Self-similar Method Research Articles

Intermittency of quantum turbulence with superfluid fractions from 0% to 96%

The intermittency of turbulent superfluid helium is explored systematically in a steady wake flow from 1.28 K up to T>2.18K using a local anemometer. This temperature range spans relative densities of superfluids from 96% down to 0%, allowing us to test numerical predictions of enhancement or depletion of intermittency at intermediate superfluid fractions. Using the so-called extended self-similarity method, scaling exponents of structure functions have been calculated. No evidence of temperature dependence is found on these scaling exponents in the upper part of the inertial cascade, where turbulence is well developed and fully resolved by the probe. This result supports the picture of a profound analogy between classical and quantum turbulence in their inertial range, including the violation of self-similarities associated with inertial-range intermittency.

A novel Self-Similar Traffic Prediction Method Based onWavelet Transform for Satellite Internet

With service types and requirements of broadband satellite internet continuously increasing, improving QoS (Quality of Service) of satellite internet has attracted extensive attention. To reduce the impact of self-similarity caused by various of service traffic sources converging on satellite communic

Anchoring Polar Magnetic Field in a Stationary Thick Accretion Disk

Abstract We investigate the properties of a hot accretion flow bathed in a poloidal magnetic field. We consider an axisymmetric viscous-resistive flow in the steady-state configuration. We assume that the dominant mechanism of energy dissipation is due to turbulence viscosity and magnetic diffusivity. A certain fraction of that energy can be advected toward the central compact object. We employ the self-similar method in the radial direction to find a system of ODEs with just one varible, θ in the spherical coordinates. For the existence and maintenance of a purely poloidal magnetic field in a rotating thick disk, we find that the necessary condition is a constant value of angular velocity along a magnetic field line. We obtain an analytical solution for the poloidal magnetic flux. We explore possible changes in the vertical structure of the disk under the influences of symmetric and asymmetric magnetic fields. Our results reveal that a polar magnetic field with even symmetry about the equatorial plane makes the disk vertically thin. Moreover, the accretion rate decreases when we consider a strong magnetic field. Finally, we notice that hot magnetized accretion flows can be fully advected even in a slim shape.

Light bullets in coupled nonlinear Schrödinger equations with variable coefficients and a trapping potential.

We analyze three-dimensional (3D) vector solitary waves in a system of coupled nonlinear Schrödinger equations with spatially modulated diffraction and nonlinearity, under action of a composite self-consistent trapping potential. Exact vector solitary waves, or light bullets (LBs), are found using the self-similarity method. The stability of vortex 3D LB pairs is examined by direct numerical simulations; the results show that only low-order vortex soliton pairs with the mode parameter values n ≤ 1, l ≤ 1 and m = 0 can be supported by the spatially modulated interaction in the composite trap. Higher-order LBs are found unstable over prolonged distances.

Combining edge difference with nonlocal self-similarity constraints for single image super-resolution

Sparse representation based nonlocal self-similarity methods have been proved to be effective for single image super-resolution. However, as the noise level increases, these methods always lead to the aggravated blurring of image small scale structures, which means the failure to preserve the edge structures. In this paper, we propose a new single image super-resolution method by combining edge difference with nonlocal self-similarity constraints. In the proposed method, firstly, we extract the image texture feature in the main direction for dictionary learning with Principal Components Analysis (PCA) to ensure the learned subdictionaries contain the image texture structures. Then, we explore the one dimensional edge difference between LR image and degraded version (e.g., blurred, noisy, and down-sampled) of the image reconstructed by the sparse representation based nonlocal self-similarity method with the leaned PCA subdictionaries and utilize it as the edge difference constraint. Thirdly, we incorporate the edge difference constraint into the sparse representation model based nonlocal self-similarity to preserve the edge structures and nonlocal self-similarity structures simultaneously. Moreover, we propose a nonlocal structure tensor optimization model to further improve image quality, which can effectively mitigate the loss of image high-frequency texture and edge information. Experiments on natural images validate that our method outperforms other state-of-the-art methods, especially for the noise image.

Explicitly self-similar solutions for the Euler/Navier–Stokes–Korteweg equations in RN

Abstract In this paper, we present a unified formulae for explicit self-similar solutions of the Euler/Navier–Stokes–Korteweg equations arising in the modeling of capillary fluids. The technique used here is to reduce Euler/Navier–Stokes–Korteweg equations into a series of solvable ordinary differential equations by making use of multi-dimensional self-similar ansatz and variable separation method.

