Assumption Of Self-similarity Research Articles

Archipelago strait exchange processes—an overview

Archipelagos consist of a set of islands forming a collection of basins interconnected by straits, and are typically characterized by widely varying spatial and temporal scales regarding geometry and forcing conditions. Focusing on the strait exchange parameterization, we describe an archipelago water exchange model in which the archipelago is subdivided into a network of discrete basins and interconnecting straits and where the time integration assumes a series of quasi-steady states. We propose an algorithm that should be sufficiently flexible to provide reasonable strait exchange estimates under the variety of forcing conditions encountered in the Stockholm archipelago. We start from the functional formulation of two-layer hydraulic theory, which allows numerical schemes to be designed that, given the forcing conditions at the ends of a given strait, distinguish between maximal and sub-maximal flow cases and solve the flow accordingly. We relax the assumption of two homogeneous layers when necessary, using an approximate method based on a self-similarity assumption and with the sea-level difference over the strait as an explicit part of the problem. This method allows exchange flows with two groups of layers to be solved for the same set of geometries that the pure two-layer theory can handle, including sill-contraction combinations and non-rectangular cross-sections. We further show how aspiration of dense water from below the sill crest can be quantified with hydraulic theory, and be included in the method for stratified strait exchange. Rotational control in wide straits and in parallel straits connecting the same two basins is treated with a simple but robust scheme. We evaluate the calculations with data from the Oxdjupet strait in the Stockholm archipelago. Simulations with a three-dimensional, non-hydrostatic numerical model are performed to compensate for sparsity in data.

Continuously stratified exchange flow through a contraction in a channel

Existing solutions for exchange flow through straits rely upon the decomposition of the flow into a finite number of layers which have constant density. In this paper we provide a solution to inviscid steady exchange flow between continuously stratified reservoirs, where it is assumed that the flow in each direction is independently self-similar. The solution requires knowledge only of the two reservoir stratifications and an imposed net barotropic throughflow. The solution includes regions of stagnant fluid which separate two counter-flowing, stably stratified layers, with the provision that the two active layers may touch at no more than one point. Comparison of the theoretical solution with numerical simulations indicates that the assumption of self-similarity is reasonable, and that the disparity between the theoretical and simulated flows can be attributed to the inclusion of diffusion and viscosity in the numerical model.

Kinematics of discretely self-similar spherically symmetric spacetimes

We summarize the consequences of the twin assumptions of (discrete) self-similarity and spherical symmetry for the global structure of a spacetime. All such spacetimes can be constructed from two building blocks, the "fan" and "splash". Each building block contains one radial null geodesic that is invariant under the self-similarity (self-similarity horizon).

The reflection-antisymmetric counterpart of the Kármán–Howarth dynamical equation

We study the isotropic, helical component in homogeneous turbulence using statistical objects which have the correct symmetry and parity properties. Using these objects we derive an analogue of the Kármán–Howarth equation, that arises due to lack of mirror-reflection-symmetry in isotropic flows. The main equation we obtain is consistent with the results of Chkhetiani [JETP 63 (1996) 768] and L’vov et al. [Exact result for the 3rd order correlations of velocity in turbulence with helicity, 1997. http://xxx.lanl.gov/abs/chao-dyn/9705016] but is derived using only velocity correlations, with no direct consideration of the vorticity or helicity. This alternative formulation offers an advantage to both experimental and numerical measurements. We also postulate, under the assumption of self-similarity, the existence of a hierarchy of scaling exponents for helical velocity correlation functions of arbitrary order, analogous to the Kolmogorov prediction for the scaling exponents of velocity structure function.

Scaling Relation to Understand Non-Detection of Cold Gas at the Cluster Center

Recent XMM-Newton observations of clusters of galaxies have indicated the soft X-ray spectra to be inconsistent with the simple isobaric cooling flow model. There is almost no feature of the cold gas expected from the model. This shows that we have not yet understood the physics of the hot gas in clusters of galaxies well. A quantitative evaluation of the behavior of gas cooling is important not only for understanding the clusters, themselves, but also for studying cosmology and galaxy formation. To clarify the problem of this reported discrepancy, we have studied scaling relations for clusters of galaxies based on the self-similarity assumption. We also propose an observational strategy to solve this problem.

