Empirical Scaling Laws Research Articles

Exploring the inverse line-source scattering problem in dielectric cylinders with deep neural networks

Abstract This study presents a novel approach utilizing deep neural networks to
address the inverse line-source scattering problem in dielectric cylinders. By employing
Multi-layer Perceptron models, we intend to identify the number, positions, and
strengths of hidden internal sources. This is performed by using single-frequency
phased data, from limited measurements of real electric and real magnetic surface fields.
Training data are generated by solving corresponding direct problems, using an exact
solution representation. Through extended numerical experiments, we demonstrate
the efficiency of our approach, including scenarios involving noise, reduced sample
sizes, and fewer measurements. Additionally, we examine the empirical scaling laws
governing model performance and conduct a local analysis to explore how our neural
networks handle the inherent ill-posedness of the considered inverse problems.

Settling of two rigidly connected spheres

Laboratory experiments and particle-resolved simulations are employed to investigate the settling dynamics of a pair of rigidly connected spherical particles of unequal size. They yield a detailed picture of the transient evolution and the terminal values of the aggregate's orientation angle and its settling and drift velocities as functions of the aspect ratio and the Galileo number $Ga$ , which denotes the ratio of buoyancy and viscous forces acting on the aggregate. At low to moderate values of $Ga$ , the aggregate's orientation and velocity converge to their terminal values monotonically, whereas for higher $Ga$ -values the aggregate tends to undergo a more complex motion. If the aggregate assumes an asymmetric terminal orientation, it displays a non-zero terminal drift velocity. For diameter ratios much larger than one and small $Ga$ , the terminal orientation of the aggregate becomes approximately vertical, whereas when $Ga$ is sufficiently large for flow separation to occur, the aggregate orients itself such that the smaller sphere is located at the separation line. Empirical scaling laws are obtained for the terminal settling velocity and orientation angle as functions of the aspect ratio and $Ga$ for diameter ratios from 1 to 4 and particle-to-fluid density ratios from 1.3 to 5. An analysis of the accompanying flow field shows the formation of vortical structures exhibiting complex topologies in the aggregate's wake, and indicates the formation of a horizontal pressure gradient across the larger sphere, which represents the main reason for the emergence of the drift velocity.

The role of heterogeneous stress in earthquake cycle models of the Hikurangi-Kermadec subduction zone

Summary Seismic and tsunami hazard modelling and preparedness are challenged by uncertainties in the earthquake source process. Important parameters such as the recurrence interval of earthquakes of a given magnitude at a particular location, the probability of multi-fault rupture, earthquake clustering, rupture directivity and slip distribution are often poorly constrained. Physics-based earthquake simulators, such as RSQSim, offer a means of probing uncertainties in these parameters by generating long-term catalogues of earthquake ruptures on a system of known faults. The fault initial stress state in these simulations is typically prescribed as a single uniform value, which can promote characteristic earthquake behaviours and reduce variability in modelled events. Here, we test the role of spatial heterogeneity in the distribution of the initial stresses and frictional properties on earthquake cycle simulations. We focus on the Hikurangi-Kermadec subduction zone, which may produce Mw > 9.0 earthquakes and likely poses a major hazard and risk to Aotearoa New Zealand. We explore RSQSim simulations of Hikurangi-Kermadec subduction earthquake cycles in which we vary the rate and state coefficients (a and b). The results are compared with the magnitude-frequency distribution (MFD) of the instrumental earthquake catalogue and with empirical slip scaling laws from global earthquakes. Our results suggest stress heterogeneity produces more realistic and less characteristic synthetic catalogues, making them particularly well suited for hazard and risk assessment. We further find that the initial stress effects are dominated by the initial effective normal stresses, since the normal stresses evolve more slowly than the shear stresses. A heterogeneous stress model with a constant pore-fluid pressure ratio and a constant state coefficient (b) of 0.003 produces the best fit to MFDs and empirical scaling laws, while the model with variable frictional properties produces the best fit to earthquake depth distribution and empirical scaling laws. This model is our preferred initial stress state and frictional property settings for earthquake modelling of the Hikurangi-Kermadec subduction interface. Introducing heterogeneity of other parameters within RSQSim (e.g. friction coefficient, reference slip rate, characteristic distance, initial state variable, etc) could further improve the applicability of the synthetic earthquake catalogues to seismic hazard problems and form the focus of future research.