Heat transfer in the cylindrical rarefied Couette flow

The efficiency of the self-similar interpolation method is demonstrated with reference to the solution of the problem of heat transfer in a rarefied gas between two coaxial cylinders rotating relative one another. The analytical solution of the problem is compared with the results obtained by direct statistical simulation. The most interesting result is the energy flux nonmonotonicity and the reversal of its sign with variation in the Knudsen number.

Statistically advanced, self-similar, radial probability density functions of atmospheric and under-expanded hydrogen jets

This paper presents improved statistical insight regarding the self-similar scalar mixing process of atmospheric hydrogen jets and the downstream region of under-expanded hydrogen jets. Quantitative planar laser Rayleigh scattering imaging is used to probe both jets. The self-similarity of statistical moments up to the sixth order (beyond the literature established second order) is documented in both cases. This is achieved using a novel self-similar normalization method that facilitated a degree of statistical convergence that is typically limited to continuous, point-based measurements. This demonstrates that image-based measurements of a limited number of samples can be used for self-similar scalar mixing studies. Both jets exhibit the same radial trends of these moments demonstrating that advanced atmospheric self-similarity can be applied in the analysis of under-expanded jets. Self-similar histograms away from the centerline are shown to be the combination of two distributions. The first is attributed to turbulent mixing. The second, a symmetric Poisson-type distribution centered on zero mass fraction, progressively becomes the dominant and eventually sole distribution at the edge of the jet. This distribution is attributed to shot noise-affected pure air measurements, rather than a diffusive superlayer at the jet boundary. This conclusion is reached after a rigorous measurement uncertainty analysis and inspection of pure air data collected with each hydrogen data set. A threshold based upon the measurement noise analysis is used to separate the turbulent and pure air data, and thusly estimate intermittency. Beta-distributions (four parameters) are used to accurately represent the turbulent distribution moments. This combination of measured intermittency and four-parameter beta-distributions constitutes a new, simple approach to model scalar mixing. Comparisons between global moments from the data and moments calculated using the proposed model show excellent agreement. This was attributed to the high quality of the measurements which reduced the width of the correctly identified, noise-affected pure air distribution, with respect to the turbulent mixing distribution. The ignitability of the atmospheric jet is determined using the flammability factor calculated from both kernel density estimated (KDE) PDFs and PDFs generated using the newly proposed model. Agreement between contours from both approaches is excellent. Ignitability of the under-expanded jet is also calculated using KDE PDFs. Contours are compared with those calculated by applying the atmospheric model to the under-expanded jet. Once again, agreement is excellent. This work demonstrates that self-similar scalar mixing statistics and ignitability of atmospheric jets can be accurately described by the proposed model. This description can be applied with confidence to under-expanded jets, which are more realistic of leak and fuel injection scenarios.

Controlled generation of nonlinear resonances through sinusoidal lattice modes in Bose–Einstein condensate

We study Bose–Einstein condensate in the combined presence of time modulated optical lattice and harmonic trap in the mean-field approach. Through the self-similar method, we show the existence of sinusoidal lattice modes in this inhomogeneous system, commensurate with the lattice potential. A significant advantage of this system is wide tunability of the parameters through chirp management. The combined effect of the interaction, harmonic trap and lattice potential leads to the generation of nonlinear resonances, exactly where the matter wave changes its direction. When the harmonic trap is switched off, the BEC undergoes a nonlinear compression for the static optical lattice potential. For better understanding of chirp management and the nature of the sinusoidal excitation, we investigate the energy spectrum of the condensate, which clearly reveals the generation of nonlinear resonances in the appropriate regime. We have also identified a classical dynamical phase transition occurring in the system, where loss of superfluidity takes the superfluid phase to an insulating state.

Self similar solution of superradiant amplification of ultrashort laser pulses in plasma

Based on the self-similar method, superradiant amplification of ultrashort laser pulses by the counterpropagating pump in a plasma is investigated. Here, we present a governing system of partial differential equations for the signal pulse and the motion of the electrons. These equations are transformed to ordinary differential equations by the self-similar method and numerically solved. It is found that the increase of the signal intensity is proportional to the square of the propagation distance and the signal frequency has a red shift. Also, depending on the pulse width, the signal breaks up into a train of short pulses or its duration decreases with the inverse square root of the distance. Moreover, we identified two distinct categories of the electrons by the phase space analysis. In the beginning, one of them is trapped in the ponderomotive potential well and oscillates while the other is untrapped. Over time, electrons of the second kind also join to the trapped electrons. In the potential well, the electrons are bunched to form an electron density grating which reflects the pump pulse into the signal pulse. It is shown that the backscattered intensity is enhanced with the increase of the electron bunching parameter which leads to the enhanced efficiency of superradiant amplification.

