Lower bound for the ground state energy of the no-pair Hamiltonian

A lower bound for the ground state energy of a one particle relativistic Hamiltonian - sometimes called no-pair operator - is provided.Comment: 5 pages, 1 figure, 1 table, Latex2e (amssymb,amsmath,graphicx

A Magnetic Localization Technique Designed for use with Magnetic Levitation Systems.

M.S. Thesis. University of Hawaiʻi at Mānoa 2017

Instability of a Pseudo-Relativistic Model of Matter with Self-Generated Magnetic Field

For a pseudo-relativistic model of matter, based on the no-pair Hamiltonian, we prove that the inclusion of the interaction with the self-generated magnetic field leads to instability for all positive values of the fine structure constant. This is true no matter whether this interaction is accounted for by the Breit potential, by an external magnetic field which is chosen to minimize the energy, or by the quantized radiation field.Comment: 13 pages, AMS-LaTe

Electromagnetic Position Sensing and Force Feedback for a Magnetic Stylus with an Interactive Display

This letter describes the design, implementation, validation, and demonstration of an electromagnetic system that can be incorporated into a graphical display to provide computer-controlled planar feedback forces on the tip of a stylus or fingertip-mounted magnet held near the display surface, according to the magnet position and virtual fixtures implemented in software. An array of magnetometer sensors is used to detect the position of the magnet, while a pair of box-shaped coils behind the display produces feedback forces on the stylus parallel to the plane of the display. Electromagnetic analysis for the system design is presented and system implementation is described. Validation results are given for force generation within a 100 mm × 100 mm area and force interaction with a virtual obstacle is demonstrated

The impact of carbon dioxide on freshwater fish behaviors

Freshwater environments have the potential to be impacted by acidification due to increases in dissolved carbon dioxide (CO2). Recent work in the marine environment suggests that increased CO2 levels due to climate change can negatively affect a fish’s ability to detect predators, home to natal environments, and perform aerobically. The potential for elevated CO2 to have similar negative impacts on freshwater communities remains understudied. The objective of our study was to quantify the effects of elevated CO2 on the behaviors of fathead minnows (Pimephales promelas) and silver carp (Hypophthalmichthys molitrix) following exposure to conspecific skin extracts (alarm cues). In fathead minnows, their response to conspecific skin extracts were significantly impaired following exposure to elevated CO2 levels for at least 96 h, while silver carp behaviors were unaltered. However, fathead minnow behaviors did return to pre-CO2 exposure in high CO2 exposed fish following 14 d of holding at ambient CO2 levels. Overall, this study suggests there may be potential impacts to freshwater fishes alarm cue behaviors following CO2 exposure but these responses may be species-specific, and will likely be abated should the CO2 stressor be removed

Electromagnetic Position Sensing and Force Feedback for a Magnetic Stylus with an Interactive Display

This letter describes the design, implementation, validation, and demonstration of an electromagnetic system that can be incorporated into a graphical display to provide computer-controlled planar feedback forces on the tip of a stylus or fingertip-mounted magnet held near the display surface, according to the magnet position and virtual fixtures implemented in software. An array of magnetometer sensors is used to detect the position of the magnet, while a pair of box-shaped coils behind the display produces feedback forces on the stylus parallel to the plane of the display. Electromagnetic analysis for the system design is presented and system implementation is described. Validation results are given for force generation within a 100 mm × 100 mm area and force interaction with a virtual obstacle is demonstrated

Characterising Probabilistic Processes Logically

In this paper we work on (bi)simulation semantics of processes that exhibit both nondeterministic and probabilistic behaviour. We propose a probabilistic extension of the modal mu-calculus and show how to derive characteristic formulae for various simulation-like preorders over finite-state processes without divergence. In addition, we show that even without the fixpoint operators this probabilistic mu-calculus can be used to characterise these behavioural relations in the sense that two states are equivalent if and only if they satisfy the same set of formulae.Comment: 18 page

Exponential localization of hydrogen-like atoms in relativistic quantum electrodynamics

We consider two different models of a hydrogenic atom in a quantized electromagnetic field that treat the electron relativistically. The first one is a no-pair model in the free picture, the second one is given by the semi-relativistic Pauli-Fierz Hamiltonian. We prove that the no-pair operator is semi-bounded below and that its spectral subspaces corresponding to energies below the ionization threshold are exponentially localized. Both results hold true, for arbitrary values of the fine-structure constant, $e^2$, and the ultra-violet cut-off, $\Lambda$, and for all nuclear charges less than the critical charge without radiation field, $Z_c=e^{-2}2/(2/\pi+\pi/2)$. We obtain similar results for the semi-relativistic Pauli-Fierz operator, again for all values of $e^2$ and $\Lambda$ and for nuclear charges less than $e^{-2}2/\pi$.Comment: 37 page

Semantic Domains for Combining Probability and Non-Determinism

AbstractWe present domain-theoretic models that support both probabilistic and nondeterministic choice. In [A. McIver and C. Morgan. Partial correctness for probablistic demonic programs. Theoretical Computer Science, 266:513–541, 2001], Morgan and McIver developed an ad hoc semantics for a simple imperative language with both probabilistic and nondeterministic choice operators over a discrete state space, using domain-theoretic tools. We present a model also using domain theory in the sense of D.S. Scott (see e.g. [G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. W. Mislove, and D. S. Scott. Continuous Lattices and Domains, volume 93 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge, 2003]), but built over quite general continuous domains instead of discrete state spaces.Our construction combines the well-known domains modelling nondeterminism – the lower, upper and convex powerdomains, with the probabilistic powerdomain of Jones and Plotkin [C. Jones and G. Plotkin. A probabilistic powerdomain of evaluations. In Proceedings of the Fourth Annual Symposium on Logic in Computer Science, pages 186–195. IEEE Computer Society Press, 1989] modelling probabilistic choice. The results are variants of the upper, lower and convex powerdomains over the probabilistic powerdomain (see Chapter 4). In order to prove the desired universal equational properties of these combined powerdomains, we develop sandwich and separation theorems of Hahn-Banach type for Scott-continuous linear, sub- and superlinear functionals on continuous directed complete partially ordered cones, endowed with their Scott topologies, in analogy to the corresponding theorems for topological vector spaces in functional analysis (see Chapter 3). In the end, we show that our semantic domains work well for the language used by Morgan and McIver