Shank's transformation revisited

AbstractA unified and self-contained approach to the block structure of Shank's table and its cross rules is presented. Wynn's regular and Cordellier's singular cross rules are derived by the Schur-complement method in a unified manner without appealing to Padé approximation. Moreover, by extending the definition of Shank's transformation to certain biinfinite sequences and by introducing a parameter it is possible to get more consistency with respect to Möbius transformations. It is well known that Padé approximants in general don't have this property

The smallest eigenvalue of Hankel matrices

Let H_N=(s_{n+m}),n,m\le N denote the Hankel matrix of moments of a positive measure with moments of any order. We study the large N behaviour of the smallest eigenvalue lambda_N of H_N. It is proved that lambda_N has exponential decay to zero for any measure with compact support. For general determinate moment problems the decay to 0 of lambda_N can be arbitrarily slow or arbitrarily fast. In the indeterminate case, where lambda_N is known to be bounded below by a positive constant, we prove that the limit of the n'th smallest eigenvalue of H_N for N tending to infinity tends rapidly to infinity with n. The special case of the Stieltjes-Wigert polynomials is discussed

Simulation of Channel Segregation During Directional Solidification of In—75 wt pct Ga. Qualitative Comparison with In Situ Observations

International audienceFreckles are common defects in industrial casting. They result from thermosolutal convection due to buoyancy forces generated from density variations in the liquid. The present paper proposes a numerical analysis for the formation of channel segregation using the three-dimensional (3D) cellular automaton (CA)—finite element (FE) model. The model integrates kinetics laws for the nucleation and growth of a microstructure with the solution of the conservation equations for the casting, while introducing an intermediate modeling scale for a direct representation of the envelope of the dendritic grains. Directional solidification of a cuboid cell is studied. Its geometry, the alloy chosen as well as the process parameters are inspired from experimental observations recently reported in the literature. Snapshots of the convective pattern, the solute distribution, and the morphology of the growth front are qualitatively compared. Similitudes are found when considering the coupled 3D CAFE simulations. Limitations of the model to reach direct simulation of the experiments are discussed

Solidification microstructures and solid-state parallels: Recent developments, future directions

Rapid advances in atomistic and phase-field modeling techniques as well as new experiments have led to major progress in solidification science during the first years of this century. Here we review the most important findings in this technologically important area that impact Our quantitative understanding of: (i) key anisotropic properties of the solid-liquid interface that govern solidification pattern evolution, including the solid-liquid interface free energy and the kinetic coefficient; (ii) dendritic solidification at small and large growth rates. with particular emphasis on orientation selection; (iii) regular and irregular eutectic and peritectic microstructures; (iv) effects of convection on microstructure formation; (v) solidification at a high Volume fraction of solid and the related formation of pores and hot cracks: and (vi) solid-state transformations as far as they relate to solidification models anti techniques. In light of this progress, critical issues that point to directions for future research in both solidification and solid-state transformations are identified. (C) 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved

Basic Module Theory over Non-Commutative Rings with Computational Aspects of Operator Algebras

The present text surveys some relevant situations and results where basic Module Theory interacts with computational aspects of operator algebras. We tried to keep a balance between constructive and algebraic aspects.Comment: To appear in the Proceedings of the AADIOS 2012 conference, to be published in Lecture Notes in Computer Scienc

Mushy-Zone Rayleigh Number to Describe Macrosegregation and Channel Segregate Formation During Directional Solidification of Metallic Alloys

A recently defined mushy-zone Rayleigh number (R-aM) that includes side-branching contributions to the mushy-zone permeability has been examined for its correlation with the longitudinal macrosegregation and channel segregate formation. The Rayleigh number shows (1) a strong correlation between the extent of longitudinal macrosegregation and increase in the mushy-zone convection and (2) a good ability to predict the formation of channel segregates during directional solidification

