Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Power Law”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Fermions, quantum gravity, and holography in two dimensions

We study a model comprising N flavors of Kähler Dirac fermion propagating on a triangulated two-dimensional disk which is constrained to have a negative average bulk curvature. Dirichlet boundary conditions are chosen for the fermions. Quantum fluctuations of the geometry are included by summing over all possible triangulations consistent with these constraints. We show in the limit N → ∞ that the partition function is dominated by a regular triangulation of two-dimensional hyperbolic space. We use strong coupling expansions and Monte Carlo simulation to show that in this limit boundary correlators of the fermions have a power law dependence on boundary separation as one expects from holography. However, we argue that this behavior breaks down for any finite number of massive fields in the thermodynamic limit and quantum fluctuations of the bulk geometry drive the theory into a nonholographic phase. In contrast, for massless fermions, we find evidence that the boundary is conformal even for finite N . This is consistent with theoretical results in quantum Liouville theory. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2024

Revisiting shear stress tensor evolution: Nonresistive magnetohydrodynamics with momentum-dependent relaxation time

This study aims to develop second-order relativistic viscous magnetohydrodynamics (MHD) derived from kinetic theory within an extended relaxation time approximation (momentum/energy dependent) for the collision kernel. The investigation involves a detailed examination of shear stress tensor evolution equations and associated transport coefficients. The Boltzmann equation is solved using a Chapman-Enskog-like gradient expansion for a charge-conserved conformal system, incorporating a momentum-dependent relaxation time. The derived relativistic nonresistive, viscous second-order MHD equations for the shear stress tensor reveal significant modifications in the coupling with dissipative charge current and magnetic field due to the momentum dependence of the relaxation time. By utilizing a power law parametrization to quantify the momentum dependence of the relaxation time, the anisotropic magnetic field-dependent shear coefficients in the Navier-Stokes limit have been investigated. The resulting viscous coefficients are seen to be sensitive to the momentum dependence of the relaxation time.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Aspects of gravitational portals and freeze-in during reheating

We conduct a systematic investigation of freeze-in during reheating while taking care to include both direct and indirect production of dark matter (DM) via gravitational portals and inflaton decay. Direct production of DM can occur via gravitational scattering of the inflaton, while indirect production occurs through scattering in the Standard Model radiation bath. We consider two main contributions to the radiation bath during reheating. The first, which may dominate at the onset of the reheating process, is produced via gravitational scattering of the inflaton. The second (and more standard contribution) comes from inflaton decay. We consider a broad class of DM production rates parametrized as R χ ∝ T n + 6 / Λ n + 2 , and inflaton potentials with a power-law form V ( ϕ ) ∝ ϕ k about the minimum. We find the relic density produced by freeze-in for each contribution to the Standard Model bath for arbitrary k and n , and compare these with the DM density produced gravitationally by inflaton scattering. We find that freeze-in production from the gravitationally produced radiation bath can exceed that of the conventional decay bath and account for the observed relic density provided that m χ > T RH , with additional k - and n -dependent constraints. For each freeze-in interaction considered, we also find m χ - and T RH -dependent limits on the beyond the Standard Model scale, Λ , for which gravitational production will exceed ordinary freeze-in production. Published by the American Physical Society 2025

Henrich, Stephen E. (ORCID:0000000323669519)↗
DOE OSTI2025

Cosmological limits on the neutrino mass sum for beyond-Λ⁢ CDM models

The sum of neutrino masses can be measured cosmologically, as the sub-eV particles behave as “hot” dark matter whose main effect is to suppress the clustering of matter compared to a universe with the same amount of purely cold dark matter. Current astronomical data provide an upper limit on ∑𝑚 𝜈 between 0.07–0.12 eV at 95% confidence, depending on the choice of data. This bound assumes that the cosmological model is Λ Cold Dark Matter (Λ⁢ CDM), where dark energy is a cosmological constant, the spatial geometry is flat, and the primordial fluctuations follow a pure power law. Here, we update studies on how the mass limit degrades if we relax these assumptions. To existing data from the Planck satellite we add new gravitational lensing data from the Atacama Cosmology Telescope, the new Type Ia supernova sample from the Pantheon+survey, and baryonic acoustic oscillation (BAO) measurements from the Sloan Digital Sky Survey and the Dark Energy Spectroscopic Instrument. Using our fiducial data combination, described in the appendix, we find the neutrino mass limit is stable to most model extensions, with such extensions degrading the limit by less than 10%. We find a broadest bound of ∑𝑚 𝜈 < 0.19 eV at 95% confidence for a model with dynamical dark energy, although this scenario is not statistically preferred over the simpler Λ ⁢CDM model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Interacting dark sector within ETHOS: Cosmological constraints from SPT cluster abundance with DES and HST weak lensing data

