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In the context of the growing use of hydrogen for decarbonization in combustion, understanding NO x emissions from hydrogen burners is crucial. This study focuses on the impact of partial premixing on NO x production in hydrogen flames using a coaxial injector with swirl. The goal is to expand conventional jet scaling laws to encompass additional physical phenomena. The flexible injection system employed allows the stabilization of various flame types depending on the operating conditions, and double-front flames are obtained in several configurations. Observing the limitations of known scaling laws, particularly in coaxial flows with low-velocity differences or swirl, we conduct experiments measuring NO x and flame volume. Two Large Eddy Simulations explore distinct flame configurations to deepen our understanding about coaxial jet and recirculating flames, especially in the presence of a secondary premixed front due to rich premixing. Our investigation delves into the relationship between NO production and strain rate, considering turbulent and strain-related timescales. Notably, the presence of a premixed flame front alters the velocity profile on the shear layer, and the observed relationship between strain and turbulence in jet flames does not hold for recirculating flames. Thanks to this new insight, we propose a novel formulation for NO x scaling in coaxial jets, leveraging existing literature on coaxial jet modeling. Additionally, we propose a simple model to represent the piloting strain rate for NO emission in recirculating flames. Intricate effects of both swirl and partial-premixing are then included in the derived NO x scaling laws. [Display omitted] • Nitrogen oxide (NO x) emissions are measured in many swirled hydrogen flames. • Large-eddy simulations are used to enlighten the formation mechanisms. • Scaling laws for NO x emissions are derived to work for different flame topologies. [ABSTRACT FROM AUTHOR]

To enhance our understanding of soil behavior at critical states, considering that natural soil is composed of granular matter, a quasi-static inertia number taking soil compaction into account is proposed. In analyzing classical triaxial test data of soil, the scaling law of quasi-statically deforming grains at the critical state is explored; a simple linear relationship is found between the coefficient of friction and the proposed number. This scaling law describes quantitatively the influence of initial compaction, shear rate, confining pressure, and particle size on the frictional strength of granular soils when they reach the critical state. The number proposed is employed to describe the scaling of volumetric behavior of granular soils undergoing quasi-static deformation. The difference between the particle volume fraction at the critical state and that at the initial compacted state is also found to be linearly correlated with the quasi-static inertia number, for soil at the critical state. [ABSTRACT FROM AUTHOR]

The three‐dimensional structure of the Tropical Cyclone's baroclinic wake is synthesized as an averaged baroclinic‐dominant response of the upper ocean. The resulting persisting sea surface depression can easily be monitored using the present‐day altimeter constellation. Following a semi‐empirical framework, these baroclinic wake signatures are linked to the inner core TC dynamic and the ocean stratification. To collect these fine‐scale parameters, spaceborne SAR instruments and Argo fleet are used, to precisely capture the maximum wind region and the irregularities of the ocean vertical structure. This combination of high‐resolution information is found paramount to fully capture the modulation of sea surface height anomalies, and its mean trend, especially for major hurricanes. Baroclinic signatures mostly range around 10–20 cm and peak at 40 cm. Deeper anomalies correspond to barotropic response, removed from the present analysis. Plain Language Summary: In the wakes of Tropical Cyclones (TCs), sea surface depressions of about 10 cm appear. These TC signatures are persistent enough to be easily monitored by the current fleet of altimeter instruments. A measured sea surface height anomaly integrates and reduces the air/sea interactions during the TC passage into a single observable metric. It mostly encodes the cyclonic wind forcing and the interior ocean state. A broad constellation of remote sensing and in‐situ instruments has been gathered to compile 200 cyclonic episodes, collecting a wide range of TC sizes, intensities, and translation speeds together with oceanic conditions. A synthetic relationship is found to robustly predict most observed sea surface height anomalies. Moreover, when high‐resolution information is available to estimate the ocean interior state and the TC radius of maximum winds. Such a diagnostic thus explains the dominant baroclinic ocean response to a TC passage, and, inversely, can be used to infer ocean stratification or forcing parameters in the absence of high‐resolution observations. Key Points: Residual sea surface height anomalies from the cold wakes of Tropical Cyclones are analyzed using a multi‐modal approach at global scaleA scaling law provides a robust interpretation of the baroclinic response to given ocean stratification and forcing conditionsHigh resolution measurements are found critical to correctly anticipate the SSHA amplitudes with localized pre‐storm ocean stratification [ABSTRACT FROM AUTHOR]

We develop a methodology to compile an objective tremor catalog by utilizing distinctive event features that differentiate tectonic tremors from non‐tremor events, and combining the envelope cross‐correlation method with clustering technique and neural network. This approach enables tremor extraction without subjective criteria, allowing for the detection of previously overlooked short‐duration tremors. The event features employed to distinguish tremors and non‐tremor events are depth, the mean amplitudes at high and low frequencies, the ratio of these two amplitudes, and event duration. The duration is defined as the minimum period that contains 50% of the seismic energy. The application of this method to western Japan detects 1.7 times more tremors than the previous studies, with the durations of 0.3–∼100 s. The events with short durations are considered low‐frequency earthquakes. The relationship between seismic moment and duration of the detected tremors is consistent with the scaling law of slow earthquakes. Plain Language Summary: Slow earthquakes are characterized by very slow underground deformation compared with regular (fast) earthquakes and are important for understanding the preparation period prior to large earthquakes. Tectonic tremors, which are a type of slow earthquakes, radiate tiny seismic waves with frequencies of several Hz, occur episodically and densely in space and time, and may last for long durations of up to several hundred seconds, which is much longer than the durations of fast earthquakes of equivalent magnitude. In this study, we detect and differentiate tectonic tremors from fast earthquakes and anthropogenic events. We do this using a set of event features, without relying on subjective criteria. The durations of the detected tremors range from 0.3 to ∼100 s, and they appear consistent with a previously proposed scaling relationship for slow earthquakes. This result suggests that fast earthquakes and slow earthquakes have different physical mechanisms. Key Points: We compile a more complete tectonic tremor catalog for western Japan using a clustering method based on event featuresEvent duration, newly defined using energy radiation, clearly separates tectonic tremors from fast earthquakesTectonic tremors, ranging in duration from 0.3 to 100 s, are consistent with the scaling law of slow earthquakes [ABSTRACT FROM AUTHOR]

