Universal Scaling Research Articles

The entropic origin of the enhancement of liquid diffusion close to a neutral confining surface.

It is known that, in the proximity of a neutral wall, liquids experience diffusion enhancement relative to their bulk diffusion, but the origin of this phenomenon is still unknown. We report a molecular dynamics simulation investigating the dynamics of a simple liquid in the proximity to a non-interacting smooth confining wall, which exhibits a strong diffusion enhancement within the liquid layers adjacent to the wall. We present an analysis of these results, demonstrating that the observed diffusion enhancement can be accounted for, with numerical accuracy, using the universal scaling law that relates the liquid diffusion rate to the excess entropy. These results show that the scaling law, which has so far only been used for the description of the bulk liquid diffusion, can be successfully used to describe the diffusion in liquids under nano-scale confinement.

Non‐Linearity in Mean Annual Peak Flow Scaling With Upstream Basin Area: Insights From Percolation Theory

ABSTRACTUnderstanding how annual peak flow, , relates to upstream basin area, , and their scaling have been one of the challenges in surface hydrology. Although a power‐law scaling relationship (i.e., ) has been widely applied in the literature, it is purely empirical, and due to its empiricism, the interpretation of its exponent, , and its variations from one basin to another is not clear. In the literature, different values of have been reported for various datasets and drainage basins of different areas. Invoking concepts of percolation theory as well as self‐affinity, we derived universal and non‐universal scaling laws to theoretically link to . In the universal scaling, we related the exponent to the fractal dimensionality of percolation, (i.e., ). In the non‐universal scaling, in addition to , the exponent was related to the Hurst exponent, , characterizing the boundaries of the drainage basin (i.e., ). The depends on the dimensionality of the drainage system (e.g., two or three dimensions) and percolation class (e.g., random or invasion percolation). We demonstrated that the theoretical universal and non‐universal bounds were in well agreement with experimental ranges of reported in the literature. More importantly, our theoretical framework revealed that greater values are theoretically expected when basins are more quasi two‐dimensional, while smaller values when basins are mainly quasi three‐dimensional. This is well consistent with the experimental data. We attributed it to the fact that small basins most probably display quasi‐two‐dimensional topography, while large basins quasi‐three‐dimensional topography.

Reynolds and Mach Number Effects on Propulsive Performance for a Pitching Airfoil

In this work, numerical simulations are conducted to investigate the effects of Reynolds (Re) and Mach (Ma) numbers on thrust characteristics for a pitching airfoil. The results show that as Re increases, the thrust performance is improved. The inverse square root of Reynolds number is demonstrated to be a universal scaling law for both thrust coefficients and drag-to-thrust crossovers across Re=1×103∼1×106 and Ma=0∼0.3. In contrast, as Ma increases above 0.1, the thrust performance is significantly reduced, especially when Ma approaches 0.3. The thrust coefficients follow the square law of the Mach number, which also exhibits universality. Furthermore, the incompressible vortex projection method and the compressible vortex projection method are employed for thrust decomposition. Before this, the full expression of the compressible vortex projection method is derived. It is revealed that as Re increases, the improvement of thrust performance is primarily attributed to the reduced flow viscous effect and, meanwhile, benefits from the formation of more intense boundary layers and vortex structures in near wake. As Ma increases, the enhancement of local flow compressibility ultimately leads to the divergence of added mass drag and thereby reduces the thrust performance.

Coarse-graining model reveals universal exponential scaling in axonal length distributions

Abstract The Exponential Distance Rule (EDR) is a well-documented phenomenon suggesting that the distribution of axonal lengths in the brain follows an exponential decay pattern. 
Nevertheless, individual-level axon data supporting this assertion is limited to Drosophila and mice, while inter-region connectome data is also accessible for macaques, marmosets, and humans. 
Although axon-level data in Drosophila and mice support the generality of the EDR, region-level data can significantly deviate from the exponential curve. 
In this study, we establish that the axon number-weighted length distribution of region-level connections converges onto a universal curve when rescaled to the mean axonal length, demonstrating similarities across different species. 
To explain these observations, we present a simple mathematical model that attributes the observed deviations from the EDR in the weighted length distribution of inter-regional connectomes to the inherent coarse-graining effect of translating from neuron-level to region-level connectomics.
We demonstrate that the qualitative predictions of the model are robust with respect to various aspects of brain region-geometry, including dimensionality, resolution, and curvature.
On the other hand, the performance of the model exhibits a monotonous dependence on the amount of region-geometry related detail incorporated into the model.
The findings validate the universality of the EDR rule across various species, paving the way for further in-depth exploration of this remarkably simple principle.

