Power-law Increase Research Articles

Turbulent magnetic field fluctuations in Saturn's magnetosphere

We analyze the statistical properties of magnetic field fluctuations measured by the Cassini spacecraft inside Saturn's magnetosphere. We introduce Saturn's magnetosphere as a new laboratory for plasma turbulence, where background magnetic field is strong (1 nT<B0≤75 nT), fluctuations are weak (<δB/B> = 0.07), and the ion plasma βi is smaller than one. We also show that the dissipation of these magnetic field fluctuations has important implications for the magnetosphere. In a case study of the second orbit of Cassini around Saturn we show that at MHD scales, the spectra and the nature of fluctuations are characterized by large‐scale nonstationary processes. The spectral slope varies between −0.8 and −1.7. At higher frequencies we observe a steeper spectrum with nearly constant power law exponent. A spectral break correlating with ion scales separates the two frequency ranges. We carry out a statistical study of high‐frequency range fluctuations using the first seven orbits of Cassini. We find that the energy density of raw frequency spectra depends on radial distance from Saturn and thermal and magnetic pressures. However, normalized spectra depend only on ion plasma βi. Closer to Saturn the spectral slope is about −2.3 and for radial distances r>9 Rs the average slope is −2.6. The fluctuations have probability density functions with increasingly non‐Gaussian tails and a power law increase of flatness with frequency, which indicates intermittency. We estimate the total energy flux contained in the turbulent cascade as 60–100 GW, which is on the same order of magnitude as needed to heat an adiabatically expanding plasma to the temperatures measured in Saturn's magnetosphere.

STEADILY INCREASING STAR FORMATION RATES IN GALAXIES OBSERVED AT 3 ≲z≲ 5 IN THE CANDELS/GOODS-S FIELD

We investigate the star formation histories (SFHs) of high redshift (3 <~ z <~ 5) star-forming galaxies selected based on their rest-frame ultraviolet (UV) colors in the CANDELS/GOODS-S field. By comparing the results from the spectral-energy-distribution-fitting analysis with two different assumptions about the SFHs --- i.e., exponentially declining SFHs as well as increasing ones, we conclude that the SFHs of high-redshift star-forming galaxies increase with time rather than exponentially decline. We also examine the correlations between the star formation rates (SFRs) and the stellar masses. When the galaxies are fit with rising SFRs, we find that the trend seen in the data qualitatively matches the expectations from a semi-analytic model of galaxy formation. The mean specific SFR is shown to increase with redshift, also in agreement with the theoretical prediction. From the derived tight correlation between stellar masses and SFRs, we derive the mean SFH of star-forming galaxies in the redshift range of 3 <~ z <~ 5, which shows a steep power-law (with power alpha = 5.85) increase with time. We also investigate the formation timescales and the mean stellar population ages of these star-forming galaxies. Our analysis reveals that UV-selected star-forming galaxies have a broad range of the formation redshift. The derived stellar masses and the stellar population ages show positive correlation in a sense that more massive galaxies are on average older, but with significant scatter. This large scatter implies that the galaxies' mass is not the only factor which affects the growth or star formation of high-redshift galaxies.

ENTROPY FLATTENING, GAS CLUMPING, AND TURBULENCE IN GALAXY CLUSTERS

Several physical processes and formation events are expected in cluster outskirts, a vast region up to now essentially not covered by observations. The recent Suzaku (X-ray) and Planck (Sunayev-Zeldovich effect) observations out to the virial radius have highlighted in these peripheral regions a rather sharp decline of the intracluster gas temperature, an entropy flattening in contrast with the theoretically expected power law increase, the break of the hydrostatic equilibrium even in some relaxed clusters, a derived gas mass fraction above the cosmic value measured from several CMB experiments, and a total X-ray mass lower than the weak lensing mass determinations. Here we present the analysis of four clusters (A1795, A2029, A2204 and A133) with the SuperModel that includes a nonthermal pressure component due to turbulence to sustain the hydrostatic equilibrium also in the cluster outskirts. In such way we obtain a correct determination of the total X-ray mass and of the gas mass fraction; this in turn allows to determine the level of the gas clumping that can affect the shape of the entropy profiles reported by the Suzaku observations. Our conclusion is that the role of the gas clumping is very marginal and that the observed entropy flattening is due to the rapid decrement of the temperature in the cluster outskirts caused by non gravitational effects. Moreover, we show that the X-ray/SZ joint analysis from ROSAT and Planck data, as performed in some recent investigations, is inadequate to discriminate between a power law increase and a flattening of the entropy.