Couette flow and heat transfer between parallel plates in a rarefied gas

The effectiveness of the self-similar interpolation method in its simplest form is demonstrated by solving the problem of a planar Couette flow in a rarefied gas between plates with different temperatures. An analytic representation of the solution is compared with the results obtained by the DSMC method. The most interesting result is the nonmonotonicity of the heat flow and the change in its sign accompanying the modification in the gas rarefaction, i.e., in the Knudsen number Kn.

Spectral analysis of structure functions and their scaling exponents in forced isotropic turbulence.

The pseudospectral method, in conjunction with a technique for obtaining scaling exponents ζ_{n} from the structure functions S_{n}(r), is presented as an alternative to the extended self-similarity (ESS) method and the use of generalized structure functions. We propose plotting the ratio |S_{n}(r)/S_{3}(r)| against the separation r in accordance with a standard technique for analyzing experimental data. This method differs from the ESS technique, which plots S_{n}(r) against S_{3}(r), with the assumption S_{3}(r)∼r. Using our method for the particular case of S_{2}(r) we obtain the result that the exponent ζ_{2} decreases as the Taylor-Reynolds number increases, with ζ_{2}→0.679±0.013 as R_{λ}→∞. This supports the idea of finite-viscosity corrections to the K41 prediction for S_{2}, and is the opposite of the result obtained by ESS. The pseudospectral method also permits the forcing to be taken into account exactly through the calculation of the energy input in real space from the work spectrum of the stirring forces.

Opposite polarity dusty plasma expansion in Earth’s mesosphere

The self-similar expansion method is applied on the fluid system of equations which describes a plasma system consisting of opposite polarity dust grains, positive ions and electrons. The resultant system of equations is solved numerically to study the properties of the plasma expansion of this system. It is found that the presence of the second species of the dust has a great effect on the properties of the expansion of the other species.

A two-dimensional study for cooling and self-gravitating accretion discs

The importance of cooling for the structure and evolution of self-gravitating accretion discs has been confirmed through the use of direct numerical simulations. In this paper, we present a two-dimensional study for self-gravitating accretion discs, to investigate the influence of the cooling rate on the latitudinal structure of such accretion discs. The disc is cooled using a simple parametrization for the cooling function, (de/dt)cool=−e/tcool with e as the internal energy and tcool as the cooling timescale. The cooling timescale is in units of the dynamical timescale, tdyn[=Ω−1], is Ωtcool=β, where β is a free parameter. The mechanism of energy dissipation is assumed to be turbulent viscosity in the disc and an α-prescription is applied for the kinematic coefficient of viscosity. To study the gravitational stability of the self-gravitating disc, we use the Toomre parameter. We obtain the radial dependence of the physical variables through the use of a self-similar method and we numerically solve the equations to obtain the latitudinal dependence of the physical variables. The solutions show that the radial velocity is smaller than the Keplerian rotational velocity; however, the disc, dependent on the values of parameters α and β and only near the zone close to the equatorial plane, can rotate in a super-Keplerian manner. With the magnitude of both parameters α and β, the disc thickness increases due to the increase of the vertical pressure gradient. The dependence of the gas density on the parameters α and β indicates two zones in the accretion disc. In the first zone near the equatorial plane, the mass density decreases by increasing these parameters. However, in the second zone, the regions with higher latitude, the mass density increases with the magnitude of parameters α and β.

Aperiodic 3D tiling by self-similar substitution method using solid unit

"There are two important aperiodic tiling methods. One is a projection method and the other is self-similar substitution method. Author applied projection and substitution method to several quasi-periodic tiling [1a] [1b] [1c] [2a] [2b] [2c]. Quantity of the information for research of aperiodic tiling except quasi-periodic tiling is not so large as that of quasi-periodic tiling. Author shows one of the substitution example. that is a ""pentomino tile"" which is made of five unit squares. First generation of a ""pentomino tile"" is composed of two original pentominos and chiral two original pentominos [3]. Author considered 3D solid body unit similar to exterior view of car-body as shown in figure, then succeeded in first generation tile using the body unit. In this study, author consider a relation between substitution and crystallographic rotation matrix and translation matrix and discuss general formulation of self-similar substitution. Caption of Figure: (left-hand) original generation, (center) First generation, (right-hand) Second generation"

Special two-soliton solution of the generalized Sine–Gordon equation with a variable coefficient

A new special two-soliton solution to the generalized Sine–Gordon equation with a variable coefficient is constructed analytically, by using the self-similar method and Hirota bilinear method. To construct this special solution, we do not utilize the pairs of one-soliton solutions, as is customarily done when solving the Sine–Gordon equation, but introduce two auxiliary self-similar variables in Hirota’s procedure. We also study features of this solution by choosing different self-similar variables. The results obtained confirm that the behavior of such Sine–Gordon solitons can be easily controlled by the selection of the self-similar variables.