How urban form impacts flooding

Urbanization and climate change are contributing to severe flooding globally, damaging infrastructure, disrupting economies, and undermining human well-being. Approaches to make cities more resilient to floods are emerging, notably with the design of flood-resilient structures, but relatively little is known about the role of urban form and its complexity in the concentration of flooding. We leverage statistical mechanics to reduce the complexity of urban flooding and develop a mean-flow theory that relates flood hazards to urban form characterized by the ground slope, urban porosity, and the Mermin order parameter which measures symmetry in building arrangements. The mean-flow theory presents a dimensionless flood depth that scales linearly with the urban porosity and the order parameter, with different scaling for disordered square- and hexagon-like forms. A universal scaling is obtained by introducing an effective mean chord length representative of the unobstructed downslope travel distance for flood water, yielding an analytical model for neighborhood-scale flood hazards globally. The proposed mean-flow theory is applied to probe city-to-city variations in flood hazards, and shows promising results linking recorded flood losses to urban form and observed rainfall extremes.

Scaling Transition of Active Turbulence from Two to Three Dimensions.

Turbulent flows are observed in low-Reynolds active fluids, which display similar phenomenology to the classical inertial turbulence but are of a different nature. Understanding the dependence of this new type of turbulence on dimensionality is a fundamental challenge in non-equilibrium physics. Real-space structures and kinetic energy spectra of bacterial turbulence are experimentally measured from two to three dimensions. The turbulence shows three regimes separated by two critical confinement heights, resulting from the competition of bacterial length, vortex size and confinement height. Meanwhile, the kinetic energy spectra display distinct universal scaling laws in quasi-2D and 3D regimes, independent of bacterial activity, length, and confinement height, whereas scaling exponents transition in two steps around the critical heights. The scaling behaviors are well captured by the hydrodynamic model wedevelop, which employs image systems to represent the effects of confining boundaries. The study suggests a framework for investigating the effect of dimensionality on non-equilibrium self-organizedsystems.

Dynamic fluctuations of current and mass in nonequilibrium mass transport processes

We study steady-state dynamic fluctuations of current and mass in several variants of random average processes on a ring of L sites. These processes violate detailed balance in the bulk and have nontrivial spatial structures: their steady states are not described by the Boltzmann–Gibbs distribution and can have nonzero spatial correlations. Using a microscopic approach, we exactly calculate the second cumulants, or the variance, ⟨Qi2(T)⟩c and ⟨Qsub2(l,T)⟩c , of cumulative (time-integrated) currents up to time T across the ith bond and across a subsystem of size l (summed over bonds in the subsystem), respectively. We also calculate the (two-point) dynamic correlation function of the subsystem mass. In particular, we show that, for large L≫1 , the second cumulant ⟨Qi2(T)⟩c of the cumulative current up to time T across the ith bond grows linearly as ⟨Qi2⟩c∼T for initial times T∼O(1) , subdiffusively as ⟨Qi2⟩c∼T1/2 for intermediate times 1≪T≪L2 , and then again linearly as ⟨Qi2⟩c∼T for long times T≫L2 . The scaled cumulant liml→∞,T→∞⟨Qsub2(l,T)⟩c/2lT of current across the subsystem of size l and up to time T converges to the density-dependent particle mobility χ(ρ) when the large subsystem-size limit is taken first, followed by the large-time limit; when the limits are reversed, it simply vanishes. Remarkably, regardless of the dynamical rules, the scaled current cumulant D⟨Qi2(T)⟩c/2χL≡W(y) as a function of scaled time y=DT/L2 can be expressed in terms of a universal scaling function W(y) , where D is the bulk-diffusion coefficient; interestingly, the intermediate-time subdiffusive and long-time diffusive growths can be connected through a single scaling function W(y) . The power spectra for current and mass are also exactly characterized by the respective scaling functions. Furthermore, we provide a microscopic derivation of equilibrium-like Green–Kubo and Einstein relations that connect the steady-state current fluctuations to an ‘operational’ mobility (i.e. the response to an external force field) and mass fluctuation, respectively.

