40 research outputs found
Zero Lyapunov exponents of the Hodge bundle
By the results of G. Forni and of R. Trevi\~no, the Lyapunov spectrum of the
Hodge bundle over the Teichm\"uller geodesic flow on the strata of Abelian and
of quadratic differentials does not contain zeroes even though for certain
invariant submanifolds zero exponents are present in the Lyapunov spectrum. In
all previously known examples, the zero exponents correspond to those
PSL(2,R)-invariant subbundles of the real Hodge bundle for which the monodromy
of the Gauss-Manin connection acts by isometries of the Hodge metric. We
present an example of an arithmetic Teichm\"uller curve, for which the real
Hodge bundle does not contain any PSL(2,R)-invariant, continuous subbundles,
and nevertheless its spectrum of Lyapunov exponents contains zeroes. We
describe the mechanism of this phenomenon; it covers the previously known
situation as a particular case. Conjecturally, this is the only way zero
exponents can appear in the Lyapunov spectrum of the Hodge bundle for any
PSL(2,R)-invariant probability measure.Comment: 47 pages, 10 figures. Final version (based on the referee's report).
A slightly shorter version of this article will appear in Commentarii
Mathematici Helvetici. A pdf file containing a copy of the Mathematica
routine "FMZ3-Zariski-numerics_det1.nb" is available at this link here:
http://w3.impa.br/~cmateus/files/FMZ3-Zariski-numerics_det1.pd
Calculus of Variations
Since its invention, the calculus of variations has been a central field of mathematics and physics, providing tools and techniques to study problems in geometry, physics and partial differential equations. On the one hand, steady progress is made on long-standing questions concerning minimal surfaces, curvature flows and related objects. On the other hand, new questions emerge, driven by applications to diverse areas of mathematics and science. The July 2012 Oberwolfach workshop on the Calculus of Variations witnessed the solutions of famous conjectures and the emerging of exciting new lines of research
Computer Science for Continuous Data:Survey, Vision, Theory, and Practice of a Computer Analysis System
Building on George Boole's work, Logic provides a rigorous foundation for the powerful tools in Computer Science that underlie nowadays ubiquitous processing of discrete data, such as strings or graphs. Concerning continuous data, already Alan Turing had applied "his" machines to formalize and study the processing of real numbers: an aspect of his oeuvre that we transform from theory to practice.The present essay surveys the state of the art and envisions the future of Computer Science for continuous data: natively, beyond brute-force discretization, based on and guided by and extending classical discrete Computer Science, as bridge between Pure and Applied Mathematics
Robot Manipulators
Robot manipulators are developing more in the direction of industrial robots than of human workers. Recently, the applications of robot manipulators are spreading their focus, for example Da Vinci as a medical robot, ASIMO as a humanoid robot and so on. There are many research topics within the field of robot manipulators, e.g. motion planning, cooperation with a human, and fusion with external sensors like vision, haptic and force, etc. Moreover, these include both technical problems in the industry and theoretical problems in the academic fields. This book is a collection of papers presenting the latest research issues from around the world
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Acoustic and Elastic Waves: Recent Trends in Science and Engineering
The present Special Issue intends to explore new directions in the field of acoustics and ultrasonics. The interest includes, but is not limited to, the use of acoustic technology for condition monitoring of materials and structures. Topics of interest (among others): • Acoustic emission in materials and structures (without material limitation) • Innovative cases of ultrasonic inspection • Wave dispersion and waveguides • Monitoring of innovative materials • Seismic waves • Vibrations, damping and noise control • Combination of mechanical wave techniques with other types for structural health monitoring purposes. Experimental and numerical studies are welcome