Power-law Characteristics Research Articles

The arrest and recession dynamics of a deflating radial hydraulic fracture in a permeable elastic medium

In this paper we describe the post injection deflation dynamics of a radially symmetric hydraulic fracture in a permeable elastic medium. Depending on the parameters of the problem, the fracture may arrest almost immediately after injection has ceased, or continue to propagate despite the fluid loss to the porous medium. After arrest the fracture continues to deflate while the stress intensity factor decreases to zero, after which it recedes until the fracture finally collapses. In order to establish rigorous numerical solutions to explore this deflation dynamics, we make use of recent research (Peirce and Detournay, 2021) that derived vertex asymptotes for the arrest and recession phases of the deflation process as well as multiscale asymptotic solutions that connect these vertex asymptotes: during arrest, through the arrest–recession transition, and during recession. If only vertex asymptotes are used to capture the arrest and recession, the solution exhibits jump discontinuities through this arrest–recession transition point. We describe how the multiscale asymptotes can be used to obtain a smooth solution valid through the arrest–recession transition. Significantly, after the arrest–recession transition, the jump-induced transients decay and the solutions using vertex asymptotes converge to those that use multiscale asymptotes. Thus unless it is important to obtain a smooth solution through the arrest–recession transition, a practical, and more efficient, approach would be to use an algorithm based solely on vertex asymptotes. We also provide numerical confirmation of the emergence, beyond the arrest–recession transition time, of the dominant balance used in the asymptotic analysis to establish the linear recession asymptote wˆ∼rˆ. We present a novel scaling analysis to establish the characteristic power laws for the arrest time, arrest radius, arrest aperture, and the deflation time, in terms of two new dimensionless parameters, which make it possible to unify the power laws between the zero and finite toughness cases. These power laws show close agreement with those obtained by regression of the numerical results over a range of the dimensionless parameters. Numerical solutions are provided to illustrate the solution landscape in parameter space and the effect that each of the dimensionless parameters has on: the duration of the period of propagation after injection has ceased, the duration of the arrest period, and the time from the initiation of recession to collapse.

Frequency-dependent transition in power-law rheological behavior of living cells

Living cells are active viscoelastic materials exhibiting diverse mechanical behaviors at different time scales. However, dynamical rheological characteristics of cells in frequency range spanning many orders of magnitude, especially in high frequencies, remain poorly understood. Here, we show that a self-similar hierarchical model can capture cell’s power-law rheological characteristics in different frequency scales. In low-frequency scales, the storage and loss moduli exhibit a weak power-law dependence on frequency with same exponent. In high-frequency scales, the storage modulus becomes a constant, while the loss modulus shows a power-law dependence on frequency with an exponent of 1.0. The transition between low- and high-frequency scales is defined by a transition frequency based on cell’s mechanical parameters. The cytoskeletal differences of different cell types or states can be characterized by changes in mechanical parameters in the model. This study provides valuable insights into potentially using mechanics-based markers for cell classification and cancer diagnosis.

Ferromagnetic resonance modulation in d -wave superconductor/ferromagnetic insulator bilayer systems

We investigate ferromagnetic resonance (FMR) modulation in $d$-wave superconductor (SC)/ferromagnetic insulator (FI) bilayer systems theoretically. The modulation of the Gilbert damping in these systems reflects the existence of nodes in the $d$-wave SC and shows power-law decay characteristics within the low-temperature and low-frequency limit. Our results indicate the effectiveness of use of spin pumping as a probe technique to determine the symmetry of unconventional SCs with high sensitivity for nanoscale thin films.

Universal Conductance Scaling of Andreev Reflections Using a Dissipative Probe.

The Majorana search is caught up in an extensive debate about the false-positive signals from nontopological Andreev bound states. We introduce a remedy using the dissipative probe to generate electron-boson interaction. We theoretically show that the interaction-induced renormalization leads to significantly distinct universal zero-bias conductance behaviors, i.e., distinct characteristic power law in temperature, for different types of Andreev reflections, that show a sharp contrast to that of a Majorana zero mode. Various specific cases have been studied, including the cases in which two charges involved in an Andreev reflection process maintain or lose coherence, and the cases for multiple Andreev bound states with or without a Majorana. A transparent list of conductance features in each case is provided to help distinguish the observed subgap states in experiments, which also promotes the identification of Majorana zero modes.