Testing for Markovian character of transfer of fluctuations in solar wind turbulence on kinetic scales.

We apply statistical analysis to search for processes responsible for turbulence in physical systems. In our previous studies, we have shown that solar wind turbulence in the inertial range of large magnetohydrodynamic scales exhibits Markov properties. We have recently extended this approach on much smaller kinetic scales. Here we are testing for the Markovian character of stochastic processes in a kinetic regime based on magnetic field and velocity fluctuations in the solar wind, measured onboard the Magnetospheric Multiscale (MMS) mission: behind the bow shock, inside the magnetosheath, and near the magnetopause. We have verified that the Chapman-Kolmogorov necessary conditions for Markov processes is satisfied for local transfer of energy between the magnetic and velocity fields also on kinetic scales. We have confirmed that for magnetic fluctuations, the first Kramers-Moyal coefficient is linear, while the second term is quadratic, corresponding to drift and diffusion processes in the resulting Fokker-Planck equation. It means that magnetic self-similar turbulence is described by generalized Ornstein-Uhlenbeck processes. We show that for the magnetic case, the Fokker-Planck equationleads to the probability density functions of the kappa distributions, which exhibit global universal scale invariance with a linear scaling and lack of intermittency. On the contrary, for velocity fluctuations, higher order Kramers-Moyal coefficients should be taken into account and hence scale invariance is not observed. However, the nonextensity parameter in Tsallis entropy provides a robust measure of the departure of the system from equilibrium. The obtained results are important for a better understanding of the physical mechanism governing turbulent systems in space and laboratory.

A universal scaling relation incorporating the cusp-to-core transition of dark matter halos

A universal scaling relation incorporating the cusp-to-core transition of dark matter halos

Corrections to Diffusion in Interacting Quantum Systems

The approach to equilibrium in interacting classical and quantum systems is a challenging problem of both theoretical and experimental interest. One useful organizing principle characterizing equilibration is the dissipative universality class, the most prevalent one being diffusion. In this paper, we use the effective field theory (EFT) of diffusion to systematically obtain universal power-law corrections to diffusion. We then employ large-scale simulations of classical and quantum systems to explore their validity. In particular, we find universal scaling functions for the corrections to the dynamical structure factor ⟨n(x,t)n⟩, in the presence of a single U(1) or SU(2) charge in systems with and without particle-hole symmetry, and present the framework to generalize the calculation to multiple charges. Classical simulations show remarkable agreement with EFT predictions for subleading corrections, pushing precision tests of effective theories for thermalizing systems to an unprecedented level. Moving to quantum systems, we perform large-scale tensor-network simulations in unitary and noisy 1D Floquet systems with conserved magnetization. We find a qualitative agreement with EFT, which becomes quantitative in the case of noisy systems. Additionally, we show how the knowledge of EFT corrections allows for fitting methods, which can improve the estimation of transport parameters at the intermediate times accessible by simulations and experiments. Finally, we explore nonlinear response in quantum systems and find that EFT provides an accurate prediction for its behavior. Our results provide a basis for a better understanding of the nonlinear phenomena present in thermalizing systems. Published by the American Physical Society 2024

Integrative catalytic pairs for efficient multi-intermediate catalysis.

Single-atom catalysts (SACs) have attracted considerable research interest owing to their combined merits of homogeneous and heterogeneous catalysts. However, the uniform and isolated active sites of SACs fall short in catalysing complex chemical processes that simultaneously involve multiple intermediates. In this Review, we highlight an emerging class of catalysts with adjacent binary active centres, which is called integrative catalytic pairs (ICPs), showing not only atomic-scale site-to-site electronic interactions but also synergistic catalytic effects. Compared with SACs or their derivative dual-atom catalysts (DACs), multi-interactive intermediates on ICPs can overcome kinetic barriers, adjust reaction pathways and break the universal linear scaling relations as the smallest active units. Starting from this active-site design principle, each single active atom can be considered as a brick to further build integrative catalytic clusters (ICCs) with desirable configurations, towards trimer or even larger multi-atom units depending on the requirement of a given reaction.

