General Scaling Laws Research Articles

Prediction of Volumetric, Specific Energy and Power Density of High-Capacity Thin Layer Battery Electrodes By Using a Novel Multi-Scale Modelling Framework

In this work, a novel modelling approach is presented, which is able to directly relate the microstructure of the active layer of thin-film batteries to the battery cell macroscopic behaviour. A general pore-scale model has been developed by mimicking the layer fabrication process. Five different electrode structures were reconstructed taking into account the interaction between the deposited particles during the layer formation. In each simulation 108particles were deposited with 5 different sticking rules. Fig.1. captures the beginning of the layer formation. Fig.1a) shows weak interaction between the particles, i.e. the layer is mainly governed by random deposition, and b) strong attractive forces, i.e. every particle sticks to the nearest neighbour. The different colours correspond to the deposition of 1000 particles, while white spaces correspond to open pores.Instead of simulating each type of reconstructed layer, the renormalization group theory is applied to analyse the effect of thickness on the properties of the active layer. It is shown, that in spite of the very different morphology, all these reconstructed layers belong to the same universality class and can be described by a general non-linear scaling law. The simulation results imply that porosity and specific surface area depend on the thickness of the electrode, which is not commonly considered in battery models. The general expression derived is incorporated into a macrohomogeneous model and the charge-discharge performance is simulated. The volumetric and specific energy and power densities are calculated and finally, the simulation results are compared with measured data at different thicknesses.The developed method offers an efficient tool not only to predict, but to design high power and high capacity batteries for automotive applications and/or scale down dimensions for microelectronics and MEMS. It can be used for fast screening of novel manufacturing technologies as well as for deeper understanding of the effect of microscale structure on the macroscopic behaviour of battery cells.

Prediction model of flow duct constriction noise

The scaling law for aerodynamic dipole type of sound from constrictions in low speed flow ducts by Nelson and Morfey is revisited. A summary of earlier published results using this scaling law is presented together with some new data. Based on this, an effort to find a general scaling law for the sound power for components with both distinct and non-distinct flow separation points are made. Special care is taken to apply the same scaling to all data based on the pressure drop. Results from both rectangular and circular ducts, duct flow velocities from 2 to 120m/s and sound power measurements made both in ducts and in reverberation chambers are presented. The computed sound power represents the downstream source output in a reflection free duct. In particular for the low frequency plane wave range strong reflections from e.g. openings can affect the sound power output. This is handled by reformulating the Nelson and Morfey model in the form of an active acoustic 2-port. The pressure loss information needed for the semi-empirical scaling law can be gained from CFD simulations. A method using Reynold Average Navier Stokes (RANS) simulations is presented, where the required mesh quality is evaluated and estimation of the dipole source strength via the use of the pressure drop is compared to using the turbulent kinetic energy.

Electron density compression and oscillating effects on laser energy absorption in overdense plasma targets.

An analytical model for energy absorption during the interaction of an ultrashort, ultraintense laser with an overdense plasma is proposed. Both the compression effect of the electron density profile and the oscillation of the electron plasma surface are self-consistently included, which exhibit significant influences on the laser energy absorption. Based on our model, the general scaling law of the compression effect depending on laser strength and initial density is derived, and the temporal variation of the laser absorption due to the boundary oscillating effect is presented. It is found that due to the oscillation of the electron plasma surface, the laser absorption rate will vibrate periodically at ω or 2ω frequency for the p-polarized and s-polarized laser, respectively. The effect of plasma collision on the laser absorption has also been investigated, which shows a considerable rise in absorption with increasing electron-ion collision frequency for both polarizations.

Reply to comments on “Surname distribution in population genetics and in statistical physics”

