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Results for “Scale Invariance”

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 1,063 records · Page 59
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A magnon band analysis of GdRu 2 Si 2 in the field-polarized state

Understanding the formation of skyrmions in centrosymmetric materials is a problem of fundamental and technological interest. GdRu 2 Si 2 is a candidate material that hosts a variety of multi-Q magnetic phases, including in zero-field. Here, inelastic neutron scattering is used to measure the spin excitations in the field-polarized phase of GdRu 2 Si 2 . Linear spin wave theory and a method of interaction invariant path analysis are used to derive a Hamiltonian accounting for the spectra. The Hamiltonian, dominated by bilinear (Ruderman-Kittel-Kasuya-Yosida) Heisenberg exchange, compares favorably to ab initio calculations. Dipolar interactions are a secondary energy scale to consider, with J D.D ~ 0.05 J RKKY . However, it is shown that in the field-polarized phase the dipolar interactions ‘self screen’ so that their effect is largely suppressed. No specific evidence for higher-order exchange is found. These aspects are discussed in the context of the lower field multi-Q states and the anisotropy of the system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2011

ON THE ORIGIN OF STELLAR MASSES

It has been a longstanding problem to determine, as far as possible, the characteristic masses of stars in terms of fundamental constants; the almost complete invariance of this mass as a function of the star-forming environment suggests that this should be possible. Here I provide such a calculation. The typical stellar mass is set by the characteristic fragment mass in a star-forming cloud, which depends on the cloud's density and temperature structure. Except in the very early universe, the latter is determined mainly by the radiation released as matter falls onto seed protostars. The energy yield from this process is ultimately set by the properties of deuterium burning in protostellar cores, which determines the stars' radii. I show that it is possible to combine these considerations to compute a characteristic stellar mass almost entirely in terms of fundamental constants, with an extremely weak residual dependence on the interstellar pressure and metallicity. This result not only explains the invariance of stellar masses, it resolves a second mystery: why fragmentation of a cold, low-density interstellar cloud, a process with no obvious dependence on the properties of nuclear reactions, happens to select a stellar mass scale such that stellar cores can ignite hydrogen. Finally, the weak residual dependence on the interstellar pressure and metallicity may explain recent observational hints of a smaller characteristic mass in the high-pressure, high-metallicity cores of giant elliptical galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

SOLAR CYCLE VARIATION OF THE INTER-NETWORK MAGNETIC FIELD

The solar inter-network magnetic field is the weakest component of solar magnetism, but it contributes most of the solar surface magnetic flux. The study of its origin has been constrained by the inadequate tempospatial resolution and sensitivity of polarization observations. With dramatic advances in spatial resolution and detecting sensitivity, the solar spectropolarimetry provided by the Solar Optical Telescope on board Hinode in an interval from the solar minimum to maximum of cycle 24 opens an unprecedented opportunity to study the cyclic behavior of the solar inter-network magnetic field. More than 1000 Hinode magnetograms observed from 2007 January to 2014 August are selected in the study. It has been found that there is a very slight correlation between sunspot number and magnetic field at the inter-network flux spectrum. From solar minimum to maximum of cycle 24, the flux density of the solar inter-network field is invariant, at 10 ± 1 G. The observations suggest that the inter-network magnetic field does not arise from flux diffusion or flux recycling of solar active regions, thereby indicating the existence of a local small-scale dynamo. Combining the full-disk magnetograms observed by the Solar and Heliospheric Observatory/Michelson Doppler Imager and the Solar Dynamics Observatory/Helioseismic and Magnetic Imager in the same period, we find that the area ratio of the inter-network region to the full disk of the Sun apparently decreases from solar minimum to maximum but always exceeds 60%, even in the phase of solar maximum.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

A new quasidilaton theory of massive gravity

We present a new quasidilaton theory of Poincare invariant massive gravity, based on the recently proposed framework of matter coupling that makes it possible for the kinetic energy of the quasidilaton scalar to couple to both physical and fiducial metrics simultaneously. We find a scaling-type exact solution that expresses a self-accelerating de Sitter universe, and then analyze linear perturbations around it. It is shown that in a range of parameters all physical degrees of freedom have non-vanishing quadratic kinetic terms and are stable in the subhorizon limit, while the effective Newton's constant for the background is kept positive.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Bounce universe from string-inspired Gauss-Bonnet gravity

