A Remark on Elastic Graphs with the Symmetric Cone Obstacle

2021 ◽  
Vol 53 (2) ◽  
pp. 1857-1885 ◽  
Author(s):  
Kensuke Yoshizawa
Keyword(s):  
Symmetric Cone

scholarly journals Elastic-instability–enabled locomotion

2021 ◽  
Vol 118 (8) ◽  
pp. e2013801118
Author(s):  
Amit Nagarkar ◽  
Won-Kyu Lee ◽  
Daniel J. Preston ◽  
Markus P. Nemitz ◽  
Nan-Nan Deng ◽  
...  
Keyword(s):  
Symmetry Breaking ◽  
Scaling Laws ◽  
Multiple Scales ◽  
Symmetric Cone ◽  
Simple Approach ◽  
Inertial Forces ◽  
Elastic Instability ◽  
Anisotropic Friction ◽  
Buckling Instability ◽  
Elastic Instabilities

Locomotion of an organism interacting with an environment is the consequence of a symmetry-breaking action in space-time. Here we show a minimal instantiation of this principle using a thin circular sheet, actuated symmetrically by a pneumatic source, using pressure to change shape nonlinearly via a spontaneous buckling instability. This leads to a polarized, bilaterally symmetric cone that can walk on land and swim in water. In either mode of locomotion, the emergence of shape asymmetry in the sheet leads to an asymmetric interaction with the environment that generates movement––via anisotropic friction on land, and via directed inertial forces in water. Scaling laws for the speed of the sheet of the actuator as a function of its size, shape, and the frequency of actuation are consistent with our observations. The presence of easily controllable reversible modes of buckling deformation further allows for a change in the direction of locomotion in open arenas and the ability to squeeze through confined environments––both of which we demonstrate using simple experiments. Our simple approach of harnessing elastic instabilities in soft structures to drive locomotion enables the design of novel shape-changing robots and other bioinspired machines at multiple scales.

scholarly journals An Arc Search Interior-Point Algorithm for Monotone Linear Complementarity Problems over Symmetric Cones

2018 ◽  
Vol 23 (1) ◽  
pp. 1-16
Author(s):  
Mohammad Pirhaji ◽  
Maryam Zangiabadi ◽  
Hossein Mansouri ◽  
Saman H. Amin
Keyword(s):  
Interior Point ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Symmetric Cone ◽  
Central Path ◽  
Interior Point Algorithm ◽  
Complexity Bound ◽  
Wide Neighborhood ◽  
Mathematical Problems

An arc search interior-point algorithm for monotone symmetric cone linear complementarity problem is presented. The algorithm estimates the central path by an ellipse and follows an ellipsoidal approximation of the central path to reach an "-approximate solution of the problem in a wide neighborhood of the central path. The convergence analysis of the algorithm is derived. Furthermore, we prove that the algorithm has the complexity bound O ( p rL) using Nesterov-Todd search direction and O (rL) by the xs and sx search directions. The obtained iteration complexities coincide with the best-known ones obtained by any proposed interior- point algorithm for this class of mathematical problems.

A long-step interior-point algorithm for symmetric cone Cartesian P*(κ)-HLCP

Optimization ◽  
2018 ◽  
Vol 67 (11) ◽  
pp. 2031-2060 ◽  
Author(s):  
S. Asadi ◽  
H. Mansouri ◽  
G. Lesaja ◽  
M. Zangiabadi
Keyword(s):  
Interior Point ◽  
Symmetric Cone ◽  
Interior Point Algorithm

scholarly journals EXTENSION OF THE OLKIN AND RUBIN CHARACTERIZATION TO THE WISHART DISTRIBUTION ON HOMOGENEOUS CONES

2011 ◽  
Vol 14 (04) ◽  
pp. 591-611 ◽  
Author(s):  
I. BOUTOURIA ◽  
A. HASSAIRI ◽  
H. MASSAM
Keyword(s):  
Wishart Distribution ◽  
Symmetric Cone ◽  
Symmetric Matrices ◽  
Riesz Distribution ◽  
Homogeneous Cones ◽  
Homogeneous Cone

The Wishart distribution on a homogeneous cone is a generalization of the Riesz distribution on a symmetric cone which corresponds to a given graph. The paper extends to this distribution, the famous Olkin and Rubin characterization of the ordinary Wishart distribution on symmetric matrices.

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