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51.
Extending fixed‐grid time integration schemes for unsteady CFD applications to moving grids, while formally preserving their numerical stability and time accuracy properties, is a nontrivial task. A general computational framework for constructing stability‐preserving ALE extensions of Eulerian multistep time integration schemes can be found in the literature. A complementary framework for designing accuracy‐preserving ALE extensions of such schemes is also available. However, the application of neither of these two computational frameworks to a multistage method such as a Runge–Kutta (RK) scheme is straightforward. Yet, the RK methods are an important family of explicit and implicit schemes for the approximation of solutions of ordinary differential equations in general and a popular one in CFD applications. This paper presents a methodology for filling this gap. It also applies it to the design of ALE extensions of fixed‐grid explicit and implicit second‐order time‐accurate RK (RK2) methods. To this end, it presents the discrete geometric conservation law associated with ALE RK2 schemes and a method for enforcing it. It also proves, in the context of the nonlinear scalar conservation law, that satisfying this discrete geometric conservation law is a necessary and sufficient condition for a proposed ALE extension of an RK2 scheme to preserve on moving grids the nonlinear stability properties of its fixed‐grid counterpart. All theoretical findings reported in this paper are illustrated with the ALE solution of inviscid and viscous unsteady, nonlinear flow problems associated with vibrations of the AGARD Wing 445.6. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
52.
P.‐W. Zhang Z.‐G. Zhou G. Li 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2009,89(9):767-788
In this paper, the behavior of four parallel non‐symmetric permeable cracks with different lengths in a functionally graded piezoelectric material plane subjected to anti‐plane shear stress loading was studied by the Schmidt method. The problem was formulated through Fourier transform into four pairs of dual integral equations, in which unknown variables are the jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi polynomials. The results show that the stress intensity factors at the crack tips depend on the lengths and spacing of cracks and the material parameters. It is also revealed that the crack shielding effect presents in functionally graded piezoelectric materials. 相似文献
53.
The application of exponential integrators based on Krylov techniques to large‐scale simulations of complex fluid flows with multiple time‐scales demonstrates the efficiency of these schemes in reducing the associated time‐step restrictions due to numerical stiffness. Savings of approximately 50% can be achieved for simulations of the three‐dimensional compressible Navier–Stokes equations while still maintaining a truncation error typical of explicit time‐stepping schemes. Exponential time integration techniques of this type are particularly advantageous for fluid flows with a wide range of temporal scales such as low‐Mach number, reactive or acoustically dominated flows. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
54.
Simulation of nano‐scale channel flows using a coupled Navier–Stokes/Molecular Dynamics (MD) method is presented. The flow cases serve as examples of the application of a multi‐physics computational framework put forward in this work. The framework employs a set of (partially) overlapping sub‐domains in which different levels of physical modelling are used to describe the flow. This way, numerical simulations based on the Navier–Stokes equations can be extended to flows in which the continuum and/or Newtonian flow assumptions break down in regions of the domain, by locally increasing the level of detail in the model. Then, the use of multiple levels of physical modelling can reduce the overall computational cost for a given level of fidelity. The present work describes the structure of a parallel computational framework for such simulations, including details of a Navier–Stokes/MD coupling, the convergence behaviour of coupled simulations as well as the parallel implementation. For the cases considered here, micro‐scale MD problems are constructed to provide viscous stresses for the Navier–Stokes equations. The first problem is the planar Poiseuille flow, for which the viscous fluxes on each cell face in the finite‐volume discretization are evaluated using MD. The second example deals with fully developed three‐dimensional channel flow, with molecular level modelling of the shear stresses in a group of cells in the domain corners. An important aspect in using shear stresses evaluated with MD in Navier–Stokes simulations is the scatter in the data due to the sampling of a finite ensemble over a limited interval. In the coupled simulations, this prevents the convergence of the system in terms of the reduction of the norm of the residual vector of the finite‐volume discretization of the macro‐domain. Solutions to this problem are discussed in the present work, along with an analysis of the effect of number of realizations and sample duration. The averaging of the apparent viscosity for each cell face, i.e. the ratio of the shear stress predicted from MD and the imposed velocity gradient, over a number of macro‐scale time steps is shown to be a simple but effective method to reach a good level of convergence of the coupled system. Finally, the parallel efficiency of the developed method is demonstrated. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
55.
