Extension the Noether's theorem to Lagrangian formulation with nonlocality

A Lagrangian formulation with nonlocality is investigated in this paper. The nonlocality of the Lagrangian is introduced by a new nonlocal argument that is defined as a nonlocal residual satisfying the zero mean condition. The nonlocal Euler-Lagrangian equation is derived from the Hamilton's principle. The Noether's theorem is extended to this Lagrangian formulation with nonlocality. With the help of the extended Noether's theorem, the conservation laws relevant to energy, linear momentum, angular momentum and the Eshelby tensor are determined in the nonlocal elasticity associated with the mechanically based constitutive model. The results show that the conservation laws exist only in the form of the integral over the whole domain occupied by body. The localization of the conservation laws is discussed in detail. We demonstrate that not every conservation law corresponds to a local equilibrium equation. Only when the nonlocal residual of conservation current exists, can a conservation law be transformed into a local equilibrium equation by localization.Comment: 13 page

SIRIS: a high resolution scanning infrared camera for examining paintings

The new SIRIS (Scanning InfraRed Imaging System) camera developed at the National Gallery in London allows highresolution images of paintings to be made in the near infrared region (900–1700 nm). Images of 5000 × 5000 pixels are made by moving a 320 × 256 pixel InGaAs array across the focal plane of the camera using two orthogonal translation stages. The great advantages of this camera over scanning infrared devices are its relative portability and that image acquisition is comparatively rapid – a full 5000 × 5000 pixel image can be made in around 20 minutes. The paper describes the development of the mechanical, optical and electronic components of the camera, including the design of a new lens. The software routines used to control image capture and to assemble the individual 320 × 256 pixel frames into a seamless mosaic image are also mentioned. The optics of the SIRIS camera have been designed so that the camera can operate at a range of resolutions; from around 2.5 pixels per millimetre on large paintings of up to 2000 × 2000 mm to 10 pixels per millimetre on smaller paintings or details of paintings measuring 500 × 500 mm. The camera is primarily designed to examine underdrawings in paintings; preliminary results from test targets and paintings are presented and the quality of the images compared with those from other cameras currently used in this field

Multi-camera digital holographic PIV: Tomographic DHPIV

The wide scale application of digital holographic particle image velocimetry (DHPIV) as a three-component three-dimensional (3C-3D) velocity field measurement tool is current restricted by the limited size and resolution of commercially available CCD arrays, resulting in a elongation of particle is the direction normal to the hologram plane. This elongation can be over an order of magnitude greater than the true particle diameter and posses significant problems for the cross-correlation analysis used in particle image velocimetry (PIV). In this paper we discuss a multi-camera method of tomographic digital holographic particle image velocimetry (Tomo-DHPIV) to reconstruct a 3D intensity field without a loss of resolution in the hologram normal direction. Application of this reconstruction technique is provided along with Monte Carlo simulations of the effects of various operating parameters

Algebraic Reconstruction Techniques for Tomographic Particle Image Velocimetry

Tomographic particle image velocimetry (Tomo-PIV) is a technique for three-component three-dimensional (3C-3D) velocity measurement based on the tomographic reconstruction of a volume intensity field from multiple two-dimensional projection. As such the performance and accuracy of this technique is highly dependant on the algorithm used for reconstruction. This paper presents an evaluation of four different tomographic reconstruction algorithms, namely multiplicative algebraic reconstruction techinique (MART); adaptive algebraic reconstruction technique (AART); improved iterative algorithm for sparse object reconstruction (IIASOR); and simultaneous iterative reconstruction technique (SIRT). Results indicate that the MART and AART algorithms provide considerably better particle field reconstructions for fewer iterations

The effect of uniaxial pressure on the magnetic anisotropy of the Mn_{12}-Ac single-molecule magnet

We study the effect of uniaxial pressure on the magnetic hysteresis loops of the single-molecule magnet Mn_{12}-Ac. We find that the application of pressure along the easy axis increases the fields at which quantum tunneling of magnetization occurs. The observations are attributed to an increase in the molecule's magnetic anisotropy constant D of 0.142(1)%/kbar. The increase in D produces a small, but measurable increase in the effective energy barrier for magnetization reversal. Density-functional theory calculations also predict an increase in the barrier with applied pressure.Comment: version accepted by EPL; 6 pages, including 7 figures. Small changes and added reference