A Simple, Single-Carbon-Nanotube Nanofludic Platform for Fundamental Transport Studies

Fundamental understanding of ionic and molecular transport phenomena in a simple model nanopore is critical for elucidating function mechanisms of much more complex biological systems, and for advancing technological areas such as membrane separation, energy harvesting/storage, and single molecule detection. For this goal, carbon nanotubes (CNTs) offer key advantages as model nanofluidic channels due to their simple chemical composition and structure (known with atomic precision), robustness, facile length and diameter control, and straightforward local functionalization at their open rim. CNTs have also very interesting fluidics properties such as enhanced pressure-driven fluid transport rates, unusually high electroosmotic flow, and ionic selectivity.Here, we present our work toward developing and validating a novel nanofluidic platform featuring an individual carbon nanotube (CNT) as the flow channel in an advanced Coulter Counter. To fabricate the CNT nanofluidic device, vertically aligned single-walled CNTs are synthesized directly on a suspended silicon nitride membrane and then bound in a solid matrix before an individual CNT is opened by focused ion beam milling. Single-molecule translocation studies with small molecular size analytes suggest the successful fabrication of a Coulter Counter with a-few-nm wide CNT nanochannel. Our initial ionic conductivity studies indicate a power-law increase of conductance with KCl concentration in CNT channels, a dependence that seems to be unique of CNT pores.

The stochastic background: scaling laws and time to detection for pulsar timing arrays

We derive scaling laws for the signal-to-noise ratio of the optimal cross-correlation statistic, and show that the large power-law increase of the signal-to-noise ratio as a function of the observation time T that is usually assumed holds only at early times. After enough time has elapsed, pulsar timing arrays enter a new regime where the signal to noise only scales as . In addition, in this regime the quality of the pulsar timing data and the cadence become relatively unimportant. This occurs because the lowest frequencies of the pulsar timing residuals become gravitational-wave dominated. Pulsar timing arrays enter this regime more quickly than one might naively suspect. For T = 10 yr observations and typical stochastic background amplitudes, pulsars with residual root-mean-squares of less than about 1 μs are already in that regime. The best strategy to increase the detectability of the background in this regime is to increase the number of pulsars in the array. We also perform realistic simulations of the NANOGrav pulsar timing array, which through an aggressive pulsar survey campaign adds new millisecond pulsars regularly to its array, and show that a detection is possible within a decade, and could occur as early as 2016.

Interface structure and flux laws in a natural double-diffusive layering

The diffusive regime of double-diffusive convection generates staircases consisting of thin high-gradient interfaces sandwiched between convectively mixed layers. Simultaneous microstructure measurements of both temperature and conductivity from the staircases in Lake Kivu are used to test flux laws and theoretical models for double diffusion. Density ratios in Lake Kivu are between one and ten and mixed layer thicknesses on average 0.7 m. The larger interface thickness of temperature (average 9 cm) compared to dissolved substances (6 cm) confirms the boundary-layer structure of the interface. Our observations suggest that the boundary-layer break-off cannot be characterized by a single critical boundary-layer Rayleigh number, but occurs within a range of O(10(2)) to O(10(4)). Heat flux parameterizations which assume that the Nusselt number follows a power law increase with the Rayleigh number Ra are tested for their exponent . In contrast to the standard estimate =1/3, we found =0.200.03 for density ratios between two and six. Therefore, we suggest a correction of heat flux estimates which are based on =1/3. The magnitude of the correction depends on Ra in the system of interest. For Lake Kivu (average heat flux 0.10 W m(-2)) with Ra=O(10(8)), corrections are marginal. In the Arctic Ocean with Ra=O(10(8)) to O(10(12)), however, heat fluxes can be overestimated by a factor of four.

