Universal Scaling Law Research Articles

Ergodic time scale and transitive dynamics in single-particle tracking

We investigate ergodic time scales in single-particle tracking by introducing a covariance measure Ω(Δ;t) for the time-averaged relative square displacement recorded in lag-time Δ at elapsed time t. The present model is established in the generalized Langevin equation with a power-law memory function. The ratio Ω(Δ;Δ)/Ω(Δ;t) is shown to obey a universal scaling law for long but finite times and is used to extract the effective ergodic time. We derive a finite-time-averaged Green-Kubo relation and find that, to control the deviations in measurement results from ensemble averages, the ratio Δ/t must be neither too small nor close to unity. Our paper connects the experimental self-averaging property of a tracer with the theoretic velocity autocorrelation function and sheds light on the transition to ergodicity.

Universal scaling law for human-to-human transmission diseases

Due to the COVID-19 pandemic, Susceptible-Infective-Recovered (SIR) models and their variants are in high demand for predicting the number of cases in urban areas. Aiming to correctly use the experience of the epidemic evolution from one local to another, we present an analysis of the transmission rate of COVID-19 as a function of population size at the metropolitan area level for the United States. Contrary to the usual hypothesis in epidemics modeling, we observe that the disease transmissibility scales with the logarithm of the local's population size. The analysis, made possible by a large amount of data available on simultaneous epidemics of the same type, is universal for any human-to-human transmission disease. We present a contact rate scaling theory that explains the results.

Spontaneous Imbibition in a Square Tube With Corner Films: Theoretical Model and Numerical Simulation

AbstractSpontaneous imbibition in an angular tube with corner films is a fundamental problem in many scientific and engineering processes. In this study, a modified interacting capillary bundle model is developed to describe the liquid imbibition dynamics in a square tube with corner films. The square tube is decomposed into several interacting subcapillaries and the local capillary pressure in each subcapillary is derived based on the specific shape of its meniscus. The conductance of each subcapillary is calculated using single‐phase lattice Boltzmann simulation. The modified interacting capillary bundle model and color‐gradient lattice Boltzmann method are used to simulate the liquid imbibition dynamics in the square tube with different fluid properties. The predictions by the modified interacting capillary bundle model match well with the lattice Boltzmann simulation results for different conditions, demonstrating the accuracy and robustness of the interacting capillary bundle model to describe the imbibition dynamics with corner films. In addition, the interacting capillary bundle model is helpful to investigate the mechanisms during spontaneous imbibition and the influences of fluid viscosity, surface tension, wetting phase contact angle and gravity on imbibition dynamics. Finally, a universal scaling law of imbibition dynamics for the main meniscus is developed and the scaling law for arc meniscus is also analyzed.

Effects of interionic pair interactions on atomic transport properties of liquid Al

The effects of parameters used for tuning the interionic pair interaction of the Ashcroft’s pseudopotential model on the temperature-dependent atomic transport properties of liquid Al have been studied employing the Universal Scaling Laws (USLs) and Hard Sphere (HS) theories of liquid metals. Temperature-dependent effective HS diameter and excess entropy are the key ingredients of the applied theories. We have calculated them by using Ashcroft’s empty core (EMC) pseudopotential and the variational modified hypernetted chain (VMHNC) integral equation theory of liquid. Obtained results clearly suggest that the core radius in the interaction plays a major role in determining atomic transport properties of liquid Al for both USLs and HS theory. It is also observed that USLs are more sensitive than HS theories in response to variation of core radius.

