General Scaling Laws Research Articles

Laser-induced extreme magnetic field in nanorod targets

The application of nano-structured target surfaces in laser-solid interaction has attracted significant attention in the last few years. Their ability to absorb significantly more laser energy promises a possible route for advancing the currently established laser ion acceleration concepts. However, it is crucial to have a better understanding of field evolution and electron dynamics during laser-matter interactions before the employment of such exotic targets. This paper focuses on the magnetic field generation in nano-forest targets consisting of parallel nanorods grown on plane surfaces. A general scaling law for the self-generated quasi-static magnetic field amplitude is given and it is shown that amplitudes up to 1 MT field are achievable with current technology. Analytical results are supported by three-dimensional particle-in-cell simulations. Non-parallel arrangements of nanorods has also been considered which result in the generation of donut-shaped azimuthal magnetic fields in a larger volume.

Universal model of individual and population mobility on diverse spatial scales

Studies of human mobility in the past decade revealed a number of general scaling laws. However, to reproduce the scaling behaviors quantitatively at both the individual and population levels simultaneously remains to be an outstanding problem. Moreover, recent evidence suggests that spatial scales have a significant effect on human mobility, raising the need for formulating a universal model suited for human mobility at different levels and spatial scales. Here we develop a general model by combining memory effect and population-induced competition to enable accurate prediction of human mobility based on population distribution only. A variety of individual and collective mobility patterns such as scaling behaviors and trajectory motifs are accurately predicted for different countries and cities of diverse spatial scales. Our model establishes a universal underlying mechanism capable of explaining a variety of human mobility behaviors, and has significant applications for understanding many dynamical processes associated with human mobility.

Fast Magnetic Reconnection: “Ideal” Tearing and the Hall Effect

Abstract One of the main questions in magnetic reconnection is the origin of triggering behavior with on/off properties that, once it is activated, accounts for the fast magnetic energy conversion to kinetic and thermal energies at the heart of explosive events in astrophysical and laboratory plasmas. Over the past decade, progress has been made on the initiation of fast reconnection via the plasmoid instability and what has been called “ideal” tearing, which sets in once current sheets thin to a critical inverse aspect ratio . As shown by Pucci & Velli, at , the timescale for the instability to develop becomes of the order of the Alfvén time and independent of the Lundquist number (here defined in terms of current sheet length L). However, given the large values of S in natural plasmas, this transition might occur for thicknesses of the inner resistive singular layer that are comparable to the ion inertial length d i . When this occurs, Hall currents produce a three-dimensional quadrupole structure of the magnetic field, and the dispersive waves introduced by the Hall effect accelerate the instability. Here we present a linear study showing how the “ideal” tearing mode critical aspect ratio is modified when Hall effects are taken into account, including more general scaling laws of the growth rates in terms of sheet inverse aspect ratio: the critical inverse aspect ratio is amended to , at which point the instability growth rate becomes Alfvénic and does not depend on either of the (small) parameters . We discuss the implications of this generalized triggering aspect ratio for recently developed phase diagrams of magnetic reconnection.

A general scaling law reveals why the largest animals are not the fastest.

Speed is the fundamental constraint on animal movement, yet there is no general consensus on the determinants of maximum speed itself. Here, we provide a general scaling model of maximum speed with body mass, which holds across locomotion modes, ecosystem types and taxonomic groups. In contrast to traditional power-law scaling, we predict a hump-shaped relationship resulting from a finite acceleration time for animals, which explains why the largest animals are not the fastest. This model is strongly supported by extensive empirical data (474 species, with body masses ranging from 30 μg to 100 tonnes) from terrestrial as well as aquatic ecosystems. Our approach unravels a fundamental constraint on the upper limit of animal movement, thus enabling a better understanding of realized movement patterns in nature and their multifold ecological consequences.