Flow and axial dispersion in a sinusoidal-walled tube: Effects of inertial and unsteady flows

In this work, we consider a sinusoidal-walled tube (a three-dimensional tube with sinusoidally-varying diameter) as a simplified conceptualization of flow in porous media. Direct numerical simulation using computational fluid dynamics (CFD) methods was used to compute velocity fields by solving the Navier–Stokes equations, and also to numerically solve the volume averaging closure problem, for a range of Reynolds numbers (Re) spanning the low-Re to inertial flow regimes, including one simulation at Re=449 for which unsteady flow was observed. The longitudinal dispersion observed for the flow was computed using a random walk particle tracking method, and this was compared to the longitudinal dispersion predicted from a volume-averaged macroscopic mass balance using the method of volume averaging; the results of the two methods were consistent. Our results are compared to experimental measurements of dispersion in porous media and to previous theoretical results for both the low-Re, Stokes flow regime and for values of Re representing the steady inertial regime. In the steady inertial regime, a power-law increase in the effective longitudinal dispersion (DL) with Re was found, and this is consistent with previous results. This rapid rate of increase is caused by trapping of solute in expansions due to flow separation (eddies). One unsteady (but non-turbulent) flow case (Re=449) was also examined. For this case, the rate of increase of DL with Re was smaller than that observed at lower Re. Velocity fluctuations in this regime lead to increased rates of solute mass transfer between the core flow and separated flow regions, thus diminishing the amount of tailing caused by solute trapping in eddies and thereby reducing longitudinal dispersion. The observed tailing was further explored through analysis of concentration skewness (third moment) and its assymptotic convergence to conventional advection–dispersion behavior (skewness=0). The method of volume averaging was applied to develop a skewness model, and demonstrated that the skewness decreases as a function of inverse square root of time. Our particle tracking simulation results were shown to conform to this theoretical result in most of the cases considered.

(Invited) Photoluminescence Efficiency of Germanium Dots Self-Assembled on Oxides

Self-assembled Ge quantum dots were formed by in-situ thermal annealing of a thin amorphous Ge layer deposited by molecular beam epitaxy either on a thin porous TiO2 layer grown on SiO2 on Si(001) or directly on the SiO2 layer itself. For samples with dot diameters ranging from 10 to 35 nm, the dot photoluminescence (PL) appeared primarily as a wide near-infrared band peaked near 800 meV. The peak energy of the PL band reflects the average dot size and its shape depends on the dot size distribution. Using tight binding and effective mass theoretical models, we have analyzed the PL spectrum in terms of the dot size distribution. The observed size distribution determined from transmission electron and atomic force microscopy allowed the determination of the nonlinear increase in the PL efficiency with decreasing dot diameter. Although the absolute intensities of the PL from the samples vary, the calculated efficiency curves are all well fitted by straight lines on a log-log plot, with essentially the same slope for all samples, thereby demonstrating that under the weak confinement regime investigated here there is a universal power-law increase in PL efficiency with decreasing dot size. Knowing this generic PL efficiency, we show that it is possible to evaluate the size distribution of Ge dots from their PL energy dependence.

DECODING THE MESSAGE FROM METEORITIC STARDUST SILICON CARBIDE GRAINS

Micron-sized stardust grains that originated in ancient stars are recovered from meteorites and analysed using high-resolution mass spectrometry. The most widely studied type of stardust is silicon carbide (SiC). Thousands of these grains have been analysed with high precision for their Si isotopic composition. Here we show that the distribution of the Si isotopic composition of the vast majority of stardust SiC grains carry the imprints of a spread in the age-metallicity distribution of their parent stars and of a power-law increase of the relative formation efficiency of SiC dust with the metallicity. This result offers a solution for the long-standing problem of silicon in stardust SiC grains, confirms the necessity of coupling chemistry and dynamics in simulations of the chemical evolution of our Galaxy, and constrains the modelling of dust condensation in stellar winds as function of the metallicity.

