ON LOCAL CURVATURE SYMMETRIES OF GRW SPACE-TIMES

2021 ◽  
Vol 88 (3) ◽  
pp. 313-325
Author(s):  
UDAY CHAND DE ◽  
SAMEH SHENAWY
Keyword(s):  
2021 ◽  
Vol 5 (2) ◽  
pp. 45
Author(s):  
Siddhant Prakash Goyal ◽  
Mohammadjavad Lashkari ◽  
Awab Elsayed ◽  
Marlon Hahn ◽  
A. Erman Tekkaya

Multiturn coils are required for manufacturing sheet metal parts with varying depths and special geometrical features using electromagnetic forming (EMF). Due to close coil turns, the physical phenomena of the proximity effect and Lorentz forces between the parallel coil windings are observed. This work attempts to investigate the mechanical consequences of these phenomena using numerical and experimental methods. A numerical model was developed in LS-DYNA. It was validated using experimental post-mortem strain and laser-based velocity measurements after and during the experiments, respectively. It was observed that the proximity effect in the parallel conductors led to current density localization at the closest or furthest ends of the conductor cross-section and high local curvature of the formed sheet. Further analysis of the forces between two coil windings explained the departure from the “inverse-distance” rule observed in the literature. Finally, some measures to prevent or reduce undesired coil deformation are provided.


2007 ◽  
Vol 111 (31) ◽  
pp. 11501-11505 ◽  
Author(s):  
Edmund P. W. Ward ◽  
Timothy J. V. Yates ◽  
José-Jesús Fernández ◽  
David E. W. Vaughan ◽  
Paul A. Midgley

2015 ◽  
Vol 112 (29) ◽  
pp. E3950-E3958 ◽  
Author(s):  
Dongsung Huh ◽  
Terrence J. Sejnowski

In a planar free-hand drawing of an ellipse, the speed of movement is proportional to the −1/3 power of the local curvature, which is widely thought to hold for general curved shapes. We investigated this phenomenon for general curved hand movements by analyzing an optimal control model that maximizes a smoothness cost and exhibits the −1/3 power for ellipses. For the analysis, we introduced a new representation for curved movements based on a moving reference frame and a dimensionless angle coordinate that revealed scale-invariant features of curved movements. The analysis confirmed the power law for drawing ellipses but also predicted a spectrum of power laws with exponents ranging between 0 and −2/3 for simple movements that can be characterized by a single angular frequency. Moreover, it predicted mixtures of power laws for more complex, multifrequency movements that were confirmed with human drawing experiments. The speed profiles of arbitrary doodling movements that exhibit broadband curvature profiles were accurately predicted as well. These findings have implications for motor planning and predict that movements only depend on one radian of angle coordinate in the past and only need to be planned one radian ahead.


1965 ◽  
Vol 22 (3) ◽  
pp. 471-479 ◽  
Author(s):  
Robert Betchov

We consider a very thin vortex filament in an unbounded, incompressible and inviscid fluid. The filament is not necessarily plane. Each portion of the filament moves with a velocity that can be approximated in terms of the local curvature of the filament. This approximation leads to a pair of intrinsic equations giving the curvature and the torsion of the filament, as functions of the time and the arc length along the filament. It is found that helicoidal vortex filaments are elementary solutions, and that they are unstable.The intrisic equations also suggest a linear mechanism that tends to produce concentrated torsion and a non-linear mechanism tending to disperse such singularities.


2021 ◽  
Author(s):  
Anil K Dasanna ◽  
Sebastian Hillringhaus ◽  
Gerhard Gompper ◽  
Dmitry A Fedosov

During the blood stage of malaria pathogenesis, parasites invade healthy red blood cells (RBC) to multiply inside the host and evade the immune response. When attached to RBC, the parasite first has to align its apex with the membrane for a successful invasion. Since the parasite's apex sits at the pointed end of an oval (egg-like) shape with a large local curvature, apical alignment is in general an energetically un-favorable process. Previously, using coarse-grained mesoscopic simulations, we have shown that optimal alignment time is achieved due to RBC membrane deformation and the stochastic nature of bond-based interactions between the parasite and RBC membrane (Hillringhaus et al., 2020). Here, we demonstrate that the parasite's shape has a prominent effect on the alignment process. The alignment times of spherical parasites for intermediate and large bond off-rates (or weak membrane-parasite interactions) are found to be close to those of an egg-like shape. However, for small bond off-rates (or strong adhesion and large membrane deformations), the alignment time for a spherical shape increases drastically. Parasite shapes with large aspect ratios such as oblate and long prolate ellipsoids are found to exhibit very long alignment times in comparison to the egg-like shape. At a stiffened RBC, spherical parasite aligns faster than any other investigated shapes. This study shows that the original egg-like shape performs not worse for parasite alignment than other considered shapes, but is more robust with respect to different adhesion interactions and RBC membrane rigidities.


2005 ◽  
Vol 358 (2) ◽  
pp. 684-692 ◽  
Author(s):  
P. Cabella ◽  
M. Liguori ◽  
F. K. Hansen ◽  
D. Marinucci ◽  
S. Matarrese ◽  
...  

1964 ◽  
Vol 8 (02) ◽  
pp. 21-28 ◽  
Author(s):  
William P. Vafakos

Equations which are applicable to uniform deep oval rings in which the local curvature of an arbitrary reference line is prescribed are derived and simplified for application to oval ring-shell combinations. Theoretical estimates of the stresses and displacements are obtained for a typical reinforcing ring of a ring-stiffened oval cylinder recently tested under hydrostatic pressure by the David Taylor Model Basin. These results are obtained by appropriately approximating the oval cross section and by assuming that the composite structure responds as an oval ring. The theoretical flange stresses are shown to be in good agreement with available test results.


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