为了求得复杂刚体重心的位置, 根据转动惯量平行轴定理, 由已知轴转动惯量和一定的几何关系推导出用于求重心的关系式, 从理论上给出两个可能重心坐标值, 再实际判断取舍.只要用实验仪器先测量刚体对3个平行转轴的转动惯量, 就可由该关系式计算得到刚体重心的位置. 这一方法有时要比直接测量重心更为简单. 相似文献
56.
The objective of this paper is to present an extension of the Lagrangian Smoothed Particle Hydrodynamics (SPH) method to solve three-dimensional shell-like structures undergoing large deformations. The present method is an enhancement of the classical stabilized SPH commonly used for 3D continua, by introducing a Reissner–Mindlin shell formulation, allowing the modeling of moderately thin structure using only one layer of particles in the shell mid-surface. The proposed Shell-based SPH method is efficient and very fast compared to the classical continuum SPH method. The Total Lagrangian Formulation valid for large deformations is adopted using a strong formulation of the differential equilibrium equations based on the principle of collocation. The resulting non-linear dynamic problem is solved incrementally using the explicit time integration scheme, suited to highly dynamic applications. To validate the reliability and accuracy of the proposed Shell-based SPH method in solving shell-like structure problems, several numerical applications including geometrically non-linear behavior are performed and the results are compared with analytical solutions when available and also with numerical reference solutions available in the literature or obtained using the Finite Element method by means of ABAQUS© commercial software. 相似文献
57.
This work discusses the performance impact from the tetrahedralization of non‐conforming meshes generated by a parallel octree method capable of handling arbitrary immersed geometries. First, we review conforming techniques for meshes created from octrees. Then we implement a tetrahedralization scheme based on templates in a parallel meshing algorithm that uses a linear octree with 2:1 balancing constraint. Besides, we also propose a change on the partitioning strategy for the same meshing algorithm to improve the octree refinement load balancing. Scalability analyses show that the chosen tetrahedralization technique preserves algorithm performance. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
58.
The hydrodynamics of fluid mixtures is receiving more and more attention in many science and engineering applications. Within the techniques for dealing with front displacements and moving boundaries between different density and/or viscosity fluids, phase fields are a class of models in which a diffusive transition region is taken into account instead of a steep interface. Although these models have a physical motivation, they require the definition of extra parameters. In order to make it less parameter dependent, the classic Allen–Cahn phase field model is modified, exploring its similarities with residual‐based discontinuity‐capturing schemes, making the phase field equation dependent on its own residual. We solve the coupling between incompressible viscous fluid flow and the phase field advective–diffusive–reactive transport to simulate the main processes in interface tension and/or buoyancy driven problems. For the solution of the Navier–Stokes and transport equations, we use a stabilized finite element formulation. The implementation has been performed using the libMesh finite element library, written in C++ , which provides support for adaptive mesh refinement and coarsening. A chemical convection benchmark problem is used to validate the proposed model, and then we solve two bubble interaction problems. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
59.
We present a novel implementation of the modal DG method for hyperbolic conservation laws in two dimensions on graphics processing units (GPUs) using NVIDIA's Compute Unified Device Architecture. Both flexible and highly accurate, DG methods accommodate parallel architectures well as their discontinuous nature produces element‐local approximations. High‐performance scientific computing suits GPUs well, as these powerful, massively parallel, cost‐effective devices have recently included support for double‐precision floating‐point numbers. Computed examples for Euler equations over unstructured triangle meshes demonstrate the effectiveness of our implementation on an NVIDIA GTX 580 device. Profiling of our method reveals performance comparable with an existing nodal DG‐GPU implementation for linear problems. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
60.
In this paper, a projection method is presented for solving the flow problems in domains with moving boundaries. In order to track the movement of the domain boundaries, arbitrary‐Lagrangian–Eulerian (ALE) co‐ordinates are used. The unsteady incompressible Navier–Stokes equations on the ALE co‐ordinates are solved by using a projection method developed in this paper. This projection method is based on the Bell's Godunov‐projection method. However, substantial changes are made so that this algorithm is capable of solving the ALE form of incompressible Navier–Stokes equations. Multi‐block structured grids are used to discretize the flow domains. The grid velocity is not explicitly computed; instead the volume change is used to account for the effect of grid movement. A new method is also proposed to compute the freestream capturing metrics so that the geometric conservation law (GCL) can be satisfied exactly in this algorithm. This projection method is also parallelized so that the state of the art high performance computers can be used to match the computation cost associated with the moving grid calculations. Several test cases are solved to verify the performance of this moving‐grid projection method. Copyright © 2004 John Wiley Sons, Ltd. 相似文献