scholarly journals Nonlinear definition of the shadowy mode in higher-order scalar-tensor theories

2021 ◽  
Vol 2021 (12) ◽  
pp. 020
Author(s):  
Antonio De Felice ◽  
Shinji Mukohyama ◽  
Kazufumi Takahashi
Keyword(s):  
Differential Equation ◽  
Coordinate System ◽  
Three Dimensional ◽  
Spacelike Hypersurface ◽  
Higher Order ◽  
Elliptic Differential Equation ◽  
Unitary Gauge ◽  
Definition Of

Abstract We study U-DHOST theories, i.e., higher-order scalar-tensor theories which are degenerate only in the unitary gauge and yield an apparently unstable extra mode in a generic coordinate system. We show that the extra mode satisfies a three-dimensional elliptic differential equation on a spacelike hypersurface, and hence it does not propagate. We clarify how to treat this “shadowy” mode at both the linear and the nonlinear levels.

Definition of Coordinate System for Three-Dimensional Data Analysis in the Foot and Ankle

2011 ◽  
Vol 32 (2) ◽  
pp. 193-199 ◽  
Author(s):  
Connor Green ◽  
Clare Fitzpatrick ◽  
David FitzPatrick ◽  
Michael Stephens ◽  
William Quinlan ◽  
...  
Keyword(s):  
Data Analysis ◽  
Coordinate System ◽  
Three Dimensional ◽  
Foot And Ankle ◽  
Definition Of

scholarly journals On the mild solutions of higher-order differential equations in Banach spaces

2003 ◽  
Vol 2003 (15) ◽  
pp. 865-880 ◽  
Author(s):  
Nguyen Thanh Lan
Keyword(s):  
Differential Equation ◽  
Banach Spaces ◽  
Mild Solutions ◽  
Higher Order ◽  
Almost Periodicity ◽  
Abstract Differential Equation ◽  
Translation Invariant ◽  
Definition Of ◽  
Translation Invariant Subspace ◽  
Higher Order Differential Equations

For the higher-order abstract differential equationu(n)(t)=Au(t)+f(t),t∈ℝ, we give a new definition of mild solutions. We then characterize the regular admissibility of a translation-invariant subspaceℳofBUC(ℝ,E)with respect to the above-mentioned equation in terms of solvability of the operator equationAX−X𝒟n=C. As applications, periodicity and almost periodicity of mild solutions are also proved.

scholarly journals On Representations for Joint Moments Using a Joint Coordinate System

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
Oliver M. O'Reilly ◽  
Mark P. Sena ◽  
Brian T. Feeley ◽  
Jeffrey C. Lotz
Keyword(s):  
Knee Joint ◽  
Coordinate System ◽  
Three Dimensional ◽  
Human Knee ◽  
Human Knee Joint ◽  
Six Dof ◽  
Clinical Description ◽  
Definition Of ◽  
Nonorthogonal Projections ◽  
Joint Coordinate System

In studies of the biomechanics of joints, the representation of moments using the joint coordinate system has been discussed by several authors. The primary purpose of this technical brief is to emphasize that there are two distinct, albeit related, representations for moment vectors using the joint coordinate system. These distinct representations are illuminated by exploring connections between the Euler and dual Euler bases, the “nonorthogonal projections” presented in a recent paper by Desroches et al. (2010, “Expression of Joint Moment in the Joint Coordinate System,” ASME J. Biomech. Eng., 132(11), p. 11450) and seminal works by Grood and Suntay (Grood and Suntay, 1983, “A Joint Coordinate System for the Clinical Description of Three-Dimensional Motions: Application to the Knee,” ASME J. Biomech. Eng., 105(2), pp. 136–144) and Fujie et al. (1996, “Forces and Moment in Six-DOF at the Human Knee Joint: Mathematical Description for Control,” Journal of Biomechanics, 29(12), pp. 1577–1585) on the knee joint. It is also shown how the representation using the dual Euler basis leads to straightforward definition of joint stiffnesses.

A Boundary Element Method for Three-Dimensional Steady Convective Heat Diffusion

2004 ◽  
Author(s):  
M. M. Grigoriev ◽  
G. F. Dargush
Keyword(s):  
Boundary Element ◽  
Convective Heat ◽  
Sparse Matrices ◽  
Three Dimensional ◽  
Higher Order ◽  
Iterative Solvers ◽  
Boundary Element Methods ◽  
Heat Diffusion ◽  
Element Formulation ◽  
Definition Of

Higher-order boundary element methods (BEM) are presented for three-dimensional steady convective heat diffusion at high Peclet numbers. An accurate and efficient boundary element formulation is facilitated by the definition of an influence domain due to convective kernels. This approach essentially localizes the surface integrations only within the domain of influence which becomes more narrowly focused as the Peclet number increases. The outcome of this phenomenon is an increased sparsity and improved conditioning of the global matrix. Therefore, iterative solvers for sparse matrices become a very efficient and robust tool for the corresponding boundary element matrices. In this paper, we consider an example problem with an exact solution and investigate the accuracy and efficiency of the higher-order BEM formulations for high Peclet numbers in the range from 1,000 to 100,000. The bi-quartic boundary elements included in this study are shown to provide very efficient and extremely accurate solutions, even on a single engineering workstation.