I can only agree with almost all the observations made in the Comments, and I will only stress some points complementing my review or suggesting new promising lines of investigation. I will also quote the most relevant recent contributions, missing in the review and suggested by the comments. Baek and Kim correctly point out the heterogeneity of surname distributions, and suggest that in general scaling laws must be seen as the most random outcome under certain constraints; hence the analysis should focus on the constraints and not on the specific dynamics [1]. In the RG approach this would correspond to focussing on the relevant field operator associated with the introduction of new surnames. Boattini and Pettner offer a convincing explaination of the relative decline of biodemography in the last decade (based especially on the advent of easier end cheaper technologies for DNA typing, and partially on the difficulties raised by polyphyletism). However they stress that there is still much interest in comparing surnames and Y-chromosome haplotypes and indicate the existence of several possible directions for a fruitful interdisciplinary approach (among them anthropology, forensics [2], genetic genealogy [3] and especially linguistics [4]). Maruvka and Shnerb underline the connection of the statistical approach to surname studies with many other developments, not only in population dymamics, but also in the theory of scale-free networks. However they raise a number of technical problems that should be the object of further analysis, among them the limiting assumptions of fixed size or fixed growth rate of the population, and the difficult comparison of theoretical models with empirical data generated by sampling [5]. As a side comment I would like to stress that the application of surname statistics to the study of nepotism in the academia has been the object also of one of the references quoted in my review [6]. Also Manrubia stresses the importance of shifting the attention from the commonalities to the dissimilarities. She also underlines the relevance of surname patterns to solve questions in history and anthropology (migratory phenomena, transmission of cultural traits) and suggests the possibility of deriving a ”surname phylogenies” in analogy with linguistic phylogenies, and exploring second and higher order contributions to the composition of human groups. Zanette emphasizes the problems raised by polyphyletism, and suggests an extensive analysis of this aspect of surname dynamics, as well as a better exploration of the mechanisms of surname mutation, possibly in connection with the study of linguistic evolution. He also stresses the lack of a rigorous analysis of the mutual compatibility of the theoretical methods applied to the study of surname dynamics. To this purpose I would like to notice that one of the aims of my review was to show that many of the results presented in the literature are substantially equivalent since they basically derive from different representations of the same Yule-Simon process.

Stability of a Unitary Bose Gas

We study the stability of a thermal (39)K Bose gas across a broad Feshbach resonance, focusing on the unitary regime, where the scattering length a exceeds the thermal wavelength λ. We measure the general scaling laws relating the particle-loss and heating rates to the temperature, scattering length, and atom number. Both at unitarity and for positive a<<λ we find agreement with three-body theory. However, for a<0 and away from unitarity, we observe significant four-body decay. At unitarity, the three-body loss coefficient, L(3) proportional λ(4), is 3 times lower than the universal theoretical upper bound. This reduction is a consequence of species-specific Efimov physics and makes (39)K particularly promising for studies of many-body physics in a unitary Bose gas.

Atomistic simulations, mesoscopic modeling, and theoretical analysis of thermal conductivity of bundles composed of carbon nanotubes

The propensity of carbon nanotubes (CNTs) to self-organize into continuous networks of bundles has direct implications for thermal transport properties of CNT network materials and defines the importance of clear understanding of the mechanisms and scaling laws governing the heat transfer within the primary building blocks of the network structures—close-packed bundles of CNTs. A comprehensive study of the thermal conductivity of CNT bundles is performed with a combination of non-equilibrium molecular dynamics (MD) simulations of heat transfer between adjacent CNTs and the intrinsic conductivity of CNTs in a bundle with a theoretical analysis that reveals the connections between the structure and thermal transport properties of CNT bundles. The results of MD simulations of heat transfer in CNT bundles consisting of up to 7 CNTs suggest that, contrary to the widespread notion of strongly reduced conductivity of CNTs in bundles, van der Waals interactions between defect-free well-aligned CNTs in a bundle have negligible effect on the intrinsic conductivity of the CNTs. The simulations of inter-tube heat conduction performed for partially overlapping parallel CNTs indicate that the conductance through the overlap region is proportional to the length of the overlap for CNTs and CNT-CNT overlaps longer than several tens of nm. Based on the predictions of the MD simulations, a mesoscopic-level model is developed and applied for theoretical analysis and numerical modeling of heat transfer in bundles consisting of CNTs with infinitely large and finite intrinsic thermal conductivities. The general scaling laws predicting the quadratic dependence of the bundle conductivity on the length of individual CNTs in the case when the thermal transport is controlled by the inter-tube conductance and the independence of the CNT length in another limiting case when the intrinsic conductivity of CNTs plays the dominant role are derived. An application of the scaling laws to bundles of single-walled (10,10) CNTs reveals that the transition from inter-tube-conductance-dominated to intrinsic-conductivity-dominated thermal transport in CNT bundles occurs in a practically important range of CNT length from ∼20 nm to ∼4 μm.

Normal conducting linac designs for low beam loading

To drive future X-ray FELs, normal-conducting linacs with a wide range of rf are being considered. In this paper, we present accelerator structure and high power rf system designs at three rf (2.856GHz, 5.712GHz and 11.424GHz) that are optimized for single bunch and multi-bunch linac operation with very low beam loading. General scaling laws for the main linac parameters are derived to serve as guidelines to optimize such linacs at other frequencies. The linac costs at the three rf are also discussed. High rf linacs are shown to provide compact, low cost and reasonably efficient drivers for X-ray FELs.

