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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Kink solutions with power law tails

We present a comprehensive review about the various facets of kink solutions with a power law tail, which have received considerable attention during the last few years. This area of research is in its early stages; although several aspects have become clear by now, there are a number of issues which have only been partially understood or not understood at all. We first discuss the aspects which are reasonably well known and then address in some detail the issues which are only partially or not understood at all. We present a wide class of higher (than sixth) order field theory models admitting implicit kink as well as mirror kink solutions where the two tails facing each other have a power law or a power-tower type fall off, whereas the other two ends not facing each other could have either an exponential or a power law tail. The models admitting implicit kink solutions where the two ends facing each other have an exponential tail while the other two ends have a power law tail are also discussed. Moreover, we present several field theory models which admit explicit kink solutions with a power law fall off; we note that in all these polynomial models while the potential V ( ϕ ) is continuous, its derivative is discontinuous. We also discuss one of the most important and only partially understood issues of the kink–kink and the kink–antikink forces in case the tails facing each other have a power law fall off. Finally, we briefly discuss the kink–antikink collisions at finite velocity and present some open questions.

power-tower tail↗
DOE OSTI2022

A Stochastic Transport Model for the Cumulative Number of Fissions and Deposited Fission Energy

The stochastic theory of neutron transport is extended to describe the cumulative distribution of fission numbers and deposited fission energy in a multiplying assembly. Solutions for the probability distributions are obtained using analytical approximations and Monte Carlo simulation in lumped geometry and in symmetric homogeneous and heterogeneous spheres. The results show the development of a power-law tail in the steady state fission number and deposited energy distributions when the medium is critical, independent of the fission neutron multiplicity distribution and domain heterogeneity. In contrast, the asymptotic decay is faster than exponential in subcritical media due to rapid chain extinction and in supercritical media due to the increasing probability of chain divergence. Here, a formal asymptotic analysis of the problem in lumped geometry with an arbitrary fission neutron multiplicity confirms the existence of power-law tails at critical.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Explicit kink solutions in several one-parameter families of higher-order field theory models

Here, we present several one-parameter families of higher-order field theory models some of which admit explicit kink solutions with an exponential tail while others admit explicit kink solutions with a power-law tail. Various properties of these families of kink solutions are examined in detail. Further, by applying the recent Manton formalism, we provide estimates for the kink–kink (KK) and antikink–kink (AK-K) acceleration and hence the ratio of the corresponding AK-K and KK forces.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Turbulence and Particle Acceleration in a Relativistic Plasma

Abstract In a collisionless plasma, the energy distribution function of plasma particles can be strongly affected by turbulence. In particular, it can develop a nonthermal power-law tail at high energies. We argue that turbulence with initially relativistically strong magnetic perturbations (magnetization parameter σ ≫ 1) quickly evolves into a state with ultrarelativistic plasma temperature but mildly relativistic turbulent fluctuations. We present a phenomenological and numerical study suggesting that in this case, the exponent α in the power-law particle-energy distribution function, f ( γ ) d γ ∝ γ − α d γ , depends on magnetic compressibility of turbulence. Our analytic prediction for the scaling exponent α is in good agreement with the numerical results.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Turbulent Acceleration of Interstellar Pickup Ions at the Heliospheric Termination Shock Forms the Global ENA Spectrum

The heliospheric energetic neutral atom spectrum observed by the Interstellar Boundary Explorer (IBEX) reveals that the heliosheath proton distribution is consistent with a power law. The origin of the spectrum is likely from interstellar pickup ions (PUIs) accelerated at the heliospheric termination shock (HTS). We present an explanation of the proton spectrum origin using a test particle simulation of PUIs accelerated at the HTS. PUIs experience preferential heating by the motional electric field in the shock foot, but do not develop a power-law tail without the presence of turbulence at wavenumbers (k) close to the PUI gyroradius scale (R g ). Voyager 2 observations of the magnetic field downstream of the HTS indicate a moderate amount of turbulence at kR g ≅ 1, (δB /B 0 ) 2 @ 0.01, which we find to be sufficient for producing a downstream suprathermal PUI tail but not at intensities observed by IBEX. Within the shock ramp, however, Voyager observed the turbulence power at much smaller scales to be nearly 100 times stronger, suggesting the possibility of strong turbulence at the PUI gyroradius scale. We show that a proton distribution can develop a power law downstream of the HTS consistent with IBEX observations if (δB /B 0 ) 2 ≳ 0.1 at kR g ≅ 1 in the shock foot. Shock drift acceleration of PUIs by the motional electric field is aided by interactions with turbulence upstream of the shock overshoot. Steepening of the IBEX proton spectrum in directions farther from the heliospheric nose suggests the HTS compression ratio and/or turbulence power weakens near the heliotail.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Distributions of Particles Accelerated by Strong Alfvénic Turbulence

