Tenseurs d'impulsion–énergie asymétriques et moment angulaire à six composantes dans le problème des deux impulsions du photon et celui de l'effet magnétodynamique

1975 ◽  
Vol 53 (21) ◽  
pp. 2355-2368 ◽  
Author(s):  
O. Costa de Beauregard
Keyword(s):  
Energy Flux ◽  
Evanescent Wave ◽  
A Priori ◽  
Momentum Conservation ◽  
Momentum Density ◽  
Total Reflection ◽  
Refractive Indices ◽  
Energy Tensor ◽  
Covariant Formulation ◽  
Minkowski Tensor

When an asymmetrical momentum–energy tensor Tij is used in the relativistic covariant formulation of the six component angular momentum conservation, and when this formulation is particularized in Newtonian style (initial and final integrals at constant times t and t + dt, origin of point instants simultaneous with t), there is a compensation of terms which substitutes the energy flux T4α for the momentum density Tα4.Three applications of this general result are given.If Tij is the Maxwell–Minkowski tensor, the integrated momentum density D × B is fully replaced by the energy flux E × H, or in other terms, the Minkowski momentum of the photon nhv/c is replaced by the Abraham momentum hv/nrc (n and nr = n cos θ are the refractive indices of the diopter for the directions normal to the equiphase planes and parallel to the extraordinary ray). This is a general solution of the photon two momenta paradox for refringent media.An analogous problem exists for the Fresnel evanescent wave associated with total reflection, in relation to the Goos–Hänchen and Imbert shifts. The solution is identical, but uses the de Broglie and Géhéniau canonical tensor (the Maxwell–Minkowski tensor, being symmetrical in vacuum, cannot be used). A third similar problem is that of the momentum [Formula: see text] 'hidden' in an electric field E = ∂V (Penfield–Haus effect). In terms of densities, the energy flux Vj is seen to appear instead of momentum density qA expected a priori (A, iV: 4 potential, j, iq: current density). In this case, the paradox is solved by using the momentum–energy tensor Akjl or Akjl – (1/2)Aijiδkl. [Translated by the Journal]

Simulation for enhancement in sensitivity of chalcogenide glasses-based fibre optic evanescent absorption sensor for malignant tissue detection

2020 ◽  
Vol 12 ◽  
Author(s):  
Ritesh Kumar Singh ◽  
Adarsh Chandra Mishra ◽  
Pooja Lohia ◽  
D.K. Dwivedi
Keyword(s):  
Evanescent Wave ◽  
Chalcogenide Glasses ◽  
Biological Tissues ◽  
Biological Species ◽  
Primary Objective ◽  
Effect Of Temperature ◽  
Refractive Indices ◽  
Core Radius ◽  
Source Illumination ◽  
Study Results

Background: Refractive index determination of biological tissues is a challenging issue. Many biological species also show vibrational signature in infrared domain. The chalcogenide-based glasses can be used to make the fiber optic evanescent wave sensors for detection of analyte. Objectives: The primary objective is to study the effect of various parameters on the sensitivity of chalcogenide glass-based evanescent wave sensor for biological tissue detection. Methods: An evanescent wave sensor has been proposed with collimated source illumination and uniform tapering. The chalcogenide materials are chosen such that the weakly guiding approximation could be followed. Complex refractive indices of liver tissue samples have been taken for the analysis of sensitivity via method of evanescent absorption coefficient. Equations for sensitivity have been solved analytically using MATLAB software. Results: The simplification of the formula for sensitivity leads to the inference that the sensitivity is a function of core radius, refractive indices of sample tissues and wavelength used. Moreover, since the refractive indices of the materials are also a function of temperature, therefore a change in temperature results into change in the profile of guiding mode. Hence the effect of temperature must also be observed. The initial simulation parameters are taken; core radius 100 µm, sensing length 4 cm and wavelength 1.0 µm. In the NIR region we have a better sensitivity of detection for all the tissues samples and the risk of photodamage of the biosamples is reduced to a good extent. It has been found that sensitivity decreases with wavelength and core radius whereas increases with temperature. It has also been shown that sensitivity is found to be better with collimated in comparison with diffused source. Conclusion: The comparative study results that one should operate at shorter NIR region of wavelength for higher sensitivity. The collimated source illumination should be preferred over diffused one for launching the light within the fiber to have high sensitivity. Further, length of sensing region should be larger but the fiber core radius should be smaller. The proposed biosensor is robust and can also be used many times if the probe (sensing region) is cleaned properly. Moreover, a small amount of analyte is enough for the detection. Thus, the proposed sensor is very useful for bio-medical applications with its high performance, accuracy and robustness.

