A method is developed for the optimal estimation of the parameters in a fully nonlinear model of flow in a channel. The data assimilated consist of values of the water surface elevation during a given interval. The me...
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A method is developed for the optimal estimation of the parameters in a fully nonlinear model of flow in a channel. The data assimilated consist of values of the water surface elevation during a given interval. The method is based on the adjoint method of optimal control. It is shown that accurate values of the parameters can be estimated, and the estimates are stable with respect to random perturbations of the data provided that data from a sufficient number of locations are available for assimilation.
We show that the statistical properties of the large scales of the Kuramoto-Sivashinsky equation in the extended system limit can be understood in terms of the dynamical behavior of the same equation in a small finite...
In order to realize light and small power supplies, this paper proposes a film-shape transformer called film transformer. The basic operating principle of this transformer is the skin effect similar to those of the co...
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In order to realize light and small power supplies, this paper proposes a film-shape transformer called film transformer. The basic operating principle of this transformer is the skin effect similar to those of the coreless transformer previously exploited by the authors. Both the primary and secondary coils composed of thin-film conductors are arranged coaxially on the one-layer film base, and the film transformer is constructed by the lamination of these films. In this paper, experimental as well as numerical studies are carried out about basic characteristics of the film transformer in order to examine possibilities in practical use. As a result, it is shown that the film transformer may be applicable to high-frequency switching power supplies.
The purpose of this paper is to study the motion of a spinless axisymmetric rigid body in a Newtonian field when we suppose the motion of the center of mass of the rigid body is on a Keplerian orbit. In this case the ...
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The purpose of this paper is to study the motion of a spinless axisymmetric rigid body in a Newtonian field when we suppose the motion of the center of mass of the rigid body is on a Keplerian orbit. In this case the system can be reduced to a Hamiltonian system with configuration space of a two-dimensional sphere. We prove that the restricted planar motion is analytical nonintegrable and we find horseshoes due to the eccentricity of the orbit. In the case I-3/I-1 > 4/3, we prove that the system on the sphere is also analytical nonintegrable.
The dynamics of velocity fluctuations, governed by the one-dimensional Burgers equation, driven by a white-in-time random force f with the spatial spectrum ‖f(k)‖2∝k−1, is considered. High-resolution numerical expe...
The dynamics of velocity fluctuations, governed by the one-dimensional Burgers equation, driven by a white-in-time random force f with the spatial spectrum ‖f(k)‖2∝k−1, is considered. High-resolution numerical experiments conducted in this work give the energy spectrum E(k)∝k−β with β=5/3±0.02. The observed two-point correlation function C(k,ω) reveals ω∝kz with the ‘‘dynamic exponent’’ z≊2/3. High-order moments of velocity differences show strong intermittency and are dominated by powerful large-scale shocks. The results are compared with predictions of the one-loop renormalized perturbation expansion.
High-resolution numerical experiments, described in this work, show that velocity fluctuations governed by the one-dimensional Burgers equation driven by a white-in-time random noise with the spectrum ‖f(k)‖2¯...
High-resolution numerical experiments, described in this work, show that velocity fluctuations governed by the one-dimensional Burgers equation driven by a white-in-time random noise with the spectrum ‖f(k)‖2¯∝k−1 exhibit a biscaling behavior: All moments of velocity differences Sn≤3(r)=‖u(x+r)-u(x)‖n¯≡‖Δu‖n¯ ∝rn/3, while Sn>3(r)∝rnξ with ξn≊1 for real n>0 [Chekhlov and Yakhot, Phys. Rev. E 51, R2739 (1995)]. The probability density function, which is dominated by coherent shocks in the interval Δu<0, is scrP(Δu,r)∝(Δu)−q with q≊4. A phenomenological theory describing the experimental findings is presented.
It is shown that the parameters in a quasi‐three‐dimensional numerical tidal model can be estimated accurately by assimilation of data from current meters and tide gauges. The tidal model considered is a semi‐linea...
