ON THE STRING EQUATION AND THE WHITHAM METHOD

1993 ◽  
Vol 08 (19) ◽  
pp. 3321-3338 ◽  
Author(s):  
F. FUCITO ◽  
A. GAMBA ◽  
M. MARTELLINI
Keyword(s):  
Numerical Simulations ◽  
Excellent Agreement ◽  
String Equation ◽  
Detailed Report ◽  
Whitham Method

We present a detailed report of the application of the Whitham method to the study of the string equation. Even though the solutions obtained with this method are not exact they are in excellent agreement with the true solutions, as we explicitly show using numerical simulations.

scholarly journals NON-LINEAR WKB ANALYSIS OF THE STRING EQUATION

1992 ◽  
Vol 06 (11n12) ◽  
pp. 2123-2147 ◽  
Author(s):  
F. FUCITO ◽  
A. GAMBA ◽  
M. MARTELLINI ◽  
O. RAGNISCO
Keyword(s):  
Numerical Simulations ◽  
Numerical Solution ◽  
Excellent Agreement ◽  
Riemann Surfaces ◽  
Analytic Approximation ◽  
String Equation ◽  
Non Linear

We apply non-linear WKB analysis to the study of the string equation. Even though the solutions obtained with this method are not exact, they approximate extremely well the true solutions, as we explicitly show using numerical simulations. “Physical” solutions are seen to be separatrices corresponding to degenerate Riemann surfaces. We obtain an analytic approximation in excellent agreement with the numerical solution found by Parisi et al. for the k=3 case.

scholarly journals Precession-driven flows in non-axisymmetric ellipsoids

2013 ◽  
Vol 737 ◽  
pp. 412-439 ◽  
Author(s):  
J. Noir ◽  
D. Cébron
Keyword(s):  
Theoretical Model ◽  
Numerical Simulations ◽  
Celestial Body ◽  
Excellent Agreement ◽  
Analytical Models ◽  
Forced Flow ◽  
Spheroidal Geometry ◽  
Strong Contrast ◽  
Do So

AbstractWe study the flow forced by precession in rigid non-axisymmetric ellipsoidal containers. To do so, we revisit the inviscid and viscous analytical models that have been previously developed for the spheroidal geometry by, respectively, Poincaré (Bull. Astronomique, vol. XXVIII, 1910, pp. 1–36) and Busse (J. Fluid Mech., vol. 33, 1968, pp. 739–751), and we report the first numerical simulations of flows in such a geometry. In strong contrast with axisymmetric spheroids, where the forced flow is systematically stationary in the precessing frame, we show that the forced flow is unsteady and periodic. Comparisons of the numerical simulations with the proposed theoretical model show excellent agreement for both axisymmetric and non-axisymmetric containers. Finally, since the studied configuration corresponds to a tidally locked celestial body such as the Earth’s Moon, we use our model to investigate the challenging but planetary-relevant limit of very small Ekman numbers and the particular case of our Moon.

scholarly journals Asteroid Families

1994 ◽  
Vol 160 ◽  
pp. 395-414 ◽  
Author(s):  
Vincenzo Zappalà ◽  
Alberto Cellino
Keyword(s):  
Numerical Simulations ◽  
Excellent Agreement ◽  
Present Review ◽  
The Family ◽  
Suitable Technique ◽  
Asteroid Families ◽  
Collisional Evolution

In spite of their widely recognized importance in the framework of the modern understanding of the asteroidal population and its collisional evolution, asteroid dynamical families have long been a puzzling subject of research, due to the disagreement among the family lists published by different authors. In the present review, the definition and meaning of asteroid families are critically discussed, as well as the various problems which have to be faced by any suitable technique of family identification. In this respect, major improvements have been achieved during the last few years. The most recent family searches show an excellent agreement both in the number of reliably identified families, and in their members. Moreover, the overall performances of the most recent techniques of family identification have been tested by means of numerical simulations, with encouraging results. For these reasons, we believe that we are presently at the beginning of an era in which detailed physical studies of families can be attempted, and observational campaigns can be planned on the basis of solid evidence, like in the case of the recent spectacular results obtained for the family associated to the large asteroid 4 Vesta.

