Macrosegregation during plane front directional solidification of Csl-1 wt. percent Tll alloy

Macrosegregation produced during vertical Bridgeman directional solidification of Csl-1 wt. pct. Tll in crucibles of varying diameter, from 0.5 to 2.0 cm, was examined. Gravity driven convection is present in the melt even in the smallest crucible diameter of 0.5 cm. Observed solutal profiles are in agreement with the analytical boundary layer model of Favier which describes macrosegregation in the presence of convection. The scintillation efficiency of Csl decreases along the specimen length as the thallium iodide content of the alloy increases

Geometric reconstruction methods for electron tomography

Electron tomography is becoming an increasingly important tool in materials science for studying the three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is seriously affected by the problems of missing wedge artefacts and nonlinear projection intensities due to diffraction effects. The former refers to the fact that data cannot be acquired over the full $180^\circ$ tilt range; the latter implies that for some orientations, crystalline structures can show strong contrast changes. To overcome these problems we introduce and discuss several algorithms from the mathematical fields of geometric and discrete tomography. The algorithms incorporate geometric prior knowledge (mainly convexity and homogeneity), which also in principle considerably reduces the number of tilt angles required. Results are discussed for the reconstruction of an InAs nanowire

Quantum de Finetti Theorems under Local Measurements with Applications

Quantum de Finetti theorems are a useful tool in the study of correlations in quantum multipartite states. In this paper we prove two new quantum de Finetti theorems, both showing that under tests formed by local measurements one can get a much improved error dependence on the dimension of the subsystems. We also obtain similar results for non-signaling probability distributions. We give the following applications of the results: We prove the optimality of the Chen-Drucker protocol for 3-SAT, under the exponential time hypothesis. We show that the maximum winning probability of free games can be estimated in polynomial time by linear programming. We also show that 3-SAT with m variables can be reduced to obtaining a constant error approximation of the maximum winning probability under entangled strategies of O(m^{1/2})-player one-round non-local games, in which the players communicate O(m^{1/2}) bits all together. We show that the optimization of certain polynomials over the hypersphere can be performed in quasipolynomial time in the number of variables n by considering O(log(n)) rounds of the Sum-of-Squares (Parrilo/Lasserre) hierarchy of semidefinite programs. As an application to entanglement theory, we find a quasipolynomial-time algorithm for deciding multipartite separability. We consider a result due to Aaronson -- showing that given an unknown n qubit state one can perform tomography that works well for most observables by measuring only O(n) independent and identically distributed (i.i.d.) copies of the state -- and relax the assumption of having i.i.d copies of the state to merely the ability to select subsystems at random from a quantum multipartite state. The proofs of the new quantum de Finetti theorems are based on information theory, in particular on the chain rule of mutual information.Comment: 39 pages, no figure. v2: changes to references and other minor improvements. v3: added some explanations, mostly about Theorem 1 and Conjecture 5. STOC version. v4, v5. small improvements and fixe

Quantitative Evaluation of Particle Morphology

In geomechanics research shape is most often qualitatively assessed. Various definitions on how to quantify shape have been applied in the literature. This paper assesses the feasibility of applying these definitions to digital images of sand grains. Firstly the way in which size can be calculated from these digital images is discussed, then the sphericity and convexity definitions proposed by Sympatec (2008) are considered. These definitions of sphericity and convexity (SQP, Cx) are relatively easy to apply. By relating SQP and Cx to the qualitative measures of particle shape that are most often used in geotechnical sample description, we argue that there is significant scope to introduce these measures to engineering practice (Altuhafi et al., 2012). We show that distributions of convexity and sphericity obtained in 2D and 3D analyses differ