Kink soliton behavior study for systems with power-law nonlinearity

In this study, we investigate the kink soliton dynamics for power-law nonlinear systems. Based on the F-expansion method, we first derive the novel kink soliton solution of the nonlinear Schrödinger equation (NLSE) with third-order dispersion term, power-law dependent nonlinearity term, linear attenuation term, and self-steepness term under appropriate parameter settings. With pictorial demonstration, we show that the obtained kink soliton solution not only has the soliton features of the classical NLSE, but also has power-law features. The theoretical results presented in our work can be used to guide the observation of soliton behavior in power-law dependent media.

High-frequency asymptotics of one integral in the theory of equilibrium radiation of electron gas

It is considered an improper integral that determines the high-frequency asymptotics of the spectral energy distribution of equilibrium radiation in an ideal electron gas. It has been established that in the "high-frequency" limit the asymptotics of this integral has a power-law character, and its value is proportional to the density of the electron gas as a function of temperature and chemical potential for arbitrary degeneracy of electrons. Keywords: equilibrium radiation, spectral energy distribution, electron gas.

Высокочастотная асимптотика одного интеграла в теории равновесного излучения электронного газа

It is considered an improper integral that determines the high-frequency asymptotics of the spectral energy distribution of equilibrium radiation in an ideal electron gas. It has been established that in the "high-frequency" limit the asymptotics of this integral has a power-law character, and its value is proportional to the density of the electron gas as a function of temperature and chemical potential for arbitrary degeneracy of electrons

The Contagion of Associated Credit Risk Based on the Real Estate Companies Network

This paper discusses the structural characteristics of the real estate company’s related network and the contagion law of the associated credit risk by constructing a model of associated credit risk contagion based on the real estate enterprise network.The study showed that the real estate companies network has the power-law characteristics of a scale-free network, the network density of parent companies is relatively high, local subsidiaries are isolated and the path becomes longer. At the same time, leading companies with different associated structures have significant differences in the impact on the rest of the companies after default. Furthermore, the credit risk of companies with complex relational structures is more difficult to affect individuals in the network.

Regularities of metal flow and defects transformation during rolling in roughing stands of a universal rail and structural mill

Experimental studies carried out in the conditions of a laboratory rolling mill have determined the regularities of the processes of metal flow and roll-out defects of billets during deformation in roughing stands of a universal rail and structural mill. In relation to the box size and gauges types "lying trapeze" and "trapeze", we have determined a significant irregularity of drawing coefficients of the surface layers by roll length and width, as well as the irregularity of drawing in the cross-section of the roll during rolling. It is shown that during deformation the surface zones adjacent to the ends of the roll are subjected to the greatest drawing, and dependence of irregularity of the drawing coefficients over the cross-section of the roll on the shape of the deformation zone has a distinct power-law character. We have established a significant effect of the drawing coefficient, as well as the location and spatial orientation of the billet defects, while the geometric dimensions of the defects don't have such influence on their roll-out coefficients. According to the obtained data, the defects located on the rolling edges are rolled out most intensively both in depth and width, and the transverse defects are rolled out the least intensively. At the same time, the rollability of any defects increases with the growth of drawing coefficient. It is determined that near the side edges of the roll there is an increase in the width (disclosure) of transverse and inclined defects relative to the rolling axis, as well as the disclosure of defects occurs at the end sections of the roll in relation to longitudinal defects. For internal defects, it was found that, similar to surface defects, an increase in the drawing coefficient during rolling contributes to an increase in their roll-out, while the rollout coefficient of internal defects in absolute value is significantly lower than this indicator for surface defects. It was determined that the minimum roll-out coefficient of internal defects occurs when they are located in the core of the sample, while the roll-out coefficient of such defects increases linearly when moving towards the roll surface. The influence of the location, spatial orientation, and drawing coefficient on the rollability of surface and internal defects is generalized in the form of regression equations. It makes it possible to use them in practice to predict the quality of finished rolled metal when changing rolling modes.

A hierarchical cellular structural model to unravel the universal power-law rheological behavior of living cells

Living cells are a complex soft material with fascinating mechanical properties. A striking feature is that, regardless of their types or states, cells exhibit a universal power-law rheological behavior which to this date still has not been captured by a single theoretical model. Here, we propose a cellular structural model that accounts for the essential mechanical responses of cell membrane, cytoplasm and cytoskeleton. We demonstrate that this model can naturally reproduce the universal power-law characteristics of cell rheology, as well as how its power-law exponent is related to cellular stiffness. More importantly, the power-law exponent can be quantitatively tuned in the range of 0.1 ~ 0.5, as found in most types of cells, by varying the stiffness or architecture of the cytoskeleton. Based on the structural characteristics, we further develop a self-similar hierarchical model that can spontaneously capture the power-law characteristics of creep compliance over time and complex modulus over frequency. The present model suggests that mechanical responses of cells may depend primarily on their generic architectural mechanism, rather than specific molecular properties.

