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Current approaches to scaling laws for planetary impact processes are reviewed. Only the simplest concepts and first-order theories that are the most determined are presented. Experimental, analytical, and calculative approaches to determining scaling laws are examined, including the advantages and deficiencies of each.
Complex fluctuation of unknown origin appear in the normal gait pattern. These fluctuations might be described as being (1) uncorrelated white noise, (2) short-range correlations, or (3) long-range correlations with power-law scaling. To test these possibilities, the stride interval of 10 healthy young men was measured as they walked for 9 min at their usual rate. From these time series we calculated scaling indexes by using a modified random walk analysis and power spectral analysis. Both indexes indicated the presence of long-range self-similar correlations extending over hundreds of steps; the stride interval at any time depended on the stride interval at remote previous times, and this dependence decayed in a scale-free (fractallike) power-law fashion. These scaling indexes were significantly different from those obtained after random shuffling of the original time series, indicating the importance of the sequential ordering of the stride interval. We demonstrate that conventional models of gait generation fail to reproduce the observed scaling behavior and introduce a new type of central pattern generator model that sucessfully accounts for the experimentally observed long-range correlations.
Universality and scaling laws are hallmarks of equilibrium phase transitions and critical phenomena. However, extending these concepts to non-equilibrium systems is an outstanding challenge. Despite recent progress in the study of dynamical phases, the universality classes and scaling laws for non-equilibrium phenomena are far less understood than those in equilibrium. In this work, using a trapped-ion quantum simulator with single-spin resolution, we investigate the non-equilibrium nature of critical fluctuations following a quantum quench to the critical point. We probe the scaling of spin fluctuations after a series of quenches to the critical Hamiltonian of a long-range Ising model. With systems of up to 50 spins, we show that the amplitude and timescale of the post-quench fluctuations scale with system size with distinct universal critical exponents, depending on the quench protocol. While a generic quench can lead to thermal critical behavior, we find that a second quench from one critical state to another (i.e. a double quench) results in a new universal non-equilibrium behavior, identified by a set of critical exponents distinct from their equilibrium counterparts. Our results demonstrate the ability of quantum simulators to explore universal scaling beyond equilibrium.
Turbulent viscosity νt and resistivity ηt are perhaps the simplest models for turbulent transport of angular momentum and magnetic fields, respectively. The associated turbulent magnetic Prandtl number Pr t ≡ ν t /η t has been well recognized to determine the final magnetic configuration of accretion disks. Here, we present an approach to determining these "effective transport" coefficients acting at different length scales using coarse-graining and recent results on decoupled kinetic and magnetic energy cascades. By analyzing the kinetic and magnetic energy cascades from a suite of high-resolution simulations, we show that our definitions of ν t , η t , and Pr t have power-law scalings in the "decoupled range." We observe that Pr t ≈ 1–2 at the smallest inertial-inductive scales, increasing to ≈5 at the largest scales. Furthermore, based on physical considerations, our analysis suggests that Pr t has to become scale independent and of order unity in the decoupled range at sufficiently high Reynolds numbers (or grid resolution) and that the power-law scaling exponents of velocity and magnetic spectra become equal. In addition to implications for astrophysical systems, the scale-dependent turbulent transport coefficients offer a guide for large-eddy simulation modeling.
A new staged plasma-focus geometry combining two Mather-type plasma-focus guns was constructed, and the current-sheet dynamics were investigated. The production of simultaneous pairs of plasma foci was achieved. The intensities of X-ray and fusion-neutron emission were measured and found to agree with the scaling law for a plasma focus. Advantages of this new geometry include the possibility of using plasma-focus type pinches in multiple arrays at power levels beyond the validity regime of the current scaling law for a single gun.
A theoretical analysis of the scaling law and the value of the threshold current for beam plasma discharge (BPD) is presented, based on the requirement for an absolute instability near the plasma frequency. It is shown that both the scaling law as well as the numerical values of Ic are consistent with the experimental data, in the low pressure regimes and for weak magnetic field experiments if the dominant particle loss mechanism is due to Bohm diffusion. The implications of the findings to electron injection in space are discussed.