Radiative natural convection is of vital importance in the process of energy storage, power generation, and thermal storage technology. As the attenuation coefficients of many heat transfer media in these fields are high enough to be considered as optically thick media, like nanofluids or molten salts in concentrated solar power or phase change thermal storage, Rosseland approximation is commonly used. In this paper, we delve into the impact of thermal radiation on the Rayleigh-Bénard (RB) convection. Theoretical analysis has been conducted by modifying the Grossmann-Lohse (GL) model. Based on turbulent dissipation theory, the corresponding scaling laws in four main regimes are proposed. Direct numerical simulation (DNS) was also performed, revealing that radiation exerts a notable influence on both flow and heat transfer, particularly on the formation of large-scale circulation. By comparing with DNS results, it is found that due to the presence of radiation, the modified Nu scaling law in small Pr range of the GL model is more suitable for predicting the transport characteristics of optical thick media with large Pr. The maximum deviation between the results of DNS and prediction model is about 10%, suggesting the summarized scaling law can effectively predict the Nu of radiative RB convection. [ABSTRACT FROM AUTHOR]

An unstably stratified flow entering into a stably stratified flow is referred to as penetrative convection, which is crucial to many physical processes and has been thought of as a key factor for extreme weather conditions. Past theoretical, numerical, and experimental studies on penetrative convection are reviewed, along with field studies providing insights into turbulence modeling. The physical factors that initiate penetrative convection, including internal heat sources, nonlinear constitutive relationships, centrifugal forces and other complicated factors are summarized. Cutting-edge methods for understanding transport mechanisms and statistical properties of penetrative turbulence are also documented, e.g., the variational approach and quasilinear approach, which derive scaling laws embedded in penetrative turbulence. Exploring these scaling laws in penetrative convection can improve our understanding of large-scale geophysical and astrophysical motions. To better the model of penetrative turbulence towards a practical situation, new directions, e.g., penetrative convection in spheres, and radiation-forced convection, are proposed. [ABSTRACT FROM AUTHOR]

In this manuscript, singularly perturbed energies with 2, 3, or 4 preferred gradients subject to incompatible Dirichlet boundary conditions are studied. This extends results on models for martensitic microstructures in shape memory alloys ( N = 2 ), a continuum approximation for the J 1 - J 3 -model for discrete spin systems ( N = 4 ), and models for crystalline surfaces with N different facets (general N). On a unit square, scaling laws are proved with respect to two parameters, one measuring the transition cost between different preferred gradients and the other measuring the incompatibility of the set of preferred gradients and the boundary conditions. By a change of coordinates, the latter can also be understood as an incompatibility of a variable domain with a fixed set of preferred gradients. Moreover, it is shown how simple building blocks and covering arguments lead to upper bounds on the energy and solutions to the differential inclusion problem on general Lipschitz domains. [ABSTRACT FROM AUTHOR]

Murray’s law, as the best-known optimal relationship between bifurcation calibers, is obtained based on the assumption of steady-state Poiseuille blood flow and is mostly accurate in small vessels. In middle sized and large vessels such as the aorta and coronary arteries, the pulsatile nature of the flow is dominant and deviations from Murray law have been observed. In the present study, a general scaling law is proposed, which describes the optimum relationship between the characteristics of bifurcations and pulsatile flow. This scaling law takes into account the deviations from Murray law in large vessels, and proposes optimal flow (i.e. less flow resistance) for the full range of the vascular system, from the small vessels to large ones such aorta. As a general scaling law, it covers both symmetrical and asymmetrical bifurcations. One of the merits of this scaling law is that bifurcation characteristics solely depend on the Womersley number of parent vessels. The diameter ratios suggested by this scaling law are in acceptable agreement with available clinical morphometric data such as those reported for coronary arteries and aortoiliac bifurcations. A numerical simulation of pulsatile flow for several Womersley numbers in bifurcation models according to the proposed scaling law and Murray law has been performed, which suggests that the general scaling law provides less flow resistance and more efficiency than Murray law in pulsatile flow. [ABSTRACT FROM AUTHOR]

We provide (upper and lower) scaling bounds for a singular perturbation model for the cubic-to-tetragonal phase transformation with (partial) displacement boundary data. We illustrate that the order of lamination of the affine displacement data determines the complexity of the microstructure. As in (Rüland and Tribuzio in ESAIM Control Optim. Calc. Var. 29:68, 2023) we heavily exploit careful Fourier space localization methods in distinguishing between the different lamination orders in the data. [ABSTRACT FROM AUTHOR]

Accurate characterization of soil hydraulic conductivity influenced by temperature under a centrifugal environment is important for hydraulic and geotechnical engineering. Therefore, a temperature-influenced scaling law for hydraulic conductivity of soil in centrifuge modeling was deduced, and a temperature-controlled falling-head permeameter apparatus specifically designed for centrifuge modeling was also developed. Subsequently, a series of temperature-controlled falling-head tests were conducted under varying centrifugal accelerations to achieve the following objectives: (1) examine the performance of the apparatus, (2) investigate the influence of temperature and centrifugal acceleration on the hydraulic conductivity of sand and its scaling factor, and (3) validate the proposed scaling law for hydraulic conductivity. The main conclusions of the study are as follows. Firstly, the apparatus demonstrated good sealing and effectively controlled the temperature of both the soil specimen and the fluid. Secondly, the hydraulic conductivity of sand was not constant but varied over time, likely due to the presence of radial seepage in addition to vertical seepage as the test progressed. Thirdly, temperature significantly influenced the hydraulic conductivity of sand and its scaling factor under the same centrifugal acceleration. Therefore, it is essential to closely monitor the temperature of models during centrifugal tests. Finally, the measured and calculated values of the scaling factor index for the hydraulic conductivity of sand showed good agreement, verifying the proposed scaling law. [ABSTRACT FROM AUTHOR]