A kinematic method for generating earthquake sequences

Computational earthquake sequence models provide generative estimates of the time, location, and size of synthetic seismic events that can be compared with observed earthquake histories and assessed as rupture forecasts. Here we describe a three-dimensional probabilistic earthquake sequence model that produces slip event time series constrained across geometrically complex non-planar fault systems. This model is kinematic in nature, integrating the time evolution of geometric moment accumulation and release with empirical earthquake scaling laws. The temporal probability of event occurrence is determined from the time history of geometric moment integrated with short-term Omori-style rate decay following each earthquake achieving long-term time-averaged moment balance. Similarly, the net geometric moment monotonically controls the probability of event localization, and seismic events release geometric moment with spatially heterogeneous slip on three-dimensional non-planar fault surfaces. We use this model to generate a synthetic earthquake sequence on the Nankai subduction zone over a 1,250-year-long interval, including 700+ MW=5.5−8.5 coseismic events, with decadal-to-centennial scale quiescent intervals quasi-periodic great earthquake clusters followed by aftershock sequences.

Equilibrium shape of a bubble in a liquid-filled horizontal capillary

Bubbles in liquid-filled capillaries feature in many practical applications. Here we describe the equilibrium shape of a bubble in a horizontal capillary of circular cross section, as computed numerically using energy minimization. The data is presented in terms of empirical scaling laws for bubble extension along and perpendicular to the tube axis, over a large range of the ratio of cylinder to bubble diameter and Bond numbers. We also consider the limiting case of a bubble underneath a flat plate, for which approximate analytical solutions are available. Furthermore, we deduce an equation for the mean curvature of the gas–liquid interface and the variation of contact areas, the latter being of relevance also for estimating the wall drag forces of flowing bubbles.

Economically optimized design point of high-field stellarator power-plant

High temperature superconductors (HTSs) expand the design space of stellarator power-plants (PPs) toward high magnetic fields B, enabling compact major radii R. The present paper scans the space of B, R and other design parameters, finding solutions that are promising from a physics and engineering standpoint, while minimizing the capital cost of the PP and the levelized cost of fusion electricity. Similarly, it identifies minimum-cost design points for next-step burning plasma stellarator experiments of fusion gain 1<Q<10 . The study assumes advanced stellarator configurations of reduced aspect ratio, heated by neutral beam injection. Plasma-facing, flowing liquid metal (LM) walls protect it from high heat and neutron fluxes. The study relies on analytical first-principle calculations, and established zero-dimensional (0D) empirical scaling laws. Power flows are illustrated by Sankey diagrams. Plasma operating contours are used to determine the reactor’s start-up path. Sensitivity analyses are conducted to identify the most critical reactor parameters within physics, engineering and costing, quantifying their influence on the economics of the PPs. Such 0D study suggests that the assumed next generation HTS, flowing LM walls, and advances in compact plasma configurations could lead to an ignited stellarator PP of aspect ratio A∼4 , R⩽4 m, B > 9 T, and normalized plasma pressure β∼5% which would minimize both the cost of electricity and capital cost while achieving a net electric power of about 1 GW.

On the electron impact cross-section maxima for dissociative and non-dissociative single ionization of molecules and radicals

Determining absolute electron impact ionization cross-sections for atoms and molecules, whether through experimental or theoretical means, poses a formidable challenge and is typically limited to a narrow selection of species. In this paper, by using measured cross-sections and polarizability data, it was obtained empirical scaling laws for total single ionization and non-dissociative single ionization cross-section maximum of neutral molecules by collisions with electrons. It is found that the total single ionization cross-sections scale linearly with the target electric static polarizability, while the non-dissociate cross-sections exhibit a saturation effect for large target polarizabilities. This saturation effect is interpreted as the increasing role of fragmentation with polarizability.