Scaling Limit of Multi-Type Invariant Measures via the Directed Landscape

Abstract This paper studies the large scale limits of multi-type invariant distributions and Busemann functions of planar stochastic growth models in the Kardar–Parisi–Zhang (KPZ) class. We identify a set of sufficient hypotheses for convergence of multi-type invariant measures of last-passage percolation (LPP) models to the stationary horizon (SH), which is the unique multi-type stationary measure of the KPZ fixed point. Our limit theorem utilizes conditions that are expected to hold broadly in the KPZ class, including convergence of the scaled last-passage process to the directed landscape. We verify these conditions for the six exactly solvable models whose scaled bulk versions converge to the directed landscape, as shown by Dauvergne and Virág. We also present a second, more general, convergence theorem with future applications to polymer models and particle systems. Our paper is the first to show convergence to the SH without relying on information about the structure of the multi-type invariant measures of the prelimit models. These results are consistent with the conjecture that the SH is the universal scaling limit of multi-type invariant measures in the KPZ class.

A universal yield stress equation for electrorheological fluids

In this study, we investigate the universality of the yield stress [τyE0, where E0 is electric field strength] for examining electrorheological (ER) fluids both experimentally and theoretically. We found that the published experimental data for the yield stress of ER fluids for various materials and measurement conditions obey a yield stress scaling equation. In other words, the ER yield stress data in the literature collapse onto a universal correlation: τ̂=1.313Ê3/2tanhÊ using scaled variables τ̂≡τyE0/τyEc and Ê≡E0/Ec. Here, Ec is critical electric field strength. Although this expression is attractive for experimentalists, this empirical equation has not been derived from first principles. We introduce a mesoscopic elementary region concept and justify this universal correlation for the first time. We decompose the ER system into a finite number of elementary regions and introduce “glueons,” which adhere to neighboring elementary regions resulting in fibrillary structures. We investigated the limiting case when the elementary region size is reduced to zero (continuum limit) and used a reaction-diffusion model to calculate glueon concentration. In modeling the reaction term (generation of glueons), we used a linear model by recognizing that the electric field activates glueons, i.e., the number of glueons increases as the electric field strength increases. In our preliminary study, we were able to justify a universal correlation by solving the glueon concentration equation using a simple geometry. The novelty of this work is the development of universality for the ER yield stress and derivation of a universal scaling equation.

تصورات الفكر الحداثي عن التشريعات الإسلامية للأسرة: دراسة تحليلية مقارنة

This study aims to contribute to the ongoing debate on the perceptions of modernity-related thought concerning family affairs in Islamic legislation. Analyzing the discourse of modernity and the issues raised therein, the researcher attempts to answer the following questions: what effect-if any- does one’s stance on religious heritage have on the study of family-related issues? what are the flaws of the modernists with respect to the family? what are the alternative perceptions that Islam presents concerning family values and legislation? To answer these questions- and to achieve the objective of his study- the researcher has used a descriptive as well as a comparative approach. In conclusion, the study has found that the flaws of the modernist approach, which adopts western secular concepts and values on a universal scale, can be traced back to its rejection of any cultural particularities stemming from religious heritage. That is why it fails to acknowledge or explain the changes witnessed in daily life in Muslim societies. Understandably, an explanation of such changes cannot be reduced exclusively to a material worldview. Identifying some features of such shortcomings, the researcher has referred to the modernists’ rejection of value-based family cohesion, and how they see it as a source of violation to women's rights. Or worse still, they see it as a form of stereotyping the gender roles in line with religious rulings. On the positive side, the study outlined some features of an alternative methodology from within the Islamic worldview- to address the issues of parent education, family upbringing based on dialogue, equality among family members, and women’s freedoms, which modernists usually raise. The study ends by urging researchers to conduct further case studies on a specific country or family institutions. The focus of such works should be on evaluating the content of the modernist discourse in international agreements, and its impact on women and children, on the identity of the family, as well as its functions and characteristics from the perspective of cultural differences among nations.