Microstructure and strength of a tantalum-tungsten alloy after cold rolling from small to large strains

Microstructural evolution of a refractory tantalum-tungsten alloy (Ta-4% W) after cold rolling from small to large von-Mises strains (0.12–2.7) was quantitatively studied using transmission electron microscopy. Grain subdivision was observed to take place at two levels. Geometrically necessary boundaries nearly paralleling to slip planes enclosed volumes further divided by diffuse cells and by remnants of Taylor lattices. With increasing strain, the diffuse cells evolved into clear incidental dislocation boundaries enclosing cells, while the Taylor lattices disappeared. Grain subdivision was thus intermediate between those observed in cell forming and in non-cell forming alloys. Meanwhile, the average misorientation angle across all boundaries increased while the average boundary spacing decreased. Distributions of the microstructural parameters at each strain level were found to exhibit universal scaling laws. The microstructural evolution was found closely linking to the observed high strength and strain hardening of this alloy. Based on measured microstructural parameters, the flow stress was calculated utilizing linearly addition of the strengthening by solutes, incidental dislocation boundaries (Taylor strengthening) and geometrically necessary boundaries (Hall-Petch equation). The relative contribution of each strength mechanism evolved with increasing strain and with microstructural evolution: solutes and friction stress dominated at small strains while boundaries dominated at larger strains. Calculated strengths were in close agreement with experimental tension tests and demonstrated an unexpectedly high and continuous parabolic hardening without transition across this large strain range.

Lattice Boltzmann Method for Marangoni forcing soap film

Marangoni surface tension forcing soap film is numerically solved by Lattice Boltzmann Method (LBM). A delicate false force term in the LBM equation is proposed to describe the Marangoni forcing soap film. The validity of LBM is elucidated by the linear theory of surface tension profile as a function of the vertical position of the soap film. The effect of thickness on the statistical behaviors of the Marangoni forcing soap film is discussed from three aspects: the energy spectrum, energy transfer and intermittency. It is found that the scaling behavior of energy spectrum is independent of the scaling constant of thickness [Formula: see text] where the range of [Formula: see text] is from 0.2 to 0.3. The scaling behavior of energy spectrum is [Formula: see text], which is in accordance with the Kraichnan theory in the inverse cascade. In the large-scale range, the energy flux cascades to the small scale which is called as a forward cascade process. In this scale range, more energy flux cascades to the small scale when the value of [Formula: see text] becomes larger. On the contrary, the backward cascade is involved in the small-scale range of the thinned film where more energy transfers to the large scale as the value of [Formula: see text] is smaller. The intermittency measured by PDF of the velocity increment exists in the turbulent soap film. The universal scaling law of the velocity structure function is identical with the 3D S-L intermittency model and our 2D intermittency theory.

A comparative study on atomic transport properties of liquid less-simple metals

We have studied the atomic transport properties of liquid less-simple metals namely Bi, Cd, Pb, Sb, Sn and Tl using universal scaling laws and hard sphere (HS) theories of liquid. Effective interionic interaction in metals has been derived from both Brettonet–Silbert (BS) and Ashcroft’s empty core pseudopotential models. For structure calculation, variational modified hypernetted chain integral equation theory has been considered. Excess entropy and effective HS diameter are the basic ingredients of the study. Obtained ingredients are found to be close with experimental data than any other available literature values when BS model has been chosen. Comparing with experimental data, obtained results for transport coefficients suggest that Faber’s HS theory is excellent for diffusion coefficient and is reasonably good for viscosity coefficient along with BS pseudopotential than any other combinations employed in this study. The probable reason may be the hybridization of s and d electrons exists in the concerned systems.

The Dynamics of Globally Unstable Air-Helium Jets and Its Impact on Jet Mixing Intensity

The paper presents experimental investigations of the low-density air-helium jets. The paper is aimed at the analysis of the flow conditions promoting the local absolute instability leading to global flow oscillations. A number of the test cases are analysed with a wide range of the shear layer thickness showing conditions favorable for the global modes and also mixing intensity triggered by such a regime. It is shown that high mixing intensity is determined not only by the global regime but also by the vortex pairing process. The results are compared with a recently proposed universal scaling law for an onset into the global mode. The results turn out to be far from this scaling law and the reasons for such discrepancies are discussed. The measurements show also that if the shear layer at the nozzle exit is thin enough the global modes are suppressed. The mechanism leading to the global mode suppression under such conditions is carefully analysed.

