Fundamental Scaling Laws Research Articles

Fundamental scaling laws of water-window X-rays from free-electron-driven van der Waals structures

Fundamental scaling laws of water-window X-rays from free-electron-driven van der Waals structures

Absorption and scattering limits of silicon nitride integrated photonics in the visible spectrum.

Visible-light photonic integrated circuits (PICs) promise scalability for technologies such as quantum information, biosensing, and scanning displays, yet extending large-scale silicon photonics to shorter wavelengths has been challenging due to the higher losses. Silicon nitride (SiN) has stood out as the leading platform for visible photonics, but the propagation losses strongly depend on the film's deposition and fabrication processes. Current loss measurement techniques cannot accurately distinguish between absorption and surface scattering, making it difficult to identify the dominant loss source and reach the platform's fundamental limit. Here we demonstrate an ultra-low loss, high-confinement SiN platform that approaches the limits of absorption and scattering across the visible spectrum. Leveraging the sensitivity of microresonators to loss, we probe and discriminate each loss contribution with unparalleled sensitivity, and derive their fundamental limits and scaling laws as a function of wavelength, film properties and waveguide parameters. Through the design of the waveguide cross-section, we show how to approach the absorption limit of the platform, and demonstrate the lowest propagation losses in high-confinement SiN to date across the visible spectrum. We envision that our techniques for loss characterization and minimization will contribute to the development of large-scale, dense PICs that redefine the loss limits of integrated platforms across the electromagnetic spectrum.

Computer Interface for Electroluminescence (EL)

The goal of Computer aided device start from the physical description of integrated circuit devices, considering both the physical configuration and related device properties and build the link between the broad range of physics and electrical behavior models that support circuit design. Physics-based modeling of devices, is distributed and lumped form is an essential part of the IC process development. It seeks to quantify the underlying understanding of the technology and abstract that knowledge to the device design level, including extraction of the key parameters that support circuit design and statistical metrology [1][2]. IC development for more than a quarter-century has been dominated by the MOS technology. In the 1970s and 1980s NMOS was favored owing to speed and area advantages, coupled with technology limitations and concerns related to isolation, parasitic effects and process complexity. During that era of NMOS-dominated LSI and the emergence of VLSI, the fundamental scaling laws of MOS technology were codified and broadly applied [3]. It was also during this period that Computer Aided Device reached maturity in terms of realizing robust process modeling (primarily one-dimensional) which then became an integral technology design tool, used universally across the industry [4]. At the same time device simulation, dominantly two-dimensional owing to the nature of MOS devices, became the work-horse of technologists in the design and scaling of devices [5]. The transition from NMOS to CMOS technology resulted in the necessity of tightly coupled and fully 2D simulators for process and device simulations [6][7].

Structure and Lehmann rotation of drops in a surfactant-doped bent-core liquid crystal.

The structure of the nematic (cholesteric) drops that form at the clearing temperature of a mixture of the bent-core molecule CB7CB and the rodlike molecule 8CB doped with a surfactant is optically determined. Using experimental observations and numerical simulations, it is demonstrated that the director field inside these drops is not escaped concentric, as previously proposed, but twisted bipolar. The Lehmann rotation of these drops in the presence of a temperature gradient is described. Their rotation velocity is shown to be proportional to the temperature gradient and to the surface twist angle of the director field and inversely proportional to the drop radius, thus revealing a fundamental scaling law for the Lehmann effect of nematic and cholesteric twisted-bipolar droplets.

Approach and separation of bundles of quantized vorticity

Bundles of quantized vorticity are believed to be the building block of the quasiclassical regime of quantum turbulence. We show that these bundles approach and separate from one another obeying a fundamental scaling law which has been observed in reconnections of single quantized vortices and classical vortex tubes.

Fundamental scaling laws of covert DDoS attacks

Botnets such as Mirai use insecure home devices to conduct distributed denial of service attacks on the Internet infrastructure. Although some of those attacks involve large amounts of traffic, they are generated from a large number of homes, which hampers their early detection. In this paper, our goal is to answer the following question: what is the maximum amount of damage that a DDoS attacker can produce at the network edge without being detected? To that aim, we consider a statistical hypothesis testing approach for attack detection at the network edge. The proposed system assesses the goodness of fit of traffic models based on the ratio of their likelihoods. Under such a model, we show that the amount of traffic that can be generated by a covert attacker scales according to the square root of the number of compromised homes. We evaluate and validate the theoretical results using real data collected from thousands of home-routers connected to a mid-sized ISP.

