Power-law Scaling Relationship Research Articles

Anomalous scaling of branching tidal networks in global coastal wetlands and mudflats

Branching networks are key elements in natural landscapes and have attracted sustained research interest across the geosciences and numerous intersecting fields. The prevailing consensus has long held that branching networks are optimized and exhibit fractal properties adhering to power-law scaling relationships. However, tidal networks in coastal wetlands and mudflats exhibit scaling properties that defy conventional power-law descriptions, presenting a longstanding enigma. Here we show that the observed atypical scaling represents a universal deviation from an ideal fractal branching network capable of fully occupying the available space. Using satellite imagery of tidal networks from diverse global locations, we identified an inherent “laziness” in this deviation—where the increased ease of channel formation paradoxically decreases the space-filling efficiency of the network. We developed a theoretical model that reproduces the ideal fractal branching network and the laziness phenomenon. The model suggests that branching networks can emerge under a localized competition principle without adhering to conventionally assumed optimization-driven processes. These results reveal the dual nature of branching networks, where “laziness” complements the well-known optimization process. This property provides more flexible strategies for controlling tidal network morphogenesis, with implications for coastal management, wetland restoration, and studies in fluvial and planetary systems.

Benchmark experimental study on cavitating flow around Clark-Y 11.7 % hydrofoil at various angles of attack under controlled levels of dissolved air

The present research aims to study cavitating flow around a CLARK-Y 11.7 % hydrofoil with variable angles of attack (α) while maintaining controlled levels of dissolved air in the operating fluid, which is water. A series of experiments were conducted using a water tunnel facility, where the cavitation characteristics were measured and observed using sensors and high-speed imaging techniques. The variables studied in the present work are cavitation number (1 ≤ σ ≤ 2.2) and angle of attack (α = 4°, 6°, 8°, 10°, and 12°), with dissolved air levels (DAL) in the range of 9.3 ppm to 13.1 ppm. The dimensionless cavity length decreases significantly with increasing values of σ/α, indicating an inverse relationship where higher cavitation numbers or lower angles of attack result in shorter cavities. The cavity length follows a power-law scaling relationship, with the empirical equation Lmax/C=4.78×σ/α−0.76.Increasing the angle of attack transitions the cavitation nature from stable (Mode I) to dynamic (Mode II) and highly oscillating (Mode III). Larger cavities result in lower Strouhal numbers, which indicates reduced vortex shedding activity. The relationship between the Strouhal number and the normalized cavitation number σ/α is characterized by the power-law equation St=0.041×σ/α0.3. The pressure coefficient at the leading-edge increases with the angle of attack at low cavitation numbers, while higher cavitation numbers lead to greater pressure coefficient differences between the leading and trailing edges.The present study offers an extensive dataset and empirical correlations that may serve as a benchmark framework, which facilitates the validation of computational and experimental models of cavitating flow under similar conditions.

Microcracking evolution and clustering fractal characteristics in coal failure under multi step and cyclic loading

During the deep mining process, coal mass encounter intricate geo-environmental stress, such as periodic weighting loading and repeatedly excavation unloading–reloading cycles, which weakens coal’s mechanical integrity and predisposing it to severe coalburst accidents. To investigate the microcracking damage mechanisms and predictive indicators in coal failure under in-situ stress analogs, the multistage step and cyclic loading experiments are conducted on cubic coal specimens. Acoustic emission (AE) technology is employed to track the spatiotemporal-energy evolution of stress-induced damages and discern the microcracking nature through AF/RA assessments, and the power-law scaling relation of AE activity near the catastrophic failure of coal is investigated. Then the clustering fractal structures of microcracking events in the stressed coal are quantified across temporal, spatial and energetic domains, utilizing correlation integral methodologies and b-value derivations from magnitude-frequency relation. Findings indicate that irrespective of the loading mode (step or cyclic), escalating stress triggers an intensification of irreversible fatigue deformations. AE characteristic parameters manifest a gradual rise, culminating in a precipitous peak coinciding with the critical failure point. This escalation adheres to a power-law correlation between AE occurrence frequency and time to failure, observable in the immediate pre-failure seconds, reflecting a universal attribute of coal fracture. Prior to ultimate failure, a marked increase in shear microcracks is discernible, despite tensile-dominated cracks (constituting about 80 % of total microcracks) prevailing as inferred from the variation of AF/RA values, aligning with an inferred “X” conjugate wedge splitting pattern from AE event density and energy mapping. The microcracking events in the loaded coal exhibit a clustering fractal structure that spans across temporal, spatial, and energetic (or magnitude) domains. Notably, the temporal fractal dimension, spatial fractal dimension, and b-value (i.e., a parameter characterized the energetic fractal dimension) all follow a parallel decrease pattern as the loading stress escalates, with a pronounced diminution becoming especially evident as the specimen approaches its catastrophic failure threshold. This insight offers fresh perspectives for predicting rock/coal dynamic disasters, emphasizing the necessity of concurrently monitoring the shift from diffuse microcracking to localized failure across time, space and energy domains. These research findings contribute to a deeper understanding of microcracking damage evolution and failure mechanism of loaded coal, and provide a foundational basis for early warning of rock failure such as the coalburst disasters.

