Power-law Exponent Research Articles

Manifestation of Rouse and Entanglement Dynamics in Non-Cross-Linked and Cross-Linked Polymers Studied by Field-Cycling and Multiple Quantum NMR.

Rubbers prepared from technical poly(butadiene) and natural poly(isoprene) are studied by field-cycling (FC) 1H NMR relaxometry to elucidate the changes of the relaxation spectrum. Starting with the non-cross-linked polymer successively cross-links are introduced via sulfur or peroxide vulcanization. Applying an advanced home-built relaxometer allows one to probe entanglement dynamics in addition to Rouse dynamics. We show that entanglement dynamics evidenced in terms of a characteristic power-law in the NMR susceptibility is still observed with an exponent identical to that in non-cross-linked linear polymers. Yet, the entanglement regime disappears more and more from the accessible frequency window upon increasing the cross-link density and a spectrally enlarged Rouse regime is revealed. Adding a swelling agent, the manifestation of the Rouse and entanglement regimes virtually does not change, yet, the apparent power-law exponents increase. Concomitant multiple-quantum (MQ) 1H NMR experiments provide information on the structure of the rubber network in terms of the residual dipolar coupling and the fraction of the network defects, i.e., persisting entangled or nonentangled chains, introduced upon cross-linking and swelling.

Dynamic analysis of viscoelastic functionally graded nanoplate

In this article, the dynamic behavior of nanoplates under time-dependent load is investigated, focusing on functionally graded viscoelastic materials and nanoscale effects. Eringen’s nonlocal elasticity theory is utilized to examine mechanical response of the nanoplate. Hamilton’s principle is utilized to derive the equations of motion, taking into account both kinetic and potential energy aspects. The obtained complex partial differential equations are then solved employing Navier method and provides an efficient way to obtain analytical solutions. The study initially performed a free vibration analysis for functionally graded nanoplate, comparing the obtained results with those available in the literature to validate the developed method. Following this validation, a parametric analysis was conducted to examine the influence of both nonlocal parameter, which accounts for nanoscale effects, and power law exponent governing material gradation on free vibration behavior of functionally graded nanoplate. Finally, as the original contribution of this study, a damped forced vibration analysis was carried out within the scope of the parametric study, investigating the effects of power law exponents, viscoelastic parameters, nonlocal parameters, and various geometric properties on functionally graded viscoelastic nanoplates’ the displacement-time relationship and maximum displacements.

Highly ordered breath figures on pure chloroform fluid surface

The natural phenomenon of water vapor condensing on a cold surface is known as breath figures (BFs). The growth process of BFs on solid and fluid surfaces has been thoroughly investigated to understand the mechanism of BFs. It is fascinating that ordered BFs can be created on volatile fluid surfaces, highlighting the significant influence of the surface on BF growth. Currently, however, the growth of ordered BFs remains unclear and ambiguous. Herein, an optical microscope was used to observe in situ the growth process of BFs on pure chloroform fluid surface under static humid conditions. The details of the obtained images were analyzed in combination with image processing. It is found that BFs are highly ordered on the pure chloroform fluid surface. The dynamics of BF growth on the volatile fluid surface presented two power-law growth exponents of 1.40 during the intermediate stage and 0.22 during the late stage. Furthermore, BFs on the chloroform surface demonstrate rapid movement throughout the growth process, indicating a strong convection current within the volatile fluid. The obtained results confirm the ordered BFs on the surface of chloroform fluid, aiding in the clarification of the mechanism behind ordered BFs on volatile fluid surfaces.

Granular memristors with tunable stochasticity.

Most realizations of memristive devices exhibit characteristic noise sometimes described as random telegraph noise. These fluctuations in current, ubiquitous in nature, carry significant implications for device performance, reliability, and the broader landscape of memristor technology applications. Here, we study inherent random fluctuations observed in silver based granular memristive devices operating under steady bias conditions. Random telegraph noise observed in our system is characterized in terms of distributions of ON and OFF times of the current flow at a particular bias. We find that these fluctuations adhere to power law statistics with , where τOFF/ON denotes the time during which the output value remains below or above a specified threshold. We follow the fluctuations for up to four decades. Significantly, unlike previous studies, we find the emergence of a new regime of behavior where the power law exponent varies as a function of applied bias. We find that our results are best described by the Marcus-Tang expression for diffusion along intersecting parabolae with bias as the driving force. The predictions of this picture of dynamics also provide a satisfactory explanation for the quiescence of the OFF/ON state of our devices.