Space-Charge Aberrations in Single-Shot Time-Resolved Transmission Electron Microscopy

In this paper, we discuss effects of space charge fields on imaging performance in a single shot time-resolved electron microscope (TEM). Using a Green's function perturbation method, we derive analytical estimates for the effects of space charge nonlinearity on the image formation process and the associated aberration coefficients. The dependence of these coefficients on the initial beam phase space distribution is elucidated. The results are validated by particle tracking simulations and provide fundamental scaling laws for the trade-off between temporal and spatial resolution in single-shot time-resolved TEM.

Scaling laws of graphs of 3D protein structures.

The application of graph theory in structural biology offers an alternative means of studying 3D models of large macromolecules such as proteins. The radius of gyration, which scales with exponent [Formula: see text], provides quantitative information about the compactness of the protein structure. In this study, we combine two proven methods, the graph-theoretical and the fundamental scaling laws, to study 3D protein models. This study shows that the mean node degree (MND) of the protein graphs, which scales with exponent 0.038, is scale-invariant. In addition, proteins that differ in size have a highly similar node degree distribution. Linear regression analysis showed that the graph parameters (radius, diameter, and mean eccentricity) can explain up to 90% of the total radius of gyration variance. Thus, the graph parameters of radius, diameter, and mean eccentricity scale match along with the same exponent as the radius of gyration. The main advantage of graph eccentricity compared to the radius of gyration is that it can be used to analyze the distribution of the central and peripheral amino acids/nodes of the macromolecular structure.

An accurate lumped convective plus radiative heat exchanger model for performance-based modelling

There are several thermo-fluid process modelling tools available on the market which can be used to analyze the off-design performance of thermal plants. These tools all offer the user with a simple convective heat exchanger component that requires the design-base process conditions as inputs. The tools would then calculate an effective overall heat transfer factor (UA) and make use of gas flow mass ratios to scale the UA value for off-design conditions. The models employed in these tools assume that the contribution of gas radiation is insignificant, hence only applies convection scaling laws. This paper presents an improved model which considers the contribution of the gas and particle radiation, as is often encountered in the first few heaters in coal fired boilers and heat recovery steam generators. A more fundamental scaling law is applied for the convection scaling and incorporates a cleanliness factor which allows for the consideration of fouling of the heater surfaces. The model’s performance was validated against a discretized tube-level heater model that solves the fundamental convection and radiation terms. The model is accurate within 1% for the cases considered, as compared to more than 20% error if radiation contribution is not considered.

Inconsistencies and Lurking Pitfalls in the Magnitude–Frequency Distribution of High-Resolution Earthquake Catalogs

AbstractEarthquake catalogs describe the distribution of earthquakes in space, time, and magnitude, which is essential information for earthquake forecasting and the assessment of seismic hazard and risk. Available high-resolution (HR) catalogs raise the expectation that their abundance of small earthquakes will help better characterize the fundamental scaling laws of statistical seismology. Here, we investigate whether the ubiquitous exponential-like scaling relation for magnitudes (Gutenberg–Richter [GR], or its tapered version) can be straightforwardly extrapolated to the magnitude–frequency distribution (MFD) of HR catalogs. For several HR catalogs such as of the 2019 Ridgecrest sequence, the 2009 L’Aquila sequence, the 1992 Landers sequence, and entire southern California, we determine if the MFD agrees with an exponential-like distribution using a statistical goodness-of-fit test. We find that HR catalogs usually do not preserve the exponential-like MFD toward low magnitudes and depart from it. Surprisingly, HR catalogs that are based on advanced detection methods depart from an exponential-like MFD at a similar magnitude level as network-based HR catalogs. These departures are mostly due to an improper mixing of different magnitude types, spatiotemporal inhomogeneous completeness, or biased data recording or processing. Remarkably, common-practice methods to find the completeness magnitude do not recognize these departures and lead to severe bias in the b-value estimation. We conclude that extrapolating the exponential-like GR relation to lower magnitudes cannot be taken for granted, and that HR catalogs pose subtle new challenges and lurking pitfalls that may hamper their proper use. The simplest solution to preserve the exponential-like distribution toward low magnitudes may be to estimate a moment magnitude for each earthquake.