This work presents a model for generating nonthermal power-law tails of particles’ energy probability density functions in turbulent collisionless plasmas, applicable to both nonrelativistic and relativistic scenarios. We propose that strong Alfvénic turbulence energizes plasma particles through curvature acceleration, particularly for particles with Larmor radii comparable to the scales of turbulence. When the energy density of the energized particles increases, the efficiency of the energy exchange process diminishes. As a result, the acceleration process saturates, leading to power-law distributions of particle momentum and energy. In the nonrelativistic case, the momentum probability density function scales as f(p)dp ∝ p −3 dp, while in the ultrarelativistic case, the energy probability density function scales as f(γ)dγ ∝ γ −3 dγ, where γ is the Lorentz factor. This model provides a unified framework for understanding particle acceleration in both energy regimes, complementing existing analytical approaches. The predicted scalings are consistent with available observations of energetic ion distributions in the heliosphere and with the findings from numerical simulations of ultrarelativistic particle acceleration in magnetically dominated plasma turbulence.

Alfven waves↗
DOE OSTI2024

Particle Acceleration in Relativistic Alfvénic Turbulence

Abstract Strong magnetically dominated Alfvénic turbulence is an efficient engine of nonthermal particle acceleration in a relativistic collisionless plasma. We argue that in the limit of strong magnetization, the type of energy distribution attained by accelerated particles depends on the relative strengths of turbulent fluctuations δ B 0 and the guide field B 0 . If δ B 0 ≪ B 0 , the particle magnetic moments are conserved, and the acceleration is provided by magnetic curvature drifts. Curvature acceleration energizes particles in the direction parallel to the magnetic field lines, resulting in log-normal tails of particle energy distribution functions. Conversely, if δ B 0 ≳ B 0 , interactions of energetic particles with intense turbulent structures can scatter particles, creating a population with large pitch angles. In this case, magnetic mirror effects become important, and turbulent acceleration leads to power-law tails of the energy distribution functions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Time–connectivity superposition and the gel/glass duality of weak colloidal gels

Colloidal gels result from the aggregation of Brownian particles suspended in a solvent. Gelation is induced by attractive interactions between individual particles that drive the formation of clusters, which in turn aggregate to form a space-spanning structure. We study this process in aluminosilicate colloidal gels through time-resolved structural and mechanical spectroscopy. Using the time–connectivity superposition principle a series of rapidly acquired linear viscoelastic spectra, measured throughout the gelation process by applying an exponential chirp protocol, are rescaled onto a universal master curve that spans over eight orders of magnitude in reduced frequency. This analysis reveals that the underlying relaxation time spectrum of the colloidal gel is symmetric in time with power-law tails characterized by a single exponent that is set at the gel point. The microstructural mechanical network has a dual character; at short length scales and fast times it appears glassy, whereas at longer times and larger scales it is gel-like. These results can be captured by a simple three-parameter constitutive model and demonstrate that the microstructure of a mature colloidal gel bears the residual skeleton of the original sample-spanning network that is created at the gel point. Our conclusions are confirmed by applying the same technique to another well-known colloidal gel system composed of attractive silica nanoparticles. The results illustrate the power of the time–connectivity superposition principle for this class of soft glassy materials and provide a compact description for the dichotomous viscoelastic nature of weak colloidal gels.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Electron energization dynamics in interaction of self-generated magnetic vortices in upstream of collisionless electron/ion shocks

Abstract Relativistic collisionless shocks are considered responsible for particle energization mechanisms leading to particle acceleration. While electron energization in shock front region of electron/ion collisionless shocks are the most studied, the mechanism of electron energization in interaction with self-generated magnetic vortices (MVs) in the upstream region is still unclear. We investigate electron energization mechanism in the upstream region of electron/ion relativistic collisionless shocks, using two dimensional particle-in-cell (PIC) simulations. We discuss mechanism of electron energization which takes place in the upstream region of the shock, where the counter stream particles interact with incoming flow. The energy gain of electrons happens during their interaction with evolving fields of self-generated magnetic vortices in this region. Three Fermi-like electron energization scenarios are discussed. Stochastic acceleration of electrons in interaction with fields of MV leads to anisotropic heating of fast electrons due to diffusion in the momentum space of electrons and, finally, synergetic effect of evolving fields of MVs leads to the formation of a power-law tail of supra-thermal particles.