The ground-based experimental tests are crucial to verify the related technologies of the drag-free satellite. This work presents a design method of the ground simulator testbed for emulating the planar dynamics of the space drag-free systems. In this paper, the planar dynamic characteristics of the drag-free satellite with double test masses are analyzed and non-dimensionalized. A simulator vehicle composed of an air bearing testbed and two inverted pendulums is devised on the basic of equivalent mass and equivalent stiffness proposed firstly in this paper. And the dynamic model of the simulator equivalent to the sensitive axis motion of the test mass and the planar motion of the satellite is derived from the Euler-Lagrange method. Then, the dynamic equivalence conditions between the space prototype system and the ground model system are derived from Pi theorem. To satisfy these conditions, the scaling laws of two systems and requirements for the inverted pendulum are put forward. Besides, the corresponding control scaling laws and a closed-loop control strategy are deduced and applied to establishing the numerical simulation experiments of underactuated system. Subsequently, the comparative simulation results demonstrate the similarity of dynamical behavior between the scaled-down ground model and the space prototype. As a result, the rationality and effectiveness of the design method are proved, facilitating the ground simulation of future gravitational wave detection satellites. [ABSTRACT FROM AUTHOR]

Murray’s law, as the best-known optimal relationship between bifurcation calibers, is obtained based on the assumption of steady-state Poiseuille blood flow and is mostly accurate in small vessels. In middle sized and large vessels such as the aorta and coronary arteries, the pulsatile nature of the flow is dominant and deviations from Murray law have been observed. In the present study, a general scaling law is proposed, which describes the optimum relationship between the characteristics of bifurcations and pulsatile flow. This scaling law takes into account the deviations from Murray law in large vessels, and proposes optimal flow (i.e. less flow resistance) for the full range of the vascular system, from the small vessels to large ones such aorta. As a general scaling law, it covers both symmetrical and asymmetrical bifurcations. One of the merits of this scaling law is that bifurcation characteristics solely depend on the Womersley number of parent vessels. The diameter ratios suggested by this scaling law are in acceptable agreement with available clinical morphometric data such as those reported for coronary arteries and aortoiliac bifurcations. A numerical simulation of pulsatile flow for several Womersley numbers in bifurcation models according to the proposed scaling law and Murray law has been performed, which suggests that the general scaling law provides less flow resistance and more efficiency than Murray law in pulsatile flow.

Understanding complex urban systems necessitates untangling the relationships between diverse urban elements such as population, infrastructure, and socioeconomic activities. Scaling laws are basic but effective rules for evaluating a city’s internal growth logic and assessing its efficiency by investigating whether urban indicators scale with population. To date, only limited research has empirically explored the scaling relations between variables of urban mobility in mega-cities at an intra-urban scale of a few meters. Using multiple urban-sensed and human-sensed data, this study proposes a thorough framework for quantifying the scaling laws in a city. To begin, urban mobility networks are built by aggregating population flows using large-scale mobile phone tracking data. To demonstrate the spatiotemporal variability of urban mobility, various network-based mobility measures are proposed. Following that, three different features of urban mobility laws are exposed, explaining spatial agglomeration, spatial hierarchical structures, and the temporal growth process. The scaling correlations between urban indicators pertaining to socioeconomic features and infrastructure and a mobility-population measure are then quantified using multi-sourced urban-sensed data. Applying this framework to the case study of Shenzhen, China revealed (a) spatial travel heterogeneity, hierarchical spatial structures, and mobility growth, and (b) not only a robust sub-linear relationship between infrastructure volume and population, but also a sub-linear relationship for socioeconomic activity. The identified scaling laws, both in terms of mobility measures and urban indicators, provide a multi-faceted portrait of the spatio-temporal variations of urban settings, allowing us to better understand intra-urban developments and, consequently, provide critical policy evaluations and suggestions for improving intra-urban efficiency in the future.

The neuromuscular junction (NMJ) has an elaborate anatomy to ensure agile and accurate signal transmission. Based on our formerly obtained expressions of the thermal and conductance induced voltage fluctuations, in this paper, the mechanisms underlying the conductance-induced voltage fluctuation are characterized from two aspects: the scaling laws with respect to either of the two system-size factors, the number of receptors or the membrane area; and the "seesaw effect" with respect to the intensive parameter, the concentration of acetylcholine. According to these mechanisms, several aspects of the NMJ anatomy are explained from a denoising perspective. Finally, the power spectra of the two types of voltage fluctuations are characterized by their specific scaling laws, based on which we explain why the endplate noise has the low-frequency property that is described by the term "seashell sound". [ABSTRACT FROM AUTHOR]

In this article, two-dimensional (2-D) Rayleigh–Bénard (RB) convection with isothermal-adiabatic boundary conditions is simulated by using the double distribution function approach of lattice Boltzmann method. The effects of isothermal-adiabatic boundary on the flow and the heat transfer characteristics in the RB system under instability, transition and turbulence are discussed in detail. The effect of the isothermal-adiabatic boundary on the scaling of Nusselt (Nu) number as a function of Rayleigh (Ra) number is analyzed. The 0.3 scaling is observed in the mixed boundary system when the Ra number is in the range of 107–108. The scaling is well consistent with that in the RB system with uniform boundaries. A comparison of the influence on the root mean square of Nu number between uniform isothermal boundary and isothermal-adiabatic boundary demonstrates that in both "transition" region and "turbulence" region, the intensity of the fluctuation of average Nu number at uniform isothermal boundary is higher than that at the isothermal-adiabatic boundary. The comparison of the fluctuation of the average Nu number between "transition" region and "turbulence" region shows that the isothermal-adiabatic boundary has a better suppression effect on the fluctuation of heat transfer in the "transition" region. The supression is related to ratio of the scale of plume and the "heat source core." When the scales are comparable, the fluctuation of average Nu number will be significantly suppressed. Flow field and temperature field further show the plumes are generated at these "heat source cores," which effectively supports the "heat source core" assumption. [ABSTRACT FROM AUTHOR]

