Lower Bounds of the Allowable Motions of One N-Dimensional Ellipsoid Contained in Another

2018 ◽  
Author(s):  
Sipu Ruan ◽  
Gregory S. Chirikjian ◽  
Jianzhong Ding
Keyword(s):  
Closed Form ◽  
Lower Bounds ◽  
Automated Assembly ◽  
First Order ◽  
Order Algebraic ◽  
Specific Configuration ◽  
Different Shapes ◽  
2D And 3D ◽  
Minkowski Difference

This paper studies the representations of a subset of the allowable motions for an N-dimensional ellipsoid inside another slightly larger ellipsoid without collision based on the idea of the Kinematics of Containment. As an extension to the previous work on the closed-form lower bounds, this paper proposes another two lower bounds based on the first-order algebraic condition of containment and the closed-form Minkowski difference between two ellipsoids respectively. Querying processes for a specific configuration of the moving ellipsoid and the calculations of the volume of the proposed lower bounds in configuration space (C-space) are introduced. Examples for the proposed lower bounds in 2D and 3D Euclidean space are implemented and the corresponding motion volumes in C-space are compared with different shapes of the ellipsoids. Finally a case study of the application on automated assembly is introduced.

The Kinematics of Containment for N-Dimensional Ellipsoids

2019 ◽  
Vol 11 (4) ◽  
Author(s):  
Sipu Ruan ◽  
Jianzhong Ding ◽  
Qianli Ma ◽  
Gregory S. Chirikjian
Keyword(s):  
Motion Planning ◽  
Lower Bounds ◽  
Convex Bodies ◽  
Practical Applications ◽  
Constraint Equations ◽  
Specific Configuration ◽  
Different Shapes ◽  
2D And 3D ◽  
Planning Problems ◽  
Simple Convex

Knowing the set of allowable motions of a convex body moving inside a slightly larger one is useful in applications such as automated assembly mechanisms, robot motion planning, etc. The theory behind this is called the “kinematics of containment (KC).” In this article, we show that when the convex bodies are ellipsoids, lower bounds of the KC volume can be constructed using simple convex constraint equations. In particular, we study a subset of the allowable motions for an n-dimensional ellipsoid being fully contained in another. The problem is addressed in both algebraic and geometric ways, and two lower bounds of the allowable motions are proposed. Containment checking processes for a specific configuration of the moving ellipsoid and the calculations of the volume of the proposed lower bounds in the configuration space (C-space) are introduced. Examples for the proposed lower bounds in the 2D and 3D Euclidean space are implemented, and the corresponding volumes in C-space are compared with different shapes of the ellipsoids. Practical applications using the proposed theories in motion planning problems and parts-handling mechanisms are then discussed.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

scholarly journals Rotary steerable systems: mathematical modeling and their case study

2021 ◽  
Vol 11 (6) ◽  
pp. 2743-2761
Author(s):  
Caetano P. S. Andrade ◽  
J. Luis Saavedra ◽  
Andrzej Tunkiel ◽  
Dan Sui
Keyword(s):  
Directional Drilling ◽  
Steering Control ◽  
Fundamental Physics ◽  
Drilling Tools ◽  
Drilling Operations ◽  
Beam Bending ◽  
Extended Reach Drilling ◽  
And Control ◽  
2D And 3D

AbstractDirectional drilling is a common and essential procedure of major extended reach drilling operations. With the development of directional drilling technologies, the percentage of recoverable oil production has increased. However, its challenges, like real-time bit steering, directional drilling tools selection and control, are main barriers leading to low drilling efficiency and high nonproductive time. The fact inspires this study. Our work aims to contribute to the better understanding of directional drilling, more specifically regarding rotary steerable system (RSS) technology. For instance, finding the solutions of the technological challenges involved in RSSs, such as bit steering control, bit position calculation and bit speed estimation, is the main considerations of our study. Classical definitions from fundamental physics including Newton’s third law, beam bending analysis, bit force analysis, rate of penetration (ROP) modeling are employed to estimate bit position and then conduct RSS control to steer the bit accordingly. The results are illustrated in case study with the consideration of the 2D and 3D wellbore scenarios.

scholarly journals An exact expression of positive periodic solution for a first-order singular equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yun Xin ◽  
Xiaoxiao Cui ◽  
Jie Liu
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Lower Bounds ◽  
Topological Degree ◽  
Order Differential Equation ◽  
Positive Periodic Solution ◽  
Exact Expression ◽  
Upper And Lower Bounds ◽  
Singular Equation ◽  
First Order