Quantifying the energetic cost tradeoffs of photovoltaic pumping systems for Sub-Saharan African smallholder farms

As solar technology has matured, irrigation using photovoltaic pumping systems (PVPSs) has gained popularity in developing markets as an effective means to alleviate poverty and increase food security. Yet, there remains a barrier to adoption; the upfront costs of PVPSs pose a financial burden for many low-income farmers. In a PVPS, the capital cost of the solar array contributes a large portion of upfront system costs. The solar pump is the largest energy consumer in the system, thus its efficiency directly impacts the size and cost of the solar array. There is a limited quantitative understanding of how solar pump efficiency affects the capital cost of the solar array. This study presents a technoeconomic framework to directly quantify the impact of solar pump efficiency on the cost of the solar array in a PVPS, for a range of hydraulic operating conditions. New empirical efficiency scaling laws were created by characterizing the efficiencies of 4-inch multistage centrifugal borehole pumps and induction motors. The utility of the technoeconomic framework is demonstrated through a case study comparing solar pump architectures with motors of different efficiencies. Results indicate that, despite the increased motor cost, the use of high-efficiency motors in solar pumps may lead to an overall cost reduction in a PVPS. Counter to the conventional capital cost-driven process, this work demonstrates that an efficiency-driven design process could improve low-cost, solar-powered system design. Engineers and system designers can leverage the presented framework during the design process to make informed decisions to achieve more cost-effective PVPSs.

Electron Impact Ionization Cross-Section Maxima of Atoms

Using measured cross-sections and polarizability data, an empirical scaling law is extracted for the electron collision single-ionization cross-section maxima of neutral atoms. We found that the cross sections scale linearly with the target’s static polarizability. We confirm this observation using our present three-body classical trajectory Monte Carlo simulations.

Numerical Investigation of the Influence of Hydrodynamic Dispersion on Solutal Natural Convection

AbstractWe investigate numerically the effect of hydrodynamic dispersion on convective dissolution of carbon dioxide in saline aquifers. Solutions of the transport equations were used to describe the dissolution process in the aquifer and provide a systematic parametric analysis of the influence of dispersion on two important measures of convective dissolution, the wavenumber, and dissolution flux. The results suggest that dispersion decreases the dissolution rate and reduces the finger wavenumber. Based on the simulated results, new empirical scaling laws that predict the dissolution rate and wavenumber were developed. The application of the new laws to two storage sites shows that the currently available predictions overestimate the dissolution rates by ∼30%. We have identified some discrepancies between published scaling laws that were obtained for the dissolution rate. While most numerical studies identify a linear scaling, experimental investigations often suggest a sublinear behavior. Our findings resolve the controversy by suggesting that dispersion, which was not considered in these past numerical studies, is the reason for the apparent sublinear scaling.

Logarithmic versus Andrade's transient creep: Role of elastic stress redistribution

Creep is defined as time-dependent deformation and rupture processes taking place within a material subjected to constant applied stress smaller than its athermal, time-independent strength. This time dependence is classically attributed to the thermal activation of local deformation events. The phenomenology of creep is characterized by several ubiquitous but empirical rheological and scaling laws. We focus here on primary creep following the onset of loading, for which a power law decay of the strain rate is observed, $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\varepsilon}}\ensuremath{\sim}{t}^{\ensuremath{-}p}$, with the exponent $p$ varying between $\ensuremath{\simeq}0.4$ and 1, this upper bound defining the so-called logarithmic creep. Although this phenomenology is known for more than a century, the physical origin of Andrade-like $(p&lt;1)$ creep remains unclear and debated. Here we show that $p&lt;1$ values arise from the interplay between thermal activation and elastic stress redistribution. The latter stimulates creep dynamics from a shortening of waiting times between successive events, is associated to material damage and, possibly, at high temperature and/or stresses, gives rise to avalanches of deformation events.