The young Hobson family: Possible binary parent body and low-velocity dispersal

Context.Asteroid families with ages younger than 1 Myr offer an interesting possibility of studying the outcomes of asteroid disruptions that are little modified by subsequent evolutionary processes.Aims.We analyze a very young asteroid family associated with (18777) Hobson in the central part of the main belt. We aim at (i) understanding its peculiar size distribution, and (ii) setting an upper limit on the characteristic dispersal velocity at subkilometer sizes corresponding to the smallest visible Hobson members.Methods.We identified the Hobson family using an up-to-date asteroid catalog. A significant increase in the number of its known members allowed us to study their size distribution and compare it with computer simulations of catastrophic disruptions. Backward orbital integrations of the heliocentric orbits allowed us to confirm the previously suggested age of Hobson and helped to estimate limits of the ejection speed.Results.The Hobson family has an unusual size distribution: two nearly equal-size bodies, followed by a population of smaller asteroids, whose distribution takes a characteristic power law. There are two possibilities to explain these data. Either a canonical impact onto a single parent body, requiring fine-tuned impact conditions that have not been studied so far, or an unconventional model for the parent object of the Hobson family, namely a binary with ≃7−9 km primary and a ≃2.5 km secondary. In the latter case, the primary was disrupted, leaving behind the largest remnant (18777) Hobson and a suite of subkilometer asteroids. The second largest asteroid, (57738) 2001 UZ160, is the nearly intact satellite of the parent binary. The excellent convergence of nominal orbits of Hobson members sets an upper limit of ≃(10−20) m s−1for the initial dispersal velocity of the known members, which is consistent with both formation models. The Hobson family provides a so far rare opportunity of studying disruptions of small asteroids in a situation in which both the material strength and reaccumulation efficiency play an important role.

Alteration of power law scaling of spontaneous brain activity in schizophrenia

Nonlinear dynamical analysis has been used to quantify the complexity of brain signal at temporal scales. Power law scaling is a well-validated method in physics that has been used to describe the dynamics of a system in the frequency domain, ranging from noisy oscillation to complex fluctuations. In this research, we investigated the power-law characteristics in a large-scale resting-state fMRI data of schizophrenia and healthy participants derived from Taiwan Aging and Mental Illness cohort. We extracted the power spectral density (PSD) of resting signal by Fourier transform. Power law scaling of PSD was estimated by determining the slope of the regression line fitting to the logarithm of PSD. t-Test was used to assess the statistical difference in power law scaling between schizophrenia and healthy participants. The significant differences in power law scaling were found in six brain regions. Schizophrenia patients have significantly more positive power law scaling (i.e., more homogenous frequency components) at four brain regions: left precuneus, left medial dorsal nucleus, right inferior frontal gyrus, and right middle temporal gyrus and less positive power law scaling (i.e., more dominant at lower frequency range) in bilateral putamen compared with healthy participants. Moreover, significant correlations of power law scaling with the severity of psychosis were found. These findings suggest that schizophrenia has abnormal brain signal complexity linked to psychotic symptoms. The power law scaling represents the dynamical properties of resting-state fMRI signal may serve as a novel functional brain imaging marker for evaluating patients with mental illness.

Dynamic Study of Intelligent Traffic Behaviour Based on Multiple Traffic Modes

With the rapid development of society, the traffic problem has become increasingly severe, and the traditional methods can no longer effectively solve the current social traffic behaviour problems. Although studies on the dynamics of human traffic behaviour based on traffic modes can effectively reveal the anomalies in traffic behaviour, few studies integrate intelligent traffic behaviour with multiple traffic modes. Based on the numerous traffic data of bike-sharing and ride-hailing in a Chinese city, this paper reveals the dynamic characteristics of various traffic behaviours in the city by combining spatiotemporal characteristics index and urban spatial structure with human traffic behaviour patterns. The experimental results show that the traffic behaviour of the town presents a double logarithmic power-law distribution in time characteristics, and there is a close interdependent dynamic relationship with the city’s spatial structure. The research in this paper can reveal the relationship between bimodal power-law distribution and spatial characteristics in complex systems and help solve social traffic problems effectively in social reality. Further research results can provide practical planning guidance for the behavioural integration of multiple traffic in smart cities.

