Parallel transport and moving frame

Author(s):  
Michel Emery
Biology Open ◽  
2021 ◽  
pp. bio.058512
Author(s):  
Yusri Dwi Heryanto ◽  
Chin-Yi Cheng ◽  
Yutaka Uchida ◽  
Kazushi Mimura ◽  
Masaru Ishii ◽  
...  

The cell movement and morphological change are two interrelated cellular processes. The integrated analysis is needed to explore the relationship between them. However, it has been challenging to investigate them as a whole. The cell trajectory can be described by its speed, curvature, and torsion. On the other hand, the 3-Dimensional (3D) cell shape can be studied by using a shape descriptor such as Spherical harmonic (SH) descriptor, which is an extension of Fourier transform in 3D space.We propose a novel method using parallel-transport (PT) to integrate these shape-movement data by using moving frames as the 3D-shape coordinate system. This moving frame is purely determined by the velocity vector. On this moving frame, the movement change will influence the coordinate system for shape analysis. By analyzing the change of the SH coefficients over time in the moving frame, we can observe the relationship between shape and movement.We illustrate the application of our approach using simulational and real datasets in this paper.


2020 ◽  
Author(s):  
Yusri Dwi Heryanto ◽  
Chin-Yi Cheng ◽  
Yutaka Uchida ◽  
Kazushi Mimura ◽  
Masaru Ishii ◽  
...  

ABSTRACTThe cell movement and morphological change are two interrelated cellular processes. The integrated analysis is needed to explore the relationship between them. However, it has been challenging to investigate them as a whole. The cell trajectory can be described by its speed, curvature, and torsion. On the other hand, the 3-Dimensional (3D) cell shape can be studied by using a shape descriptor such as Spherical harmonic (SH) descriptor which is an extension of Fourier transform in 3D space.To integrate these shape-movement data, we propose a method to use a parallel-transport (PT) moving frame as the 3D-shape coordinate system. This moving frame is purely determined by the velocity vector. On this moving frame, the movement change will influence the coordinate system for shape analysis. By analyzing the change of the SH coefficients over time in the moving frame, we can observe the relationship between shape and movement.We illustrate the application of our approach using simulational and real datasets in this paper.


1987 ◽  
Vol 95 ◽  
Author(s):  
J. P. Conde ◽  
S. Aljishi ◽  
D. S. Shen ◽  
V. Chu ◽  
Z E. Smith ◽  
...  

AbstractWe study the dark conductivity σd, dark conductivity activation energy Ea and photoconductivity σph of a-Si:H,F/a-Si,Ge:H,F superlattices both perpendicular and parallel to the plane of the layers. In parallel transport, both the σph and σd are dominated by the alloy layer characteristics with the superposition of carrier confinement quantum effects. In perpendicular transport, the σd shows an interplay of quantum mechanical tunneling through the barriers and of classical thermal emission over the barrier layer and the σph is controlled by the decreasing absorption by the silicon barrier layer as the optical gap Eopt of the structure decreases.We also found that the multilayer structure allows to grow lower gap a-Si,Ge:H,F alloys than achievable under the same deposition conditions for bulk materials. This stabilizing effect allowed us to study low-gap superlattice structures and extract information about these very low gap (<1.2 eV) a- Si,Ge:H,F alloys.


2010 ◽  
Vol 08 (03) ◽  
pp. 517-528 ◽  
Author(s):  
M. A. JAFARIZADEH ◽  
M. MAHDIAN

This paper is concerned with the spin–momentum correlation in single-particle quantum states, which is described by the mixed states under Lorentz transformations. For convenience, instead of using the superposition of momenta we use only two momentum eigenstates (p1 and p2) that are perpendicular to the Lorentz boost direction. Consequently, in 2D momentum subspace we show that the entanglement of spin and momentum in the moving frame depends on the angle between them. Therefore, when spin and momentum are perpendicular the measure of entanglement is not an observer-dependent quantity in the inertial frame. Likewise, we have calculated the measure of entanglement (by using the concurrence) and have shown that entanglement decreases with respect to the increase in observer velocity. Finally, we argue that Wigner rotation is induced by Lorentz transformations and can be realized as a controlling operator.


1995 ◽  
Author(s):  
Meng-Hsuan Chung ◽  
Andrew M. Wo

The effect of blade row axial spacing on vortical and potential disturbances and gust response is studied for a compressor stator/rotor configuration near design and at high loadings using 2D incompressible Navier-Stokes and potential codes, both written for multistage calculations. First, vortical and potential disturbances downstream of the isolated stator in the moving frame are defined; these disturbances exclude blade row interaction effects. Then, vortical and potential disturbances for the stator/rotor configuration are calculated for axial gaps of 10%, 20%, and 30% chord. Results show that the potential disturbance is uncoupled; the potential disturbance calculated from the isolated stator configuration is a good approximation for that from the stator/rotor configuration for all three axial gaps. The vortical disturbance depends strongly on blade row interactions. Low order modes of vortical disturbance are of substantial magnitude and decay much more slowly downstream than do those of potential disturbance. Vortical disturbance decays linearly with increasing mode except very close to the stator trailing edge. For a small axial gap, lower order modes of both vortical and potential disturbances must be included to determine the rotor gust response.


2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Leiming Ning ◽  
Jichang Chen ◽  
Mingbo Tong

A high-fidelity cargo airdrop simulation requires the accurate modeling of the contact dynamics between an aircraft and its cargo. This paper presents a general and efficient contact-friction model for the simulation of aircraft-cargo coupling dynamics during an airdrop extraction phase. The proposed approach has the same essence as the finite element node-to-segment contact formulation, which leads to a flexible, straightforward, and efficient code implementation. The formulation is developed under an arbitrary moving frame with both aircraft and cargo treated as general six degrees-of-freedom rigid bodies, thus eliminating the restrictions of lateral symmetric assumptions in most existing methods. Moreover, the aircraft-cargo coupling algorithm is discussed in detail, and some practical implementation details are presented. The accuracy and capability of the present method are demonstrated through four numerical examples with increasing complexity and fidelity.


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