scholarly journals Computations of Eigenvalues and Resonances on Perturbed Hyperbolic Surfaces with Cusps

2019 ◽  
Author(s):  
Michael Levitin ◽  
Alexander Strohmaier
Keyword(s):  
Finite Element Method ◽  
Numerical Experiments ◽  
Compact Manifold ◽  
Good Accuracy ◽  
Scattering Matrix ◽  
Direct Computation ◽  
Simple Method ◽  
Manifold With Boundary ◽  
Arithmetic Surfaces ◽  
Genus One

Abstract In this paper we describe a simple method that allows for a fast direct computation of the scattering matrix for a surface with hyperbolic cusps from the Neumann-to-Dirichlet map on the compact manifold with boundary obtained by removing the cusps. We illustrate that even if the Neumann-to-Dirichlet map is obtained by a finite element method (FEM) one can achieve good accuracy for the scattering matrix. We give various interesting examples of how this can be used to investigate the behaviour of resonances under conformal perturbations or when moving in Teichmüller space. For example, based on numerical experiments we rediscover the four arithmetic surfaces of genus one with one cusp. This demonstrates that it is possible to identify arithmetic objects using FEM. All the videos accompanying this paper are available with its online version, or externally either at michaellevitin.net/hyperbolic.html or as a dedicated YouTubeplaylist.

scholarly journals A Simple Method for Evaluating the Bioactive Phenolic Compounds’ Presence in Brazilian Craft Beers

Molecules ◽  
2021 ◽  
Vol 26 (16) ◽  
pp. 4716
Author(s):  
Marcelo Coelho Silva ◽  
Jeancarlo Pereira dos Anjos ◽  
Lilian Lefol Nani Guarieiro ◽  
Bruna A. Souza Machado
Keyword(s):  
Phenolic Compounds ◽  
Caffeic Acid ◽  
Good Accuracy ◽  
Limit Of Detection ◽  
Coumaric Acid ◽  
Simple Method ◽  
Craft Beer ◽  
Extraction Step ◽  
Satisfactory Precision ◽  
Craft Beers

There are a significant number of analytical methodologies employing different techniques to determine phenolic compounds in beverages. However, these methods employ long sample preparation processes and great time consumption. The aim of this paper was the development of a simple method for evaluating the phenolic compounds’ presence in Brazilian craft beers without a previous extraction step. Catechin, caffeic acid, epicatechin, p-coumaric acid, hydrated rutin, trans-ferulic acid, quercetin, kaempferol, and formononetin were analyzed in fifteen different craft beers. The method showed good linearity (R2 ≥ 0.9966). The limit of detection ranged from 0.08 to 0.83 mg L−1, and limits of quantification were between 0.27 and 2.78 mg L−1. The method showed a satisfactory precision (RSD ≤ 16.2%). A good accuracy was obtained by the proposed method for all phenolic compounds in craft beer (68.6% ˂ accuracy ˂ 112%). Catechin showed higher concentrations (up to 124.8 mg L−1) in the samples, followed by epicatechin (up to 51.1 mg L−1) and caffeic acid (up to 8.13 mg L−1). Rutin and formononetin were observed in all analyzed samples (0.52 mg L−1 to 2.40 mg L−1), and kaempferol was less present in the samples. The presence of plant origin products was determinant for the occurrence of the highest concentrations of phenolic compounds in Brazilian craft beers.

Development of a Method for the Prediction of Pressure-Viscosity Coefficients of Lubricating Oils Based on Free-Volume Theory

1989 ◽  
Vol 111 (1) ◽  
pp. 121-128 ◽  
Author(s):  
C. S. Wu ◽  
E. E. Klaus ◽  
J. L. Duda
Keyword(s):  
Free Volume ◽  
Good Accuracy ◽  
Temperature Relationship ◽  
Free Volume Theory ◽  
Simple Method ◽  
Lubricating Oils ◽  
Viscosity Coefficients ◽  
Data Points

A simple method based on free-volume theory to predict the pressure-viscosity coefficients of liquid lubricants has been developed. The method only requires the viscosity-temperature relationship and the viscosity at the temperature of interest. The method provides good accuracy when it was tested for 162 data points for various fluid types over wide ranges of temperature and viscosity.

scholarly journals CONFIGURATION CATEGORIES AND HOMOTOPY AUTOMORPHISMS

2018 ◽  
Vol 62 (1) ◽  
pp. 13-41
Author(s):  
MICHAEL S. WEISS
Keyword(s):  
Compact Manifold ◽  
Geometric Conditions ◽  
Homeomorphism Group ◽  
Manifold With Boundary ◽  
Smooth Compact Manifold

AbstractLet M be a smooth compact manifold with boundary. Under some geometric conditions on M, a homotopical model for the pair (M, ∂M) can be recovered from the configuration category of M \ ∂M. The grouplike monoid of derived homotopy automorphisms of the configuration category of M \ ∂M then acts on the homotopical model of (M, ∂M). That action is compatible with a better known homotopical action of the homeomorphism group of M \ ∂M on (M, ∂M).

