Science, Art and Geometrical Imagination

From the geocentric, closed world model of Antiquity to the wraparound universe models of relativistic cosmology, the parallel history of space representations in science and art illustrates the fundamental role of geometric imagination in innovative findings. Through the analysis of works of various artists and scientists like Plato, Durer, Kepler, Escher, Grisey or the present author, it is shown how the process of creation in science and in the arts rests on aesthetical principles such as symmetry, regular polyhedra, laws of harmonic proportion, tessellations, group theory, etc., as well as beauty, conciseness and emotional approach of the world.Comment: 22 pages, 28 figures, invited talk at the IAU Symposium 260 "The Role of Astronomy in Society and Culture", UNESCO, 19-23 January 2009, Paris, Proceedings to be publishe

ColDICE: a parallel Vlasov-Poisson solver using moving adaptive simplicial tessellation

Resolving numerically Vlasov-Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conforming, self-adaptive simplicial tessellation of which the vertices follow the Lagrangian equations of motion. The algorithm is implemented both in six- and four-dimensional phase-space. Refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase-space sheet at second order relying on additional tracers created when needed at runtime. In order to preserve in the best way the Hamiltonian nature of the system, refinement is anisotropic and constrained by measurements of local Poincar\'e invariants. Resolution of Poisson equation is performed using the fast Fourier method on a regular rectangular grid, similarly to particle in cells codes. To compute the density projected onto this grid, the intersection of the tessellation and the grid is calculated using the method of Franklin and Kankanhalli (1993) generalised to linear order. As preliminary tests of the code, we study in four dimensional phase-space the evolution of an initially small patch in a chaotic potential and the cosmological collapse of a fluctuation composed of two sinusoidal waves. We also perform a "warm" dark matter simulation in six-dimensional phase-space that we use to check the parallel scaling of the code.Comment: Code and illustration movies available at: http://www.vlasix.org/index.php?n=Main.ColDICE - Article submitted to Journal of Computational Physic

Fast Non-Parametric Learning to Accelerate Mixed-Integer Programming for Online Hybrid Model Predictive Control

Today's fast linear algebra and numerical optimization tools have pushed the frontier of model predictive control (MPC) forward, to the efficient control of highly nonlinear and hybrid systems. The field of hybrid MPC has demonstrated that exact optimal control law can be computed, e.g., by mixed-integer programming (MIP) under piecewise-affine (PWA) system models. Despite the elegant theory, online solving hybrid MPC is still out of reach for many applications. We aim to speed up MIP by combining geometric insights from hybrid MPC, a simple-yet-effective learning algorithm, and MIP warm start techniques. Following a line of work in approximate explicit MPC, the proposed learning-control algorithm, LNMS, gains computational advantage over MIP at little cost and is straightforward for practitioners to implement