Abstract The main purpose of this paper is to obtain an exact expression of the positive periodic solution for a first-order differential equation with attractive and repulsive singularities. Moreover, we prove the existence of at least one positive periodic solution for this equation with an indefinite singularity by applications of topological degree theorem, and give the upper and lower bounds of the positive periodic solution.

scholarly journals Note on constructing a family of solvable sine-type difference equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ahmed El-Sayed Ahmed ◽  
Bratislav Iričanin ◽  
Witold Kosmala ◽  
Stevo Stević ◽  
Zdeněk Šmarda
Keyword(s):  
General Solution ◽  
Closed Form ◽  
Difference Equations ◽  
First Order ◽  
Solvable In Closed Form

AbstractWe obtain a family of first order sine-type difference equations solvable in closed form in a constructive way, and we present a general solution to each of the equations.

scholarly journals Nucleation is more than critical: A case study of the electroweak phase transition in the NMSSM

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Sebastian Baum ◽  
Marcela Carena ◽  
Nausheen R. Shah ◽  
Carlos E. M. Wagner ◽  
Yikun Wang
Keyword(s):  
Phase Transition ◽  
Parameter Space ◽  
Local Minima ◽  
Critical Temperatures ◽  
Electroweak Phase Transition ◽  
First Order ◽  
Vacuum Structure ◽  
The Universe ◽  
Scalar Sector

Abstract Electroweak baryogenesis is an attractive mechanism to generate the baryon asymmetry of the Universe via a strong first order electroweak phase transition. We compare the phase transition patterns suggested by the vacuum structure at the critical temperatures, at which local minima are degenerate, with those obtained from computing the probability for nucleation via tunneling through the barrier separating local minima. Heuristically, nucleation becomes difficult if the barrier between the local minima is too high, or if the distance (in field space) between the minima is too large. As an example of a model exhibiting such behavior, we study the Next-to-Minimal Supersymmetric Standard Model, whose scalar sector contains two SU(2) doublets and one gauge singlet. We find that the calculation of the nucleation probabilities prefers different regions of parameter space for a strong first order electroweak phase transition than the calculation based solely on the critical temperatures. Our results demonstrate that analyzing only the vacuum structure via the critical temperatures can provide a misleading picture of the phase transition patterns, and, in turn, of the parameter space suitable for electroweak baryogenesis.

scholarly journals Macroscopic and Multi-Scale Models for Multi-Class Vehicular Dynamics with Uneven Space Occupancy: A Case Study

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 102
Author(s):  
Maya Briani ◽  
Emiliano Cristiani ◽  
Paolo Ranut
Keyword(s):  
Road Network ◽  
Real Data ◽  
Second Order ◽  
Heavy Vehicles ◽  
First Order ◽  
Multi Scale ◽  
Stop And Go ◽  
Scale Models ◽  
Road Space

In this paper, we propose two models describing the dynamics of heavy and light vehicles on a road network, taking into account the interactions between the two classes. The models are tailored for two-lane highways where heavy vehicles cannot overtake. This means that heavy vehicles cannot saturate the whole road space, while light vehicles can. In these conditions, the creeping phenomenon can appear, i.e., one class of vehicles can proceed even if the other class has reached the maximal density. The first model we propose couples two first-order macroscopic LWR models, while the second model couples a second-order microscopic follow-the-leader model with a first-order macroscopic LWR model. Numerical results show that both models are able to catch some second-order (inertial) phenomena such as stop and go waves. Models are calibrated by means of real data measured by fixed sensors placed along the A4 Italian highway Trieste–Venice and its branches, provided by Autovie Venete S.p.A.

Microstructure Sensitive Design with First Order Homogenization Theories and Finite Element Codes

2005 ◽  
Vol 495-497 ◽  
pp. 23-30 ◽  
Author(s):  
Surya R. Kalidindi ◽  
J. Houskamp ◽  
G. Proust ◽  
H. Duvvuru
Keyword(s):  
Finite Element ◽  
Inverse Problems ◽  
Mechanical Design ◽  
Materials Design ◽  
Mathematical Framework ◽  
First Order

A mathematical framework called Microstructure Sensitive Design (MSD) has been developed recently to solve inverse problems of materials design, where the goal is to identify the class of microstructures that are predicted to satisfy a set of designer specified objectives and constraints [1]. This paper demonstrates the application of the MSD framework to a specific case study involving mechanical design. Processing solutions to obtain one of the elements of the desired class of textures are also explored within the same framework.

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