Geometric aspects of 2-walk-regular graphs

A t-walk-regular graph is a graph for which the number of walks of given length between two vertices depends only on the distance between these two vertices, as long as this distance is at most t. Such graphs generalize distance-regular graphs and t-arc-transitive graphs. In this paper, we will focus on 1- and in particular 2-walk-regular graphs, and study analogues of certain results that are important for distance-regular graphs. We will generalize Delsarte’s clique bound to 1-walk-regular graphs, Godsil’s multiplicity bound and Terwilliger’s analysis of the local structure to 2-walk-regular graphs. We will show that 2-walk-regular graphs have a much richer combinatorial structure than 1-walk-regular graphs, for example by proving that there are finitely many non-geometric 2-walk-regular graphs with given smallest eigenvalue and given diameter (a geometric graph is the point graph of a special partial linear space); a result that is analogous to a result on distance-regular graphs. Such a result does not hold for 1-walk-regular graphs, as our construction methods will show

Production of gliders by collisions in Rule 110

We investigate the construction of all the periodic structures or “gliders” up to now known in the evolution space of the one-dimensional cellular automaton Rule 110. The production of these periodic structures is developed and presented by means of glider collisions. We provide a methodology based on the phases of each glider to establish the necessary conditions for controlling and displaying the collisions of gliders from the initial configuration

Spin-polarized Tunneling in Hybrid Metal-Semiconductor Magnetic Tunnel Junctions

We demonstrate efficient spin-polarized tunneling between a ferromagnetic metal and a ferromagnetic semiconductor with highly mismatched conductivities. This is indicated by a large tunneling magnetoresistance (up to 30%) at low temperatures in epitaxial magnetic tunnel junctions composed of a ferromagnetic metal (MnAs) and a ferromagnetic semiconductor (GaMnAs) separated by a nonmagnetic semiconductor (AlAs). Analysis of the current-voltage characteristics yields detailed information about the asymmetric tunnel barrier. The low temperature conductance-voltage characteristics show a zero bias anomaly and a V^1/2 dependence of the conductance, indicating a correlation gap in the density of states of GaMnAs. These experiments suggest that MnAs/AlAs heterostructures offer well characterized tunnel junctions for high efficiency spin injection into GaAs.Comment: 14 pages, submitted to Phys. Rev.

Virtual Constraints and Hybrid Zero Dynamics for Realizing Underactuated Bipedal Locomotion

Underactuation is ubiquitous in human locomotion and should be ubiquitous in bipedal robotic locomotion as well. This chapter presents a coherent theory for the design of feedback controllers that achieve stable walking gaits in underactuated bipedal robots. Two fundamental tools are introduced, virtual constraints and hybrid zero dynamics. Virtual constraints are relations on the state variables of a mechanical model that are imposed through a time-invariant feedback controller. One of their roles is to synchronize the robot's joints to an internal gait phasing variable. A second role is to induce a low dimensional system, the zero dynamics, that captures the underactuated aspects of a robot's model, without any approximations. To enhance intuition, the relation between physical constraints and virtual constraints is first established. From here, the hybrid zero dynamics of an underactuated bipedal model is developed, and its fundamental role in the design of asymptotically stable walking motions is established. The chapter includes numerous references to robots on which the highlighted techniques have been implemented.Comment: 17 pages, 4 figures, bookchapte

Visualization of Frequent Itemsets with Nested Circular Layout and Bundling Algorithm

International audienceFrequent itemset mining is one of the major data mining issues. Once generated by algorithms, the itemsets can be automatically processed, for instance to extract association rules. They can also be explored with visual tools, in order to analyze the emerging patterns. Graphical itemsets representation is a convenient way to obtain an overview of the global interaction structure. However, when the complexity of the database increases, the network may become unreadable. In this paper, we propose to display itemsets on concentric circles, each one being organized to lower the intricacy of the graph through an optimization process. Thanks to a graph bundling algorithm, we finally obtain a compact representation of a large set of itemsets that is easier to exploit. Colors accumulation and interaction operators facilitate the exploration of the new bundle graph and to illustrate how much an itemset is supported by the data

Theory of coherent acoustic phonons in InGaN/GaN multi-quantum wells

A microscopic theory for the generation and propagation of coherent LA phonons in pseudomorphically strained wurzite (0001) InGaN/GaN multi-quantum well (MQW) p-i-n diodes is presented. The generation of coherent LA phonons is driven by photoexcitation of electron-hole pairs by an ultrafast Gaussian pump laser and is treated theoretically using the density matrix formalism. We use realistic wurzite bandstructures taking valence-band mixing and strain-induced piezo- electric fields into account. In addition, the many-body Coulomb ineraction is treated in the screened time-dependent Hartree-Fock approximation. We find that under typical experimental conditions, our microscopic theory can be simplified and mapped onto a loaded string problem which can be easily solved.Comment: 20 pages, 17 figure

On Aharonov-Casher bound states

In this work bound states for the Aharonov-Casher problem are considered. According to Hagen's work on the exact equivalence between spin-1/2 Aharonov-Bohm and Aharonov-Casher effects, is known that the $\boldsymbol{\nabla}\cdot\mathbf{E}$ term cannot be neglected in the Hamiltonian if the spin of particle is considered. This term leads to the existence of a singular potential at the origin. By modeling the problem by boundary conditions at the origin which arises by the self-adjoint extension of the Hamiltonian, we derive for the first time an expression for the bound state energy of the Aharonov-Casher problem. As an application, we consider the Aharonov-Casher plus a two-dimensional harmonic oscillator. We derive the expression for the harmonic oscillator energies and compare it with the expression obtained in the case without singularity. At the end, an approach for determination of the self-adjoint extension parameter is given. In our approach, the parameter is obtained essentially in terms of physics of the problem.Comment: 11 pages, matches published versio

Renormalized Path Integral for the Two-Dimensional Delta-Function Interaction

A path-integral approach for delta-function potentials is presented. Particular attention is paid to the two-dimensional case, which illustrates the realization of a quantum anomaly for a scale invariant problem in quantum mechanics. Our treatment is based on an infinite summation of perturbation theory that captures the nonperturbative nature of the delta-function bound state. The well-known singular character of the two-dimensional delta-function potential is dealt with by considering the renormalized path integral resulting from a variety of schemes: dimensional, momentum-cutoff, and real-space regularization. Moreover, compatibility of the bound-state and scattering sectors is shown.Comment: 26 pages. The paper was significantly expanded and numerous equations were added for the sake of clarity; the main results and conclusions are unchange

A Comparison of 37-Ca(p,n) Cross Sections to 37-Ca β-Decay

This research was sponsored by the National Science Foundation Grant NSF PHY-931478