Exploring patterns in precipitation intensity–duration–area–frequency relationships using weather radar data

Abstract. Accurate estimations of extreme precipitation return levels are critical for many hydrological applications. Extreme precipitation is highly variable in both space and time; therefore, to better understand and manage the related risks, knowledge of their probability at different spatial–temporal scales is crucial. We employ a novel non-asymptotic framework to estimate extreme return levels (up to 100 years) at multiple spatial–temporal scales from weather radar precipitation estimates. The approach reduces uncertainties and enables the use of relatively short archives typical of weather radar data (12 years in this case). We focus on the eastern Mediterranean, an area of high interest due to its sharp climatic gradient, containing Mediterranean, semi-arid, and arid areas across a few tens of kilometres, and its susceptibility to flash flood. At-site intensity–duration–area–frequency relations are derived from radar precipitation data at various scales (10 min–24 h, 0.25–500 km2) across the study area, using ellipses of varying axes and orientations to account for the spatial component of storms. We evaluate our analysis using daily rain gauge data over areas for which sufficiently dense gauge networks are available. We show that extreme return levels derived from radar precipitation data for 24 h and 100 km2 are generally comparable to those derived from averaging daily rain gauge data over a similar areal scale. We then analyse differences in multi-scale extreme precipitation over coastal, mountainous, and desert regions. Our study reveals that the power-law scaling relationship between precipitation and duration (simple scaling) weakens for increasing area sizes. This finding has implications for temporal downscaling. Additionally, precipitation intensity varies significantly for different area sizes at short durations but becomes more similar at long durations, suggesting that, in the region, areal reduction factors may not be necessary for computing return levels over long durations. Furthermore, the reverse orographic effect, which causes decreased precipitation for hourly and sub-hourly durations, diminishes for larger areas. Finally, we discuss the effects of orography and coastline proximity on extreme precipitation intensity over different spatial–temporal scales.

Explaining neural scaling laws

The population loss of trained deep neural networks often follows precise power-law scaling relations with either the size of the training dataset or the number of parameters in the network. We propose a theory that explains the origins of and connects these scaling laws. We identify variance-limited and resolution-limited scaling behavior for both dataset and model size, for a total of four scaling regimes. The variance-limited scaling follows simply from the existence of a well-behaved infinite data or infinite width limit, while the resolution-limited regime can be explained by positing that models are effectively resolving a smooth data manifold. In the large width limit, this can be equivalently obtained from the spectrum of certain kernels, and we present evidence that large width and large dataset resolution-limited scaling exponents are related by a duality. We exhibit all four scaling regimes in the controlled setting of large random feature and pretrained models and test the predictions empirically on a range of standard architectures and datasets. We also observe several empirical relationships between datasets and scaling exponents under modifications of task and architecture aspect ratio. Our work provides a taxonomy for classifying different scaling regimes, underscores that there can be different mechanisms driving improvements in loss, and lends insight into the microscopic origin and relationships between scaling exponents.