Kinetics of Charge Carriers across a Graphene-Silicon Schottky Junction

We perform a comparative study on the transfer velocity of charge carriers across two-dimensional and (2D) three-dimensional (3D) graphene-silicon and 3D-3D $\mathrm{Au}$-silicon Schottky junctions. Within the framework of classical thermionic emission theory, the transfer velocity of carriers across the $\mathrm{Au}$-$\mathrm{Si}$ interface is determined as $\overline{v}\ensuremath{\sim}{10}^{7}$ cm/s that is thoroughly consistent with the average thermal velocity of carriers in silicon. In contrast, the graphene-$\mathrm{Si}$ interface discloses a much lower transfer velocity of $\overline{v}\ensuremath{\sim}{10}^{1}$ cm/s, i.e., nearly 6 orders of magnitude smaller than the thermal velocity of carriers in silicon. Utilizing the ${T}^{1}$ universal scaling law for vertical 2D-3D Schottky junctions, we determine the effective out-of-plane velocity of charge carriers in graphene as ${v}_{\ensuremath{\perp}}^{\ensuremath{\ast}}\ensuremath{\sim}{10}^{0}$ cm/s. This indicates current flow across the graphene-$\mathrm{Si}$ contact is substantially limited by ${v}_{\ensuremath{\perp}}^{\ensuremath{\ast}}$. Moreover, by analyzing experimental activation-energy data, we uncover a general correlation between the kinetics of charge carriers and the potential barrier at the graphene-$\mathrm{Si}$ interface. It is found that the transfer velocity increases almost exponentially with the Schottky barrier height, which cannot be explained in the framework of classical theory. Considering nonconserving ${\mathbf{k}}_{\ensuremath{\parallel}}$ scattering strength as an exponential function of Schottky barrier height, ${T}^{1}$ scaling theory leads to a comprehensive interpretation of experimental data. This study sheds light on the electronic processes across 2D-3D interfaces.

A dimensionless number for predicting universal processing parameter boundaries in metal powder bed additive manufacturing

One of the main challenges facing selective laser melting processes is finding suitable process parameters to achieve maximum density (pore-free) parts. In this letter, two newly discovered dimensionless numbers are presented that correlate process parameters to a part’s density allowing for an initial estimation of suitable process parameters without the need for extensive modeling or experimentation. The prediction is achieved by utilizing the Buckingham-Π theorem and the implementation of Pawlowski’s matrix transformation method. The universality of the new dimensionless numbers is verified by applying them to selective laser melting data for eight different metals and alloy systems, obtained both experimentally and gathered from the literature. The dimensionless numbers allow for identification of process parameters that will result in a maximum density regime in the as-built part. Finally, a universal scaling law is introduced that can aid in quantitative prediction of process parameters that result in the highest as-built density.

Scaling Laws of Collective Ride-Sharing Dynamics.

Ride-sharing services may substantially contribute to future sustainable mobility. Their collective dynamics intricately depend on the topology of the underlying street network, the spatiotemporal demand distribution, and the dispatching algorithm. The efficiency of ride-sharing fleets is thus hard to quantify and compare in a unified way. Here, we derive an efficiency observable from the collective nonlinear dynamics and show that it exhibits a universal scaling law. For any given dispatcher, we find a common scaling that yields data collapse across qualitatively different topologies of model networks and empirical street networks from cities, islands, and rural areas. A mean-field analysis confirms this view and reveals a single scaling parameter that jointly captures the influence of network topology and demand distribution. These results further our conceptual understanding of the collective dynamics of ride-sharing fleets and support the evaluation of ride-sharing services and their transfer to previously unserviced regions or unprecedented demand patterns.