Naseri, N.↗
DOE OSTI2020

Nonthermal electron and ion acceleration by magnetic reconnection in large laser-driven plasmas

Magnetic reconnection is a fundamental plasma process that is thought to play a key role in the production of nonthermal particles associated with explosive phenomena in space physics and astrophysics. Experiments at high-energy-density facilities are starting to probe the microphysics of reconnection at high Lundquist numbers and large system sizes. We have performed particle-in-cell (PIC) simulations to explore particle acceleration for parameters relevant to laser-driven reconnection experiments. We study particle acceleration in large system sizes that may be produced soon with the most energetic laser drivers available, such as at the National Ignition Facility. In these conditions, we show the possibility of reaching the multi-plasmoid regime, where plasmoid acceleration becomes dominant. Our results show the transition from X point to plasmoid-dominated acceleration associated with the merging and contraction of plasmoids that further extend the maximum energy of the power-law tail of the particle distribution for electrons. We also find for the first time a system-size-dependent emergence of nonthermal ion acceleration in driven reconnection, where the magnetization of ions at sufficiently large sizes allows them to be contained by the magnetic field and energized by direct X point acceleration. For feasible experimental conditions, electrons and ions can attain energies of ϵ max , e / k B T e > 100 and ϵ max , i / k B T i > 1000 . Using PIC simulations with binary Monte Carlo Coulomb collisions, we study the impact of collisionality on plasmoid formation and particle acceleration. The implications of these results for understanding the role reconnection plays in accelerating particles in space physics and astrophysics are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Hidden domain boundary dynamics toward crystalline perfection

A central paradigm of nonequilibrium physics concerns the dynamics of heterogeneity and disorder, impacting processes ranging from the behavior of glasses to the emergent functionality of active matter. Understanding these complex mesoscopic systems requires probing the microscopic trajectories associated with irreversible processes, the role of fluctuations and entropy growth, and the timescales on which nonequilibrium responses are ultimately maintained. Approaches that illuminate these processes in model systems may enable a more general understanding of other heterogeneous nonequilibrium phenomena, and potentially define ultimate speed and energy cost limits for information processing technologies. Here, we apply ultrafast single-shot X-ray photon correlation spectroscopy to resolve the nonequilibrium, heterogeneous, and irreversible mesoscale dynamics during a light-induced phase transition in a (PbTiO 3 ) 16 /(SrTiO 3 ) 16 superlattice. Such ferroelectric superlattice systems are a useful platform to study phase transitions and topological dynamics due to their high degree of tunability. This provides an approach for capturing the nucleation of the light-induced phase, the formation of transient mesoscale defects at the boundaries of the nuclei, and the eventual annihilation of these defects, even in systems with complex polarization topologies. We identify a nonequilibrium correlation response spanning >10 orders of magnitude in timescales, with multistep behavior similar to the plateaus observed in supercooled liquids and glasses. We further show how the observed time-dependent long-time correlations can be understood in terms of stochastic and non-Markovian dynamics of domain walls, encoded in waiting-time distributions with power-law tails. This work defines possibilities for probing the nonequilibrium and correlated dynamics of disordered and heterogeneous media.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Sonic horizons and causality in phase transition dynamics

A system gradually driven through a symmetry-breaking phase transition is subject to the Kibble-Zurek mechanism (KZM). As a consequence of the critical slowing down, its state cannot follow local equilibrium, and its evolution becomes nonadiabatic near the critical point. In the simplest approximation, that stage can be regarded as an “impulse” where the state of the system remains unchanged. It leads to the correct KZM scaling laws. However, such a “freeze-out” might suggest that the coherence length of the nascent order parameter remains unchanged as the critical region is traversed. By contrast, the original causality-based discussion emphasized the role of the sonic horizon: Domains of the broken symmetry phase can expand with a velocity limited by the speed of the relevant sound. This effect was demonstrated in the quantum Ising chain where the dynamical exponent z = 1 and quasiparticles excited by the transition have a fixed speed of sound. To elucidate the role of the sonic horizon, in this paper we study two systems with z > 1 where the speed of sound is no longer fixed, and the fastest excited quasiparticles set the size of the sonic horizon. Their effective speed decays with increasing transition time. In the extreme case, the dynamical exponent z can diverge such as in the Griffiths region of the random Ising chain where the localization of excited quasiparticles freezes the growth of the correlation range when the critical region is traversed. Of particular interest is an example with z < 1 , the long-range extended Ising chain, where there is no upper limit to the velocity of excited quasiparticles with small momenta. Initially, the power-law tail of the correlation function grows adiabatically, but in the nonadiabatic stage it lags behind the adiabatic evolution.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Spin dynamics of the antiferromagnetic Heisenberg model on a kagome bilayer