A scaling approach for high-frequency vibration analysis of line-coupled plates

A scaling approach is proposed for the vibration analysis of line-coupled plates at high frequencies. It extends earlier scaling approaches for an isolated system to coupled systems. Based on the power flow balance in the plate assembly, a general scaling law is derived and a scaled model is built accordingly. Due to the dynamic similitude in a statistical sense, the scaled model is able to simulate the dynamics of the original system at high frequencies. Numerical examples validate the efficiency of the approach and suggest the application of finite element methods in the high-frequency vibration analysis.

Basic investigations of electrostatic turbulence and its interaction with plasma and suprathermal ions in a simple magnetized toroidal plasma

Progress in basic understanding of turbulence and its influence on the transport both of the plasma bulk and of suprathermal components is achieved in the TORPEX simple magnetized torus. This configuration combines a microwave plasma production scheme with a quasi-equilibrium generated by a toroidal magnetic field, onto which a small vertical component is superimposed, simulating a simplified form of tokamak scrape-off layers. After having clarified the formation of blobs in ideal interchange turbulence, TORPEX experiments elucidated the mechanisms behind the blob motion, with a general scaling law relating their size and speed. The parallel currents associated with the blobs, responsible for the damping of the charge separation that develops inside them, hence determining their cross-field velocity, have been measured. The blob dynamics is influenced by creating convective cells with biased electrodes, arranged in an array on a metal limiter. Depending on the biasing scheme, radial and vertical blob velocities can be varied. Suprathermal ion transport in small-scale turbulence is also investigated on TORPEX. Suprathermal ions are generated by a miniaturized lithium source, and are detected using a movable double-gridded energy analyser. We characterize vertical and radial spreading of the ion beam, associated with the ideal interchange-dominated plasma turbulence, as a function of the suprathermal ion energy and the plasma temperature. Experimental results are in good agreement with global fluid simulations, including in cases of non-diffusive behaviour. To investigate the interaction of plasma and suprathermal particles with instabilities and turbulence in magnetic configurations of increasing complexity, a closed field line configuration has recently been implemented on TORPEX, based on a current-carrying wire suspended in the vacuum chamber. First measurements indicate the creation of circular symmetric profiles centred on the magnetic axis, and instabilities driven in the region of strong gradients, with a strong ballooning character.

Constriction Resistance and Current Crowding in Vertical Thin Film Contact

The constriction resistance and the current flow pattern are calculated analytically in a vertical thin film contact in which the thin film base is an equipotential surface. Both Cartesian and cylindrical thin film contacts are studied. The resistivities and the geometric dimensions in the individual contact members may assume arbitrary values. General scaling laws are constructed for the constriction resistance for arbitrary resistivity ratios and geometric aspect ratios. The analytic solutions are validated using a simulation code. Current crowding at the edges is displayed. In the limit of small film thickness, we show that current crowding in the vertical contact is far less serious than the current crowding in the horizontal contact. The data show that the normalized constriction resistance depends predominantly on the geometry of the thin film, but is relatively insensitive to the height and to the resistivity of the member with which the thin film is in contact.

Entanglement in permutation symmetric states, fractal dimensions, and geometric quantum mechanics

We study the von Neumann and Rényi bipartite entanglement entropies in the thermodynamic limit of many-body quantum states with spin-s sites that possess full symmetry under exchange of sites. It turns out that there is essentially a one-to-one correspondence between such thermodynamic states and probability measures on CP2s. Let a measure be supported on a set of possibly fractal real dimension d with respect to the Study–Fubini metric of CP2s. Let m be the number of sites in a subsystem of the bipartition. We give evidence that in the limit m → ∞, the entanglement entropy diverges like (d/2)logm. Further, if the measure is supported on a submanifold of CP2s and can be described by a density f with respect to the metric induced by the Study–Fubini metric, we give evidence that the correction term is simply related to the entropy associated with f: the geometric entropy of geometric quantum mechanics. This extends results obtained by the authors in a recent letter where the spin- case was considered. Here we provide more examples as well as detailed accounts of the ideas and computations leading to these general results. For special choices of the state in the spin-s situation, we recover the scaling behaviour previously observed by Popkov et al, showing that their result is but a special case of a more general scaling law.