scholarly journals Simulation of a rotating strong gravity that reverses time

2021 ◽  
pp. 7-16
Author(s):  
Yoshio Matsuki ◽  
Petro Bidyuk
Keyword(s):  
Angular Momentum ◽  
Gravitational Field ◽  
Momentum Density ◽  
Polar Coordinates ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Strong Gravity ◽  
The Past ◽  
Stress Energy ◽  
The Future

In this research we simulated how time can be reversed with a rotating strong gravity. At first, we assumed that the time and the space can be distorted with the presence of a strong gravity, and then we calculated the angular momentum density of the rotating gravitational field. For this simulation we used Einstein’s field equation with spherical polar coordinates and the Euler’s transformation matrix to simulate the rotation. We also assumed that the stress-energy tensor that is placed at the end of the strong gravitational field reflects the intensities of the angular momentum, which is the normal (perpendicular) vector to the rotating axis. The result of the simulation shows that the angular momentum of the rotating strong gravity changes its directions from plus (the future) to minus (the past) and from minus (the past) to plus (the future), depending on the frequency of the rotation.

scholarly journals Proca tubes with the flux of the longitudinal chromoelectric field and the energy flux/momentum density

2020 ◽  
Vol 80 (11) ◽  
Author(s):  
Vladimir Dzhunushaliev ◽  
Vladimir Folomeev
Keyword(s):  
Angular Momentum ◽  
Scalar Field ◽  
Electric Field ◽  
Energy Flux ◽  
Momentum Density ◽  
Proton Spin ◽  
Longitudinal Electric Field ◽  
Cylindrically Symmetric ◽  
Electric And Magnetic Fields ◽  
Higgs Scalar

AbstractWe consider non-Abelian SU(3) Proca theory with a Higgs scalar field included. Cylindrically symmetric solutions describing classical tubes either with the flux of a longitudinal electric field or with the energy flux (and hence with nonzero momentum density) are obtained. It is shown that, in quantum Proca theory, there can exist tubes both with the flux of the longitudinal electric field and with the energy flux/momentum density simultaneously. An imaginary particle – Proca proton – in which ‘quarks’ are connected by tubes with nonzero momentum density is considered. It is shown that this results in the appearance of the angular momentum related to the presence of the non-Abelian electric and magnetic fields in the tube, and this angular momentum is a part of the Proca proton spin.

scholarly journals Characterisation of Biological Materials at THz Frequencies by Attenuated Total Reflection: Lard

2020 ◽  
Vol 10 (23) ◽  
pp. 8692
Author(s):  
Zoltan Vilagosh ◽  
Alireza Lajevardipour ◽  
Dominique Appadoo ◽  
Soon Hock Ng ◽  
Saulius Juodkazis ◽  
...  
Keyword(s):  
Penetration Depth ◽  
Evanescent Wave ◽  
Total Internal Reflection ◽  
Complex Refractive Index ◽  
Biological Tissues ◽  
Total Reflection ◽  
Attenuated Total Reflection ◽  
Frustrated Total Internal Reflection ◽  
Model Sample ◽  
Difference Time

The penetration depth of an evanescent wave in Attenuated Total Reflection (ATR) is dependent on the wavelength of the radiation utilised. At THz frequencies, the penetration depth into biological tissues is in the order of 0.1 to 0.5 mm; rendered pig lard was used as a model sample in this study. A method for the direct measurement of the evanescent wave penetration depth is presented which allows for the estimation of the dispersion of the complex refractive index by using the reflection of the evanescent wave from varying sample depths. The method employs frustrated total internal reflection, and has been demonstrated by using the THz/Far-IR beamline at the Australian synchrotron, and modelled using finite difference time domain (FDTD) simulations.

