Exact Random Walk Distributions using Noncommutative Geometry

Using the results obtained by the non commutative geometry techniques applied to the Harper equation, we derive the areas distribution of random walks of length $N$ on a two-dimensional square lattice for large $N$, taking into account finite size contributions.Comment: Latex, 3 pages, 1 figure, to be published in J. Phys. A : Math. Ge

Magneto-optical properties of Co|Pt multilayer systems

We are reporting, for the first time in the literature, theoretical Kerr spectra of Co|Pt multilayer systems as obtained on a first principles basis including multiple reflections and interferences from all the boundaries in-between the layers.Comment: 4 pages (LaTeX), 1 (a,b) figures (Encapsulated PostScript), J. Appl. Physics, in pres

Symmetry of Quantum Torus with Crossed Product Algebra

In this paper, we study the symmetry of quantum torus with the concept of crossed product algebra. As a classical counterpart, we consider the orbifold of classical torus with complex structure and investigate the transformation property of classical theta function. An invariant function under the group action is constructed as a variant of the classical theta function. Then our main issue, the crossed product algebra representation of quantum torus with complex structure under the symplectic group is analyzed as a quantum version of orbifolding. We perform this analysis with Manin's so-called model II quantum theta function approach. The symplectic group Sp(2n,Z) satisfies the consistency condition of crossed product algebra representation. However, only a subgroup of Sp(2n,Z) satisfies the consistency condition for orbifolding of quantum torus.Comment: LaTeX 17pages, changes in section 3 on crossed product algebr

Vacuum Compatibility of 3D-Printed Materials

The fabrication fidelity and vacuum properties are tested for currently available 3D-printed materials including polyamide, glass, acrylic, and sterling silver. The silver was the only material found to be suitable to ultrahigh vacuum environments due to outgassing and sublimation observed in other materials.Comment: 3 pages, 2 figures, preprin

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

Self-Defense Against Robots and Drones

Robots can pose-or can appear to pose-a threat to life, property, and privacy. May a landowner legally shoot down a trespassing drone? Can she hold a trespassing autonomous car as security against damage done or further torts? Is the fear that a drone may be operated by a paparazzo or Peeping Tom sufficient grounds to disable or interfere with it? How hard may you shove if the office robot rolls over your foot? This Article addresses all those issues and one more. what rules and standards we could put into place to make the resolution of those questions easier and fairer to all concerned The default common-law legal rules governing each of these perceived threats are somewhat different, although reasonableness always plays an important role in defining legal rights and options. In certain cases-drone overflights, autonomous cars-national,s tate, and even local regulations may trump the common law. Because it is in most cases obvious that humans can use force to protect themselves against actual physical attack, this Article concentrates on the more interesting cases of (1) robot (and especially drone) trespass and (2) responses to perceived threats other than physical attack by robots-notably the risk that the robot (or drone) may be spying-perceptions which may not always be justified, but which sometimes may nonetheless be considered reasonable in law

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

Magnetic layers with periodic point perturbations

We study spectral properties of a spinless quantum particle confined to an infinite planar layer with hard walls which interacts with a periodic lattice of point perturbations and a homogeneous magnetic field perpendicular to the layer. It is supposed that the lattice cell contains a finite number of impurities and the flux through the cell is rational. Using the Landau-Zak transformation, we convert the problem into investigation of the corresponding fiber operators which is performed by means of Krein's formula. This yields an explicit description of the spectral bands which may be absolutely continuous or degenerate, depending on the parameters of the model.Comment: LaTeX 2e, 30 pages; with minor revisions, to appear in Rep. Math. Phy