On the theory of grain growth in systems with anisotropic boundary mobility

We analyze grain growth kinetics in systems with anisotropic grain boundary mobility. In contrast to most previous studies of grain growth dynamics, we relax self-similarity assumptions that strongly constrain the dynamics and statistics during microstructural evolution in polycrystalline materials. We derive analytical expressions for the average growth rate within each topological class of n-sided grains as well as for the growth rate of the average grain area; we explain the results using underlying symmetries. Although anisotropic grain growth may in general be non-linear in time, we show, even in the absence of the self-similarity constraint, that the evolution kinetics obeys the von Neumann–Mullins relationship in the two limiting cases of textured and fully random microstructure with a time dependence solely determined by changes in the misorientation distribution. Our analytical results agree well with recent computer simulations using a generalized phase field approach.

Seismic expression and kinematics of a fault-related fold termination: Rosario structure, Maracaibo Basin, Venezuela

Fold terminations are primary features of deformed belts and are critical elements in understanding the 3-D kinematics of fault-related folds. Typically, such terminations form due to loss of displacement on the genetically-related thrust fault and/or to along-strike change in fault attitude, forming a lateral or oblique ramp. To unambiguously determine the mechanism responsible for a given fault-related fold termination, footwall cutoffs and along-strike displacement variation must be constrained. Reflection seismic data can provide the detail necessary to uniquely describe these features. The Rosario structure in the Maracaibo Basin, Venezuela is an example of a natural fault-related fold that possesses a southern termination whose fold/fault geometry and along-strike displacement variation are constrained by industry reflection seismic and well data. We interpret that the fold plunge near the southern termination is due to an along-strike decrease in displacement. The fault geometry associated with the southern termination changes from a flat–ramp–flat at the crest of the structure where displacement is greatest to simply a ramp near the lateral fault tip, without forming a lateral or oblique ramp. We combine these observations regarding displacement and fault geometry with the assumption that along-strike spatial variations reflect temporal variations during development of a fault-related fold to propose a kinematic model for the Rosario structure. Specifically, we suggest that the structure first initiated as an isolated fault ramp within the ‘stiff’ carbonate and clastic units. With increased shortening, the fault grew to link with upper and lower detachments in the weaker shale units to create a hybridized fault-bend fold. Our model suggests a possible explanation for the evolution of the Rosario structure, and also provides an alternative to existing pseudo-three-dimensional models for fault-related fold growth that relaxes the rigidity in the assumption of along-strike self-similarity.

Coarse-graining and self-similarity of price fluctuations

We propose a new approach for analyzing price fluctuations in their strongly correlated regime ranging from minutes to months. This is done by employing a self-similarity assumption for the magnitude of coarse-grained price fluctuation or volatility. The existence of a Cramér function, the characteristic function for self-similarity, is confirmed by analyzing real price data from a stock market. We also discuss the close interrelation among our approach, the scaling-of-moments method and the multifractal approach for price fluctuations.

Self-similar BEC dynamics: accuracy and applications

We discuss a simplified description of the dynamics ofinhomogeneous dilute Bose-Einstein condensates (BECs), based on theassumption that the time-evolving BEC preserves its shape (i.e. thedensity profile remains similar to the initial profile). While thevalidity of the self-similarity assumption is not a priori obvious,weshow that this description becomes exact in the opposite limitsof large and small condensates contained by time-dependent sphericallysymmetric harmonic oscillator trap potentials. We discussapplications of this simple description and we show how the insightsderived from it suggest that phase-coherent BECs expanding fromoptical lattice sites can be used for the purpose of imaging.