The verification approach of large beam type space structures is verified. The proposed verification approach consists of two parts. The first part is to remove the gravity effect on the tested substructure and to identify the on-orbit dynamic characteristics of the substructure by using the measurements of the ground test. A scaling law is also established to define the critical length of the structure which can be tested in 1-g field without incurring a buckling problem. The second part is to develop an adequate scaling law to extrapolate the dynamic characteristics of the prototype structure by using results from the substructure. The verification approaches are demonstrated on two typical structural configurations, the feed support structure of a wrap-rip antenna and a candidate shuttle flight experiment. The results indicate that it is practical to verify the on-orbit dynamic characteristics of these structures by using the proposed approach.
Laboratory impact experiments were performed to investigate the conditions that produce large-scale damage in rock targets. Aluminum cylinders (6.3 mm diameter) impacted basalt cylinders (69 mm diameter) at speeds ranging from 0.7 to 2.0 km/s. Diagnostics included measurements of the largest fragment mass, velocities of the largest remnant and large fragments ejected from the periphery of the target, and X-ray computed tomography imaging to inspect some of the impacted targets for internal damage. Significant damage to the target occurred when the kinetic energy per unit target mass exceeded roughly 1/4 of the energy required for catastrophic shattering (where the target is reduced to one-half its original mass). Scaling laws based on a rate-dependent strength were developed that provide a basis for extrapolating the results to larger strength-dominated collisions. The threshold specific energy for widespread damage was found to scale with event size in the same manner as that for catastrophic shattering. Therefore, the factor of four difference between the two thresholds observed in the lab also applies to larger collisions. The scaling laws showed that for a sequence of collisions that are similar in that they produce the same ratio of largest fragment mass to original target mass, the fragment velocities decrease with increasing event size. As a result, rocky asteroids a couple hundred meters in diameter should retain their large ejecta fragments in a jumbled rubble-pile state. For somewhat larger bodies, the ejection velocities are sufficiently low that large fragments are essentially retained in place, possibly forming ordered "brick-pile" structures.
Magnetized liner inertial fusion (MagLIF) is a z-pinch magneto-inertial-fusion concept studied at the Z Pulsed Power Facility of Sandia National Laboratories. Two important metrics characterizing current delivery to a z-pinch load are the peak current and the current-rise time, which is roughly the time interval to reach the peak current. It is known that, when driving a z-pinch load with a longer current-rise time, the performance of the z-pinch decreases. However, a theory to understand and quantify this effect is still lacking. Here, in this paper, we utilize a framework based on similarity scaling to analytically investigate the variations in the performance of MagLIF loads when varying the current-rise time, or equivalently, the implosion timescale. To maintain similarity between the implosions, we provide scaling prescriptions of experimental input parameters defining a MagLIF load and derive the expected scaling laws for stagnation conditions and for various performance metrics. We compare predictions of the theory to 2D numerical simulations using the radiation, magneto-hydrodynamic code hydra. For several metrics, we find acceptable agreement between the theory and simulations. Our results show that the voltage φload near the MagLIF load follows a weak scaling law φload ∝$t_{φ}^{-0.12}$ with respect to the characteristic timescale t φ of the voltage source, instead of the ideal φload ∝$t_{φ}^{-1}$ scaling. This occurs because the imploding height of the MagLIF load must increase to preserve end losses. As a consequence of the longer imploding liners, the required total laser preheat energy and delivered electric energy increase. Overall, this study helps understand the trade-offs of the MagLIF design space when considering future pulsed-power generators with shorter and longer current-rise times.