Energetics of spreading droplets and role of capillary waves at low Weber numbers below 10

In this study, we investigate the energy conversion and dissipation mechanisms of spreading droplets on a solid surface at a low Weber number regime, which neither conventional energy-balance-based theories nor empirical scaling laws can completely explain. The energetic analysis presented in this study shows that on a hydrophilic surface, the actual primary energy source driving the spreading process is the initial surface energy not the initial kinetic energy. The conventional energy-balance-based approaches are found to be valid only for the spreading process on a hydrophobic surface. Particular attention is also paid to the roles of the capillary waves. The capillary waves are found to play significant roles in all of the important flow physics, that is, the interfacial structure, the oscillatory motions and the rapid collapse of the liquid film, the onset of the viscous regime, and the energy loss mechanism. It is also shown that the energy dissipation caused by the capillary-wave-induced phenomena can be estimated to be 25%–35% and 55%–65% of the total energy loss for a hydrophilic and a hydrophobic surface, respectively, at the low Weber number regime.

Nowcasting earthquakes in Iran: A quantitative analysis of earthquake hazards through natural times

Despite the extremely complex earthquake generation mechanism in a driven nonlinear threshold system, simple empirical scaling laws apply to the collective behavior of earthquakes in a network of geological faults. The physical interpretation of these properties and associated relations exhibit a wealth of information to study earthquake processes and consequent earthquake hazards in a defined area. In this article, an area-source-based earthquake nowcasting method is implemented to statistically determine the current state of earthquake hazards at several cities of Iran through the formulation of a discrete time-series of cumulative interevent counts, known as natural times. Use of natural times to mark the evolution of the seismic process, rather than the passage of clock time, essentially provides spatiotemporal and clustering invariable properties. Statistical inference of natural time counts corresponding to M ≥ 6.0 events results in an earthquake potential score (%) as Ahvaz (94), Hamadan (50), Isfahan (98), Karaj (76), Kerman (78), Kermanshah (73), Mashhad (40), Qom (92), Rasht (21), Shiraz (98), Tabriz (45), Tehran (78), Urmia (51), and Zahedan (53). These nowcast values provide a snapshot of the current progression of a city in its earthquake cycle of large-sized events and thus facilitate better decision-making, city-planning, and earthquake awareness, leading to an efficient seismic risk reduction strategy in the densely populated study region.

Amplification effect of near-field ground motion around deep tunnels based on finite fracturing seismic source model

Dynamic failure of rock masses around deep tunnels, such as fault-slip rockburst and seismic-induced collapse, can pose a significant threat to tunnel construction safety. One of the most significant factors that control the accuracy of its risk assessment is the estimation of the ground motion around a tunnel caused by seismicity events. In general, the characteristic parameters of ground motion are estimated in terms of empirical scaling laws. However, these scaling laws make it difficult to accurately estimate the near-field ground motion parameters because the roles of control factors, such as tunnel geometry, damage zone distribution, and seismic source parameters, are not considered. For this, the finite fracturing seismic source model (FFSSM) proposed in this study is used to simulate the near-field ground motion characteristics around deep tunnels. Then, the amplification effects of ground motion caused by the interaction between seismic waves and deep tunnels and corresponding control factors are studied. The control effects of four factors on the near-field ground motion amplification effect are analyzed, including the main seismic source wavelength, tunnel span, tunnel shape, and range of damage zones. An empirical formula for the maximum amplification factor ( α m ) of the near-field ground motion around deep tunnels is proposed, which consists of four control factors, i.e. the wavelength control factor ( F λ ), tunnel span factor ( F D ), tunnel shape factor ( F s ) and excavation damage factor ( F d ). This empirical formula provides an easy approach for accurately estimating the ground motion parameters in seismicity-prone regimes and the rock support design of deep tunnels under dynamic loads.