We research the spin dynamics of a classical Heisenberg antiferromagnet with nearest-neighbor interactions on a quasi-two-dimensional kagome bilayer. This geometrically frustrated lattice consists of two kagome layers connected by a triangular-lattice linking layer. By combining Monte Carlo with precessional spin dynamics simulations, we compute the dynamical structure factor of the classical spin liquid in the kagome bilayer and investigate the thermal and dilution effects. While the low-frequency and long-wavelength dynamics of the cooperative paramagnetic phase is dominated by spin diffusion, weak magnon excitations persist at higher energies, giving rise to the half-moon pattern in the dynamical structure factor. In the presence of spin vacancies, the dynamical properties of the diluted system can be understood within the two-population picture. The spin diffusion of the “correlated” spin clusters is mainly driven by the zero-energy weather-vane modes, giving rise to an autocorrelation function that decays exponentially with time. On the other hand, the diffusive dynamics of the quasifree “orphan” spins leads to a distinctive longer-time power-law tail in the autocorrelation function. We discuss the implications of our work for the glassy behaviors observed in the archetypal frustrated magnet SrCr 9p Ga 12-9 pO 19 (SCGO).

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Eikonal spin-dependent odderon and gluon Sivers function of a proton and its small-𝑥 evolution

The matrix element in the proton of the eikonal Odderon operator, with a helicity flip, has been shown to correspond to the dipole gluon Sivers function. We employ a three quark light-front model of the proton to determine the Sivers function at moderately small 𝑥 0 ∼ 0.1 and transverse momentum 𝑘 ⊥ ≲ 1 GeV. The model light-cone (LC) wave function predicts the properties of 𝑥⁢𝑓$^{⊥⁢𝑔}_{1⁢𝑇⁡}$(𝑥,𝑘 ⊥ ) such as its overall magnitude, the position of its peak in 𝑘 ⊥ , and its behavior at small 𝑘 ⊥ . We then compute numerically the Balitsky-Fadin-Kuraev-Lipatov anomalous dimension characterizing the power-law tail at 𝑘 ⊥ ≳ 1.5 GeV of the gluon Sivers function at small (but preasymptotic) LC momentum fractions 𝑥 ∼ 𝑥 0 ⁢𝑒 −1/𝛼 𝑠 : 𝑥⁢𝑓$^{⊥⁢𝑔}_{1⁢𝑇⁡}$⁡(𝑥,𝑘 ⊥ ) ∼ 𝑘$^{−3.3}_{⊥}$.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

What Sets the Star Formation Rate of Molecular Clouds? The Density Distribution as a Fingerprint of Compression and Expansion Rates

We use a suite of 3D simulations of star-forming molecular clouds, with and without stellar feedback, magnetic fields, and driven turbulence, to study the compression and expansion rates of the gas as functions of density. We show that, around the mean density, supersonic turbulence promotes rough equilibrium between the amounts of compressing and expanding gas, consistent with continuous gas cycling between high- and low-density states. We find that the inclusion of protostellar jets produces rapidly expanding and compressing low-density gas. We find that the gas mass flux peaks at the transition between the lognormal and power-law forms of the density probability distribution function (PDF). This is consistent with the transition density tracking the post-shock density, which promotes an enhancement of mass at this density (i.e., shock compression and filament formation). At high densities, the gas dynamics are dominated by self-gravity: the compression rate in all of our runs matches the rate of the run with only gravity, suggesting that processes other than self-gravity have little effect at these densities. The net gas mass flux becomes constant at a density below the sink formation threshold, where it equals the star formation rate. The density at which the net gas mass flux equals the star formation rate is one order of magnitude lower than our sink threshold density, corresponds to the formation of the second power-law tail in the density PDF, and sets the overall star formation rates of these simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Predicting Water Cycle Characteristics from Percolation Theory and Observational Data

