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The exponentiated Gumbel distribution with climate application
No full textThe Gumbel distribution is perhaps the most widely applied statistical distribution for climate modeling. In this article we introduce a distribution that generalizes the standard Gumbel distribution in the same way the exponentiated exponential distribution generalizes the standard exponential distribution. We refer to this new distribution as the exponentiated Gumbel distribution. We provide a comprehensive treatment of the mathematical properties of this new distribution and illustrate its use for modeling rainfall data from Orlando, Florida. Among the mathematical properties, we derive the analytical shapes of the corresponding probability density function and the hazard rate function, calculate expressions for the nth moment and the asymptotic distribution of the extreme order statistics, and investigate the variation of the skewness and kurtosis measures. We also discuss estimation by the method of maximum likelihood. Copyright © 2005 John Wiley & Sons, Ltd
Natural transformations of tensor algebras and representations of combinatorial groups
No full textNatural linear and coalgebra transformations of tensor algebras are studied. The representations of certain combinatorial groups are given. These representations are connected to natural transformations of tensor algebras and to the groups of the homotopy classes of maps from the James construction to loop spaces. Applications to homotopy theory appear in a sequel
A high resolution scheme for Eulerian gas-solid two-phase isentropic flow
Get PDFNumerical solutions of the equations governing two-phase isentropic flow of a solid granular material dispersed in a gas are investigated. Both the dispersed and continuous phases are treated as continua and an Eulerian description of the flow is adopted. We present an inviscid model with a general pressure term from which a number of variant models can be obtained. A high resolution scheme is presented to obtain numerical approximations of the equations in each of the models. We investigate whether the chosen numerical scheme is suitable for the equations governing the models and use the numerical results to obtain quantitative and qualitative insight into the predictions of each of the models. Three test cases, new to the literature, are considered, and the numerical results compared
Time-dependent solutions for particle size segregation in shallow granular avalanches
Get PDFRapid shallow granular free-surface flows develop in a wide range of industrial and geophysical flows, ranging from rotating kilns and blenders to rock-falls, snow slab-avalanches and debris-flows. Within these flows, grains of different sizes often separate out into inversely graded layers, with the large particles on top of the fines, by a process called kinetic sieving. In this paper, a recent theory is used to construct exact time-dependent two-dimensional solutions for the development of the particle-size distribution in inclined chute flows. The first problem assumes the flow is initially homogeneously mixed and is fed at the inflow with homogeneous material of the same concentration. Concentration shocks develop during the flow and the particles eventually separate out into inversely graded layers sufficiently far downstream. Sections with a monotonically decreasing shock height, between these layers, steepen and break in finite time. The second problem assumes that the material is normally graded, with the small particles on top of the coarse ones. In this case, shock waves, concentration expansions, non-centred expanding shock regions and breaking shocks develop. As the parameters are varied, nonlinearity leads to fundamental topological changes in the solution, and, in simple-shear, a logarithmic singularity prevents a steady-state solution from being attained
Almost Sure Relative Stability of the Overshoot of Power Law Boundaries
Get PDFWe give necessary and sufficient conditions for the almost sure (a.s.)
relative stability of the overshoot of a random walk when it exits from a
two-sided symmetric region with curved boundaries. The boundaries are
of power-law type, ±rn^b, r > 0, n = 1, 2, · · · , where 0 ≤ b < 1, b 6= 1/2.
In these cases, the a.s. stability occurs if and only if the mean step length
of the random walk is finite and nonzero, or the step length has a finite
variance and mean zero
How chaotic are strange nonchaotic attractors?
Get PDFWe show that the classic examples of quasi-periodically forced maps with strange nonchaotic
attractors described by Grebogi et al and Herman in the mid-1980s have some chaotic properties.
More precisely, we show that these systems exhibit sensitive dependence on initial conditions,
both on the whole phase space and restricted to the attractor. The results also remain valid
in more general classes of quasiperiodically forced systems. Further, we include an elementary
proof of a classic result by Glasner and Weiss on sensitive dependence, and we clarify the
structure of the attractor in an example with two-dimensional bers also introduced by Grebogi
et al
oomph-lib — An Object-Oriented Multi-Physics Finite-Element Library
Get PDFThis paper discusses certain aspects of the design and implementation
of oomph-lib, an object-oriented multi-physics finite-element library, available
as open-source software at http://www.oomph-lib.org. The main aim of the library
is to provide an environment that facilitates the robust, adaptive solution
of multi-physics problems by monolithic discretisations, while maximising the potential
for code re-use. This is achieved by the extensive use of object-oriented
programming techniques, including multiple inheritance, function overloading and
template (generic) programming, which allow existing objects to be (re-)used in
many different ways without having to change their original implementation.
These ideas are illustrated by considering some specific issues that arise when
implementing monolithic finite-element discretisations of large-displacement fluidstructure-
interaction problems within an Arbitrary Lagrangian Eulerian (ALE)
framework. We also discuss the development of wrapper classes that permit the
generic and efficient evaluation of the so-called “shape derivatives”, the derivatives
of the discretised fluid equations with respect to those solid mechanics degrees of
freedom that affect the nodal positions in the fluid mesh. Finally, we apply the
methodology in several examples
Rationality as conformity
No full textWe argue in favour of identifying one aspect of rational choice with the tendency to conform to the choice you expect another like-minded, but non-communicating, agent to make and study this idea in the very basic case where the choice is from a non-empty subset K of 2^A and no further structure or knowledge of A is assumed
Isomorphism classes for Banach vector bundle structures of second tangents
No full textOn a smooth Banach manifold M,$the equivalence classes of curves
that agree up to acceleration form the second order tangent bundle
T^2M of M.
This is a vector bundle in the presence of a linear connection on
M and the corresponding local structure is heavily dependent on
the choice of connection. In this paper we study the extent of this
dependence and we prove that it is closely related to the notions
of conjugate connections and
second order differentials. In particular, the vector bundle structure on
T^2M remains invariant under conjugate connections with respect
to diffeomorphisms of M