A computational model of insect campaniform sensilla predicts encoding of forces during walking

Control of forces is essential in both animals and walking machines. Insects measure forces as strains in their exoskeletons via campaniform sensilla (CS). Deformations of cuticular caps embedded in the exoskeleton excite afferents that project to the central nervous system. CS afferent firing frequency (i.e. ‘discharge’) is highly dynamic, correlating with the rate of change of the force. Discharges adapt over time to tonic forces and exhibit hysteresis during cyclic loading.In this study we characterized a phenomenological model that predicts CS discharge, in which discharge is proportional to the instantaneous stimulus force relative to an adaptive variable. In contrast to previous studies of sensory adaptation, our model (1) is nonlinear and (2) reproduces the characteristic power-law adaptation with first order dynamics only (i.e. no ‘fractional derivatives’ are required to explain dynamics). We solve the response of the system analytically in multiple cases and use these solutions to derive the dynamics of the adaptive variable. We show that the model can reproduce responses of insect CS to many different force stimuli after being tuned to reproduce only one response, suggesting that the model captures the underlying dynamics of the system. We show that adaptation to tonic forces, rate-sensitivity, and hysteresis are different manifestations of the same underlying mechanism: the adaptive variable. We tune the model to replicate the dynamics of three different CS groups from two insects (cockroach and stick insect), demonstrating that it is generalizable. We also invert the model to estimate the stimulus force given the discharge recording from the animal. We discuss the adaptive neural and mechanical processes that the model may mimic and the model’s use for understanding the role of load feedback in insect motor control. A preliminary model and results were previously published in the proceedings of the Conference on Biohybrid and Biomimetic Systems.

Vulnerability assessment of China–Europe Railway Express multimodal transport network under cascading failures

Transshipment and transnational long-haul transport make the multimodal transport network (MTN) vulnerable when subjected to unexpected disturbances, which may cause cascading failures. Therefore, this paper presents a dynamic layered road–rail MTN to measure the vulnerability of China–Europe Railway Express (CR Express) MTN. The statistical analysis of the topological characteristics and the final simulation results show that the layered road–rail MTN with priority connection mechanism exhibits power-law distribution characteristics. The final simulation results reveal that the road–rail MTN shows a better ability to suppress the risk cascading propagation when the transshipment coupling enhances the dynamic flexibility of the network. Although the optimal inter-layer transshipment coupling changes positively with the external disturbance and negatively with the intra-layer coupling in special cases, the moderate inter-layer coupling is still the most effective in improving the anti-cascading ability of general MTN. These findings provide recommendations for the CR Express MTN to suppress the cascading failures.

Exploring the possible gluon condensation signature in gamma-ray emission from pulsars

The very high energy gamma-ray emissions from pulsars are usually considered to be dominated by leptonic scenario since the hadronic flux is weak. We point out that the gluon condensation predicted by a nonlinear QCD evolution equation may greatly enhance the cross sections of proton-target interactions and give rise to a characteristic broken power law in the gamma-ray spectra. The result is used to explore the gluon condensation signature in the observed gamma-ray spectra from pulsars.

Time-averaged mean squared displacement ratio test for Gaussian processes with unknown diffusion coefficient.

The time-averaged mean squared displacement (TAMSD) is one of the most common statistics used for the analysis of anomalous diffusion processes. Anomalous diffusion is manifested by non-linear (mostly power-law) characteristics of the process in contrast to normal diffusion where linear characteristics are expected. One can distinguish between sub- and super-diffusive processes. We consider Gaussian anomalous diffusion models and propose a new approach used for their testing. This approach is based on the TAMSD ratio statistic for different time lags. Similar to the TAMSD, this statistic exhibits a specific behavior in the anomalous diffusion regime. Through its structure, it is independent of the diffusion coefficient, which, in general, does not influence anomalous diffusion behavior. Thus, the TAMSD ratio-based approach does not require preliminary knowledge of the diffusion coefficient's value, in contrast to the TAMSD-approach, where this value is crucial in the testing procedure. Based on the quadratic form representation of the TAMSD ratio, we calculate its main characteristics and propose a step-by-step testing procedure that can be applied for any Gaussian process. For the anomalous diffusion model used here, namely, the fractional Brownian motion, we demonstrate the effectiveness of the proposed methodology. We show that the new approach outperforms the TAMSD-based one, especially for small sample sizes. Finally, the methodology is applied to the real data from the financial market.

