We reformulate the renormalization group (RNG) and the e{open}-expansion for derivation of turbulence models. The procedure is developed for the Navier-Stokes equations and the transport equations for the kinetic ener...
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A two-species reaction-diffusion model is used to study bifurcations in one-dimensional excitable media. Numerical continuation is used to compute branches of traveling waves and periodic steady states, and linear sta...
A two-species reaction-diffusion model is used to study bifurcations in one-dimensional excitable media. Numerical continuation is used to compute branches of traveling waves and periodic steady states, and linear stability analysis is used to determine bifurcations of these solutions. It is shown that the sequence of symmetry-breaking bifurcations which lead from the homogeneous excitable state to stable traveling waves can be understood in terms of an O(2)-symmetric normal form.
The performance of the i-line AZ Spectralith resist under typical working conditions is examined. A study of primary lens aberrations including spherical aberration, coma, and astigmatism is presented for a lines and ...
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The wakes of bluff objects and in particular of circular cylinders are known to undergo a ‘fast ’ transition, from a laminar two-dimensional state a t Reynolds number 200 to a turbulent state a t Reynolds number 400...
The wakes of bluff objects and in particular of circular cylinders are known to undergo a ‘fast ’ transition, from a laminar two-dimensional state a t Reynolds number 200 to a turbulent state a t Reynolds number 400. The process has been documented in several eXperimental mvestigations, but the underlying physical mechanisms have remained largely unknown so far. In this paper, the transition process is investigated numerically, through direct simulation of the NavierStokes equations at representative Reynolds numbers, up to 500. A high-order timeaccurate, miXed spectral/spectral element technique is used. It is shown that the wake first becomes three-dimensional, as a result of a secondary instability of the two-dimensional vorteX street. This secondary instability appears at a Reynolds number close to 200. For slightly supercritical Reynolds numbers, a harmonic state develops, in which the flow oscillates at its fundamental frequency (Strouhal number) around a spanwise modulated time-average flow. In the near wake the modulation wavelength of the time-average flow is half of the spanwise wavelength of the perturbation flow, consistently with linear instability theory. The vorteX filaments have a spanwise wavy shape in the near wake, and form rib-like structures further downstream. At higher Reynolds numbers the three-dimensional flow oscillation undergoes a period-doubling bifurcation, in which the flow alternates between two different states. Phase-space analysis of the flow shows that the basic limit cycle has branched into two connected limit cycles. In physical space the period doubling appears as the shedding of two distinct types of vorteX filaments. Further increases of the Reynolds number result in a cascade of period-doubling bifurcations, which create a chaotic state in the flow at a Reynolds number of about 500. The flow is characterized by broadband power spectra, and the appearance intermittent phenomena. It is concluded that the wake undergoes transit
The usual formula for the scalar aerial image of an isolated object due to a projection lens system has been generalized beyond the paraxial approximation in an attempt to extend scalar diffraction theory to include n...
The usual formula for the scalar aerial image of an isolated object due to a projection lens system has been generalized beyond the paraxial approximation in an attempt to extend scalar diffraction theory to include numerical aperture (NA) values up to about 0.6. Beyond this regime, or certainly beyond NA=0.7, polarization effects need to be included, thereby demanding a full vector treatment and invalidating the present scalar formulation. A key point to the present scalar result without the paraxial approximation is the predicted functional dependence of the aerial image on magnification as NA increases. A second key point is that the usual scaling of λ/NA for the object dimensions and λ/NA2 for defocus become invalid for high NA systems. Numerical results of illustrative test cases are shown.
A Monte Carlo scheme for the search of extensive conserved quantities in lattice gas automata models is described. It is based on an approximation to the microscopic dynamics and it amounts to estimating the dimension...
A Monte Carlo scheme for the search of extensive conserved quantities in lattice gas automata models is described. It is based on an approximation to the microscopic dynamics and it amounts to estimating the dimension of the eigenspace with eigenvalue 1 of a linear operator related to the lattice gas automata model evolution operator linearized around equilibrium distributions. The applicability of this technique is limited to models with collision rules satisfying semi-detailed balance.
Intermittency effects in turbulence are discussed from a dynamical point of view. A two-fluid model is developed to describe quantitatively the non-gaussian statistics of turbulence at small scales. With a self-simila...
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Intermittency effects in turbulence are discussed from a dynamical point of view. A two-fluid model is developed to describe quantitatively the non-gaussian statistics of turbulence at small scales. With a self-similarity argument, the model gives rise to the entire set of inertial range scaling exponents for normalized velocity structure functions. The results are in excellent agreement with experimental and numerical measurements. The model suggests a physical mechanism of intermittency, namely the self-interaction of turbulence structures.
A simple fluctuation argument A la Landau suggests why probability density functions of velocity gradients of turbulent velocity fields are often found to have a close to exponential tail. The detailed functional form...
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A simple fluctuation argument A la Landau suggests why probability density functions of velocity gradients of turbulent velocity fields are often found to have a close to exponential tail. The detailed functional form depends on the assumptions made concerning the intermittency.
We describe here a new technique and a package for rapid reconstruction of smooth surfaces from scattered data points. This method is based on a fast recurrent algorithm for the Delauney triangulation followed by rati...
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We describe here a new technique and a package for rapid reconstruction of smooth surfaces from scattered data points. This method is based on a fast recurrent algorithm for the Delauney triangulation followed by rational interpolation inside triangles. Preprocessing of data includes sorting and takes N log(N) time. Afterwards the computational cost is a linear function of the amount of data. This technique enables a user to construct a surface of any class of smoothness and degree of convergence. Our package reconstructs surfaces that can be uniquely projected either on a plane or on a sphere. The graphical section of this package includes three dimensional transformations, shading, hidden surface removal, interactive adding points into triangulation by mouse, etc. The graphics has been implemented on Iris-4D, SUN-4 and IBM-5080.
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.
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