We use galaxy cluster abundance measurements from the South Pole Telescope enhanced by multicomponent matched filter confirmation and complemented with mass information obtained using weak-lensing data from Dark Energy Survey Year 3 (DES Y3) and targeted Hubble Space Telescope observations for probing deviations from the cold dark matter paradigm. Concretely, we consider a class of dark sector models featuring interactions between dark matter (DM) and a dark radiation (DR) component within the framework of the effective theory of structure formation (ETHOS). We focus on scenarios that lead to power suppression over a wide range of scales, and thus can be tested with data sensitive to large scales, as realized, for example, for DM–DR interactions following from an unbroken non-Abelian 𝑆⁢𝑈⁡(𝑁) gauge theory (interaction rate with power-law index 𝑛 = 0 within the ETHOS parametrization). Cluster abundance measurements are mostly sensitive to the amount of DR interacting with DM, parametrized by the ratio of DR temperature to the cosmic microwave background (CMB) temperature, 𝜉 DR = 𝑇 DR /𝑇 CMB . We find an upper limit 𝜉 DR < 17% at 95% credibility. When the cluster data are combined with Planck 2018 CMB data along with baryon acoustic oscillation (BAO) measurements we find 𝜉 DR < 10%, corresponding to a limit on the abundance of interacting DR that is around 3 times tighter than that from CMB + BAO data alone. We also discuss the complementarity of weak lensing informed cluster abundance studies with probes sensitive to smaller scales, explore the impact on our analysis of massive neutrinos, and comment on a slight preference for the presence of a nonzero interacting DR abundance, which enables a physical solution to the 𝑆 8 tension.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Uniqueness criteria for the Virasoro-Shapiro amplitude

The scattering amplitudes of string theory exhibit many extraordinary properties. But are they the unique mathematical objects to do so? Recently, it has been shown how the spectrum and amplitudes of open string theory follow directly from the assumptions of faster than power-law falloff at high energies and a property dubbed level truncation. At present there is no analogous principle for closed string scattering, which is famously rigid and naively impervious to modification. In this paper we analytically bootstrap the spectrum and four-point amplitudes of the closed string—together with a parametrized space of deformations—from conditions on high-energy falloff and level truncation. While these deformations exhibit the same Regge scaling as pure gravity, in the tensionless limit they reproduce remarkable extremal amplitudes that have appeared in bottom-up studies of positivity.

Field & string theory models & techniques↗
DOE OSTI2025

Emergent hydrodynamic mode on SU(2) plaquette chains and quantum simulation

We search for emergent hydrodynamic modes in real-time Hamiltonian dynamics of 2+1-dimensional SU(2) lattice gauge theory on a quasi-one-dimensional plaquette chain, by numerically computing symmetric correlation functions of energy densities on lattice sizes of about 20 with the local Hilbert space truncated at 𝑗 max = $\frac{1}{2}$. Because of the Umklapp processes, we only find a mode for energy diffusion. The symmetric correlator exhibits transport peak near zero frequency with a width approximately proportional to momentum squared at small momentum, when the system is fully quantum ergodic, as indicated by the eigenenergy level statistics. This transport peak leads to a power-law 𝑡 −$\frac{1}{2}$ decay of the symmetric correlator at late time, also known as the long-time tail, as well as diffusionlike spreading in position space. We also introduce a quantum algorithm for computing the symmetric correlator on a quantum computer and find it gives results consistent with exact diagonalization when tested on the IBM emulator. Finally we discuss the future prospect of searching for the sound modes.

