The finite-difference method is a numerical technique for obtaining approximate solutions to differential equations. The main
objective of the present study is to give a new aspect to the finite-difference method by using a variational derivative.
By applying this formulation, accurate values of the buckling loads of beams and frames with various end supports are obtained.
The performance of this formulation is verified by comparison with numerical examples in the literature
__________
Published in Prikladnaya Mekhanika, Vol. 41, No. 7, pp. 139–144, July 2005. 相似文献
For an arbitrary poset H and measure ρ on H × R (where R is the real axis), we construct a monotone decreasing stochastic field ηρ and compute its finite-dimensional distributions. In the case where H is a Λ-semilattice and the measure ρ satisfies additional conditions, we compute various characteristics of the field ηρ such as the expectation of the field value at a point, variance of the field value at a point, and correlation function of the field. The described construction of random fields gives a new method for constructing positive definite functions on posets. Bibliography: 6 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 301, 2003, pp. 92–143. 相似文献
The Ac behaviour of PLZT 6/80/20 ferroelectric ceramics was analyzed around and above the phase transition. Two relaxation processes are identified, showing that the so-called ‘universal relaxation law’ holds for the ceramics. A critical point in the values of the Ac conductivity, around the temperature corresponding to the maximum of the dielectric losses, is observed below the transition temperature due to the relaxor behaviour. The frequency dependence of the Ac conductivity at various temperatures and the hysteresis loops show classical relaxor behaviour with a diffuse phase transition. 相似文献
3-Hydroxy-4-hydroxymethyl pyrrolidin-2-ones, easily prepared from the Baylis–Hillman adduct 1-ethyl-4-methyl-2-hydroxy-3-methylenebutanedioate, are useful intermediates in the synthesis of bioactive compounds. In order to understand the mechanism involved in this reaction, vibrational and Montecarlo molecular mechanics conformational analysis on 1-ethyl-4-methyl-2-hydroxy-3-methylenebutanedioate were carried out, confirming the existence of a low energy intramolecular H-bonded five-member ring. 相似文献
The title compound [systematic name: 8‐chloro‐11‐(piperidin‐4‐ylidene)‐6,11‐dihydro‐5H‐benzo[4,5]cyclohepta[2,1‐b]pyridine], C19H19ClN2, was crystallized from ethyl acetate. The interesting feature of the reported structure is that it does not contain any strong hydrogen bonds, although the molecule contains a secondary NH group, which is a good hydrogen‐bond donor. 相似文献
We introduce a new construction algorithm for digital nets for integration in certain weighted tensor product Hilbert spaces. The first weighted Hilbert space we consider is based on Walsh functions. Dick and Pillichshammer calculated the worst-case error for integration using digital nets for this space. Here we extend this result to a special construction method for digital nets based on polynomials over finite fields. This result allows us to find polynomials which yield a small worst-case error by computer search. We prove an upper bound on the worst-case error for digital nets obtained by such a search algorithm which shows that the convergence rate is best possible and that strong tractability holds under some condition on the weights.
We extend the results for the weighted Hilbert space based on Walsh functions to weighted Sobolev spaces. In this case we use randomly digitally shifted digital nets. The construction principle is the same as before, only the worst-case error is slightly different. Again digital nets obtained from our search algorithm yield a worst-case error achieving the optimal rate of convergence and as before strong tractability holds under some condition on the weights. These results show that such a construction of digital nets yields the until now best known results of this kind and that our construction methods are comparable to the construction methods known for lattice rules.
We conclude the article with numerical results comparing the expected worst-case error for randomly digitally shifted digital nets with those for randomly shifted lattice rules.
Mo2Ni3Si/NiSi metal silicide composite coatings with a fine microstructure consisting of Mo2Ni3Si primary dendrites and the interdendritic Mo2Ni3Si/NiSi eutectics were fabricated on austenitic stainless steel AISI 321 by laser cladding process. Small amplitude reciprocating sliding wear resistance of the coatings is evaluated as functions of normal load and slip amplitude and the wear mechanisms were discussed based on worn surface morphology observations. Results showed that the Mo2Ni3Si/NiSi coatings have excellent small amplitude reciprocating sliding wear resistance. 相似文献
Some polythermal sections of the Ni-Bi-Se system have been investigated by DTA, X-ray powder diffraction, microstructural analysis, and microhardness measurements. The liquidus surface has been constructed for this system. The compounds NiBi2Se4 and Ni3Bi2Se2 are formed by dystectic reactions and melt at 1088 and 980 K, respectively. The regions of primary and joint phase crystallization have been determined. A commutation of Bi2Se3-based thermoelements with a metal nickel bus-bar has been proposed. 相似文献
Catalytic properties of silica-supported heteropolyacids (HPA) in a mechanical mixture with reduced Me-Ce oxides (Me = Ni,
Pd) in n-hexane isomerization are studied. The role of each component of the mixed oxides (Ce and, typically, Ni and Pd) and their
optimum content has been illuminated: cerium is not only beneficial for eliminating or preventing coke deposition but is also
effective for maintaining the Keggin structure of the highly-organized HPA during the reaction and probably allows a better
dispersion of the second metal species. Nickel and palladium, present as Ni0 and Pd0, reinforce the activation of the alkane, which is difficult to obtain by means of a direct attack by an acid, and, thus,
enhance noticeably the activity of the catalyst. The best mechanical mixtures are obtained with 30–70 wt % NiCeO-HPW/SiO2 and 50–50 wt % Pd0.1CeO-HPW/SiO2. These mixtures have the highest efficiency for a Ni/(Ni + W) atomic ratio of 0.66 and a Pd/(Pd + W) ratio of 0.40, respectively.
Finally, the conversion of n-hexane is in the order HPW > HSiW > HBW, which seems to be consistent with the order of their acid strength as per the literature,
but the isomerization selectivity appears to be slightly higher on HSiW.
Published in Russian in Kinetika i Kataliz, 2006, Vol. 47, No. 1, pp. 24–28.
The text was submitted by the authors in English. 相似文献
We study the motion of envelope solitons on anharmonic atomic chains in the presence of dissipation and thermal fluctuations. We consider the continuum limit of the discrete system and apply an adiabatic perturbation theory which yields a system of stochastic integro-differential equations for the collective variables of the ansatz for the perturbed envelope soliton. We derive the Fokker-Planck equation of this system and search for a statistically equivalent system of Langevin equations, which shares the same Fokker-Planck equation. We undertake an analytical analysis of the Langevin system and derive an expression for the variance of the soliton position Var[xs] which predicts a stronger than linear time dependence of Var[xs] (superdiffusion). We compare these results with simulations for the discrete system and find they agree well. We refer to recent studies where the diffusion of pulse solitons were found to exhibit a superdiffusive behaviour on longer time scales.Received: 28 June 2004, Published online: 26 November 2004PACS:
05.10.Gg Stochastic analysis methods - 05.45.Yv Solitons - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 05.50. + q Lattice theory and statistics 相似文献