Modeling of comet water production. I. Sensitivity to macro- and micro-model parameters

This study investigates the impact of microscopic and macroscopic cometary surface properties on water production variations with heliocentric distance, focusing on dust layer thickness, grain size, nucleus shape, and spin axis orientation. We employed a two-layer thermophysical model to calculate effective gas production, incorporating a dust layer of porous aggregates of submillimeter- and millimeter-sized grains. The model includes radiative thermal conductivity and permeability for volatile diffusion and considers dust layer evolution and tensile strength. We examined different cometary nucleus shape models based on spacecraft observations and calculated power-law exponents for water production rates as functions of heliocentric distance. A two-layer outgassing model with fixed layer properties showed minimal qualitative differences from a simpler water ice sublimation model. The study reaffirms the critical role of the spin axis inclination and illuminated cross-section variation with the heliocentric distance in gas production. Using 67P/Churyumov-Gerasimenko's orbital parameters, the study demonstrates that dust accumulation and layer growth significantly alter production rate exponents. Additionally, considering tensile strength in a homogeneous spherical nucleus model revealed the potential for local dust crust removal near perihelion. Macroscopic properties such as nucleus shape and spin axis orientation significantly influence water production rate variations with heliocentric distance. Microscopic surface characteristics and dust layer growth also play crucial roles in cometary activity. Incorporating tensile strength and dust removal mechanisms into models provides a more accurate representation of comet activity, particularly near perihelion. This refined model enhances our understanding of comet outgassing, highlighting the importance of detailed surface property data for an accurate interpretation of observations.

Prediction of Fretting Wear Lifetime of a Coated System

This article proposes a model of predicting the fretting wear lifetime of a low-friction coating. The proposed model incorporates multiple factors that influence the fretting wear damage of coatings: the imposed contact load, imposed average velocity, coating hardness, and initial surface roughness of counterparts. The fretting wear lifetime of coatings, defined as the number of cycles critical to friction coefficient evolution, was collected from the literature. For the purpose of identifying parameters in the model, experimental fretting wear lifetime data were analyzed. The results show that the fretting wear lifetime of a coating can be described by an inverse power law regarding the contact load, imposed average velocity, and initial surface roughness of counterparts. In contrast, the fretting wear lifetime of a coating was observed to increase with increased coating hardness. It was observed that the exponents of the inverse power law varied with respect to the type of coating. The proposed fretting wear lifetime model enables the prediction of coating lifetime under various fretting conditions.

Comparing prediction efficiency in the BTW and Manna sandpiles

The state-of-the-art in the theory of self-organized criticality reveals that a certain inactivity precedes extreme events, which are located on the tail of the event probability distribution with respect to their sizes. The existence of the inactivity allows for the prediction of these events in advance. In this work, we explore the predictability of the Bak–Tang–Wiesenfeld (BTW) and Manna models on the square lattice as a function of the lattice length. For both models, we use an algorithm that forecasts the occurrence of large events after a fall in activity. The efficiency of the prediction can be universally described in terms of the event size divided by an appropriate power-law function of the lattice length. The power-law exponents are projected to be 2.75 and 3 for the Manna and BTW models respectively. The scaling with the exponent 2.75 is known for collapsing of the entire size-frequency relationship in the Manna model. However, the correspondence between events on different lattices in the BTW model requires a variety of exponents where 3 is the largest. This indicates that in thermodynamic limit, prediction does exist in the Manna but not in the BTW model, at least based on inactivity. The difference in the universality classes may underline the difference in the prediction.

