scholarly journals A line element algorithm for curve flow problems in the plane

1993 ◽  
Vol 35 (2) ◽  
pp. 244-261 ◽  
Author(s):  
Stephen Roberts
Keyword(s):  
Flame Propagation ◽  
Mean Curvature Flow ◽  
Line Element ◽  
Particle Method ◽  
Normal Velocity ◽  
Flow Problems ◽  
Curve Flow ◽  
Marker Particle ◽  
Line Elements ◽  
Element Algorithm

AbstractIn this paper we shall describe a numerical method for the solution of curve flow problems in which the normal velocity of the curve depends locally on the position, normal and curvature of the curve. The method involves approximating the curve by a number of line elements (segments) which are only allowed to move in a direction normal to the element. Hence the normal of each line element remains constant throughout the evolution. In regions of high curvature elements naturally tend to accumulate. The method easily deals with the formation of cusps as found in flame propagation problems and is computationally comparable to a naive marker particle method. As a test of the method we present a number of numerical experiments related to mean curvature flow and flows associated with flame propagation and bushfires.

scholarly journals A hypercontinuous hypersmooth Schwarzschild line element transformation

1997 ◽  
Vol 20 (1) ◽  
pp. 201-204
Author(s):  
Robert A. Herrmann
Keyword(s):  
Black Hole ◽  
Gravitational Field ◽  
Line Element ◽  
Spherical Body ◽  
Physical World ◽  
Natural World ◽  
Transformation Process ◽  
Transformation Procedure ◽  
Alteration Processes ◽  
Line Elements

In this paper, a new derivation for one of the black hole line elements is given since the basic derivation for this line element is flawed mathematically. This derivation postulates a transformation procedure that utilizes a transformation function that is modeled by an ideal nonstandard physical world transformation process that yields a connection between an exterior Schwarzschild line element and distinctly different interior line element. The transformation is an ideal transformation in that in the natural world the transformation is conceived of as occurring at an unknown moment in the evolution of a gravitationally collapsing spherical body with radius greater than but near to the Schwarzsclfild radius. An ideal transformation models this transformation in a manner independent of the objects standard radius. It yields predicted behavior based upon a Newtonian gravitational field prior to the transformation, predicted behavior after the transformation for a field internal to the Schwarzschild surface and predicted behavior with respect to field alteration processes during the transformation.

Topology Synthesis of Electrothermal Compliant (ETC) Mechanisms Using Line Elements

2001 ◽  
Author(s):  
Nilesh D. Mankame ◽  
G. K. Ananthasuresh
Keyword(s):  
Line Element ◽  
Elastic Behavior ◽  
Optimal Topology ◽  
Dimensional Model ◽  
Mechanism Synthesis ◽  
Straightforward Manner ◽  
One Dimensional ◽  
Element Approach ◽  
Synthesis Procedure ◽  
Line Elements

Abstract This paper presents a line element based approach to the synthesis of electrothermally actuated compliant (ETC) mechanisms. A line element is a one-dimensional model of the electrical, thermal and elastic behavior of a beam-like continuum. In contrast to topology synthesis of ETC mechanisms by a continuum element based approach, the line element based approach offers significant conceptual and practical advantages. The line element approach allows for accurate modeling of surface heat transfer in a straightforward manner. Moreover, this approach results in clean geometries that are easy to fabricate. The line element based ETC mechanism synthesis procedure is used to study the influence of the direction of output and the electrical and thermal resistance of the workpiece on the resulting optimal topology. Solutions obtained from this procedure are compared with results from continuum based optimal synthesis procedures as well as intuitive designs reported in literature. The ability of the procedure to generate non-intuitive topologies is also demonstrated through design examples.

scholarly journals Intron Retention and TE Exonization Events inZRANB2

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Sang-Je Park ◽  
Jae-Won Huh ◽  
Young-Hyun Kim ◽  
Heui-Soo Kim ◽  
Kyu-Tae Chang
Keyword(s):  
Line Element ◽  
Intron Retention ◽  
World Monkey ◽  
Expression Patterns ◽  
Pcr Amplification ◽  
Rt Pcr ◽  
Old World ◽  
Old World Monkey ◽  
Evolutionary Features ◽  
Line Elements

The Zinc finger, RAN-binding domain-containing protein 2 (ZRANB2), contains arginine/serine-rich (RS) domains that mediate its function in the regulation of alternative splicing. TheZRANB2gene contains 2 LINE elements (L3b, Plat_L3) between the 9th and 10th exons. We identified the exonization event of a LINE element (Plat_L3). Using genomic PCR, RT-PCR amplification, and sequencing of primate DNA and RNA samples, we analyzed the evolutionary features ofZRANB2transcripts. The results indicated that 2 of the LINE elements were integrated in human and all of the tested primate samples (hominoids: 3 species; Old World monkey: 8 species; New World monkey: 6 species; prosimian: 1 species). Human, rhesus monkey, crab-eating monkey, African-green monkey, and marmoset harbor the exon derived from LINE element (Plat_L3). RT-PCR amplification revealed the long transcripts and their differential expression patterns. Intriguingly, these long transcripts were abundantly expressed in Old World monkey lineages (rhesus, crab-eating, and African-green monkeys) and were expressed via intron retention (IR). Thus, theZRANB2gene produces 3 transcript variants in which the Cterminus varies by transposable elements (TEs) exonization and IR mechanisms. Therefore,ZRANB2is valuable for investigating the evolutionary mechanisms of TE exonization and IR during primate evolution.

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