The fate of water and water-soluble toxic wastes in the subsurface is of high importance for many scientific and practical applications. Although solute transport is proportional to water flow rates, theoretical and experimental studies show that heavy-tailed (power-law) solute transport distribution can cause chemical transport retardation, prolonging clean-up time-scales greatly. However, no consensus exists as to the physical basis of such transport laws. In percolation theory, the scaling behavior of such transport rarely relates to specific medium characteristics, but strongly to the dimensionality of the connectivity of the flow paths (for example, two- or three-dimensional, as in fractured-porous media or heterogeneous sediments), as well as to the saturation characteristics (i.e., wetting, drying, and entrapped air). In accordance with the proposed relevance of percolation models of solute transport to environmental clean-up, these predictions also prove relevant to transport-limited chemical weathering and soil formation, where the heavy-tailed distributions slow chemical weathering over time. The predictions of percolation theory have been tested in laboratory and field experiments on reactive solute transport, chemical weathering, and soil formation and found accurate. Recently, this theoretical framework has also been applied to the water partitioning at the Earth’s surface between evapotranspiration, ET, and run-off, Q, known as the water balance. A well-known phenomenological model by Budyko addressed the relationship between the ratio of the actual evapotranspiration (ET) and precipitation, ET/P, versus the aridity index, ET 0 /P, with P being the precipitation and ET 0 being the potential evapotranspiration. Existing work was able to predict the global fractions of P represented by Q and ET through an optimization of plant productivity, in which downward water fluxes affect soil depth, and upward fluxes plant growth. In the present work, based likewise on the concepts of percolation theory, we extend Budyko’s model, and address the partitioning of run-off Q into its surface and subsurface components, as well as the contribution of interception to ET. Using various published data sources on the magnitudes of interception and information regarding the partitioning of Q, we address the variability in ET resulting from these processes. The global success of this prediction demonstrated here provides additional support for the universal applicability of percolation theory for solute transport as well as guidance in predicting the component of subsurface run-off, important for predicting natural flow rates through contaminated aquifers.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Novel deformation function creating or destroying any number of even kink solutions

Here, we present a one-parameter family of deformation functions f(Φ) which have novel properties. Firstly, the deformation function is its own inverse. We show that a class of potentials remains invariant under this deformation. Further, when applied to a certain class of kink bearing potentials, one obtains potentials which are not bounded from below. Besides, we show that there is a wide class of potentials having power law kink tails which are connected by this deformation but the corresponding kink tails of the two potentials have different asymptotic behavior. Finally, we show that when this deformation function is applied to an appropriate one-parameter family of potentials having two kink solutions, it creates new potentials with an arbitrary even number (2n) of kink solutions. Conversely, by starting from this potential with 2n kink solutions the deformation function annihilates 2n-2 kinks and we get back the potential which we started with having only two kink solutions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

River Dynamics Control Transit Time Distributions and Biogeochemical Reactions in a Dam-Regulated River Corridor

Residence Time Distributions (RTDs) exert an important control on biogeochemical translation in the hydrological systems. Previous tracer studies have revealed that RTDs often followed time-invariant exponential, lognormal, or heavy-tailed RTDs that have power-law behavior for long tails in headwater or low-order streams. However, there is a recognition that RTDs can be more complicated and time-variable in response to dynamic hydrological forcing. Here, we use particle tracking to estimate RTDs along the Hanford Reach of the Columbia River and to quantify the influences of river stage fluctuations. Particle tracking is conducted using the velocity field from high-resolution 3D groundwater flow simulations. The effects of hydrological forcing on the residence time distribution were evaluated by varying river flow boundary conditions and releasing particles in different time windows. Our results revealed that dynamic stage fluctuations created rapidly changing losing-gaining conditions in the river and led to highly transient RTDs, which contributes to multiple modes of RTDs. Dam-induced high-frequency (sub-daily) flow variation contributes to the short-time (sub-daily) component of the RTDs. Deviation of the reactant consumption under the single-mode assumption compared to the multimodal RTDs is relatively small (~5%) and appears when the Damköhler number was close to one.More specifically, high-frequency (daily) dam-induced stage variations have higher impacts on biogeochemical reactions with faster reaction rate, and can potentially increase the reactant consumption by 26.68%. Based on these findings, we suggest that current river basin models could be improved by including bank storage and more complex RTDs influenced by both short and long term river stage fluctuations.

54 ENVIRONMENTAL SCIENCES↗