A game theoretic complex network model to estimate the epidemic threshold under individual vaccination behaviour and adaptive social connections

In today’s interconnected world, the spread of information is closely linked to infectious disease dynamics. Public awareness plays a crucial role, as individual vaccination decisions significantly impact collective efforts to combat emerging health threats. This study explores disease transmission within a framework integrating social connections, information sharing, and individual vaccination decisions. We introduce a behaviour-prevalence model on an adaptive multiplex network, where the physical layer (Layer-II) captures disease transmission under vaccination. In contrast, the virtual layer (Layer-I) represents adaptive social contacts and the flow of information, shaping vaccination decisions within a socially influenced environment. We derive analytical expressions for the epidemic threshold using the microscopic Markov Chain Method (MMCM). Simulation results highlight that adaptive social contacts lead to a higher epidemic threshold than non-adaptive networks. Additionally, network characteristics, such as the power-law exponent in scale-free networks, significantly impact infection spread within populations. Our results reveal that changes in perceived infection risk and an individual’s sensitivity to non-vaccinated neighbour’s status strongly influence vaccine uptake across populations. These insights can guide public health officials in developing targeted vaccination programs that address the evolving dynamics of social connections, information dissemination, and vaccination choice in the digital era.

Haar wavelet analysis of axisymmetric vibration of 2-D functionally graded porous thin annular plate resting on the Winkler foundation

Purpose In this paper, free axisymmetric vibration analysis of a two-directional functionally graded porous thin annular plate resting on the Winkler foundation is presented utilizing the classical plate theory (CPT). The mechanical properties are considered to be varying in the radial-thickness plane.Design/methodology/approach Based on the CPT, the governing differential equation of motion is derived. The highest-order derivative of displacement is approximated by Haar wavelets and successive lower-order derivatives are obtained by integration. The integration coefficients are calculated using boundary conditions. The fundamental frequency for clamped-clamped, clamped-simply supported, simply supported-clamped and simply supported-simply supported boundary conditions is obtained.Findings The effects of the porosity coefficient, the coefficient of radial variation, the exponent of power law, the foundation parameter, the aspect ratio and boundary conditions are investigated on fundamental frequency. A convergence study is conducted to validate the present analysis. The accuracy and reliability of the Haar wavelets are shown by comparing frequencies with those available in the literature. Three-dimensional mode shapes in the fundamental mode for all four boundary conditions are presented.Originality/value Based on the Haar wavelet method, a free axisymmetric vibration model of a porous thin annular plate is solved in which 2-D variation of mechanical properties is considered.

Filtered Point Processes Tractably Capture Rhythmic And Broadband Power Spectral Structure in Neural Electrophysiological Recordings.

Neural electrophysiological recordings arise from interacting rhythmic (oscillatory) and broadband (aperiodic) biological subprocesses. Both rhythmic and broadband processes contribute to the neural power spectrum, which decomposes the variance of a neural recording across frequencies. Although an extensive body of literature has successfully studied rhythms in various diseases and brain states, researchers only recently have systematically studied the characteristics of broadband effects in the power spectrum. Broadband effects can generally be categorized as 1) shifts in power across all frequencies, which correlate with changes in local firing rates and 2) changes in the overall shape of the power spectrum, such as the spectral slope or power law exponent. Shape changes are evident in various conditions and brain states, influenced by factors such as excitation to inhibition balance, age, and various diseases. It is increasingly recognized that broadband and rhythmic effects can interact on a sub-second timescale. For example, broadband power is time-locked to the phase of <1 Hz rhythms in propofol induced unconsciousness. Modeling tools that explicitly deal with both rhythmic and broadband contributors to the power spectrum and that capture their interactions are essential to help improve the interpretability of power spectral effects. Here, we introduce a tractable stochastic forward modeling framework designed to capture both narrowband and broadband spectral effects when prior knowledge or theory about the primary biophysical processes involved is available. Population-level neural recordings are modeled as the sum of filtered point processes (FPPs), each representing the contribution of a different biophysical process such as action potentials or postsynaptic potentials of different types. Our approach builds on prior neuroscience FPP work by allowing multiple interacting processes and time-varying firing rates and by deriving theoretical power spectra and cross-spectra. We demonstrate several properties of the models, including that they divide the power spectrum into frequency ranges dominated by rhythmic and broadband effects, and that they can capture spectral effects across multiple timescales, including sub-second cross-frequency coupling. The framework can be used to interpret empirically observed power spectra and cross-frequency coupling effects in biophysical terms, which bridges the gap between theoretical models and experimental results.

