Search results for "Geometric analysis"
showing 10 items of 23 documents
Molecular correlation functions for uniaxial ellipsoids in the isotropic state
2006
We perform event-driven molecular dynamics simulations of a system composed by uniaxial hard ellipsoids for different values of the aspect-ratio and packing fraction . We compare the molecular orientational-dependent structure factors previously calculated within the Percus-Yevick approximation with the numerical results. The agreement between theoretical and numerical results is rather satisfactory. We also show that, for specific orientational quantities, the molecular structure factors are sensitive to the particle shape and can be used to distinguish prolate from oblate ellipsoids. A first-order theoretical expansion around the spherical shape and a geometrical analysis of the configura…
Assouad Type Dimensions in Geometric Analysis
2021
We consider applications of the dual pair of the (upper) Assouad dimension and the lower (Assouad) dimension in analysis. We relate these notions to other dimensional conditions such as a Hausdorff content density condition and an integrability condition for the distance function. The latter condition leads to a characterization of the Muckenhoupt Ap properties of distance functions in terms of the (upper) Assouad dimension. It is also possible to give natural formulations for the validity of Hardy–Sobolev inequalities using these dual Assouad dimensions, and this helps to understand the previously observed dual nature of certain cases of these inequalities. peerReviewed
The tree of life in the southern porch of the cathedral of Palermo: survey and geometric analysis
2016
This study focuses one of the most puzzling works of art made in Palermo at the end of the medieval age: the tree of life, a rich geometrical decoration with animal and human figures in the southern porch of the Cathedral of Palermo. Topographic and SfM photogrammetric methods produced a detailed orthophoto of the porch. Images collected during restoration have been rectified and superimposed to the orthophoto. The geometrical analysis of the decorative patterns reveals a complex design and meaningful links between the decoration and the general architectural layout of the porch.
Qualitative Theory of Differential Equations, Difference Equations, and Dynamic Equations on Time Scales
2016
We are pleased to present this special issue. This volume reflects an increasing interest in the analysis of qualitative behavior of solutions to differential equations, difference equations, and dynamic equations on time scales. Numerous applications arising in the engineering and natural sciences call for the development of new efficient methods and for the modification and refinement of known techniques that should be adjusted for the analysis of new classes of problems. The twofold goal of this special issue is to reflect both the state-of-the-art theoretical research and important recent advances in the solution of applied problems.
A geometric analysis of the effects of noise on Berry phase
2007
In this work we describe the effect of classical and quantum noise on the Berry phase. It is not a topical review article but rather an overview of our work in this field aiming at giving a simple pictorial intuition of our results.
The latent geometry of the human protein interaction network
2017
Abstract Motivation A series of recently introduced algorithms and models advocates for the existence of a hyperbolic geometry underlying the network representation of complex systems. Since the human protein interaction network (hPIN) has a complex architecture, we hypothesized that uncovering its latent geometry could ease challenging problems in systems biology, translating them into measuring distances between proteins. Results We embedded the hPIN to hyperbolic space and found that the inferred coordinates of nodes capture biologically relevant features, like protein age, function and cellular localization. This means that the representation of the hPIN in the two-dimensional hyperboli…
Multiresolution Analysis for Meshes with Appearance Attributes
2005
International audience; We present a new multiresolution analysis framework for irregular meshes with attributes based on the lifting scheme. We introduce a surface prediction operator to compute the detail coefficients for the geometry and the attributes of the model. Attribute analysis gives appearance information to complete the geometrical analysis of the model. A set of experimental results are given to show the efficiency of our framework. We present two applications to adaptive visual-ization and denoising.
Geometric Analysis of Type B Aortic Dissections Shows Aortic Remodeling After Intervention Using Multilayer Stents
2020
Recently, multilayer stents for type B aortic dissections (TBAD) have been proposed to decrease false lumen flow, increase and streamline true lumen flow, and retain branch vessel patency. We aimed to provide a protocol with standardized techniques to investigate aortic remodeling of TBAD by multilayer flow modulators (MFM) in static geometric and hemodynamic analyses. Combining existing literature and new insights, a standardized protocol was designed. Using pre- and postoperative CT scans, geometric models were constructed, lumen dimensions were calculated, computational fluid dynamics (CFD) models were composed, and velocity and pressures were calculated. Sixteen TBAD cases treated with …
U.I.R.D.A. – Unbuilt Italian Rationalism Digital Archive
2018
For twenty years, the architecture of Italian rationalism through the digital modelling has been investigated. Very often, the production of a model and the consequent representation of tridimensional views, in many case studies, as outcome of the research on architecture have been considered. Actually, the digital model, intended as a critical tool, has to be conceived as a ‘starting point' for graphic analysis of architecture and not as the outcome. Indeed, it is associated to other graphics, sometimes not ‘deducted' from the model, useful for the understanding/translation of architecture. The construction of the model is not the construction of a simple image, operation, which is often c…
Dal rilievo alla ricostruzione del progetto: la torre Pisana nel Palazzo Reale di Palermo
2017
The paper focuses the survey and representation of the Pisana Tower in the Royal Palace of Palermo. The tower, which has recently been inserted in the UNESCO World Heritage List, was built in the XII century under the patronage of Norman kings. Along the centuries, the tower has undergone several transformations, to fit ever-changing uses. The coexistence of such heterogeneous elements, combined with the fragmentation of the passages connecting the levels of the tower, conceal the original unity and the typology of this historical building. Researches focusing the study of monuments deeply transformed along their history, even when based on the cooperation of multidisciplinary scholarships,…