Master equation for She–Leveque scaling and its classification in terms of other Markov models of developed turbulence

The statistics of velocity increments in homogeneous and isotropic turbulence exhibit universal features in the limit of infinite Reynolds numbers. After Kolmogorov’s scaling law from 1941, many turbulence models aim for capturing these universal features, some are known to have an equivalent formulation in terms of Markov processes. We derive the Markov process equivalent to the particularly successful scaling law postulated by She and Leveque. The Markov process is a jump process for velocity increments in scale r in which the jumps occur randomly but with deterministic width in u. From its master equation we establish a prescription to simulate the She–Leveque process and compare it with Kolmogorov scaling. To put the She–Leveque process into the context of other established turbulence models on the Markov level, we derive a diffusion process for using two properties of the Navier–Stokes equation. This diffusion process already includes Kolmogorov scaling, extended self-similarity and a class of random cascade models. The fluctuation theorem of this Markov process implies a ‘second law’ that puts a loose bound on the multipliers of the random cascade models. This bound explicitly allows for instances of inverse cascades, which are necessary to satisfy the fluctuation theorem. By adding a jump process to the diffusion process, we go beyond Kolmogorov scaling and formulate the most general scaling law for the class of Markov processes having both diffusion and jump parts. This Markov scaling law includes She–Leveque scaling and a scaling law derived by Yakhot.

Experimental investigations on characteristics of stable water electrospray in air without discharge.

An experimental study was conducted to resolve previous conflicting results on water electrospray in air at atmospheric pressure. Using a small flow rate relative to that used in previous studies and a small nonmetallic nozzle, we observed stable electrospray of water in air without discharge and distinguished three distinct operating regimes for applied voltage and flow rate. The well-known cone-jet mode was observed and the general scaling law of the generated droplet size in the cone-jet mode was confirmed by direct visualization of the meniscus, jet, and generated droplets. We also observed and analyzed whipping motion in the electrified water jet.

Optimal Sizing and Comparison of Permanent Magnet Thrust Bearings

The aim of this paper is to study different permanent magnet (PM) bearings geometries based on PM rings with a minimum volume of PM for a given load. Simple and general scaling laws (SCLs) are proposed for each bearing geometry to predict its behavior. These SCLs allow a fast sizing of those geometries, as a function of the number of PM rings, the load reference, the air gap, and the remanent flux density. Those SCLs are derived for optimized topologies without any constraint on the geometrical parameters, as well as for optimized geometries with a constraint on the PM dimensions. For both cases, SCLs for the thrust-bearing stiffness are also proposed.

General wave optics propagation scaling law.

A general far-field wave propagation scaling law is developed. The formulation is simple but predicts diffraction peak irradiance accurately in the far field, regardless of the near-field beam type or geometry, including laser arrays. We also introduce the concept of the equivalent uniform circular beam that generates a far-field peak irradiance and power-in-the-bucket that are the same as an arbitrary laser source. Applications to clipped Gaussian beams with an obscuration, both as a single beam and as an array of beams, are shown.

Scale-invariant radio jets and varying black hole spin

Compact radio cores associated with relativistic jets are often observed in both active galactic nuclei and X-ray binaries. Their radiative properties follow some general scaling laws which primarily depend on their masses and accretion rates. However, it has been suggested that the black hole spin can also strongly influence the power and radio flux of these. Here, we attempt to estimate the dependency of the radio luminosity of steady jets launched by accretion disks on black hole mass, accretion rate and spin using numerical simulations. We make use of 3D GRMHD simulations of accretion disks around low-luminosity black holes in which the jet radio emission is produced by the jet sheath. We find that the radio flux increases roughly by a factor of 6 as the back hole spin increases from a~0 to a=0.98. This is comparable to the increase in accretion power with spin, meaning that the ratio between radio jet and accretion power is hardly changing. Although our jet spine power scales as expected for the Blandford-Znajek process, the dependency of jet radio luminosity on the black hole spin is somewhat weaker. Also weakly rotating black holes can produce visible radio jets. The overall scaling of the radio emission with black hole mass and accretion rate is consistent with the scale-invariant analytical models used to explain the fundamental plane of black hole activity. Spin does not introduce a significant scatter in this model. The jet-sheath model can describe well resolved accreting systems, such as SgrA* and M87, as well as the general scaling behavior of low-luminosity black holes. Hence the model should be applicable to a wide range of radio jets in sub-Eddington black holes. The black hole spin has an effect on the production of visible radio jet, but it may not be the main driver to produce visible radio jets. An extension of our findings to powerful quasars remains speculative.

