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This is a general work on gravitational lensing. We present new expressions for the optical scalars and the deflection angle in terms of the energy-momentum tensor components of matter distributions. Our work generalizes standard references…
We present a new compressed representation of free trajectories of moving objects. It combines a partial-sums-based structure that retrieves in constant time the position of the object at any instant, with a hierarchical…
Translations between different nonmonotonic formalisms always have been an important topic in the field, in particular to understand the knowledge-representation capabilities those formalisms offer. We provide such an investigation in terms…
We derive new equations using the mixed-frame approach for one- and two-dimensional (axisymmetric) time-dependent radiation transport and the associated couplings with matter. Our formulation is multi-group and multi-angle and includes…
A formula for the apparent rotation of a relativistically moving object has been known for some time, but it seems not to have been realized that this formula has a very pretty interpretation in terms of formal group laws. Version 2…
I provide a pedagogical introduction to the notion of pseudomomentum for waves in a medium, and show how changes in pseudomomentum may sometimes be used to compute real forces. I then explain how these ideas apply to sound waves in a fluid.…
A global model is presented that can be used to study attitude maneuvers of a rigid spacecraft in a circular orbit about a large central body. The model includes gravity gradient effects that arise from the non-uniform gravity field and…
The major difficulty when one teaches about non-inertial reference frames in undergraduate courses on Classical Mechanics is to find an intuitive way to derive the Coriolis acceleration. Indeed, there is a factor of 2 in the formula for the…
Lorentz transformation equations provide us a set of relations between the spacetime coordinates as observed from two different inertial frames. In case, one of the frames is moving with a uniform rectilinear acceleration we have Rindler's…
We consider continuous, translation-commuting transformations of compact, translation-invariant families of mappingsfrom finitely generated groups into finite alphabets. It is well-known that such transformations and spaces can be described…
We propose the use of ponderomotive forces to entangle the motions of different atoms. Two situations are analyzed: one where the atoms belong to the same optical cavity and interact with the same radiation field mode; the other where each…
This paper explores the chaotic properties of an advection system expressed in difference equations form. In the beginning the Aref's blinking vortex system is examined. Then several new lines are explored related to the sink problem (one…
The attitude space has been parameterized in various ways for practical purposes. Different representations gain preferences over others based on their intuitive understanding, ease of implementation, formulaic simplicity, and physical as…
We introduce a system where an elastic lattice of particles is moved slowly at a constant velocity under the influence of a local external potential, construct a rigid-body model through simplification processes, and show that the two…
This thesis is devoted to algorithmic aspects of the implementation of Cartan's moving frame method to the problem of the equivalence of submanifolds under a Lie group action. We adopt a general definition of a moving frame as an…
A new computational framework for the simulation of turbulent flow through complex objects and along irregular boundaries is presented. This is motivated by the application of metal foams in compact heat-transfer devices, or as catalyst…
We discuss implications of the cosmological frame principle which states that cosmological effects of modified gravity must be stable as solutions of each of the corresponding sets of dynamical equations holding in the two…
To use robots in more unstructured environments, we have to accommodate for more complexities. Robotic systems need more awareness of the environment to adapt to uncertainty and variability. Although cameras have been predominantly used in…
We discuss neutrino oscillations in vacuum from the point of view of a uniformly accelerated observer. A covariant definition of quantum phase is introduced with the aim of generalizing the standard expression of the oscillation amplitude…
Simple physical models of a measuring rod and of a clock are used to demonstrate the contraction of objects and clock retardation in special relativity. It is argued that the models could help in promoting student understanding of special…