A proposal to change the leap-second adjustments to coordinated universal time

The definition of Coordinated Universal Time (UTC) in 1972 balanced the needs of the time and frequency community for a universal time scale that was traceable to the definition of frequency in the SI system of units with the needs of the astronomical community for a time scale that was closely linked to UT1, a time scale related to the rotation of Earth. The balance between these two considerations has changed very significantly since 1972, and there is widespread agreement that the method of relating UTC to UT1 should be changed by increasing the magnitude of the maximum tolerance between the two scales to more than the current limit of 0.9 s. We propose to realize this decision by means of an algorithmic adjustment process based on the variation in the length of the day over the previous centuries. We use these historical data to extrapolate the length of the day for a century into the future, and to compute a periodic rate adjustment to UTC based on this extrapolation. The adjustment process will not use time steps. The magnitude of the periodic rate adjustment will be re-considered every century, but the basic adjustment algorithm will not change. We suggest a maximum tolerance between UT1 and UTC that is large enough to absorb the irregular and unpredictable variations in the length of the day with respect to the long-term average increase in this value but plays no role in determining the parameters of the adjustment process that is proposed. We also propose that the adjustment be implemented at 12 UTC on 1 January or on another date that is close to a universal holiday in all time zones.

Trends in the oxygen adsorption energy derived from the thermodynamic potential model for the oxygen evolution reaction

Across the last years, substantial efforts were done to understand the limitations of the oxygen evolution reaction (OER) catalysts and to develop robust ones such as to solve the efficiency problem in water splitting. Fundamental understanding represents a pathway towards designing superior catalysts. In this direction, several descriptors (ηTD, ESSI, Gmax(η)) have been derived based on the adsorption energies of the OER intermediate moieties (∆EHO*/∆EO*/∆EHOO*) for faster screening of the materials. A universal scaling between the adsorption energies of HO* and HOO* was established for a wide range of materials and in many cases was shown to govern the minimum theoretical overpotential. On the other hand, the scaling between the adsorption energies of HO* and O* fragments have a large scattering along the trendline. In this work we derive five trends for the O* adsorption energies based on theoretical overpotential intervals, using data collected from the published studies employing DFT calculations for OER. It is shown that the best materials have an adsorption energy for HO* placed within a limited interval, yet sufficiently large for a pool of promising catalysts (-0.5,1.5 eV), and that the adsorption energies of O* scales with that of HO* at a slope of one and an intercept of 1.81 eV. Furthermore, a decrease of the intercept for the scaling between HOO* and HO* from 3.14 (valid for all data analyzed) to 3.03 eV is found. For three of the other four trends, the slope of the adsorption energies of O*/HO*scaling is one with intercepts closer either to HOO* (2.2/2.78) or to HO*(1.43/0.78) adsorption energies. For each set of data, the scaling between HOO* and HO* adsorption energies varies from 3 to 3.37 eV. Separately, the trends for O* adsorption energies were analyzed for the TiO2(110) semiconducting rutile surface when doped with transition metals and modified (i) with HO* or H* co-adsorbed fragments that act as charge donor/acceptor moieties or (ii) when the surface was provided with an excess or a lack of electrons. The analysis was performed using the data collected from the published literature, supplemented by additional calculations. Clear trends based on the amount of charge were obtained when standard GGA functionals were used. An understanding for the origin of the large variation of the oxygen adsorption energies for the systems that have similar adsorption energies for the HO*/HOO* is provided. However, when the Hubbard corrected GGA functional is used, some trends change. Clearly, it is still a challenge describing accurately and in a cost-effective manner the adsorption of OER moieties on the undoped or doped transition metal oxides, especially for O*. A strategy to get further insight into the origin of large variations of oxygen adsorption energies for the materials that have similar adsorption energies of HO* and HOO* is discussed.

Harmonizing tau positron emission tomography in Alzheimer's disease: The CenTauR scale and the joint propagation model.

