Stress–energy–momentum tensors in higher order variational calculus

2000 ◽  
Vol 34 (1) ◽  
pp. 41-72 ◽  
Author(s):  
A. Fernández ◽  
P.L. Garcı́a ◽  
C. Rodrigo
Keyword(s):  
Variational Calculus ◽  
Higher Order ◽  
Stress Energy

scholarly journals Higher-order Hahn’s quantum variational calculus

2012 ◽  
Vol 75 (3) ◽  
pp. 1147-1157 ◽  
Author(s):  
Artur M.C. Brito da Cruz ◽  
Natália Martins ◽  
Delfim F.M. Torres
Keyword(s):  
Variational Calculus ◽  
Higher Order

GEOMETRIC STUDY OF HAMILTON'S VARIATIONAL PRINCIPLE

1991 ◽  
Vol 03 (04) ◽  
pp. 379-401 ◽  
Author(s):  
JOSÉ F. CARIÑENA ◽  
CARLOS LÓPEZ
Keyword(s):  
Variational Calculus ◽  
Higher Order ◽  
Lagrangian Mechanics ◽  
Lagrange Equations ◽  
Order Case ◽  
Helmholtz Conditions ◽  
Higher Order Tangent Bundle ◽  
Order Tangent ◽  
Geometric Study

Higher order tangent bundle geometry and sections along maps are used in Geometrical Mechanics in order to develop an intrinsic variational calculus. The role of variational derivative as the bundle operator associated to exterior differential on the set of trajectories is remarked. Euler-Lagrange equations and Poincaré-Cartan form are rederived in this way. Helmholtz conditions for the inverse problem of Lagrangian Mechanics are geometrically obtained for the general higher order case.

scholarly journals Bundle-theoretic methods for higher-order variational calculus

2014 ◽  
Vol 6 (1) ◽  
pp. 99-120 ◽  
Author(s):  
Michał Jóźwikowski ◽  
◽  
Mikołaj Rotkiewicz
Keyword(s):  
Variational Calculus ◽  
Higher Order

Foundations of higher-order variational theory on Grassmann fibrations

2014 ◽  
Vol 11 (07) ◽  
pp. 1460023 ◽  
Author(s):  
Zbyněk Urban ◽  
Demeter Krupka
Keyword(s):  
Vector Fields ◽  
Variational Principles ◽  
Variational Calculus ◽  
Higher Order ◽  
Noether Theorem ◽  
Variational Theory ◽  
Lagrange Equations ◽  
Variation Formula ◽  
One Dimensional ◽  
The First Variation

A setting for higher-order global variational analysis on Grassmann fibrations is presented. The integral variational principles for one-dimensional immersed submanifolds are introduced by means of differential 1-forms with specific properties, similar to the Lepage forms from the variational calculus on fibred manifolds. Prolongations of immersions and vector fields to the Grassmann fibrations are defined as a geometric tool for the variations of immersions, and the first variation formula in the infinitesimal form is derived. Its consequences, the Euler–Lagrange equations for submanifolds and the Noether theorem on invariant variational functionals are proved. Examples clarifying the meaning of the Noether theorem in the context of variational principles for submanifolds are given.

Consideration of interlaminar strain–energy continuity in composite plate analysis using improved higher order theory

2018 ◽  
Vol 42 (3) ◽  
pp. 211-221
Author(s):  
Temesgen Takele Kasa
Keyword(s):  
Composite Laminates ◽  
Strain Energy ◽  
Variational Calculus ◽  
Order Theory ◽  
Higher Order ◽  
Refined Theory ◽  
Total Potential ◽  
Lagrange Multiplier Technique ◽  
Plate Analysis ◽  
Higher Order Theory

The main goal of this paper is to suggest an improved higher order refined theory for analysing perfectly bonded stacked composite laminates with the usual lamination configurations. The analysis incorporates continuous flexural and in-plane displacements at the interfaces. Furthermore, the transverse shear stress is continuous and constrained with the Lagrange multiplier technique by introducing 14 new unknown variables that are expressed in terms of the interfacial strain energy, which is assuming to be continuous throughout the thickness of the laminate. To determine the newly introduced flexural and in-plane unknown variables, the total potential energy is minimised using variational calculus. The numerical results are compared with those from existing reliable published papers. In general, the proposed approach is sufficient for analysing laminate structures with the required accuracy.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Quantitative EPMA of nitrogen : A tricky element in the electron-probe microanalyzer

1992 ◽  
Vol 50 (2) ◽  
pp. 1622-1623
Author(s):  
G.F. Bastin ◽  
H.J.M. Heijligers
Keyword(s):  
Background Subtraction ◽  
Electron Probe ◽  
Detection System ◽  
Higher Order ◽  
Light Elements ◽  
Strong Suppression ◽  
Electron Probe Microanalyzer ◽  
Quantitative Epma ◽  
Peak Count ◽  
Lead Stearate

Among the ultra-light elements B, C, N, and O nitrogen is the most difficult element to deal with in the electron probe microanalyzer. This is mainly caused by the severe absorption that N-Kα radiation suffers in carbon which is abundantly present in the detection system (lead-stearate crystal, carbonaceous counter window). As a result the peak-to-background ratios for N-Kα measured with a conventional lead-stearate crystal can attain values well below unity in many binary nitrides . An additional complication can be caused by the presence of interfering higher-order reflections from the metal partner in the nitride specimen; notorious examples are elements such as Zr and Nb. In nitrides containing these elements is is virtually impossible to carry out an accurate background subtraction which becomes increasingly important with lower and lower peak-to-background ratios. The use of a synthetic multilayer crystal such as W/Si (2d-spacing 59.8 Å) can bring significant improvements in terms of both higher peak count rates as well as a strong suppression of higher-order reflections.

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