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Shock waves, dead-zones and particle-free regions in rapid granular free surface flows
Get PDFShock waves, dead zones and particle-free regions form when a thin surface avalanche of granular material flows around an obstacle or over a change in the bed topography. Understanding and modelling these flows is of considerable practical interest for industrial processes, as well as for the design of defences to protect buildings, structures and people from snow avalanches, debris flows and rockfalls. These flow phenomena also yield useful constitutive information that can be used to improve existing avalanche models. In this paper a simple hydraulic theory, first suggested in the Russian literature, is generalized to model quasi-two-dimensional flows around obstacles. Exact and numerical solutions are then compared with laboratory experiments. These indicate that the theory is adequate to quantitatively describe the formation of normal shocks, oblique shocks, dead zones and granular vacua. Such features are generated by the flow around a pyramidal obstacle, which is typical of some of the defensive structures in use today
Modelling the adaptive permeability of porcine iliac arteries to acute changes in mural shear
No full textThe hypothesis that much of the uptake of macromolecules by the vascular wall takes place while the endothelial lining is adapting to changes in its hemodynamic environment is being tested by a series of in vivo measurements of the uptake of Evans-blue-dye-labeled albumin by porcine iliac arteries subjected to acute changes in blood flow. The uptake data are interpreted through an ad hoc model of the dynamic permeability response that is proposed to accompany alterations in mural shear.The model is able to correlate, with a single set of parameters, the vascular response to a variety of experimental protocols, including sustained step increases and decreases in shear, and alternations in shear of various periods. The best-fit parameters of the model suggest that the adaptive response to an increase in shear proceeds with a latency of sim 1.5 min and a time constant of sim 90 min that is substantially shorter than the response to a decrease in shear. © 2003 Biomedical Engineering Society.
PAC2003: 8710+e, 8719Rr, 8719U
Scaling of the turbulence transition threshold in a pipe
No full textWe report the results of an experimental investigation of the transition to turbulence in a pipe over approximately an order of magnitude range in the Reynolds number Re. A novel scaling law is uncovered using a systematic experimental procedure which permits contact to be made with modern theoretical thinking. The principal result we uncover is a scaling law which indicates that the amplitude of perturbation required to cause transition scales as O(Re–1)
On modelling mean-covariance structures in longitudinal studies
No full textWe exploit a reparameterisation of the marginal covariance matrix arising in longitudinal studies (Pourahmadi, 1999, 2000) to model, jointly, the mean and covariance structures in terms of three polynomial functions of time.By reanalysing Kenward's (1987) cattle data, we compare model selection procedures based on regressogram estimation with these based on a global search of the model space. Using a BIC-based model selection criterion to identify the optimum degree triple of the three polynomials, we show that the use of a saturated mean model is not optimal and explain why regressogram-based model estimation may be misleading. We also suggest a new computational method for finding the global optimum based on a criterion involving three pairwise saturated profile likelihoods
Limit Behavior of the "Horizontal-Vertical" Random Walk and Some Extensions of the Donsker-Prokhorov Invariance Principle
Get PDFWe consider a two-dimensional random walk that moves in the horizontal direction on the half-plane {y>x} and in the vertical direction on the half-plane {y ≤ x}. The limit behavior (as the time interval between two steps and the size of each step tend to zero) of this "horizontal-vertical" random walk is investigated. In order to solve this problem, we prove an extension of the Donsker—Prokhorov invariance principle. The extension states that the discrete-time stochastic integrals with respect to the appropriately renormalized one-dimensional random walk converge in distribution to the corresponding stochastic integral with respect to a Brownian motion. This extension enables us to construct a discrete-time approximation of the local time of a Brownian motion. We also provide discrete-time approximations of skew Brownian motions
Flow in Collapsible Tubes and Past Other Highly Compliant Boundaries
Get PDFThis chapter gives an overview of the main physiological applications of
collapsible tube
ows and reviews the major theoretical and computational
developments of the past twenty-ve years, ranging from lumped-parameter
models to three-dimensional Navier{Stokes simulations. We also discuss
some of the signicant questions that, despite substantial progress, still
remain open
-Orthogonal Matrices: Properties and Generation
Get PDFA real, square matrix is -orthogonal if ,
where the signature matrix J = \diag(\pm 1).