Nonasymptotic Multicast Throughput and Delay in Multihop Wireless Networks

Previous works on multicast capacity mainly focus on deriving asymptotic order results in large-scale wireless networks. While they can explore the general scaling laws of throughput capacity, it is also of great interest for practical concern to predict the exact achievable throughput in networks with an arbitrary finite number of nodes. In this paper, we investigate the nonasymptotic throughput and delay of multihop wireless networks for multicast applications wherein for each source node, $k$ nodes are randomly selected as receivers. It is challenging for the exact performance analysis since multicast transmission has a dynamic nature due to the following factors: 1) random distribution of nodes; 2) bursty traffic arrivals; and 3) different timescales for transient analysis. To tackle the problem, we propose an explicit analytical model and develop a multicast routing scheme, which accounts for these aspects. With our proposed model, we derive lower bound (LB) and upper bound (UB) on nonasymptotic multicast throughput and delay using stochastic network calculus. We show that the performance results hold for all timescales and network sizes and are strongly correlated to data burstiness and the number of receivers. While we investigate from a nonasymptotic point of view, our results can also cover the asymptotic scaling laws. Simulations are conducted to further verify the accuracy of the analytical bounds.

Mechanical Properties of the Boron Nitride Analog of Graphyne: Scaling Laws and Failure Patterns

Recent years have witnessed the explosive growth of interest in novel two‐dimensional materials beyond graphene, such as the boron nitride analogue BNyne. Here, the authors perform steered molecular dynamics (MD) simulations to probe the structure, mechanical properties, and failure of BNyne with a range of triple‐single‐bond linker numbers. The authors develop a set of general scaling laws for the cumulative effects of linkers based on MD, allowing extrapolation to extended BNynes. Results indicate that the number of linkers, and thus density, is a vital metric of material strength and stiffness. We find that BNyne is stronger in the armchair direction but stiffer in the zigzag direction. These findings are promising as the application of this strong, anisotropic 2D material becomes closer to reality.

Mean First Passage Time in Single File Dynamics

We derive the general scaling law of the mean first passage time (MFPT) in single file dynamics; the process where many real particles move in a channel of length [Formula: see text] with absorbing boundaries, where the particles and the channel have about the same cross section. We derive the relation [Formula: see text], here we compute the MFPT when the channel is free (all particles are absorbed, where the average is over many trajectories), [Formula: see text] is the number of particles in the channel at initiation, [Formula: see text] is the many-particle effect and the quantity MFPT[Formula: see text] is the MFPT of the free particle. When at initiation the density is fixed in basic files [Formula: see text] and therefore e.g. [Formula: see text] (basic stochastic dynamics). We also compute the MFPT in diverse files; for example, in a file with heterogeneous particles, in deterministic files, in slow files and in files with long-range interactions. When the particle density is not fixed yet scales with 1/length from the origin, [Formula: see text]; yet, interactions might increase (attractive) or decrease (repulsive) the many-particle effect relative to [Formula: see text]. In slow files, [Formula: see text] (in the number of jumps). We explain these valuable results with various methods and approaches, e.g., we derive a general mapping from the mean square displacement scaling law to the MFPT scaling law. We also connect the results with real life activities. Special Issue Comments: Mean first passage scaling law in single file dynamics and various particular results in files are derived in this project. The project is related to the Special Issue projects about heterogeneous files and slow files,[Formula: see text] expansions in files,[Formula: see text] files with force[Formula: see text] and the first passage time in files.[Formula: see text]

Guided Formation of 3D Helical Mesostructures by Mechanical Buckling: Analytical Modeling and Experimental Validation.

