Crystallography and Surface Structure: An Introduction for Surface Scientists and Nanoscientists

A valuable learning tool as well as a reference, this book provides students and researchers in surface science and nanoscience with the theoretical crystallographic foundations, which are necessary to understand local structure and symmetry of bulk crystals, including ideal and real single crystal surfaces. The author deals with the subject at an introductory level, providing numerous graphic examples to illustrate the mathematical formalism. The book brings together and logically connects many seemingly disparate structural issues and notations used frequently by surface scientists and nanoscientists. Numerous exercises of varying difficulty, ranging from simple questions to small research projects, are included to stimulate discussions about the different subjects

Simultaneous global exact controllability of an arbitrary number of 1D bilinear Schrödinger equations

International audienceWe consider a system of an arbitrary number of \textsc{1d} linear Schrödinger equations on a bounded interval with bilinear control. We prove global exact controllability in large time of these $N$ equations with a single control. This result is valid for an arbitrary potential with generic assumptions on the dipole moment of the considered particle. Thus, even in the case of a single particle, this result extends the available literature. The proof combines local exact controllability around finite sums of eigenstates, proved with Coron's return method, a global approximate controllability property, proved with Lyapunov strategy, and a compactness argument

Molecular Formula Identification using High Resolution Mass Spectrometry: Algorithms and Applications in Metabolomics and Proteomics

Wir untersuchen mehrere theoretische und praktische Aspekte der Identifikation der Summenformel von Biomolekülen mit Hilfe von hochauflösender Massenspektrometrie. Durch die letzten Forschritte in der Instrumentation ist die Massenspektrometrie (MS) zur einen der Schlüsseltechnologien für die Analyse von Biomolekülen in der Proteomik und Metabolomik geworden. Sie misst die Massen der Moleküle in der Probe mit hoher Genauigkeit, und ist für die Messdatenerfassung im Hochdurchsatz gut geeignet. Eine der Kernaufgaben in der MS-basierten Proteomik und Metabolomik ist die Identifikation der Moleküle in der Probe. In der Metabolomik unterliegen Metaboliten der Strukturaufklärung, beginnend bei der Summenformel eines Moleküls, d.h. der Anzahl der Atome jedes Elements. Dies ist der entscheidende Schritt in der Identifikation eines unbekannten Metabolits, da die festgelegte Formel die Anzahl der möglichen Molekülstrukturen auf eine viel kleinere Menge reduziert, die mit Methoden der automatischen Strukturaufklärung weiter analysiert werden kann. Nach der Vorverarbeitung ist die Ausgabe eines Massenspektrometers eine Liste von Peaks, die den Molekülmassen und deren Intensitäten, d.h. der Anzahl der Moleküle mit einer bestimmten Masse, entspricht. Im Prinzip können die Summenformel kleiner Moleküle nur mit präzisen Massen identifiziert werden. Allerdings wurde festgestellt, dass aufgrund der hohen Anzahl der chemisch legitimer Formeln in oberen Massenbereich eine exzellente Massengenaugkeit alleine für die Identifikation nicht genügt. Hochauflösende MS erlaubt die Bestimmung der Molekülmassen und Intensitäten mit hervorragender Genauigkeit. In dieser Arbeit entwickeln wir mehrere Algorithmen und Anwendungen, die diese Information zur Identifikation der Summenformel der Biomolekülen anwenden

The Statistical Foundations of Entropy

In the last two decades, the understanding of complex dynamical systems underwent important conceptual shifts. The catalyst was the infusion of new ideas from the theory of critical phenomena (scaling laws, renormalization group, etc.), (multi)fractals and trees, random matrix theory, network theory, and non-Shannonian information theory. The usual Boltzmann–Gibbs statistics were proven to be grossly inadequate in this context. While successful in describing stationary systems characterized by ergodicity or metric transitivity, Boltzmann–Gibbs statistics fail to reproduce the complex statistical behavior of many real-world systems in biology, astrophysics, geology, and the economic and social sciences.The aim of this Special Issue was to extend the state of the art by original contributions that could contribute to an ongoing discussion on the statistical foundations of entropy, with a particular emphasis on non-conventional entropies that go significantly beyond Boltzmann, Gibbs, and Shannon paradigms. The accepted contributions addressed various aspects including information theoretic, thermodynamic and quantum aspects of complex systems and found several important applications of generalized entropies in various systems

www.springerreference.com/docs/html/chapterdbid/60497.html Mechanical Computing: The Computational Complexity of Physical Devices

- Mechanism: A machine or part of a machine that performs a particular task computation: the use of a computer for calculation.- Computable: Capable of being worked out by calculation, especially using a computer.- Simulation: Used to denote both the modeling of a physical system by a computer as well as the modeling of the operation of a computer by a mechanical system; the difference will be clear from the context. Definition of the Subject Mechanical devices for computation appear to be largely displaced by the widespread use of microprocessor-based computers that are pervading almost all aspects of our lives. Nevertheless, mechanical devices for computation are of interest for at least three reasons: (a) Historical: The use of mechanical devices for computation is of central importance in the historical study of technologies, with a history dating back thousands of years and with surprising applications even in relatively recent times. (b) Technical & Practical: The use of mechanical devices for computation persists and has not yet been completely displaced by widespread use of microprocessor-based computers. Mechanical computers have found applications in various emerging technologies at the micro-scale that combine mechanical functions with computational and control functions not feasible by purely electronic processing. Mechanical computers also have been demonstrated at the molecular scale, and may also provide unique capabilities at that scale. The physical designs for these modern micro and molecular-scale mechanical computers may be based on the prior designs of the large-scale mechanical computers constructed in the past. (c) Impact of Physical Assumptions on Complexity of Motion Planning, Design, and Simulation: The study of computation done by mechanical devices is also of central importance in providing lower bounds on the computational resources such as time and/or space required to simulate a mechanical syste

Discrete Breathers

Nonlinear classical Hamiltonian lattices exhibit generic solutions in the form of discrete breathers. These solutions are time-periodic and (typically exponentially) localized in space. The lattices exhibit discrete translational symmetry. Discrete breathers are not confined to certain lattice dimensions. Necessary ingredients for their occurence are the existence of upper bounds on the phonon spectrum (of small fluctuations around the groundstate) of the system as well as the nonlinearity in the differential equations. We will present existence proofs, formulate necessary existence conditions, and discuss structural stability of discrete breathers. The following results will be also discussed: the creation of breathers through tangent bifurcation of band edge plane waves; dynamical stability; details of the spatial decay; numerical methods of obtaining breathers; interaction of breathers with phonons and electrons; movability; influence of the lattice dimension on discrete breather properties; quantum lattices - quantum breathers. Finally we will formulate a new conceptual aproach capable of predicting whether discrete breather exist for a given system or not, without actually solving for the breather. We discuss potential applications in lattice dynamics of solids (especially molecular crystals), selective bond excitations in large molecules, dynamical properties of coupled arrays of Josephson junctions, and localization of electromagnetic waves in photonic crystals with nonlinear response.Comment: 62 pages, LaTeX, 14 ps figures. Physics Reports, to be published; see also at http://www.mpipks-dresden.mpg.de/~flach/html/preprints.htm