1,479 research outputs found
On Kottler's path: origin and evolution of the premetric program in gravity and in electrodynamics
In 1922, Kottler put forward the program to remove the gravitational
potential, the metric of spacetime, from the fundamental equations in physics
as far as possible. He successfully applied this idea to Newton's
gravitostatics and to Maxwell's electrodynamics, where Kottler recast the field
equations in premetric form and specified a metric-dependent constitutive law.
We will discuss the basics of the premetric approach and some of its beautiful
consequences, like the division of universal constants into two classes. We
show that classical electrodynamics can be developed without a metric quite
straightforwardly: the Maxwell equations, together with a local and linear
response law for electromagnetic media, admit a consistent premetric
formulation. Kottler's program succeeds here without provisos. In Kottler's
approach to gravity, making the theory relativistic, two premetric
quasi-Maxwellian field equations arise, but their field variables, if
interpreted in terms of general relativity, do depend on the metric. However,
one can hope to bring the Kottler idea to work by using the teleparallelism
equivalent of general relativity, where the gravitational potential, the
coframe, can be chosen in a premetric way.Comment: 72 pages latex with 6 figures; based on an invited talk given at the
Annual Meeting of the German Physical Society (DPG) in Berlin on 20 March
2015, Working Group on Philosophy of Physics (AGPhil); a short version will
be submitted to IJMP
Clouding tracing: Visualization of the mixing of fluid elements in convection-diffusion systems
This paper describes a highly interactive method for computer visualization of the basic physical process of dispersion and mixing of fluid elements in convection-diffusion systems. It is based on transforming the vector field from a traditionally Eulerian reference frame into a Lagrangian reference frame. Fluid elements are traced through the vector field for the mean path as well as the statistical dispersion of the fluid elements about the mean position by using added scalar information about the root mean square value of the vector field and its Lagrangian time scale. In this way, clouds of fluid elements are traced and are not just mean paths. We have used this method to visualize the simulation of an industrial incinerator to help identify mechanisms for poor mixing
The Kummer tensor density in electrodynamics and in gravity
Guided by results in the premetric electrodynamics of local and linear media,
we introduce on 4-dimensional spacetime the new abstract notion of a Kummer
tensor density of rank four, . This tensor density is, by
definition, a cubic algebraic functional of a tensor density of rank four
, which is antisymmetric in its first two and its last two
indices: . Thus,
, see Eq.(46). (i) If is identified with the
electromagnetic response tensor of local and linear media, the Kummer tensor
density encompasses the generalized {\it Fresnel wave surfaces} for propagating
light. In the reversible case, the wave surfaces turn out to be {\it Kummer
surfaces} as defined in algebraic geometry (Bateman 1910). (ii) If is
identified with the {\it curvature} tensor of a Riemann-Cartan
spacetime, then and, in the special case of general
relativity, reduces to the Kummer tensor of Zund (1969). This is related to the {\it principal null directions} of the curvature. We
discuss the properties of the general Kummer tensor density. In particular, we
decompose irreducibly under the 4-dimensional linear group
and, subsequently, under the Lorentz group .Comment: 54 pages, 6 figures, written in LaTex; improved version in accordance
with the referee repor
Dynamic Maps: Representations of Change in Geospatial Modeling and Visualization
By coining the descriptive phrase ―user-centric geographic cosmology, Goodchild (1998), challenges the geographically oriented to address GIS in the broadest imaginable context: as interlocutor between persons and geo-phenomena. This investigation responds both in a general way, and more specifically, to the representations of change in GIS modeling and visualization leading to dynamic mapping.
The investigation, consisting of a report and a series of experiments, explores and demonstrates prototype workarounds that enhance GIS capabilities by drawing upon ideas, techniques, and components from agent-based modeling and visualization software, and suggests shifts at the conceptual, methodological, and technical levels.
The workarounds and demonstrations presented here are four-dimensional visualizations, representing changes and behaviors of different types of entities such as living creatures, mobile assets, features, structures, and surfaces, using GIS, agent-based modeling and animation techniques. In a typical case, a creature begins as a point feature in GIS, becomes a mobile and interactive object in agent-based modeling, and is fleshed out to three dimensions in an animated representation. In contrast, a land surface remains much the same in all three stages. The experiments address change in location, orientation, shape, visual attributes, viewpoint, scale, and speed in applications representing predator-prey, search and destroy, sense and locate and urban sprawl. During the experiments, particular attention is paid to factors of modeling and visualization involved in engaging human sensing and cognitive abilities
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