Reduced basis catalogs for gravitational wave templates

We introduce a reduced basis approach as a new paradigm for modeling, representing and searching for gravitational waves. We construct waveform catalogs for non-spinning compact binary coalescences, and we find that for accuracies of 99% and 99.999% the method generates a factor of about $10-10^5$ fewer templates than standard placement methods. The continuum of gravitational waves can be represented by a finite and comparatively compact basis. The method is robust under variations in the noise of detectors, implying that only a single catalog needs to be generated.Comment: Minor changes in some of the phrasing to match the version as published in PR

Heat flow and calculus on metric measure spaces with Ricci curvature bounded below - the compact case

We provide a quick overview of various calculus tools and of the main results concerning the heat flow on compact metric measure spaces, with applications to spaces with lower Ricci curvature bounds. Topics include the Hopf-Lax semigroup and the Hamilton-Jacobi equation in metric spaces, a new approach to differentiation and to the theory of Sobolev spaces over metric measure spaces, the equivalence of the L^2-gradient flow of a suitably defined "Dirichlet energy" and the Wasserstein gradient flow of the relative entropy functional, a metric version of Brenier's Theorem, and a new (stronger) definition of Ricci curvature bound from below for metric measure spaces. This new notion is stable w.r.t. measured Gromov-Hausdorff convergence and it is strictly connected with the linearity of the heat flow.Comment: To the memory of Enrico Magenes, whose exemplar life, research and teaching shaped generations of mathematician

Fractional Operators, Dirichlet Averages, and Splines

Fractional differential and integral operators, Dirichlet averages, and splines of complex order are three seemingly distinct mathematical subject areas addressing different questions and employing different methodologies. It is the purpose of this paper to show that there are deep and interesting relationships between these three areas. First a brief introduction to fractional differential and integral operators defined on Lizorkin spaces is presented and some of their main properties exhibited. This particular approach has the advantage that several definitions of fractional derivatives and integrals coincide. We then introduce Dirichlet averages and extend their definition to an infinite-dimensional setting that is needed to exhibit the relationships to splines of complex order. Finally, we focus on splines of complex order and, in particular, on cardinal B-splines of complex order. The fundamental connections to fractional derivatives and integrals as well as Dirichlet averages are presented

Wet Granular Materials

Most studies on granular physics have focused on dry granular media, with no liquids between the grains. However, in geology and many real world applications (e.g., food processing, pharmaceuticals, ceramics, civil engineering, constructions, and many industrial applications), liquid is present between the grains. This produces inter-grain cohesion and drastically modifies the mechanical properties of the granular media (e.g., the surface angle can be larger than 90 degrees). Here we present a review of the mechanical properties of wet granular media, with particular emphasis on the effect of cohesion. We also list several open problems that might motivate future studies in this exciting but mostly unexplored field.Comment: review article, accepted for publication in Advances in Physics; tex-style change

Immunohistochemical Detection of MYC-driven Diffuse Large B-Cell Lymphomas

Diffuse large B cell lymphoma (DLBCL) is a clinically and genetically heterogeneous disease. A small subset of DLBCLs has translocations involving the MYC locus and an additional group has a molecular signature resembling Burkitt lymphoma (mBL). Presently, identification of such cases by morphology is unreliable and relies on cytogenetic or complex molecular methods such as gene transcriptional profiling. Herein, we describe an immunohistochemical (IHC) method for identifying DLBCLs with increased MYC protein expression. We tested 77 cases of DLBCL and identified 15 cases with high MYC protein expression (nuclear staining in >50% of tumor cells). All MYC translocation positive cases had increased MYC protein expression by this IHC assay. In addition, gene set enrichment analysis (GSEA) of the DLBCL transcriptional profiles revealed that tumors with increased MYC protein expression (regardless of underlying MYC translocation status) had coordinate upregulation of MYC target genes, providing molecular confirmation of the IHC results. We then generated a molecular classifier derived from the MYC IHC results in our cases and employed it to successfully classify mBLs from two previously reported independent case series, providing additional confirmation that the MYC IHC results identify clinically important subsets of DLBCLs. Lastly, we found that DLBCLs with high MYC protein expression had inferior overall survival when treated with R-CHOP. In conclusion, the IHC method described herein can be used to readily identify the biologically and clinically distinct cases of MYC-driven DLBCL, which represent a clinically significant subset of DLBCL cases due to their inferior overall survival