Hamiltonian systems↗
DOE OSTI2020

Hotspot parameter scaling with velocity and yield for high-adiabat layered implosions at the National Ignition Facility

Here, in this paper, we present a study on hotspot parameters in indirect-drive, inertially confined fusion implosions as they proceed through the self-heating regime. The implosions with increasing nuclear yield reach the burning-plasma regime, hotspot ignition, and finally propagating burn and ignition. These implosions span a wide range of alpha heating from a yield amplification of 1.7–2.5. We show that the hotspot parameters are explicitly dependent on both yield and velocity and that by fitting to both of these quantities the hotspot parameters can be fit with a single power law in velocity. The yield scaling also enables the hotspot parameters extrapolation to higher yields. This is important as various degradation mechanisms can occur on a given implosion at fixed implosion velocity which can have a large impact on both yield and the hotspot parameters. The yield scaling also enables the experimental dependence of the hotspot parameters on yield amplification to be determined. The implosions reported have resulted in the highest yield (1.73×10 16 ±2.6%), yield amplification, pressure, and implosion velocity yet reported at the National Ignition Facility.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Distinct critical behaviors from the same state in quantum spin and population dynamics perspectives

There is a deep connection between the ground states of transverse-field spin systems and the late-time distributions of evolving viral populations—within simple models, both are obtained from the principal eigenvector of the same matrix. However, that vector is the wave-function amplitude in the quantum spin model, whereas it is the probability itself in the population model. We show that this seemingly minor difference has significant consequences: Phase transitions that are discontinuous in the spin system become continuous when viewed through the population perspective, and transitions that are continuous become governed by new critical exponents. We introduce a more general class of models that encompasses both cases and that can be solved exactly in a mean-field limit. Numerical results are also presented for a number of one-dimensional chains with power-law interactions. We see that well-worn spin models of quantum statistical mechanics can contain unexpected new physics and insights when treated as population-dynamical models and beyond, motivating further studies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Cell dynamics simulations of coupled charge and magnetic phase transformation in correlated oxides

In this work, we present a comprehensive numerical study on the kinetics of phase transition that is characterized by two nonconserved scalar order parameters coupled by a special linear-quadratic interaction. This particular Ginzburg-Landau theory has been proposed to describe the coupled charge and magnetic transition in nickelates and the collinear stripe phase in cuprates. The inhomogeneous state of such systems at low temperatures consists of magnetic domains separated by quasimetallic domain walls where the charge order is reduced. By performing large-scale cell dynamics simulations, we find a two-stage phase-ordering process in which a short period of independent evolution of the two order parameters is followed by a correlated coarsening process. The long-time growth and coarsening of magnetic domains is shown to follow the Allen-Cahn power law. We further show that the nucleation-and-growth dynamics during phase transformation to the ordered states is well described by the Kolmogorov-Johnson-Mehl-Avrami theory in two dimensions. On the other hand, the presence of quasimetallic magnetic domain walls in the ordered states gives rise to a very different kinetics for transformation to the high-temperature paramagnetic phase. In this scenario, the phase transformation is initiated by the decay of magnetic domain walls into two insulator-metal boundaries, which subsequently move away from each other. Implications of our findings to recent nano-imaging experiments on nickelates are also discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Phase-space entropy cascade and irreversibility of stochastic heating in nearly collisionless plasma turbulence

We consider a nearly collisionless plasma consisting of a species of “test particles” in one spatial and one velocity dimension, stirred by an externally imposed stochastic electric field—a kinetic analog of the Kraichnan model of passive advection. The mean effect on the particle distribution function is turbulent diffusion in velocity space—known as stochastic heating. Accompanying this heating is the generation of fine-scale structure in the distribution function, which we characterize with the collisionless (Casimir) invariant C 2 ∝ ∫ ∫ d x d v 〈 f 2 〉 —a quantity that here plays the role of (negative) entropy of the distribution function. We find that C 2 is transferred from large scales to small scales in both position and velocity space via a phase-space cascade enabled by both particle streaming and nonlinear interactions between particles and the stochastic electric field. We compute the steady-state fluxes and spectrum of C 2 in Fourier space, with k and s denoting spatial and velocity wave numbers, respectively. In our model, the nonlinearity in the evolution equation for the spectrum turns into a fractional Laplacian operator in k space, leading to anomalous diffusion. Whereas even the linear phase mixing alone would lead to a constant flux of C 2 to high s (towards the collisional dissipation range) at every k , the nonlinearity accelerates this cascade by intertwining velocity and position space so that the flux of C 2 is to both high k and high s simultaneously. Integrating over velocity (spatial) wave numbers, the k -space ( s -space) flux of C 2 is constant down to a dissipation length (velocity) scale that tends to zero as the collision frequency does, even though the rate of collisional dissipation remains finite. The resulting spectrum in the inertial range is a self-similar function in the ( k , s ) plane, with power-law asymptotics at large k and s . Our model is fully analytically solvable, but the asymptotic scalings of the spectrum can also be found via a simple phenomenological theory whose key assumption is that the cascade is governed by a “critical balance” in phase space between the linear and nonlinear timescales. We argue that stochastic heating is made irreversible by this entropy cascade and that, while collisional dissipation accessed via phase mixing occurs only at small spatial scales rather than at every scale as it would in a linear system, the cascade makes phase mixing even more effective overall in the nonlinear regime than in the linear one. Published by the American Physical Society 2024