Global Energetics of Solar Flares. XII. Energy Scaling Laws

Abstract In this study we test 18 versions of five fundamental energy scaling laws that operate in large solar flares. We express scaling laws in terms of the magnetic potential field energy E p , the mean potential field strength B p , the free energy E free, the dissipated magnetic flare energy E diss, the magnetic length scale L, the thermal length scale L th, the mean helically twisted flux tube radius R, the sunspot radius r, the emission-measure-weighted flare temperature T e , the electron density n e , and the total emission measure EM, measured from a data set of 173 GOES M- and X-class flare events. The five categories of physical scaling laws include (i) a scaling law of the potential field energy, (ii) a scaling law for helical twisting, (iii) a scaling law for Petschek-type magnetic reconnection, (iv) the Rosner–Tucker–Vaiana scaling law, and (v) the Shibata–Yokoyama scaling law. We test the self-consistency of these theoretical scaling laws with observed parameters by requiring two criteria: a cross-correlation coefficient of CCC > 0.5 between the theoretically predicted scaling laws and observed values, and a linear regression fit with a slope of α ≈ 1 within one standard deviation σ. These two criteria enable us (i) to corroborate some existing (or modified) scaling laws, (ii) to reject other scaling laws that are not consistent with the observations, (iii) to probe the dimensionality of flare geometries, and (iv) to predict various energy parameters based on tested scaling laws.

Covert Capacity of Bosonic Channels

We investigate the quantum-secure covert-communication capabilities of lossy thermal-noise bosonic channels, the quantum-mechanical model for many practical channels. We determine the expressions for the covert capacity of these channels: $L_{\text{no-EA}}$, when Alice and Bob share only a classical secret, and $L_{\text{EA}}$, when they benefit from entanglement assistance. We find that entanglement assistance alters the fundamental scaling law for covert communication. Instead of $L_{\text{no-EA}}\sqrt{n}-r_{\text{no-EA}}(n)$, $r_{\text{no-EA}}(n)=o(\sqrt{n})$, entanglement assistance allows $L_{\text{EA}}\sqrt{n}\log n-r_{\text{EA}}(n)$, $r_{\text{EA}}(n)=o(\sqrt{n}\log n)$, covert bits to be transmitted reliably over $n$ channel uses.

Explicit Characterization of Performance of a Class of Networked Linear Control Systems

We quantify performance of a class of interconnected linear dynamical networks with arbitrary nodal dynamics. It is shown that the steady-state variance of the output, which is equivalent to the squared $\mathcal {H}_2$ norm of the network, as a performance measure, can be expressed explicitly as a summation of a rational function over the Laplacian eigenvalues of the underlying graph of the network. Our results generalize the existing works on $\mathcal {H}_2$ -norm characterization for the first- and second-order consensus networks to general consensus-type linear dynamical networks with arbitrary nodal dynamics. We characterize several fundamental limits and scaling laws for the performance of this class of networks. To show the practical usefulness of our results, we discuss how to design decentralized observer-based output feedback mechanisms and how to analyze the performance of composite networks. Numerous examples support our theoretical contributions.

New Figure-of-Merit Combining Semiconductor and Multi-Level Converter Properties

Figures-of-Merit (FOMs) are widely-used to compare power semiconductor materials and devices and to motivate research and development of new technology nodes. These material- and device-specific FOMs, however, fail to directly translate into quantifiable performance in a specific power electronics application. Here, we combine device performance with specific bridge-leg topologies to propose the extended FOM, or X-FOM, a Figure-of-Merit that quantifies bridge-leg performance in multi-level (ML) topologies and supports the quantitative comparison and optimization of topologies and power devices. To arrive at the proposed X-FOM, we revisit the fundamental scaling laws of the on-state resistance and output capacitance of power semiconductors to first propose a revised device-level semiconductor Figure-of-Merit (D-FOM). The D-FOM is then generalized to a multi-level topology with an arbitrary number of levels, output power, and input voltage, resulting in the X-FOM that quantitatively compares hard-switched semiconductor stage losses and filter stage requirements across different bridge-leg structures and numbers of levels, identifies the maximum achievable efficiency of the semiconductor stage, and determines the loss-optimal combination of semiconductor die area and switching frequency. To validate the new X-FOM and showcase its utility, we perform a case study on candidate bridge-leg structures for a three-phase 10 kW photovoltaic (PV) inverter, with the X-FOM showing that (a) the minimum hard-switching losses are an accurate approximation to predict the theoretically maximum achievable efficiency and relative performance between bridge-legs and (b) the 3-level bridge-leg outperforms the 2-level configuration, despite utilizing a SiC MOSFET with a lower D-FOM than in the 2-level case.