This study presents the turbulence characteristics and the scaling laws in a horizontal submerged wall jet on an array of hemispherical macro-rough elements forming an open-channel boundary. The flow field was measured by an acoustic Doppler system, called Vectrino. The turbulence characteristics on a macro-rough boundary, being different from those on smooth boundary, are discussed from the perspective of decay of the local-peak parameters, similarity, and growth of the length scales. The vector plots, streamwise velocity flow field, and the jet velocity variations show that the decay rate of jet velocity in a submerged jet on a macro-rough boundary is initially sharp and then gradually drops down to become independent of streamwise distance. The growth rate of the jet boundary layer thickness is initially slow and then becomes fast as it tends to reach the free surface. On the other hand, the plots of the Reynolds shear stress and turbulence intensities, and the variations of their local-peak magnitudes reveal the gradual damping of these parameters with the streamwise distance. These results encapsulate the recovery of a submerged jet on a macro-rough boundary to become an open channel flow. The most important outcome is that the streamwise velocity, Reynolds shear stress, and turbulence intensities in the fully developed zone are found to be self-similar when the velocity is scaled with the local-peak velocity against jet half-width, and the Reynolds shear stress and turbulence intensities are scaled with their respective local-peak magnitudes against half-width of Reynolds shear stress. The boundary shear stress diminishes with an increase in streamwise distance. [ABSTRACT FROM AUTHOR]

Understanding complex urban systems necessitates untangling the relationships between diverse urban elements such as population, infrastructure, and socioeconomic activities. Scaling laws are basic but effective rules for evaluating a city's internal growth logic and assessing its efficiency by investigating whether urban indicators scale with population. To date, only limited research has empirically explored the scaling relations between variables of urban mobility in mega-cities at an intra-urban scale of a few meters. Using multiple urban-sensed and human-sensed data, this study proposes a thorough framework for quantifying the scaling laws in a city. To begin, urban mobility networks are built by aggregating population flows using large-scale mobile phone tracking data. To demonstrate the spatiotemporal variability of urban mobility, various network-based mobility measures are proposed. Following that, three different features of urban mobility laws are exposed, explaining spatial agglomeration, spatial hierarchical structures, and the temporal growth process. The scaling correlations between urban indicators pertaining to socioeconomic features and infrastructure and a mobility-population measure are then quantified using multi-sourced urban-sensed data. Applying this framework to the case study of Shenzhen, China revealed (a) spatial travel heterogeneity, hierarchical spatial structures, and mobility growth, and (b) not only a robust sub-linear relationship between infrastructure volume and population, but also a sub-linear relationship for socioeconomic activity. The identified scaling laws, both in terms of mobility measures and urban indicators, provide a multi-faceted portrait of the spatio-temporal variations of urban settings, allowing us to better understand intra-urban developments and, consequently, provide critical policy evaluations and suggestions for improving intra-urban efficiency in the future. [ABSTRACT FROM AUTHOR]

Deviation from the optimal bifurcation structure causes abnormal hemodynamic stress, increasing the risk of cerebral aneurysm initiation at the arterial bifurcation apexes of the Circle of Willis. Although Murray's law describes the optimal relationship between bifurcation calibers, major arterial bifurcations within the Circle of Willis show deviations from this law. This study introduces a novel scaling law that describes the optimum relationship between bifurcation characteristics based on pulsatile flow and the internal surface of vessels. The proposed scaling law applies to major intracranial arteries, such as the basilar, internal carotid and common carotid arteries, encompassing both symmetrical and asymmetrical bifurcations. One of the merits of this scaling law is its sole dependence on the Womersley number of parent vessels to determine bifurcation characteristics. The diameter ratios suggested by these relationships are in good agreement with available clinical morphometric data. Numerical simulations of pulsatile flow for several Womersley numbers indicate that the flow resistance and temperature stability of the proposed scaling law are preferable to those of Murray's law. That might be the reason this scaling law is the optimality principle governing the major cerebral arteries, particularly those arterial blood vessels responsible for the brain's thermoregulatory, because the brain's thermoregulatory and temperature stability are the physiological and anatomical constraints of the human brain. [ABSTRACT FROM AUTHOR]

In this study, we comprehensively investigated the scaling law for elastic properties of three-dimensional honeycomb-like graphenes (3D graphenes) using hybrid neural network potential-based molecular dynamics simulations and theoretical analyses. The elastic constants were obtained as functions of honeycomb hole size, denoted by the graphene wall length L. All five independent elastic constants in the large-L limit are proportional to L−1. The associated coefficients are combinations of elastic constants of two-dimensional graphene. High-order terms including L−2 and L−3 emerge for finite L values. They have three origins, the distorted areas close to the joint lines of 3D graphenes, the variation in solid angles between graphene plates, and the bending distortion of graphene plates. Significantly, the chirality becomes essential with decreasing L because the joint line structures are different between the armchair and zigzag-type 3D graphenes. Our findings provide insights into the elastic properties of graphene-based superstructures and can be used for further studies on graphene-based materials. [ABSTRACT FROM AUTHOR]

Abstract We develop a methodology to compile an objective tremor catalog by utilizing distinctive event features that differentiate tectonic tremors from non‐tremor events, and combining the envelope cross‐correlation method with clustering technique and neural network. This approach enables tremor extraction without subjective criteria, allowing for the detection of previously overlooked short‐duration tremors. The event features employed to distinguish tremors and non‐tremor events are depth, the mean amplitudes at high and low frequencies, the ratio of these two amplitudes, and event duration. The duration is defined as the minimum period that contains 50% of the seismic energy. The application of this method to western Japan detects 1.7 times more tremors than the previous studies, with the durations of 0.3–∼100 s. The events with short durations are considered low‐frequency earthquakes. The relationship between seismic moment and duration of the detected tremors is consistent with the scaling law of slow earthquakes.

Abstract The three‐dimensional structure of the Tropical Cyclone's baroclinic wake is synthesized as an averaged baroclinic‐dominant response of the upper ocean. The resulting persisting sea surface depression can easily be monitored using the present‐day altimeter constellation. Following a semi‐empirical framework, these baroclinic wake signatures are linked to the inner core TC dynamic and the ocean stratification. To collect these fine‐scale parameters, spaceborne SAR instruments and Argo fleet are used, to precisely capture the maximum wind region and the irregularities of the ocean vertical structure. This combination of high‐resolution information is found paramount to fully capture the modulation of sea surface height anomalies, and its mean trend, especially for major hurricanes. Baroclinic signatures mostly range around 10–20 cm and peak at 40 cm. Deeper anomalies correspond to barotropic response, removed from the present analysis.

Abstract 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.

