34,381 research outputs found
Convergence of a cell-centered finite volume discretization for linear elasticity
We show convergence of a cell-centered finite volume discretization for
linear elasticity. The discretization, termed the MPSA method, was recently
proposed in the context of geological applications, where cell-centered
variables are often preferred. Our analysis utilizes a hybrid variational
formulation, which has previously been used to analyze finite volume
discretizations for the scalar diffusion equation. The current analysis
deviates significantly from previous in three respects. First, additional
stabilization leads to a more complex saddle-point problem. Secondly, a
discrete Korn's inequality has to be established for the global discretization.
Finally, robustness with respect to the Poisson ratio is analyzed. The
stability and convergence results presented herein provide the first rigorous
justification of the applicability of cell-centered finite volume methods to
problems in linear elasticity
Stable cell-centered finite volume discretization for Biot equations
In this paper we discuss a new discretization for the Biot equations. The
discretization treats the coupled system of deformation and flow directly, as
opposed to combining discretizations for the two separate sub-problems. The
coupled discretization has the following key properties, the combination of
which is novel: 1) The variables for the pressure and displacement are
co-located, and are as sparse as possible (e.g. one displacement vector and one
scalar pressure per cell center). 2) With locally computable restrictions on
grid types, the discretization is stable with respect to the limits of
incompressible fluid and small time-steps. 3) No artificial stabilization term
has been introduced. Furthermore, due to the finite volume structure embedded
in the discretization, explicit local expressions for both momentum-balancing
forces as well as mass-conservative fluid fluxes are available.
We prove stability of the proposed method with respect to all relevant
limits. Together with consistency, this proves convergence of the method.
Finally, we give numerical examples verifying both the analysis and convergence
of the method
Analysis of Human Spleen Contamination
Besides carbon, oxygen and nitrogen, numerous other elements and their compounds are significant in the body of humans and other animals. Accumulation of some elements and their compounds is recognized by clinical and biochemical evaluation. The physical-chemical properties and topical characteristics of elements in tissues may play a crucial role in evaluation their effect on human body. The ^57^Fe Mössbauer measurement was used for evaluation of iron–oxide biomagnetic nanoparticles composition and properties. Absorption spectra of the powdered spleen recorded at 77K and 300K were measured and subsequently analyzed. From fitted data it is possible to obtain material composition as well as discuss the mean particle size (received from decrease hyperfine field in comparison with bulk value)
A spatial version of the It\^{o}-Stratonovich correction
We consider a class of stochastic PDEs of Burgers type in spatial dimension
1, driven by space-time white noise. Even though it is well known that these
equations are well posed, it turns out that if one performs a spatial
discretization of the nonlinearity in the "wrong" way, then the sequence of
approximate equations does converge to a limit, but this limit exhibits an
additional correction term. This correction term is proportional to the local
quadratic cross-variation (in space) of the gradient of the conserved quantity
with the solution itself. This can be understood as a consequence of the fact
that for any fixed time, the law of the solution is locally equivalent to
Wiener measure, where space plays the role of time. In this sense, the
correction term is similar to the usual It\^{o}-Stratonovich correction term
that arises when one considers different temporal discretizations of stochastic
ODEs.Comment: Published in at http://dx.doi.org/10.1214/11-AOP662 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Integral equation for spin dependent unintegrated parton distributions incorporating double ln^2(1/x) effects at low x
In this paper we derive an integral equation for the evolution of
unintegrated (longitudinally) polarized quark and gluon parton distributions.
The conventional CCFM framework is extended at small x in order to incorporate
the QCD expectations concerning the double ln^2(1/x) resummation at low x for
the integrated distributions. Complete Altarelli-Parisi splitting functions are
included, that makes the formalism compatible with the LO Altarelli-Parisi
evolution at large and moderately small values of x. The obtained modified
polarized CCFM equation is shown to be partially diagonalized by the
Fourier-Bessel transform. Results of the numerical solution for this modified
CCFM equation for the non-singlet quark distributions are presented.Comment: 24 pages, 3 figures, LaTeX, some discussion added, none of the
results changed, version to appear in Phys. Rev.
On approximate pseudo-maximum likelihood estimation for LARCH-processes
Linear ARCH (LARCH) processes were introduced by Robinson [J. Econometrics 47
(1991) 67--84] to model long-range dependence in volatility and leverage. Basic
theoretical properties of LARCH processes have been investigated in the recent
literature. However, there is a lack of estimation methods and corresponding
asymptotic theory. In this paper, we consider estimation of the dependence
parameters for LARCH processes with non-summable hyperbolically decaying
coefficients. Asymptotic limit theorems are derived. A central limit theorem
with -rate of convergence holds for an approximate conditional
pseudo-maximum likelihood estimator. To obtain a computable version that
includes observed values only, a further approximation is required. The
computable estimator is again asymptotically normal, however with a rate of
convergence that is slower than Comment: Published in at http://dx.doi.org/10.3150/09-BEJ189 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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