Heavy-tailed Independent Component Analysis

Independent component analysis (ICA) is the problem of efficiently recovering a matrix $A \in \mathbb{R}^{n\times n}$ from i.i.d. observations of $X=AS$ where $S \in \mathbb{R}^n$ is a random vector with mutually independent coordinates. This problem has been intensively studied, but all existing efficient algorithms with provable guarantees require that the coordinates $S_i$ have finite fourth moments. We consider the heavy-tailed ICA problem where we do not make this assumption, about the second moment. This problem also has received considerable attention in the applied literature. In the present work, we first give a provably efficient algorithm that works under the assumption that for constant $\gamma > 0$, each $S_i$ has finite $(1+\gamma)$-moment, thus substantially weakening the moment requirement condition for the ICA problem to be solvable. We then give an algorithm that works under the assumption that matrix $A$ has orthogonal columns but requires no moment assumptions. Our techniques draw ideas from convex geometry and exploit standard properties of the multivariate spherical Gaussian distribution in a novel way.Comment: 30 page

Three-dimensionality of space and the quantum bit: an information-theoretic approach

It is sometimes pointed out as a curiosity that the state space of quantum two-level systems, i.e. the qubit, and actual physical space are both three-dimensional and Euclidean. In this paper, we suggest an information-theoretic analysis of this relationship, by proving a particular mathematical result: suppose that physics takes place in d spatial dimensions, and that some events happen probabilistically (not assuming quantum theory in any way). Furthermore, suppose there are systems that carry "minimal amounts of direction information", interacting via some continuous reversible time evolution. We prove that this uniquely determines spatial dimension d=3 and quantum theory on two qubits (including entanglement and unitary time evolution), and that it allows observers to infer local spatial geometry from probability measurements.Comment: 13 + 22 pages, 9 figures. v4: some clarifications, in particular in Section V / Appendix C (added Example 39