In this work, we study the thermoelectric transport properties of fractional quantum Hall systems based on an exact diagonalization calculation. Based on the relation between the thermoelectric response and thermal entropy, we demonstrate that thermoelectric Hall conductivity $α_{xy}$ has power-law scaling $α_{xy} ∝ T^η$ for gapless composite Fermi-liquid states at filling numbers $\textit{ν}$ = 1/2 and 1/4 at low temperatures ($\textit{T}$), with an exponent η ~ 0.5 distinctly different from Fermi liquids. The power-law scaling remains unchanged for different forms of interaction including Coulomb and short-range ones, demonstrating the robustness of non-Fermi-liquid behavior of these interacting systems at low $\textit{T}$. In contrast, for the 1/3 fractional quantum Hall state, $α_xy$ vanishes at low $\textit{T}$ with an activation gap associated with neutral collective modes rather than charged quasiparticles. Our results establish another manifestation of the non-Fermi-liquid nature of quantum Hall fluids at a finite temperature.
An axial fan was designed at NASA Glenn Research Center using tools developed for aircraft turbine engines. The fan unit design size, flow rate and pressure rise were chosen to be broadly in the range of the Orion cabin fan. A ground test prototype was built and tested, confirming design predictions. Pressure rise and flow rate measurements were conducted over a range of fan speeds while in-duct and radiated acoustic measurements were collected. Unsteady flow measurements were acquired between the rotor and stator. These methods are a hybrid of the techniques used for small fans and those used for aircraft engine component tests. A larger version of the fan was recently designed, based on the original fan, using aerodynamic scaling laws resulting in a design with approximately twice the flow rate and twice the pressure-rise compared to the original fan. The mechanical structure was optimized using generative design for low weight. The paper discusses this larger fan design including the scaling laws, the predicted performance and acoustics.
The influence of specimen polishing, configuration, and size on the transverse tension strength of two glass-epoxy materials, and one carbon-epoxy material, loaded in three and four point bending was evaluated. Polishing machined edges, arid/or tension side failure surfaces, was detrimental to specimen strength characterization instead of yielding a higher, more accurate, strength as a result of removing inherent manufacture and handling flaws. Transverse tension strength was typically lower for longer span lengths due to the classical weakest link effect. However, strength was less sensitive to volume changes achieved by increasing specimen width. The Weibull scaling law typically over-predicted changes in transverse tension strengths in three point bend tests and under-predicted changes in transverse tension strengths in four point bend tests. Furthermore, the Weibull slope varied with specimen configuration, volume, and sample size. Hence, this scaling law was not adequate for predicting transverse tension strength of heterogeneous, fiber-reinforced, polymer matrix composites.
This is the official code for the ICML 2024 paper "Adversarial Robustness Limits via Scaling-Law and Human-Alignment Studies". This code extends that of Wang et al. (2023) to facilitate state-of-the-art CIFAR-10 adversarial robustness, via training of WideResNet models on various large synthetic datasets. The code also facilitates derivation of the various scaling laws put forth in our ICML paper, which we use to compute efficient training settings.
The influence of specimen polishing, specimen configuration, and specimen size on the transverse tension strength of two glass epoxy materials loaded in three and four point bending was evaluated. Polishing machined edges, and/or tension side failure surfaces, was detrimental to specimen strength characterization instead of yielding a higher, more accurate, strength as a result of removing inherent manufacture and handling flaws. Transverse tension strength was sensitive to span length due to the classical weakest link effect. However, strength was less sensitive to volume changes achieved by increasing specimen width. The Weibull scaling law over-predicted changes in transverse tension strengths in three point bend tests and under-predicted changes in transverse tension strengths in four point bend tests. Furthermore, the Weibull slope varied with specimen configuration, volume, and sample size. Hence, the utility of this scaling law for predicting transverse tension strength is unclear.
Scaling relations between coronal base pressure and longitudinal photospheric magnetic field strength are tested for the case of a single active region observed for five solar rotations from Skylab. The evolution of measureable quantities, such as coronal thermal energy content, total longitudinal photospheric magnetic flux, region scale size, and peak energy density, is traced throughout the five rotations observed. The theoretically derived scaling law of Golub et al. (1980) is found to provide an acceptable fit to the data throughout the entire evolutionary history of the region from an age of about 3 days to the fully evolved state in which the mature active region merges into the general large-scale structure of the quiet corona. An alternative scaling law obtained by including the results of Galeev et al. (1981), however, is found to provide a somewhat better fit to the data. The study is seen as providing additional justification for the belief that magnetic field-related heating is the operative mechanism in the solar corona.
