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31.
We describe and interpret computer simulations of the time evolution of a binary alloy on a cubic lattice, with nearest neighbor interactions favoring like pairs of atoms. Initially the atoms are arranged at random; the time evolution proceeds by random interchanges of nearest neighbor pairs, using probabilities compatible with the equilibrium Gibbs distribution at temperatureT. For temperatures 0.59Tc, 0.81 Tc, and 0.89T
c, with density of A atoms equal to that in the B-rich phase at coexistence, the density C1 of clusters ofl A atoms approximately satisfies the following empirical formulas: C1 w(1 –)3 andC
1, (1 –)4Q1w1 (2 l 10). Herew is a parameter and we defineQ
l
=
K
e
–E(K)
, where the sum goes over all translationally nonequivalentl-particle clusters andE(K) is the energy of formation of the clusterK. Forl > 10,Q
1 is not known exactly; so we use an extrapolation formulaQ
l
Aw
s
–l
l
– exp(–bl
), wherew
s is the value ofw at coexistence. The same formula (withw > w
s) also fits the observed values of C, (for small values ofl) at densities greater than the coexistence density (forT=0.59Tc): When the supersaturation is small, the simulations show apparently metastable states, a theoretical estimate of whose lifetime is compatible with the observations. For higher supersaturation the system is observed to undergo a slow process of segregation into two coexisting phases (andw therefore changes slowly with time). These results may be interpreted as a more quantitative formulation (and confirmation) of ideas used in standard nucleation theory. No evidence for a spinodal transition is found.Supported by AFOSR Grant No. 73-2430D and by ERDA Contract No. EY-76-C-02-3077*000. 相似文献
32.
We investigate the stationary nonequilibrium (heat transporting) states of the Lorentz gas. This is a gas of classical point particles moving in a region gL containing also fixed (hard sphere) scatterers of radiusR. The stationary state considered is obtained by imposing stochastic boundary conditions at the top and bottom of , i.e., a particle hitting one of these walls comes off with a velocity distribution corresponding to temperaturesT
1 andT
2 respectively,T
1 <T
2. Letting be the average density of the randomly distributed scatterers we show that in the Boltzmann-Grad limit,,R 0 with the mean free path fixed, the stationary distribution of the Lorentz gas converges in theL
1-norm to the stationary distribution of the corresponding linear Boltzmann equation with the same boundary conditions. In particular, the steady state heat flow in the Lorentz gas converges to that of the linear Boltzmann equation, which is known to behave as (T
2-T
1)/L for largeL, whereL is the distance from the bottom to the top wall: i.e., Fourier's law of heat conduction is valid in the limit. The heat flow converges even in probability. Generalizations of our result for scatterers with a smooth potential as well as the related diffusion problem are discussed.Research supported in part by NSF Grant no. Phy 77-22302.On leave of absence from the Fachbereich Physik der Universität, München. Work supported by a DFG fellowship. 相似文献
33.
The B → X (2870–3100 Å) and D → X (2250–2370 Å) band systems of 136Xe35Cl are photographed and vibrationally analyzed. A simultaneous least-squares fit of 41 band-heads in the B-X system and 35 in D-X yields, in part, the following constants (in cm?1): TeB = 32 405.8, TeD = 42 347.9, ωeB = 194.75, ωeD = 204.34, ωeX = 26.22. The ground state dissociation energy (″e) is estimated to be 281 ± 10 cm?1. Potential curves are derived for all three states through Franck-Condon calculations. From these curves the D-state internuclear distance is 0.09 ± .02 Å smaller than the B-state distance. 相似文献
34.
Alexandre Joel Chorin 《Communications in Mathematical Physics》1991,141(3):619-631
The thermodynamic functions and scaling exponents (including the Kolmogorov and Flory exponents) of a vortex filament in thermal equilibrium are calculated, giving a quantitative content to earlier qualitative analyses. The numerical results uncover a percolation property of vortex filaments near the maximum entropy state. The implications of the results for the onset of turbulence, for the structure of its inertial range, and for superfluid vortices are discussed. In particular, it is shown that vortex stretching pushes a vortex system to a polymeric state and a Kolmogorov spectrum.This work was supported in part by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under contract DE-AC03-76SF-00098, and in part by the National Science Foundation under grant number DMS89-19074 相似文献
35.