Tau-positron emission tomography (PET) outcome data of patients with Alzheimer's disease (AD) cannot currently be meaningfully compared or combined when different tracers are used due to differences in tracer properties, instrumentation, and methods of analysis. Using head-to-head data from five cohorts with tau PET radiotracers designed to target tau deposition in AD, we tested a joint propagation model (JPM) to harmonize quantification (units termed "CenTauR" [CTR]). JPM is a statistical model that simultaneously models the relationships between head-to-head and anchor point data. JPM was compared to a linear regression approach analogous to the one used in the amyloid PET Centiloid scale. A strong linear relationship was observed between CTR values across brain regions. Using the JPM approach, CTR estimates were similar to, but more accurate than, those derived using the linear regression approach. Preliminary findings using the JPM support the development and adoption of a universal scale for tau-PET quantification. Tested a novel joint propagation model (JPM) to harmonize quantification of tau PET. Units of common scale are termed "CenTauRs". Tested a Centiloid-like linear regression approach. Using five cohorts with head-to-head tau PET, JPM outperformed linearregressionbased approach. Strong linear relationship was observed between CenTauRs values across brain regions.

Necessary and sufficient conditions for Kolmogorov’s flux laws on T2 and T3

Necessary and sufficient conditions for the third order Kolmogorov universal scaling flux laws are derived for the stochastically forced incompressible Navier Stokes equations on the torus in 2D and 3D. This paper rigorously generalises the result of (Bedrossian 2019 Commun. Math. Phys. 367 1045–75) to functions which are heavy-tailed in Fourier space or have local finite time singularities in the inviscid limit. In other words, we have rigorously derived the existence of the well known physical relationships, the direct and inverse cascades. Furthermore we show that the rate of the direct cascade is proportional to the amount of energy ‘escaping to infinity’ in spectral space as well as a measure of the total singularities within the solution. Similarly, an inverse cascade is proportional to the amount of energy that moves towards the k = 0 Fourier mode in the invisicid limit.

The Cost of Impatience in Dynamic Matching: Scaling Laws and Operating Regimes

We study matching queues with abandonment. The simplest of these is the two-sided queue with servers on one side and customers on the other, both arriving dynamically over time and abandoning if not matched by the time their patience elapses. We identify nonasymptotic and universal scaling laws for the matching loss due to abandonment, which we refer to as the “cost of impatience.” The scaling laws characterize the way in which this cost depends on the arrival rates and the (possibly different) mean patience of servers and customers. Our characterization reveals four operating regimes identified by an operational measure of patience that brings together mean patience and utilization. The four regimes subsume the regimes that arise in asymptotic (heavy-traffic) approximations. The scaling laws, specialized to each regime, reveal the fundamental structure of the cost of impatience and show that its order of magnitude is fully determined by (i) a “winner-take-all” competition between customer impatience and utilization, and (ii) the ability to accumulate inventory on the server side. Practically important is that when servers are impatient, the cost of impatience is, up to an order of magnitude, given by an insightful expression where only the minimum of the two patience rates appears. Considering the trade-off between abandonment and capacity costs, we characterize the scaling of the optimal safety capacity as a function of costs, arrival rates, and patience parameters. We prove that the ability to hold inventory of servers means that the optimal safety capacity grows logarithmically in abandonment cost and, in turn, slower than the square-root growth in the single-sided queue. This paper was accepted by Baris Ata, stochastic models and simulation. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.01513 .

Universal scaling in far-from-equilibrium quantum systems: An equivalent differential approach

Recent progress in out-of-equilibrium closed quantum systems has significantly advanced the understanding of mechanisms behind their evolution toward thermalization. Notably, the concept of nonthermal fixed points (NTFPs)-responsible for the emergence of spatiotemporal universal scaling in far-from-equilibrium systems-has played a crucial role in both theoretical and experimental investigations. In this work, we introduce a differential equation that has the universal scaling associated with NTFPs as a solution. The advantage of working with a differential equation, rather than only with its solution, is that we can extract several insightful properties not necessarily present in the solution alone. How the differential equation is derived allows physical interpretation of the universal exponents in terms of the time dependence of the amplitude of the distributions and their momentum scaling. Employing two limiting cases of the equation, we determined the universal exponents related to the scaling using the distributions near just two momentum values. We established a solid agreement with previous investigations by validating this approach with three distinct physical systems. This consistency highlights the universal nature of scaling due to NTFPs and emphasizes the predictive capabilities of the proposed differential equation. Moreover, under specific conditions, the equation predicts a power-law related to the ratio of the two universal exponents, leading to implications concerning particle and energy transport. This suggests that the observed power-laws in far-from-equilibrium turbulent fluids could be related to the universal scaling due to NTFPs, potentially offering insights into the study of turbulence.