On quantum mechanics with a magnetic field on R^n and on a torus T^n, and their relation

We show in elementary terms the equivalence in a general gauge of a U(1)-gauge theory of a scalar charged particle on a torus T^n = R^n/L to the analogous theory on R^n constrained by quasiperiodicity under translations in the lattice L. The latter theory provides a global description of the former: the quasiperiodic wavefunctions defined on R^n play the role of sections of the associated hermitean line bundle E on T^n, since also E admits a global description as a quotient. The components of the covariant derivatives corresponding to a constant (necessarily integral) magnetic field B = dA generate a Lie algebra g_Q and together with the periodic functions the algebra of observables O_Q . The non-abelian part of g_Q is a Heisenberg Lie algebra with the electric charge operator Q as the central generator; the corresponding Lie group G_Q acts on the Hilbert space as the translation group up to phase factors. Also the space of sections of E is mapped into itself by g in G_Q . We identify the socalled magnetic translation group as a subgroup of the observables' group Y_Q . We determine the unitary irreducible representations of O_Q, Y_Q corresponding to integer charges and for each of them an associated orthonormal basis explicitly in configuration space. We also clarify how in the n = 2m case a holomorphic structure and Theta functions arise on the associated complex torus. These results apply equally well to the physics of charged scalar particles on R^n and on T^n in the presence of periodic magnetic field B and scalar potential. They are also necessary preliminary steps for the application to these theories of the deformation procedure induced by Drinfel'd twists.Comment: Latex2e file, 22 pages. Final version appeared in IJT

Entropy on the von Neumann lattice and its evaluation

Based on the recently introduced averaging procedure in phase space, a new type of entropy is defined on the von Neumann lattice. This quantity can be interpreted as a measure of uncertainty associated with simultaneous measurement of the position and momentum observables in the discrete subset of the phase space. Evaluating for a class of the coherent states, it is shown that this entropy takes a stationary value for the ground state, modulo a unit cell of the lattice in such a class. This value for the ground state depends on the ratio of the position lattice spacing and the momentum lattice spacing. It is found that its minimum is realized for the perfect square lattice, i.e., absence of squeezing. Numerical evaluation of this minimum gives 1.386....Comment: 14 pages, no figures; J. Phys. A, in pres

Performance experiments with alternative advanced teleoperator control modes for a simulated solar maximum satellite repair

Experiments are described which were conducted at the JPL Advanced Teleoperator Lab to demonstrate and evaluate the effectiveness of various teleoperator control modes in the performance of a simulated Solar Max Satellite Repair (SMSR) task. THe SMSR was selected as a test because it is very rich in performance capability requirements and it actually has been performed by two EVA astronauts in the Space Shuttle Bay in 1984. The main subtasks are: thermal blanket removal; installation of a hinge attachment for electrical panel opening; opening of electrical panel; removal of electrical connectors; relining of cable bundles; replacement of electrical panel; securing parts and cables; re-mate electrical connectors; closing of electrical panel; and reinstating thermal blanket. The current performance experiments are limited to thermal blanket cutting, electrical panel unbolting and handling electrical bundles and connectors. In one formal experiment even different control modes were applied to the unbolting and reinsertion of electrical panel screws subtasks. The seven control modes are alternative combinations of manual position and rate control with force feedback and remote compliance referenced to force-torque sensor information. Force-torque sensor and end effector position data and task completion times were recorded for analysis and quantification of operator performance

A philosophical context for methods to estimate origin-destination trip matrices using link counts.

