Scaling Law

In this paper, the linear thermocapillary stability of a liquid layer coating a thick wall with finite thermal conductivity is studied under the assumption that the heat flux in the liquid obeys the Cattaneo-Christov constitutive equation. The interplay between stationary and oscillatory instability modes is examined through plots of codimension-two points. It is demonstrated that the damping of heat flux, induced by the thermal relaxation time in the Cattaneo-Christov model, plays a crucial role in destabilizing the system. Additionally, the wall's thickness, thermal conductivity, and specific heat capacity are identified as key factors influencing the system's stability in the monotonic mode. These properties also significantly affect the critical wavenumbers and frequencies associated with oscillatory convection.

We study the relaxational dynamics of flux lines in high-temperature superconductors with random pinning using Langevin dynamics. At high temperatures the dynamics is stationary and the fluctuation dissipation theorem (FDT) holds. At low temperatures the system does not equilibrate with its thermal bath: a simple multiplicative aging is found, the FDT is violated and we found that an effective temperature characterizes the slow modes of the system. The generic features of the evolution -scaling laws -are dictated by the ones of the single elastic line in a random environment.

Off-equilibrium dynamics and effective temperature of flux lines with random pinning and the vortex glass phase S. BUSTINGORRY, Centro Atomico Bariloche, Argentina, L.F. CUGLIANDOLO, LPTHE, Jussieu, France and LPT, Ecole Normale Superieure, France , D. DOMINGUEZ, Centro Atomico Bariloche, Argentina -We investigate the low-temperature off-equilibrium dynamics of elastic lines embedded in three-dimensional disordered media using Langevin dynamics. The model describes interacting vortex lines in high-temperature superconductors with random pinning. We first study the case of isolated flux lines. At high temperatures the dynamics is stationary and the fluctuation dissipation theorem (FDT) holds. At low temperatures a simple multiplicative aging is found, as recently observed numerically in the directed polymer problem in (1+1) dimensions or analytically in the 2d XY model in the spin-wave approximation. Besides, the FDT is violated and we found a well defined effective temperature characterizing the slow modes of the system. This implies the existence of a dynamic crossover between a high-temperature equilibrium dynamic phase and a low-temperature glassy dynamic phase. We then discuss how the off-equilibrium dynamics and effective temperature are affected when the flux line interactions are taken into account and its relationship with the vortex glass phase.

Simulations of agent-based models have shown that the stylized facts (unit-root, fat tails and volatility clustering) of financial markets have a possible explanation in the interactions among agents. However, the complexity, originating from the presence of non-linearity and interactions, often limits the analytical approach to the dynamics of these models. In this paper we show that even a very simple model of a financial market with heterogeneous interacting agents is capable of reproducing realistic statistical properties of returns, in close quantitative accordance with the empirical analysis. The simplicity of the system also permits some analytical insights using concepts from statistical mechanics and physics. In our model, the traders are divided into two groups: fundamentalists and chartists, and their interactions are based on a variant of the herding mechanism introduced by Kirman . The statistical analysis of our simulated data shows long-term dependence in the auto-correlations of squared and absolute returns and hyperbolic decay in the tail of the distribution of the raw returns, both with estimated decay parameters in the same range like empirical data. Theoretical analysis, however, excludes the possibility of 'true' scaling behavior because of the Markovian nature of the underlying process and the finite set of possible realized returns. The model, therefore, only mimics power law behavior. Similarly as with the phenomenological volatility models analyzed in LeBaron [25], the usual statistical tests are not able to distinguish between true or pseudo-scaling laws in the dynamics of our artificial market.

Simple models for ruptures along a heterogeneous earthquake fault zone are studied, focussing on the interplay between the roles of disorder and dynamical effects. A class of models are found to operate naturally at a critical point whose properties yield power law scaling of earthquake statistics. Various dynamical effects can change the behavior to a distribution of small events combined with characteristic system size events. The studies employ various analytic methods as well as simulations.

Simple models for ruptures along a heterogeneous earthquake fault zone are studied, focussing on the interplay between the roles of disorder and dynamical effects. A class of models are found to operate naturally at a critical point whose properties yield power law scaling of earthquake statistics. Various dynamical effects can change the behavior to a distribution of small events combined with characteristic system size events. The studies employ various analytic methods as well as simulations.

Simple models for ruptures along a heterogeneous earthquake fault zone are studied, focussing on the interplay between the roles of disorder and dynamical effects. A class of models are found to operate naturally at a critical point whose properties yield power law scaling of earthquake statistics. Various dynamical effects can change the behavior to a distribution of small events combined with characteristic system size events. The studies employ various analytic methods as well as simulations.