A Method to Generate Initial Fault Stresses for Physics-Based Ground-Motion Prediction Consistent with Regional Seismicity

ABSTRACTNear-field ground motion is the major blind spot of seismic hazard studies, mainly because of the challenges in accounting for source effects. Initial stress heterogeneity is an important component of physics-based approaches to ground-motion prediction that represents source effects through dynamic earthquake rupture modeling. We hypothesize that stress heterogeneity on a fault primarily originates from past background seismicity. We develop a new method to generate stochastic stress distributions as a superposition of residual stresses left by the previous ruptures that are consistent with regional distributions of earthquake size and hypocentral depth. We validate our method on Mw 7 earthquake models suitable for California by obtaining a satisfactory agreement with empirical earthquake scaling laws and ground-motion prediction equations. To avoid the excessive seismic radiation produced by dynamic models with abrupt arrest at preset rupture borders, we achieve spontaneous rupture arrest by incorporating a growth of fracture energy as a function of hypocentral distance. Our analyses of rupture and ground motion reveal particular signatures of the initial stress heterogeneity: rupture can locally propagate at supershear speed near the highly stressed areas; the position of high-stress and low-stress areas due to initial stress heterogeneity determines how the peak ground-motion amplitudes and polarization spatially vary along the fault, as low-stress areas slow down the rupture and decrease stress drop. We also find that the medium stratification in the fault zone amplifies fault slip and consequent ground motion, which requires understanding the interaction between site effects and rupture dynamics. Our approach advances our understanding of the relations between dynamic features of earthquake ruptures and the statistics of regional seismicity, and our capability to integrate information about regional seismicity into near-field ground-motion prediction.

Performance Analysis of an Electron Cyclotron Resonance Thruster with Various Propellants

The performance of an electron cyclotron resonance thruster is analyzed for operation with argon, krypton, xenon, and water vapor to understand how mass utilization efficiency and frozen flow losses vary across propellant type. The device was operated from 20 to 220 W for flow rates of 0.06–0.4 mg/s. Thrust performance is measured using an inverted pendulum thrust stand, and plasma characteristics are measured using a retarding potential analyzer, ExB probe, Langmuir probe, and emissive probe. Specific impulse is generally found to decrease as the ratio of mass flow rate over power () increases. Probe measurements indicate that this trend is attributed to a combination of lower propellant mass utilization and decreased electron temperatures. The mass utilization efficiency is found to increase with the ratio of thruster length to ionization mean free path for all propellants; however, the data do not support existing theoretical scaling laws, and a more accurate empirical scaling law is proposed. The decrease in electron temperature with also drives an increase in the relative frozen flow losses, which are found to be about a factor of two higher for water propellant. Multiply charged ions did not constitute a significant fraction of the plume for the atomic species. Mass utilization efficiency and frozen flow losses describe the trends in the thrust efficiency but not the overall magnitude, which suggests that microwave coupling and diffusion to the walls are dominant loss processes.

Slow spin dynamics of cluster spin-glass spinel Zn(FeRu x )2O4: role of Jahn–Teller active spin-1/2 Cu2+ ions at B-sites