-orthogonal matrices arise in the analysis and numerical solution of various
matrix problems involving indefinite inner products, including,
in particular,
the downdating of Cholesky factorizations.
We present techniques and tools useful in the analysis,
application and construction of these matrices,
giving a self-contained treatment that provides new insights.
First, we define and explore the properties of the exchange operator,
which maps -orthogonal matrices to orthogonal matrices and vice versa.
Then we show how the exchange operator can be used to obtain a
hyperbolic CS decomposition of a -orthogonal matrix
directly from the usual CS decomposition
of an orthogonal matrix.
We employ the decomposition to derive an algorithm for constructing random
-orthogonal matrices with specified norm and condition number.
We also give a short proof of the fact that -orthogonal matrices
are optimally scaled
under two-sided diagonal scalings.
We introduce the indefinite polar decomposition
and investigate two iterations for
computing the -orthogonal polar factor:
a Newton iteration involving only matrix inversion
and a Schulz iteration involving only matrix \mult.
We show that these iterations can be used to -orthogonalize
a matrix that is not too far from being -orthogonal
Nilpotent orbits in good characteristic and the Kempf-Rousseau theory
Get PDFLet G be a connected reductive algebraic group over an algebraically closed field k of characteristic p>0, Image, and suppose that p is a good prime for the root system of G. In this paper, we give a fairly short conceptual proof of Pommerening's theorem [Pommerening, J. Algebra 49 (1977) 525–536; J. Algebra 65 (1980) 373–398] which states that any nilpotent element in Image is Richardson in a distinguished parabolic subalgebra of the Lie algebra of a Levi subgroup of G. As a by-product, we obtain a short noncomputational proof of the existence theorem for good transverse slices to the nilpotent G-orbits in Image (for earlier proofs of this theorem see [Kawanaka, Invent. Math. 84 (1986) 575–616; Premet, Trans. Amer. Math. Soc. 347 (1995) 2961–2988; Spaltenstein, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 31 (1984) 283–286]). We extend recent results of Sommers [Internal. Math. Res. Notices 11 (1998) 539–562] to reductive Lie algebras of good characteristic thus providing a satisfactory approach to computing the component groups of the centralisers of nilpotent elements in Image and unipotent elements in G. Earlier computations of these groups in positive characteristics relied, mostly, on work of Mizuno [J. Fac. Sci. Univ. Tokyo Sect. IA Math. 24 (1977) 525–563; Tokyo J. Math. 3 (1980) 391–459]. Our approach is based on the theory of optimal parabolic subgroups for G-unstable vectors, also known as the Kempf–Rousseau theory, which provides a good substitute for the Image-theory prominent in the characteristic zero case
A Chart of Backward Errors for Singly and Doubly Structured Eigenvalue Problems
Get PDFWe present a chart of structured backward errors for approximate eigenpairs of singly and doubly structured eigenvalue problems. We aim to give, wherever possible, formulae that are inexpensive to compute so that they can be used routinely in practice. We identify a number of problems for which the structured backward error is within a factor of the unstructured backward error. This paper collects, unifies, and extends existing work on this subject
Recursive calculation of dominant singular subspaces.
Get PDFIn this paper we show how to compute recursively an approximation of the left and
right dominant singular subspaces of a given matrix. In order to perform as few as possible operations
on each column of the matrix, we use a variant of the classical Gram–Schmidt algorithm to estimate
this subspace. The method is shown to be particularly suited for matrices with many more rows than
columns. Bounds for the accuracy of the computed subspace are provided. Moreover, the analysis
of error propagation in this algorithm provides new insights in the loss of orthogonality typically
observed in the classical Gram–Schmidt method