Finding new local minima in lens design landscapes by constructing saddle points

2009 ◽  
Vol 48 (6) ◽  
pp. 063001 ◽  
Author(s):  
Florian Bociort
Keyword(s):  
Saddle Points ◽  
Lens Design ◽  
Local Minima

scholarly journals Obtaining new local minima in lens design by constructing saddle points

2015 ◽  
Vol 23 (5) ◽  
pp. 6679 ◽  
Author(s):  
Maarten van Turnhout ◽  
Pascal van Grol ◽  
Florian Bociort ◽  
H. Paul Urbach
Keyword(s):  
Saddle Points ◽  
Lens Design ◽  
Local Minima

Gas-Phase Clustering of NO+ with H2S and H2O

2007 ◽  
Vol 72 (8) ◽  
pp. 1122-1138 ◽  
Author(s):  
Milan Uhlár ◽  
Ivan Černušák
Keyword(s):  
Hydrogen Bonds ◽  
Water Molecule ◽  
Gas Phase ◽  
Saddle Points ◽  
Solvent Molecule ◽  
Local Minima ◽  
Additional Water ◽  
Three Body ◽  
Rain Formation ◽  
Stable Structures

The complex NO+·H2S, which is assumed to be an intermediate in acid rain formation, exhibits thermodynamic stability of ∆Hº300 = -76 kJ mol-1, or ∆Gº300 = -47 kJ mol-1. Its further transformation via H-transfer is associated with rather high barriers. One of the conceivable routes to lower the energy of the transition state is the action of additional solvent molecule(s) that can mediate proton transfer. We have studied several NO+·H2S structures with one or two additional water molecule(s) and have found stable structures (local minima), intermediates and saddle points for the three-body NO+·H2S·H2O and four-body NO+·H2S·(H2O)2 clusters. The hydrogen bonds network in the four-body cluster plays a crucial role in its conversion to thionitrous acid.

Existence of local minima in lens design

1991 ◽  
Author(s):  
Michael J. Kidger ◽  
Paul T. Leamy
Keyword(s):  
Lens Design ◽  
Local Minima

scholarly journals Chaotic behavior in an algorithm to escape from poor local minima in lens design

2009 ◽  
Vol 17 (8) ◽  
pp. 6436 ◽  
Author(s):  
Maarten van Turnhout ◽  
Florian Bociort
Keyword(s):  
Chaotic Behavior ◽  
Lens Design ◽  
Local Minima

scholarly journals Transition pathways connecting crystals and quasicrystals

2021 ◽  
Vol 118 (49) ◽  
pp. e2106230118
Author(s):  
Jianyuan Yin ◽  
Kai Jiang ◽  
An-Chang Shi ◽  
Pingwen Zhang ◽  
Lei Zhang
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
Saddle Points ◽  
Energy Functional ◽  
Computational Method ◽  
Local Minima ◽  
Free Energy Functional ◽  
Transition Pathways ◽  
Critical Nuclei ◽  
Quasicrystalline State

Due to structural incommensurability, the emergence of a quasicrystal from a crystalline phase represents a challenge to computational physics. Here, the nucleation of quasicrystals is investigated by using an efficient computational method applied to a Landau free-energy functional. Specifically, transition pathways connecting different local minima of the Lifshitz–Petrich model are obtained by using the high-index saddle dynamics. Saddle points on these paths are identified as the critical nuclei of the 6-fold crystals and 12-fold quasicrystals. The results reveal that phase transitions between the crystalline and quasicrystalline phases could follow two possible pathways, corresponding to a one-stage phase transition and a two-stage phase transition involving a metastable lamellar quasicrystalline state, respectively.

Locating the local minima in lens design with machine learning

2021 ◽  
Author(s):  
Anna V. Kononova ◽  
Ofer M. Shir ◽  
Teus Tukker ◽  
Pierluigi Frisco ◽  
Shutong Zeng ◽  
...  
Keyword(s):  
Machine Learning ◽  
Lens Design ◽  
Local Minima

Lens design and local minima

1981 ◽  
Vol 20 (3) ◽  
pp. 384 ◽  
Author(s):  
Berlyn Brixner
Keyword(s):  
Lens Design ◽  
Local Minima

A random walk to local minima and saddle points on a potential energy surface. A strategy based on simulated annealing

1996 ◽  
Vol 250 (2) ◽  
pp. 238-246 ◽  
Author(s):  
P. Chaudhury ◽  
P. Dutta ◽  
P. Bandyopadhyay ◽  
P. Sarkar ◽  
S.P. Bhattacharyya
Keyword(s):  
Simulated Annealing ◽  
Random Walk ◽  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Saddle Points ◽  
Local Minima

scholarly journals Barrier Trees of Degenerate Landscapes

2002 ◽  
Vol 216 (2) ◽  
Author(s):  
Christoph Flamm ◽  
Ivo L. Hofacker ◽  
Peter F. Stadler ◽  
Michael T. Wolfinger
Keyword(s):  
Saddle Points ◽  
Local Minima ◽  
Energy Barriers ◽  
Definition Of ◽  
Barrier Trees

The heights of energy barriers separating two (macro-)states are useful for estimating transition frequencies. In non-degenerate landscapes the decomposition of a landscape into basins surrounding local minima connected by saddle points is straightforward and yields a useful definition of macro-states. In this work we develop a rigorous concept of barrier trees for degenerate landscapes. We present a program that efficiently computes such barrier trees, and apply it to two well known examples of landscapes.

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