Power-law Scaling Relationship Research Articles

Kinetics of sol-to-gel transition in irreversible particulate systems

A comprehensive theory encompassing the kinetics of the sol-to-gel transition is yet to be formulated due to break-down of the mean-field Smoluchowski Equation. Using high temporal-resolution Monte Carlo simulation of irreversible aggregation systems, we show that this transition has three distinct regimes with kinetic exponent z∈1,2 corresponding to aggregation of sol clusters proceeding to the ideal gel point (IGP); z∈2,5.7 for gelation of sol clusters beyond IGP; and z∈2,3.5 for a hitherto unidentified regime involving aggregation of gels when monomer-dense. We further establish universal power-law scaling relationships that connect the kinetics of these three regimes. Improved parameterizations are performed on the characteristic timescale parameters that define each regime.

Numerical study on the dynamic process of single plume flow in thermal convection with polymers

A direct numerical simulation of single plume flow in thermal convection with polymers was carried out in a domain with 1:3 as the width to height ratio. The heat transport ability is weakened by adding polymers within the here-investigated governing parameter range. However, it is promoted when the maximum polymer extension L is increased. The distribution of vertical velocity and temperature indicates that the plume in the polymer solution case is speeded up and widens bigger as compared to that in the Newtonian fluid case. Inside the plume, polymer chains tend to release energy at the position where the velocity is decelerated. The ratio of Nusselt numbers (Nu/NuNew) shows the power-law scaling relation with the governing parameter L2/Wi in polymer solution cases, which is only applicable for moderate Wi and small L. The present study can give direct insight into the observation about plumes in turbulent thermal convection experiments. It is therefore useful for the analysis of heat transport in thermal convection with polymers.

X-Ray Properties of SPT-selected Galaxy Clusters at 0.2 < z < 1.5 Observed with XMM-Newton

Abstract We present measurements of the X-ray observables of the intracluster medium (ICM), including luminosity L X , ICM mass M ICM, emission-weighted mean temperature T X , and integrated pressure Y X , that are derived from XMM-Newton X-ray observations of a Sunyaev–Zel’dovich effect (SZE) selected sample of 59 galaxy clusters from the South Pole Telescope SPT-SZ survey that span the redshift range 0.20 < z < 1.5. We constrain the best-fit power-law scaling relations between X-ray observables, redshift, and halo mass. The halo masses are estimated based on previously published SZE observable-to-mass scaling relations, calibrated using information that includes the halo mass function. Employing SZE-based masses in this sample enables us to constrain these scaling relations for massive galaxy clusters (M 500 ≥ 3 × 1014 M ⊙) to the highest redshifts where these clusters exist without concern for X-ray selection biases. We find that the mass trends are steeper than self-similarity in all cases, and with ≥2.5σ significance in the case of L X and M ICM. The redshift trends are consistent with the self-similar expectation, but the uncertainties remain large. Core-included scaling relations tend to have steeper mass trends for L X . There is no convincing evidence for a redshift-dependent mass trend in any observable. The constraints on the amplitudes of the fitted scaling relations are currently limited by the systematic uncertainties on the SZE-based halo masses, but the redshift and mass trends are limited by the X-ray sample size and the measurement uncertainties of the X-ray observables.

Impacts of changing spatial scales on CPUE–factor relationships of Ommastrephes bartramii in the northwest Pacific

AbstractThe selection of spatial scales is of particular importance in modeling relationships between fishery abundance and its influencing factors, because these relationships are significantly affected by spatial scale. Here, we explore the spatial scale effects of catch per unit effort (CPUE)–factor relationships for Ommastrephes bartramii in the northwest Pacific. The original commercial fishery data and oceanographic factors were tessellated to 12 spatial scales from 5′ to 60′ with an interval of 5′. Under the original scale and 12 tessellated scales, we constructed the generalized additive models (GAMs) to model the relationships between the O. bartramii CPUE and the influencing factors, including Year, Month, Latitude (Lat), Longitude (Lon), sea surface salinity (SSS), sea surface temperature (SST), sea surface chlorophyll‐a (Chl‐a) concentration, and sea surface height (SSH). Our multi‐scale analysis showed that the relationships are sensitive to spatial scales. Among the factors, Year, Month, and SSS share quadratic polynomial scaling relations; Lat, SST, and Chl‐a illustrate power law scaling relations; Lon has a linear scaling relation; and SSH presents an exponential scaling relation. Considering the scale sensitivity of the factor sort‐order and the accumulation of explained residual deviance in GAM, we suggest 30′–45′ as the optimal range of spatial scales for analyzing the CPUE–factor relationships for O. bartramii. Our research improves understanding of the impacts of changing scales in fisheries and provides a potential method for the selection of a suitable spatial scale for fisheries analysis and resource surveying.

