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41.
Amnon Aharony 《Journal of statistical physics》1984,34(5-6):931-939
Both the infinite cluster and its backbone are self-similar at the percolation threshold,p
c
. This self-similarity also holds at concentrationsp nearp
c
, for length scalesL which are smaller than the percolation connectedness length,. ForL<, the number of bonds on the infinite cluster scales asL
D
, where the fractal dimensionalityD is equal to(d-/v). Geometrical fractal models, which imitate the backbone and on which physical models are exactly solvable, are presented. Above six dimensions, one has D=4 and an additional scaling length must be included. The effects of the geometrical structure of the backbone on magnetic spin correlations and on diffusion at percolation are also discussed. 相似文献
42.
The lattice Boltzmann method (LBM) is coupled with the multiple-relaxation-time (MRT) collision model and the three-dimensional 19-discrete-velocity (D3Q19) model to resolve intermittent behaviors on small scales in isotropic turbulent flows. The high-order scaling exponents of the velocity structure functions, the probability distribution functions of Lagrangian accelerations, and the local energy dissipation rates are investigated. The self-similarity of the space-time velocity structure functions is explored using the extended self-similarity (ESS) method, which was originally developed for velocity spatial structure functions. The scaling exponents of spatial structure functions at up to ten orders are consistent with the experimental measurements and theoretical results, implying that the LBM can accurately resolve the intermittent behaviors. This validation provides a solid basis for using the LBM to study more complex processes that are sensitive to small scales in turbulent flows, such as the relative dispersion of pollutants and mesoscale structures of preferential concentration of heavy particles suspended in turbulent flows. 相似文献
43.
M. Baurngaertel M. E. De Rosa J. Machado M. Masse Prof. H. H. Winter 《Rheologica Acta》1992,31(1):75-82
The relaxation behavior of polymers with long linear flexible chains of uniform length has been investigated by means of dynamic mechanical analysis. The relaxation time spectrum (H()) follows a scaling relationship with two self-similar regions, one for the entanglement and terminal zone, and a second one for the transition to the glass. This can be described in its most general form (termed BSW spectrum) as H() = H
e
ne
+ H
g
–
n
g
for < max and H() = 0 for max < , where H
e
, H
g
, n
e
, n
g
are material constants and max is the molecular weight dependent cut-off of the self-similar behavior. In this study, the dynamic mechanical response has been measured and analyzed for four highly entangled, nearly monodisperse polybutadienes with molecular weights from 20000 to 200000. The data are well represented by the BSW spectrum with scaling exponents of n
e
= 0.23 and n
g
= 0.67. The values of the exponents obtained in this work are about the same as those found for polystyrene samples in a previous study. This suggests that the two types of polymers have a similar relaxation pattern. However, at this point further refinement of the experiments is needed before being able to draw definite conclusions about the universality of the exponents.Dedicated to Professor Arthur S. Lodge on the occasion of his 70th birthday and his retirement from the University of Wisconsin. 相似文献
44.
Large eddy simulation (LES) is coupled with a turbine model to study the structure of the wake behind a vertical-axis wind turbine (VAWT). In the simulations, a tuning-free anisotropic minimum dissipation model is used to parameterise the subfilter stress tensor, while the turbine-induced forces are modelled with an actuator line technique. The LES framework is first validated in the simulation of the wake behind a model straight-bladed VAWT placed in the water channel and then used to study the wake structure downwind of a full-scale VAWT sited in the atmospheric boundary layer. In particular, the self-similarity of the wake is examined, and it is found that the wake velocity deficit can be well characterised by a two-dimensional multivariate Gaussian distribution. By assuming a self-similar Gaussian distribution of the velocity deficit, and applying mass and momentum conservation, an analytical model is developed and tested to predict the maximum velocity deficit downwind of the turbine. Also, a simple parameterisation of VAWTs for LES with very coarse grid resolutions is proposed, in which the turbine is modelled as a rectangular porous plate with the same thrust coefficient. The simulation results show that, after some downwind distance (x/D ≈ 6), both actuator line and rectangular porous plate models have similar predictions for the mean velocity deficit. These results are of particular importance in simulations of large wind farms where, due to the coarse spatial resolution, the flow around individual VAWTs is not resolved. 相似文献
45.
