Constructive Field Theory and Applications: Perspectives and Open Problems

In this paper we review many interesting open problems in mathematical physics which may be attacked with the help of tools from constructive field theory. They could give work for future mathematical physicists trained with the constructive methods well within the 21st century

On Automated Lemma Generation for Separation Logic with Inductive Definitions

Separation Logic with inductive definitions is a well-known approach for deductive verification of programs that manipulate dynamic data structures. Deciding verification conditions in this context is usually based on user-provided lemmas relating the inductive definitions. We propose a novel approach for generating these lemmas automatically which is based on simple syntactic criteria and deterministic strategies for applying them. Our approach focuses on iterative programs, although it can be applied to recursive programs as well, and specifications that describe not only the shape of the data structures, but also their content or their size. Empirically, we find that our approach is powerful enough to deal with sophisticated benchmarks, e.g., iterative procedures for searching, inserting, or deleting elements in sorted lists, binary search tress, red-black trees, and AVL trees, in a very efficient way

Strong, Ultra-narrow Peaks of Longitudinal and Hall Resistances in the Regime of Breakdown of the Quantum Hall Effect

With unusually slow and high-resolution sweeps of magnetic field, strong, ultra-narrow (width down to $100 {\rm \mu T}$) resistance peaks are observed in the regime of breakdown of the quantum Hall effect. The peaks are dependent on the directions and even the history of magnetic field sweeps, indicating the involvement of a very slow physical process. Such a process and the sharp peaks are, however, not predicted by existing theories. We also find a clear connection between the resistance peaks and nuclear spin polarization.Comment: 5 pages with 3 figures. To appear in PR

Frequency Scaling of Microwave Conductivity in the Integer Quantum Hall Effect Minima

We measure the longitudinal conductivity $\sigma_{xx}$ at frequencies $1.246 {\rm GHz} \le f \le 10.05$ GHz over a range of temperatures $235 {\rm mK} \le T \le 4.2$ K with particular emphasis on the Quantum Hall plateaus. We find that $Re(\sigma_{xx})$ scales linearly with frequency for a range of magnetic field around the center of the plateaus, i.e. where $\sigma_{xx}(\omega) \gg \sigma_{xx}^{DC}$. The width of this scaling region decreases with higher temperature and vanishes by 1.2 K altogether. Comparison between localization length determined from $\sigma_{xx}(\omega)$ and DC measurements on the same wafer show good agreement.Comment: latex 4 pages, 4 figure

Quantum Transport in a Nanosize Silicon-on-Insulator Metal-Oxide-Semiconductor

An approach is developed for the determination of the current flowing through a nanosize silicon-on-insulator (SOI) metal-oxide-semiconductor field-effect transistors (MOSFET). The quantum mechanical features of the electron transport are extracted from the numerical solution of the quantum Liouville equation in the Wigner function representation. Accounting for electron scattering due to ionized impurities, acoustic phonons and surface roughness at the Si/SiO2 interface, device characteristics are obtained as a function of a channel length. From the Wigner function distributions, the coexistence of the diffusive and the ballistic transport naturally emerges. It is shown that the scattering mechanisms tend to reduce the ballistic component of the transport. The ballistic component increases with decreasing the channel length.Comment: 21 pages, 8 figures, E-mail addresses: [email protected]

Optimizing Multi-Photon Fluorescence Microscopy Light Collection from Living Tissue by Non-Contact Total Emission Detection (TEDII)

Farrando Sicilia, Jordi; Fuente Fuente, Carlo

Demonstration of Prognostics-Enabled Decision Making Algorithms on a Hardware Mobile Robot Test Platform

Prognostics-enabled Decision Making (PDM) is an emerging research area that aims to integrate prognostic health information and knowledge about the future operating conditions into the process of selecting subsequent actions for the system. Previous work developing and testing PDM algorithms has been done in simulation; this paper describes the effort leading to a successful demonstration of PDM algorithms on a hardware mobile robot platform. The hardware platform, based on the K11 planetary rover prototype, was modified to allow injection of selected fault modes related to the rovers electrical power subsystem. The PDM algorithms were adapted to the hardware platform, including development of a software module framework, a new route planner, and modifications to increase the algorithms robustness to sensor noise and system timing issues. A set of test scenarios was chosen to demonstrate the algorithms capabilities. The modifications to run with a hardware platform, the test scenarios, and the test results are described in detail. The results show a successful use of PDM algorithms on a hardware test platform to optimize mission planning in the presence of electrical system faults

Dynamical scaling of the quantum Hall plateau transition

Using different experimental techniques we examine the dynamical scaling of the quantum Hall plateau transition in a frequency range f = 0.1-55 GHz. We present a scheme that allows for a simultaneous scaling analysis of these experiments and all other data in literature. We observe a universal scaling function with an exponent kappa = 0.5 +/- 0.1, yielding a dynamical exponent z = 0.9 +/- 0.2.Comment: v2: Length shortened to fulfil Journal criteri

GTI-space : the space of generalized topological indices

A new extension of the generalized topological indices (GTI) approach is carried out torepresent 'simple' and 'composite' topological indices (TIs) in an unified way. Thisapproach defines a GTI-space from which both simple and composite TIs represent particular subspaces. Accordingly, simple TIs such as Wiener, Balaban, Zagreb, Harary and Randićconnectivity indices are expressed by means of the same GTI representation introduced for composite TIs such as hyper-Wiener, molecular topological index (MTI), Gutman index andreverse MTI. Using GTI-space approach we easily identify mathematical relations between some composite and simple indices, such as the relationship between hyper-Wiener and Wiener index and the relation between MTI and first Zagreb index. The relation of the GTI space with the sub-structural cluster expansion of property/activity is also analysed and some routes for the applications of this approach to QSPR/QSAR are also given