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Unsteady fronts in the spin-down of a fluid-filled torus
No full textWe report the results of an experimental investigation into fluid motion induced by the deceleration to rest of a rigidly rotating fluid-filled torus. Transition to a transient turbulent state is found where the onset of the complicated motion is triggered by a small scale wavelike instability. The wave forms on a front that propagates from the inner wall of the toroidal container after it is stopped. We reveal the origins of the front through a combination of careful experimental measurements, boundary-layer analysis and computation of the axisymmetric Navier--Stokes equations
Scaling, Sensitivity and Stability in the Numerical Solution of Quadratic Eigenvalue Problems
No full textThe most common way of solving the quadratic eigenvalue problem (QEP)
(\l^2 M + \l D + K)x=0 is to convert it into a linear problem
(\l X + Y)z=0 of twice the dimension and solve the linear problem
by the QZ algorithm or a Krylov method.
In doing so, it is important to understand the influence of the linearization
process on the accuracy and stability of the computed solution.
We discuss these issues for three particular linearizations:
the standard companion linearization
and two linearizations that preserve symmetry in the problem.
For illustration we employ
a model QEP describing the motion of
a beam simply supported at both ends and damped at the midpoint.
We show that the above linearizations lead to poor numerical results
for the beam problem,
but that a two-parameter scaling proposed by Fan, Lin and Van Dooren
cures the instabilities.
We also show that half of the eigenvalues of the beam QEP are pure imaginary
and are eigenvalues of the undamped problem.
Our analysis makes use of recently developed theory explaining the sensitivity
and stability of linearizations,
the main conclusions of which are summarized.
As well as arguing that
scaling should routinely be used,
we give guidance on how to choose a linearization
and illustrate the practical value of condition numbers and backward errors
Lie powers and Witt vectors
Get PDFIn the study of Lie powers of a module in prime characteristic , a basic role is played by certain modules introduced by Bryant and Schocker. The isomorphism types of the are not fully understood, but these modules fall into infinite families , one family for each positive integer not divisible by , and there is a recursive formula for the modules within . Here we use combinatorial methods and Witt vectors to show that each module in is isomorphic to a direct sum of tensor products of direct summands of the th tensor power
A consensus yeast metabolic network reconstruction obtained from a community approach to systems biology
Get PDFGenomic data allow the large-scale manual or semi-automated assembly of metabolic network reconstructions, which provide highly curated organism-specific knowledge bases. Although several genome-scale network reconstructions describe Saccharomyces cerevisiae metabolism, they differ in scope and content, and use different terminologies to describe the same chemical entities. This makes comparisons between them difficult and underscores the desirability of a consolidated metabolic network that collects and formalizes the 'community knowledge' of yeast metabolism. We describe how we have produced a consensus metabolic network reconstruction for S. cerevisiae. In drafting it, we placed special emphasis on referencing molecules to persistent databases or using database-independent forms, such as SMILES or InChI strings, as this permits their chemical structure to be represented unambiguously and in a manner that permits automated reasoning. The reconstruction is readily available via a publicly accessible database and in the Systems Biology Markup Language (http://www.comp-sys-bio.org/yeastnet). It can be maintained as a resource that serves as a common denominator for studying the systems biology of yeast. Similar strategies should benefit communities studying genome-scale metabolic networks of other organisms
Solar Grand Minima and Random Fluctuations in Dynamo Parameters
No full textAbstract We consider to what extent the long-term dynamics of cyclic solar activity in
the form of Grand Minima can be associated with random fluctuations of the parameters
governing the solar dynamo.We consider fluctuations of the alpha coefficient in the conventional
Parker migratory dynamo, and also in slightly more sophisticated dynamo models, and
demonstrate that they can mimic the gross features of the phenomenon of the occurrence of
Grand Minima over suitable parameter ranges. The temporal distribution of these Grand
Minima appears chaotic, with a more or less exponential waiting time distribution, typical
of Poisson processes. In contrast, however, the available reconstruction of Grand Minima
statistics based on cosmogenic isotope data demonstrates substantial deviations from this
exponential law.We were unable to reproduce the non-Poissonic tail of the waiting time distribution
either in the framework of a simple alpha-quenched Parker model or in its straightforward
generalization, nor in simple models with feedback on the differential rotation. We
suggest that the disagreement may only be apparent and is plausibly related to the limited
observational data, and that the observations and results of numerical modeling can be consistent
and represent physically similar dynamo regimes
On filling-in missing conditional probabilities in causal networks
Get PDFThis paper considers the problem and appropriateness of filling-in missing conditional probabilities in causal networks by the use of maximum entropy. Results generalizing earlier work of Rhodes, Garside & Holmes are
proved straightforwardly by the direct application of principles satisfied by the maximum entropy inference process under the assumed uniqueness of the maximum entropy solution. It is however demonstrated that the implicit assumption of uniqueness in the Rhodes, Garside & Holmes papers may fail even in the case of inverted trees. An alternative approach to
filling in missing values using the limiting centre of mass inference process
is then described which does not suffer this shortcoming, is trivially computationally feasible and arguably enjoys more justification in the context
when the probabilities are objective (for example derived from frequencies)
than by taking maximum entropy values
On the entropy flows to disorder
Get PDFGamma distributions, which contain the exponential as a
special case, have a distinguished place in the representation of
near-Poisson randomness for statistical processes; typically, they represent
distributions of spacings between events or voids among objects.
Here we look at the properties of the
Shannon entropy function and calculate its corresponding flow curves, relating
them to examples of constrained degeneration from ordered processes.
We consider also univariate and bivariate gamma, as well as Weibull distributions
since these include exponential distributions
Lie powers of relation modules for groups
No full textMotivated by applications to abstract group theory, we study Lie powers of relation modules. The relation module
associated to a free presentation of a group is the abelianization of , with
-action given by conjugation in . The degree Lie power is the homogeneous component of degree in
the free Lie ring on (equivalently, it is the relevant quotient of the lower central series of ). We
show that after reduction modulo a prime this becomes a projective -module, provided and is
not divisible by
A Lemon is not a Monstar: visualization of singularities of symmetric second rank tensor fields in the plane.
Get PDFIn the visualization of the topology of second rank symmetric tensor fields in the plane one can extract some key
points (degenerate points), and curves (separatrices) that characterize the qualitative behaviour of the whole
tensor field. This can provide a global structure of the whole tensor field, and effectively reduce the complexity of
the original data. To construct this global structure it is important to classify those degenerate points accurately.
However, in existing visualization techniques, a degenerate point is only classified into two types: trisector and
wedge types. In this work, we will apply the theory from the analysis of binary differential equations and demonstrate that, topologically, a simple degenerate point should be classified into three types: star (trisector), lemon
and monstar. The later two types were mistakenly regarded as a single type in the existing visualization techniques