In TEXTOR the long-range time dependence of edge plasma fluctuations has been investigated. The results indicate that the tail of the autocorrelation function decays as a power law for time lags longer than the local decorrelation time. The frequency spectra of the fluctuations show similar features to those obtained in "sandpile" models. Using rescaled range (R/S) analysis techniques the self-similarity parameters have been estimated for the potential fluctuation data detected by Langmuir probes. The results show that the Hurst exponents are well above 0.5 over the self-similarity range at all the measured radial locations. All these facts reveal the self-similar character of the electrostatic fluctuations at the plasma edge of TEXTOR, consistent with plasma transport as characterized by self-organized criticality (SOC). Furthermore, we have analyzed in this respect discharges in which an edge transport barrier was created by means of edge biasing, hitherto limited to floating potential measurements in the scrape off layer outside the barrier region. The results show a decrease of fluctuating amplitudes, a reduction of decorrelation time of local turbulence and, surprisingly, a concomitant increase of the Hurst exponent. This result implies that the mechanisms governing the decorrelation of local turbulence may differ from those governing the decorrelation of SOC transport events. 相似文献
47.
K. R. Krishnan 《Queueing Systems》1996,22(3-4):277-285
Recent Bellcore studies have shown that high-speed data traffic exhibits long-range dependence, characterized byH>0.5, whereH is the Hurst parameter of the traffic. In the wake of those studies, there has been much interest in developing tractable analytical models for traffic with long-range dependence, for use in performance evaluation and traffic engineering. Norros has used a traffic model known as Fractional Brownian Motion (FBM) to derive several analytical results on the behavior of a queue subject to such an arrival process. In this paper, we derive a new class of results, also based on the FBM model, which reveal rather curious and unexpected crossover properties of the Hurst parameter of the traffic, as regards its effect on the behavior of queues. These results, together with those of Norros, serve to enhance our understanding of the significance of the Hurst parameterH for traffic engineering. In particular, Krishnan and Meempat have used the crossover property derived here to explain, in part, a gap that existed between the results of two sets of Bellcore studies, one casting doubt on the usefulness of Markovian traffic models and methods whenH>0.5, and the other furnishing an example of successful traffic engineering with Markovian methods for traffic known to haveH>0.5. The results derived here can be used to obtainconservative estimates of the multiplexing gains achieved when independent traffic sources with the same Hurst parameterH are multiplexed for combined transmission. In turn, such estimates yield guidelines for the engineering of ATM links that are subject to traffic with long-range dependence. 相似文献
48.
We provide general conditions for normalized, time-scaled stochastic integrals of independently scattered, Lévy random measures
to converge to a limit. These integrals appear in many applied problems, for example, in connection to models for Internet
traffic, where both large scale and small scale asymptotics are considered. Our result is a handy tool for checking such convergence.
Numerous examples are provided as illustration. Somewhat surprisingly, there are examples where rescaling towards large times
scales yields a Gaussian limit and where rescaling towards small time scales yields an infinite variance stable limit, and
there are examples where the opposite occurs: a Gaussian limit appears when one converges towards small time scales and an
infinite variance stable limit occurs when one converges towards large time scales.
相似文献
49.
50.
We define and prove the existence of a fractional Brownian motion indexed by a collection of closed subsets of a measure space.
This process is a generalization of the set-indexed Brownian motion, when the condition of independance is relaxed. Relations
with the Lévy fractional Brownian motion and with the fractional Brownian sheet are studied. We prove stationarity of the
increments and a property of self-similarity with respect to the action of solid motions. Moreover, we show that there no
“really nice” set indexed fractional Brownian motion other than set-indexed Brownian motion. Finally, behavior of the set-indexed
fractional Brownian motion along increasing paths is analysed.
相似文献