The correspondence principle postulated for the description of hydrodynamic turbulence [Phys. Rev. Lett. 57, 1722 (1986)] combined with the theory of thermal boundary layer [B. Castaing et al. (private communication)]...
The correspondence principle postulated for the description of hydrodynamic turbulence [Phys. Rev. Lett. 57, 1722 (1986)] combined with the theory of thermal boundary layer [B. Castaing et al. (private communication)] is applied to high Rayleigh number convection in a Bénard cell. Quantitative interpretation of recent experimental data [B. Castaing et al. (private communication)] is presented. The predicted intermittency exponent following from comparison of the theory with experiment is 0.175<μ<0.275. A crucial experimental test of the renormalization group theory of turbulence is proposed.
The equations of motion describing inviscid fluid flow are solved numerically in two dimensions for the case where the flow can be described by patches of constant vorticity. The case where the vorticity is described ...
The equations of motion describing inviscid fluid flow are solved numerically in two dimensions for the case where the flow can be described by patches of constant vorticity. The case where the vorticity is described initially by two circular patches is studied in detail. The numerical evidence indicates that when the minimum distance between the two patches is initially less than the radius of the patches a singularity forms in finite time on the boundary curves of the patches. The singularity appears to be a jump discontinuity in the tangent vector of the boundary curve.
Deviations from classical scaling behavior are shown to result in flattened energy and dissipation–fluctuation inertial‐range spectra in fully developed turbulence.
Deviations from classical scaling behavior are shown to result in flattened energy and dissipation–fluctuation inertial‐range spectra in fully developed turbulence.
A new dimensional analysis for high Rayleigh number thermal convection is proposed to give an alternative interpretation of the scaling laws observed recently by Castaing et al. [J. Fluid Mech. (in press)]. The key as...
A new dimensional analysis for high Rayleigh number thermal convection is proposed to give an alternative interpretation of the scaling laws observed recently by Castaing et al. [J. Fluid Mech. (in press)]. The key assumption in the present approach is that the central fluctuating temperature field actively interacts with the turbulent velocity field, and this interaction leads to a velocity inertial subrange that deviates significantly from Kolmogorov’s freely cascading inertial range.
A new algorithm based on spectral element discretization and non-oscillatory ideas is developed for the solution of hyperbolic partial differential equations. A conservative formulation is proposed based on cell avera...
A new algorithm based on spectral element discretization and non-oscillatory ideas is developed for the solution of hyperbolic partial differential equations. A conservative formulation is proposed based on cell averaging and reconstruction procedures, that employs a staggered grid of Gauss-Chebyshev and Gauss-Lobatto Chebyshev discretizations. The non-oscillatory reconstruction procedure is based on ideas similar to those proposed by Cai et al. (Math. Comput. 52, 389 (1989)) but employs a modified technique which is more robust and simpler in terms of determining the location and strength of a discontinuity. It is demonstrated through model problems of linear advection, inviscid Burgers equation, and one-dimensional Euler system that the proposed algorithm leads to stable, non-oscillatory accurate results. Exponential accuracy away from the discontinuity is realized for the inviscid Burgers equation example.
A time-independent field theoretical framework for turbulence is suggested, based upon a variational principle for a stationary solution of the Fokker-Planck equation. We obtain a functional equation for the effective...
A time-independent field theoretical framework for turbulence is suggested, based upon a variational principle for a stationary solution of the Fokker-Planck equation. We obtain a functional equation for the effective Action of this spatial field theory and investigate its general properties and some numerical solutions. The equation is completely universal, and allows for the scale invariant solutions in the inertial range. The critical indices are not fixed at the kinematical level, but rather should be found from certain eigenvalue conditions, as in the field theory of critical phenomena. Unlike the Wyld field theory, there are no divergences in our Feynman integrals, due to some magic cancellations. The simplest possible Gaussian approximation yields crude but still reasonable results (there are deviations from Kolmogorov scaling in 3 dimensions, but at 2.7544 dimensions it would be exact). Our approach allows us to study some new problems, such as spontaneous parity breaking in 3d turbulence. It turns out that with the appropriate helicity term added to the velocity correlation function, logarithmic infrared divergences arise in our field theory which effectively eliminates these terms. In order to build a quantitative theory of turbulence, one should consider more sophisticated Ansatz for the effective Action, which would require serious numerical work.