Universal scaling laws of collective human flow patterns in urban regions

Detail observation of human locations became available recently by the development of information technology such as mobile phones with GPS (Global Positioning System). We analyzed temporal changes of global human flow patterns in urban regions based on mobile phones’ GPS data in 9 large cities in Japan. By applying a new concept of drainage basins in analogous to river flow patterns, we discovered several universal scaling relations. These include, the number of moving people in a drainage basin of diameter L is proportional to L^3 in the morning rush hour, which is surprisingly different from reasonable intuition of proportionality to the 2 dimensional area, L^2. We show that this unexpected 3 dimensional feature is related to the strong attraction of the city center to become a 3 dimensional structure due skyscrapers.

From universal profiles to universal scaling laws in X-ray galaxy clusters

As the end products of the hierarchical process of cosmic structure formation, galaxy clusters present some predictable properties, like those mostly driven by gravity, and some others more affected by astrophysical dissipative processes that can be recovered from observations and that show remarkable universal behaviour once rescaled by halo mass and redshift. However, a consistent picture that links these universal radial profiles and the integrated values of the thermodynamical quantities of the intracluster medium, also quantifying the deviations from the standard self-similar gravity-driven scenario, has to be demonstrated. In this work we use a semi-analytic model based on a universal pressure profile in hydrostatic equilibrium within a cold dark matter halo with a defined relation between mass and concentration to reconstruct the scaling laws between the X-ray properties of galaxy clusters. We also quantify any deviation from the self-similar predictions in terms of temperature dependence of a few physical quantities such as the gas mass fraction, the relation between spectroscopic temperature and its global value, and, if present, the hydrostatic mass bias. This model allows us to reconstruct both the observed profiles and the scaling laws between integrated quantities. We use the Planck Early Sunyaev-Zeldovich sample, a Planck-selected sample of objects homogeneously analysed in X-rays, to calibrate the predicted scaling laws between gas mass, temperature, luminosity, and total mass. Our universal model reproduces well the observed thermodynamic properties and provides a way to interpret the observed deviations from the standard self-similar behaviour, also allowing us to define a framework to modify accordingly the characteristic physical quantities that renormalise the observed profiles. By combining these results with the constraints on the observed YSZ − T relation we show how we can quantify the level of gas clumping affecting the studied sample, estimate the clumping-free gas mass fraction, and suggest the average level of hydrostatic bias present.

A universal scaling law of mammalian touch

For most mammals, touch is the first sense to develop. They must feel vibrations on the surface of their skin to enable them to respond to various stimuli in their environment, a process called vibrotaction. But how do mammals perceive these vibrations? Through mathematical modeling of the skin and touch receptors, we show that vibrotaction is dominated by "surface" Rayleigh waves traveling cooperatively through all layers of the skin and bone. Applying our model to experimental data, we identify a universal scaling law for the depth of touch receptors across multiple species, indicating an evolutionarily conserved constant in the sensation of vibrations.

Experimental study on electrohydrodynamic atomization (EHDA) in stable cone-jet with middle viscous and low conductive liquid

The cone-jet is one of the most interesting means in electrohydrodynamic atomization (EHDA) for wide applications because of highly charged and monodisperse drops. The pulsating and stable cone-jet modes in EHDA of diethyleneglycol (DEG) are observed by means of high-speed photography technology, as well as the breakup modes transition of electrified jet from varicose to kink instability. The conductive liquid is driven to form a liquid cone at the outlet of the capillary tube, and form a permanent jet from the apex of the cone by the tangential electric stress. With an increase in electric potential, the cone angle and jet length increase. The electrified meniscus and the cone may appear convex, linear sides and concave in cone jet regime, which depends on the static equilibrium of forces exists at each point of electrified liquid surface. The jet breakup modes with multi-jet, varicose and kink instabilities are successively recorded as liquid flow rates increasing. The jet breakup transition depends on flow rate. The drops size rises proportionally with an increase in liquid flow rate or a decrease in electric potential in stable cone-jet mode. The dimensionless diameter d/d0 as a function of the dimensionless flow rate qV/qm is in good agreement with the universal scaling laws.