Urban heat island (UHI) and nitrogen dioxide (NO2) concentration in the air are two significant health hazards arising from urbanization. While much research has focused on the local urban context and micro-conditions for sources and exposures in particular case-studies, the effect of the overall level of urban agglomeration, as measured by population size, remains underreported. We compile the literature that explicitly discusses the relationship between UHI or NO2 and population size. We synthesize methods and findings qualitatively, then perform a quantified meta-analysis using comparable data from the corpus. We find that the corpus from which population size effects can be retrieved is very thin given the level of urbanization trends and the health impact. Despite a variety of functional specifications, data gathering processes, and metrics, the literature generally agrees on a significant effect of population size on both UHI and NO2. After pooling data we estimate that each 10-fold increase in population, increases the temperature gap between the city and countryside by almost 2 °C or a 40 % increase when cities get very large. We find that NO2 scales similarly, with a 40 % increase in concentration each time the city population is multiplied by 10. These numbers represent very important health threat given the current urbanization rate and the distribution of city population sizes. We also call for more studies to be conducted, across larger sets of cities, using observed data at higher resolution and comparable city definitions.

The ability to transfer microdroplets between fluid phases offers numerous advantages in various fields. This study focuses on the stability and morphology of a sessile oil microdropletduring the transfer from underwater to air. A distinct transition in microdroplet dynamics is observed, characterized by a shift from a scenario dominated by Marangoni forces to one dominated by capillary forces. In the former regime, the oil microdroplets spread in response to the contact between the water‐air interface and the water‐oil interface. The spreading distance follows a power law relationship of t3/4, reflecting the balance between Marangoni forces and viscous forces. On the other hand, in the capillarity‐dominated regime, the oil microdroplets remain stable at the contact line and after being transferred into the air. The crossover between these two regimes is identified in the parameter space defined by three factors: the approaching velocity of the solid‐water‐air contact line (vcl), the radius of the oil microdroplet (ro), and the radius of the water drop (rw). Furthermore, how to use the four‐phase contact line for shaping oil microdroplets is demonstrated using a full liquid process by the contact line lithography. [ABSTRACT FROM AUTHOR]

• GNSS-TEC data showed ionospheric changes immediately before the 2008 M w 7.9 Wenchuan earthquake, China. • TEC trend showed positive changes in trends ∼1/2 h before the earthquake and the anomaly reached ∼5 % of the background. • These anomalies are mostly consistent with worldwide trends of past examples for ∼20 earthquakes. Ionospheric disturbances associated with large earthquakes can be observed with global navigation satellite system (GNSS) receivers on the ground as changes in total electron content (TEC). In addition to coseismic disturbances ∼10 min after earthquakes caused by acoustic-gravity waves from epicenters, there have been reports on changes immediately before very large earthquakes. We show such disturbances for the 2008 Wenchuan earthquake (M w 7.9), China, started ∼ 37 min before the main shock and reached ∼5 percent of the background value. The results of past ∼20 cases with M w 7.3 or more exhibit simple relationships that the leading times scale with fault lengths and the intensities of the anomalies relative to the backgrounds scale with fault areas. We demonstrate that the anomaly immediately before the 2008 Wenchuan earthquake fits well with these trends but with slightly longer leading time and stronger intensity. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Understanding the dynamic characteristics of deep-sea explosions is essential to improve the survivability and combat capability of deep-sea equipment. In this paper, by considering the practical underwater conditions, we investigated the mechanical effects of the deep-sea 1-kg-trinitrotoluene (TNT) explosion with charge depths ranging from 1 to 10 km through numerical simulation and dimensional analysis. The shock wave overpressure, the positive overpressure pulse, the bubble pulse, and the energy distribution for various depth explosions were analyzed systematically. The simulation results showed that the charge depth was negligible for the peak overpressure of the shock wave. However, the positive overpressure pulse, the shock wave energy, the maximum bubble radius, the bubble energy, and the bubble period decrease significantly with increasing the charge depth. Then, the dimensional analysis for deep-sea TNT explosion was performed to reveal the key dimensionless parameters, from which the scaling laws of the shock wave overpressure and the overpressure pulse were obtained. By fitting the simulation results, the dimensionless equations were proposed, providing an effective method for predicting the peak overpressure and the positive overpressure pulse of shock wave for underwater TNT explosion over a wide range of water depths. [ABSTRACT FROM AUTHOR]

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Spin glass coherence lengths can be extracted from experiment and from numerical simulations. They encompasses the correlated region, and their growth in time makes them a useful tool for exploration of spin glass dynamics. Because they play the role of a fundamental length scale, they control the transition from the reversible to the chaotic state. This review explores their use for spin glass properties, ranging from scaling laws to rejuvenation and memory. [ABSTRACT FROM AUTHOR]

Time series of large samples of instantaneous velocity fields with a 7.26δ0.99×1.18δ0.99 size in a turbulent boundary layer have been obtained by experimental measurement using time-resolved particle image velocimetry (TRPIV) with a four-camera array. The resultant experimental Reynolds number (Reτ) is 1046. The continuous spatial wavelet transform has been employed to convert the streamwise velocity fluctuations into multi-scale components in the streamwise direction at all wall-normal positions. The distribution of turbulence kinetic energy across all spatial scales and all wall-normal positions are determined from the multi-scale wavelet coefficients. The continuous temporal wavelet transform has also been utilized to resolve the temporal series of longitudinal velocity fluctuations into multi-scale temporal components at all wall-normal positions. The use of the multi-scale wavelet coefficients delivered the turbulent kinetic energy distribution across all temporal scales and all wall-normal positions. Moreover, the distribution of multi-scale flatness factors with spatial scales and normal position, before and after removal of multi-scale coherent structures, has been calculated. The turbulent structures are detected by zero-crossing the wavelet coefficients. The conditional sampling scheme and spatial phase-locked method have been employed to establish typical multi-scale structures at different wall-normal positions. The universality of the small-scale structures has been confirmed where the associated vorticity is characterized by an alternating positive and negative quadrupole along the longitudinal direction and wall-normal direction, while the streamlines can be considered a dynamic system composed of a saddle point and focal points. The scaling exponent Ϛ(p), before and after the removal of the coherent structures, has been calculated, confirming that the multi-scale coherent structures are responsible for the anomalous scaling law. [ABSTRACT FROM AUTHOR]

