Reduced coordinates on the configuration space of three and four atoms

1992 ◽  
Vol 46 (4) ◽  
pp. 2133-2146 ◽  
Author(s):  
P. Dallot ◽  
P. D. Bristowe ◽  
M. Demazure
Keyword(s):  
Configuration Space ◽  
Reduced Coordinates

scholarly journals Semi-Classical Localisation Properties of Quantum Oscillators on a Noncommutative Configuration Space

2015 ◽  
Vol 22 (04) ◽  
pp. 1550021 ◽  
Author(s):  
Fabio Benatti ◽  
Laure Gouba
Keyword(s):  
Phase Space ◽  
Configuration Space ◽  
Classical Limit ◽  
Coherent States ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Wigner Functions ◽  
Quantum Mechanical Oscillators ◽  
Mechanical Oscillators ◽  
Space Noncommutativity

When dealing with the classical limit of two quantum mechanical oscillators on a noncommutative configuration space, the limits corresponding to the removal of configuration-space noncommutativity and position-momentum noncommutativity do not commute. We address this behaviour from the point of view of the phase-space localisation properties of the Wigner functions of coherent states under the two limits.

scholarly journals Topological representation of cloth state for robot manipulation

2021 ◽  
Author(s):  
Fabio Strazzeri ◽  
Carme Torras
Keyword(s):  
State Space ◽  
Configuration Space ◽  
Common Ground ◽  
Low Complexity ◽  
Flag Manifold ◽  
Infinite Dimensional ◽  
Articulated Objects ◽  
Research Goal ◽  
State Graphs ◽  
Deformable Materials

AbstractForty years ago the notion of configuration space (C-space) revolutionised robot motion planning for rigid and articulated objects. Despite great progress, handling deformable materials has remained elusive because of their infinite-dimensional shape-state space. Finding low-complexity representations has become a pressing research goal. This work tries to make a tiny step in this direction by proposing a state representation for textiles relying on the C-space of some distinctive points. A stratification of the configuration space for n points in the cloth is derived from that of the flag manifold, and topological techniques to determine adjacencies in manipulation-centred state graphs are developed. Their algorithmic implementation permits obtaining cloth state–space representations of different granularities and tailored to particular purposes. An example of their usage to distinguish between cloth states having different manipulation affordances is provided. Suggestions on how the proposed state graphs can serve as a common ground to link the perception, planning and manipulation of textiles are also made.

scholarly journals Stringy canonical forms and binary geometries from associahedra, cyclohedra and generalized permutohedra

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Song He ◽  
Zhenjie Li ◽  
Prashanth Raman ◽  
Chi Zhang
Keyword(s):  
Large Class ◽  
Configuration Space ◽  
Moduli Space ◽  
Cluster Algebras ◽  
Configuration Spaces ◽  
Minkowski Sum ◽  
Canonical Forms ◽  
Infinite Class ◽  
Special Cases ◽  
Generalized Associahedra

Abstract Stringy canonical forms are a class of integrals that provide α′-deformations of the canonical form of any polytopes. For generalized associahedra of finite-type cluster algebras, there exist completely rigid stringy integrals, whose configuration spaces are the so-called binary geometries, and for classical types are associated with (generalized) scattering of particles and strings. In this paper, we propose a large class of rigid stringy canonical forms for another class of polytopes, generalized permutohedra, which also include associahedra and cyclohedra as special cases (type An and Bn generalized associahedra). Remarkably, we find that the configuration spaces of such integrals are also binary geometries, which were suspected to exist for generalized associahedra only. For any generalized permutohedron that can be written as Minkowski sum of coordinate simplices, we show that its rigid stringy integral factorizes into products of lower integrals for massless poles at finite α′, and the configuration space is binary although the u equations take a more general form than those “perfect” ones for cluster cases. Moreover, we provide an infinite class of examples obtained by degenerations of type An and Bn integrals, which have perfect u equations as well. Our results provide yet another family of generalizations of the usual string integral and moduli space, whose physical interpretations remain to be explored.

ADD-RRV for motion planning in complex environments

Robotica ◽  
2021 ◽  
pp. 1-18
Author(s):  
Peng Cai ◽  
Xiaokui Yue ◽  
Hongwen Zhang
Keyword(s):  
Principal Component Analysis ◽  
Motion Planning ◽  
Configuration Space ◽  
Principal Component ◽  
Component Analysis ◽  
Planning Method ◽  
Complex Environments ◽  
Local Configuration ◽  
Narrow Passage

Abstract In this paper, we present a novel sampling-based motion planning method in various complex environments, especially with narrow passages. We use online the results of the planner in the ADD-RRT framework to identify the types of the local configuration space based on the principal component analysis (PCA). The identification result is then used to accelerate the expansion similar to RRV around obstacles and through narrow passages. We also propose a modified bridge test to identify the entrance of a narrow passage and boost samples inside it. We have compared our method with known motion planners in several scenarios through simulations. Our method shows the best performance across all the tested planners in the tested scenarios.

