We have developed and implemented a selfconsistent density functional method using standard norm-conserving pseudopotentials and a flexible, numerical linear combination of atomic orbitals basis set, which includes multiple-zeta and polarization orbitals. Exchange and correlation are treated with the local spin density or generalized gradient approximations. The basis functions and the electron density are projected on a real-space grid, in order to calculate the Hartree and exchange-correlation potentials and matrix elements, with a number of operations that scales linearly with the size of the system. We use a modified energy functional, whose minimization produces orthogonal wavefunctions and the same energy and density as the Kohn-Sham energy functional, without the need for an explicit orthogonalization. Additionally, using localized Wannier-like electron wavefunctions allows the computation time and memory required to minimize the energy to also scale linearly with the size of the system. Forces and stresses are also calculated efficiently and accurately, thus allowing structural relaxation and molecular dynamics simulations.

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The SIESTA method for ab initio order-N materials simulation

Complex dynamical systems, ranging from ecosystems to financial markets and the climate, can have tipping points at which a sudden shift to a contrasting dynamical regime may occur. Although predicting such critical points before they are reached is extremely difficult, work in different scientific fields is now suggesting the existence of generic early-warning signals that may indicate for a wide class of systems if a critical threshold is approaching.

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Early-warning signals for critical transitions

The field of metaheuristics for the application to combinatorial optimization problems is a rapidly growing field of research. This is due to the importance of combinatorial optimization problems for the scientific as well as the industrial world. We give a survey of the nowadays most important metaheuristics from a conceptual point of view. We outline the different components and concepts that are used in the different metaheuristics in order to analyze their similarities and differences. Two very important concepts in metaheuristics are intensification and diversification. These are the two forces that largely determine the behavior of a metaheuristic. They are in some way contrary but also complementary to each other. We introduce a framework, that we call the I&D frame, in order to put different intensification and diversification components into relation with each other. Outlining the advantages and disadvantages of different metaheuristic approaches we conclude by pointing out the importance of hybridization of metaheuristics as well as the integration of metaheuristics and other methods for optimization.

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Metaheuristics in combinatorial optimization: Overview and conceptual comparison

Complex networks arise in a wide range of biological and sociotechnical systems. Epidemic spreading is central to our understanding of dynamical processes in complex networks, and is of interest to physicists, mathematicians, epidemiologists, and computer and social scientists. This review presents the main results and paradigmatic models in infectious disease modeling and generalized social contagion processes.

Epidemic processes in complex networks

Wavelets were developed independently by mathematicians, quantum physicists, electrical engineers and geologists, but collaborations among these fields during the last decade have led to new and varied applications. What are wavelets, and why might they be useful to you? The fundamental idea behind wavelets is to analyze according to scale. Indeed, some researchers feel that using wavelets means adopting a whole new mind-set or perspective in processing data. Wavelets are functions that satisfy certain mathematical requirements and are used in representing data or other functions. Most of the basic wavelet theory has now been done. The mathematics have been worked out in excruciating detail, and wavelet theory is now in the refinement stage. This involves generalizing and extending wavelets, such as in extending wavelet packet techniques. The future of wavelets lies in the as-yet uncharted territory of applications. Wavelet techniques have not been thoroughly worked out in such applications as practical data analysis, where, for example, discretely sampled time-series data might need to be analyzed. Such applications offer exciting avenues for exploration. >

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An introduction to wavelets

Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering

Partial Contents: 1. Ideal Polymer Chain. A Freely Jointed Chain. Flexibility of a Polymer Chain. Size of an Ideal Polymer Chain. 2. Polymer Chains with Volume Interactions. Basic Definitions and Methods. Polymer Chain Models of Systems with Volume Interactions. Basic Definitions in the Theory of Volume Interactions in Polymer Systems. Perturbation Theory for Polymer Coils with Volume Interactions. 3. Single Macromolecule with Volume Interactions. Swelling of a Polymer Coil in Good Solvent (excluded volume problem). Renormalization Group and S-expansion Methods Applied to the Excluded Volume Problem. Properties of Polymer Coils with Excluded Volume (the scaling concept and the notion of a blob). 4. Polymer solutions and melts. Basic Preliminary Data and Definitions. Theory of Polymer Solutions and Melts in the Self-Consistent Field Approximation. Appendix. Flory Lattice Theory of Polymer Solutions and Melts. 5. Other Polymer Systems. Polymer Mixtures and Block Copolymers. Liquid- Crystal Polymers. High Elasticity of Polymer Networks. Methods of Polymer Network Synthesis. 6. Dynamic Properties of Polymer Solutions and Melts. The Rouse Model: a Phantom Chain in Immobile Solvent. The

Statistical physics of macromolecules

Senior level/graduate level text/reference presenting state-of-the- art numerical techniques to solve the wave equation in heterogeneous fluid-solid media. Numerical models have become standard research tools in acoustic laboratories, and thus computational acoustics is becoming an increasingly important branch of ocean acoustic science. The first edition of this successful book, written by the recognized leaders of the field, was the first to present a comprehensive and modern introduction to computational ocean acoustics accessible to students. This revision, with 100 additional pages, completely updates the material in the first edition and includes new models based on current research. It includes problems and solutions in every chapter, making the book more useful in teaching (the first edition had a separate solutions manual). The book is intended for graduate and advanced undergraduate students of acoustics, geology and geophysics, applied mathematics, ocean engineering or as a reference in computational methods courses, as well as professionals in these fields, particularly those working in government (especially Navy) and industry labs engaged in the development or use of propagating models.

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Susan McKay

Papers

Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering

Statistical physics of macromolecules

Computational Ocean Acoustics

Data Reduction and Error Analysis for the Physical Sciences

Monte Carlo Simulation in Statistical Physics