Scaling relationship between CO pollution and population size over major US metropolitan statistical areas

As the world’s population is projected to reach 9.7 billion by 2050, large and small cities will continue to expand. There are few studies investigating how the size of cities affects air pollution. Carbon monoxide (CO), a precursor of ozone and a by-product of incomplete combustion, is a common air pollutant. The major sources of CO in the US urban areas are motor vehicles. Here we examined the scaling relation of CO concentrations over major US metropolitan statistical areas (MSAs) using Measurement Of Pollution in The Troposphere (MOPITT) surface CO retrievals and National Emissions Inventory (NEI) data. We found significant power-law scaling relationships between CO and population (r2 of 0.30 for MOPITT average CO concentration and r2 of 0.71 for NEI total CO emission). We found decreasing CO trends from 2000 to 2015 using MOPITT and EPA CO ground measurements. Sublinear scaling relationships (scaling coefficient β < 1) suggest that larger MSAs are more combustion-efficient in terms of CO emissions. We found a weaker scaling relation and smaller scaling coefficient from MOPITT CO concentrations than from NEI total CO emission data. This pattern may be attributed to the differences between the two CO datasets: annual average of monthly MOPITT CO concentration at 1° by 1° spatial resolution versus the NEI annual CO emissions compiled from emission inventories and estimated from mobile source emissions models. Future research is needed to investigate the capability of using satellite observations to study scaling relations between air pollutants and population.

The impact of spatial scale on local Moran’s I clustering of annual fishing effort for Dosidicus gigas offshore Peru

The spatial scale (fishing grid) of fisheries research affects the observed spatial patterns of fisheries resources such as catch-per-unit-effort (CPUE) and fishing effort. We examined the scale impact of high value (HH) clusters of the annual fishing effort for Dosidicus gigas offshore Peru from 2009 to 2012. For a multi-scale analysis, the original commercial fishery data were tessellated to twelve spatial scales from 6′ to 72′ with an interval of 6′. Under these spatial scales, D. gigas clusters were identified using the Anselin Local Moran’s I. Statistics including the number of points, mean CPUE, standard deviation (SD), skewness, kurtosis, area and centroid were calculated for these HH clusters. We found that the z-score of global Moran’s I and the number of points for HH clusters follow a power law scaling relationship from 2009 to 2012. The mean effort and its SD also follow a power law scaling relationship from 2009 to 2012. The skewness follows a linear scaling relationship in 2010 and 2011 but fluctuates with spatial scale in 2009 and 2012; kurtosis follows a logarithmic scale relationship in 2009, 2011 and 2012 but a linear scale relationship in 2010. Cluster area follows a power law scaling relationship in 2010 and 2012, a linear scaling relationship in 2009, and a quadratic scaling relationship in 2011. Based on the peaks of Moran’s I indices and the multi-scale analysis, we conclude that the optimum scales are 12′ in 2009 – 2011 and 6′ in 2012, while the coarsest allowable scales are 48′ in 2009, 2010 and 2012, and 60′ in 2011. Our research provides the best spatial scales for conducting spatial analysis of this pelagic species, and provides a better understanding of scaling behavior for the fishing effort of D. gigas in the offshore Peruvian waters.

The Dependence of Solar Wind Burst Size on Burst Duration and Its Invariance Across Solar Cycles 23 and 24

AbstractTime series of solar wind variables are bursty in nature. Bursts, or excursions, in the time series of solar wind parameters are associated with various transient structures in the solar wind plasma and are often the drivers of increased space weather activity in Earth's magnetosphere. We define bursts by setting a threshold value of the time series and identifying how often, and for how long, it is exceeded. This allows us to study how the statistical distributions and scaling properties of burst parameters vary over solar cycles 23 and 24. We find that the distributions of burst duration and integrated burst size vary over the solar cycle and between the equivalent phases of consecutive cycles. However, there exists a single power law scaling relation between burst size and duration, with a joint area‐duration scaling exponent α that is independent of the solar cycle. This provides a solar cycle invariant constraint between possible sizes and durations of solar wind bursts that can occur.

