332,568 research outputs found
Holistic projection of initial conditions onto a finite difference approximation
Modern dynamical systems theory has previously had little to say about finite
difference and finite element approximations of partial differential equations
(Archilla, 1998). However, recently I have shown one way that centre manifold
theory may be used to create and support the spatial discretisation of \pde{}s
such as Burgers' equation (Roberts, 1998a) and the Kuramoto-Sivashinsky
equation (MacKenzie, 2000). In this paper the geometric view of a centre
manifold is used to provide correct initial conditions for numerical
discretisations (Roberts, 1997). The derived projection of initial conditions
follows from the physical processes expressed in the PDEs and so is
appropriately conservative. This rational approach increases the accuracy of
forecasts made with finite difference models.Comment: 8 pages, LaTe
The inertial dynamics of thin film flow of non-Newtonian fluids
Consider the flow of a thin layer of non-Newtonian fluid over a solid
surface. I model the case of a viscosity that depends nonlinearly on the
shear-rate; power law fluids are an important example, but the analysis here is
for general nonlinear dependence. The modelling allows for large changes in
film thickness provided the changes occur over a large enough lateral length
scale. Modifying the surface boundary condition for tangential stress forms an
accessible base for the analysis where flow with constant shear is a neutral
critical mode, in addition to a mode representing conservation of fluid.
Perturbatively removing the modification then constructs a model for the
coupled dynamics of the fluid depth and the lateral momentum. For example, the
results model the dynamics of gravity currents of non-Newtonian fluids even
when the flow is not very slow
Accurately model the Kuramoto--Sivashinsky dynamics with holistic discretisation
We analyse the nonlinear Kuramoto--Sivashinsky equation to develop accurate
discretisations modeling its dynamics on coarse grids. The analysis is based
upon centre manifold theory so we are assured that the discretisation
accurately models the dynamics and may be constructed systematically. The
theory is applied after dividing the physical domain into small elements by
introducing isolating internal boundaries which are later removed.
Comprehensive numerical solutions and simulations show that the holistic
discretisations excellently reproduce the steady states and the dynamics of the
Kuramoto--Sivashinsky equation. The Kuramoto--Sivashinsky equation is used as
an example to show how holistic discretisation may be successfully applied to
fourth order, nonlinear, spatio-temporal dynamical systems. This novel centre
manifold approach is holistic in the sense that it treats the dynamical
equations as a whole, not just as the sum of separate terms.Comment: Without figures. See
http://www.sci.usq.edu.au/staff/aroberts/ksdoc.pdf to download a version with
the figure
Crystals of an Insoluble Carbonate of Copper Grown under a Soda Solution
Copia digital. Madrid : Ministerio de Educación, Cultura y Deporte, 201
Testing the Limits of Antidiscrimination Law: The Business, Legal, and Ethical Ramifications of Cultural Profiling at Work
While courts have rarely ruled in favor of plaintiffs bringing discrimination claims based on identity performance, legal scholars have argued that discrimination on the basis of certain cultural displays should be prohibited because it creates a work environment that is heavily charged with ethnic and racial discrimination. Drawing upon empirical studies of diversity management, stereotyping, and group dynamics, we describe how workplace cultural profiling often creates an unproductive atmosphere of heightened scrutiny and identity performance constraints that lead workers (especially those from marginalized groups) to behave in less authentic, less innovative ways in diverse organizational settings
Quantizing the line element field
A metric with signature (-+++) can be constructed from a metric with
signature (++++) and a double-sided vector field called the line element field.
Some of the classical and quantum properties of this vector field are studied.Comment: 9 page
A theory of bundles over posets
In algebraic quantum field theory the spacetime manifold is replaced by a
suitable base for its topology ordered under inclusion. We explain how certain
topological invariants of the manifold can be computed in terms of the base
poset. We develop a theory of connections and curvature for bundles over posets
in search of a formulation of gauge theories in algebraic quantum field theory
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