Purpose: Kinetic vibration energy from bridges under traffic excitations and human activity is extensively recognized as an alternative energy for the threat of energy crisis. Methods: In this study, we propose a simple-structure contact-separation TENG applied to the bridge environments for converting this low-frequency vibrational energy into electrical power, which is utilized to develop the new scaling laws considering the effects of the host structure and the energy harvester coherently. Results: Laboratory tests are established to prove its feasibility as a high-output performance harvester and investigate how the factors influence the output performance, especially considering the frequency of the host. To simulate the TENG's working mechanism theoretically, a series of output expressions, mainly including dimensionless expressions composed of two compound variables, are carried out. These novel and simple scaling laws consisting of two dimensionless variables are used to analyze the simultaneous effects on the output performance of all critical parameters. More importantly, the effects of the dynamic and structural characteristics of the host structure are considered with the proposed scaling laws. Conclusions: This significant contribution could offer general optimization guidance of the contact-separation TENG for acquiring optimal output performance by considering the integration of the TENGs and the host structure. [ABSTRACT FROM AUTHOR]

Radiative natural convection is of vital importance in the process of energy storage, power generation, and thermal storage technology. As the attenuation coefficients of many heat transfer media in these fields are high enough to be considered as optically thick media, like nanofluids or molten salts in concentrated solar power or phase change thermal storage, Rosseland approximation is commonly used. In this paper, we delve into the impact of thermal radiation on the Rayleigh-Bénard (RB) convection. Theoretical analysis has been conducted by modifying the Grossmann-Lohse (GL) model. Based on turbulent dissipation theory, the corresponding scaling laws in four main regimes are proposed. Direct numerical simulation (DNS) was also performed, revealing that radiation exerts a notable influence on both flow and heat transfer, particularly on the formation of large-scale circulation. By comparing with DNS results, it is found that due to the presence of radiation, the modified Nu scaling law in small Pr range of the GL model is more suitable for predicting the transport characteristics of optical thick media with large Pr. The maximum deviation between the results of DNS and prediction model is about 10%, suggesting the summarized scaling law can effectively predict the Nu of radiative RB convection.

Accurate characterization of soil hydraulic conductivity influenced by temperature under a centrifugal environment is important for hydraulic and geotechnical engineering. Therefore, a temperature-influenced scaling law for hydraulic conductivity of soil in centrifuge modeling was deduced, and a temperature-controlled falling-head permeameter apparatus specifically designed for centrifuge modeling was also developed. Subsequently, a series of temperature-controlled falling-head tests were conducted under varying centrifugal accelerations to achieve the following objectives: (1) examine the performance of the apparatus, (2) investigate the influence of temperature and centrifugal acceleration on the hydraulic conductivity of sand and its scaling factor, and (3) validate the proposed scaling law for hydraulic conductivity. The main conclusions of the study are as follows. Firstly, the apparatus demonstrated good sealing and effectively controlled the temperature of both the soil specimen and the fluid. Secondly, the hydraulic conductivity of sand was not constant but varied over time, likely due to the presence of radial seepage in addition to vertical seepage as the test progressed. Thirdly, temperature significantly influenced the hydraulic conductivity of sand and its scaling factor under the same centrifugal acceleration. Therefore, it is essential to closely monitor the temperature of models during centrifugal tests. Finally, the measured and calculated values of the scaling factor index for the hydraulic conductivity of sand showed good agreement, verifying the proposed scaling law.

The laws governing life should be as simple as possible; however, theoretical investigations into allometric laws have become increasingly complex, with the long-standing debate over the scaling exponent in allometric laws persisting. This paper re-examines the same biological phenomenon using two different scales. On a macroscopic scale, a cell surface appears smooth, but on a smaller scale, it exhibits a fractal-like porous structure. To elaborate, a few examples are given. Employing the two-scale fractal theory, we theoretically predict and experimentally verify the scaling exponent values for basal, active, and maximal metabolic rates. This paper concludes that Rubner's 2/3 law and Kleiber's 3/4 law are two facets of the same truth, manifested across different scale approximations. [ABSTRACT FROM AUTHOR]

An elegant calculation is carried out to investigate the effects of the non‐ideality of classical plasma on the energy levels of the hydrogenic atoms held in a spherical cage. Organized effect of the non‐ideal classical plasma is described by an analytical pseudopotential which contains the Debye length D and non‐ideality parameter γ as parameters. Convergent results for the bound states are obtained variationally by utilizing a large trail function containing cosine term which automatically takes care of the requisite boundary conditions. For the plasma‐free case, our results are in excellent agreement with the most accurate results available in the literature. An inclusive study is made to explore the changes emerging in the energy levels due to the variation of the plasma parameters and cage size. Special emphasis is made on the determination of critical cage size precisely. The present study specifically reveals that the increasing plasma non‐ideality leads to the elongation of the critical cage size. Moreover, it is empirically found that the critical cage size for a given hydrogenic atom can be obtained from a scaling law. [ABSTRACT FROM AUTHOR]

In an ecosystem, environmental changes as a result of natural and human processes can cause some key parameters of the system to change with time. Depending on how fast such a parameter changes, a tipping point can occur. Existing works on rate-induced tipping, or R-tipping, offered a theoretical way to study this phenomenon but from a local dynamical point of view, revealing, e.g., the existence of a critical rate for some specific initial condition above which a tipping point will occur. As ecosystems are subject to constant disturbances and can drift away from their equilibrium point, it is necessary to study R-tipping from a global perspective in terms of the initial conditions in the entire relevant phase space region. In particular, we introduce the notion of the probability of R-tipping defined for initial conditions taken from the whole relevant phase space. Using a number of real-world, complex mutualistic networks as a paradigm, we find a scaling law between this probability and the rate of parameter change and provide a geometric theory to explain the law. The real-world implication is that even a slow parameter change can lead to a system collapse with catastrophic consequences. In fact, to mitigate the environmental changes by merely slowing down the parameter drift may not always be effective: Only when the rate of parameter change is reduced to practically zero would the tipping be avoided. Our global dynamics approach offers a more complete and physically meaningful way to understand the important phenomenon of R-tipping. [ABSTRACT FROM AUTHOR]