We explore cosmology with a bounce in Gauss-Bonnet gravity where the Gauss-Bonnet invariant couples to a dynamical scalar field. In particular, the potential and and Gauss-Bonnet coupling function of the scalar field are reconstructed so that the cosmological bounce can be realized in the case that the scale factor has hyperbolic and exponential forms. Furthermore, we examine the relation between the bounce in the string (Jordan) and Einstein frames by using the conformal transformation between these conformal frames. It is shown that in general, the property of the bounce point in the string frame changes after the frame is moved to the Einstein frame. Moreover, it is found that at the point in the Einstein frame corresponding to the point of the cosmological bounce in the string frame, the second derivative of the scale factor has an extreme value. In addition, it is demonstrated that at the time of the cosmological bounce in the Einstein frame, there is the Gauss-Bonnet coupling function of the scalar field, although it does not exist in the string frame.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Reinforcement Learning of Structured Stabilizing Control for Linear Systems With Unknown State Matrix

This paper delves into designing feedback control gains for a continuous-time linear quadratic regulator (LQR) problem that is constrained to certain predefined structure with unknown state matrix. We bring forth the ideas from reinforcement learning (RL) in conjunction with sufficient stability and performance guarantees in order to design these structured gains using the trajectory measurements of states and controls. Here we first formulate a model-based framework using dynamic programming (DP) to embed the structural constraint to the LQR gain computation in the continuous-time setting, and then subsequently, formulate a policy iteration RL algorithm that can alleviate the requirement of known state matrix in conjunction with maintaining the feedback gain structure. The design enables a distributed learning control design which is necessary for many large-scale cyber-physical systems. Theoretical guarantees are provided for stability and convergence of the structured reinforcement learning (SRL) algorithm. We validate our theoretical results with numerical simulations on a multi-agent networked linear time-invariant (LTI) dynamic system.

42 ENGINEERING↗
NASA NTRS1996

Symmetries in Turbulent Boundary Layer Flows

The objective is the development of a new theory which enables the algorithmic computation of all self-similar mean velocity profiles. The theory is based on Liegroup analysis and unifies a large set of self-similar solutions for the mean velocity of stationary parallel turbulent shear flows. The results include the logarithmic law of the wall, an algebraic law, the viscous sublayer, the linear region in the middle of a Couette flow and in the middle of a rotating channel flow, and a new exponential mean velocity profile not previously reported. Experimental results taken in the outer parts of a high Reynolds number flat-plate boundary layer, strongly support the exponential profile. From experimental as well as from DNS data of a turbulent channel flow the algebraic scaling law could be confirmed in both the center region and in the near wall region. In the case of the logarithmic law of the wall, the scaling with the wall distance arises as a result of the analysis and has not been assumed in the derivation. The crucial part of the derivation of all the different mean velocity profiles is to consider the invariance of the equation for the velocity fluctuations at the same time as the invariance of the equation for the velocity product equations. The latter is the dyad product of the velocity fluctuations with the equation for the velocity fluctuations. It has been proven that all the invariant solutions are also consistent with similarity of all velocity moment equations up to any arbitrary order.

Oberlack, M.↗
NASA NTRS2003

Microwave Cavity Clocks On Space Station

We describe the status of a microwave cavity clock experiment to perform improved tests of Local Position Invariance and Lorentz Invariance on the International Space Station in conjunction with atomic clocks. Significant improvements over present bounds are expected in both cases. The oscillators can also be used to enhance the performance of atomic clocks at short time scales for other experiments.

Lipa, J. a.↗
NASA NTRS2010

A Singular Perturbation Approach for Time-Domain Assessment of Phase Margin

This paper considers the problem of time-domain assessment of the Phase Margin (PM) of a Single Input Single Output (SISO) Linear Time-Invariant (LTI) system using a singular perturbation approach, where a SISO LTI fast loop system, whose phase lag increases monotonically with frequency, is introduced into the loop as a singular perturbation with a singular perturbation (time-scale separation) parameter Epsilon. First, a bijective relationship between the Singular Perturbation Margin (SPM) max and the PM of the nominal (slow) system is established with an approximation error on the order of Epsilon(exp 2). In proving this result, relationships between the singular perturbation parameter Epsilon, PM of the perturbed system, PM and SPM of the nominal system, and the (monotonically increasing) phase of the fast system are also revealed. These results make it possible to assess the PM of the nominal system in the time-domain for SISO LTI systems using the SPM with a standardized testing system called "PM-gauge," as demonstrated by examples. PM is a widely used stability margin for LTI control system design and certification. Unfortunately, it is not applicable to Linear Time-Varying (LTV) and Nonlinear Time-Varying (NLTV) systems. The approach developed here can be used to establish a theoretical as well as practical metric of stability margin for LTV and NLTV systems using a standardized SPM that is backward compatible with PM.

