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121.
JérÔme Jaffré 《Transport in Porous Media》1995,21(3):195-207
When simulating two-phase flow in porous media, one has to consider the case where there is a discontinuity in the medium. There relative permeabilities and capillary pressure functions may change and we address the problem of calculating the convective part of the numerical flux at the interface between the two rock types. Several solutions are compared. 相似文献
122.
Traditional mathematical models of multiphase flow in porous media use a straightforward extension of Darcys equation. The key element of these models is the appropriate formulation of the relative permeability functions. It is well known that for one-dimensional flow of three immiscible incompressible fluids, when capillarity is neglected, most relative permeability models used today give rise to regions in the saturation space with elliptic behavior (the so-called elliptic regions). We believe that this behavior is not physical, but rather the result of an incomplete mathematical model. In this paper we identify necessary conditions that must be satisfied by the relative permeability functions, so that the system of equations describing three-phase flow is strictly hyperbolic everywhere in the saturation triangle. These conditions seem to be in good agreement with pore-scale physics and experimental data. 相似文献
123.
Rheological models of complex fluids with a physically restricted microstructure are analyzed to obtain general classes of
dynamical evolution equations for these materials. These classes insure that the appropriate mathematical constraints, associated
with each type of physical restriction, are consistently incorporated into the corresponding model development. Describing
the microstructure of the complex fluid with a second-rank tensor variable, a general class of dynamical evolution equations
is derived for three physically meaningful constraints associated with constancy of the invariants of this microstructural
tensor. The physical rationale for each of these constraints is discussed, and a corresponding set of constrained dynamical
evolution equations is derived in general terms.
Abdellatif Ait-Kadi passed away suddenly during the course of this research. The surviving authors express their gratitude
to Abdellatif for our many hours of productive work and companionship. 相似文献
124.
Hysteresis phenomena in multi-phase flow in porous media has been recognized by many researchers and widely believed to have significant effects on the flow. In an attempt to account for these effects, a theoretical model for history-dependent relative permeabilities is considered. This model is incorporated into 1-D two-phase nondiffusive flow system and the corresponding flow is predicted. Flow history is observed to have a notable impact on the saturation profile and fluids breakthrough. 相似文献
125.
Dai Tian-min 《应用数学和力学(英文版)》2003,24(10):1134-1140
The existing various couple stress theories have been carefully restudied.The purpose is to propose a coupled Noether’s theorem and to reestablish rather complete conservation laws and balance equations for couple stress elastodynamics. The new concrete forms of various conservation laws of couple stress elasticity are derived. The precise nature of these conservation laws which result from the given invariance requirements are established. Various special cases are reduced and the results of micropolar continua may be naturally transited from the results presented in this paper. 相似文献
126.
127.
We study 2×2 systems of hyperbolic conservation laws near an umbilic point. These systems have Undercompressive shock wave solutions, i.e., solutions whose viscous profiles are represented by saddle connections in an associated family of planar vector fields. Previous studies near umbilic points have assumed that the flux function is a quadratic polynomial, in which case saddle connections lie on invariant lines. We drop this assumption and study saddle connections using Golubitsky-Schaeffer equilibrium bifurcation theory and the Melnikov integral, which detects the breaking of heteroclinic orbits. The resulting information is used to construct solutions of Riemann problems. 相似文献
128.
本文提出了构造Birkhoff系统守恒律的积分因子方法。首先,给出了Birkhoff方程的积分因子的定义,研究了Birkhoff系统的守恒量存在必要条件;其次,建立了系统的积分因子与守恒律的对应关系,并给出了用于确定积分因子的广义Killing方程,最后,建立了守恒定理的逆定理。文末,举例说明结果的应用。 相似文献
129.
We show how one can construct conservation laws of Euler-Lagrange-type equations via Noether-type symmetry operators associated with what we term partial Lagrangians. This is even in the case when a system does not directly have a usual Lagrangian, e.g. scalar evolution equations. These Noether-type symmetry operators do not form a Lie algebra in general. We specify the conditions under which they do form an algebra. Furthermore, the conditions under which they are symmetries of the Euler-Lagrange-type equations are derived. Examples are given including those that admit a standard Lagrangian such as the Maxwellian tail equation, and equations that do not such as the heat and nonlinear heat equations. We also obtain new conservation laws from Noether-type symmetry operators for a class of nonlinear heat equations in more than two independent variables. 相似文献
130.
Sérgio H. Faria 《Continuum Mechanics and Thermodynamics》2003,15(2):147-159
Recently, there appeared in this journal a short review article by Müller ((2002), 14: 227–229), in which it was argued that
the internal energy of a reacting mixture of liquid crystals should not be an objective quantity (i.e., a quantity independent
of the referential frame). Such a paradoxical conclusion has revealed the urging necessity for a better comprehension of the
interactions taking place in structured mixtures, specially when referred to non-inertial observers. This work shows that
Müller's paradox is avoided when all inertial effects are carefully accounted for. Further, it predicts interesting phenomena
without analogue in reacting mixtures of structureless fluids: internal inertial effects, produced by a combination of mass exchanges (e.g. by chemical reactions or phase changes) with the extra degrees of freedom
posed by the microstructure. Such effects clarify the reasons why inertial forces and couples acting on a mixture do not always
coincide with the sum of the inertial forces and couples exerted upon its individual constituents. The present conclusions
establish a reinterpretation of some fundamental concepts of continuum mechanics and thermodynamics, including a deeper understanding
of the manner in which total energy and momenta are conserved in complex media.
Received: July 25, 2002 / Published online: February 17, 2003
Communicated by Kolumban Hutter, Darmstadt
e-mail: faria@mechanik.tu-darmstadt.de 相似文献