Niobium and tantalum oxides as model materials for resistive switching effect

Celem współczesnej nauki jest znalezienie nowych rozwiązań dla wciąż zmieniającego się świata. Jednym z wyzwań jakie stawiają sobie naukowcy jest znalezienie nowego materiału dla pamięci nieulotnych o dużej gęstości zapisu, który w coraz to mniejszej scali, nanoskali, pozwoli na zapisanie coraz większej ilości danych. Takimi materiałami mogą być tlenki metali przejściowych, które bazując na reakcji redoks, wykazują zdolność do zmiany oporu pod wpływem przyłożonego pola elektrycznego. Jednakże wiedza o fizycznych podstawach tego zjawiska jest wciąż ograniczona. Do tej pory nie zostało jasno i klarownie przedstawione wyjaśnienie natury zjawiska przełączania rezystywnego, a co za tym idzie jego aplikacja w urządzeniach elektronicznych, może być nadal problematyczna. Niniejsza praca doktorska została poświęcona tlenkom metali przejściowych jakim są tlenki niobu i tantalu. Chociaż jak się często podkreśla są to materiały wciąż badane od wielu lat i wydaje się, że posiadamy już duży zasób wiedzy na ich temat, to nadal są miejsca, gdzie materiały te potrafią nas zaskoczyć. Praca ta została podzielona na dwie części. Pierwsza została poświęcona monokryształowi Nb₂O₅ natomiast w drugiej badania były skoncentrowane na cienkich warstwach Nb-O i Ta-O. W pracy przedstawiono wyniki badań podstawowych właściwości fizykochemicznych materiału przed oraz po redukcji termicznej. Temperatury od 800°C -1000°C znacząco redukują monokryształ Nb₂O₅. Natomiast w cienkich warstwach amorficznych Nb-O czy Ta-O o złożonej strukturze wewnętrznej, w której skład wchodzą warstwy pięciotlenków, zaobserwowano ten efekt w znacznie niższych temperaturach. Nawet niewielka zmiana temperatury (300°C dla Nb-O i 600°C dla Ta-O) wpływa na stopień redukcji warstwy. Wpływ temperatury ma również silenie znaczenia na przewodnictwo. W cienkich warstwach zaobserwowano przełączanie oporności typu bipolarnego. Natomiast w krysztale ten sam efekt również był zauważalny, lecz znacznie słabszy. Można było, podobnie jak w cienkich warstwach, zmodyfikować jego powierzchnie w celu zapisania informacji przy pomocy igły z mikroskopu sił atomowych. Reasumując przedstawione wyniki badań w tej pracy pozwalają w szerszy sposób spojrzeć na problem chemicznej i strukturalnej niestabilności tlenków metali przejściowych (Nb, Ta) w krysztale jak i cienkich warstwach. Pokazują wpływ tych zmian na ich przewodnictwo, które może być lokalnie kontrolowane, pozwalając na łatwiejszą aplikacje tych materiałów

Global Scale Impacts

Global scale impacts modify the physical or thermal state of a substantial fraction of a target asteroid. Specific effects include accretion, family formation, reshaping, mixing and layering, shock and frictional heating, fragmentation, material compaction, dilatation, stripping of mantle and crust, and seismic degradation. Deciphering the complicated record of global scale impacts, in asteroids and meteorites, will lead us to understand the original planet-forming process and its resultant populations, and their evolution in time as collisions became faster and fewer. We provide a brief overview of these ideas, and an introduction to models.Comment: A chapter for Asteroids IV, a new volume in the Space Science Series, University of Arizona Press (Patrick Michel, Francesca E. DeMeo, William F. Bottke, Eds.

Structural studies on Functional Materials using Solid-State NMR, Powder X-ray Diffraction and DFT Calculations

Analytical and theoretical techniques were used in this work for structural studies of framework materials. One and two dimensional 31P and 17O solid state NMR experiments highlight subtle thermally induced structural changes in (MoO2)2P2O7 pyrophosphate, tungsten trioxide WO3 and negative thermal expansion ZrW2O8. DFT methods using CASTEP software to calculate 31P and 17O NMR parameters are performed on these structures and discussed in comparison to experimental results, published structures and thermal mechanisms

A review of mechanoluminescence in inorganic solids : compounds, mechanisms, models and applications

Mechanoluminescence (ML) is the non-thermal emission of light as a response to mechanical stimuli on a solid material. While this phenomenon has been observed for a long time when breaking certain materials, it is now being extensively explored, especially since the discovery of non-destructive ML upon elastic deformation. A great number of materials have already been identified as mechanoluminescent, but novel ones with colour tunability and improved sensitivity are still urgently needed. The physical origin of the phenomenon, which mainly involves the release of trapped carriers at defects with the help of stress, still remains unclear. This in turn hinders a deeper research, either theoretically or application oriented. In this review paper, we have tabulated the known ML compounds according to their structure prototypes based on the connectivity of anion polyhedra, highlighting structural features, such as framework distortion, layered structure, elastic anisotropy and microstructures, which are very relevant to the ML process. We then review the various proposed mechanisms and corresponding mathematical models. We comment on their contribution to a clearer understanding of the ML phenomenon and on the derived guidelines for improving properties of ML phosphors. Proven and potential applications of ML in various fields, such as stress field sensing, light sources, and sensing electric (magnetic) fields, are summarized. Finally, we point out the challenges and future directions in this active and emerging field of luminescence research