Unveiling the reproduction number scaling in characterizing social contagion coverage

The spreading of diseases depends critically on the reproduction number, which gives the expected number of new cases produced by infectious individuals during their lifetime. Here we reveal a widespread power-law scaling relationship between the variance and the mean of the reproduction number across simple and complex contagion mechanisms on various network structures. This scaling relation is verified on an empirical scientific collaboration network and analytically studied using generating functions. Specifically, we explore the impact of the scaling law of the reproduction number on the expected size of cascades of contagions. We find that the mean cascade size can be inferred from the mean reproduction number, albeit with limitations in capturing spreading variations. Nonetheless, insights derived from the tail of the distribution of the reproduction number contribute to explaining cascade size variation and allow the distinction between simple and complex contagion mechanisms. Our study sheds light on the intricate dynamics of spreading processes and cascade sizes in social networks, offering valuable insights for managing contagion outbreaks and optimizing responses to emerging threats.

Layer-dependence study of two-dimensional ferromagnets: Fe3GeTe2 and Fe5Ge2Te2

We have investigated the electrical transport properties of nanodevices fabricated from exfoliated flakes of two-dimensional metallic ferromagnets Fe3GeTe2 (FGT) and Fe5Ge2Te2 (FG2T) down to below three layers in thickness. The per-layer anomalous Hall conductivity even in thick FGT and FG2T devices is found to be much smaller than ∼e2h, the approximate value calculated for thick undoped crystals. Moreover, we obtain a power-law scaling relation between the per-layer anomalous Hall and per-layer longitudinal conductivities with an exponent close to 1.6, which agrees with the universal value for poor ferromagnetic conductors. Both FGT and FG2T devices show clear layer-dependent Curie temperatures and layer-dependent perpendicular magnetic anisotropy, with FG2T dominating the former and FGT dominating the latter for all thicknesses. Despite their declining trend as the device thickness decreases, both Curie temperature and magnetic anisotropy retain a significant fraction of their bulk values (>60% and >80% of the bulk values, respectively, even in the thinnest FG2T device), indicating attractive potential for practical applications.

Quasi-three-dimensional hydrodynamics of the corona region of laser irradiation of a slab

Abstract This paper introduces and establishes a quasi-three-dimensional physical model of the interaction between laser and slab target. In contrast to previous one-dimensional analytical models, this paper innovatively fits the real laser conditions, based on an isothermal, homogeneous expansion similarity solution of the ideal hydrodynamic equations, using this simple model, the evolution law and analytical formula of key parameters (e.g., temperature, density, and scale length) in the corona region under certain conditions are given. The analytical solution agrees well with the relevant computational hydrodynamics simulation results. For constant laser irradiation, the analytical solution provides a meaningful power-law scaling relationship. The model provides a set of mathematical and physical tools that provide theoretical support for adjusting parameters in experiments.

Unraveling power-law scaling through exponential cell division dynamics

A primary objective of biology is the development of universal laws that define how organic form develops and how it evolves as a function of size, both ontogenetically and across evolutionary time. Scaling theory has been essential in reaching this goal by giving a complete perspective point, particularly in illuminating the fundamental biological features produced within scaling exponents defining families of equations. Nonetheless, the theoretical basis of the allometric equation within scaling theory are inadequately explained, particularly when it comes to establishing links between micro-level processes at the cellular level and macro-level phenomena. We proposed an unlimited cell bipartition, resulting in an exponential growth in cell numbers during an individual’s lifespan, to bridge this conceptual gap between cellular processes and allometric scaling. The power-law scaling between body mass and organ weight was produced by the synchronous exponential increments and the allometric exponent is rate of logarithmic cell proliferation rate. Substituting organ weight for erythrocyte weight aided in the development of a power-law scaling relationship between body mass and metabolic rate. Furthermore, it is critical to understand how cell size affects the exponent in power-law scaling. We find that a bigger exponent will result from an increase in the average weight of organ cells or a decrease in the average weight of all cells. Furthermore, cell proliferation dynamics showed a complex exponential scaling between body mass and longevity, defying the previously reported power-law scaling. We discovered a quadratic link between longevity and logarithmic body mass. Notably, all of the parameters included in these relationships are explained by indices linked to cell division and embryonic development. This research adds to our understanding of the complex interaction between cellular processes and overarching scaling phenomena in biology.

Beyond the kill: The allometry of predation behaviours among large carnivores.