This paper creates a philosophical structure for classifying methods which estimate origin-destination matrices using link counts. It is claimed that the motivation for doing so is to help real-life transport planners use matrix estimation methods effectively, especially in terms of trading-off observational data with prior subjective input (typically referred to as 'professional judgement'). The paper lists a number of applications that require such methods, differentiating between relatively simple and highly complex applications. It is argued that a sound philosophical perspective is particularly important for estimating trip matrices in the latter type of application. As a result of this argument, a classification structure is built up through using concepts of realism, subjectivity, empiricism and rationalism. Emphasis is put on the fact that, in typical transport planning applications, none of these concepts is useful in its extreme form. The structure is then used to make a review of methods for estimating trip matrices using link counts, covering material published over the past 30 years. The paper concludes by making recommendations, both philosophical and methodological, concerning both practical applications and further research

A three-dimensional electrostatic actuator with a locking mechanism for a new generation of atom chips

A micromachined three-dimensional electrostatic actuator that is optimized for aligning and tuning optical microcavities on atom chips is presented. The design of the 3D actuator is outlined in detail, and its characteristics are verified by analytical calculations and finite element modelling. Furthermore, the fabrication process of the actuation device is described and preliminary fabrication results are shown. The actuation in the chip plane which is used for mirror positioning has a working envelope of 17.5 ?m. The design incorporates a unique locking mechanism which allows the out-of-plane actuation that is used for cavity tuning to be carried out once the in-plane actuation is completed. A maximum translation of 7 ?m can be achieved in the out-of-plane direction

Experimental determination of grain density function of AZ91/SiC composite with different mass fractions of SiC and undercoolings using heterogeneous nucleation model

The grain density, Nv, in the solid state after solidification of AZ91/SiC composite is a function of maximum undercooling, ΔT, of a liquid alloy. This type of function depends on the characteristics of heterogeneous nucleation sites and number of SiC present in the alloy. The aim of this paper was selection of parameters for the model describing the relationship between the grain density of primary phase and undercooling. This model in connection with model of crystallisation, which is based on chemical elements diffusion and grain interface kinetics, can be used to predict casting quality and its microstructure. Nucleation models have parameters, which exact values are usually not known and sometimes even their physical meaning is under discussion. Those parameters can be obtained after mathematical analysis of the experimental data. The composites with 0, 1, 2, 3 and 4wt.% of SiC particles were prepared. The AZ91 alloy was a matrix of the composite reinforcement SiC particles. This composite was cast to prepare four different thickness plates.They were taken from the region near to the thermocouple, to analyze the undercooling for different composites and thickness plates and its influence on the grain size. The microstructure and thermal analysis gave set of values that connect mass fraction of SiC particles, and undercooling with grain size. These values were used to approximate nucleation model adjustment parameters. Obtained model can be very useful in modelling composites microstructure

Spring 1981 Conference Issue

Fifty Years of Turf Management Education at the University of Massachusetts (page 3) Commentary: A Case for Conditional Optimism (7) Fiftieth Annual Turf Conference and Fifth Industrial Show (10) Dollar Spot Fungicide Trials --1980 (12) Tree News (14) Insurance Requirements (16) UMass Turfgrass Research Fund (18) Exams (19

Theory of a magnetic microscope with nanometer resolution

We propose a theory for a type of apertureless scanning near field microscopy that is intended to allow the measurement of magnetism on a nanometer length scale. A scanning probe, for example a scanning tunneling microscope (STM) tip, is used to scan a magnetic substrate while a laser is focused on it. The electric field between the tip and substrate is enhanced in such a way that the circular polarization due to the Kerr effect, which is normally of order 0.1% is increased by up to two orders of magnitude for the case of a Ag or W tip and an Fe sample. Apart from this there is a large background of circular polarization which is non-magnetic in origin. This circular polarization is produced by light scattered from the STM tip and substrate. A detailed retarded calculation for this light-in-light-out experiment is presented.Comment: 17 pages, 8 figure

Control of Dynamic Systems via Neural Networks

This report is devoted to the problem of controlling a class of linear time-invariant dynamic systems via controllers based on additive neural network models. In particular, the tracking and stabilization problems are considered. First, we show how to transform the problem of tracking a reference signal by a control system into the stabilization problem. Then, some concepts from the variable structure control theory are utilized to construct stabilizing controllers. In order to facilitate the stability analysis of the closed-loop systems we employ a special state space transformation. This transformation allows us also to reveal connections between the proposed controllers and the additive neural network models

Atmospheric Co2 And O3 Alter The Flow Of 15n In Developing Forest Ecosystems

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/116984/1/ecy200788102630.pd