Structural and hydrodynamic controls on fluid travel time distributions across fracture networks

Fracture networks are preferential flow paths playing a critical role in a wide range of environmental and industrial problems. Their complex multiscale structure leads to broad distributions of fluid travel times, affecting many biogeochemical processes. Yet, the relationship between the fracture network structures, their hydrodynamic properties, and the resulting anomalous transport dynamics remains unclear. We use a large database of fracture network models to investigate the factors controlling fluid velocity and travel-time distributions across a wide range of networks, from synthetic to field-calibrated models, with aperture variability at both fracture and network scales. Analysis reveals that transport statistics have generic properties across investigated networks, including notably heavy-tailed travel time distributions. Networks of increasing complexity and heterogeneity lead to broader velocity distributions and more channeled velocity fields, where flow concentrates in a narrow channel web in the three-dimensional (3D) fracture structure. While heterogeneity in point-velocity statistics increases travel-time variability, channeling tends to reduce it. This counterintuitive phenomenon challenges current theories, which assume that long travel time power law exponents are determined solely by point-velocity statistics. By analyzing velocity and travel time statistics for different flow structures, we develop a coupled Continuous Time Random Walk framework capturing the unexpected control of the velocity field's spatial structure on anomalous transport in fracture networks. This leads to a unique class of random walk models capturing the respective roles of velocity heterogeneity and spatial structure on transport in networks. These findings open a prospective for characterizing, modeling, and predicting transport dynamics in complex networks, with potential applications to geological, biological, and engineered networks.

Full-scale experiments on fire smoke spreading respectively under natural and hybrid ventilation in a real urban road tunnel with shafts

In the past two decades, some shallow-buried urban road tunnels with shafts (URTS) have been built and operated in large cities in China, and successfully released the traffic congestion. However, uncertainties of fire smoke exhausting and individual safety have still been worried. Here, an idea of installing and operating the axial exhaust fans inside the unit shafts near to the fire source is proposed, then a hybrid ventilation is formed that combines both natural and mechanical ventilation. Three sets of full-scale fire experiments were carried out on a real URTS in Nanjing China. A 1.6 m (length) × 1.6 m (width) pan was placed on the ground in middle of the 264 m longest buried section. Diesel oil was used as the fire source. Fire 1 was conducted in a hot summer under pure natural ventilation without fan working. Fires 2 and 3 were conducted in a cold winter respectively without and with three SHANGFENG HTF-Ⅱ-5.5C fans working. Smoke parameters of temperature, velocity and CO concentration were recorded by monitors respectively under the ceiling, inside the shafts, on the shaft tops and at the shaft bottoms. Inhibition coefficient fi is proposed to evaluate the influence of the fans working on the smoke flow of those non-fanned shafts. Results show that the dual power-law exponent function provided a better fit for the ceiling temperature decay, and the decay coefficients ranged from 0.042 to 0.069 with the sortation: Fire 2 > Fire 3 > Fire 1. On top openings of the shafts, parameters reached up to 47 °C in temperature, 4.6 m/s in velocity, and 120 ppm in CO concentration. Mass flow rates of the unit shafts differed in range of 0.24 ∼ 2.03 kg/(s·m2) that decreased away from the fire sources in Fires 1 and 2, but increased away from the fanned-shafts in Fire 3. Wang model provides a better similar result to that under measurement. The coefficients fi ranged from −0.5 to 1.29. The fan operations did promote the smoke discharge of the non-fanned shafts close tightly to the fanned shafts, but reduce the discharge some far away from the fanned shafts. This study provides on-site data in URTS firing, and ascertains the useful of operating the shaft axial fans in promoting the smoke control.

Static, free vibration, and buckling analysis of functionally graded plates using the dual mesh control domain method

In this paper, the Dual Mesh Control Domain Method (DMCDM) put forward by Reddy is applied to solve linear static, free vibration, and buckling problems of functionally graded plates modeled using the First-Order Shear Deformation Theory (FSDT). The material properties are assumed to vary continuously through the thickness of the plate according to a power-law. Formulations are presented for linear triangular (3-noded) and bilinear quadrilateral (4-noded) primal elements of arbitrary shape. The influence of the power-law exponents, length to thickness ratio, boundary conditions, and plate skewness on the numerical solution is systematically analyzed. Additionally, the numerical solutions using the DMCDM are compared against those from the Finite Element Method (FEM) to demonstrate the robustness of the DMCDM as a strong competitor to well-established numerical techniques such as the FEM.