The costs of foraging can be high while also carrying significant risks, especially for consumers feeding at the top of the food chain. To mitigate these risks, many predators supplement active hunting with scavenging and kleptoparasitic behaviours, in some cases specializing in these alternative modes of predation. The factors that drive differential utilization of these tactics from species to species are not well understood. Here, we use an energetics approach to investigate the survival advantages of hunting, scavenging and kleptoparasitism as a function of predator, prey and potential competitor body sizes for terrestrial mammalian carnivores. The results of our framework reveal that predator tactics become more diverse closer to starvation, while the deployment of scavenging and kleptoparasitism is strongly constrained by the ratio of predator to prey body size. Our model accurately predicts a behavioural transition away from hunting towards alternative modes of predation with increasing prey size for predators spanning an order of magnitude in body size, closely matching observational data across a range of species. We then show that this behavioural boundary follows an allometric power-law scaling relationship where the predator size scales with an exponent nearing 3/4 with prey size, meaning that this behavioural switch occurs at relatively larger threshold prey body size for larger carnivores. We suggest that our approach may provide a holistic framework for guiding future observational efforts exploring the diverse array of predator foraging behaviours.

Exploring the low-mass regime of galaxy-scale strong lensing: Insights into the mass structure of cluster galaxies

Context. Several recent studies have highlighted a discrepancy between the strong lensing (SL) properties of observed cluster galaxies and the predictions of Λ cold dark matter (CDM) cosmological hydrodynamical simulations. This discrepancy can be interpreted as the result of observed cluster members being more compact than their simulated counterparts. Aims. In this work, we aim at a direct measurement of the compactness of a few selected galaxy-scale lenses in massive clusters, testing the accuracy of the scaling laws adopted to describe the members in SL models of galaxy clusters. Methods. We selected the multiply imaged sources MACS J0416.1−2403 ID14 (z = 3.221), MACS J0416.1−2403 ID16 (z = 2.095), and MACS J1206.2−0847 ID14 (z = 3.753). Eight multiple images were observed for the first SL system, and six for the latter two. We focused on the main deflector of each galaxy-scale SL system (identified as members 8971, 8785, and 3910, respectively), and modelled its total mass distribution with a truncated isothermal sphere. To account for the lensing effects of the remaining components of the cluster, we took the most accurate SL model of its mass distribution available. To include the uncertainty and the systematics affecting the cluster-scale mass models, we explored the posterior probability distribution of its parameters and extracted 100 cluster mass distributions. For each of them, we optimised the mass parameters of the galaxy-scale lens: the bootstrapping procedure allowed us to obtain a realistic estimate of the uncertainty on their values. Results. We measured a truncation radius value of 6.1−1.1+2.3 kpc, 4.0−0.4+0.6 kpc, and 5.2−1.1+1.3 kpc for members 8971, 8785, and 3910, corresponding to total mass values of M = 1.2−0.1+0.3 × 1011 M⊙, M = 1.0−0.1+0.2 × 1010 M⊙, and M = 6.3−1.1+1.0 × 1010 M⊙, respectively. Alternative non-truncated models with a higher number of free parameters do not lead to an improved description of the SL system and show some parametric degeneracies. We measured the stellar-to-total mass fraction within the effective radius for the three cluster members, finding 0.51 ± 0.21, 1.0 ± 0.4, and 0.39 ± 0.16, respectively. Conclusions. We find that a parameterisation of the physical properties of cluster galaxies in SL models based on power-law scaling relations with respect to the observed total luminosity cannot accurately describe the compactness of the members over their full total mass range. Our results, instead, agree with recent modelling of the cluster members based on the Fundamental Plane relation. Finally, we report good agreement between our predicted values of the stellar-to-total mass fraction within the effective radius and those of early-type galaxies from the Sloan Lens ACS Survey. Our work significantly extends the regimes of the current samples of lens galaxies, towards the mass range that will be probed by the Euclid, Rubin, and James Webb Telescopes.

A Review on the Coalescence of Confined Drops with a Focus on Scaling Laws for the Growth of the Liquid Bridge.

