The metric properties of the reduced nuclear configuration space: Remarks

1993 ◽  
Vol 13 (1) ◽  
pp. 205-208 ◽  
Author(s):  
Zbigniew Zimpel
Keyword(s):  
Configuration Space ◽  
Metric Properties ◽  
Nuclear Configuration

Conformer specific nonadiabatic reaction dynamics in the photodissociation of partially deuterated thioanisoles (C6H5S-CH2D and C6H5S-CHD2)

2017 ◽  
Vol 19 (29) ◽  
pp. 18902-18912 ◽  
Author(s):  
So-Yeon Kim ◽  
Jeongmook Lee ◽  
Sang Kyu Kim
Keyword(s):  
Configuration Space ◽  
Reaction Dynamics ◽  
Conical Intersection ◽  
Nuclear Configuration

Multidimensional aspects of the conical intersection in the nuclear configuration space have been explored by partial H/D substitution of the methyl moiety of pre-dissociating thioanisole.

Reaction topology of excited state potential energy hypersurfaces

1983 ◽  
Vol 61 (5) ◽  
pp. 956-961 ◽  
Author(s):  
Paul G. Mezey
Keyword(s):  
Excited State ◽  
Potential Energy ◽  
Configuration Space ◽  
Mathematical Framework ◽  
Molecular Systems ◽  
Energy Expectation ◽  
State Potential ◽  
Charge Space ◽  
Reaction Topology ◽  
Nuclear Configuration

Topology ("rubber geometry") is an exceptionally suitable mathematical framework for a global quantum chemical description of the fundamental relations between nonrigid molecular systems, chemical reactions, and many photochemical processes. In Reaction Topology the concept of nuclear geometry is replaced by open subsets of an abstract nuclear configuration space nR. The ground and various excited state energy expectation value functionals induce a sequence of topologies in the nuclear configuration space nR, leading to a consistent topological description of molecular structure, excimers, exciplexes, and reaction mechanisms. Utilizing earlier results on topological properties of the abstract nuclear charge space wZ, a theorem is proven on the ordering of excited state potential energy hypersurfaces for sequences of isoelectronic molecules.

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.

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