Lubricated revolute joints in rigid multibody systems

The main purpose of this work is to present a general methodology for modeling lubricated revolute joints in constrained rigid multibody systems. In the dynamic analysis of journal-bearings, the hydrodynamic forces, which include both squeeze and wedge effects, generated by the lubricant fluid, oppose the journal motion. The hydrodynamic forces are obtained by integrating the pressure distribution evaluated with the aid of Reynolds’ equation, written for the dynamic regime. The hydrodynamic forces built up by the lubricant fluid are evaluated from the system state variables and included into the equations of motion of the multibody system. Numerical examples are presented in order to demonstrate the use of the methodologies and procedures described in this work.Fundação para a Ciência e a Tecnologia (FCT

Dimension reduction in heterogeneous parametric spaces with application to naval engineering shape design problems

We present the results of the first application in the naval architecture field of a methodology based on active subspaces properties for parameter space reduction. The physical problem considered is the one of the simulation of the hydrodynamic flow past the hull of a ship advancing in calm water. Such problem is extremely relevant at the preliminary stages of the ship design, when several flow simulations are typically carried out by the engineers to assess the dependence of the hull total resistance on the geometrical parameters of the hull, and others related with flows and hull properties. Given the high number of geometric and physical parameters which might affect the total ship drag, the main idea of this work is to employ the active subspaces properties to identify possible lower dimensional structures in the parameter space. Thus, a fully automated procedure has been implemented to produce several small shape perturbations of an original hull CAD geometry, in order to exploit the resulting shapes and to run high fidelity flow simulations with different structural and physical parameters as well, and then collect data for the active subspaces analysis. The free form deformation procedure used to morph the hull shapes, the high fidelity solver based on potential flow theory with fully nonlinear free surface treatment, and the active subspaces analysis tool employed in this work have all been developed and integrated within SISSA mathLab as open source tools. The contribution will also discuss several details of the implementation of such tools, as well as the results of their application to the selected target engineering problem

Spatial rigid-multi-body systems with lubricated spherical clearance joints : modeling and simulation

The dynamic modeling and simulation of spatial rigid-multi-body systems with lubricated spherical joints is the main purpose of the present work. This issue is of paramount importance in the analysis and design of realistic multibody mechanical systems undergoing spatial motion. When the spherical clearance joint is modeled as dry contact; i.e., when there is no lubricant between the mechanical elements which constitute the joint, a body-to-body (typically metal-to-metal) contact takes place. The joint reaction forces in this case are evaluated through a Hertzian-based contact law. A hysteretic damping factor is included in the dry contact force model to account for the energy dissipation during the contact process. The presence of a fluid lubricant avoids the direct metal-to-metal contact. In this situation, the squeeze film action, due to the relative approaching motion between the mechanical joint elements, is considered utilizing the lubrication theory associated with the spherical bearings. In both cases, the intra-joint reaction forces are evaluated as functions of the geometrical, kinematical and physical characteristics of the spherical joint. These forces are then incorporated into a standard formulation of the system’s governing equations of motion as generalized external forces. A spatial four bar mechanism that includes a spherical clearance joint is considered here as example. The computational simulations are carried out with and without the fluid lubricant, and the results are compared with those obtained when the system is modeled with perfect joints only. From the general results it is observed that the system’s performance with lubricant effect presents fewer peaks in the kinematic and dynamic outputs, when compared with those from the dry contact joint model.Fundação para a Ciência e a Tecnologia (FCT