The effects of the carrier-envelope phase (CEP) of a few-cycle attosecond pulse on ionized electron momentum and energy spectra are analyzed, both with and without an additional few-cycle IR pulse. In the absence of an IR pulse, the CEP-induced asymmetries in the ionized electron momentum distributions are shown to vary as the 3/2 power of the attosecond pulse intensity. These asymmetries are also found to satisfy an approximate scaling law involving the frequency and intensity of the attosecond pulse. In the presence of even a very weak IR pulse (having an intensity of the order of 10 11 -10 12 W cm -2 ), the attosecond pulse CEP-induced asymmetries in the ionized electron momentum distributions are found to be significantly augmented. In addition, for higher IR laser intensities, we observe for low electron energies peaks separated by the IR photon energy in one electron momentum direction along the laser polarization axis; in the opposite direction, we find structured peaks that are spaced by twice the IR photon energy. Possible physical mechanisms for such asymmetric, low-energy structures in the ionized electron momentum distribution are proposed. Our results are based on singleactive-electron solutions of the three-dimensional, time-dependent Schrödinger equation including atomic potentials appropriate for the H and He atoms.

The American Physical Society Shear-Layer Interactions Between Surface-Mounted Obstacles at Varying Streamwise Spacings T. KIM, J.L. BEST, K.T. CHRISTENSEN, University of Illinois at Urbana-Champaign -Surface obstacles occur in a variety of flows, such as roughness elements in engineering flows and barchan dunes in natural eolian environments on both the Earth and Mars. Depending upon the arrangement and spacing between such obstacles, the flow over one obstacle can significantly alter the flow over those positioned downstream. Such flow interactions occur in fields of barchan dunes that are closely spaced and aligned in the flow direction, and where flow sheltering may play a significant role. To better understand these flow interactions, experiments were conducted for a pair of identical, upright cylinders extending into the log layer and aligned at various spacings in the streamwise direction of a turbulent channel flow at Re τ ∼ 1200. Particle-image velocimetry measurements of the flow around the cylinders reveal strong interactions between the shear layers generated downstream of the cylinders, and particularly a weakening of the downstream-most shear layer for small cylinder spacings (< 4 -6D). Modifications of the vortex-shedding processes at the downstream cylinder are under investigation, as these interactions are thought to play a critical role in the formation and evolution of surface obstacles when the surface is cohesionless and mobile.

Source scaling relations have been obtained for earthquakes in eastern North America and other co'ntinental interiors, and compared with a relation obtained for earthquakes in western North America. The scaling relation for eastern North American earthquakes was constructed from measurements of seismic moment and source duration obtained by the waveform modeling of seismic body waves. The events used include nine events of mbLg magnitude 4. 7 to 5.8 that occurred after 1960, and four earlier events with magnitudes between 5.5 and 6.6. The scaling relation for events in other continental interiors was used for comparative purposes and to provide constraints for larger magnitudes. Detailed analysis of the uncertainties in the scaling relations has allowed the resolution of two important issues concerning the source scaling of earthquakes in eastern North America. First, the source characteristics of earthquakes in eastern North America and other continental interiors are consistent with constant stress drop scaling, and are inconsistent with nonconstant scaling models such as that of Nuttli (1983). Second, the stress drops of earthquakes in eastern North America and other continental interiors are not significantly different from those of earthquakes in western North America, and have median values of approximately 100 bars. The source parameters of earthquakes in eastern North America are consistent with a single constant stress drop scaling relation, whereas the source parameters of earthquakes in western North America are much more variable and show significant departures from an average scaling relation in which stress drop decreases slightly with seismic moment.

The formation of a crater is a complex process, which can be analyzed with numerical simulations and/or observational methods. This work reports a preliminary analysis of some craters on Mercury, based on the Mariner 10 images. The physical and dynamical properties of the projectile may not derive from the knowledge of the crater alone, since the size of an impact crater depends on many parameters. We have calculated the diameter of the projectile using the scaling law of . It is performed for different projectile compositions and impact velocities, assuming an anorthositic composition of the surface. The melt volume production at the initial phases of the crater formation is also calculated by the experimental law proposed by O'Keefe and Ahrens (, 1982), giving the ratio between melt and projectile mass.

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When a long gas slug rises in a vertical tube "lled with liquid, the liquid ahead of the slug is displaced and runs down along the tube wall, thus originating a counter-current annular #ow. The present work was undertaken to experimentally demonstrate that when the density of gas slugs, rising in stagnant liquid, is raised above certain limits, the wetted-wall #ow around the slugs is subject to #ooding instability; curiously, the available correlations on #ooding would not predict this occurrence at the low gas velocities involved. In our experiments, the movement of slugs of argon rising in water, inside tubes of internal diameters 21.0 and 32.8 mm, was followed by means of fast response di!erential pressure transducers. Experiments were performed at absolute pressures of up to 6.1 MPa and from the signals of the pressure transducers it was inferred that gas slugs, with a total length of around 2 m, became unstable above 2.1 MPa, in the smaller tube, and above around 1.0 MPa in the larger one. Simple physical arguments, about the origin of #ooding instability in wetted-wall #ows, are used to derive approximate scaling laws for the phenomenon. The predictions from these scaling laws are shown to be in very good agreement with the experimental "ndings in the present work and with those of Nakazatomi et al. (1992, JSME International Journal, Series II, 35, 388}394), in their study of the rise of long slugs of nitrogen in water, at pressures of up to 20 MPa. Finally, our work suggests that in wetted-wall tubes operated with high-density gas, the velocity at which the #ooding instability sets in may be signi"cantly lower than that above which there is liquid carry over, at the top of the tube, and this calls for increased caution in the de"nition of #ooding.