It is shown that the parameters in a quasi‐three‐dimensional numerical tidal model can be estimated accurately by assimilation of data from current meters and tide gauges. The tidal model considered is a semi‐linearized one in which advective nonlinearities are neglected but nonlinear bottom friction is included. The parameters estimated are the eddy viscosity, bottom friction coefficient, water depth and wind drag coefficient, the first three of which are allowed to be position‐dependent. The adjoint method is used to construct the gradient of a cost function defined as a certain norm of the difference between computed and observed current and surface elevations. On the basis of a number of tests, it is shown that very effective estimation of the nodal values of the parameters can be achieved using the current data either alone or in combination with elevation data. When random errors are introduced into the data, the estimated parameters are quite sensitive to the magnitude of the errors, and in particular the eddy viscosity is unstably sensitive. The sensitivity of the viscosity can be stabilized by incorporating an appropriate penalty term in the cost function or alternatively by reducing the number of estimated viscosity values via a finite element approximation. Once stabilized, the sensitivity of the estimates to data errors is significantly reduced by assimilating a longer data record.RésuméOn montre que les paramètres d'un modèle numérique quasi trois dimensions de la marée peuvent être estimés avec exactitude en assimilant les données de courantomètres et de marégraphes. Le modèle de la marée examiné est semi linéarisé et les non linéarités advectives y sont négligées mais la friction de fond non linéaire est incluse. On a estimé les coeffecients de viscosité, de friction de fond, de la profondeur de l'eau et de traînée du vent, allouant les trois premiers d'être translatables. La méthode adjointe est utilisée pour construire le gradient d'une fonction de
The theory of the focusing NLS equation under periodic boundary conditions, together with the Floquet spectral theory of its associated Zakharov-Shabat liner operator L, is developed in sufficient detail for later use...
The theory of the focusing NLS equation under periodic boundary conditions, together with the Floquet spectral theory of its associated Zakharov-Shabat liner operator L, is developed in sufficient detail for later use in studies of perturbations of the NLS equation. ''Counting lemmas'' for the non-selfadjoint operator L, are established which control its spectrum and show that all of its eccentricities are finite in number and must reside within a finite disc D in the complex eigenvalue plane. The radius of the disc D is controlled by the H-1 norm of the potential q. For this integrable NLS Hamiltonian system, unstable tori are identified, and Backlund transformations are then used to construct global representations of their stable and unstable manifolds - ''whiskered tori'' for the NLS pde. The Floquet discriminant DELTA(lambda;q) used to introduce a natural sequence of NLS constants of motion, [F(j)(q) = DELTA(lambda = lambda(j)c(q);q), where lambda(j)c denotes the j(th) critical point of the Floquet discriminant DELTA(lambda)]. A Taylor series expansion of the constants F(j)(q), with explicit representations of the first and second variations, is then used to study neighborhoods of the whiskered tori. In particular, critical tori with hyperbolic structure are identified through the first and second variations of F(j)(q), which themselves are expressed in terms of quadratic products of eigenfunctions of L. The second variation permits identification, within the disc D, of important bifurcations m the spectral configurations of the operator L. The constant F(j)(q), as the height of the Floquet discriminant over the critical point lambda(j)c, admits a natural interpretation as a Morse function for NLS isospectral level sets. This Morse interpretation is studied in some detail. It is valid globally for the infinite tail, {F(j)(q)}\j\>N, which is associated with critical points outside the disc D. Within this disc, the interpretation is only valid locally, with the s
A new mechanism for the creation of structures in two-dimensional turbulence is investigated. The forced Navier-Stokes equations are solved numerically in a periodic square in the limit of zero viscosity. The force is...
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A new mechanism for the creation of structures in two-dimensional turbulence is investigated. The forced Navier-Stokes equations are solved numerically in a periodic square in the limit of zero viscosity. The force is a white-in-time random noise acting in a narrow band of high wavenumbers. The inverse-cascade process and the presence of the boundary lead ultimately to a pile-up of energy in the lowest wavenumber (Bose condensation). In the asymptotic limit where the enstrophy cascade range is negligible, Bose condensation is solely responsible for the generation of coherent vortices and intermittency in the system. We present the evolution of the velocity and vorticity fields through the later stages of the condensate state, and explore the possible implications for atmospheric turbulence constrained by the periodic domain about the earth.
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