Signature of outflows in strong Mg ii absorbers in quasar sightlines

Abstract We report a correlation between velocity offset (β = v/c) of strong Mg ii absorption systems and the bolometric luminosity (Lbol) of quasars in SDSS-DR7. We find that β shows a power-law increase with Lbol, with a slope ∼1/4. We find that such a relation of β with Lbol is expected for outflows driven by scattering of black hole radiation by dust grains, and which are launched from the innermost dust survival radius. Our results indicate that a significant fraction of the strong Mg ii absorbers, in the range of β = 0–0.4, may be associated with the quasars themselves.

The field-induced laws of thermodynamic properties in the two-dimensional spin-1 ferromagnetic Heisenberg model with the exchange and single-ion anisotropies

Green's function method is applied to investigate the two-dimensional spin-1 ferromagnetic Heisenberg model with the exchange and single-ion anisotropies. In the presence of the magnetic field, the effects of the anisotropies and field on the thermodynamic properties are obtained within the random phase approximation combining with Anderson–Callen approximation. The field-induced laws are found for the thermodynamic properties. Field dependences of heights of the susceptibility maximum and specific heat maximum fit well to power laws. The linear increase at high fields is shown for positions of the susceptibility maximum and specific heat maximum. A power law at low fields occurs for the position of the susceptibility maximum. At the positions of the maxima, the magnetization and internal energy display the power-law increase and linear decrease with the field, respectively. The exponents of the power laws are dependent of the anisotropies, as well as the slopes of the linear laws. Our results do not support the 2/3 power law which was obtained by the Landau theory.

Eruption forerunners from multiparameter monitoring and application for eruptions time predictability (Piton de la Fournaise)

Volcanic eruptions impact on societal risk, and volcanic hazard assessment is a necessary ingredient for decision‐makers. However, the prediction of volcanic eruptions remains challenging due to the complexity and the non‐linearity of volcanic processes. Identified forerunners such as increasing seismicity or deformation of the volcanic edifice prior to eruption are not deterministic. In this study, we use statistical methods to identify and discriminate precursory patterns to eruptions, on three sets of observables of Piton de la Fournaise volcano. We analyzed the short‐term (i.e. the inter‐eruptive period) time series of the seismicity rate, the deformation and the seismic velocity changes (deduced from seismic noise cross‐correlations) over the period 1999–2006, with two main goals. First, we characterize the average pre‐eruptive time patterns before 22 eruptions using superposed epoch analysis for the three observables. Using daily rate values, we resolve (1) a velocity change within 100–50 days from the eruptions onsets, then a plateau value up to eruption onset; (2) a power law increase in seismicity rate from noise level 15–10 days before eruption time; (3) an increase of displacement rate on the eruption day. These results support a three step mechanism leading to magma transfers toward the surface. Second we use pattern recognition techniques and the formalization of error diagrams to quantify the predictive power of each forerunner either as used independently or as combined to each other. We show that when seismicity rate alone performs the best prediction in the failure to predict versus alarm duration space, the combination of the displacement and seismicity data reduces the false alarm rate. We further propose a tool which explores the prediction results in order to optimize prediction strategy for decision‐makers, as a function of the risk value.

Nuclear fusion of deuterons with light nuclei driven by Coulomb explosion of nanodroplets

Theoretical-computational studies of table-top laser-driven nuclear fusion of high energy (up to 15 MeV) deuterons with 7Li, 6Li, T, and D demonstrate the attainment of high fusion yields. The reaction design constitutes a source of Coulomb exploding deuterium nanodroplets driven by an ultraintense, near-infrared, femtosecond Gaussian laser pulse (peak intensity 2 × 1018–5 × 1019 W cm−2) and a solid, hollow cylindrical target containing the second reagent. The exploding nanodroplets source is characterized by the deuteron kinetic energies, their number, and the laser energy absorbed by a nanodroplet. These were computed by scaled electron and ion dynamics simulations, which account for intra-nanodroplet laser intensity attenuation and relativistic effects. The fusion yields Y are determined by the number of the source deuterons and by the reaction probability. When laser intensity attenuation is weak within a single nanodroplet and throughout the nanodroplets assembly, Y exhibits a power law increase with increasing the nanodroplet size. Y is maximized for the nanodroplet size and laser intensity corresponding to the "transition" between the weak and the strong intensity attenuation domains. The dependence of Y on the laser pulse energy W scales as W2 for weak assembly intensity attenuation, and as W for strong assembly intensity attenuation. This reaction design attains the highest table-top fusion efficiencies (up to 4 × 109 J−1 per laser pulse) obtained up to date.