scholarly journals Notes on cluster algebras and some all-loop Feynman integrals

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Song He ◽  
Zhenjie Li ◽  
Qinglin Yang
Keyword(s):  
Configuration Space ◽  
Strong Evidence ◽  
Wilson Loop ◽  
Cluster Algebra ◽  
Cluster Algebras ◽  
Gauge Invariant ◽  
Feynman Integrals ◽  
Cluster Function ◽  
Invariant Description ◽  
Cluster Configuration

Abstract We study cluster algebras for some all-loop Feynman integrals, including box-ladder, penta-box-ladder, and double-penta-ladder integrals. In addition to the well-known box ladder whose symbol alphabet is $$ {D}_2\simeq {A}_1^2 $$ D 2 ≃ A 1 2 , we show that penta-box ladder has an alphabet of D3 ≃ A3 and provide strong evidence that the alphabet of seven-point double-penta ladders can be identified with a D4 cluster algebra. We relate the symbol letters to the u variables of cluster configuration space, which provide a gauge-invariant description of the cluster algebra, and we find various sub-algebras associated with limits of the integrals. We comment on constraints similar to extended-Steinmann relations or cluster adjacency conditions on cluster function spaces. Our study of the symbol and alphabet is based on the recently proposed Wilson-loop d log representation, which allows us to predict higher-loop alphabet recursively; by applying it to certain eight-point and nine-point double-penta ladders, we also find D5 and D6 cluster functions respectively.

scholarly journals Safe Path Planning Algorithms for Mobile Robots Based on Probabilistic Foam

Sensors ◽  
2021 ◽  
Vol 21 (12) ◽  
pp. 4156
Author(s):  
Luís B. P. Nascimento ◽  
Dennis Barrios-Aranibar ◽  
Vitor G. Santos ◽  
Diego S. Pereira ◽  
William C. Ribeiro ◽  
...  
Keyword(s):  
Path Planning ◽  
Mobile Robots ◽  
Configuration Space ◽  
Autonomous Robot ◽  
Breadth First Search ◽  
Propagation Process ◽  
Robot Systems ◽  
And Performance ◽  
Safe Path ◽  
High Clearance

The planning of safe paths is an important issue for autonomous robot systems. The Probabilistic Foam method (PFM) is a planner that guarantees safe paths bounded by a sequence of structures called bubbles that provides safe regions. This method performs the planning by covering the free configuration space with bubbles, an approach analogous to a breadth-first search. To improve the propagation process and keep the safety, we present three algorithms based on Probabilistic Foam: Goal-biased Probabilistic Foam (GBPF), Radius-biased Probabilistic Foam (RBPF), and Heuristic-guided Probabilistic Foam (HPF); the last two are proposed in this work. The variant GBPF is fast, HPF finds short paths, and RBPF finds high-clearance paths. Some simulations were performed using four different maps to analyze the behavior and performance of the methods. Besides, the safety was analyzed considering the new propagation strategies.

scholarly journals Inverse design of glass structure with deep graph neural networks

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Qi Wang ◽  
Longfei Zhang
Keyword(s):  
Neural Networks ◽  
Monte Carlo ◽  
Configuration Space ◽  
Glass Structure ◽  
Stable State ◽  
Specific Property ◽  
Inverse Design ◽  
Data Driven ◽  
Common Belief ◽  
Graph Neural Networks

AbstractDirectly manipulating the atomic structure to achieve a specific property is a long pursuit in the field of materials. However, hindered by the disordered, non-prototypical glass structure and the complex interplay between structure and property, such inverse design is dauntingly hard for glasses. Here, combining two cutting-edge techniques, graph neural networks and swap Monte Carlo, we develop a data-driven, property-oriented inverse design route that managed to improve the plastic resistance of Cu-Zr metallic glasses in a controllable way. Swap Monte Carlo, as a sampler, effectively explores the glass landscape, and graph neural networks, with high regression accuracy in predicting the plastic resistance, serves as a decider to guide the search in configuration space. Via an unconventional strengthening mechanism, a geometrically ultra-stable yet energetically meta-stable state is unraveled, contrary to the common belief that the higher the energy, the lower the plastic resistance. This demonstrates a vast configuration space that can be easily overlooked by conventional atomistic simulations. The data-driven techniques, structural search methods and optimization algorithms consolidate to form a toolbox, paving a new way to the design of glassy materials.

t+t clustering in He-isotopes

2006 ◽  
Vol 21 (31n33) ◽  
pp. 2499-2502
Author(s):  
S. Aoyama ◽  
N. Itagaki ◽  
K. Arai ◽  
K. Katō ◽  
M. Oi
Keyword(s):  
Configuration Space ◽  
Ground State ◽  
Cluster Component ◽  
Theoretical Approaches ◽  
He Isotopes

t+t clustering in He isotopes is investigated by using two theoretical approaches. A role of the t+t cluster component in the ground state is examined with AMD triple-S, allowing the wider configuration space containing simultaneously the "t+t+valence neutrons" structure and "4 He +valence neutrons" structure. We understand the importance of the t + t component even for the ground state. Further, t + t resonances are investigated with RGM type approach. We obtained many t + t states as resonances near to t + t threshold.

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