Characterization of Calcium Phosphate Structures obtained by 3D Printing

Image processing is a technique that is increasingly being used to extract, quickly and easily, different parameters used to characterize three-dimensional structures that, through other conventional characterization techniques, would take much longer and be more expensive. The objective of this study is to analyse the macroscopic attributes (filament geometry, porosity, specific surface and concavity), of three-dimensional structures of calcium phosphate with different filament morphologies from the images obtained by computed micro-tomography (Micro- CT). The study compares the results obtained with three software (CTAn, ImageJ and MeshMixer), as well as those obtained from theoretical calculations from 2D measurements. The sections of the different nozzles used by scanning electron microscopy (SEM) have also been characterized, comparing them with the sections of the printed filaments. In order to determine the degree of concavity of the different structures, an estimation of this parameter has been made both in 3D, using an extension of ImageJ software, as in 2D, from the images of the filament sections (Micro-CT) and nozzles (SEM). The study has allowed quantifying the degree of deviation in the different morphological parameters between the nozzles and the printed filaments, although the fact of having used imaging techniques (SEM and Micro-CT) with different resolution may also have influenced the observed differences. For porosity, the different software used have given similar values and it has been observed that when structures with a fixed pore size are printed (as in this case), a smaller filament measure increases the porosity of the material. Regarding the specific surface, the calculation of meshes has not given good results, and this may be due to an error when reconstructing the mesh from the Micro-CT images by the 3D Viewer extension of the ImageJ program. On the other hand, it has been observed that, for specific surface calculations, not only the shape of the filament is important, but also the measurement of its section; the filaments with a small section are repeated more throughout the piece and therefore the total value of specific surface is larger than those pieces with larger sections. Finally, in the case of concavity, the two ways of calculation (2D and 3D) have given similar results, and the 2D comparison of the section of the nozzle and the section of the filament have revealed the existing deviation between both of them.El processament d´imatges és una eina que s´està utilitzant cada vegada més per extreure, de manera senzilla i ràpida, diferents paràmetres utilitzats per caracteritzar estructures tridimensionals que, mitjançant altres tècniques de caracterització trigaríem molt més temps i serien més costoses. L'objectiu d'aquest estudi és analitzar els atributs macroscòpics (geometria dels filaments, porositat, superfície específica i concavitat), d'estructures tridimensionals de fosfat de calci amb diferents morfologies dels filaments a partir de les imatges obtingudes per micro-tomografia computeritzada (Micro-CT). A l’estudi es comparen els resultats obtinguts amb tres softwares (CTAN, ImageJ i MeshMixer), així com els obtinguts a partir dels càlculs teòrics a partir de mesures en 2D. També s’han caracteritzat les seccions dels diferents broquets d’impressió utilitzats mitjançant microscòpia electrònica de rastreig (SEM), comparant-los amb la secció dels filaments impresos. Pel que fa a la determinació del grau de concavitat de les diferents estructures, s'ha fet una estimació d’aquest paràmetre tant en 3D, utilitzat una extensió del software ImageJ, com en 2D, a partir de les imatges de les seccions dels filaments (Micro-CT) i dels broquets d’impressió (SEM). L’estudi ha permès quantificar el grau de desviació existent en els diferents paràmetres morfològics entre els broquets d’impressió i els filaments impresos, malgrat que el fet d’haver utilitzat tècniques d’imatge (SEM i micro-CT) amb diferent resolució també pot haver influït en les diferències observades. Pel que fa a la porositat, els diferents softwares emprats han resultat en valors similars i s'ha observat que quan s'imprimeix estructures amb una mida de porus fix (com és en aquest cas), una mida de filament menor augmenta la porositat del material. Respecte a la superfície específica, el càlcul per malles no ha donat bons resultats, i això pot ser degut a un error a l'hora de reconstruir la malla a partir de les imatges de Micro-CT per l'extensió 3D Viewer de el programa ImageJ. D´altra banda, s´ha pogut observar que, per als càlculs de superfície especifica, no només és important la forma del filament, sinó també la mida de la seva secció; els filaments con una secció petita es repeteixen més al llarg de la peça i per tant el valor total de superfície especifica és més gran que en peces amb una secció més gran. Finalment, en el cas de la concavitat, les dues formes de càlcul (3D i 2D) han donat resultats semblants, i la comparativa en 2D de la secció del broquet d’impressió i la secció del filament ha posat de manifest la desviació existent entre ambdues.El procesamiento de imágenes es una técnica que cada vez se está usando más para extraer, de manera rápida y sencilla, diferentes parámetros utilizados para caracterizar estructuras tridimensionales que, mediante otras técnicas de caracterización convencionales llevarían mucho más tiempo y serían más costosas. El objetivo de este estudio es analizar los atributos macroscópicos (geometría de los filamentos, porosidad, superficie específica y concavidad), de estructuras tridimensionales de fosfato de calcio con diferentes morfologías de filamentos a partir de las imágenes obtenidas por micro-tomografía computarizada (Micro-CT). En el estudio se comparan los resultados obtenidos con tres softwares (CTAn, ImageJ y MeshMixer), así como los obtenidos a partir de los cálculos teóricos a partir de medidas en 2D. También se han caracterizado las secciones de las diferentes boquillas de impresión utilizadas mediante microscopia electrónica de rastreo (SEM), comparándolos con las secciones de los filamentos impresos. Para poder determinar el grado de concavidad de las diferentes estructuras, se ha hecho una estimación de este parámetro tanto en 3D, utilizando una extensión del software ImageJ, como en 2D, a partir de las imágenes de las secciones de los filamentos (Micro-CT) y de las boquillas de impresión (SEM). El estudio ha permitido cuantificar el grado de desviación existente en los diferentes parámetros morfológicos entre las boquillas de impresión y los filamentos impresos, a pesar de que el hecho de haber usado técnicas de imagen (SEM y Micro-CT) con diferente resolución también puede haber influido en las diferencias observadas. Para la porosidad, los diferentes softwares usados han dado valores similares y se ha observado que cuando se imprimen estructuras con una medida de poro fija (como es en este caso), una medida de filamento menor aumenta la porosidad del material. Respecto a la superficie específica, el cálculo de mallas no ha dado buenos resultados, y esto se puede deber a un error a la hora de reconstruir la malla a partir de las imágenes de Micro-CT por la extensión 3D Viewer del programa ImageJ. Por otra parte, se ha podido observar que, para los cálculos de superficie específica, no solo es importante la forma del filamento, sino también la medida de su sección; los filamentos con una sección pequeña se repiten más a lo largo de la pieza y por tanto el valor total de superficie específica es más grande que aquellas piezas con secciones más grandes. Finalmente, en el caso de la concavidad, las dos maneras de cálculo (2D y 3D) han dado resultados similares, y la comparación en 2D de la sección de la boquilla de impresión y la sección del filamento han puesto de manifiesto la desviación existente entre ambos