Form Of Scaling Laws Research Articles

Scaling law of real traffic jams under varying travel demand

The escalation of urban traffic congestion has reached a critical extent due to rapid urbanization, capturing considerable attention within urban science and transportation research. Although preceding studies have validated the scale-free distributions in spatio-temporal congestion clusters across cities, the influence of travel demand on that distribution has yet to be explored. Using a unique traffic dataset during the COVID-19 pandemic in Shanghai 2022, we present empirical evidence that travel demand plays a pivotal role in shaping the scaling laws of traffic congestion. We uncover a noteworthy negative linear correlation between the travel demand and the traffic resilience represented by scaling exponents of congestion cluster size and recovery duration. Additionally, we reveal that travel demand broadly dominates the scale of congestion in the form of scaling laws, including the aggregated volume of congestion clusters, the number of congestion clusters, and the number of congested roads. Subsequent micro-level analysis of congestion propagation also unveils that cascade diffusion determines the demand sensitivity of congestion, while other intrinsic components, namely spontaneous generation and dissipation, are rather stable. Our findings of traffic congestion under diverse travel demand can profoundly enrich our understanding of the scale-free nature of traffic congestion and provide insights into internal mechanisms of congestion propagation.

Unsteady aerodynamics of porous aerofoils

Abstract

Long‐range correlations of soil water content time series under tillage and different cover crops in a semi‐arid vineyard

AbstractWe explored the suitability of multifractal detrended fluctuation analysis (MFDFA) to characterize the temporal dynamics of soil water content (SWC), we analysed the origin of the multifractality of time series of the dynamic of SWC and we investigated how this dynamic was affected by different soil treatments and depths, through the characterization of long‐range correlations. Temporal data of SWC from conventional tillage and two different cover crops at three different depths in a Mediterranean vineyard were examined. The dataset spanned 18 months in 30‐min intervals. We investigated if SWC dynamics, as reflected by long‐range dependencies, can be detected and quantified by MFDFA in the form of scaling laws. We analysed the randomly shuffled series associated with temporal data of SWC to investigate if the detected multifractality of the data reflected either a broad density function of the values of the series or different long‐range correlations for small and large fluctuations in the dataset. Finally, the impact of treatment and depth on the variation of long‐range dependencies was studied. Our results suggest that the time records of soil moisture in a Mediterranean vineyard show a multifractal behaviour compatible with complex patterns of long‐range correlations. Moreover, this complex structure is affected by depth, as depicted by the statistically significant variation of the generalized Hurst exponent h(0), which controls the logarithmic mean of the fluctuation of SWC over a period of time. No significant interactions between treatments and depth was found. This suggests that soil properties that influence soil water dynamics at each depth are not affected by cover crop treatments. This could be due to the fact that the experiment lasted less than 2 years and no long‐term interactions were present at this time interval.Highlights Multifractal detrended fluctuation analysis (MFDFA) characterizes soil water content dynamics. MFDFA detects the influence of soil depth on long‐range correlations. Time series of soil moisture are multifractals compatible with complex patterns of long‐range correlations. Long‐range dependencies are affected by depth but no interaction has been found between soil treatment and depth.

Geometric localization in supported elastic struts

Localized deformation patterns are a common motif in morphogenesis and are increasingly finding applications in materials science and engineering, in such instances as mechanical memories. Here, we describe the emergence of spatially localized deformations in a minimal mechanical system by exploring the impact of growth and shear on the conformation of a semi-flexible filament connected to a pliable shearable substrate. We combine numerical simulations of a discrete rod model with theoretical analysis of the differential equations recovered in the continuum limit to quantify (in the form of scaling laws) how geometry, mechanics and growth act together to give rise to such localized structures in this system. We find that spatially localized deformations along the filament emerge for intermediate shear modulus and increasing growth. Finally, we use experiments on a 3D-printed multi-material model system to demonstrate that external control of the amount of shear and growth may be used to regulate the spatial extent of the localized strain texture.

Critical temperature estimation of bulk and confined atomic fluid using vapour−liquid interfacial free energy

The critical temperatures of bulk and confined atomic fluids are investigated using values of the vapour−liquid interfacial free energy of coexistence obtained from grand-canonical transition-matrix Monte Carlo simulations using a histogram reweighting technique. The temperature corresponding to zero interfacial free energy of coexistence is the estimated critical temperature for the system under investigation. Slit width of confined atomic fluid for this investigation is varied from 40 to 1 fluid particle diameter. The obtained critical temperatures have shown nonlinear monotonic trend with inverse of slit width. Moreover, five different linear regimes of critical temperature are observed in the studied range of slit width. Interestingly, in the slit width range of less than two fluid particle diameters, the critical temperature approaches two-dimensional value and remains approximately indifferent with a decrease in slit width up to one fluid particle diameter. This investigation also reveals that the critical temperature of bulk and confined atomic fluid estimated using the vapour−liquid interfacial free energy of coexistence is within reasonable accuracy with that obtained using the simplified form of scaling law.