The surface-tension-driven coalescence of drops has been extensively studied because of the omnipresence of the phenomenon and its significance in various natural and engineering systems. When two drops come into contact, a liquid bridge is formed between them and then grows in its lateral dimensions. As a result, the two drops merge to become a bigger drop. The growth dynamics of the bridge are governed by a balance between the driving force and the viscous and inertial resistances of involved liquids, and it is usually represented by power-law scaling relations on the temporal evolution of the bridge dimension. Such scaling laws have been well-characterized for the coalescence of unconfined or freely suspended drops. However, drops are often confined by solid or liquid surfaces and thus are a different shape from spheres, which affects their coalescence dynamics. As such, the coalescence of confined drops poses more complicated interfacial fluid dynamics challenges compared to that of unconfined drops. Although there have been several studies on the coalescence of confined drops, they have not been systematically reviewed in terms of the properties and geometry of the confining surface. Thus, we aim to review the current literature on the coalescence of confined drops in three categories: drop coalescence on a solid surface, drop coalescence on a deformable surface, and drop coalescence between two parallel surfaces with a small gap (i.e., Hele-Shaw cell), with a focus on power-law scaling relations, and to suggest challenges and outlooks for future research on the phenomena.

Local and global measures of the shear moduli of jammed disk packings.

Strain-controlled isotropic compression gives rise to jammed packings of repulsive, frictionless disks with either positive or negative global shear moduli. We carry out computational studies to understand the contributions of the negative shear moduli to the mechanical response of jammed disk packings. We first decompose the ensemble-averaged, global shear modulus as 〈G〉=(1-F_{-})〈G_{+}〉+F_{-}〈G_{-}〉, where F_{-} is the fraction of jammed packings with negative shear moduli and 〈G_{+}〉 and 〈G_{-}〉 are the average values from packings with positive and negative moduli, respectively. We show that 〈G_{+}〉 and 〈|G_{-}|〉 obey different power-law scaling relations above and below pN^{2}∼1. For pN^{2}>1, both 〈G_{+}〉N and 〈|G_{-}|〉N∼(pN^{2})^{β}, where β∼0.5 for repulsive linear spring interactions. Despite this, 〈G〉N∼(pN^{2})^{β^{'}} with β^{'}≳0.5 due to the contributions from packings with negative shear moduli. We show further that the probability distribution of global shear moduli P(G) collapses at fixed pN^{2} and different values of p and N. We calculate analytically that P(G) is a Γ distribution in the pN^{2}≪1 limit. As pN^{2} increases, the skewness of P(G) decreases and P(G) becomes a skew-normal distribution with negative skewness in the pN^{2}≫1 limit. We also partition jammed disk packings into subsystems using Delaunay triangulation of the disk centers to calculate local shear moduli. We show that the local shear moduli defined from groups of adjacent triangles can be negative even when G>0. The spatial correlation function of local shear moduli C(r[over ⃗]) displays weak correlations for pn_{sub}^{2}<10^{-2}, where n_{sub} is the number of particles within each subsystem. However, C(r[over ⃗]) begins to develop long-ranged spatial correlations with fourfold angular symmetry for pn_{sub}^{2}≳10^{-2}.

Predicting movement speed of beetles from body size and temperature

Movement facilitates and alters species interactions, the resulting food web structures, species distribution patterns, community structures and survival of populations and communities. In the light of global change, it is crucial to gain a general understanding of how movement depends on traits and environmental conditions. Although insects and notably Coleoptera represent the largest and a functionally important taxonomic group, we still know little about their general movement capacities and how they respond to warming. Here, we measured the exploratory speed of 125 individuals of eight carabid beetle species across different temperatures and body masses using automated image-based tracking. The resulting data revealed a power-law scaling relationship of average movement speed with body mass. By additionally fitting a thermal performance curve to the data, we accounted for the unimodal temperature response of movement speed. Thereby, we yielded a general allometric and thermodynamic equation to predict exploratory speed from temperature and body mass. This equation predicting temperature-dependent movement speed can be incorporated into modeling approaches to predict trophic interactions or spatial movement patterns. Overall, these findings will help improve our understanding of how temperature effects on movement cascade from small to large spatial scales as well as from individual to population fitness and survival across communities.