Efficient Source-To-Fiber Coupling Method Using a Diamond Rod: Theory and Application to Multimode Evanescent-Wave IR Absorption Spectroscopy

1993 ◽  
Vol 47 (11) ◽  
pp. 1751-1759 ◽  
Author(s):  
Roy E. Jonas ◽  
Mark S. Braiman
Keyword(s):  
Evanescent Wave ◽  
Unit Length ◽  
Refractive Indices ◽  
Ir Absorption ◽  
Optical Losses ◽  
Close Match ◽  
Blackbody Source ◽  
Rod Theory ◽  
Higher Order Modes ◽  
Optical Modes

The use of a diamond rod to couple a blackbody source optically to a chalcogenide glass fiber is described and shown to be useful for evanescent-wave IR absorbance measurements. One end of a short 0.5-mm-diameter diamond rod abuts an optical fiber of the same diameter; the other end is in direct contact with a glowing silicon carbide IR source. The close match of the refractive indices of SiC, diamond, and AsSeTe fiber reduces optical losses at the interfaces, allowing a high overall throughput as well as transmission into the fiber of a wider range of transverse optical modes than is available with the use of through-air focusing methods. Use of the higher-order modes for evanescent-wave spectroscopy leads to increases in sensitivity, due both to increased evanescent pathlength and to a larger number of internal reflections per unit length.

Convective variational approach to relativistic thermodynamics of dissipative fluids

1991 ◽  
Vol 433 (1887) ◽  
pp. 45-62 ◽  
Keyword(s):  
Traditional Approach ◽  
Chemical Constituents ◽  
Momentum Density ◽  
Energy Tensor ◽  
Cauchy Type ◽  
Entropy Current ◽  
Master Function ◽  
Relativistic Thermodynamic ◽  
Set Up ◽  
Generalized Variation

Using guidelines provided by Noether identities arising from a generalized variation procedure of convective type, a new (nonlinear and exactly self-consistent) category of relativistic thermodynamic models is developed for the systematic representation of viscous conducting fluid media (allowing for several independent charged or neutral chemical constituents). Apart from the provision of a set of dissipation coefficients of the usual (reactivity, resistivity, and viscosity) type, the specification of a particular model is determined just by giving the algebraic dependence a single ‘master function’, ͘ Λ say, on the relevant dynamical variables, which are supposed here to consist of an entropy current 4-vector and a set of particle current 4-vectors corresponding to the various chemical constituents, together with a set of symmetric (rank 3) viscosity tensors, which are considered as being dynamically independent of the corresponding current vectors except in the degenerate limit of linear viscosity. The master function is set up as a generalization of an ordinary lagrangian function, to which it reduces in the relevant non - dissipative limit, and, as in the conservative case, it is used for the construction of derived quantities in such a way that appropriate self-consistency conditions are satisfied as identities. In particular the relevant stress-momentum-energy tensor is obtained directly in terms of the independent variables and of their dynamical conjugates (whose role is hidden in the traditional approach as developed by Israel & Stewart), which are set of ordinary 4-momentum (not 4-momentum density) covectors associated with the independent currents, and a set of generalised Cauchy type strain (not strain - rate) tensors associated with the independent viscous stress contributions. The range of application of the category obtained in this way is intended to include that of the standard (Israel-Stewart) formalism to which it is expected to be effectively equivalent in the limit of sufficiently small deviations from thermodynamic equilibrium.

The use of a slit in determining refractive indices with the microscope

1917 ◽  
Vol 18 (84) ◽  
pp. 130-132
Author(s):  
John William Evans
Keyword(s):  
Crystal Structure ◽  
Refractive Index ◽  
Optical Properties ◽  
Critical Angle ◽  
Total Reflection ◽  
Index Of Refraction ◽  
Refractive Indices ◽  
Object Image ◽  
Ordinary Object

Certain optical properties of crystals, and more particularly the refractive index, may be determined either in the directions-image, often referred to as the 'image in convergent light', or in the ordinary object-image in which the object itself is seen. In the former case, in which the index of refraction is 'usually determined by means of the critical angle of total-reflection, every point in the image corresponds to a single direction of propagation of the wave-front through the crystal-structure and to the two corresponding directions of vibration. One of these can, however, be eliminated by the insertion of a nicol in an approximate position, and thus all ambiguity in the determination of the refractive index is removed.