The statistical properties of aftershock sequences are associated with three empirical scaling relations: (1) Gutenberg-Richter frequency-magnitude scaling, (2) Ba˚th's law for the magnitude of the largest aftershock, and (3) the modified Omori's law for the temporal decay of aftershocks. In this paper these three laws are combined to give a relation for the aftershock decay rate that depends on only a few parameters. This result is used to study the temporal properties of aftershock sequences of several large California earthquakes. A review of different mechanisms and models of aftershocks are also given. The scale invariance of the process of stress transfer caused by a main shock and the heterogeneous medium in which aftershocks occur are responsible for the occurrence of scaling laws. We suggest that the observed partitioning of energy could play a crucial role in explaining the physical origin of Ba˚th's law. We also study the stress relaxation process in a simple model of damage mechanics and find that the rate of energy release in this model is identical to the rate of aftershock occurrence described by the modified Omori's law.

We analyze the avalanche size distribution of the Abelian Manna model on two different fractal lattices with the same dimension dg = ln 3/ ln 2, with the aim to probe for scaling behavior and to study the systematic dependence of the critical exponents on the dimension and structure of the lattices. We show that the scaling law D(2 -τ ) = dw generalizes the corresponding scaling law on regular lattices, in particular hypercubes, where dw = 2. Furthermore, we observe that the lattice dimension dg, the fractal dimension of the random walk on the lattice dw, and the critical exponent D, form a plane in 3D parameter space, i.e. they obey the linear relationship D = 0.632(3)dg + 0.98(1)dw -0.49(3).

The combination of detailed topographic leveling on the southwest segment of the El Asnam thrust fault with existing seismic and geologic data implies that the geometry of this fault involves shallow dipping flats and steep ramps. The fault appears to be growing along strike toward the southwest end, where the main shock initiated in 1980. From a depth of about 10 km, the main thrust appears to ramp to the basement-Cenozoic cover interface on a plane soiking N40°E and dipping 50°-550 to the nonhwest. Along the southwest segment where folding has not yet developed, the thrust continues steeply through the Cenozoic cover to the near surface where it flattens, causing normal faulting. Along the central and nonheast segments, which display a more evolved fold structure, the deep thrust probably flattens at a depth of 5-6 km, into a decollement along the Cenozoic-Jurassic interface before ramping to the surface. The Sara El Marouf and Kef El Mes anticlines have thus formed as fault propagation folds. Normal faults at Beni Rached probably branch with the thrust to maintain kinematic compatibility between the deep ramp and decollement The greater separation ( -1 km) between the normal faults at Beni Rached and the thrust where it crosses Oued Cheliff than along the southwest segment (-1 km) reflects the greater depth of the ramp to flat bend. We infer that the September 9, 1954, eanhquake activated only the central deep segment of the main thrust together with the Beni Rached normal faults, while that of October 10, 1980, activated the whole system of flat decollements, ramp thrusts and compatibility normal faults. Further complexities of the faulting in map view are related to changes of strike of the thrust (in particular nonh of Oued Cheliff). The most active tectonic deformation in Nonh Africa occurs in a roughly E-W trending thrust belt that has formed as a result of crustal shortening induced by the convergence between the African and European plates [e.g., McKenzie, 1972; Tapponnier, 1977]. The El Asnam fault zone belongs to that belt and has been the site of two large, recent eanhquakes

High-accuracy three-dimensional numerical simulations of miscible displacements with gravity override in homogeneous porous media are carried out for the quarter five-spot configuration. Special emphasis is placed on describing the influence of viscous and gravitational effects on the overall displacement dynamics in terms of the vorticity variable. Even for neutrally buoyant displacements, three-dimensional effects are seen to change the character of the flow significantly, in contrast to earlier findings for rectilinear displacements. At least in part this can be attributed to the time dependence of the most dangerous vertical instability mode. Density differences influence the flow primarily by establishing a narrow gravity layer, in which the effective Péclet number is enhanced owing to the higher flow rate. However, buoyancy forces of a certain magnitude can lead to a pinch-off of the gravity layer, thereby slowing it down. Overall, an increase of the gravitational parameter is found to enhance mostly the vertical perturbations, while larger Pe values act towards amplifying horizontal disturbances. The asymptotic rate of growth of the mixing length varies only with Péclet number. For large Péclet numbers, an asymptotic value of 0.7 is observed. A scaling law for the thickness of the gravity layer is obtained as well. In contrast to immiscible flow displacements, it is found to increase with the gravity parameter.