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Competition between roughness and strength for scale-dependent surfaces

Rocks famously have scale-dependent strength, yet the actual dependence is notoriously hard to measure or incorporate into any theoretical framework. Natural rough surfaces present an opportunity to solve the problem. Surfaces sliding in shear evolve as protrusions collide. These asperities can deform or break, thus creating a new surface shape. In particular, natural surfaces have roughness at all scales as well as scale-dependent strength. Based on a scaling analysis, we have previously suggested that the scale-dependent aspect ratio of steady-state surfaces should be proportional to the scale-dependent shear strain at yield. If true, scale-dependent strength could easily be inferred from natural surfaces. Thus, moving beyond the scaling argument to a rigorous treatment of scale-dependent strength for multiscale rough surfaces in shear is important. However, analytic frameworks for analyzing multiscale problems are challenging, as conventional continuum mechanics typically involves a single value for a material property across scales. Here, in this work, we build on the formalism of Persson (2001) that presents a method to compute contact area for rough surfaces with a prescribed topographic spectrum using a stochastic differential equation. The Persson formalism allows for plastic yield under normal loading of otherwise elastic materials and leaves open the possibility of scale-dependent yield stress. In this study, we pursue this route to develop a theory and numerical results for the yielding of a rough, elastoplastic surface with scale-dependent yield stress. Here, we examine surfaces for which the power spectrum of the topography 𝐶 and yield stress 𝑌 follow power laws as a function of scale 𝜆, such that 𝐶∼𝜆 −𝑚 and 𝑌∼𝜆 −𝑛 , respectively. In this formal treatment of the problem, we focus on surfaces in contact and the resulting yield and do not impose shear. Numerical solutions show that the deviation from the elastic scaling solution is bounded as expected by the prior 1D heuristic scaling argument that anticipates the Hurst exponent as 1−𝑛. We also show that the plasticity is expected to erode the contacts if 𝑚 is lower than 𝑛−3, which corresponds to a Hurst exponent lower than 1−𝑛/2. This result is rigorously sound for 2D, i.e., realistic surfaces, and quantitatively different than the prior scaling argument. The theory now permits a correspondingly quantitative approach to interpreting natural surfaces.

elasticity↗
DOE OSTI2021

Adiabatic behavior of an elliptical vortex in a time-dependent external strain flow

The adiabatic behavior of two-dimensional (2D) fluid vortices subject to slowly varying, time-dependent external strain flows is studied theoretically, and experimentally using magnetized non-neutral electron plasmas. Here the E × B drift dynamics of the electrons perpendicular to the magnetic field are analogous to the motion of fluid vorticity under the 2D Euler equations describing ideal fluids. A low-dimensional elliptical vortex patch model is used along with a WKB approximation to derive a formula for the breaking of an adiabatic invariant due to the changing external flow. The invariant is interpreted as the amplitude of a perturbative oscillation about a stable fixed point corresponding to a steady elliptical vortex. Smooth, hyperbolic tangent and piecewise linear ramp functions are considered for the external strain time dependence. Standard exponential breaking is observed in the former case, whereas the latter exhibits a power-law breaking curve with periodic modulation. It is found that a driving term in the equations of motion contributes the majority of the breaking whereas the frequency variation plays a weaker, but significant role. The experimental data agree closely with the theoretical model. The most significant deviation is due to inviscid damping behavior associated with the smooth edges of the experimental vortices, which tends to reduce the amplitude of the oscillation. Finally, the results are compared and contrasted with other related experimental, numerical, and theoretical work.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Learning unknown physics of non-Newtonian fluids

Here, we use physics-informed neural networks (PINNs) to learn viscosity models of two non-Newtonian systems (polymer melts and suspensions of particles) using only velocity measurements. For synthetic velocity data generated with the power-law viscosity model, the PINN-inferred viscosity model agrees with the analytical model for shear rates with large absolute values but deviates for shear rates near zero where the analytical model has an unphysical singularity. Once the viscosity model is learned the PINN method can solve the momentum conservation equation using only the boundary conditions.