Shock dispersal of dilute particle clouds

2018 ◽  
Vol 841 ◽  
pp. 732-745 ◽  
Author(s):  
Theo G. Theofanous ◽  
Vladimir Mitkin ◽  
Chih-Hao Chang
Keyword(s):  
Numerical Simulations ◽  
Excellent Agreement ◽  
Volume Fraction ◽  
Essential Feature ◽  
Particle Volume Fraction ◽  
Effective Field ◽  
Blast Waves ◽  
Particle Volume ◽  
Report Data ◽  
The Mathematical Model

We present experiments and numerical simulations for an elementary paradigm of disperse multiphase flow: highly dilute, homogeneous, finite-dimension clouds of particles (curtains) hit by shock/blast waves in one dimension. In the experiments (particle volume fraction ${<}1\,\%$) the blasts that follow the shocks vary from low subsonic to supersonic, and we report data on curtain expansions and volume fraction distributions. The particle-resolving numerical simulations, run for the supersonic case, yield excellent agreement with all of these experimental data. We find that the essential feature for these good predictions is a flow choking phenomenon that entails a (particle) dispersive character of the flow down a volume fraction gradient (as at the downstream portions of the curtain). A most basic effective-field model is made to capture this gas dynamics by emulating the wake behind each particle, as seen in the particle-resolving direct Euler simulation (DES). On this basis, standard drag laws yield excellent agreement with the dispersive behaviour found in the experiment/DES, thus revealing a physics-based path to eventual well posedness of the mathematical model.

Influence of Inlet Boundary Conditions on Simulations of an Asymmetric Diffuser With the V2F Turbulence Model

2015 ◽  
Author(s):  
James Crawford ◽  
A. M. Birk
Keyword(s):  
Experimental Data ◽  
Boundary Conditions ◽  
Numerical Simulations ◽  
Excellent Agreement ◽  
Turbulence Model ◽  
Two Dimensional ◽  
Ansys Fluent ◽  
Inlet Velocity

A set of numerical simulations were performed on an asymmetric, two dimensional diffuser using ANSYS Fluent 14.0, a commercially available RANS based CFD code. The ν′2¯-f turbulence model, which has previously been shown to be a good model for this geometry, was implemented through a user defined function, and the influence of inlet boundary conditions was evaluated. It was shown that the inlet velocity and turbulence profiles had a significant effect on the calculated performance of the diffuser, especially in terms of the onset of diffuser stall. It was shown that when the boundary conditions were set appropriately, excellent agreement with LES and experimental data was obtained.

scholarly journals Photonic generation of picosecond pulse doublets from the nonlinear splitting of super-Gaussian pulses

2020 ◽  
Vol 238 ◽  
pp. 11012
Author(s):  
Christophe Finot
Keyword(s):  
Fourier Transform ◽  
Optical Fiber ◽  
Numerical Simulations ◽  
Excellent Agreement ◽  
Energy Efficient ◽  
Picosecond Pulse ◽  
Photonic Generation ◽  
Temporal Compression ◽  
Nonlinear Focusing ◽  
Temporal Pulse

We experimentally demonstrate the generation of temporal pulse doublets from the propagation of initial super-Gaussian waveforms in an optical fiber with anomalous dispersion. The nonlinear focusing dynamics leads to picosecond structures that are characterized both in amplitude and phase. Their close-to-Gaussian Fourier-transform limited shape is found in excellent agreement with numerical simulations. This single-stage reshaping scheme is energy efficient, can sustain GHz repetition rates and temporal compression factors around 10 are demonstrated.

scholarly journals Starved Lubrication of Elliptical EHD Contacts

2004 ◽  
Vol 126 (1) ◽  
pp. 105-111 ◽  
Author(s):  
B. Damiens ◽  
C. H. Venner ◽  
P. M. E. Cann ◽  
A. A. Lubrecht
Keyword(s):  
Numerical Model ◽  
Film Thickness ◽  
Numerical Simulations ◽  
Excellent Agreement ◽  
Experimental Approach ◽  
Operating Conditions ◽  
Inlet Region ◽  
Inlet Length ◽  
Thickness Measurements ◽  
Circular Contact