The dynamic behavior of RMSprop and Adam algorithms is studied through a combination of careful numerical experiments and theoretical explanations. Three types of qualitative features are observed in the training loss...
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In secure multi-party computations (SMC), parties wish to compute a function on their private data without revealing more information about their data than what the function reveals. In this paper, we investigate two ...
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Disordered hyperuniform many-particle systems are recently discovered exotic states of matter, characterized by the complete suppression of normalized infinite-wavelength density fluctuations, as in perfect crystals, ...
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Disordered hyperuniform many-particle systems are recently discovered exotic states of matter, characterized by the complete suppression of normalized infinite-wavelength density fluctuations, as in perfect crystals, while lacking conventional long-range order, as in liquids and glasses. In this work, we begin a program to quantify the structural properties of nonhyperuniform and hyperuniform networks. In particular, large two-dimensional (2D) Voronoi networks (graphs) containing approximately 10,000 nodes are created from a variety of different point configurations, including the antihyperuniform hyperplane intersection process (HIP), nonhyperuniform Poisson process, nonhyperuniform random sequential addition (RSA) saturated packing, and both non-stealthy and stealthy hyperuniform point processes. We carry out an extensive study of the Voronoi-cell area distribution of each of the networks by determining multiple metrics that characterize the distribution, including their average areas and corresponding variances as well as higher-order cumulants (i.e., skewness γ1 and excess kurtosis γ2). We show that the HIP distribution is far from Gaussian, as evidenced by a high skewness (γ1=3.16) and large positive excess kurtosis (γ2=16.2). The Poisson (with γ1=1.07 and γ2=1.79) and non-stealthy hyperuniform (with γ1=0.257 and γ2=0.0217) distributions are Gaussian-like distributions, since they exhibit a small but positive skewness and excess kurtosis. The RSA (with γ1=0.450 and γ2=−0.0384) and the highest stealthy hyperuniform distributions (with γ1=0.0272 and γ2=−0.0626) are also non-Gaussian because of their low skewness and negative excess kurtosis, which is diametrically opposite of the non-Gaussian behavior of the HIP. The fact that the cell-area distributions of large, finite-sized RSA and stealthy hyperuniform networks (e.g., with N≈10,000 nodes) are narrower, have larger peaks, and smaller tails than a Gaussian distribution implies that in the thermodynamic limit th
Four-Dimensional Simplicial Quantum Gravity is simulated using the dynamical triangulation approach. We studied simplicial manifolds of spherical topology and found the critical line for the cosmological constant as a...
Four-Dimensional Simplicial Quantum Gravity is simulated using the dynamical triangulation approach. We studied simplicial manifolds of spherical topology and found the critical line for the cosmological constant as a function of the gravitational one, separating the phases of opened and closed Universe. When the bare cosmological constant approaches this line from above, the four-volume grows: we reached about 5 x 10(4) simplexes, which proved to be sufficient for the statistical limit of infinite volume. However, for the genuine continuum theory of gravity, the parameters of the lattice model should be further adjusted to reach the second order phase transition point, where the correlation length grows to infinity. We varied the gravitational constant, and we found the first order phase transition, similar to the one found in three-dimensional model, except in 4D the fluctuations are rather large at the transition point, so that this is close to the second order phase transition. The average curvature in cutoff units is large and positive in one phase (gravity), and small negative in another (antigravity). We studied the fractal geometry of both phases, using the heavy particle propagator to define the geodesic map, as well as with the old approach using the shortest lattice paths. The heavy propagator geodesic appeared to be much smoother, so that the scaling laws were found, corresponding to finite fractal dimensions: D+ approximately 2.3 in the gravity phase and D- approximately 4.6 in the antigravity phase. Similar, but somewhat lower numbers were obtained from the heat kernel singularity. The influence of the alpha-R2 terms in 2, 3 and 4 dimensions is discussed.
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