Richardson and Reynolds number effects on the near field of buoyant plumes: flow statistics and fluxes

The near-field characteristics of highly buoyant plumes, commonly referred to as lazy plumes, remain relatively poorly understood across a range of flow conditions, particularly compared with our understanding of far-field characteristics. Here, we perform fully resolved three-dimensional numerical simulations of round helium plumes to characterize the effects of different inlet Richardson, ${Ri}_0$ , and Reynolds, ${Re}_0$ , numbers on first- and second-order statistical moments as well as average vertical fluxes in the near field. For sufficiently high ${Re}_0$ at a particular ${Ri}_0$ , heavy air can penetrate the core of the plume, reminiscent of spikes in the classical Rayleigh–Taylor instability. In the most turbulent simulation, this penetration becomes so strong that a recirculation zone forms along the centreline of the plume. Vertical fluxes are found to scale linearly with vertical distance from the plume inlet, consistent with experimental and numerical observations (Jiang &amp; Luo, Flow Turbul. Combust., vol. 64, 2000, pp. 43–69; Kaye &amp; Hunt, Intl J. Heat Fluid Flow, vol. 30, 2009, pp. 1099–1105). We analytically derive this linear scaling from the governing equations by making a radial entrainment hypothesis whereby ambient fluid is entrained, on average, only in the radial direction at a finite distance from the inlet. Through this derivation, we identify physical mechanisms that can cause these relationships to remain only approximately valid for the present simulations. Lastly, we identify near-field power-law scaling relations for the flux magnitudes based on ${Ri}_0$ , and also examine vertical profiles of the non-dimensional Richardson number flux. Ultimately, insights from the present simulations are used to define near-, intermediate- and far-field regions in buoyant plumes.

Emergent Scaling of Dissolved Oxygen (DO) in Freshwater Streams Across Contiguous USA

AbstractDissolved oxygen (DO) indicates the overall stream water quality and ecosystem health. We investigated emergent scaling of DO with the dominant environmental drivers in freshwater (non‐coastal) streams across the contiguous United States. Available data of monthly to quarterly sampling frequencies during 1998–2015 were obtained for 86 U.S. streams. Data analytics indicated water temperature (Tw) and pH (a proxy of carbon dioxide) dominating the key environmental process components of DO concentrations in the freshwater streams. The “climatic” process component (comprising Tw and net radiation) had, respectively, ∼3 and ∼9 times stronger control on DO than the “biogeochemical” (total nitrogen, total phosphorus, pH, and specific conductivity) and “hydro‐atmospheric” exchange (stream flow and atmospheric pressure) components. The predominant climatic control on stream DO was linked to the high extent of vegetated land (on average ∼53%) and steep slope (∼10%) in the draining watersheds, despite the notable presence of agricultural land (∼35%). An emergent power law scaling relationship was then developed to acceptably predict DO (mg/l) based on Tw (K) and pH, with the approximate exponents of −15/2 and 1/2, respectively (Nash‐Sutcliffe Efficiency = 0.72–0.73). The scaling law demonstrated the underlying organizing principles such as the depletion of stream DO due to reduced dissolution and increased metabolic respiration with the increasing temperature and nutrients. The scaling law was persistent across the various U.S. streams, representing gradients in climate, hydrology, biogeochemistry, and land use/cover. The findings would help understand and manage water quality and ecosystem health in freshwater streams across the United States and beyond.

Predicting sub-millimetre flux densities from global galaxy properties

ABSTRACT Recent years have seen growing interest in post-processing cosmological simulations with radiative transfer codes to predict observable fluxes for simulated galaxies. However, this can be slow, and requires a number of assumptions in cases where simulations do not resolve the interstellar medium (ISM). Zoom-in simulations better resolve the detailed structure of the ISM and the geometry of stars and gas; however, statistics are limited due to the computational cost of simulating even a single halo. In this paper, we make use of a set of high-resolution, cosmological zoom-in simulations of massive ($M_{\star }\gtrsim 10^{10.5}\, \rm {M_{\odot }}$ at z = 2), star-forming galaxies from the FIRE suite. We run the skirt radiative transfer code on hundreds of snapshots in the redshift range 1.5 &amp;lt; z &amp;lt; 5 and calibrate a power-law scaling relation between dust mass, star formation rate, and $870\, \mu \rm {m}$ flux density. The derived scaling relation shows encouraging consistency with observational results from the sub-millimetre-selected AS2UDS sample. We extend this to other wavelengths, deriving scaling relations between dust mass, stellar mass, star formation rate, and redshift and sub-millimetre flux density at observed-frame wavelengths between $\sim \! 340$ and $\sim \! 870\, \mu \rm {m}$. We then apply the scaling relations to galaxies drawn from EAGLE, a large box cosmological simulation. We show that the scaling relations predict EAGLE sub-millimetre number counts that agree well with previous results that were derived using far more computationally expensive radiative transfer techniques. Our scaling relations can be applied to other simulations and semi-analytical or semi-empirical models to generate robust and fast predictions for sub-millimetre number counts.