Three-dimensional (3D) helical mesostructures are attractive for applications in a broad range of microsystem technologies, due to their mechanical and electromagnetic properties as stretchable interconnects, radio frequency antennas and others. Controlled compressive buckling of 2D serpentine-shaped ribbons provides a strategy to formation of such structures in wide ranging classes of materials (from soft polymers to brittle inorganic semiconductors) and length scales (from nanometer to centimeter), with an ability for automated, parallel assembly over large areas. The underlying relations between the helical configurations and fabrication parameters require a relevant theory as the basis of design for practical applications. Here, we present an analytic model of compressive buckling in serpentine microstructures, based on the minimization of total strain energy that results from various forms of spatially dependent deformations. Experiments at micro- and millimeter-scales, together with finite element analyses (FEA), were exploited to examine the validity of developed model. The theoretical analyses shed light on general scaling laws in terms of three groups of fabrication parameters (related to loading, material and 2D geometry), including a negligible effect of material parameters and a square root dependence of primary displacements on the compressive strain. Furthermore, analytic solutions were obtained for the key physical quantities (e.g., displacement, curvature and maximum strain). A demonstrative example illustrates how to leverage the analytic solutions in choosing the various design parameters, such that brittle fracture or plastic yield can be avoided in the assembly process.

The predator-prey power law: Biomass scaling across terrestrial and aquatic biomes.

Ecosystems exhibit surprising regularities in structure and function across terrestrial and aquatic biomes worldwide. We assembled a global data set for 2260 communities of large mammals, invertebrates, plants, and plankton. We find that predator and prey biomass follow a general scaling law with exponents consistently near ¾. This pervasive pattern implies that the structure of the biomass pyramid becomes increasingly bottom-heavy at higher biomass. Similar exponents are obtained for community production-biomass relations, suggesting conserved links between ecosystem structure and function. These exponents are similar to many body mass allometries, and yet ecosystem scaling emerges independently from individual-level scaling, which is not fully understood. These patterns suggest a greater degree of ecosystem-level organization than previously recognized and a more predictive approach to ecological theory.

A general scaling law for ecology

Macroecology Despite the huge diversity of ecological communities, they can have unexpected patterns in common. Hatton et al. describe a general scaling law that relates total predator and prey biomass in terrestrial and aquatic animal communities (see the Perspective by Cebrian). They draw on data from many thousands of population counts of animal communities ranging from plankton to large mammals, across a wide range of biomes. They find a ubiquitous pattern of biomass scaling, which may suggest an underlying organization in ecosystems. It seems that communities follow systematic changes in structure and dynamics across environmental gradients. Science , this issue [10.1126/science.aac6284][1]; see also p. [1053][2] [1]: /lookup/doi/10.1126/science.aac6284 [2]: /lookup/doi/10.1126/science.aad0684

The coronal temperatures of low-mass main-sequence stars

Aims. We study the X-ray emission of low-mass main-sequence stars to derive a reliable general scaling law between coronal temperature and the level of X-ray activity.Methods. We collect ROSAT measurements of hardness ratios and X-ray luminosities for a large sample of stars to derive which stellar X-ray emission parameter is most closely correlated with coronal temperature. We calculate average coronal temperatures for a sample of 24 low-mass main-sequence stars with measured emission measure distributions (EMDs) collected from the literature. These EMDs are based on high-resolution X-ray spectra measured by XMM-Newton and Chandra . Results. We confirm that there is one universal scaling relation between coronal average temperature and surface X-ray flux, F X , that applies to all low-mass main-sequence stars. We find that coronal temperature is related to F X by T cor = 0.11 FX 0.26 , where T cor is in MK and F X is in erg s-1 cm-2 .