Testing for the Presence of Self‐Similarity of Gaussian Time Series Having Stationary Increments

A method for testing for the presence of self‐similarity of a Gaussian time series with stationary increments is presented. The test is based on estimation of the distance between the time series and a set of time series containing all the fractional Brownian motions. This distance is constructed from two estimations of multiscale generalized quadratic variations expectations. The second one requires regression estimates of the self‐similarity index H. Two estimations of H are then introduced. They present good robustness and computing time properties compared with the Whittle approach, with nearly similar convergence rate. The test is applied on simulated and real data. The self‐similarity assumption is notably accepted for the famous Nile River data.

Multiradii modeling of counterflow spray diffusion flames

A multiradii spray flame model is derived in a kinetic framework in which the droplets' distribution function is taken as a sum of delta products. The droplet class equations are obtained by taking moments of the Boltzmann-type spray equation. The gas-phase equations are coupled to the droplets equations through various integral sources terms. In the counterflow geometry, using a self-similar assumption, multiradii counterflow spray flame models are then obtained as exact solutions of multidimensional small Mach number governing equations. The structure of multiradii counterflow spray flames is investigated numerically. To solve the discretized system of equation, a fully coupled adaptive computation was conducted between the gas and liquid phase. The equations are discretized by using a finite difference, and highly optimized libraries were used in order to evaluate thermochemistry and transport properties. We first investigate an n -heptane counterflow monodisperse spray flame studied experimentally by Chen and Gomez. We then investigate a multiradii methanol spray flame studied experimentally by Gomez and coworkers. The multiradii approach is used in order to describe accurately the multiple size behavior, which is found to be strongly radius-dependent. Good agreement is found in both cases up to experimental uncertainties in the measured injection velocities and class number densities.

Scaling down: On the Challenge of Estimating Abundance from Occurrence Patterns

Scaling down: On the Challenge of Estimating Abundance from Occurrence Patterns

Final fate of the spherically symmetric collapse of a perfect fluid

The final fate of the spherically symmetric collapse of a perfect fluid which follows the $\gamma$-law equation of state and adiabatic condition is investigated. Full general relativistic hydrodynamics is solved numerically using a retarded time coordinate, the so-called observer time coordinate. Thanks to this coordinate, the causal structure of the resultant space-time is automatically constructed. Then, it is found that a globally naked, shell-focusing singularity can occur at the center from relativistically high-density, isentropic and time symmetric initial data if $\gamma \alt 1.01$ within the numerical accuracy. The result is free from the assumption of self-similarity. The upper limit of $\gamma$ with which a naked singularity can occur from generic initial data is consistent with the result of Ori and Piran based on the assumption of self-similarity.

The spill plume in smoke control design

Abstract Using recent data, obtained by Morgan, Poreh and colleagues, we produce correlations for the mass flow of a two-dimensional plume emerging normal to the straight edge of a flat horizontal surface—the balcony—and rising up into a uniform atmosphere (the spill plume). A comparison is made with an earlier correlation of the same data by Poreh et al . which required values of the layer depth, D B , in addition to those of the layer flow per unit length of line plume, M ′ B . The treatment of Poreh et al . followed others assuming the linear relationship typical of far-field line plumes between the mass flow M ′ and the height z with a correction Δ—the virtual source. This linearity is a theoretical consequence of self-similarity (and a constant entrainment coefficient) in the velocity and temperature profiles across the plume, but recent, as yet unpublished, studies including some by computational fluid dynamics (CFD) cast doubt on the existence of self-similarity for these plumes at the low heights relevant in practice. However, a dimensional analysis of the flow does not require the assumption of self-similarity and we have demonstrated the linearity as a conclusion and not an assumption. The effective entrainment coefficient is, as found by Poreh et al ., less than the value 0·16 found by Lee and Emmons and used in early work by Morgan and Marshall. The lower figure of 0·11 is consistent with other recent work on line plumes. The experimental values of D B , the layer depth reported by Poreh et al ., are in reasonable agreement with theoretical values for small increases in temperatures only. Experiments in model atria by Hansell, Morgan and Marshall which are not fully two-dimensional are discussed. Our correlation of them can be reconciled with that obtained by Law and subsequently used by the Chartered Institution of Building Service Engineers (CIBSE).