Size scaling of large landslides from incomplete inventories

Abstract. Landslide inventories have become cornerstones for estimating the relationship between the frequency and size of slope failures, thus informing appraisals of hillslope stability, erosion, and commensurate hazard. Numerous studies have reported how larger landslides are systematically rarer than smaller ones, drawing on probability distributions fitted to mapped landslide areas or volumes. In these models, much uncertainty concerns the larger landslides (defined here as affecting areas ≥ 0.1 km2) that are rarely sampled and often projected by extrapolating beyond the observed size range in a given study area. Relying instead on size-scaling estimates from other inventories is problematic because landslide detection and mapping, data quality, resolution, sample size, model choice, and fitting method can vary. To overcome these constraints, we use a Bayesian multi-level model with a generalised Pareto likelihood to provide a single, objective, and consistent comparison grounded in extreme value theory. We explore whether and how scaling parameters vary between 37 inventories that, although incomplete, bring together 8627 large landslides. Despite the broad range of mapping protocols and lengths of record, as well as differing topographic, geological, and climatic settings, the posterior power-law exponents remain indistinguishable between most inventories. Likewise, the size statistics fail to separate known earthquakes from rainfall triggers and event-based triggers from multi-temporal catalogues. Instead, our model identifies several inventories with outlier scaling statistics that reflect intentional censoring during mapping. Our results thus caution against a universal or solely mechanistic interpretation of the scaling parameters, at least in the context of large landslides.

Characteristic Analysis of Vertical Tidal Profile Parameters at Tidal Current Energy Site

Many mathematical models have been proposed to estimate vertical tidal current profiles. However, as previous studies have shown that tidal current energy sites have different characteristics in their vertical tidal current profiles, it is necessary to estimate the profiles from field-measured data for practical purposes. In this study, we measured layered tidal currents over two months using an acoustic Doppler current profiler (ADCP) to analyze the characteristics of vertical tidal current profiles at the Jangjuk Strait, a candidate site for tidal current energy. As a result, the power law parameter α and bed roughness β were estimated as 4.51–12.41 and 0.38–0.42, respectively. Additionally, the maximum roughness length representing seabed roughness in the logarithmic profile was estimated as 0.221 m, and the estimated friction velocity was 0.038–0.194 m/s. Furthermore, a high correlation was observed between the depth-averaged tidal current velocity and friction velocities at all sites during flood and ebb tide conditions. A high correlation was also found between the bed roughness, roughness length, and power law exponent at relatively deeper sites. Tidal current energy sites display distinct characteristics compared to other sea areas. Therefore, it is essential to account for field conditions when conducting numerical modeling and design.

Electromagnetic frequency prediction pattern for electrical circuited shell based on FSTT theory using electromagnetic wave prediction method

This research focuses on electromagnetic analysis of electrical circuited shell to predict possible failure using wave prediction method. The equation is established considering axial and lateral hydrostatic pressure based on first order shear deformation theory of shell motion using the wave propagation approach and classic Flügge shell equations. For validation of accuracy of this research method, a comparison carried out with experimental data. With this method the effects of circuit parameters as well as different t power-law exponent on the frequencies are investigated. The results showed fantastic agreement between the present method and experimental ones.

Converging profile relationships for offshore wind speed and turbulence intensity

Abstract. This paper reduces uncertainty in the quantification of offshore wind speed and turbulence intensity. A range of industry standard relationships, including those from International Electrotechnical Commission (IEC) and International Organization for Standardization (ISO), are compared with an extensive set of met mast data collected offshore northwestern Europe over recent decades. Analysis initially focused on over 1000 independent storm peak events identified within the 10 min mean wind speed data. Time series and coherent vertical profiles were subjected to detailed scrutiny and analysis, considering wind speeds at various averaging periods, turbulence intensity and gust factors. Most peak events were associated with neutral atmospheric conditions, so they were well represented by the ISO Frøya profile, with a shear close to the IEC power law exponent of α= 0.11. A new pragmatic approximation of atmospheric stability in terms of relative shear is outlined, bringing together key elements of the IEC and ISO standards. New empirical relationships to quantify offshore wind ambient turbulence intensity are described. A simple generalised form of gust factor relationship is adopted, with a coefficient that varies with averaging period. Distinct recommendations are made for estimating peak 10 min mean winds from peaks in 1 or 3 h mean winds. Finally, a simplified workflow for the estimation of extreme offshore winds is used to show how IEC and ISO relationships can be effectively combined.