Confinement effects on an ultra-cold matter wave-packet by a square well impurity near the de-localization threshold: analytic solutions, scaling, and width properties

The determination of the maximum number of atoms and the density profile of an ultra-cold wave-packet, under confinement conditions by an attractive impurity near the de-localization threshold, have been an open problem in ultra-cold atom physics. In this work, we study the effect of a wave-guide impurity on an ultra-cold matter wave-packet at the threshold of de-localization. The impurity is modeled by a 1-D square well potential with depth V 0 and length 2R 0. Coupling of the square well potential to a contact impurity of strength β at the center is also considered. The time-independent non-linear Schrodinger equation describing a Bose-Einstein condensate at the delocalization threshold is exactly solved. The density profile, maximum non-linear coupling constant, g max, and maximum number of atoms, N max, prompt to be localized by the defect potential in the ground and first excited states are also reported. It is shown that g max and the density profiles become only functions of the reduced impurity size ξ = √V 0 R 0. It is also found that the first excited state at the threshold of de-localization exists only for ξ ≥ π/(2√2), always holding a lower number of atoms than the corresponding ground state for the same reduced impurity size. Also, the addition of a repulsive contact impurity leads to a non-linear coupling constant at the de-localization threshold lower than that of the square well potential. In spite of the non-linear character of the Gross-Pitaevskii equation, it is found that a general scaling-law holds for defects with the same ξ, related with the same g max, having the same reduced density profile in the quasi-free direction. We report the full width at half maximum for the wave-function and density profile, finding a large spread for small reduced confining conditions. Implications of these results for the determination of the wave-packet properties under confinement in atom chip and Bose-Einstein condensates are presented with the aim to motivate further experimental work.

Energy efficiency of adiabatic superconductor logic

Adiabatic superconductor logic (ASL), including adiabatic quantum-flux-parametron (AQFP) logic, exhibits high energy efficiency because its bit energy can be decreased below the thermal energy through adiabatic switching operations. In the present paper, we present the general scaling laws of ASL and compare the energy efficiency of ASL with those of other energy-efficient logics. Also, we discuss the minimum energy-delay product (EDP) of ASL at finite temperature. Our study shows that there is a maximum temperature at which the EDP can reach the quantum limit given by ħ/2, which is dependent on the superconductor material and the Josephson junction quality, and that it is reasonable to operate ASL at cryogenic temperatures in order to achieve an EDP that approaches ħ/2.

ON THE DIVERSITY OF MAGNETIC INTERACTIONS IN CLOSE-IN STAR-PLANET SYSTEMS

Magnetic interactions between close-in planets and their host star can play an important role in the secular orbital evolution of the planets, as well as the rotational evolution of their host. As long as the planet orbits inside the Alfv\'en surface of the stellar wind, the magnetic interaction between the star and the planet can modify the wind properties and also lead to direct angular momentum transfers between the two. We model these star-planet interactions using compressible magneto-hydrodynamic (MHD) simulations, and quantify the angular momentum transfers between the star, the planet, and the stellar wind. We study the cases of magnetized and non-magnetized planets and vary the orbital radius inside the Alfv\'en surface of the stellar wind. Based on a grid of numerical simulations, we propose general scaling laws for the modification of the stellar wind torque, for the torque between the star and the planet, and for the planet migration associated with the star-planet magnetic interactions. We show that when the coronal magnetic field is large enough and the star is rotating sufficiently slowly, the effect of the magnetic star-planet interaction is comparable to tidal effects and can lead to a rapid orbital decay.

Scaling laws to understand tidal dissipation in fluid planetary layers and stars

AbstractTidal dissipation is known as one of the main drivers of the secular evolution of planetary systems. It directly results from dissipative mechanisms that occur in planets and stars' interiors and strongly depends on the structure and dynamics of the bodies. This work focuses on the mechanism of viscous friction in stars and planetary layers. A local model is used to study tidal dissipation. It provides general scaling laws that give a qualitative overview of the different possible behaviors of fluid tidal waves. Furthermore, it highlights the sensitivity of dissipation to the tidal frequency and the roles played by the internal parameters of the fluid such as rotation, stratification, viscosity and thermal diffusivity that will impact the spins/orbital architecture in planetary systems.