Effect of finite sampling time on estimation of Brownian fluctuation

AbstractWe present a study of the effect of finite detector integration/exposure time $E$, in relation to interrogation time interval ${\rm\Delta}t$, on analysis of Brownian motion of small particles using numerical simulation of the Langevin equation for both free diffusion and hindered diffusion near a solid wall. The simulation result for free diffusion recovers the known scaling law for the dependence of estimated diffusion coefficient on $E/{\rm\Delta}t$, i.e. for $0\leqslant E/{\rm\Delta}t\leqslant 1$ the estimated diffusion coefficient scales linearly as $1-(E/{\rm\Delta}t)/3$. Extending the analysis to the parameter range $E/{\rm\Delta}t\geqslant 1$, we find a new nonlinear scaling behaviour given by $(E/{\rm\Delta}t)^{-1}[1-((E/{\rm\Delta}t)^{-1})/3]$, for which we also provide an exact analytical solution. The simulation of near-wall diffusion shows that hindered diffusion of particles parallel to a solid wall, when normalized appropriately, follows with a high degree of accuracy the same form of scaling laws given above for free diffusion. Specifically, the scaling laws in this case are well represented by $1-((1+{\it\epsilon})(E/{\rm\Delta}t))/3$, for $E/{\rm\Delta}t\leqslant 1$, and $(E/{\rm\Delta}t)^{-1}[1-((1+{\it\epsilon})(E/{\rm\Delta}t)^{-1})/3]$, for $E/{\rm\Delta}t\geqslant 1$, where the small parameter ${\it\epsilon}$ depends on the size of the near-wall domain used in the estimation of the diffusion coefficient and value of $E$. For the range of parameters reported in the literature, we estimate ${\it\epsilon}<0.03$. The near-wall simulations also show a bias in the estimated diffusion coefficient parallel to the wall even in the limit $E=0$, indicating an overestimation which increases with increasing time delay ${\rm\Delta}t$. This diffusion-induced overestimation is caused by the same underlying mechanism responsible for the previously reported overestimation of mean velocity in near-wall velocimetry.

Shielding Effects in Polymer‐Polymer Reactions, 6

Pairs of linear chains – the end segment of one of each fixed at a surface – are analyzed for the relative probability of mutual contact formation between particularly specified segments i and j belonging to different chains within these pairs. Several positions are of general interest only, while other portray specific experimental conditions, e.g., the basic step in surface initiated Z‐RAFT polymerization (contact of the end of the free chain with the anchored segment of the fixed one). Contact probabilities are calculated for athermal cubic lattice chains by means of exact enumeration. Basic results are chain‐length dependences of shielding factors Kij in form of scaling laws and changes of size and shape properties of the involved molecules while approaching and penetration as functions of chain separation.

User capacity scaling laws for fading multiple-access channels

In this paper, the maximum number of simultaneous active transmitters (i.e. user capacity) is obtained in the many user case for fading multiple-access channels in which a minimum rate must be maintained for all active users. The results are presented in the form of scaling laws as the number of transmitters increases and three commonly used fading models, namely, Rayleigh, Rician and Nakagami are considered. It is shown that in all three cases, the user capacity scales double logarithmically with the number of users and differs only by constants depending on the distributions. We also show that the scheduling policy maximizing the number of simultaneous active transmitters can be implemented in a distributed fashion.

The Implications of Scaling Approaches for Understanding Resilience and Reorganization in Ecosystems

ABSTRACT Managing ecosystems for resilience—the capacity to maintain function in response to perturbation—is among the most pressing ecological and socioeconomic imperatives of our time. The variability of biological and ecological systems at multiple scales in time and space makes this task even more challenging, yet diverse ecological systems often display striking regularities. These regularities often take the form of scaling laws, which describe how the structure and function of the system change systematically with scale. In this article, we review recent work on the scaling of human settlement sizes and fertility as well as the size distributions of forests. We demonstrate that systematic departures from expected ecological scaling relationships may indicate particular structuring processes (e.g., fire) or the perturbation and reorganization of ecosystems. In sum, we argue that scaling provides a powerful tool for understanding resilience and change in ecological systems.

