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51.
For three‐dimensional flows with one inhomogeneous spatial coordinate and two periodic directions, the Karhunen–Loeve procedure is typically formulated as a spatial eigenvalue problem. This is normally referred to as the direct method (DM). Here we derive an equivalent formulation in which the eigenvalue problem is formulated in the temporal coordinate. It is shown that this so‐called method of snapshots (MOS) has some numerical advantages when compared to the DM. In particular, the MOS can be formulated purely as a matrix composed of scalars, thus avoiding the need to construct a matrix of matrices as in the DM. In addition, the MOS avoids the need for so‐called weight functions, which emerge in the DM as a result of the non‐uniform grid typically employed in the inhomogeneous direction. The avoidance of such weight functions, which may exhibit singular behaviour, guarantees satisfaction of the boundary conditions. The MOS is applied to data sets recently obtained from the direct simulation of turbulence in a channel in which viscoelasticity is imparted to the fluid using a Giesekus model. The analysis reveals a steep drop in the dimensionality of the turbulence as viscoelasticity is increased. This is consistent with the results that have been obtained with other viscoelastic models, thus revealing an essential generic feature of polymer‐induced drag reduced turbulent flows. Published in 2006 by John Wiley & Sons, Ltd. 相似文献
52.
This is a review paper of basic knowledge and recent advances in the area of spatial solitons in Kerr and Kerr-like media. We consider spatial bright and dark solitons, solitons in waveguide geometries, optical bullets, vortex solitons and, briefly, dissipative cases. In our treatment, we use a Hamiltonian approach when considering stability issues. 相似文献
53.
Flowing and static gas-phase samples of HNO3 in O2 and N2 were analyzed by long-path ultraviolet/visible (UV/VIS) spectroscopy to reveal the presence of both NO2 and NO3, the concentrations of which were calculated using differential absorption cross sections. NO2 is produced predominantly by the heterogeneous decomposition of HNO3, whereas NO3 is generated in the gas phase by the thermal decomposition of N2O5, a product of the self-disproportionation of liquid HNO3. © 1993 John Wiley & Sons, Inc. 相似文献
54.
N. V. Pratsevityi 《Ukrainian Mathematical Journal》1998,50(8):1233-1241
We study the fractal properties of a convolution of two Cantor distributions. By using the method of characteristic functions,
we establish sufficient conditions for the singularity of the convolution of an arbitrary finite number of distributions of
random variables with independent s-adic digits. We disprove the hypothesis on the validity of a “singular analog” of the Jessen-Wintner theorem for anomalously
fractal distributions.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 8, pp. 1082–1088, August, 1998.
The present work was partially supported by the International Soros Program of Educational Support in Exact Sciences (grant
No. APU 061086). 相似文献
55.
The gauge compensation fields induced by the differential operators of the Stueckelberg-Schrödinger equation are discussed, as well as the relation between these fields and the standard Maxwell fields; An action is constructed and the second quantization of the fields carried out using a constraint procedure. The properties of the second quantized matter fields are discussed. 相似文献
56.
57.
A. N. Urumbaev 《Ukrainian Mathematical Journal》1997,49(2):320-326
We show that the modified method for finite-dimensional approximation of solutions of Fredholm integral equations of the first
kind presented in this paper is more economical than traditional methods for finite-dimensional approximation.
Institute of Mathematies, Ukrainian Academy of Science, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49,
No. 2, pp. 289–295, February, 1997. 相似文献
58.
A numerical study of confined jets in a cylindrical duct is carried out to examine the performance of two recently proposed turbulence models: an RNG-based K-? model and a realizable Reynolds stress algebraic equation model. The former is of the same form as the standard K-? model but has different model coefficients. The latter uses an explicit quadratic stress-strain relationship to model the turbulent stresses and is capable of ensuring the positivity of each turbulent normal stress. The flow considered involves recirculation with unfixed separation and reatachment points and severe adverse pressure gradients, thereby providing a valuable test of the predictive capability of the models for complex flows. Calculations are performed with a finite volume procedure. Numerical credibility of the solutions is ensured by using second-order-accurate differencing schemes and sufficiently fine grids. Calculations with the standard K-? model are also made for comparison. Detailed comparisons with experiments show that the realizable Reynolds stress algebraic equation model consistently works better than does the standard K-? model in capturing the essential flow features, while the RNG-based K-? model does not seem to give improvements over the standard K-? model under the flow conditions considered. 相似文献
59.
Modeling and numerical simulations of the convective flows induced by the vibration of the monocrystal during crystal growth have been performed for two configurations simulating the Cz and FZ methods. This permitted to emphasize the role of different vibrational mechanisms in the formation of the average flows. It is shown that an appropriate combination of these mechanisms can be used to counteract the usual convective flows (buoyancy- and/or thermocapillary-driven) inherent to crystal growth processes from the liquid phase. While vibrational convection is rather complex due to these identified mechanisms, the new modeling used in the present paper opens up very promising perspectives to efficiently control heat and mass transfer during real industrial applications of crystal growth from the liquid phase. 相似文献
60.
H.-J. Sue E. I. Garcia-Meitin N. A. Orchard 《Journal of Polymer Science.Polymer Physics》1993,31(5):595-608
The fracture behavior of a core-shell rubber (CSR) modified epoxy is investigated using both fracture mechanics and microscopy tools. The CSR-modified epoxy is found to be toughened via numerous line-array cavitations of the CSR particles, followed by plastic flow of the epoxy matrix. The toughening effect via the above craze-like damage process is found to be as effective as that of the well-known widespread rubber cavitation/matrix shear yielding mechanisms. The conditions for triggering the craze-like damage appear to be both stress state and rubber concentration dependent. The type of rubber tougheners utilized also plays a critical role in triggering this rather unusual craze-like damage in epoxy systems. © 1993 John Wiley & Sons, Inc. 相似文献