This paper focuses on the lubrication behavior of starved elliptical Elasto-HydroDynamic (EHD) contacts. Starvation is governed by the amount of lubricant available in the inlet region and can result in much thinner films than occurring under fully flooded conditions. Therefore, it would be desirable to be able to predict the onset and severity of starvation and to be able to relate film reduction directly to the operating conditions and lubricant properties. The aim of this work is to explore the influence of these parameters on starvation. A combined modeling and experimental approach has been employed. The numerical model has been developed from an earlier circular contact study [1]. In this model, the amount and distribution of the lubricant in the inlet region determines the onset of starvation and predicts the film decay in the contact. Numerical simulations for a uniform layer on the surface show that a single parameter, characteristic of the inlet length of the contact in the fully flooded regime, determines the starved behavior. Film thickness measurements under starved conditions were performed to validate this theory. For a circular contact excellent agreement was found. In theory the same mechanism applies to elliptic contacts, however, the behavior is more complicated.

scholarly journals Properties of galaxy dark matter halos from weak lensing

2004 ◽  
Vol 220 ◽  
pp. 439-445 ◽  
Author(s):  
Henk Hoekstra ◽  
Howard K.C. Yee ◽  
Michael D. Gladders
Keyword(s):  
Dark Matter ◽  
Numerical Simulations ◽  
Excellent Agreement ◽  
Gravitational Lensing ◽  
Strong Support ◽  
Alternative Theories Of Gravity ◽  
Dark Matter Halos ◽  
Imaging Data ◽  
Average Mass ◽  
Theories Of Gravity

We present the results of a study of the average mass profile around galaxies using weak gravitational lensing. We use 45.5 deg2 of RC band imaging data from the Red-Sequence Cluster Survey (RCS) and define a sample of ~ 1.2 × 105 lenses with 19.5 < RC < 21, and a sample of ~ 1.5 × 106 background galaxies with 21.5 < R < 24.We constrain the power law scaling relations between the B-band luminosity and the mass and size of the halo, and find that the results are in excellent agreement with observed luminosity–line-width relations. Under the assumption that the luminosity does not evolve with redshift, the best fit NFW model yields a mass M200 = (8.8±0.7) × 1011h–1M⊙ and a scale radius rs = I6.7+3.7–3.0h–1 kpc for a galaxy with a fiducial luminosity of Lb = 1010h–2LB⊙. the latter result is in excellent agreement with predictions from numerical simulations for a halo of this mass. We also observe a signficant anisotropy of the lensing signal around the lenses, implying that the halos are flattened and aligned with the light distribution. We find an average (projected) halo ellipticity of 〈ehalo〉 = 0.20+0.04–0.05, in fair agreement with results from numerical simulations of CDM. Alternative theories of gravity (without dark matter) predict an isotropic lensing signal, which is excluded with 99.5% confidence. Hence, our results provide strong support for the existence of dark matter.

scholarly journals Analytical Models for Distribution of the Envelope and Phase of Linearly Modulated Signals in AWGN Channel

2014 ◽  
Vol 60 (1) ◽  
pp. 70-73 ◽  
Author(s):  
Taleb Moazzeni ◽  
Yingtao Jiang ◽  
Henry Selvaraj ◽  
Tianding Chen
Keyword(s):  
Numerical Simulations ◽  
Excellent Agreement ◽  
Numerical Experiments ◽  
Theoretical Models ◽  
Analytical Models ◽  
Awgn Channel ◽  
Signal Constellations ◽  
Modulated Signals ◽  
Analytical Expressions

Abstract In this paper, analytical expressions for the distribution of the envelope and phase of linearly modulated signals such as BPSK,M-PSK, andM-QAM in AWGN are presented.We perform numerical simulations for different orders of signal constellations. The results show that the proposed theoretical models are in excellent agreement with the estimated distributions from various numerical experiments.

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