Jean Bricmont Jean-Raymond Fontaine Joel L. Lebowitz Thomas Spencer 《Communications in Mathematical Physics》1981,78(3):363-371
We consider perturbations of a massless Gaussian lattice field on ? d ,d≧3, which preserves the continuous symmetry of the Hamiltonian, e.g., $$ - H = \sum\limits_{< x,y > } {(\phi _x - \phi _y )^2 + T(\phi _x - \phi _y )^4 ,\phi _x \in \mathbb{R}.} $$ It is known that for allT>0 the correlation functions in this model do not decay exponentially. We derive a power law upper bound for all (truncated) correlation functions. Our method is based on a combination of the log concavity inequalities of Brascamp and Lieb, reflection positivity and the Fortuin, Kasteleyn and Ginibre (F.K.G.) inequalities. 相似文献
36.
We study the partial differential equation which arose originally as a scaling limit in the study of interface fluctuations in a certain spin system. In that application x lies in R, but here we study primarily the periodic case × R S1. We establish existence, uniqueness, and regularity of solutions, locally in time, for positive initial data in H1(S1), and prove the existence of several families of Lyapunov functions for the evolution. From the latter we establish a sharp connection between existence globally in time and positivity preservation: if [0], T*) is a maximal half open interval of existence for a positive solution of the equation, with T* < ∞, then limtT* w(t,·) exists in C1(S1) but vanishes at some point. We show further that if T* > (1 + √3)/16π2 √3 then T* = ∞ and limt∞ w(t,.) exists and is constant. We discuss also some explicit solutions and propose a generalization to higher dimensions. © 1994 John Wiley & Sons, Inc. 相似文献
37.
When p = c/n and c goes from less than one to greater than one, the random graph G(n, p) experiences the double jump. The first order language is too weak to recognize this change while there are properties expressable in the second order monadic language for which the change is clear. © 1994 John Wiley & Sons, Inc. 相似文献
38.
Joel Keizer 《Journal of statistical physics》1983,31(3):485-497
The relationship between fluctuating irreversible thermodynamics and theories of irreversible processes which include the thermodynamic fluxes as independent variables is explored. It is shown that the usual fluctuating linear theory of irreversible thermodynamics is a contraction of the extended theory. This contraction contains non-Markovian effects dependent upon the relaxation times associated with the thermodynamic fluxes. In the limit that these relaxation times are small, the extended theory is shown to be equivalent to the usual fluctuating thermodynamic theory. A critique of the extended theories is given from the point of view of the mechanistic statistical theory of irreversible processes. 相似文献
39.
We derive microscopically precise identities for the geometry of small clusters in the equilibrium states of the two-dimensional Ising model with emphasis on near-critical phenomena. 相似文献
40.
An emission system of I2 in Ar in the region 2830–2890 Å is examined under high resolution and found to display fine violet-degraded band structure. This system is interpreted as a charge-transfer transition originating from an ion-pair state near 47 000 cm?1 and terminating on a weakly bound state which dissociates to two ground-state atoms. This interpretation is supported by spectral simulations employing a bound-free model. The transition is tentatively assigned as , according to which the excited state becomes the fourth ion-pair state near 47 000 cm?1 to be experimentally characterized, and the lower state is the last component of the lowest 3Π state to be identified. The vibrational assignments include about 45 bands in 127I2 and 129I2, spanning v′ = 0–4 and v″ = 6–19, but with the numbering of the lower state remaining uncertain by several units. The main spectroscopic constants for the excited state are Te = 47 070 cm?1, ?e = 105.7 cm?1, ?exe = 0.49 cm?1. The spectral simulations place the lower state's potential curve 34 650 cm?1 below the upper state at R = R′e, with slope ?850 cm?1/Å. For our “best” numbering of the lower state, ?e = 20.5 cm?1, ?exe = 0.29 cm?1, Te = 12 190 cm?1, and De = 360 cm?1. 相似文献