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

Application of high-resolution field-emission LVSEM, backscatter imaging, immunogold staining to definition of the spatial distributions of two human neutrophil adherence receptors

1993 ◽  
Vol 51 ◽  
pp. 36-37
Author(s):  
Robert D. Nelson ◽  
Sharon R. Hasslen ◽  
Stanley L. Erlandsen
Keyword(s):  
Cell Surface ◽  
Surface Membrane ◽  
Three Dimensional ◽  
Human Neutrophils ◽  
Spatial Distributions ◽  
Immunogold Staining ◽  
Functional Control ◽  
Neutrophil Adherence ◽  
Definition Of ◽  
Mode Of Attachment

Receptors are commonly defined in terms of number per cell, affinity for ligand, chemical structure, mode of attachment to the cell surface, and mechanism of signal transduction. We propose to show that knowledge of spatial distribution of receptors on the cell surface can provide additional clues to their function and components of functional control.L-selectin and Mac-1 denote two receptor populations on the neutrophil surface that mediate neutrophil-endothelial cell adherence interactions and provide for targeting of neutrophil recruitment to sites of inflammation. We have studied the spatial distributions of these receptors using LVSEM and backscatter imaging of isolated human neutrophils stained with mouse anti-receptor (primary) antibody and goat anti-mouse (secondary) antibody conjugated to 12 nm colloidal gold. This combination of techniques provides for three-dimensional analysis of the expression of these receptors on different surface membrane domains of the neutrophil: the ruffles and microvilli that project from the cell surface, and the cell body between these projecting structures.

scholarly journals Proposing 3D Thermal Technology for Heritage Building Energy Monitoring

2021 ◽  
Vol 13 (8) ◽  
pp. 1537
Author(s):  
Antonio Adán ◽  
Víctor Pérez ◽  
José-Luis Vivancos ◽  
Carolina Aparicio-Fernández ◽  
Samuel A. Prieto
Keyword(s):  
Computer Vision ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Building Energy ◽  
Energy Monitoring ◽  
3D Computer Vision ◽  
Building Monitoring ◽  
Heritage Buildings ◽  
Heritage Building ◽  
Definition Of

The energy monitoring of heritage buildings has, to date, been governed by methodologies and standards that have been defined in terms of sensors that record scalar magnitudes and that are placed in specific positions in the scene, thus recording only some of the values sampled in that space. In this paper, however, we present an alternative to the aforementioned technologies in the form of new sensors based on 3D computer vision that are able to record dense thermal information in a three-dimensional space. These thermal computer vision-based technologies (3D-TCV) entail a revision and updating of the current building energy monitoring methodologies. This paper provides a detailed definition of the most significant aspects of this new extended methodology and presents a case study showing the potential of 3D-TCV techniques and how they may complement current techniques. The results obtained lead us to believe that 3D computer vision can provide the field of building monitoring with a decisive boost, particularly in the case of heritage buildings.

scholarly journals Zur exakten Behandlung von kollektiven Rotationen Teil A: Theorie / On the Exact Treatment of Collective Rotations Part A: Theory

1973 ◽  
Vol 28 (2) ◽  
pp. 206-215
Author(s):  
Hanns Ruder
Keyword(s):  
Coordinate System ◽  
Perturbation Expansion ◽  
Rotational Energy ◽  
The Body ◽  
System A ◽  
N Body Problem ◽  
Definition Of ◽  
Fixed System ◽  
Body Fixed Coordinate System ◽  
Groundstate Energy

Basic in the treatment of collective rotations is the definition of a body-fixed coordinate system. A kinematical method is derived to obtain the Hamiltonian of a n-body problem for a given definition of the body-fixed system. From this exact Hamiltonian, a consequent perturbation expansion in terms of the total angular momentum leads to two exact expressions: one for the collective rotational energy which has to be added to the groundstate energy in this order of perturbation and a second one for the effective inertia tensor in the groundstate. The discussion of these results leads to two criteria how to define the best body-fixed coordinate system, namely a differential equation and a variational principle. The equivalence of both is shown.

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