Studies on active and capable faults produce data that presently have a key role in the broad field of earthquake geology, as well as in planning engineering works and land use. In regions with high deformation rates, the approach through paleoseismology could be sufficient to collect data necessary to depict active faults behavior. By contrast, a similar approach may be inappropriate in tectonic domains which are characterized by slower deformation rates, like Italy. In such areas, Neotectonics as expressed by Carlo Bosi in 1992 -"integrated set of researches with the aim to define the Plio-Quaternary tectonic evolution defined through a temporal scan of hundreds of thousands of years" -provides valuable insights into studying active tectonics and related faulting. Indeed, through the evolutionary perspective, which goes far beyond a "static" multidisciplinary approach, Neotectonics appears as a necessary procedure to define the active faulting setting of a region, representing the effect of the current tectonic regime. Hence, the structural settings produced by Neotectonics represent the basis for seismotectonic settings, as they incorporate those faults that are active seismogenic, which can be capable or not. Overall, this has effects in terms of definition: a fault can be considered active if it exhibits evidence of movements within a time frame consistent with the ongoing tectonic regime of the region, unless it is sealed by deposits and/or landforms not younger than a time span (from the present) whose duration encompasses a significant number of seismic cycles on the respective fault. Neotectonics, defined as a procedure, permits to connect active faults to their "engine", that is tectonics. This sets the basis for its methodological predictive effectiveness in seismotectonic studies.

Studies on active and capable faults produce data that presently have a key role in the broad field of earthquake geology, as well as in planning engineering works and land use. In regions with high deformation rates, the approach through paleoseismology could be sufficient to collect data necessary to depict active faults behavior. By contrast, a similar approach may be inappropriate in tectonic domains which are characterized by slower deformation rates, like Italy. In such areas, Neotectonics as expressed by Carlo Bosi in 1992-"integrated set of researches with the aim to define the Plio-Quaternary tectonic evolution defined through a temporal scan of hundreds of thousands of years"-provides valuable insights into studying active tectonics and related faulting. Indeed, through the evolutionary perspective, which goes far beyond a "static" multidisciplinary approach, Neotectonics appears as a necessary procedure to define the active faulting setting of a region, representing the effect of the current tectonic regime. Hence, the structural settings produced by Neotectonics represent the basis for seismotectonic settings, as they incorporate those faults that are active seismogenic, which can be capable or not. Overall, this has effects in terms of definition: a fault can be considered active if it exhibits evidence of movements within a time frame consistent with the ongoing tectonic regime of the region, unless it is sealed by deposits and/or landforms not younger than a time span (from the present) whose duration encompasses a significant number of seismic cycles on the respective fault. Neotectonics, defined as a procedure, permits to connect active faults to their "engine", that is tectonics. This sets the basis for its methodological predictive effectiveness in seismotectonic studies.

Collisional heat transport in a stochastic magnetic field configuration is investigated. Well above stochastic threshold, a numerical solution of a Chirikov-Taylor model shows a short-time nonlocal regime, but at large time the Rechester-Rosenbluth effective diffusion is confirmed. Near stochastic threshold, subdiffusive behavior is observed for short mean free paths. The nature of this subdiffusive behavior is understood in terms of the spectrum of islands in the stochastic sea.

We study time-varying realized volatility and related correlation measures as proxies for the true volatility and correlation. We investigate measures of Two-Scale realized Absolute Volatility (TSAV) and correlation (TSACORxy) which are helpful to cope effectively with the ...

for an Invited Paper for the MAR15 Meeting of the American Physical Society Mechanical properties of 3D ceramic nanolattices LUCAS MEZA, California Institute of Technology Developments in advanced nanoscale fabrication techniques have allowed for the creation of 3-dimensional hierarchical structural meta-materials that can be designed with arbitrary geometry. These structures can be made on length scales spanning multiple orders of magnitude, from tens of nanometers to hundreds of microns. The smallest features are controllable on length scales where materials have been shown to exhibit size effects in their mechanical properties. Combining novel nanoscale mechanical properties with a 3-dimensional architecture enables the creation of new classes of materials with tunable and unprecedented mechanical properties. We present the fabrication and mechanical deformation of hollow tube alumina nanolattices that were fabricated using two-photon lithography direct laser writing (DLW), atomic layer deposition (ALD), and oxygen plasma etching. Nanolattices were designed in a number of different geometries including octet-truss, octahedron, and 3D Kagome. Additionally, a number of structural parameters were varied including tube wall thickness (t), tube major axis (a), and unit cell size (L). The resulting nanolattices had a range of densities from ρ = 4 to 250 mg/cm 3 . Uniaxial compression and cyclic loading tests were performed on the nanolattices to obtain the yield strength and modulus. In these tests, a marked change in the deformation response was observed when the wall thickness was reduced below 20nm; thick-walled nanolattices (t>20nm) underwent catastrophic, brittle failure, which transitioned to a gradual, ductilelike deformation as wall thickness was reduced. Thick-walled nanolattices also exhibited no recovery after compression, while thin-walled structures demonstrated notable recovery, with some recovering by 98% after compression to 50% strain and by 80% when compressed to 90% strain. Across all geometries, unit cell sizes, and wall thicknesses, we found a consistent power law relation between strength and modulus with relative density of E ∝ ρ 1.6 and σ y ∝ ρ 1.75 . This scaling marks an improvement over other lightweight and ultralight materials, which normally scale as E ∝ ρ 2 or E ∝ ρ 3 , but does not meet the analytic upper bound of a linear scaling with relative density that is predicted for stretching dominated geometries like the octet-truss.