Scaling of square-prism shear layers

Scaling characteristics, essential to the mechanisms of transition in square-prism shear layers, were explored experimentally. In particular, the evolution of the dominant instability modes as a function of Reynolds number were reported in the range $1.5\times 10^{4}\lesssim Re_{D}\lesssim 7.5\times 10^{4}$. It was found that the ratio between the shear layer frequency and the shedding frequency obeys a power-law scaling relation. Adherence to the power-law relationship, which was derived from hot-wire measurements, has been supported by two additional and independent scaling considerations, namely, by particle image velocimetry measurements to observe the evolution of length and velocity scales in the shear layer during transition, and by comparison to direct numerical simulations to illuminate the properties of the front-face boundary layer. The nonlinear dependence of the shear layer instability frequency is sustained by the influence of $Re_{D}$ on the thickness of the laminar front-face boundary layer. In corroboration with the original scaling argument for the circular cylinder, the length scale of the shear layer was the only source of nonlinearity in the frequency ratio scaling, within the range of Reynolds numbers reported. The frequency ratio scaling may therefore be understood by the influence of $Re_{D}$ on the appropriate length scale of the shear layer. This length scale was observed to be the momentum thickness evaluated at a transition point, defined where the Kelvin–Helmholtz instability saturates.

Preliminary laboratory investigations of ejecta emplacement dynamics and morphology with planetary applications

The preponderance of impact craters and the associated crater ejecta facies are leading agents of geomorphic change across the Solar System. Interpretation of planetary landscape evolution, sample provenance, and regolith gardening all benefit from a thorough understanding of ejecta emplacement dynamics. Constraining the type and range of these dynamics has eluded experimentation even as the effects of primary impacts have become well-constrained from experiments and numerical simulations and have been shown to follow power law scaling relationships. To address the knowledge gap surrounding granular ejecta emplacement, we built and characterized a novel ejecta emplacement catapult and showed it to accurately reproduce the ejecta mass and velocity profiles predicted for in-flight natural ejecta curtains. Based on this dynamic similarity to larger, natural systems, we proceeded with a preliminary exploratory suite of experiments to constrain runout and erosion efficiencies of flowing ejecta. Our quantitative results at low speeds may suggest a new set of scaling relationships for erosion via ballistic ejecta versus crater formation and erosion from hypervelocity clustered projectiles. Our results also show significant ejecta runout efficiencies of ∼1–2 (only slightly below the efficiencies of terrestrial debris flows 12 decades more voluminous) with important erosive efficiencies of ∼2–4%. Our qualitative results reveal a stochastic and heterogeneous system: ejecta “saltation” and implantation, and regolith exhumation, erosion, and shearing. Together with the initial results showing ejecta emplacement to be violently dynamic, the development of this new laboratory technique will enable more detailed studies to better inform interpretations of sample provenance, ejecta stratigraphy, and geochemical boundaries.

Graphene Helicoid: Distinct Properties Promote Application of Graphene Related Materials in Thermal Management

The extremely high thermal conductivity of graphene has received great attention both in experiments and calculations. Obviously, new feature in thermal properties is of primary importance for application of graphene-based materials in thermal management in nanoscale. Here, we studied the thermal conductivity of graphene helicoid, a newly reported graphene-related nanostructure, using molecular dynamics simulation. Interestingly, in contrast to the converged cross-plane thermal conductivity in multi-layer graphene, axial thermal conductivity of graphene helicoid keeps increasing with thickness with a power law scaling relationship, which is a consequence of the divergent in-plane thermal conductivity of two-dimensional graphene. Moreover, the large overlap between adjacent layers in graphene helicoid also promotes higher thermal conductivity than multi-layer graphene. Furthermore, in the small strain regime (< 10%), compressive strain can effectively increase the thermal conductivity of graphene helicoid, while in the ultra large strain regime (~100% to 500%), tensile strain does not decrease the heat current, unlike that in generic solid-state materials. Our results reveal that the divergence in thermal conductivity, associated with the anomalous strain dependence and the unique structural flexibility, make graphene helicoid a new platform for studying fascinating phenomena of key relevance to the scientific understanding and technological applications of graphene-related materials.