THREE-DIMENSIONAL ATMOSPHERIC CIRCULATION MODELS OF HD 189733b AND HD 209458b WITH CONSISTENT MAGNETIC DRAG AND OHMIC DISSIPATION

We present the first three-dimensional circulation models for extrasolar gas giant atmospheres with geometrically and energetically consistent treatments of magnetic drag and ohmic dissipation. Atmospheric resistivities are continuously updated and calculated directly from the flow structure, strongly coupling the magnetic effects with the circulation pattern. We model the hot Jupiters HD 189733b (Teq \approx 1200 K) and HD 209458b (Teq \approx 1500 K) and test planetary magnetic field strengths from 0 to 30 G. We find that even at B = 3 G the atmospheric structure and circulation of HD 209458b are strongly influenced by magnetic effects, while the cooler HD 189733b remains largely unaffected, even in the case of B = 30 G and super-solar metallicities. Our models of HD 209458b indicate that magnetic effects can substantially slow down atmospheric winds, change circulation and temperature patterns, and alter observable properties. These models establish that longitudinal and latitudinal hot spot offsets, day-night flux contrasts, and planetary radius inflation are interrelated diagnostics of the magnetic induction process occurring in the atmospheres of hot Jupiters and other similarly forced exoplanets. Most of the ohmic heating occurs high in the atmosphere and on the day side of the planet, while the heating at depth is strongly dependent on the internal heat flux assumed for the planet, with more heating when the deep atmosphere is hot. We compare the ohmic power at depth in our models, and estimates of the ohmic dissipation in the bulk interior (from general scaling laws), to evolutionary models that constrain the amount of heating necessary to explain the inflated radius of HD 209458b. Our results suggest that deep ohmic heating can successfully inflate the radius of HD 209458b for planetary magnetic field strengths of B \geq 3 - 10 G.

A Concept Model about Allometric Scaling of Hierarchical Energy Flow through Plant Biosystems

Ecologists have long sought a general metabolic scaling law (e.g., the 3/4 power law), although the size-independent mass-special metabolic ratemay have been selected for over evolutionary time. Here, we outline four hierarchical energy processes along the path of energy flow. These processes are represented as the scaling exponents of mass-dependent energy flow (e.g., a 1/4-scaling rule for individuals and a 1/3-scaling rule for populations). Individuals and populations have evolved as the conduits of energy flow. Interestingly, the mass-dependent hierarchical energy flow can help explain the development of a tree population. Our theory highlights that mass-dependent hierarchical energy flow may act as a metabolic integrator and suggests an energetic explanation of the evolution of plant biosystems from the individual to the community level.

Scaling of layer spacing of charged particles under slit-pore confinement: an effect of concentration or of effective particle diameter?

This paper tests the generality of the scaling law for layer spacing of charged particles under confinement and resolves the established contradictions in the literature. The present determined layer spacings λ, also called the wavelength of oscillatory force, by colloidal probe atomic force microscopy are compared to previously obtained ones, Δh, also called step size, by using a thin film pressure balance. For charged particles, e.g. silica nanoparticles and micelles of anionic surfactant, the layer spacing under confinement is found to depend solely on the particle number density ρ in the relation λ (or Δh) =ρ−1/3. The previous description for the layer spacing using the effective particle diameter 2(R + κ−1) is not general and only applicable at specific conditions of particle volume fraction and ionic strength. We claim that when particles are dominated by electrostatic repulsion and in a low pressure reservoir, ρ−1/3 is a general scaling law for layer spacing of particles, which indicates that particles under confinement are still randomly distributed in a fluid-like manner as they are in bulk. As a side-effect an equation to obtain the ionic strength I of colloidal suspension from measured conductivity is established. Ionic strength I is needed to determine the values for Debye length κ−1, which are in very good agreement with the theoretical ones.

Onset of chaotic phase synchronization in complex networks of coupled heterogeneous oscillators

Existing studies on network synchronization focused on complex networks possessing either identical or nonidentical but simple nodal dynamics. We consider networks of both complex topologies and heterogeneous but chaotic oscillators, and investigate the onset of global phase synchronization. Based on a heuristic analysis and by developing an efficient numerical procedure to detect the onset of phase synchronization, we uncover a general scaling law, revealing that chaotic phase synchronization can be facilitated by making the network more densely connected. Our methodology can find applications in probing the fundamental network dynamics in realistic situations, where both complex topology and complicated, heterogeneous nodal dynamics are expected.