Probing the universality of topological defect formation in a quantum annealer: Kibble-Zurek mechanism and beyond

The number of topological defects created in a system driven through a quantum phase transition exhibits a power-law scaling with the driving time. This universal scaling law is the key prediction of the Kibble-Zurek mechanism (KZM), and testing it using a hardware-based quantum simulator is a coveted goal of quantum information science. Here we provide such a test using quantum annealing. Specifically, we report on extensive experimental tests of topological defect formation via the one-dimensional transverse-field Ising model on two different D-Wave quantum annealing devices. We find that the quantum simulator results can indeed be explained by the KZM for open-system quantum dynamics with phase-flip errors, with certain quantitative deviations from the theory likely caused by factors such as random control errors and transient effects. In addition, we probe physics beyond the KZM by identifying signatures of universality in the distribution and cumulants of the number of kinks and their decay, and again find agreement with the quantum simulator results. This implies that the theoretical predictions of the generalized KZM theory, which assumes isolation from the environment, applies beyond its original scope to an open system. We support this result by extensive numerical computations. To check whether an alternative, classical interpretation of these results is possible, we used the spin-vector Monte Carlo model, a candidate classical description of the D-Wave device. We find that the degree of agreement with the experimental data from the D-Wave annealing devices is better for the KZM, a quantum theory, than for the classical spin-vector Monte Carlo model, thus favoring a quantum description of the device. Our work provides an experimental test of quantum critical dynamics in an open quantum system, and paves the way to new directions in quantum simulation experiments.

Scaling law for the propagation speed of domino toppling

It is essential for domino game players to have a quick estimate of dominoes’ propagation speed without engaging in complicated multi-body dynamics simulation. This research article uses directed dimensional analysis to propose a universal scaling law, v=λghf(δλ), for the speed of domino toppling motion. As an application, two approximate power laws were formulated by curve fitting of both theoretical and experimental data. The fitted power laws, v∼δλhg, show that the domino propagation speed is proportional to the square root of the domino separation λ, thickness δ, and the reciprocation of the domino height h. The obtained scaling law might not only be useful for players but also help them understand domino toppling energy transfer cascades.

Universal scaling laws for metallic wrinkling on soft spherical substrates

The surface wrinkling of metal films on spherical polydimethylsiloxane (PDMS) substrates was induced by thermal contraction. A novel scaling law among wrinkle wavelength, film thickness, and substrate radius was discovered experimentally and rationalized theoretically, with scaling exponent being constant and coefficient being material-dependent. The theoretical predictions agree well with the existing experimental data of other spherical shell/core systems, with shell/core modulus ratio spanning several orders of magnitude, indicative of the universality and robustness. The results shed new light on the wrinkling phenomenon of spherical surfaces and demonstrate a predictive pathway to create wrinkling patterns on demand.

Universal scaling laws in droplet coalescence: A dissipative particle dynamics study

We report simulation studies on two-droplet coalescence in two-dimensions using Dissipative Particle Dynamics (DPD), a commonly used mesoscopic method for simulating soft matter systems. When two droplets undergo coalescence, the temporal evolution of bridge or neck radius rb(t) follows definite scaling laws which are derived by balancing relevant inertial/viscous stresses with the interfacial tension stresses. We successfully validated these scaling laws by varying viscosity ratio of droplet and surrounding fluids. Furthermore, for a given regime, we show collapse of rb(t) data when simulation time t is appropriately scaled.

Moving, Reproducing, and Dying Beyond Flatland: Malthusian Flocks in Dimensions d>2.

We show that "Malthusian flocks"-i.e., coherently moving collections of self-propelled entities (such as living creatures) which are being "born" and "dying" during their motion-belong to a new universality class in spatial dimensions d>2. We calculate the universal exponents and scaling laws of this new universality class to O(ε) in an ε=4-d expansion, and find these are different from the "canonical" exponents previously conjectured to hold for "immortal" flocks (i.e., those without birth and death) and shown to hold for incompressible flocks in d>2. Our expansion should be quite accurate in d=3, allowing precise quantitative comparisons between our theory, simulations, and experiments.