Summary The convergence of semi-discrete and discrete linear approximation schemes is analysed for nonlinear degenerate parabolic systems of porous medium type. The enthalpy formulation and variational technique are used. The semi-discretization used reduces the original parabolic P.D.E. to linear elliptic P.D.E. The algebraic correction arising from nonlinearities is treated by Newton-like iterations in finite steps. Some numerical experiments are discussed and compared with the analytical solutions.Supported by the Alexander von Humboldt-Foundation in 1989, and by SFB 123, University Heidelberg 相似文献
Three new complexes with 3,6‐dichlorobenzene‐1,2‐dithiol (bdtCl2), namely methyltriphenylphosphonium bis(3,6‐dichlorobenzene‐1,2‐dithiolato‐κ2S,S′)cobaltate(1−), (C19H18P)[Co(C6H2Cl2S2)2], (I), bis(methyltriphenylphosphonium) bis(3,6‐dichlorobenzene‐1,2‐dithiolato‐κ2S,S′)cuprate(2−) dimethyl sulfoxide disolvate, (C19H18P)2[Cu(C6H2Cl2S2)2]·2C2H6OS, (II), and methyltriphenylphosphonium bis(3,6‐dichlorobenzene‐1,2‐dithiolato‐κ2S,S′)cuprate(1−), (C19H18P)[Cu(C6H2Cl2S2)2], (III), have been synthesized and characterized by single‐crystal X‐ray diffraction. The X‐ray structure analyses of all three complexes confirm that the four donor S atoms form a slightly distorted square‐planar coordination arrangement around the central metal atom. An interesting finding for both the CuII and CuIII complexes, i.e. (II) and (III), respectively, is that the coordination polyhedra are principally the same and differ only slightly with respect to the interatomic distances. 相似文献
This study is concerned with the investigation of the impact of heat flux on the fire hazard and the effective heat of combustion of sunflower seed hull pellets. Pellets produced by pressing common sunflower seed hulls (Helianthus annuus L.) were investigated. The samples were dried on water content of 0 mass% at a temperature of 103 ± 2 °C. The fire hazard and the heat of combustion have been determined via the cone calorimeter and by the testing procedure per ISO 5660-1:2015 at three heat fluxes (25, 35 and 50 kW m−2). The peak heat release rate increases with the increasing of the heat flux from 446 (at a heat flux of 25 kW m−2) to 601 kW m−2 (at a heat flux of 50 kW m−2). The carbon monoxide yield lies in the interval from 82.50 (at a heat flux of 25 kW m−2) to 154.15 g kg−1 (at a heat flux of 50 kW m−2). The effective heat of combustion decreases with the increasing of the heat flux from 15.84 (at a heat flux of 25 kW m−2) to 14.58 MJ kg−1 (at a heat flux of 50 kW m−2).
A pure stress formulation of linear nonhomogeneous anisotropic elastodynamics with continuously distributed defects (EcDD) is proposed, and well known solutions of ECDD corresponding to stationary and moving concentrated plastic fields in an infinite body are recovered by direct integration of the stress field equation. A new interpretation of the solutions is given. 相似文献
A new scheme that combines conventional matrix diagonalization with the recently proposed diagonalization-free algorithm has been developed to obtain the density matrix for the next self-consistent-field iteration from the Fock matrix of the current iteration. In this manner, the advantages of the two methods are combined. The more rapid convergence of the diagonalization-free algorithm for density matrices rather close to self consistence and the more robust convergence of the conventional matrix diagonalization further away from self-consistence. The scheme has been implemented in the one- and two-component self-consistent-field procedures in the program system TURBOMOLE. The number of iterations is typically reduced by about 10%, but savings are usually much larger for slowly converging cases. 相似文献
Steady state analysis of a combined hybrid process consisting of a reactive distillation column, pervaporation unit, and a
distillation column is presented. This process configuration was first presented by Steinigeweg and Gmehling (2004) for the
transesterification of methyl acetate and butanol to butyl acetate and methanol. This system is characteristic for its low
reaction rate and complex phase equilibrium. Steinigeweg and Gmehling (2004) have shown that the combination of reactive distillation
and pervaporation is favourable since conversions close to 100 % can be reached with a reasonable size of the reactive section
in the reactive distillation column. The aim of this paper is to show that although high conversion can be achieved, very
complicated steady state behaviour must be expected. The presented analysis is based on mathematical modelling of a process
unit, where the steady-state analysis, including continuation and bifurcation analyses, was used. Multiple steady states were
predicted for the studied system; three steady states with conversions higher than 98 %. However, not all predicted steady
states met the maximal allowed temperature condition in the reactive section (catalyst maximal operation temperature of 393
K). The presence of multiple steady states reduces the operability and controllability of the reactive distillation column
during its start-up and during the occurrence of any variation of operating parameters because the system can be shifted from
one steady state to another one (concurrent exceeding the maximal allowed temperature) with unwanted consequences, e.g. production
loss. Therefore, design and subsequent operation of such a complicated system is an ambitious task requiring knowledge of
any possible system behaviour. 相似文献
Polymeric salicylatocopper(II) complexes of unusual composition [C u(X‐ sal)2( μ‐denia)(H2O)]n [denia = diethylnicotinamide, and X‐sal = 5‐methylsalicylate ( 1 ), 3‐methylsalicylate ( 2 ), 4‐methoxysalicylate ( 3 ), 3,5‐dichlorosalicylate ( 4 ) and 3,5‐dibromosalicylate ( 5 )] were synthesized and characterized. Magnetic measurements were performed in the temperature range 1.8–300 K. The structural unit of all complexes consists of a CuII atom, which is monodentately coordinated by the pair of X‐salicylate anions in trans positions. Water and the diethylnicotinamide ligand occupy the other two basal plane positions of the tetragonal pyramid. The axial positions are occupied by a diethylnicotinamide oxygen atom of neighboring structural units, thus forming a spiral polymeric structure parallel to b axis. Magnetic measurements showed that all complexes 1 – 5 exhibit a susceptibility maximum at about 6–8 K. The obtained data fit to Bleaney–Bowers equation gave singlet‐triplet energy gaps 2J = –8.60 cm–1 for 1 , 2J = –6.57 cm–1 for 2 , 2J = –8.57 cm–1 for 3 , 2J = –6.82 cm–1 for 4 , and 2J = –6.45 cm–1 for 5 . The supramolecular structure based on hydrogen bonds [described by supramolecular synthons R22(10) and R22(12)] is the pathway for antiferromagnetic interactions of the magnetically coupled pairs of copper atoms of neighboring chains within the 2D supramolecular layers. The results of the magnetic measurements suggest involvement of the COO groups in the magnetic interaction pathway for all five complexes. 相似文献
Synthesis of trihydroxylated pyrrolizidines, the enantiomer of 2-epihyacinthacine A2 and indolizidine analogues of the natural alkaloids is reported. The key step of these syntheses is the stereoselective samarium diodide-induced coupling of the chiral nitrone prepared from d-ribose with methyl acrylate. The nitrone derived from d-ribose possessing C2/C3 syn configuration reacted with methyl acrylate in the presence of samarium diiodide in excellent yield and diastereoselectivity, with only the anti-diastereomer being detected. 相似文献