Crossover of Charge Fluctuations across the Strange Metal Phase Diagram

A normal metal exhibits a valence plasmon, which is a sound wave in its conduction electron density. The mysterious strange metal is characterized by non-Boltzmann transport and violates most fundamental Fermi liquid scaling laws. A fundamental question is: Do strange metals have plasmons? Using momentum-resolved inelastic electron scattering (M-EELS) we recently showed that, rather than a plasmon, optimally-doped Bi$_{2.1}$Sr$_{1.9}$Ca$_{1.0}$Cu$_{2.0}$O$_{8+x}$ (Bi-2212) exhibits a featureless, temperature-independent continuum with a power-law form over most energy and momentum scales [M. Mitrano, PNAS 115, 5392-5396 (2018)]. Here, we show that this continuum is present throughout the fan-shaped, strange metal region of the phase diagram. Outside this region, dramatic changes in spectral weight are observed: In underdoped samples, spectral weight up to 0.5 eV is enhanced at low temperature, biasing the system towards a charge order instability. The situation is reversed in the overdoped case, where spectral weight is strongly suppressed at low temperature, increasing quasiparticle coherence in this regime. Optimal doping corresponds to the boundary between these two opposite behaviors at which the response is temperature-independent. Our study suggests that plasmons do not exist as well-defined excitations in Bi-2212, and that a featureless continuum is a defining property of the strange metal, which is connected to a peculiar crossover where the spectral weight change undergoes a sign reversal.

Species–area relationships in continuous vegetation: Evidence from Palaearctic grasslands

AbstractAimSpecies–area relationships (SARs) are fundamental scaling laws in ecology although their shape is still disputed. At larger areas, power laws best represent SARs. Yet, it remains unclear whether SARs follow other shapes at finer spatial grains in continuous vegetation. We asked which function describes SARs best at small grains and explored how sampling methodology or the environment influence SAR shape.LocationPalaearctic grasslands and other non‐forested habitats.TaxaVascular plants, bryophytes and lichens.MethodsWe used the GrassPlot database, containing standardized vegetation‐plot data from vascular plants, bryophytes and lichens spanning a wide range of grassland types throughout the Palaearctic and including 2,057 nested‐plot series with at least seven grain sizes ranging from 1 cm2 to 1,024 m2. Using nonlinear regression, we assessed the appropriateness of different SAR functions (power, power quadratic, power breakpoint, logarithmic, Michaelis–Menten). Based on AICc, we tested whether the ranking of functions differed among taxonomic groups, methodological settings, biomes or vegetation types.ResultsThe power function was the most suitable function across the studied taxonomic groups. The superiority of this function increased from lichens to bryophytes to vascular plants to all three taxonomic groups together. The sampling method was highly influential as rooted presence sampling decreased the performance of the power function. By contrast, biome and vegetation type had practically no influence on the superiority of the power law.Main conclusionsWe conclude that SARs of sessile organisms at smaller spatial grains are best approximated by a power function. This coincides with several other comprehensive studies of SARs at different grain sizes and for different taxa, thus supporting the general appropriateness of the power function for modelling species diversity over a wide range of grain sizes. The poor performance of the Michaelis–Menten function demonstrates that richness within plant communities generally does not approach any saturation, thus calling into question the concept of minimal area.

(Invited) Ultrafast X-Ray Studies of Interfacial Energy- and Charge-Transfer Dynamics

The success of many emerging molecular electronics concepts hinges on an atomistic understanding of the underlying electronic dynamics. Processes evolving on spatial and temporal scales spanning orders of magnitude have to be connected in order to gain a comprehensive understanding of the fundamental dynamics and scaling laws that enable molecular, interfacial, and macroscopic charge and energy transport. Time-domain X-ray spectroscopy techniques have the potential to provide a deeper understanding of electronic dynamics in complex, heterogeneous systems owing to their elemental site specificity and sensitivity to local valence electron configurations. We present femtosecond to picosecond time-resolved X-ray photoelectron spectroscopy (TRXPS) studies of photoinduced charge transfer dynamics in nanoporous films of N3 dye-sensitized ZnO and bilayer heterojunctions consisting of copper phthalocyanine (CuPc) electron donors and C60 acceptors. For the N3/ZnO system, differential TRXPS line shifts provide site-specific access to the locations of intermittently trapped electrons, interfacial dipoles, as well as charge delocalization and recombination dynamics. For the CuPc/C60 heterojunction, a deeper understanding of the predominant energy transport and charge generation mechanisms is achieved. Contrary to common belief, fast intersystem crossing from initially excited singlet excitons to triplet excitons within the bulk of the donor domain is not a loss channel but the triplet excitons contribute to a significantly larger extent to the time-integrated interfacial charge generation than the initially excited interfacial singlet excitons. The TRXPS data provide direct access to the diffusivity of the triplet excitons in the CuPc donor domain DCuPc = (1.8 ±1.2) × 10−5 cm2/s and their diffusion length Ldiff = (8 ± 3) nm. Preliminary TRXPS results will be presented for a model system for plasmon-enabled photocatalytic nano-assemblies consisting of a nanoporous TiO2 layer sensitized with gold nanoparticles (Au NPs). Clear differences between the temporal responses of the Au4f and Ti2p photolines are observed, indicating both the interfacial site-specificity of photoinduced electronic dynamics and the capacity of TRXPS to distinguish them. Figure 1