Evaluation of energy barrier of CoFeB/MgO magnetic tunnel junctions with perpendicular easy axis using retention time measurement

We investigate the energy barrier E that determines the thermal stability factor Δ, of CoFeB/MgO magnetic tunnel junctions (MTJs) with a perpendicular easy axis by retention time measurement as a function of temperature T and junction diameter D. E decreases with increasing T for all the studied MTJs. The temperature at which any particular value of E is obtained tends to decrease with decreasing D, indicating that the magnetization reversal in the MTJs is described by reversal models other than the nucleation model. We find that the temperature dependence of E correlates with that of spontaneous magnetization through the power law scaling relationship, which enables us to determine Δ at temperatures different from those used in the retention time measurement.

Universal statistics of vortex tangles in three-dimensional random waves

The tangled nodal lines (wave vortices) in random, three-dimensional wavefields are studied as an exemplar of a fractal loop soup. Their statistics are a three-dimensional counterpart to the characteristic random behaviour of nodal domains in quantum chaos, but in three dimensions the filaments can wind around one another to give distinctly different large scale behaviours. By tracing numerically the structure of the vortices, their conformations are shown to follow recent analytical predictions for random vortex tangles with periodic boundaries, where the local disorder of the model ‘averages out’ to produce large scale power law scaling relations whose universality classes do not depend on the local physics. These results explain previous numerical measurements in terms of an explicit effect of the periodic boundaries, where the statistics of the vortices are strongly affected by the large scale connectedness of the system even at arbitrarily high energies. The statistics are investigated primarily for static (monochromatic) wavefields, but the analytical results are further shown to directly describe the reconnection statistics of vortices evolving in certain dynamic systems, or occurring during random perturbations of the static configuration.

Sediment rating and annual cycles of suspended sediment in German upland rivers

Sediment flux of lowland rivers is dominated by suspended transport, but data is often sparse and analysis largely relies on rating relationships. However, suspended sediment concentration is by no means constant in both, space and time. Here we analyse the variability of sediment rating curves and the seasonality of suspended sediment concentration in German waterways, as recorded by 10 gauging stations with catchment areas between 2600 - 22000 km2. Our data reveal a distinct break in power-law scaling relationships for all stations, with increased scaling exponents above threshold discharges close to the geometric mean. We attribute this mainly to the activation of sediment sources that resist mobilisation at lower flows. Furthermore, all stations show a counter-clockwise hysteresis effect throughout the year, where summer discharges have a higher sediment load than comparable winter discharges. Though the reasons for this pattern need further investigation, preliminary results show a strong correlation with rainfall erosivity and land-use parameters.

Expansion of major urban areas in the US Great Plains from 2000 to 2009 using satellite scatterometer data

A consistent dataset delineating and characterizing changes in urban environments will be valuable for socioeconomic and environmental research and for sustainable urban development. Remotely sensed data have been long used to map urban extent and infrastructure at various spatial and spectral resolutions. Although many datasets and approaches have been tried, there is not yet a universal way to map urban extents across the world. Here we combined a microwave scatterometer (QuikSCAT) dataset at ~1km posting with percent impervious surface area (%ISA) data from the National Land Cover Dataset (NLCD) that was generated from Landsat data, and ambient population data from the LandScan product to characterize and quantify growth in nine major urban areas in the US Great Plains from 2000 to 2009. Nonparametric Mann-Kendall trend tests on backscatter time series from urban areas show significant expanding trends in eight of nine urban areas with p-values ranging 0.032 to 0.001. The sole exception is Houston, which has a substantial non-urban backscatter at the northeastern edge of the urban core. Strong power law scaling relationships between ambient population and either urban area or backscatter power (r2 of 0.96 in either model) with sub-linear exponents (β of 0.911 and 0.866, respectively) indicate urban areas become more compact with more vertical built-up structure than lateral expansion to accommodate the increased population. Increases in backscatter and %ISA datasets between 2001 and 2006 show agreement in both magnitude and direction for all urban areas except Minneapolis-St. Paul (MSP), likely due to the presence of many lakes and ponds throughout the MSP metropolitan area. We conclude discussing complexities in the backscatter data caused by large metal structures and rainfall.