Abstract The ability to transfer microdroplets between fluid phases offers numerous advantages in various fields. This study focuses on the stability and morphology of a sessile oil microdropletduring the transfer from underwater to air. A distinct transition in microdroplet dynamics is observed, characterized by a shift from a scenario dominated by Marangoni forces to one dominated by capillary forces. In the former regime, the oil microdroplets spread in response to the contact between the water‐air interface and the water‐oil interface. The spreading distance follows a power law relationship of t3/4, reflecting the balance between Marangoni forces and viscous forces. On the other hand, in the capillarity‐dominated regime, the oil microdroplets remain stable at the contact line and after being transferred into the air. The crossover between these two regimes is identified in the parameter space defined by three factors: the approaching velocity of the solid‐water‐air contact line (vcl), the radius of the oil microdroplet (ro), and the radius of the water drop (rw). Furthermore, how to use the four‐phase contact line for shaping oil microdroplets is demonstrated using a full liquid process by the contact line lithography.

Spin glass coherence lengths can be extracted from experiment and from numerical simulations. They encompasses the correlated region, and their growth in time makes them a useful tool for exploration of spin glass dynamics. Because they play the role of a fundamental length scale, they control the transition from the reversible to the chaotic state. This review explores their use for spin glass properties, ranging from scaling laws to rejuvenation and memory.

Reliable service of indispensable titanium alloys in aeroengines is limited by titanium fire with unclear critical conditions. In this study, critical conditions in the form of parameter phase diagrams for secondary burning were determined by molten droplet ignition. Finite element analysis (FEA) reveals that the molten droplet size (R0), relative oxygen content (Pr), and initial temperature (T0) significantly affect titanium fire following power exponential laws. In addition, Pr and T0 affect ablation synergically, and a unified empirical relationship for critical ablation of titanium alloy is established. Furthermore, the critical T0 of a typical TC4 alloy under 20% Pr is higher than 973 K, which explains the reliable service performance of TC4 alloy at ≤ 873 K in compressors in commerical air engines. In addition, the critical empirical conditions are consistent with the FEA results, and the deviation occurs due to oxidation at T0 ≥ 673 K. Moreover, the ablated TC4 alloy can be divided into five characteristic zones, and loose and porous oxide scales are formed at the front of the titanium fire. The present study points the way towards long-lifetime services of TC4 alloys through sound titanium fire protection strategies.

Scaling laws are ubiquitous in modern biological systems. However, whether such patterns existed in deep-time biological systems is less investigated; the best-known example is the scaling law between the frequency and size of extinction events. Here, I show that the variation rates of biodiversity, origination intensity, extinction intensity, and body size of marine animals during the last 540 million years exhibited scaling laws. I then derive a general form of these scaling laws from a conceptual model with some principles of thermodynamics and assumptions about the global biological system. The results in this study suggest that the scaling laws systematically appearing in the biological metrics characterizing different aspects of the evolutionary processes of marine animals likely belong to the same universality class and probably derived from a set of common factors.

In this work, single-phase BaZr0.05Ti0.95O3 (BZT) ceramic was prepared through a conventional solid-state reaction route. The structural identity was analyzed by X-ray diffraction (XRD) and Rietveld refinement, which reveals the single-phase perovskite structure of the synthesized sample having an orthorhombic structure and space group Amm2. Scanning electron microscope (SEM) study gives an idea about the well-dense grains with clear grain boundaries of the BZT sample. Frequency and amplitude-dependent Polarization-Electric field (P-E) and Strain-Electric field (S-E) loops were studied. The parameters like remnant polarization (Ec), coercive field (Pr), loop area (), energy storage efficiency (η), field-induced maximum strain (Smax) and inverse piezoelectric coefficient (d33*) were calculated. The scaling behavior of the hysteresis loops area as a function of frequency and field strength is studied. The thermal conductivity and thermal diffusivity as a function of temperature were investigated.

Self‐diffusion of poly(acrylic acid) (PAA) in dilute solution is studied by pulsed field gradient (PFG)‐NMR, also known as DOSY, and correlated to molecular weight with scaling laws at varying pH. Fitting a diffusion coefficient distribution model to PFG‐NMR data, the molecular weight polydispersity of commercial PAA samples is quantified. Due to good agreement with GPC data, diffusion measurements offer a viable alternative to estimate chain length properties with minimal sample preparation. Similar results are achieved by dynamic light scattering (DLS), however, with lower precision. The evolution of the scaling exponent with increasing pH indicates a transition from a globular state in highly acidic conditions (ν = 0.46) to a partially stretched conformation with a maximum at pH 5 (ν = 0.67). At higher pH, counterion screening counteracts chain expansion, while an unexpected increase in the width of the diffusion coefficient distribution occurs. A universal scaling law of the diffusivity applies for a chain length range of 25 ≤ N ≤ 1585, albeit with distinctly different scaling exponents. While opposing arguments are brought forward in recent literature concerning the pH‐dependence of short‐chain conformations, analysis supports the view that chain conformation is significantly affected by pH, even for short chains. [ABSTRACT FROM AUTHOR]

Block copolymers are a class of materials that are particularly interesting with respect to their capability to self-assemble in ordered structures. In this context, the coupling between environment and dynamics is particularly relevant given that movements at the molecular level influence various properties of macromolecules. Mixing the polymer with a second macromolecule appears to be an easy method for studying these relationships. In this work, we studied blends of poly(methyl methacrylate) (PMMA) and a block copolymer composed of PMMA as the first block and poly(3-methyl-4-[6-(methylacryloyloxy)-hexyloxy]-4′-pentyloxy azobenzene) as the second block. The relaxational properties of these blends were investigated via electron spin resonance (ESR) spectroscopy, which is sensitive to nanometric length scales. The results of the investigations on the blends were related to the dynamic behavior of the copolymers. At the nanoscale, the study revealed the presence of heterogeneities, with slow and fast dynamics available for molecular reorientation, which are further modulated by the ability of the block copolymers to form supramolecular structures. For blends, the heterogeneities at the nanoscale were still detected. However, it was observed that the presence of the PMMA as a major component of the blends modified their dynamic behavior. [ABSTRACT FROM AUTHOR]

