A Periodic Orbit Bifurcation Analysis of Vibrationally Excited Isotopologues of Sulfur Dioxide and Water Molecules: Symmetry Breaking Substitutions†

2010 ◽  
Vol 114 (36) ◽  
pp. 9836-9847 ◽  
Author(s):  
Frederic Mauguiere ◽  
Michael Rey ◽  
Vladimir Tyuterev ◽  
Jaime Suarez ◽  
Stavros C. Farantos
Keyword(s):  
Sulfur Dioxide ◽  
Periodic Orbit ◽  
Symmetry Breaking ◽  
Bifurcation Analysis ◽  
Water Molecules ◽  
Vibrationally Excited

Symmetry-breaking bifurcations in resonant surface waves

1989 ◽  
Vol 199 ◽  
pp. 495-518 ◽  
Author(s):  
Z. C. Feng ◽  
P. R. Sethna
Keyword(s):  
Normal Form ◽  
Symmetry Breaking ◽  
Surface Waves ◽  
Bifurcation Analysis ◽  
Internal Resonance ◽  
Travelling Waves ◽  
Chaotic Behaviour ◽  
Derived Set ◽  
Parameter Values ◽  
Theoretical Results

Surface waves in a nearly square container subjected to vertical oscillations are studied. The theoretical results are based on the analysis of a derived set of normal form equations, which represent perturbations of systems with 1:1 internal resonance and with D4 symmetry. Bifurcation analysis of these equations shows that the system is capable of periodic and quasi-periodic standing as well as travelling waves. The analysis also identifies parameter values at which chaotic behaviour is to be expected. The theoretical results are verified with the aid of some experiments.

ROBUST METHOD FOR EXPERIMENTAL BIFURCATION ANALYSIS

2002 ◽  
Vol 12 (08) ◽  
pp. 1909-1913 ◽  
Author(s):  
GERRIT LANGER ◽  
ULRICH PARLITZ
Keyword(s):  
Symmetry Breaking ◽  
Bifurcation Analysis ◽  
Duffing Oscillator ◽  
Period Doubling ◽  
Robust Method ◽  
Periodically Driven ◽  
Experimental Systems ◽  
Saddle Node ◽  
Electronic Implementation

We present a robust method to locate and continue period-doubling, saddle-node and symmetry-breaking bifurcations of periodically driven experimental systems. The method is illustrated from results obtained for an electronic implementation of a Duffing oscillator.

HETERODIMENSIONAL CYCLE BIFURCATION WITH ORBIT-FLIP

2010 ◽  
Vol 20 (02) ◽  
pp. 491-508 ◽  
Author(s):  
QIUYING LU ◽  
ZHIQIN QIAO ◽  
TIANSI ZHANG ◽  
DEMING ZHU
Keyword(s):  
Periodic Orbit ◽  
Bifurcation Analysis ◽  
Homoclinic Orbit ◽  
Heteroclinic Orbit ◽  
Moving Frame ◽  
Homoclinic Loop ◽  
Orbit Flip ◽  
Local Moving Frame

The local moving frame approach is employed to study the bifurcation of a degenerate heterodimensional cycle with orbit-flip in its nontransversal orbit. Under some generic hypotheses, we provide the conditions for the existence, uniqueness and noncoexistence of the homoclinic orbit, heteroclinic orbit and periodic orbit. And we also present the coexistence conditions for the homoclinic orbit and the periodic orbit. But it is impossible for the coexistence of the periodic orbit and the persistent heterodimensional cycle or the coexistence of the homoclinic loop and the persistent heterodimensional cycle. Moreover, the double and triple periodic orbit bifurcation surfaces are established as well. Based on the bifurcation analysis, the bifurcation surfaces and the existence regions are located. An example of application is also given to demonstrate our main results.