We report the slow spin dynamics of cluster spin-glass (SG) spinel Zn(FeRu x )2O4 by means of detailed -magnetization and -susceptibility studies combined with the heat capacity analysis. Two specific compositions (x = 0.5, 0.75) have been investigated in detail along with the substitution of Jahn–Teller (JT) active spin-1/2 Cu2+ ions at B-sites. Measurements based on the frequency and temperature dependence of -susceptibility () and the subsequent analysis using the empirical scaling laws such as: (a) Vogel–Fulcher law and (b) Power law reveal the presence of cluster SG state below the characteristic freezing temperature (17.77 K (x = 0.5) and 14 K (x = 0.75)). Relaxation dynamics of both the compositions follow the non-mean field de Almeida–Thouless (AT)-line approach , with an ideal value of φ = 3. Nevertheless, the analysis of temperature dependent high field -susceptibility, (, T) provides evidence for Gabay–Toulouse type mixed-phase (coexistence of SG and ferrimagnetic (FiM)) behaviour. Further, in the case of Cu0.2Zn0.8FeRuO4 system, slowly fluctuating magnetic clusters persist even above the short-range FiM ordering temperature () and their volume fraction vanishes completely across ∼6. This particular feature of the dynamics has been very well supported by the time decay of the thermoremanent magnetization and heat-capacity studies. We employed the high temperature series expansion technique to determine the symmetric exchange coupling () between the spins which yields eV for Cu0.2Zn0.8FeRuO4 representing the dominant intra-sublattice ferromagnetic interactions due to the dilute incorporation of the JT active Cu2+ ions. However, the antiferromagnetic coupling is predominant in ZnFeRuO4 and Cu0.2Zn0.8Fe0.5Ru1.5O4 systems. Finally, we deduced the magnetic phase diagram in the plane using the characteristic parameters obtained from the field variations of both - and -magnetization measurements.

Multiple photodetachment of oxygen anions via K -shell excitation and ionization: Direct double-detachment processes and subsequent deexcitation cascades

Experimental cross sections for m-fold photodetachment (m=2-5) of oxygen anions via K-shell excitation and ionization were measured in the photon-energy range of 525-1500 eV using the photon-ion merged-beams technique at a synchrotron light source. The measured cross sections exhibit clear signatures of direct double detachment, including double K-hole creation. The shapes of the double-detachment cross sections as a function of photon energy are in accord with Pattard's [J. Phys. B 35, L207 (2002)] empirical scaling law. We have also followed the complex deexcitation cascades that evolve subsequently to the initial double-detachment events by systematic large-scale cascade calculations. The resulting theoretical product charge-state distributions are in good agreement with the experimental findings.

Pulse temporal scaling of LIDT for anti-reflective coatings deposited on lithium triborate crystals.

Anti-reflective (AR) coatings minimize photon losses of optics when it comes to the transmission of light, thus, are broadly used for imaging and laser applications. However, the maximum output power in high-power lasers is limited by the so-called laser-induced damage threshold (LIDT) parameter of optical elements. Often AR coated nonlinear crystals are responsible for such limitations, however, LIDT data is rather scarce. Thus, only limited understanding about LIDT pulse temporal scaling laws for AR coatings exists, which also lacks the specificity about fatigue effect of distinct failure modes. To expand the present knowledge four identical lithium triborate (LBO) crystals were prepared. Each crystal had one side coated with the AR@1064+532 nm coating and the opposite side coated with the AR@355 nm coating. Multiple LIDT tests were then conducted following 1-on-1 and S-on-1 testing protocols at UV and IR wavelengths while varying laser pulse duration. Empirical scaling laws are then investigated for different failure modes and later interpreted using a numerical model.

Scaling characteristics of the hull girder's ultimate strength subjected to the combined hogging moment and bottom lateral pressure: An empirically modified scaling criterion

The ultimate strength of the ship hull girder under combined loads is closer to the load-carrying capacity during the actual sailing for considering the negative effect of the secondary load in some cases. Scaled models are designed to represent the prototype in ultimate strength experiments. To study the effect of the bottom lateral pressure on the scaled hull girder under combined loads thoroughly, a series of hull girders of a 10,000TEU container ship under different scale combinations of geometric length and plate thickness are analyzed. The relevant changes in the characteristics of ultimate strength and collapse behaviors caused by bottom lateral pressure are investigated. Results show that the ultimate hogging moment predicted by the traditional or the empirical scaling law proposed in the reference is significantly different from that obtained by numerical analysis when the scale ratio of the plate thickness is much smaller than the geometric scale ratio for ignoring the significant effect of the bottom lateral pressure. Correspondingly, an empirical scaling criterion is proposed to improve the accuracy of the converting process of the ultimate strength between scaled models and the full-scale prototype. Finally, the applicability of the proposed scaling criterion is verified by numerical results of a series of simplified hull girder models.