Polyelectrolyte complex micelles are hydrophilic nanoparticles that self-assemble in aqueous environments due to associative microphase separation between oppositely charged blocky polyelectrolytes. In this work, we employ a suite of physical characterization tools to examine the effect of charged block length mismatch on the equilibrium structure of double diblock polyelectrolyte complex micelles (D-PCMs) by mixing a diverse library of peptide and synthetic charged-neutral block polyelectrolytes with a wide range of charged block lengths (25–200 units) and chemistries. Early work on D-PCMs suggested that this class of micelles can only be formed from blocky polyelectrolytes with identical charged block lengths, a phenomenon referred to as chain length recognition. Here, we use salt annealing to create PCMs at equilibrium, which shows that chain length recognition, a longstanding hurdle to repeatable self-assembly from mismatched polyelectrolytes, can be overcome. Interestingly, D-PCM structure–property relationships display a range of values that vary systematically with the charged block lengths and chemical identity of constituent polyelectrolyte pairings and cannot be described by generalizable scaling laws. We discuss the interdependent growth behavior of the radius, ionic pair aggregation number, and density in the micelle core for three chemically distinct diblock pairings and suggest a potential physical mechanism that leads to this unique behavior. By comparing the results of these D-PCMs to the scaling laws recently developed for single diblock polyelectrolyte complex micelles (S-PCMs: diblock + homopolymer), we observe that D-PCM design schemes reduce the size and aggregation number and restrict their growth to a function of charged block length relative to S-PCMs. Understanding these favorable attributes enables more predictive use of a wider array of charged molecular building blocks to anticipate and control macroscopic properties of micelles spanning countless storage and delivery applications.
In this paper we study the three-dimensional (3D) structure of hot (T(sub e) approximately equals 1.5 - 2.5 MK) loops in solar active region NOAA 7986, observed on 1996 August 30 with the Extreme-ultraviolet Imaging Telescope (EIT) onboard the Solar and Heliospheric Observatory (SoHO). This complements a first study on cooler (T(sub e) approximately equals 1.0 - 1.5 MK) loops of the same active region, using the same method of Dynamic Stereoscopy to reconstruct the 3D geometry. We reconstruct the 3D-coordinates x(s), y(s), z(s), the density n(sub e)(s), and temperature profile T(sub e)(s) of 35 individual loop segments (as function of the loop coordinate s) using EIT 195 A and 284 A images. The major findings are: (1) All loops are found to be in hydrostatic equilibrium, in the entire temperature regime of T(sub e) = 1.0 - 2.5 MK; (2) The analyzed loops have a height of 2-3 scale heights, and thus only segments extending over about one vertical scale height have sufficient emission measure contrast for detection; (3) The temperature gradient over the lowest scale height is of order dT/ds is approximately 1 - 4 K/km; (4) The radiative loss rate is found to exceed the conductive loss rate by about two orders or magnitude, making thermal conduction negligible to explain the temperature structure of the loops; (5) A steady-state can only be achieved when the heating rate E(sub H) matches the radiative loss rate in hydrostatic equilibrium, requiring a heat deposition length lambda(sub H) of the half density scale height lambda, predicting a scaling law with the loop base pressure, EH varies as p(sub 0 exp 2). This favors coronal heating mechanisms that operate near the loop footpoints; (6) We find a reciprocal correlation between the loop pressure p(sub 0) and loop length L, i.e. p(sub 0) varies as 1/L, implying a scaling law of the steady-state requirement with loop length, i.e. E(sub H ) varies as 1/L(exp 2). The heating rate shows no correlation with the loop-aligned magnetic field component B(sub z) at the footpoints, but is correlated with the azimuthal field B(sub phi) = Bz(RDelta Phi/L) of a twisted loop, and is thus consistent with heating mechanisms based on field-aligned currents.
Low gravity slosh simulation parameters and scaling law used to extrapolate data to full scale spacecraft systems