State Univ -Columbus -Laser driven target normal sheath acceleration (TNSA) of ions has been widely studied due to its fundamental importance, use as a probe, and for possible applications such as cancer therapy and neutron generation. Much of this work has been conducted on thin foils with peak ion energy and yield optimized using laser parameters such as energy and spot size. Micro-structured targets, however, have demonstrated increased peak ion energy and yield by controlling and enhancing mechanisms preferential to TNSA. Novel micro-structured targets were developed using optical lithography techniques on thin substrates at the OSU NanoSystem Laboratory. Variable structure height (0.5-2 micron) and transverse patterning (up to 1 micron resolution) permit the survey of a range of structured target variables in the study of ion acceleration. We describe the development of these targets and an experiment investigating the enhancement of TNSA ions from lithography produced micro-structured targets conducted at the Scarlet Laser Facility. Experimental results show increased proton and Carbon yield >2 MeV and higher peak Carbon energy from structured targets.

We report direct domain observations of Barkhausen avalanches at criticality in Co and MnAs thin films investigated by means of a magneto-optical microscope magnetometer, capable of time-resolved domain observation in real time. Through a statistical analysis of the fluctuating size of Barkhausen jump from numerous repetitive experiments for each sample, the distribution of Barkhausen jump size is found to exhibit a power-law scaling behavior with the critical exponent of $1.33 in both systems. This value is consistent with the twodimensional prediction of a theoretical model proposed by Cizeau et al. [Phys. Rev. Lett. 79 (1997) 4669].

DNA ligases specifically recognize and seal double stranded nicked DNA by catalyzing the formation of a phospho-diester bond between the 3 0 OH and 5 0 phosphate termini. In physiological conditions these ubiquitous enzymes are essential for DNA replication, repair and recombination, while in tumor cells they can play a critical role in apoptosis resistance. Chlorella virus ligase is a pluripotent ATP-dependent ligase composed by two domains, a N-terminal nucleotidyltransferase domain, hosting the catalytic site, and a C-terminal OB-domain, both of which participate to DNA binding. A number of crystallographic studies have elucidated important structural details of the nick-sealing process. DNA binding, in particular, appears to require a large reorientation of the two domains, as well as relevant structural rearrangements localized mainly in the N-terminal region (1). Indeed this protein appears to be a highly dynamic system whose internal motions are closely linked to both the DNA recognition and to the catalytic process. So far, however, the actual nature of these motions is still largely unknown, not only for Chlorella virus ligase, but also for the entire protein family. We therefore tried to close this gap by undertaking the analysis of the dynamic properties of Chlorella virus liagase by solution NMR spectroscopy.

We measure interaction forces between pairs of charged PMMA colloidal particles suspended in a relatively low-polar medium (5 ε 8) directly from the deviations of particle positions inside two time-shared optical traps. The particles are confined to optical point traps; one is held in a stationary trap and the other particle is brought closer in small steps while tracking the particle positions using confocal microscopy. From the observed particle positions inside the traps we calculate the interparticle forces using an ensemble-averaged particle displacement-force relationship. The force measurements are confirmed by independent measurements of the different parameters using electrophoresis and a scaling law for the liquid-solid phase transition. When increasing the salt concentration by exposing the sample to UV light, the force measurements agree well with the classical DLVO theory assuming a constant surface potential. On the other hand, when adding tetrabutylammonium chloride (TBAC) to vary the salt concentration, surface charge regulation seems to play an important role.

Based on kinetic Monte Carlo simulations, we show that modulated wires and island gratings can be formed at vicinal surfaces. The modulation (grating) wavelength along the steps can be tailored by external conditions (coverage and temperature) and intrinsic surface properties (diffusion, terrace width) via a scaling law. Above 220 K a thermodynamic saturation value for the wavelength occurs, which depends only on the terrace width. This morphological behavior can be understood in terms of nucleation arguments applied to heteroepitaxial growth of Ag on stepped Pt(1 1 1) surfaces.

We derive analytic expressions, and approximate them in closed form, for the effective detection aperture for Cerenkov radio emission from ultra-high-energy neutrinos striking the Moon. The resulting apertures are in good agreement with recent Monte Carlo simulations and support the conclusion of James & Protheroe ( ) that neutrino flux upper limits derived from the GLUE search were too low by an order of magnitude. We also use our analytic expressions to derive scaling laws for the aperture as a function of observational and lunar parameters. We find that at low frequencies downward-directed neutrinos always dominate, but at higher frequencies, the contribution from upward-directed neutrinos becomes increasingly important, especially at lower neutrino energies. Detecting neutrinos from Earth near the GZK regime will likely require radio telescope arrays with extremely large collecting area (A e ∼ 10 6 m 2 ) and hundreds of hours exposure time. Higher energy neutrinos are most easily detected using lower frequencies. Lunar surface roughness is a decisive factor for obtaining detections at higher frequencies (ν ∼ > 300 MHz) and higher energies (E ∼ > 10 21 eV).