A PRIORI PRESSURE FIELD CONSTRUCTION ITERATIVE METHOD FOR THE SOLUTION OF THE STEADY-STATE NAVIER–STOKES EQUATIONS USING GENERAL FINITE-VOLUME CO-LOCATED GRIDS

2007 ◽  
Vol 04 (04) ◽  
pp. 567-601
Author(s):  
JOSE A. LAMAS
Keyword(s):  
Iterative Method ◽  
Pressure Field ◽  
Stokes Equations ◽  
A Priori ◽  
Mass Conservation ◽  
Momentum Conservation ◽  
Navier Stokes ◽  
Pressure Equation ◽  
Navier Stokes Equations ◽  
Correction Equations

An iterative method has been developed for the solution of the Navier–Stokes equations and implemented using finite volumes with co-located variable arrangement. A pressure equation is obtained combining algebraic momentum and mass conservation equations resulting in a self-consistent set of equations. An iterative procedure solves the pressure equation consistently with mass conservation and then updates velocities based on momentum equations without introducing velocity or pressure correction equations. The process is repeated until velocities satisfy both mass and momentum conservation. Tests demonstrate a priori pressure field solution consistent with mass conservation, and solution of hydrostatic problems in one iteration.

On the Nature of the Evanescent Wave

2013 ◽  
Vol 67 (2) ◽  
pp. 126-131 ◽  
Author(s):  
Milan Milosevic
Keyword(s):  
Theoretical Result ◽  
Experimental Method ◽  
Evanescent Wave ◽  
Research Topic ◽  
Total Reflection ◽  
Attenuated Total Reflection ◽  
Entire Field ◽  
Mental Picture ◽  
Basic Understanding ◽  
Atr Spectroscopy

This is an unusual paper in that it does not address a particular research topic or present a novel experimental method or a new theoretical result. This paper addresses our basic understanding of the nature of the evanescent wave, the wave that is the basis of the entire field of Attenuated Total Reflection (ATR) spectroscopy. I recently had the opportunity to reexamine the foundations of ATR spectroscopy and was surprised to have had to change my own mental picture of the evanescent wave that I have built over the last 25 years. Over the years I have had numerous discussions with a large number of workers in the field as well as with my former mentor, and one of the originators and the principal developer of ATR spectroscopy, the late N.J. Harrick. Everything brought up in all these discussions was perfectly consistent with my old mental picture of the evanescent wave. Thus, I believe that the picture of the evanescent wave that I had is virtually universally held by workers in the field. This paper describes the new picture of the evanescent wave that emerged from said reexamination process.

Robust Control for Coordinated Motion of Flexible Space Manipulator Based on the Augmentation Approach

2010 ◽  
Author(s):  
Zhiyong Chen ◽  
Li Chen
Keyword(s):  
Robust Control ◽  
A Priori ◽  
Joint Space ◽  
Momentum Conservation ◽  
Network Control ◽  
Coordinated Motion ◽  
Space Manipulator ◽  
Assumed Mode Method ◽  
Uncertainty Bound ◽  
Mode Method

In this paper, the coordinated control of a flexible space manipulator system with a front flexible link is discussed. With the assumed mode method and linear momentum conservation of the system, the dynamics of the manpulator is derived in Lagrangian formulation. By using the augmentation approach, a robust control scheme for the coordinated motion between the spacecraft’s attitude and arm’s joints of the flexible space manipulator with bounded external disturbances and uncertain parameters to track the desired trajectories in joint space is proposed. It is designed based on a priori knowledge about the uncertainty-bound and possesses the advantage that it can greatly reduce the calculation time needed by the adaptive or neural network control schemes. Simulation results show that the presented controller can stabilize the system to track the desired trajectories and keep the vibration amplitude of the flexible arm to be relatively low-level.

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