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161.
We studied the low speed fracture regime (10−4-10−9 m s−1) in different glassy materials (soda-lime glass, glass ceramics) with variable but controlled length scale of heterogeneity. The chosen mechanical system enabled us to work in pure mode I (tensile) and at a fixed load on double cleavage drilled compression specimen. The internal residual stresses of studied samples were carefully relaxed by appropriate thermal treatment. By means of optical and atomic force microscopy techniques fracture surfaces have been examined. We have shown for the first time that the crack front line underwent an out-of-plane oscillating behavior as a result of a reproducible sequence of instabilities. The wavelength of such a phenomenon is in the micrometer range and its amplitude in the nanometer range. These features were observed for different glassy materials providing that a typical length scale characterizing internal heterogeneities was lower than a threshold limit estimated to few nanometers. This effect is the first clear experimental evidence of crack path instabilities in the low speed regime in a uniaxial loading experiment. This phenomenon has been interpreted by referring to the stability criterion for a straight crack propagation as presented by Adda-Bedia et al. [Phys. Rev. Lett. 76 (1996) 1497]. 相似文献
162.
163.
164.
165.
Homogeneously prepared tosylcelluloses (TC) with degrees of substitution (DS) of DSTos 0.1–1.8 were used as intermediates for the synthesis of methylaminocelluloses (MAC) by nucleophilic substitution with methylamine. TC with DSTos up to 1.1 were shown to be valuable intermediates for selective synthesis of MAC with DSMA varying from 0.1 to approximately 1. No nucleophilic substitution was observed at higher DSTos. At the chosen reaction conditions (60 °C, 48 h) residual tosyl moieties remained unchanged and little hydrolysis took place. The samples obtained were characterized by means of elemental analysis, FTIR and 13C CP/MAS NMR spectroscopy. 13C CP/MAS NMR spectroscopy was found to be an efficient tool for quantification of DSMA. Furthermore, the swelling behaviour in water was investigated and preliminary tests concerning the bilirubin adsorption capacity of MAC were carried out. 相似文献
166.
Matthew D. Horton 《Linear algebra and its applications》2007,425(1):130-142
After defining and exploring some of the properties of Ihara zeta functions of digraphs, we improve upon Kotani and Sunada’s bounds on the poles of Ihara zeta functions of undirected graphs by considering digraphs whose adjacency matrices are directed edge matrices. 相似文献
167.
We study a generalized Crank–Nicolson scheme for the time discretization of a fractional wave equation, in combination with
a space discretization by linear finite elements. The scheme uses a non-uniform grid in time to compensate for the singular
behaviour of the exact solution at t = 0. With appropriate assumptions on the data and assuming that the spatial domain is convex or smooth, we show that the
error is of order k
2 + h
2, where k and h are the parameters for the time and space meshes, respectively. 相似文献
168.
A new preconditioned conjugate gradient (PCG)-based domain decomposition method is given for the solution of linear equations
arising in the finite element method applied to the elliptic Neumann problem. The novelty of the proposed method is in the
recommended preconditioner which is constructed by using cyclic matrix. The resulting preconditioned algorithms are well suited
to parallel computation. 相似文献
169.
Summary.
This paper is concerned with a high order convergent
discretization for the semilinear reaction-diffusion problem:
,
for , subject to ,
where .
We assume that on
, which
guarantees uniqueness of a solution to
the problem. Asymptotic properties of
this solution are discussed. We consider a
polynomial-based three-point
difference scheme on a simple piecewise
equidistant mesh of Shishkin type.
Existence and local uniqueness of a solution
to the scheme are analysed. We
prove that the scheme is almost fourth order
accurate in the discrete maximum
norm, uniformly in the perturbation parameter
. We present numerical
results in support of this result.
Received February 25, 1994 相似文献
170.
A conjecture of Toft [17] asserts that any 4-critical graph (or equivalently, every 4-chromatic graph) contains a fully odd subdivision ofK
4. We show that if a graphG has a degree three nodev such thatG-v is 3-colourable, then eitherG is 3-colourable or it contains a fully oddK
4. This resolves Toft's conjecture in the special case where a 4-critical graph has a degree three node, which is in turn used to prove the conjecture for line-graphs. The proof is constructive and yields a polynomial algorithm which given a 3-degenerate graph either finds a 3-colouring or exhibits a subgraph that is a fully odd subdivision ofK
4. (A graph is 3-degenerate if every subgraph has some node of degree at most three.) 相似文献