The characterization of turbulent heat and moisture transport during a gust-front event over the Indian peninsula

The ramifications of gust-front on atmospheric surface layer turbulence is a vexing issue, with nearly no information available over the Indian region where such events are not uncommon. Over the Indian peninsula, our recent field-experimental study has shown that a cold pool associated with the gust-front creates two distinct regimes in ASL turbulence, where temperature fluctuations display contrasting behavior. In this work, we use a multi-level observational dataset to evaluate the corresponding impacts on the moisture fluctuations and turbulent heat and moisture transport. We discover that the topology of the turbulent structures, which govern the temperature and moisture fluctuations, clearly exhibit a regime-wise distinction. In the first regime, the structures in temperature and moisture fluctuations are inclined in the vertical, while demonstrating a self-similarity in their time scales by being related through a power-law distribution. The inclination angle is inferred from the vertical shifts in the peak positions of the cross-correlation coefficients. However, in the second regime, the vertical inclination disappears for the temperature structures with hardly any change observed for the moisture. Moreover, the power-law exponents of the turbulent temperature time scales remain sensitive to the regimes, although no such effect is visible in the power-law character of the moisture time scales. Additionally, the dissimilarity in the heat and moisture transport is investigated through a novel polar-quadrant based approach that separates phases and amplitudes of the flux-transporting motions.

Asymmetric Rydberg blockade of giant excitons in Cuprous Oxide

The ability to generate and control strong long-range interactions via highly excited electronic states has been the foundation for recent breakthroughs in a host of areas, from atomic and molecular physics to quantum optics and technology. Rydberg excitons provide a promising solid-state realization of such highly excited states, for which record-breaking orbital sizes of up to a micrometer have indeed been observed in cuprous oxide semiconductors. Here, we demonstrate the generation and control of strong exciton interactions in this material by optically producing two distinct quantum states of Rydberg excitons. This is made possible by two-color pump-probe experiments that allow for a detailed probing of the interactions. Our experiments reveal the emergence of strong spatial correlations and an inter-state Rydberg blockade that extends over remarkably large distances of several micrometers. The generated many-body states of semiconductor excitons exhibit universal properties that only depend on the shape of the interaction potential and yield clear evidence for its vastly extended-range and power-law character.

Power law model for subjective mental workload and validation through air traffic control human-in-the-loop simulation

We provide evidence for a power law relationship between the subjective one-dimensional Instantaneous Self Assessment workload measure (five-level ISA-WL scale) and the radio communication of air traffic controllers (ATCOs) as an objective task load variable. It corresponds to Stevens’ classical psychophysics relationship between physical stimulus and subjective response, with characteristic power law exponent γ of the order of 1. The theoretical model was validated in a human-in-the loop air traffic control simulation experiment with traffic flow as environmental stimulus that correlates positively with ATCOs frequency and duration of radio calls (task load, RC-TL) and their reported ISA-WL. The theoretical predictions together with nonlinear regression-based model parameter estimates expand previously published results that quantified the formal logistic relationship between the subjective ISA measure and simulated air traffic flow (Fürstenau et al. in Theor Issues Ergon Sci 21(6): 684–708, 2020). The present analysis refers to a psychophysics approach to mental workload suggested by (Gopher and Braune in Hum Factors 26(5): 519–532, 1984) that was recently used by (Bachelder and Godfroy-Cooper in Pilot workload esimation: synthesis of spectral requirements analysis and Weber's law, SCL Tech, San Diego, 2019) for pilot workload estimation, with a corresponding power law exponent in the typical range of Stevens’ exponents. Based on the hypothesis of cognitive resource limitation, we derived the power law by combination of the two logistic models for ISA-WL and communication TL characteristics, respectively. Despite large inter-individual variance, the theoretically predicted logistic and power law parameter values exhibit surprisingly close agreement with the regression-based estimates (for averages across participants). Significant differences between logistic ISA-WL and RC-TL scaling parameters and the corresponding Stevens exponents as ratio of these parameters quantify the TL/WL dissociation with regard to traffic flow. The sensitivity with regard to work conditions of the logistic WL-scaling parameter as well as the power law exponent was revealed by traffic scenarios with a non-nominal event: WL sensitivity increased significantly for traffic flow larger than a critical value. Initial analysis of a simultaneously measured new neurophysiological (EEG) load index (dual frequency head maps, DFHM, (Radüntz in Front Physiol 8: 1–15, 2017)) provided evidence for the power law to be applicable to the DFHM load measure as well.