The height of thick and solid plants, such as woody plants, is proportional to two-thirds of the power of their diameter at breast height. However, this rule cannot be applied to herbaceous plants that are thin and soft because the mechanisms supporting their bodies are fundamentally different. This study aims to clarify the rigidity control mechanism resulting from turgor pressure caused by internal water in herbaceous plants to formulate the corresponding scaling law. We modeled a herbaceous plant as a cantilever with the ground side as a fixed end, and the greatest height was formulated considering the axial tension force from the turgor pressure. The scaling law describing the relationship between the height and diameter in terms of the turgor pressure was theoretically derived. Moreover, we proposed a plant classification rule based on stress distribution. [ABSTRACT FROM AUTHOR]

The study of slow slip events is essential to elucidating the slip mechanisms and frictional properties of plate interfaces. We imaged the aseismic slip at the plate interface between the subducting Philippine Sea Plate and overriding Amur Plate beneath Shikoku Island, Japan, by applying a network inversion filter to the position time series obtained from Global Navigation Satellite System data spanning January 2012 to April 2022. The results show long‐term slow slip events in the Bungo Channel, central Shikoku, and the Kii Channel, which started from 2018. We also identified 39 short‐term slow slip events associated with low‐frequency tremors. The estimated moment magnitudes of the Bungo Channel, central Shikoku, and Kii Channel slow slip events were Mw7.0, Mw6.4, and Mw6.3, respectively, with a rigidity of 30 GPa. The estimated moment magnitudes of the short‐term slow slip events ranged from Mw5.7 to Mw6.4. Most of the detected short‐term slow slip events are associated with low‐frequency tremor, and many showed propagation through the spatial domain. Events with magnitudes of ≥Mw6.30 typically consist of subevents. The slip rate of short‐term slow slip events ranges from 1 to 7 mm/day, which is considerably larger than the plate convergence rate. The short‐term slow slip events are 6 to 40 days, and follow the accepted scaling law between slip event duration and total magnitude. The short‐term slow slip event zone is consistent with a three‐segment hypothesis. The short‐term slow slip event in northwest Shikoku and long‐term slow slip event in central Shikoku may be correlated. Plain Language Summary: We identified three independent long‐term slow slip events that have occurred since 2018 in the Bungo Channel, central Shikoku, and the Kii Channel. We also identified 39 short‐term slow slip events in the Shikoku region. We clearly imaged the spatio‐temporal evolution of short‐term slow slip events for selected cases. Large short‐term slow slip events consist of several subevents, which are clearly imaged in this study. Key Points: We identified short‐ and long‐term slow slip events in Japan using the GNSS network and network inversion filterWe identified spatial and temporal propagation of long‐term and short‐term slow slip events along the Nankai TroughWe determined a correlation between short‐term slow slip events in northwest Shikoku and long‐term slow slip events in central Shikoku [ABSTRACT FROM AUTHOR]

Abstract This study identifies structure pairs with the potential for simultaneous rupture in a coseismic period and quantifies their rupture recurrence intervals. To assess the potential for a multiple-structure rupture, we calculated the probability of Coulomb stress triggering between seismogenic structures in Taiwan. We assumed that a multiple-structure rupture would occur if two structures could trigger each other by enhancing the plane with thresholds of a Coulomb stress increase and the distance between the structures and identified various sets of seismogenic structure pairs accordingly. We discussed the uncertainty of multiple-structure pair identification from various thresholds of stress change and structure distances, effective friction coefficient, and rotation of rake angles. To estimate the recurrence intervals for multiple-structure ruptures, we implemented a scaling law and the Gutenberg-Richter law in which the slip rate could be partitioned based on the magnitudes of the individual structure and multiple-structure ruptures. Considering that one structure may be involved in multiple cases of multiple-structure ruptures, we developed new formulas for slip partitioning in a complex fault system. By implementing the range of rupture area and slip rate of each structure, the magnitudes and recurrence intervals of multiple-structure ruptures could be estimated. We discussed the epistemic uncertainties of recurrence interval from deviations of slip rate and rupture area, various empirical formula of rupture parameters. The multiple-structure rupture with a larger characteristic magnitude would be crucial for the safety evaluation of infrastructures.

Numerous experiments have shown that the loads applied to Nb3Sn strands and cables can reduce their critical current. Experiments, performed on uniaxially loaded strands, allowed to define clear laws to describe the evolution of the critical surface as a function of the applied current, field, temperature and strain. It is, however, still unclear how these laws can be applied to superconducting magnets. The present paper proposes a methodology to estimate the critical current and temperature margin reduction on superconducting magnets due to stress on the superconducting material. The methodology is tested on the MQXF magnets, a quadrupole developed for the High Luminosity LHC project, and successfully validated by comparing computed strain with data from strain gauge measurements. Results suggested that, because of the stresses arising in winding during assembly, cool-down and powering, the current limit of the magnet is lower than the expected short sample limit, and that the most critical region does not coincide with the peak field location.

Understanding of mass transfer in gas-liquid slug flow is imperative to design and optimize micro-reactors. There exist extensive studies on symmetric bubbles by the phase volume monitor technique, whereas deformed bubbles are rarely studied due to the limitation of volume calculation methods. In this work, CO2-water and N2-water two-phase flows were investigated in a square microchannel, obtaining annular flow, slug flow, and bubbly flow. A flow pattern map was then proposed and compared with the literature. A 3D slicing technique was developed to measure the volume and interfacial area of bubble, including symmetric bubbles and deformed bubbles, by slicing the bubble along the streamwise direction. Scaling laws of the important parameters that characterize the micro-reactors were proposed. Mass transfer coefficients kLa were quantified from the time-changing volume. The empirical correlation involving dimensionless numbers were fitted, which shows accurate predictive performance for mass transfer coefficients in this study and literatures. The bigger index of Reynolds number ReG indicated that gas flow condition is the main influencing factor during mass transfer process. To have a better universality, a new semi-theoretical model involving the ratio of the size of the liquid and gas phases LL/LG was developed based on the Pigford and Higbie penetration theory because experimental data confirms that the degree of bubble deformation is related to LL/LG. The semi-theoretical model shows a satisfactory agreement over the whole range of slug flow in this study.