A novel probabilistic model to explain drainage network evolution

River channels self-organize to form tree-like networks that follow certain statistical laws, such as Horton's laws and Hack's law, which is perhaps the reason why simple statistical models are often used to explain river network evolution. However, statistical models generally do not attempt to explain the differences between network structures. Here we address this issue by incorporating certain physically meaningful variables in a statistical modeling framework. The model allows the network to grow in a headward direction via probabilistic decisions based on two free parameters. Simulations performed over a planar matrix result in tree-like networks exhibiting power-law scaling relationships as displayed by real river networks. The two parameters are shown to be capable of explaining the variation of key network characteristics such as compactness coefficient and Hack's exponent. The uniqueness of the model thus lies in its ability to generate networks with different shapes and characteristics.

Allometric scaling relationships in mouse placenta.

Fetal growth and maturation are highly intertwined with placental development during pregnancy. Here we used placental vascular morphology measurements (depth and span) as well as the umbilical artery (UA) diameter of previously published studies on three different mouse strains (C57BL6/J, CD-1 and BALB/c), which were exposed to different conditions (combination antiretroviral therapy, chronic maternal hypoxia and malaria infection) at different embryonic days, to test the hypothesis that placental vascularization and specifically the UA size affect conceptus weight. Interaction of each study parameter with embryonic day, strain and exposure to treatments are studied to investigate the stability of the scaling relationships across and/or within strains and conditions. In addition, the effect of UA diameter on the placental growth measurements (depth and span) is studied. These results show that the power-law scaling relationship of conceptus weight and placental depth with the UA diameter is conserved across strains and conditions with the scaling exponent of approximately 3/8 and 5/8, respectively. By contrast, the relationship between conceptus weight and either the placental span or depth is different between strains and conditions, suggesting multiple mechanisms of vascular adaptation.

Modulation of Diffusion Mechanism and Its Correlation with Complexation in Aqueous Deep Eutectic Solvents.

Aqueous mixtures of deep eutectic solvents (DESs) have gained traction recently as an effective template to tailor their physicochemical properties. But detailed microscopic insights into the effects of water on the molecular relaxation phenomenon in DESs are not entirely understood. DESs are strong network-forming liquids due to the extensive hydrogen bonding and complex formation between their species, and therefore, water can behave as a controlled disruptor altering the microscopic structure and dynamics in DESs. In this study, the role of water in the diffusion mechanism of acetamide in the aqueous mixtures of DESs synthesized using acetamide and lithium perchlorate is investigated using molecular dynamics (MD) simulation and quasielastic neutron scattering (QENS). The acetamide dynamics comprises localized diffusion within transient cages and a jump diffusion process across cages. The jump diffusion process is observed to be strongly enhanced by about a factor of 10 as the water content in the system is increased. Meanwhile, the geometry of the localized dynamics is unaltered by addition of water, but the localized diffusion becomes significantly faster and more heterogeneous with increasing water concentration. The accelerating effects of water on localized diffusion are also substantiated by QENS experiments. The water concentration in the DES is observed to control the solvation structure of lithium ions, with the ions becoming significantly hydrated at 20 wt % water. The formation of interwater and water-acetamide hydrogen bonds is observed. The increase in water concentration is found to increase the number of H-bonds; however, their lifetimes are found to decrease substantially. Similarly, the lifetimes of acetamide-lithium complexes are also found to be diminished by increasing water concentration. A power-law scaling relationship between lifetimes and diffusion constants is established, elucidating the extent of coupling between diffusive processes and hydrogen bonding and microscopic complexation. This study demonstrates the ability to use water as an agent to probe the role of structural relaxation and complex lifetimes of diffusive processes at different time and length scales.