Zhu, J. Jim↗
DOE OSTI2011

The path integral for the statistical sum of the microcanonical ensemble in cosmology

The path integral is calculated for the statistical sum of the microcanonical ensemble in a generic time-parametrization invariant gravitational model with the Friedman-Robertson-Walker (FRW) metric. This represents the first example of a systematic calculation of the Faddeev-Popov gauge-fixed path integral in the minisuperspace sector of quantum cosmology. The gauge fixing procedure, together with gauging out local diffeomorphisms, also handles the residual symmetries associated with the conformal Killing vector of the FRW metric and incorporates the Batalin-Vilkovisky quantization technique for gauge theories with linearly dependent generators. For a subset of saddle-point instantons, characterized by a single oscillation of the FRW scale factor, this technique is designed to obtain the one-loop statistical sum in the recently suggested model of cosmological initial conditions generated by a conformal field theory with a large number of quantum species.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Avoidance of singularities in asymptotically safe Quantum Einstein Gravity

New general spherically symmetric solutions have been derived with a cosmological “constant” Λ as a source. This Λ term is not constant but it satisfies the properties of the asymptotically safe gravity at the ultraviolet fixed point. The importance of these solutions comes from the fact that they may describe the near to the centre region of black hole spacetimes as this is modified by the Renormalization Group scaling behaviour of the fields. The consistent set of field equations which respect the Bianchi identities is derived and solved. One of the solutions (with conventional sign of temporal-radial metric components) is timelike geodesically complete, and although there is still a curvature divergent origin, this is never approachable by an infalling massive particle which is reflected at a finite distance due to the repulsive origin. Another family of solutions (of both signatures) range from a finite radius outwards, they cannot be extended to the centre of spherical symmetry, and the curvature invariants are finite at the minimum radius.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Plasma β scaling of anisotropic magnetic field fluctuations in the solar wind flux tube

Based on various observations, it has been suggested that at 1 AU, solar wind consists of 'spaghetti'-like magnetic field structures that have the magnetic topology of flux tubes. It is also observed that the plasma fluctuation spectra at 1 AU show a plasma β dependence. Reconciling these two sets of observations and using the Invariance Principle, Bhattacharjee et al. suggested that the plasma inside every flux tube may become unstable with respect to pressure-driven instabilities and gives rise to fluctuation spectra that depend on the local plasma β. The present work is the first direct numerical simulation of such a flux tube. We solve the full magnetohydrodynamic equations using the DEBS code and show that if the plasma inside the flux tube is driven unstable by spatial inhomogeneities in the background plasma pressure, the observed nature of the fluctuating power spectra agrees reasonably well with observations, as well as the analytical prediction of Bhattacharjee et al.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Spontaneous magnetization of a vacuum in the hot Universe and intergalactic magnetic fields

We review the spontaneous magnetization of the vacuum of non-Abelian gauge fields at high temperature. The standard model of particles is investigated as a particular example. By using both analytic methods of quantum field theory and gauge field theory on a lattice, we determine the Abelian (chromo)magnetic fields in the restored phase of the model at high temperatures T ≥ T{sub ew}. The fields are stable and temperature dependent, B = B(T). We investigate the mechanisms of the field stabilization in detail. The screening parameters for electric and magnetic fields—the Debye, m{sub D}(B, T), and magnetic, m{sub magn}(B, T), masses—are calculated. It is shown that, in the field presence, the former one is smaller than at zero field. The magnetic mass of the (chromo)magnetic fields is determined to be zero, as for usual U(1) magnetic field. We also show that the vacuum magnetization stops at temperatures below the electroweak phase transition temperature, T ≤ T{sub ew}, when a scalar condensate creates. These properties make reasonable a possibility that the intergalactic magnetic fields observed recently were spontaneously generated in the hot Universe at the reheating epoch due to vacuum polarization of non-Abelian gauge fields. We present a procedure for estimating the field strengths B(T) at different temperatures. In particular, the value of B(T{sub ew}) ∼ 10{sup 14} G, at T{sub ew} is estimated with taking into consideration the observed intergalactic magnetic field B{sub 0} ∼ 10{sup −15} G. The magnetic field scale is also estimated. Some model dependent peculiarities of the phenomena studied are briefly discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2013