Nonlinear power-law creep of cell cortex: A minimal model

Experiments have revealed that biological cells exhibit a universal power-law rheology, but the underlying mechanisms remain elusive. Here, we present a minimal model to explain the power-law creep of cell cortex, which is abstracted as chains of crosslinkers with random binding energies. Using this model, we show that when both the load and chain length are small, the logarithm of both the strain and time scales with the fraction of unbound crosslinkers, leading to power-law creep with a constant exponent, as observed in many experiments. Increasing the load alters the latter relationship between time and unbinding fraction, and thus, increases the power-law exponent, explaining the stress-induced nonlinearity in some experiments. Increasing the chain length alters this relationship as well, and as a result, the exponent grows proportionally with the chain length, explaining the crosslinker-density-induced nonlinearity in other experiments. This work provides a mesoscopic explanation for the linear and nonlinear power-law creep of cell cortex and may serve as a basis for understanding the cytoskeletal mechanics.

Dynamic speculation and efficiency in European natural gas markets during the COVID-19 and Russia-Ukraine crises

Efficiency and dynamic speculation literature focused on financial and crude oil markets whereas empirical studies on natural gas markets are limited. This study examines market efficiency and dynamic speculation in major European natural gas hubs (the Zeebrugge (ZEE) hub of Belgium, Title Transfer Facility (TTF) hub of the Netherlands, and National Balancing Point (NBP) hub of the UK) during the COVID-19 pandemic and Russia-Ukraine conflict. Using the Asymmetric multifractal detrended fluctuation analysis (A-MFDFA) and the power law exponent (PLE) approach, we show that European natural gas markets exhibit an asymmetric multifractal behavior and long-memory effects, with variations observed during crises. The ZEE hub in Belgium and the NBP hub in the UK demonstrate a higher multifractality under different trends during the COVID-19 pandemic and the Russia-Ukraine conflict, respectively. Notably, the TTF hub in the Netherlands emerges as the most efficient market during all subperiods. Moreover, our results, using the PLE approach, suggest that European gas market inefficiencies during crises can be attributed to speculative strategies that create self-perpetuating dynamics and diminish market transparency, leading to heightened risk and volatility in gas prices. Our findings underscore the need for regulatory intervention to mitigate excessive speculation and enhance transparency in gas markets. Diversifying gas supplies and fortifying European gas hubs emerge as pivotal strategies to bolster resilience and stability during crises.

Differentiating neurodegenerative diseases based on EEG complexity

Neurodegenerative diseases are common causes of impaired mobility and cognition in the elderly. Among them, tauopathies and α-synucleinopathies were considered. The neurodegenerative processes and relative differential diagnosis were addressed through a qEEG non-linear analytic method. Study aims were to test accuracy of the power law exponent β applied to EEG in differentiating neurodegenerative diseases and to explore differences in neuronal connectivity among different neurodegenerative processes based on β. N = 230 patients with a diagnosis of tauopathy or α-synucleinopathy and at least one artifact-free EEG recording were selected. Periodogram was applied to EEG signal epochs from continuous recordings. Power law exponent β was determined by the slope of the signal power spectrum versus frequency in logarithmic scale. A data-driven clustering based on β values was performed to identify independent subgroups. Data-driven clustering based on β differentiated tauopathies (overall lower β values) from α-synucleinopathies (higher β values) with high sensitivity and specificity. Tauopathies also presented lower values in the correlation coefficients matrix among frontal sites of recording. In conclusion, significant differences in β values were found between tauopathies and α-synucleinopathies. Hence, β is proposed as a possible biomarker of differential diagnosis and neuronal connectivity.