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1.
We study the number of determining modes necessary for continuous data assimilation in the two-dimensional incompressible Navier–Stokes equations. Our focus is on how the spatial structure of the body forcing affects the rate of continuous data assimilation and the number of determining modes. We treat this problem analytically by proving a convergence result depending on the H
–1 norm of f and computationally by considering a family of forcing functions with identical Grashof numbers that are supported on different annuli in Fourier space. The rate of continuous data assimilation and the number of determining modes is shown to depend strongly on the length scales present in the forcing. 相似文献
2.
Obilade Titi 《应用数学学报(英文版)》1990,6(1):35-39
This paper presents an algorithmic procedure for a busy-period subcomponent analysis of bulk queues. A component of interest for many server queues is the periodt
k to reduce congestion from a levelk to levelk-1. For anM
(x)/M/c system with the possibility of total or partial rejection of batches, it is demonstrated that the expected length of busy periods, the proportion of delayed batch and the steady state queue length probabilities can be easily obtained. The procedure is based on the nested partial sums and monotonic properties of expected lengths of the busy periods.Formerly University of Ife. 相似文献
3.
Isaiah R. Speight Dr. Igor Huskić Dr. Mihails Arhangelskis Dr. Hatem M. Titi Dr. Robin S. Stein Prof. Timothy P. Hanusa Prof. Tomislav Friščić 《Chemistry (Weinheim an der Bergstrasse, Germany)》2020,26(8):1811-1818
The “disappearing polymorph” phenomenon is well established in organic solids, and has had a profound effect in pharmaceutical materials science. The first example of this effect in metal-containing systems in general, and in coordination-network solids in particular, is here reported. Specifically, attempts to mechanochemically synthesize a known interpenetrated diamondoid (dia) mercury(II) imidazolate metal–organic framework (MOF) yielded a novel, more stable polymorph based on square-grid (sql) layers. Simultaneously, the dia-form was found to be highly elusive, observed only as a short-lived intermediate in monitoring solvent-free synthesis and not at all from solution. The destabilization of a dense dia-framework relative to a lower dimensionality one is in contrast to the behavior of other imidazolate MOFs, with periodic density functional theory (DFT) calculations showing that it arises from weak interactions, including structure-stabilizing agostic C−H⋅⋅⋅Hg contacts. While providing a new link between MOFs and crystal engineering of organic solids, these findings highlight a possible role for agostic interactions in directing topology and stability of MOF polymorphs. 相似文献
4.
In this work we derive lower bounds for the Hausdorff and fractal dimensions of the global attractor of the Sabra shell model
of turbulence in different regimes of parameters. We show that for a particular choice of the forcing term and for sufficiently
small viscosity term ν, the Sabra shell model has a global attractor of large Hausdorff and fractal dimensions proportional
to log ν −1 for all values of the governing parameter ε, except for ε =1. The obtained lower bounds are sharp, matching the upper bounds
for the dimension of the global attractor obtained in our previous work. Moreover, the complexity of the dynamics of the shell
model increases as the viscosity ν tends to zero, and we describe a precise scenario of successive bifurcations for different
parameters regimes. In the “three-dimensional” regime of parameters this scenario changes when the parameter ε becomes sufficiently
close to 0 or to 1. We also show that in the “two-dimensional” regime of parameters, for a certain non-zero forcing term,
the long-term dynamics of the model becomes trivial for every value of the viscosity.
AMS Subject Classifications: 76F20, 76D05, 35Q30 相似文献
5.
Summary. In this paper, we study the regularity and long-time behavior of the solutions to the Moore-Greitzer model of an axial-flow
compressor. In particular, we prove that this dissipative system of evolution equations possesses a global invariant inertial
manifold, and therefore its underlying long-time dynamics reduces to that of an ordinary differential system. Furthermore,
we show that the solutions of this model belong to a Gevrey class of regularity (real analytic in the spatial variables).
As a result, one can show the exponentially fast convergence of the Galerkin approximation method to the exact solution, an
evidence of the reliability of the Galerkin method as a computational scheme in this case. The rigorous results presented
here justify the readily available low-dimensional numerical experiments and control designs for stabilizing certain states
and traveling wave solutions for this model. 相似文献
6.
Peter Constantin E Weinan Edriss S. Titi 《Communications in Mathematical Physics》1994,165(1):207-209
We give a simple proof of a result conjectured by Onsager [1] on energy conservation for weak solutions of Euler's equation. 相似文献
7.
Three-dimensional solutions with helical symmetry are shown to form an invariant subspace for the Navier-Stokes equations. Uniqueness of weak helical solutions in the sense of Leray is proved, and these weak solutions are shown to be regular (strong) solutions existing for arbitrary time t. The global universal attractor for the infinite-dimensional dynamical system generated by the corresponding semi-group of helical flows is shown to be compact and finite-dimensional. The Hausdorff and fractal dimensions of the global attractors are estimated in terms of the governing physical parameters and in terms of the helical parameters for several problems in the class, with the most detailed results obtained for rotating Hagen-Poiseuille (pipe) flow. In this case, the dimension, either Hausdorff or fractal, up to an absolute constant is bounded from above by
, where is the axial wavenumber, n is the azimuthal wavenumber and Re is the Reynolds number based on the radius of the pipe. These upper bounds are independent of the rotation rate. 相似文献
8.
In this paper we provide a sufficient condition, in terms of only one of the nine entries of the gradient tensor, that is,
the Jacobian matrix of the velocity vector field, for the global regularity of strong solutions to the three-dimensional Navier–Stokes
equations in the whole space, as well as for the case of periodic boundary conditions. 相似文献
9.
In this paper we develop and use successive averaging methods for explaining the regularization mechanism in the the periodic Korteweg–de Vries (KdV) equation in the homogeneous Sobolev spaces Ḣs for s ≥ 0. Specifically, we prove the global existence, uniqueness, and Lipschitz‐continuous dependence on the initial data of the solutions of the periodic KdV. For the case where the initial data is in L2 we also show the Lipschitz‐continuous dependence of these solutions with respect to the initial data as maps from Ḣs to Ḣs for s ∈(−1,0]. © 2010 Wiley Periodicals, Inc. 相似文献
10.
Claude Bardos Uriel Frisch Walter Pauls Samriddhi Sankar Ray Edriss S. Titi 《Communications in Mathematical Physics》2010,293(2):519-543
We consider a modification of the three-dimensional Navier–Stokes equations and other hydrodynamical evolution equations with
space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an operator whose
Fourier symbol grows exponentially as e|k|/kd{{{\rm e}^{|k|/k_{\rm d}}}} at high wavenumbers |k|. Using estimates in suitable classes of analytic functions, we show that the solutions with initially finite energy become
immediately entire in the space variables and that the Fourier coefficients decay faster than e-C(k/kd) ln(|k|/kd){{{\rm e}^{-C(k/k_{\rm d})\,{\rm ln}(|k|/k_{\rm d})}}} for any C < 1/(2 ln 2). The same result holds for the one-dimensional Burgers equation with exponential dissipation but can be improved:
heuristic arguments and very precise simulations, analyzed by the method of asymptotic extrapolation of van der Hoeven, indicate
that the leading-order asymptotics is precisely of the above form with C = C
* = 1/ ln 2. The same behavior with a universal constant C
* is conjectured for the Navier–Stokes equations with exponential dissipation in any space dimension. This universality prevents
the strong growth of intermittency in the far dissipation range which is obtained for ordinary Navier–Stokes turbulence. Possible
applications to improved spectral simulations are briefly discussed. 相似文献