An evolutionary theory for interpreting urban scaling laws

We try here to illustrate the relevance of an evolutionary theory of urban systems for explaining their hierarchical properties. The largest cities became larger because they were successful in adopting many successive innovations. Larger cities capture innovations in a continuous way (through adaptation, imitation, anticipation), and they concentrate a larger part of anything « new » at any time. Their functions demonstrate a higher level of complexity or sophistication of their urban activity and society. The most advanced technologies concentrate in largest cities, the common place activities are ubiquitous, whereas old ones remain in small towns only (or, in economic terms, there are increasing, constant or decreasing returns to urban scale). Such regularities can be expressed in the form of scaling laws that were recognised as revealing specific constraints on the structure and evolution of complex systems in physics and biology. Approaching urban activities by scaling laws provides a linkage between the concepts of urban function, city size, and innovation cycles. Over time, there is a substitution among the activities of the largest cities, where the oldest technologies and professions are replaced by the new ones, while the old ones are relatively concentrating in the smallest towns. Such an evolution is observed within urban systems where cities are fully connected and interdependent. There are processes of cooperation through exchanges of information and learning that enable an incremental diffusion of innovation and a continuous adaptation of urban activities and society in all parts of the system. Meanwhile, there are also processes of competition between cities that enhance their capacity to innovate and to levy the benefits of innovation. A distributed process of urban growth including a slight but continuing advantage for the largest cities is the result of that competitive process, while the successive adaptation of the urban functions follows the economic and social innovation cycles.

Hyperfine Induced Transitions as Diagnostics of Isotopic Composition and Densities of Low‐Density Plasmas

The J = 0 --> J' = 0 radiative transitions, usually viewed as allowed through two-photon decay, may also be induced by the hyperfine (HPF) interaction in atoms or ions having a nonzero nuclear spin. We compute new and review existing decay rates for the nsnp P-3(J)0 --> nS(2 1)S(J'= 0) transitions in ions of the Be (n = 2) and Mg (n = 3) isoelectronic sequences. The HPF induced decay rates for the J = 0 --> J' = 0 transitions are many orders of magnitude larger than those for the competing two-photon processes, and when present are typically 1 or 2 orders of magnitude smaller than the decay rates of the magnetic quadrupole (J = 2 --> J' = 0) transitions for these ions. Several HPF induced transitions are potentially of astrophysical interest in ions of C, N, Na, Mg, Al, Si, K, Cr, Fe, and Ni. We highlight those cases that may be of particular diagnostic value for determining isotopic abundance ratios and/or electron densities from UV or EUV emission-line data. We present our atomic data in the form of scaling laws so that, given the isotopic nuclear spin and magnetic moment, a simple expression yields estimates for HPF induced decay rates. We examine some UV and EUV solar and nebular data in light of these new results and suggest possible applications for future study. We could not find evidence for the existence of HPF induced lines in the spectra we examined, but we demonstrate that existing data have come close to providing interesting upper limits. For the planetary nebula SMC N2, we derive an upper limit of 0.1 for C-13/C-12 from Goddard High-Resolution Spectrograph data obtained by Clegg. It is likely that more stringent limits could be obtained using newer data with higher sensitivities in a variety of objects. (Less)

Random walks on fractals

Random walks (RWs) and related stochastic techniques have become ubiquitous tools in many areas of physics recently. Fractals are no exception. Random walks on fractals have an added interest: random walk trails (e.g. sample paths of Brownian motion) are themselves fractal in general, and interesting kinds of behavior emerge when they occur on fractal structures, in the form of scaling laws. In the case of random Factals, one has a “random walk on a random walk”. This is an instance of a so-called “random” random walk, in the study of which considerable progress has recently been made.

Simulation of polymer chains in elongational flow. Kinetics of chain fracture and fragment distribution

In this paper the Brownian dynamics technique for computer simulation of the fracture of polymer chains in a dilute solution subjected to elongational flow was used. Individual randomly coiled chains are placed at the stagnation point of a steady, uniaxial flow, and their evolution with time is monitored for chain fracture. The chains are modeled either as Rouse chains with a cutoff spring length, or as chains of springs obeying a Morse potential. Kinetic parameters are the first-order kinetic constant and the half-life time. The dependence of these parameters with elongational rate and chain length is expressed in the form of scaling laws, and the results are compared for the two models. Also studied was the size distribution of the resulting fracture fragments, finding that it may vary from sharply peaked to uniform, depending on the strength of the flow.

Squeezing versus photon-number fluctuations.

After deriving a general formula for the quantum probability distribution function higher moments, we apply it to the multiphoton squeezed states [the usual Gaussian and the new non-Gaussian Weyl-Heisenberg, SU(2), and SU(1,1)]. The resulting moments are discussed as functions of the photon-number fluctuations. General criteria are considered to determine optimal squeezing properties with respect to photon-number noise. There result interesting generalized uncertainty relations in the form of scaling laws.