the magnetic domains, in the configurational space of the spin variables, and in the magnetic noise spectrum. We discuss possible experimental manifestations of these effects in iron-pnictide superconductors. Furthermore, our work establishes the random Baxter-field model as a more complete alternative to the random-field Ising model to describe complex electronic nematic phenomena in the presence of disorder.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Transverse eV Ion Heating by Random Electric Field Fluctuations in the Plasmasphere
Charged particle acceleration in the Earth inner magnetosphere is believed to be mainly due to the local resonant wave-particle interaction or particle transport processes. However, the Van Allen Probes have recently provided interesting evidence of a relatively slow transverse heating of eV ions at distances about 2-3 Earth radii during quiet times. Waves that are able to resonantly interact with such very cold ions are generally rare in this region of space, called the plasmasphere. Thus, non-resonant wave-particle interactions are expected to play an important role in the observed ion heating. We demonstrate that stochastic heating by random transverse electric field fluctuations of whistler (and possibly electromagnetic ion cyclotron) waves could explain this weak and slow transverse heating of H+ and O+ ions in the inner magnetosphere. The essential element of the proposed model of ion heating is the presence of trains of random whistler (hiss) wave packets, with significant amplitude modulations produced by strong wave damping, rapid wave growth, or a superposition of wave packets of different frequencies, phases, and amplitudes. Such characteristics correspond to measured characteristics of hiss waves in this region. Using test particle simulations with typical wave and plasma parameters, we demonstrate that the corresponding stochastic transverse ion heating reaches 0.07-0.2 eV/h for protons and 0.007-0.015 eV/h for O+ ions. This global temperature increase of the Maxwellian ion population from an initial Ti approx. 0.3 eV could potentially explain the observations.
Artemyev, A. V.↗
Charged-particle transport in turbulent astrophysical plasmas
The effect of electromagnetic fluctuations, or plasma turbulence, on the motion of the individual particles in a plasma is investigated. Two alternative methods are used to find a general equation governing the time-evolution of a distribution of charged particles subject to both an external force field and the random fields of the fluctuations. It is found that, for the high-temperature, low-density plasmas frequently encountered in the study of astrophysics, the presence of even a small amount of turbulence can have a very important effect on the behavior of the plasma. Two problems in which turbulence plays an important role are treated.
Newman, C. E., Jr.↗
End-to-end learning of multiple sequence alignments with differentiable Smith–Waterman
Abstract Motivation Multiple sequence alignments (MSAs) of homologous sequences contain information on structural and functional constraints and their evolutionary histories. Despite their importance for many downstream tasks, such as structure prediction, MSA generation is often treated as a separate pre-processing step, without any guidance from the application it will be used for. Results Here, we implement a smooth and differentiable version of the Smith–Waterman pairwise alignment algorithm that enables jointly learning an MSA and a downstream machine learning system in an end-to-end fashion. To demonstrate its utility, we introduce SMURF (Smooth Markov Unaligned Random Field), a new method that jointly learns an alignment and the parameters of a Markov Random Field for unsupervised contact prediction. We find that SMURF learns MSAs that mildly improve contact prediction on a diverse set of protein and RNA families. As a proof of concept, we demonstrate that by connecting our differentiable alignment module to AlphaFold2 and maximizing predicted confidence, we can learn MSAs that improve structure predictions over the initial MSAs. Interestingly, the alignments that improve AlphaFold predictions are self-inconsistent and can be viewed as adversarial. This work highlights the potential of differentiable dynamic programming to improve neural network pipelines that rely on an alignment and the potential dangers of optimizing predictions of protein sequences with methods that are not fully understood. Availability and implementation Our code and examples are available at: https://github.com/spetti/SMURF. Supplementary information Supplementary data are available at Bioinformatics online.
59 BASIC BIOLOGICAL SCIENCES↗
The rotation of photospheric magnetic fields: A random walk transport model
In an earlier study of solar differential rotation, we showed that the transport of magnetic flux across latitudes acts to establish quasi-stationary patterns, therby accounting for the observed rigid rotation of the large-scale photospheric field. In that paper, the effect of supergranular convection was represented by a continuum diffusion, limiting the applicability of the calculations to large spatial scales. Here we extend the model to scales comparable to that of the supergranulation itself by replacing the diffusive transport with a discrete random walk process. Rotation curves are derived by cross-correlating the simulated photospheric field maps for a variety of time lags and spatial resolutions. When the lag between maps is relatively short less than or approximately = 15 days), the midlatitude correlation functions show two distinct components: a broad feature associated with the large-scale unipolar patterns and a narrow feature originating from small magnetic structures encompossing from one to several supergranular cells. By fitting the broad component we obtain the rigid rotation profile of the patterns, whereas by fitting the narrow component, we recover the differential rate of the photospheric plasma itself. For time lags of 1 month or greater, only the broad feature associated with the long-lived patterns remains clearly identifiable in the simulations.
Wang, Y. -M.↗
Three velocity component, nonhomogeneous atmospheric boundary layer turbulence modeling
The vertical nonhomogeneous character of turbulence in the atmospheric boundary layer results in a non-stationary turbulence process relative to an aircraft during takeoff and landing despite the fact that the turbulence statistics can be horizontally homogeneous. The simulation of the three components of the turbulent winds which include the nonstationary aspect of atmospheric turbulence is the subject of this paper. A procedure is developed and demonstrated to generate the three components of a turbulence ramdom process field, u sub i(x,z) where x and z denote horizontal and vertical coordinates and u sub i, i = 1,2,3 are the three orthogonal components of the turbulent random field. This field satisfies any desired one point auto spectra as well as two point statistics (interlevel correlations). By use of Taylors frozen eddy hypothesis we can transform the turbulent random field into the time domain and obtain the random turbulence along an aircraft trajectory.
Perlmutter, M.↗