Identifying the sources of the highest energy cosmic rays is a fundamental unsolved problem in both high-energy physics and astrophysics. Ultra-high energy (UHE) neutrinos provide a key probe to the nature and location of cosmic ray engines since they travel essentially ...

Recent progress in the numerical calculation of memory functions from molecular dynamics simulations allowed gaining a deeper insight into the relaxation dynamics of liquids and proteins. The concept of memory functions goes back to the work of R. Zwanzig on the generalized Langevin equation, and it was the basis for the development of various dynamical models for liquids. We present brie y a method for the numerical calculation of memory functions, which is then applied to study their scaling behavior in normal and fractional Brownian dynamics. It has been shown recently that the model of fractional Brownian dynamics constitutes effectively a link between protein dynamics on the nanosecond time scale, which is accessible to molecular dynamics simulations and thermal neutron scattering, and the much longer time scale of functional protein dynamics, which can be studied by uorescence correlation spectroscopy. ¥¤ ¢´μ ¡Ò²μ ¶μ± § ´μ, ÎÉμ ³μ¤¥²Ó Ë• ±Í¨μ´´μ°¡•μÊ´μ¢¸±μ°¤¨´ ³¨±¨Ê¸É ´ ¢²¨¢ ¥É ÔË-Ë¥±É¨¢´ÊÕ ¸¢Ö §Ó ³¥¦¤Ê ¤¨´ ³¨±μ°¡¥²±μ¢ ´ ´ ´μ¸¥±Ê´¤´μ³ ¢•¥³¥´´μ³ ³ ¸ÏÉ ¡¥, ¤μ¸ÉÊ ¶´μ°¤ ²Ö ³μ¤¥²¨•μ¢ ´¨Ö ¢ ³μ²¥±Ê²Ö•´μ°¤¨´ ³¨±¥ ¨ ¶•¨É¥ ¶²μ¢μ³ • ¸¸¥Ö´¨¨´¥°É•μ´μ¢, ¨¤¨´ ³¨±μ°Ë Ê´±Í¨μ´ ²Ó´ÒÌ ¡¥²±μ¢ ´ ¡μ²ÓÏ¨Ì ¢•¥³¥´´ÒÌ ³ ¸ÏÉ ¡ Ì, ±μÉμ•ÊÕ ³μ¦´μ ¨¸¸²¥¤μ¢ ÉÓ Ë²Êμ•¥¸-Í¥´É´μ°±μ••¥²ÖÍ¨μ´´μ°¸ ¶¥±É•μ¸±μ ¶¨¥°.

Surfactants non-monotonically modify the onset of Faraday waves 1 STEPHEN STRICKLAND, Dickinson College, MICHAEL SHEARER, KAREN DANIELS, North Carolina State University -When a water-filled container is vertically vibrated, subharmonic Faraday waves emerge once the driving from the vibrations exceeds viscous dissipation. In the presence of an insoluble surfactant, a viscous boundary layer forms at the contaminated surface to balance the Marangoni and Boussinesq stresses. For linear gravity-capillary waves in an undriven fluid, the surfactant-induced boundary layer increases the amount of viscous dissipation. In our analysis and experiments, we consider whether similar effects occur for nonlinear Faraday (gravity-capillary) waves. Assuming a finite-depth, infinite-breadth, low-viscosity fluid, we derive an analytic expression for the onset acceleration up to second order in ϵ = √

This paper discusses the scaling laws of the flow structures around geometrically similar fire whirls, an insight that will be necessary when applying laboratory-scale data to real-scale fire whirls in urban or wildland fires. A fixed-frame-type fire-whirl generator is used to form geometrically similar fire whirls of three different scales. A particle image velocimetry (PIV) technique is used to measure the tangential (rotational) and the radial velocity components around the fire whirls. Scaling analysis is then conducted to derive two pi numbers, namely, the Reynolds number and the Froude number. Measured tangential velocity distributions are nearly uniform in the vertical direction when the height from the floor is greater than ~1 cm, where the velocity profiles are found to be well correlated using the Froude number, suggesting that viscosity plays only a minor role. Near the floor, on the other hand, the magnitude of tangential velocity is reduced, leading to an enhanced radial inflow toward the flame, a phenomenon similar to the Ekman layer. This inflow layer pushes the flame toward the fuel surface, increasing the heat input from the flame to the fuel and hence the burning rate. It is found that the Froude number can also correlate the radial velocity distributions near the floor.

This short communication proposes a new scaling law, on the basis of which scale-model experiments on a large-scale wind-aided fire phenomenon can be designed. The proposed scaling law takes into account the Froude number, which is defined using the flame height. The results of two different scale-model experiments on the fire whirls observed after the Great Kanto Earthquake are reported. The wind velocities in the scale-model experiments are determined using the proposed scaling law. The scale-model experiments successfully reproduce fire whirls similar to those observed after the Earthquake, thus validating the proposed scaling law.

