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1.
The governing dynamics of fluid flow is stated as a system of partial differential equations referred to as the Navier-Stokes system. In industrial and scientific applications, fluid flow control becomes an optimization problem where the governing partial differential equations of the fluid flow are stated as constraints. When discretized, the optimal control of the Navier-Stokes equations leads to large sparse saddle point systems in two levels. In this paper, we consider distributed optimal control for the Stokes system and test the particular case when the arising linear system can be compressed after eliminating the control function. In that case, a system arises in a form which enables the application of an efficient block matrix preconditioner that previously has been applied to solve complex-valued systems in real arithmetic. Under certain conditions, the condition number of the so preconditioned matrix is bounded by 2. The numerical and computational efficiency of the method in terms of number of iterations and execution time is favorably compared with other published methods.  相似文献   
2.
Summary A class of preconditioning methods depending on a relaxation parameter is presented for the solution of large linear systems of equationAx=b, whereA is a symmetric positive definite matrix. The methods are based on an incomplete factorization of the matrixA and include both pointwise and blockwise factorization. We study the dependence of the rate of convergence of the preconditioned conjugate gradient method on the distribution of eigenvalues ofC –1 A, whereC is the preconditioning matrix. We also show graphic representations of the eigenvalues and present numerical tests of the methods.  相似文献   
3.
A brief survey is given to show that harmonic averages enter in a natural way in the numerical solution of various variable coefficient problems, such as in elliptic and transport equations, also of singular perturbation types. Local Green’s functions used as test functions in the Petrov-Galerkin finite element method combined with harmonic averages can be very efficient and are related to exact difference schemes.  相似文献   
4.
Two‐by‐two block matrices arise in various applications, such as in domain decomposition methods or when solving boundary value problems discretised by finite elements from the separation of the node set of the mesh into ‘fine’ and ‘coarse’ nodes. Matrices with such a structure, in saddle point form arise also in mixed variable finite element methods and in constrained optimisation problems. A general algebraic approach to construct, analyse and control the accuracy of preconditioners for matrices in two‐by‐two block form is presented. This includes both symmetric and nonsymmetric matrices, as well as indefinite matrices. The action of the preconditioners can involve element‐by‐element approximations and/or geometric or algebraic multigrid/multilevel methods. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   
5.
Lipid vesicles can be connected by membrane nanotubes to build networks with promising bioanalytical properties. Here we characterize electrophoretic transport in such membrane tubes, with a particular eye to how their soft-material nature influences the intratube migration. In the absence of field, the tube radius is 110 +/- 26 nm, and it remains in this range during electrophoresis even though the applied electric field causes a slight decrease in the tube radius (approximately 6-11%). The electrophoretic velocity of the membrane wall (labeled with quantum dots) varies linearly with the field strength. Intratube migration is studied with latex spheres of radii 15, 50, 100, and 250 nm. The largest particle size does not enter the tube at fields strengths lower than 1250 V/m because the energy cost for expanding the tube around the particles is too high. The smaller particles migrate with essentially the same velocity as the membrane at low fields. Above 250 V/cm, the 15 nm particles exhibit an upward deviation from linear behavior and in fact migrate faster than in free solution whereas the 100 nm particles deviate downward. We propose that these nonlinear effects arise because of lipid adsorption to the particles (dominating for 15 nm particles) and a pistonlike compression of the solvent in front of the particles (dominating for 100 nm). As expected from such complexities, existing theories for a sphere migrating in a rigid-wall cylinder cannot explain our velocity results in lipid nanotubes.  相似文献   
6.
We study numerically the filtering capabilities of a nanoscale network of two micrometer-sized containers joined by a nanotube, one of which hosts an enzymatic chemical reaction. Spatiotemporal chemical signals of substrate molecules are injected into the network. The substrate propagates by diffusion and reacts with enzymes distributed in the network prior to the injections. The dimensions of the network are tailored in a way that the transport and enzymatic reaction rates are comparable in size, a situation in which the overall behavior is highly influenced by the geometry and topology of the network. This property is crucial for the functionality of the filter developed in here. It is demonstrated that input signals can be classified in a crude way using a simple setup (a two-container network) and that the classification can be tuned by changing the geometry of the network (the length of the tube connecting the two containers). The filter device we investigate can also be viewed as a primitive chemistry-based computational element in the sense that the information encoded in the signals is processed using chemical reactions. In particular, it is demonstrated that the two-container device may filter out signals based on the average injection frequency.  相似文献   
7.
Complex valued systems of equations with a matrix R + 1S where R and S are real valued arise in many applications. A preconditioned iterative solution method is presented when R and S are symmetric positive semi‐definite and at least one of R, S is positive definite. The condition number of the preconditioned matrix is bounded above by 2, so only very few iterations are required. Applications when solving matrix polynomial equation systems, linear systems of ordinary differential equations, and using time‐stepping integration schemes based on Padé approximation for parabolic and hyperbolic problems are also discussed. Numerical comparisons show that the proposed real valued method is much faster than the iterative complex symmetric QMR method. Copyright © 2000 John Wiley & Sons, Ltd.  相似文献   
8.
An experimental analysis of valved pulsejets based on the Curtis-Dyna design and the concomitant results are discussed in the current paper. By altering the combustor length, the tail pipe length and by adding a flare at the aft-end, twelve different pulsejet configurations are tested. An axially-distributed array of piezoelectric pressure sensors and ion probes reveal the pressure and combustion dynamics inside these devices. Evidence is attained to support the claim that valved Curtis-Dyna pulsejets of the tested configurations behave like a Helmholtz resonator. Each cycle of a pulsejet is composed of temporally and spatially restrained combustion events. Altering the geometry induces an amplitude modulated low frequency instability inside the pulsejet that is characterized by sinusoidally-varying peak cycle pressures. The operating frequency, peak pressures and combustion activity of the pulsejets are characterized to reveal that reliable pulsejet operation requires proper amount of coupling — defined by low time lags — between the pressure peaks and combustion events.  相似文献   
9.
10.
Eigenvalue and condition number estimates for preconditioned iteration matrices provide the information required to estimate the rate of convergence of iterative methods, such as preconditioned conjugate gradient methods. In recent years various estimates have been derived for (perturbed) modified (block) incomplete factorizations. We survey and extend some of these and derive new estimates. In particular we derive upper and lower estimates of individual eigenvalues and of condition number. This includes a discussion that the condition number of preconditioned second order elliptic difference matrices is O(h−1). Some of the methods are applied to compute certain parameters involved in the computation of the preconditioner.  相似文献   
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