Direct Simulation of a Solidification Benchmark Experiment

International audienceA solidification benchmark experiment is simulated using a three-dimensional cellular automaton-finite element solidification model. The experiment consists of a rectangular cavity containing a Sn-3 wt pct Pb alloy. The alloy is first melted and then solidified in the cavity. A dense array of thermocouples permits monitoring of temperatures in the cavity and in the heat exchangers surrounding the cavity. After solidification, the grain structure is revealed by metallography. X-ray radiography and inductively coupled plasma spectrometry are also conducted to access a distribution map of Pb, or macrosegregation map. The solidification model consists of solutions for heat, solute mass, and momentum conservations using the finite element method. It is coupled with a description of the development of grain structure using the cellular automaton method. A careful and direct comparison with experimental results is possible thanks to boundary conditions deduced from the temperature measurements, as well as a careful choice of the values of the material properties for simulation. Results show that the temperature maps and the macrosegregation map can only be approached with a three-dimensional simulation that includes the description of the grain structure

Direct and Inverse Computation of Jacobi Matrices of Infinite Homogeneous Affine I.F.S

We introduce a new set of algorithms to compute Jacobi matrices associated with measures generated by infinite systems of iterated functions. We demonstrate their relevance in the study of theoretical problems, such as the continuity of these measures and the logarithmic capacity of their support. Since our approach is based on a reversible transformation between pairs of Jacobi matrices, we also discuss its application to an inverse / approximation problem. Numerical experiments show that the proposed algorithms are stable and can reliably compute Jacobi matrices of large order.Comment: 20 pages 6 figure

Columnar and Equiaxed Solidification of Al-7 wt.% Si Alloys in Reduced Gravity in the Framework of the CETSOL Project

International audienceDuring casting, often a dendritic microstructure is formed, resulting in a columnar or an equiaxed grain structure, or leading to a transition from columnar to equiaxed growth (CET). The detailed knowledge of the critical parameters for the CET is important because the microstructure affects materials properties. To provide unique data for testing of fundamental theories of grain and microstructure formation, solidification experiments in microgravity environment were performed within the European Space Agency Microgravity Application Promotion (ESA MAP) project Columnar-to-Equiaxed Transition in SOLidification Processing (CETSOL). Reduced gravity allows for purely diffusive solidification conditions, i.e., suppressing melt flow and sedimentation and floatation effects. On-board the International Space Station, Al-7 wt.% Si alloys with and without grain refiners were solidified in different temperature gradients and with different cooling conditions. Detailed analysis of the microstructure and the grain structure showed purely columnar growth for nonrefined alloys. The CET was detected only for refined alloys, either as a sharp CET in the case of a sudden increase in the solidification velocity or as a progressive CET in the case of a continuous decrease of the temperature gradient. The present experimental data were used for numerical modeling of the CET with three different approaches: (1) a front tracking model using an equiaxed growth model, (2) a three-dimensional (3D) cellular automaton–finite element model, and (3) a 3D dendrite needle network method. Each model allows for predicting the columnar dendrite tip undercooling and the growth rate with respect to time. Furthermore, the positions of CET and the spatial extent of the CET, being sharp or progressive, are in reasonably good quantitative agreement with experimental measurements

Endogenous retroviral signatures predict immunotherapy response in clear cell renal cell carcinoma

Human endogenous retroviruses (hERVs) are remnants of exogenous retroviruses that have integrated into the genome throughout evolution. We developed a computational workflow, hervQuant, which identified more than 3,000 transcriptionally active hERVs within The Cancer Genome Atlas (TCGA) pan-cancer RNA-Seq database. hERV expression was associated with clinical prognosis in several tumor types, most significantly clear cell renal cell carcinoma (ccRCC). We explored two mechanisms by which hERV expression may influence the tumor immune microenvironment in ccRCC: (i) RIG-I-like signaling and (ii) retroviral antigen activation of adaptive immunity. We demonstrated the ability of hERV signatures associated with these immune mechanisms to predict patient survival in ccRCC, independent of clinical staging and molecular subtyping. We identified potential tumor-specific hERV epitopes with evidence of translational activity through the use of a ccRCC ribosome profiling (Ribo-Seq) dataset, validated their ability to bind HLA in vitro, and identified the presence of MHC tetramer-positive T cells against predicted epitopes. hERV sequences identified through this screening approach were significantly more highly expressed in ccRCC tumors responsive to treatment with programmed death receptor 1 (PD-1) inhibition. hervQuant provides insights into the role of hERVs within the tumor immune microenvironment, as well as evidence that hERV expression could serve as a biomarker for patient prognosis and response to immunotherapy. © 2018 American Society for Clinical Investigation. All rights reserved