Transient slowing down relaxation dynamics of the supercooled dusty plasma liquid after quenching

The spatiotemporal evolutions of microstructure and motion in the transient relaxation toward the steady supercooled liquid state after quenching a dusty plasma Wigner liquid, formed by charged dust particles suspended in a low pressure discharge, are experimentally investigated through direct optical microscopy. It is found that the quenched liquid slowly evolves to a colder state with more heterogeneities in structure and motion. Hopping particles and defects appear in the form of clusters with multiscale cluster size distributions. Via the structure rearrangement induced by the reduced thermal agitation from the cold thermal bath after quenching, the temporarily stored strain energy can be cascaded through the network to different newly distorted regions and dissipated after transferring to nonlinearly coupled motions with different scales. It leads to the observed self-similar multiscale slowing down relaxation with power law increases of structural order and structural relaxation time, the similar power law decreases of particle motions at different time scales, and the stronger and slower fluctuations with increasing waiting time toward the new steady state.

Studying the Effects of Internet Exchange Points on Internet Topology

The recent uncovering of a high number of peering links at Internet eXchange Point (IXP) locations across the world has made these exchange switches a critical component of the Internet Autonomous System (AS) level ecosystem. Studies concentrating on the Internet topology evolution have surmised that numerous links hidden at these exchange points hold the key towards solving the missing links problem in studying the evolution of the AS-level topology of the Internet. In this work, we study the e?ect of this?set of hitherto unseen peering links on the visible Internet topology. Starting with a set of measurements determining the growth of IXPs in the inter-domain routing architecture of the Internet and continuing with a more advanced graph based metric analysis of available Internet topology data, we conclude that IXP links follow power law increase characteristics while exhibiting definitive clustering characteristics. Moreover, these additional links a?ect the joint degree distributions of nodes with higher degrees while?leaving most other types of nodes unchanged. We conclude that the currently inferred AS-level maps of the Internet demonstrate considerable variations with the incorporation of these new links and could eventually lead to a remodeling of our understanding of Internet topology evolution.

Source-based strengthening of sub-micrometer Al fibers

The origin of the improved mechanical properties of sub-micron single crystals and whiskers is still debated, but studies generally concentrate solely on size effects. In comparison, the role of the initial defect content, linked to the crystal size, has been given less consideration. We show using in situ SEM and TEM tensile testing of sub-micron Al fibers prepared using selective etching of a eutectic alloy that multiplication of dislocations through intermittent spiral sources directly causes a power-law increase of the yield stress with decreasing cross-sectional size. The size effect and resulting mechanical response are directly linked to the initial defect density and the distance between the source and the surface. In the absence of dislocations, fibers elastically reach high stresses with limited to no plasticity, reminiscent of whisker behavior.

Comprehensive analysis of earthquake source spectra and swarms in the Salton Trough, California

[1] We study earthquakes within California's Salton Trough from 1981 to 2009 from a precisely relocated catalog. We process the seismic waveforms to isolate source spectra, station spectra and travel-time dependent spectra. The results suggest an average P wave Q of 340, agreeing with previous results indicating relatively high attenuation in the Salton Trough. Stress drops estimated from the source spectra using an empirical Green's function (EGF) method reveal large scatter among individual events but a low median stress drop of 0.56 MPa for the region. The distribution of stress drop after applying a spatial-median filter indicates lower stress drops near geothermal sites. We explore the relationships between seismicity, stress drops and geothermal injection activities. Seismicity within the Salton Trough shows strong spatial clustering, with 20 distinct earthquake swarms with at least 50 events. They can be separated into early-Mmax and late-Mmax groups based on the normalized occurrence time of their largest event. These swarms generally have a low skew value of moment release history, ranging from −9 to 3.0. The major temporal difference between the two groups is the excess of seismicity and an inverse power law increase of seismicity before the largest event for the late-Mmax group. All swarms exhibit spatial migration of seismicity at a statistical significance greater than 85%. A weighted L1-norm inversion of linear migration parameters yields migration velocities from 0.008 to 0.8 km/hour. To explore the influence of fluid injection in geothermal sites, we also model the migration behavior with the diffusion equation, and obtain a hydraulic diffusion coefficient of approximately 0.25 m2/s for the Salton Sea geothermal site, which is within the range of expected values for a typical geothermal reservoir. The swarms with migration velocities over 0.1 km/hour cannot be explained by the diffusion curve, rather, their velocity is consistent with the propagation velocity of creep and slow slip events. These variations in migration behavior allow us to distinguish among different driving processes.