Self-similarity and scaling relations for microearthquakes at Mt. Etna volcano (Italy)

In this study, forty-eight Etnean microearthquakes, recorded with a local network of three seismic digital stations, have been analysed in order to infer source properties and scaling relations. Seismic moments, fault radii, stress drops and seismic energies have been determined from the SH displacement spectra using the source model of Brune (1970, 1971). The Equivalent Wood-Anderson magnitude (MWAeq) has been estimated for the whole data set. The relationship between log-stress drop and log-moment is linear up to a moment of 10 12 N m, whereas for higher moments the slope of the regression-straight line is not significantly different from zero. For moments less than 10 12 N m, there is no significant trend in the log-moment as a function of source radius, whereas for higher moments the log-moment increases with radius. The main conclusion is that the stress drop is the dominant scaling factor for moments less than 10 12 N m, against the self-similarity assumption (Aki, 1967): we hypothesize that such a deviation from self-similarity is related to a heterogeneous medium with barriers on the fault. On the contrary, for higher moments, the source dimension becomes the controlling factor and self-similarity holds. The relationships between log-energy and log-moment, MWAeq and log-moment, MWAeq and log-energy show a high degree of linear correlation. Finally, the whole data set is consistent with the Gutenberg-Richter magnitude-energy relation.

On the self-similarity assumption in dynamic models for large eddy simulations

The consistency between dynamic models for large eddy simulations and their underlying self-similarity assumption is discussed. The interpretation of the resolved field is shown to be fully determined by the choice of the test-filter. Consequences for comparison to direct numerical simulations and experimental results are presented.

Relaxation phenomena in disordered systems

In this article we discuss how the assumptions of self-similarity imposed on the distribution of independently relaxing modes, as well as on their amplitude and characteristic times, manifest in the global relaxation phenomena. We also review recent applications of such approach to the description of relaxation phenomena in microemulsions and molecular glasses.

Naked singularities in a self-similar Tolman-Bondi spacetime

Following Lake and Zannias we show that naked strong curvature singularities develop in Tolman-Bondi inhomogeneous spherically symmetric spacetimes for all the three cases of a bound, unbound and marginally bound gravitational collapse. It is observed that the assumption of self-similarity rather than the spherical symmetry is crucial in determining the nature of the singularity in any gravitationally collapsing configuration.

Self-similar solutions of laser produced blast waves

The aerodynamics of the blast wave produced by laser ablation is studied using the piston analogy. The unsteady one-dimensional gasdynamic equations governing the flow are solved under assumption of self-similarity. The solutions are utilized to obtain analytical expressions for the velocity, density, pressure and temperature distributions. The results predict all the experimentally observed features of the laser produced blast waves.

Study of the thermocapillary layer preceding slow, steadily spreading flames over liquid fuels

Flames spreading slowly over liquid fuels are preceded by a region of preheated liquid set in motion by thermocapillary effect. A steady spreading may be achieved when the structure of this region moves as a whole and in solidarity with the flame. A theoretical analysis shows that this advancing thermocapillary region may have a self-similar structure in the form of a boundary layer attached to the liquid surface. Furthermore, a series of experiments on flame spreading over pure aliphatic alcohols has been performed to study this thermocapillary region and to compare the experimental findings with the theoretical predictions. Surface temperatures ahead of the flame were obtained from image processing of infrared video records of the liquid surface and by a series of thermocouples located on the fuel surface. These surface-temperature profiles are shown to be quite well correlated by a square root fit as predicted by the boundary-layer theory, in such a way that the temperature increases as the square root of the distance to the leading edge of the thermocapillary layer. The self-similarity assumption is not valid near the flame because of strong surface currents responsible for the boundary-layer detachment. Some discrepancies between theory and experiments can be explained in terms of heat and momentum losses induced by the channel walls.