Time of first entry into a region with curved boundary

1979 ◽  
Vol 19 (4) ◽  
pp. 582-595 ◽  
Author(s):  
A. A. Mogul'skii ◽  
E. A. Pecherskii
Keyword(s):  
Curved Boundary

scholarly journals Analytical solution for torsion of cylindrical orthotropic annular wedge-shaped bars reinforced by thin shells

2021 ◽  
Author(s):  
István Ecsedi ◽  
Attila Baksa
Keyword(s):  
Analytical Solution ◽  
Cross Section ◽  
Analytical Method ◽  
Torsional Rigidity ◽  
Circular Ring ◽  
Thin Shells ◽  
Elastic Wedge ◽  
Curved Boundary ◽  
Cylindrically Orthotropic ◽  
Boundary Surfaces

AbstractThis paper deals with the Saint-Venant torsion of elastic, cylindrically orthotropic bar whose cross section is a sector of a circular ring shaped bar. The cylindrically orthotropic homogeneous elastic wedge-shaped bar strengthened by on its curved boundary surfaces by thin isotropic elastic shells. An analytical method is presented to obtain the Prandtl’s stress function, torsion function, torsional rigidity and shearing stresses. A numerical example illustrates the application of the developed analytical method.

scholarly journals Motion of Multiple Robot in a Curved Boundary & Obstacles

2019 ◽  
Vol 9 (1) ◽  
pp. 6011-6014
Keyword(s):  
Curve Fitting ◽  
The Other ◽  
Multiple Robots ◽  
Curved Boundary ◽  
Medical Supplies ◽  
Straight Line ◽  
Multiple Robot ◽  
Assembly Operations ◽  
Curve Equation ◽  
Made In

An attempt is made in this paper to gain the flexibility of movement of robots around the boundary of the workspace, where in many robots are moving at a time in the presence of the static curved obstacles. The boundary of the workspace may be a straight line or curve shaped. The obstacle may be polygonal or curved shaped. A program is developed for the motion of the multiple robots to move from its origin location to the desired location without colliding with the boundary, the other moving robots and the static obstacles. The program is based on the curve fitting technique. As and when the robot comes close to the curved boundary or curved barrier, it will trace the path formed by the curve equation using the technique of curve fitting. Since there are multiple robots, the path planning ensures the robots to reach their targets in minimum time. During tracing the path, if more than one robot is following the same path, priority is assigned to such robots. Multiple robots finds application in assembly operations, medical supplies and meals to patients, disinfecting the rooms for patients etc.

Handling Blending Features in Form Feature Recognition Using Convex Decomposition

1994 ◽  
Author(s):  
Sreekumar Menon ◽  
Yong Se Kim
Keyword(s):  
Feature Recognition ◽  
Boundary Representation ◽  
Recognition Method ◽  
Geometric Information ◽  
Polyhedral Model ◽  
Curved Boundary ◽  
Convex Decomposition ◽  
Geometric Objects ◽  
Form Features ◽  
Form Feature

Abstract Form features intrinsic to the product shape can be recognized using a convex decomposition called Alternating Sum of Volumes with Partitioning (ASVP). However, the domain of geometric objects to which ASVP decomposition can be applied had been limited to polyhedral solids due to the difficulty of convex hull construction for solids with curved boundary faces. We develop an approach to extend the geometric domain to solids having cylindrical and blending features. Blending surfaces are identified and removed from the boundary representation of the solid, and a polyhedral model of the unblended solid is generated while storing the cylindrical geometric information. From the ASVP decomposition of the polyhedral model, polyhedral form features are recognized. Form feature decomposition of the original solid is then obtained by reattaching the stored blending and cylindrical information to the form feature components of its polyhedral model. In this way, a larger domain of solids can be covered by the feature recognition method using ASVP decomposition. In this paper, handling of blending features in this approach is described.

scholarly journals On Durbin's Series for the Density of First Passage Times

2011 ◽  
Vol 48 (03) ◽  
pp. 713-722
Author(s):  
P. Zipkin
Keyword(s):  
Pointwise Convergence ◽  
First Passage Time ◽  
Convergent Series ◽  
Passage Time ◽  
Partial Sums ◽  
First Passage ◽  
Substitution Method ◽  
Curved Boundary ◽  
Weiner Process ◽  
Passage Times

Durbin (1992) derived a convergent series for the density of the first passage time of a Weiner process to a curved boundary. We show that the successive partial sums of this series can be expressed as the iterates of the standard substitution method for solving an integral equation. The calculation is thus simpler than it first appears. We also show that, under a certain condition, the series converges uniformly. This strengthens Durbin's result of pointwise convergence. Finally, we present a modified procedure, based on scaling, which sometimes works better. These approaches cover some cases that Durbin did not.

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