TURBULENT CLUSTERING OF PROTOPLANETARY DUST AND PLANETESIMAL FORMATION

We study clustering of inertial particles in turbulent flows and discuss its applications to dust particles in protoplanetary disks. Using numerical simulations, we compute the radial distribution function (RDF), which measures the probability of finding particle pairs at given distances, and the probability density function of the particle concentration. The clustering statistics depend on the Stokes number, $St$, defined as the ratio of the particle friction timescale, $\tau_{\rm p} $, to the Kolmogorov timescale in the flow. In the dissipation range, the clustering intensity strongly peaks at $St \simeq 1$, and the RDF for $St \sim 1$ shows a fast power-law increase toward small scales, suggesting that turbulent clustering may considerably enhance the particle collision rate. Clustering at inertial-range scales is of particular interest to the problem of planetesimal formation. At these scales, the strongest clustering is from particles with $\tau_{\rm p}$ in the inertial range. Clustering of these particles occurs primarily around a scale where the eddy turnover time is $\sim\tau_{\rm p}$. Particles of different sizes tend to cluster at different locations, leading to flat RDFs between different particles at small scales. In the presence of multiple particle sizes, the overall clustering strength decreases as the particle size distribution broadens. We discuss particle clustering in recent models for planetesimal formation. We point out that, in the model based on turbulent clustering of chondrule-size particles, the probability of finding strong clusters that can seed planetesimals may have been significantly overestimated. We discuss various clustering mechanisms in simulations of planetesimal formation by gravitational collapse of dense clumps of meter-size particles, in particular the contribution from turbulent clustering due to the limited numerical resolution.

Research on the Evolutionary Model of A Kind of Vertex-splitting Network

A problem is presented about the evolutionary process of the vertex splitting complex network. The rule of the evolution is: every newly-added vertex is the copy of or is split from the existing vertex. The analytic equation set of this network evolutionary model and arithmetic of iteration are put forward. A series of simulation calculation prove that the complex network is Scale Free Network and the power-law increases along with the increment of the splitting similarity degree of λ ( t ) and even approaches to +∞. When the initial degree of each new vertex is constant, the evolutionary process of the network is similar to that of the BA model.

Role of diffusion in scaling of polymer chain aggregates found in vapor deposition polymerization

Polymer chain aggregates grown by (1+1)-dimensional Monte Carlo simulations of vapor deposition polymerization (VDP) were studied. The dynamic scaling behavior of polymer chain length distribution n(s)(t) was studied as a function of chain length (s), deposition time (t), and the ratio G=D/F of deposition rate (F) and free monomer diffusion (D). The dynamic scaling approach was employed to highlight the dependence of n(s)(t) on t, s, and G. With an increase in t, we found a power law increase in n(s)(t) and total number of polymer chains N(total)(t), given by N(total)(t)~t(ω) and n(s)(t)~t(ω) with exponent ω=1.01(2) that was invariant for a range of G=10 to 10^{4}. For small s and t=10^{3}, 5×10^{3}, and 10^{4}, n_{s}(t) decreased according to n(s)(t)~s(-τ) with τ=0.58(2). As G was increased from 10 to 10(4), we observed a systematic influence of G on the rescaled n(s)(t) data that prevented the manifestation of unique scaling function for polymer chain aggregates. The dependence of scaling functions of n(s)(t) on G elucidates the sensitivity of polymer chain aggregates to G and is thought to be a characteristic of VDP.