Two Emission Mechanisms in the Fermi Bubbles: A Possible Signal of Annihilating Dark Matter

We study the variation of the spectrum of the Fermi Bubbles with Galactic latitude. Far from the Galactic plane (|b| > 30 degrees), the observed gamma-ray emission is nearly invariant with latitude, and is consistent with arising from inverse Compton scattering of the interstellar radiation field by cosmic-ray electrons with an approximately power-law spectrum. The same electrons in the presence of microgauss-scale magnetic fields can also generate the the observed microwave "haze". At lower latitudes (b < 20 degrees), in contrast, the spectrum of the emission correlated with the Bubbles possesses a pronounced spectral feature peaking at 1-4 GeV (in E^2 dN/dE) which cannot be generated by any realistic spectrum of electrons. Instead, we conclude that a second (non-inverse-Compton) emission mechanism must be responsible for the bulk of the low-energy, low-latitude emission. This second component is spectrally similar to the excess GeV emission previously reported from the Galactic Center (GC), and also appears spatially consistent with a luminosity per volume falling approximately as r^-2.4, where r is the distance from the GC. We argue that the spectral feature visible in the low-latitude Bubbles is the extended counterpart of the GC excess, now detected out to at least 2-3 kpc from the GC. The spectrum and angular distribution of the signal is consistent with that predicted from ~10 GeV dark matter particles annihilating to leptons, or from ~50 GeV dark matter particles annihilating to quarks, following a distribution similar to the canonical Navarro-Frenk-White (NFW) profile. We also consider millisecond pulsars as a possible astrophysical explanation for the signal, as observed millisecond pulsars possess a spectral cutoff at approximately the required energy. Any such scenario would require a large population of unresolved millisecond pulsars extending at least 2-3 kpc from the GC.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Coping with silent and fail-stop errors at scale by combining replication and checkpointing

This paper provides a model and an analytical study of replication as a technique to cope with silent errors, as well as a mixture of both silent and fail-stop errors on large-scale platforms. Compared with fail-stop errors that are immediately detected when they occur, silent errors require a detection mechanism. To detect silent errors, many application-specific techniques are available, either based on algorithms (e.g., ABFT), invariant preservation or data analytics, but replication remains the most transparent and least intrusive technique. We explore the right level (duplication, triplication or more) of replication for two frameworks: (i) when the platform is subject to only silent errors, and (ii) when the platform is subject to both silent and fail-stop errors. A higher level of replication is more expensive in terms of resource usage but enables to tolerate more errors and to even correct some errors, hence there is a trade-off to be found. Replication is combined with checkpointing and comes with two flavors: process replication and group replication. Process replication applies to message-passing applications with communicating processes. Each process is replicated, and the platform is composed of process pairs, or triplets. Group replication applies to black-box applications, whose parallel execution is replicated several times. The platform is partitioned into two halves (or three thirds). In both scenarios, results are compared before each checkpoint, which is taken only when both results (duplication) or two out of three results (triplication) coincide. Otherwise, one or more silent errors have been detected, and the application rolls back to the last checkpoint, as well as when fail-stop errors have struck. We provide a detailed analytical study for all of these scenarios, with formulas to decide, for each scenario, the optimal parameters as a function of the error rate, checkpoint cost, and platform size. We also report a set of extensive simulation results that nicely corroborates the analytical model.

Checkpointing↗
DOE OSTI2015

STATISTICS OF THE VELOCITY GRADIENT TENSOR IN SPACE PLASMA TURBULENT FLOWS

In the last decade, significant advances have been presented for the theoretical characterization and experimental techniques used to measure and model all of the components of the velocity gradient tensor in the framework of fluid turbulence. Here, we attempt the evaluation of the small-scale velocity gradient tensor for a case study of space plasma turbulence, observed in the Earth's magnetosheath region by the CLUSTER mission. In detail, we investigate the joint statistics P(R, Q) of the velocity gradient geometric invariants R and Q, and find that this P(R, Q) is similar to that of the low end of the inertial range for fluid turbulence, with a pronounced increase in the statistics along the so-called Vieillefosse tail. In the context of hydrodynamics, this result is referred to as the dissipation/dissipation-production due to vortex stretching.

79 ASTRONOMY AND ASTROPHYSICS↗