Fractal-Based Wavelet Filter for Separating Geophysical or Geochemical Anomalies from Background

The widely used wavelet filtering technique holds potential to approach anomaly–background separation in geophysical and geochemical data processing. Wavelet statistics provide crucial information on such filtering methods. In general, conventional (Gaussian-type) statistical modeling is insufficient to adequately describe the heavily tailed and sharply peaked (at zero) distribution of the wavelet coefficients of irregular geo-anomaly patterns. This paper demonstrates that the cumulative (frequency) number of the wavelet coefficient yields a power-law scaling relationship with the coefficient based on wavelet transform of a fractal/singular measure. This wavelet coefficient–cumulative number power-law model is proven to be more flexible and appropriate than the Gaussian model for characterizing the scaling nature of the coefficient distribution. Accordingly, a fractal-based filtering technique is developed based on the wavelet statistical model to decompose mixed patterns into components based on the distinct self-similarities identified in the wavelet domain. The decomposition scheme of the fractal-based wavelet filtering method considers not only the coefficient frequency distribution but also the fractal spectrum of singularities and the self-similarity of real-world features. Finally, a synthetic data test and real applications from two metallogenic provinces of China are used to validate the proposed fractal filtering method for anomaly–background separation and identification of geophysical or geochemical anomalies related to mineralization and other geological features.

A Spatial Biosurveillance Synthetic Data Generator in R

ObjectiveTo develop a spatially accurate biosurveillance synthetic datagenerator for the testing, evaluation, and comparison of new outbreakdetection techniques.IntroductionDevelopment of new methods for the rapid detection of emergingdisease outbreaks is a research priority in the field of biosurveillance.Because real-world data are often proprietary in nature, scientists mustutilize synthetic data generation methods to evaluate new detectionmethodologies. Colizza et. al. have shown that epidemic spread isdependent on the airline transportation network [1], yet current datagenerators do not operate over network structures.Here we present a new spatial data generator that models thespread of contagion across a network of cities connected by airlineroutes. The generator is developed in the R programming languageand produces data compatible with the popular `surveillance’ softwarepackage.MethodsColizza et. al. demonstrate the power-law relationships betweencity population, air traffic, and degree distribution [1]. We generate atransportation network as a Chung-Lu random graph [2] that preservesthese scale-free relationships (Figure 1).First, given a power-law exponent and a desired number of cities,a probability mass function (PMF) is generated that mirrors theexpected degree distribution for the given power-law relationship.Values are then sampled from this PMF to generate an expecteddegree (number of connected cities) for each city in the network.Edges (airline connections) are added to the network probabilisticallyas described in [2]. Unconnected graph components are each joinedto the largest component using linear preferential attachment. Finally,city sizes are calculated based on an observed three-quarter power-law scaling relationship with the sampled degree distribution.Each city is represented as a customizable stochastic compartmentalSIR model. Transportation between cities is modeled similar to [2].An infection is initialized in a single random city and infection countsare recorded in each city for a fixed period of time. A consistentfraction of the modeled infection cases are recorded as daily clinicvisits. These counts are then added onto statically generated baselinedata for each city to produce a full synthetic data set. Alternatively,data sets can be generated using real-world networks, such as the onemaintained by the International Air Transport Association.ResultsDynamics such as the number of cities, degree distribution power-law exponent, traffic flow, and disease kinetics can be customized.In the presented example (Figure 2) the outbreak spreads over a 20city transportation network. Infection spreads rapidly once the morepopulated hub cities are infected. Cities that are multiple flights awayfrom the initially infected city are infected late in the process. Thegenerator is capable of creating data sets of arbitrary size, length, andconnectivity to better mirror a diverse set of observed network types.ConclusionsNew computational methods for outbreak detection andsurveillance must be compared to established approaches. Outbreakmitigation strategies require a realistic model of human transportationbehavior to best evaluate impact. These actions require test data thataccurately reflect the complexity of the real-world data they wouldbe applied to. The outbreak data generated here represents thecomplexity of modern transportation networks and are made to beeasily integrated with established software packages to allow for rapidtesting and deployment.Randomly generated scale-free transportation network with a power-lawdegree exponent ofλ=1.8. City and link sizes are scaled to reflect their weight.An example of observed daily outbreak-related clinic visits across a randomlygenerated network of 20 cities. Each city is colored by the number of flightsrequired to reach the city from the initial infection location. These generatedcounts are then added onto baseline data to create a synthetic data set forexperimentation.KeywordsSimulation; Network; Spatial; Synthetic; Data

Intrinsic α helix propensities compact hydrodynamic radii in intrinsically disordered proteins.