COMBINED MULTIPOINT REMOTE AND IN SITU OBSERVATIONS OF THE ASYMMETRIC EVOLUTION OF A FAST SOLAR CORONAL MASS EJECTION

We present an analysis of the fast coronal mass ejection (CME) of 2012 March 7, which was imaged by both STEREO spacecraft and observed in situ by MESSENGER, Venus Express, Wind and Mars Express. Based on detected arrivals at four different positions in interplanetary space, it was possible to strongly constrain the kinematics and the shape of the ejection. Using the white-light heliospheric imagery from STEREO-A and B, we derived two different kinematical profiles for the CME by applying the novel constrained self-similar expansion method. In addition, we used a drag-based model to investigate the influence of the ambient solar wind on the CME's propagation. We found that two preceding CMEs heading in different directions disturbed the overall shape of the CME and influenced its propagation behavior. While the Venus-directed segment underwent a gradual deceleration (from ~2700 km/s at 15 R_sun to ~1500 km/s at 154 R_sun), the Earth-directed part showed an abrupt retardation below 35 R_sun (from ~1700 to ~900 km/s). After that, it was propagating with a quasi-constant speed in the wake of a preceding event. Our results highlight the importance of studies concerning the unequal evolution of CMEs. Forecasting can only be improved if conditions in the solar wind are properly taken into account and if attention is also paid to large events preceding the one being studied.

Rarefaction wave in relativistic steady magnetohydrodynamic flows

We construct and analyze a model of the relativistic steady-state magnetohydrodynamic rarefaction that is induced when a planar symmetric flow (with one ignorable Cartesian coordinate) propagates under a steep drop of the external pressure profile. Using the method of self-similarity, we derive a system of ordinary differential equations that describe the flow dynamics. In the specific limit of an initially homogeneous flow, we also provide analytical results and accurate scaling laws. We consider that limit as a generalization of the previous Newtonian and hydrodynamic solutions already present in the literature. The model includes magnetic field and bulk flow speed having all components, whose role is explored with a parametric study.

Dynamic Gesture Recognition using a Model-based Temporal Self-similarity and its Application to Taebo Gesture Recognition

There has been a lot of attention paid recently to analyze dynamic human gestures that vary over time. Most attention to dynamic gestures concerns with spatio-temporal features, as compared to analyzing each frame of gestures separately. For accurate dynamic gesture recognition, motion feature extraction algorithms need to find representative features that uniquely identify time-varying gestures. This paper proposes a new feature-extraction algorithm using temporal self-similarity based on a hierarchical human model. Because a conventional temporal self-similarity method computes a whole movement among the continuous frames, the conventional temporal self-similarity method cannot recognize different gestures with the same amount of movement. The proposed model-based temporal self-similarity method groups body parts of a hierarchical model into several sets and calculates movements for each set. While recognition results can depend on how the sets are made, the best way to find optimal sets is to separate frequently used body parts from less-used body parts. Then, we apply a multiclass support vector machine whose optimization algorithm is based on structural support vector machines. In this paper, the effectiveness of the proposed feature extraction algorithm is demonstrated in an application for taebo gesture recognition. We show that the model-based temporal self-similarity method can overcome the shortcomings of the conventional temporal self-similarity method and the recognition results of the model-based method are superior to that of the conventional method.

Longitudinal and transverse structure functions in decaying nearly homogeneous and isotropic turbulence

Streamwise evolution of longitudinal and transverse velocity structure functions in a decaying homogeneous and nearly isotropic turbulence is reported for Reynolds numbers Reλ up to 720. First, two theoretical relations between longitudinal and transverse structure functions are examined in the light of recently derived relations and the results show that the low-order transverse structure functions can be well approximated by longitudinal ones within the sub-inertial range. Reconstruction of fourth-order transverse structure functions with a recently proposed relation by Grauer et al. is comparatively less valid than the relation already proposed by Antonia et al. Secondly, extended self-similarity methods are used to measure the scaling exponents up to order eight and the streamwise evolution of scaling exponents is explored. The scaling exponents of longitudinal structure functions are, at first location, close to Zybin's model, and at the fourth location, close to She—Leveque model. No obvious trend is found for the streamwise evolution of longitudinal scaling exponents, whereas, on the contrary, transverse scaling exponents become slightly smaller with the development of a steamwise direction. Finally, the stremwise variation of the order-dependent isotropy ratio indicates the turbulence at the last location is closer to isotropic than the other three locations.