A generalization of the asymptotic behavior of Palais-Smale sequences on a manifold with boundary

2018 ◽  
Vol 29 (10) ◽  
pp. 1850069
Author(s):  
Hong Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Value Problem ◽  
Mean Curvature ◽  
Compact Manifold ◽  
Boundary Value ◽  
Fundamental Solutions ◽  
Curvature Equation ◽  
Mean Curvature Equation ◽  
Manifold With Boundary ◽  
Prescribed Mean Curvature Equation

In this paper, we study the asymptotic behavior of Palais-Smale sequences associated with the prescribed mean curvature equation on a compact manifold with boundary. We prove that every such sequence converges to a solution of the associated equation plus finitely many “bubbles” obtained by rescaling fundamental solutions of the corresponding Euclidean boundary value problem.

scholarly journals A BDDC Preconditioner for the RotatedQ1FEM for Elliptic Problems with Discontinuous Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yaqin Jiang
Keyword(s):  
Finite Element Method ◽  
Elliptic Equations ◽  
Numerical Experiments ◽  
Mesh Size ◽  
Discontinuous Coefficients ◽  
Schwarz Methods ◽  
Additive Schwarz ◽  
Variational Form ◽  
Second Order Elliptic Equations ◽  
Additive Schwarz Methods

We propose a BDDC preconditioner for the rotatedQ1finite element method for second order elliptic equations with piecewise but discontinuous coefficients. In the framework of the standard additive Schwarz methods, we describe this method by a complete variational form. We show that our method has a quasioptimal convergence behavior; that is, the condition number of the preconditioned problem is independent of the jumps of the coefficients and depends only logarithmically on the ratio between the subdomain size and the mesh size. Numerical experiments are presented to confirm our theoretical analysis.

Approximation of the Vibration Modes of a Plate and Shells Coupled With a Fluid

2006 ◽  
Vol 73 (6) ◽  
pp. 1005-1010 ◽  
Author(s):  
E. Hernández
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Compressible Fluid ◽  
Numerical Experiments ◽  
Vibration Modes ◽  
Solid Interface ◽  
Thin Structure ◽  
Fluid Equations ◽  
Element Method

We consider a method to compute the vibration modes of an elastic thin structure (shell or plate) in contact with a compressible fluid. For the structure, the classical Naghdi equations, based on the Reissner–Mindlin hypothesis, are considered and its approximation using the mixed interpolation of tensorial component 4 finite element method. The fluid equations are discretized by using Raviart–Thomas elements, and a non-conforming coupling is used on the fluid-solid interface. Numerical experiments are reported, assessing the efficiency of this coupled scheme.

A Finite Element Method Study of Combined Hydraulic and Thermal Autofrettage Process

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Rajkumar Shufen ◽  
Uday S. Dixit
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Residual Stresses ◽  
Surface Temperature ◽  
Hydraulic Pressure ◽  
Simple Method ◽  
Inner Surface ◽  
Set Up ◽  
Element Method ◽  
Autofrettage Pressure

Autofrettage is a metal working process of inducing compressive residual stresses in the vicinity of the inner surface of a thick-walled cylindrical or spherical pressure vessel for increasing its pressure capacity, fatigue life, and stress-corrosion resistance. The hydraulic autofrettage is a class of autofrettage processes, in which the vessel is pressurized using high hydraulic pressure to cause the partial plastic deformation followed by unloading. Despite its popularity, the requirement of high pressure makes this process costly. On the other hand, the thermal autofrettage is a simple method, in which the residual stresses are set up by first maintaining a temperature difference across the thickness of the vessel and then cooling it to uniform temperature. However, the increase in the pressure carrying capacity in thermal autofrettage process is lesser than that in the hydraulic autofrettage. In the present work, a combined hydraulic and thermal autofrettage process of a thick-walled cylinder is studied using finite element method package ABAQUS® for aluminum and SS304 steel. The strain-hardening and Bauschinger effects are considered and found to play significant roles. The results show that the combined autofrettage can achieve desired increase in the pressure capacity of thick-walled cylinders with relatively small autofrettage pressure. For example, in a SS304 cylinder of wall-thickness ratio of 3, an autofrettage pressure of 150 MPa enhances the pressure capacity by 41%, but the same pressure with a 36 °C higher inner surface temperature than outer surface temperature can enhance the pressure capacity by 60%.

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