Proteins that lack tertiary stability under normal conditions, known as intrinsically disordered, exhibit a wide range of biological activities. Molecular descriptions for the biology of intrinsically disordered proteins (IDPs) consequently rely on disordered structural models, which in turn require experiments that assess the origins to structural features observed. For example, while hydrodynamic size is mostly insensitive to sequence composition in chemically denatured proteins, IDPs show strong sequence-specific effects in the hydrodynamic radius (Rh ) when measured under normal conditions. To investigate sequence-modulation of IDP Rh , disordered ensembles generated by a hard sphere collision model modified with a structure-based parameterization of the solution energetics were used to parse the contributions of net charge, main chain dihedral angle bias, and excluded volume on hydrodynamic size. Ensembles for polypeptides 10-35 residues in length were then used to establish power-law scaling relationships for comparison to experimental Rh from 26 IDPs. Results showed the expected outcomes of increased hydrodynamic size from increases in excluded volume and net charge, and compaction from chain-solvent interactions. Chain bias representing intrinsic preferences for α helix and polyproline II (PPII ), however, modulated Rh with intricate dependence on the simulated propensities. PPII propensities at levels expected in IDPs correlated with heightened Rh sensitivity to even weak α helix propensities, indicating bias for common (φ, ψ) are important determinants of hydrodynamic size. Moreover, data show that IDP Rh can be predicted from sequence with good accuracy from a small set of physicochemical properties, namely intrinsic conformational propensities and net charge. Proteins 2017; 85:296-311. © 2016 Wiley Periodicals, Inc.

Target material dependence of positron generation from high intensity laser-matter interactions

The effective scaling of positron-electron pair production by direct, ultraintense laser-matter interaction is investigated for a range of target materials and thicknesses. An axial magnetic field, acting as a focusing lens, was employed to measure positron signals for targets with atomic numbers as low as copper (Z = 29). The pair production yield was found to be consistent with the Bethe-Heitler mechanism, where the number of positrons emitted into a 1 steradian cone angle from the target rear was found to be proportional to Z2. The unexpectedly low scaling results from Coulomb collisions that act to stop or scatter positrons into high angles. Monte Carlo simulations support the experimental results, providing a comprehensive power-law scaling relationship for all elemental materials and densities.

DYNAMICAL MASS MEASUREMENTS OF CONTAMINATED GALAXY CLUSTERS USING MACHINE LEARNING

ABSTRACT We study dynamical mass measurements of galaxy clusters contaminated by interlopers and show that a modern machine learning algorithm can predict masses by better than a factor of two compared to a standard scaling relation approach. We create two mock catalogs from Multidark’s publicly available N-body MDPL1 simulation, one with perfect galaxy cluster membership information and the other where a simple cylindrical cut around the cluster center allows interlopers to contaminate the clusters. In the standard approach, we use a power-law scaling relation to infer cluster mass from galaxy line-of-sight (LOS) velocity dispersion. Assuming perfect membership knowledge, this unrealistic case produces a wide fractional mass error distribution, with a width of . Interlopers introduce additional scatter, significantly widening the error distribution further ( ). We employ the support distribution machine (SDM) class of algorithms to learn from distributions of data to predict single values. Applied to distributions of galaxy observables such as LOS velocity and projected distance from the cluster center, SDM yields better than a factor-of-two improvement ( ) for the contaminated case. Remarkably, SDM applied to contaminated clusters is better able to recover masses than even the scaling relation approach applied to uncontaminated clusters. We show that the SDM method more accurately reproduces the cluster mass function, making it a valuable tool for employing cluster observations to evaluate cosmological models.

Infrasonic and seismic eruption tremors and their relation to magma discharge rate: A case study for the 2011 eruption of Shinmoe-dake, Japan

Infrasound monitoring is a useful tool to capture surface activity of volcanoes. Previous works have attempted to connect observations of infrasonic eruption tremors with magma discharge rate that is an important parameter to characterize an eruption. Power law scaling relations with different power indices have been proposed based on various datasets and models. Independently, different power law relations have been proposed between seismic eruption tremors and magma discharge rate. The 2011 eruption of Shinmoe-dake, Japan, provides an excellent dataset with which to investigate these relationships for a sustained explosive eruption sequence. Magma discharge rates are well constrained by geodetic, geologic, and remote sensing methods. Seismic and infrasonic data were recorded close to the vent. Linear power law relationships are found to fit all pairs of variables (seismic eruption tremor power, infrasonic eruption tremor power, and magma discharge rate) in the quasi-stable or slowly growing stages of th...