Extended graphynes: simple scaling laws for stiffness, strength and fracture

The mono-atomistic structure and chemical stability of graphene provides a promising platform to design a host of novel graphene-like materials. Using full atomistic first-principles based ReaxFF molecular dynamics, here we perform a systematic comparative study of the stability, structural and mechanical properties of graphynes - a variation of the sp(2) carbon motif wherein the characteristic hexagons of graphene are linked by sp(1) acetylene (single- and triple-bond) carbyne-like chains. The introduction of acetylene links introduces an effective penalty in terms of stability, elastic modulus (i.e., stiffness), and failure strength, which can be predicted as a function of acetylene repeats, or, equivalently, lattice spacing. We quantify the mechanical properties of experimental accessible graphdiyne, with a modulus on the order of 470 to 580 GPa and a ultimate strength on the order of 36 GPa to 46 GPa (direction dependent). We derive general scaling laws for the cumulative effects of additional acetylene repeats, formulated through a simple discrete spring-network framework, allowing extrapolation of mechanical performance to highly extended graphyne structures. Onset of local tensile buckling results in a transitional regime characterized by a severe reduction of strength (ultimate stress), providing a new basis for scaling extended structures. Simple fracture simulations support the scaling functions, while uncovering a "two-tier" failure mode for extended graphynes, wherein structural realignment facilitates stress transfer beyond initial failure. Finally, the specific modulus and strength (normalized by areal density) is found to be near-constant, suggesting applications for light-weight, yet structurally robust molecular components.

Turbulent flow in a machine honed rough pipe for large Reynolds numbers: General roughness scaling laws

An alternate inner wall variable, for flow over a transitional rough pipe surface, is defined as the ratio of normal coordinate measured above the mean roughness level to the wall roughness scale. The Reynolds equations for mean turbulent flow in a transitional rough pipe, in two layers (inner and outer) are considered. The predictions of the mean velocity and friction factor in fully developed turbulent flow in a rough pipe flow, presented here, covers all types of roughness. The data for a particular case of the machine honed Princeton superpipe roughness, analogous to inflectional type roughness of Nikuradse, is presented, as two expressions using our roughness scale. The velocity profile and friction factor, on a transitional rough wall, are shown to be governed by the new log laws, which are explicitly independent of the transitional wall roughness. Further, the inflectional roughness has also been connected with geometric roughness parameters; like, arithmetic mean roughness, mean peak to valley heights roughness, root mean square (rms), roughness based on texture measure; and the friction factor implicit and approximate explicit formulas have also been proposed. In entire transition region between fully smooth and fully rough wall, monotonic roughness of Colebrook (Moody Chart) over estimaton the friction factor when compared with present inlectional roughness.

Constructing arbitrary steane code single logical qubit fault-tolerant gates

We present a simple method for constructing optimal fault-tolerant approximations of arbitrary unitary gates using an arbitrary discrete universal gate set. The method presented is numerical and scales exponentially with the number of gates used in the approximation. However, for the specific case of arbitrary single-qubit gates and the fault-tolerant gates permitted by the concatenated 7-qubit Steane code, we find gate sequences sufficiently long and accurate to permit the fault-tolerant factoring of numbers thousands of bits long. A general scaling law of how rapidly these fault-tolerant approximations converge to arbitrary single-qubit gates is also determined.

Constructing arbitrary Steane code single logical qubit fault-tolerant gates

We present a simple method for constructing optimal fault-tolerant approximations of arbitrary unitary gates using an arbitrary discrete universal gate set. The method presented is numerical and scales exponentially with the number of gates used in the approximation. However, for the specific case of arbitrary single-qubit gates and the fault-tolerant gates permitted by the concatenated 7-qubit Steane code, we find gate sequences sufficiently long and accurate to permit the fault-tolerant factoring of numbers thousands of bits long. A general scaling law of how rapidly these fault-tolerant approximations converge to arbitrary single-qubit gates is also determined.

The rank-size scaling law and entropy-maximizing principle

The rank-size regularity known as Zipf’s law is one of the scaling laws and is frequently observed in the natural living world and social institutions. Many scientists have tried to derive the rank-size scaling relation through entropy-maximizing methods, but they have not been entirely successful. By introducing a pivotal constraint condition, I present here a set of new derivations based on the self-similar hierarchy of cities. First, I derive a pair of exponent laws by postulating local entropy maximizing. From the two exponential laws follows a general hierarchical scaling law, which implies the general form of Zipf’s law. Second, I derive a special hierarchical scaling law with the exponent equal to 1 by postulating global entropy maximizing, and this implies the pure form of Zipf’s law. The rank-size scaling law has proven to be one of the special cases of the hierarchical scaling law, and the derivation suggests a certain scaling range with the first or the last data point as an outlier. The entropy maximization of social systems differs from the notion of entropy increase in thermodynamics. For urban systems, entropy maximizing suggests the greatest equilibrium between equity for parts/individuals and efficiency of the whole.