Elements of the analytic structure of anomalous scaling and intermittency in fully developed hydrodynamic turbulence are described. We focus here on the structure functions of velocity differences that satisfy inertial range scaling laws Sn(R) ∼ R ζn , and the correlation of energy dissipation Kǫǫ(R) ∼ R -µ . The goal is to understand the exponents ζn and µ from first principles. In paper II of this series it was shown that the existence of an ultraviolet scale (the dissipation scale η) is associated with a spectrum of anomalous exponents that characterize the ultraviolet divergences of correlations of gradient fields. The leading scaling exponent in this family was denoted ∆. The exact resummation of ladder diagrams resulted in the calculation of ∆ which satisfies the scaling relation ∆ = 2 -ζ2. In this paper we continue our analysis and show that nonperturbative effects may introduce multiscaling (i.e. ζn not linear in n) with the renormalization scale being the infrared outer scale of turbulence L. It is shown that deviations from K41 scaling of Sn(R) (ζn = n/3) must appear if the correlation of dissipation is mixing (i.e. µ > 0). We derive an exact scaling relation µ = 2ζ2 -ζ4. We present analytic expressions for ζn for all n and discuss their relation to experimental data. One surprising prediction is that the time decay constant τn(R) ∝ R zn of Sn(R) scales independently of n: the dynamic scaling exponent zn is the same for all n-order quantities, zn = ζ2.

In this Letter we suggest a simple and physically transparent analytical model of pressure driven turbulent wall-bounded flows at high but finite Reynolds numbers Re. The model provides an accurate quantitative description of the profiles of the mean-velocity and Reynolds-stresses (second order correlations of velocity fluctuations) throughout the entire channel or pipe, for a wide range of Re, using only three Re-independent parameters. The model sheds light on the long-standing controversy between supporters of the century-old log-law theory of von-Kàrmàn and Prandtl and proposers of a newer theory promoting power laws to describe the intermediate region of the mean velocity profile.

. Convective plume generated by a local heat source, located on the top of the small rubber cylinder, which is located in the center of the bottom of the rectangular cell. To simulate the hot-spot green laser has been used. Roll-type large-scale convective flow was generated by heating of the one vertical sides of cavity. Influence of power of hot point on the shape of plume has been investigated. It is shown that the presence of cellular convective motion may lead to the formation of a strange spiral convective plume. This plume looks like Archimedes spiral replaced on vertical plane. Physical mechanism of the formation of strange spiral plume and application of obtained results for mantle convection problems are discussed.

The space--time structure of rainfall is one of most complex problem to be solve in geophysics and atmosphere sciences. Rainfall has been studied in similar fashion as turbulence phenomena, therefore, many mathematical tools applied to the study of turbulence have also been used for the description of rainfall. The tools to be shown in this chapter were born in the fractal theory for explaining complexity and non-linear processes; they are related to the analysis of multi-scaling dynamics and the emergence of complex patterns. The Fractal-Multifractal approach and Multiplicative Random Cascade models will be discussed in the chapter, furthermore, some applications of these techniques for the analysis of rainfall will also be exhibited.

Different cortical regions vary systematically in their morphology. Here we investigate if the scaling law of cortical morphology, which was previously demonstrated across both human subjects and mammalian species, still holds within a single cortex across different brain regions. By topologically correcting for regional curvature, we could analyse how different morphological parameters co-vary within single cortices. We show in over 1500 healthy individuals that, despite their morphological diversity, regions of the same cortex obey the same universal scaling law, and age morphologically at similar rates. In Alzheimer's disease, we observe a premature ageing in the morphological parameters that was nevertheless consistent with the scaling law. The premature ageing effect was most dramatic in the temporal lobe. Thus, while morphology can vary substantially across cortical regions, subjects, and species, it always does so in accordance with a common scaling law, suggesting that the underlying processes driving cortical gyrification are universal.

In order to model volatility, the daily adjusted close prices are used to get the daily log returns. What we hope to see are clusters of high volatility periods and clusters of low volatility periods. The log returns of each stock are plotted below.

In the last 20 yr, over 600 impact flashes have been documented on the lunar surface. This wealth of data presents a unique opportunity to study the meteoroid flux of the Earth–Moon environment, and in recent years the physical properties of the impactors. However, other than through serendipitous events, there has not been yet a systematic search and discovery of the craters associated to these events. Such a meteoroid-crater link would allow us to get insight into the crater formation via these live observations of collisions. Here, we present the pynaple (python NAC Automated Pair Lunar Evaluator) software pipeline for locating newly formed craters using the location and epoch of an observed impact flash. We present the first results from pynaple, having been implemented on the 2017-09-27 impact flash. A rudimentary analysis on the impact flash and linked impact crater is also performed, finding that the crater’s ejecta pattern indicates an impact angle between 10–30°, and althou...