Body size-dependent energy storage causes Kleiber's law scaling of the metabolic rate in planarians.

Kleiber's law, or the 3/4 -power law scaling of the metabolic rate with body mass, is considered one of the few quantitative laws in biology, yet its physiological basis remains unknown. Here, we report Kleiber's law scaling in the planarian Schmidtea mediterranea. Its reversible and life history-independent changes in adult body mass over 3 orders of magnitude reveal that Kleiber's law does not emerge from the size-dependent decrease in cellular metabolic rate, but from a size-dependent increase in mass per cell. Through a combination of experiment and theoretical analysis of the organismal energy balance, we further show that the mass allometry is caused by body size dependent energy storage. Our results reveal the physiological origins of Kleiber's law in planarians and have general implications for understanding a fundamental scaling law in biology.

Fundamental scaling laws for the direct-write chemical vapor deposition of nanoscale features: modeling mass transport around a translating nanonozzle.

The nanometer placement of nanomaterials, such as nanoribbons and nanotubes, at a specific pitch and orientation on a surface, remains an unsolved fundamental problem in nanotechnology. In this work, we introduce and analyze the concept of a direct-write chemical vapor deposition (CVD) system that enables the in-place synthesis of such structures with control over orientation and characteristic features. A nanometer scale pore or conduit, called the nanonozzle, delivers precursor gases for CVD locally on a substrate, with spatial translation of either the nozzle or the substrate to enable a novel direct write (DW) tool. We analyze the nozzle under conditions where it delivers reactants to a substrate while translating at a constant velocity over the surface at a fixed reaction temperature. We formulate and solve a multi-phase three-dimensional reaction and diffusion model of the direct-write operation, and evaluate specific analytically-solvable limits to determine the allowable operating conditions, including pore dimensions, reactant flow rates, and nozzle translation speed. A Buckingham Π analysis identifies six dimensionless quantities crucial for the design and operation of the direct-write synthesis process. Importantly, we derive and validate what we call the ribbon extension inequality that brackets the allowable nozzle velocity relative to the CVD growth rate - a key constraint to enabling direct-write operation. Lastly, we include a practical analysis using attainable values towards the experimental design of such a system, building the nozzle around a commercially available near-field scanning optical microscopy (NSOM) tip as a feasible example.

The angular momentum-mass relation: a fundamental law from dwarf irregulars to massive spirals

In a Λ CDM Universe, the specific stellar angular momentum (j*) and stellar mass (M*) of a galaxy are correlated as a consequence of the scaling existing for dark matter haloes (jh ∝2∕3). The shape of this law is crucial to test galaxy formation models, which are currently discrepant especially at the lowest masses, allowing to constrain fundamental parameters, such as, for example, the retained fraction of angular momentum. In this study, we accurately determine the empirical j*−M* relation (Fall relation) for 92 nearby spiral galaxies (from S0 to Irr) selected from the Spitzer Photometry and Accurate Rotation Curves (SPARC) sample in the unprecedented mass range 7 ≲ log M*∕M⊙≲ 11.5. We significantly improve all previous estimates of the Fall relation by determining j* profiles homogeneously for all galaxies, using extended HI rotation curves, and selecting only galaxies for which a robust j* could be measured (converged j*(<R) radial profile). We find the relation to be well described by a single, unbroken power-law j* α M*α over the entire mass range, with α = 0.55 ± 0.02 and orthogonal intrinsic scatter of 0.17 ± 0.01 dex. We finally discuss some implications of this fundamental scaling law for galaxy formation models and, in particular, the fact that it excludes models in which discs of all masses retain the same fraction of the halo angular momentum.