42 ENGINEERING↗
DOE OSTI2020

Nematic Correlation Length in Iron-Based Superconductors Probed by Inelastic X-Ray Scattering

Nematicity is ubiquitous in electronic phases of high-T c superconductors, particularly in the Fe-based systems. We used inelastic x-ray scattering to extract the temperature-dependent nematic correlation length ξ from the anomalous softening of acoustic phonon modes in FeSe, underdoped Ba(Fe 0.97 Co 0.03 ) 2 As 2 , and optimally doped Ba(Fe 0.94 Co 0.06 ) 2 As 2 . In all cases, we find that. is well described by a power law (T - T 0 ) -1/2 extending over a wide temperature range. Combined with the previously reported Curie-Weiss behavior of the nematic susceptibility, these results point to the mean-field character of the nematic transition, which we attribute to a sizable nematoelastic coupling that is likely detrimental to superconductivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Operator Lévy Flight: Light Cones in Chaotic Long-Range Interacting Systems

We argue that chaotic power-law interacting systems have emergent limits on information propagation, analogous to relativistic light cones, which depend on the spatial dimension d and the exponent α governing the decay of interactions. Using the dephasing nature of quantum chaos, we map the problem to a stochastic model with a known phase diagram. A linear light cone results for α ≥ $\textit{d}$ + 1/2. We also provide a Lévy flight (long-range random walk) interpretation of the results and show consistent numerical data for 1D long-range spin models with 200 sites.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Topological Singularity Induced Chiral Kohn Anomaly in a Weyl Semimetal

The electron-phonon interaction (EPI) is instrumental in a wide variety of phenomena in solid-state physics, such as electrical resistivity in metals, carrier mobility, optical transition, and polaron effects in semiconductors, lifetime of hot carriers, transition temperature in BCS superconductors, and even spin relaxation in diamond nitrogen-vacancy centers for quantum information processing. However, due to the weak EPI strength, most phenomena have focused on electronic properties rather than on phonon properties. One prominent exception is the Kohn anomaly, where phonon softening can emerge when the phonon wave vector nests the Fermi surface of metals. In this paper, we report a new class of Kohn anomaly in a topological Weyl semimetal (WSM), predicted by field-theoretical calculations, and experimentally observed through inelastic x-ray and neutron scattering on WSM tantalum phosphide. Compared to the conventional Kohn anomaly, the Fermi surface in a WSM exhibits multiple topological singularities of Weyl nodes, leading to a distinct nesting condition with chiral selection, a power-law divergence, and non-negligible dynamical effects. Our work brings the concept of the Kohn anomaly into WSMs and sheds light on elucidating the EPI mechanism in emergent topological materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Characteristics of the Diffuse Astrophysical Electron and Tau Neutrino Flux with Six Years of IceCube High Energy Cascade Data

In this work, we report on the first measurement of the astrophysical neutrino flux using particle showers (cascades) in IceCube data from 2010-2015. Assuming standard oscillations, the astrophysical neutrinos in this dedicated cascade sample are dominated (~90%) by electron and tau flavors. The flux, observed in the sensitive energy range from 16 TeV to 2.6 PeV, is consistent with a single power-law model as expected from Fermi-type acceleration of high energy particles at astrophysical sources. We find the flux spectral index to be γ=2.53±0.07 and a flux normalization for each neutrino flavor of $\phi$ astro =1.66$_{-0.27}^{+0.25}$ at E 0 =100 TeV, in agreement with IceCube's complementary muon neutrino results and with all-neutrino flavor fit results. In the measured energy range we reject spectral indices γ≤2.28 at ≥3σ significance level. Because of high neutrino energy resolution and low atmospheric neutrino backgrounds, this analysis provides the most detailed characterization of the neutrino flux at energies below ~100 TeV compared to previous IceCube results. Results from fits assuming more complex neutrino flux models suggest a flux softening at high energies and a flux hardening at low energies (p value ≥0.06). The sizable and smooth flux measured below ~100 TeV remains a puzzle. In order to not violate the isotropic diffuse gamma-ray background as measured by the Fermi Large Area Telescope, it suggests the existence of astrophysical neutrino sources characterized by dense environments which are opaque to gamma rays.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