The performance of multi-channel multi-hop ad hoc network is evaluated in the paper. The performances of multi-hop ad hoc network with single channel IEEE 802.11 MAC for different topologies are given. The scaling laws of throughputs for large scale of ad hoc networks are presented. The theoretical guaranteed throughput bound for multi-channel systems for grid topology are proposed. The results will help to choose the proper parameters for multi-hop ad hoc network evaluations. Mobile Ad Hoc Networks (MANETs) are an emerging technology that allows establishing an instant communication network for civilian and military applications, without relying on pre-existing fixed network infrastructure [1], [2]. The nodes in a MANET can dynamically join and leave the network, frequently, often without warning, and possibly without disruption to other nodes' communication. The nodes in the network can be highly mobile, thus the network topology is rapidly changing. The main difference between the ad hoc networking technology and the cellular technology lies in the fact that nodes in an ad hoc network posses traffic routing and relaying ability. Target applications of mobile ad hoc network range from collaborative, distributed mobile computing (sensors, conferences, conventions) to disaster recovery (such as fire, flood, earthquake), law enforcement (crowd control, search and rescue) and tactical communications (digital battlefields) [1], [2]. An ad hoc network is self-organizing and communications takes place mostly through multi-hop routing. Mobility of the network nodes, limited resource (e.g., bandwidth and energy supply) and potentially large number of mobile nodes make the routing and management of ad hoc networks extremely challenging. Many papers (e.g., [3]) have investigated the performance of routing protocols based on the 2Mbps IEEE 802.11 WLAN protocols. In such studies, the number of nodes in the network usually ranges from 20 to 100 and the traffic generation per active node ranges from 2 to 4 packets per second. From these studies, one can observe that the throughput of an ad hoc network with large number nodes is relatively low. Furthermore, many papers (e.g., [4]) have also investigated the TCP performance over mobile ad hoc networks. Such works have shown that the TCP throughput is likewise quite low and TCP

The performance of multi-channel multi-hop ad hoc network is evaluated in the paper. The performances of multi-hop ad hoc network with single channel IEEE 802.11 MAC for different topologies are given. The scaling laws of throughputs for large scale of ad hoc networks are presented. The theoretical guaranteed throughput bound for multi-channel systems for grid topology are proposed. The results will help to choose the proper parameters for multi-hop ad hoc network evaluations. Mobile Ad Hoc Networks (MANETs) are an emerging technology that allows establishing an instant communication network for civilian and military applications, without relying on pre-existing fixed network infrastructure [1], [2]. The nodes in a MANET can dynamically join and leave the network, frequently, often without warning, and possibly without disruption to other nodes' communication. The nodes in the network can be highly mobile, thus the network topology is rapidly changing. The main difference between the ad hoc networking technology and the cellular technology lies in the fact that nodes in an ad hoc network posses traffic routing and relaying ability. Target applications of mobile ad hoc network range from collaborative, distributed mobile computing (sensors, conferences, conventions) to disaster recovery (such as fire, flood, earthquake), law enforcement (crowd control, search and rescue) and tactical communications (digital battlefields) [1], [2]. An ad hoc network is self-organizing and communications takes place mostly through multi-hop routing. Mobility of the network nodes, limited resource (e.g., bandwidth and energy supply) and potentially large number of mobile nodes make the routing and management of ad hoc networks extremely challenging. Many papers (e.g., [3]) have investigated the performance of routing protocols based on the 2Mbps IEEE 802.11 WLAN protocols. In such studies, the number of nodes in the network usually ranges from 20 to 100 and the traffic generation per active node ranges from 2 to 4 packets per second. From these studies, one can observe that the throughput of an ad hoc network with large number nodes is relatively low. Furthermore, many papers (e.g., [4]) have also investigated the TCP performance over mobile ad hoc networks. Such works have shown that the TCP throughput is likewise quite low and TCP

We propose a procedure for analyzing and characterizing complex networks. We apply this to the social network as constructed from email communications within a medium sized university with about 1700 employees. Email networks provide an accurate and nonintrusive description of the flow of information within human organizations. Our results reveal the self-organization of the network into a state where the distribution of community sizes is self-similar. This suggests that a universal mechanism, responsible for emergence of scaling in other self-organized complex systems, as, for instance, river networks, could also be the underlying driving force in the formation and evolution of social networks.

A three dimensional thermal analysis of a Lorentz force accelerator featuring an open heat pipe as a propellant feeding system is made in order to correct heat transfer problems that became apparent during attempts to operate the device. Specifically, the tem-perature profile along the multi-channel cathode of the thruster, which is also the open end of the heat pipe, was such that the cathode tip stayed at a tem-perature well below the vapor point of lithium thus causing lithium vapor to condense in the cathode. An empirically inspired solution was first implemented and consisted in outfitting the cathode assembly with a series of closed heat pipes that are heated form out-side the truster. However, the heat pipes failed to operate properly due to nearby thermal sinks that caused them to choke. The numerical thermal model showed what these sinks are and was instrumental in the implementation of a scheme that resulted in the successful operation of the thruster.