On the stabilization of the carbonate dianion by sulfur dioxide

2010 ◽  
Vol 88 (11) ◽  
pp. 1125-1135 ◽  
Author(s):  
Friedrich Grein ◽  
Justin K. Chan ◽  
Idlir Liko
Keyword(s):  
Sulfur Dioxide ◽  
Oxygen Atom ◽  
Gas Phase ◽  
Single Point ◽  
Basis Set ◽  
Water Molecules ◽  
Electron Detachment ◽  
Optimized Geometries

The stabilization in the gas phase of the carbonate dianion [Formula: see text] by SO2 molecules is being investigated. The geometries of various isomers of [Formula: see text] (SO2)n and [Formula: see text] (SO2)n, for n = 1–4, have been optimized by the B3PW91/6−311+G(3df) method. Single-point CCSD and CCSD(T) energies at the DFT-optimized geometries were obtained for n = 1–3, using the 6−311+G(d) basis set. For n = 1 and 2, the monoanionic clusters are adiabatically more stable than the dianionic ones. However, starting at n = 3, they become less stable. The CCSD adiabatic electron detachment energy of the dianionic cluster switches from −0.39 eV for n = 2 to +0.20 eV for n = 3. The vertical electron detachment energy turns positive at n = 2, with a CCSD value of 1.35 eV. Several of the less stable dianionic, and most of the monoionic clusters, are characterized by the transfer of an oxygen atom from CO3 to SO2, forming [Formula: see text] or [Formula: see text] units, owing to [Formula: see text] + CO2 being more stable than [Formula: see text] + SO2. For the stabilization of the sulfate dianion by stepwise hydration, studied both experimentally and theoretically by other groups, a minimum of three water molecules was required.

Asymmetric transport of water molecules through a hydrophobic conical channel

RSC Advances ◽  
2014 ◽  
Vol 4 (76) ◽  
pp. 40193-40198 ◽  
Author(s):  
Jiaye Su ◽  
Keda Yang ◽  
Hongxia Guo
Keyword(s):  
Symmetry Breaking ◽  
Water Molecules ◽  
Nanoscale Systems ◽  
Conical Channel

Unlike macroscale systems, symmetry breaking could lead to surprising results for nanoscale systems.

scholarly journals Symmetry Breaking and Bifurcations in the Periodic Orbit Theory. II: Spheroidal Cavity

2002 ◽  
Vol 108 (5) ◽  
pp. 853-901 ◽  
Author(s):  
A. G. Magner ◽  
K.-i. Arita ◽  
S. N. Fedotkin ◽  
K. Matsuyanagi
Keyword(s):  
Periodic Orbit ◽  
Symmetry Breaking ◽  
Periodic Orbit Theory ◽  
Spheroidal Cavity ◽  
Orbit Theory

State- and bond-selected photodissociation and bimolecular reaction of water

1990 ◽  
Vol 332 (1625) ◽  
pp. 259-272 ◽  
Keyword(s):  
Room Temperature ◽  
Reaction Dynamics ◽  
Bimolecular Reaction ◽  
Water Molecules ◽  
Vibrational States ◽  
Vibrationally Excited ◽  
Stretching Vibration ◽  
Different Populations ◽  
H 20 ◽  
Selection Of

It is possible to exploit the isolation of the 0 —H stretching vibration in H 20 and HOD to control the photodissociation and reaction dynamics in water molecules excited in the region of the third overtone (4rOH) of the 0 -H stretch. In vibrationally mediated photodissociation of H 20, the selection of different initial stretching states having roughly the same energy leads to drastically different populations of the vibrational states of the OH photolysis product. By exciting the O-H stretching overtone in HOD, we can selectively photolyze that bond. In bimolecular reaction experiments, we react H 20 (4rOH) with H atoms to produce H 2 and OH. The reaction, which is endothermic, proceeds at an undetectable rate in our room temperature measurements. Vibrationally excited water, however, reacts at roughly the gas kinetic collision rate. Applying this technique to HOD (4rOH) allows us to demonstrate bond selected bimolecular chemistry in which the reaction produces only OD. This observation suggests a general approach to assessing bond controlled reactions in a variety of systems.

Reactive and inelastic collisions of H atoms with vibrationally excited water molecules

1999 ◽  
Vol 110 (6) ◽  
pp. 2963-2970 ◽  
Author(s):  
G. Lendvay ◽  
K. S. Bradley ◽  
G. C. Schatz
Keyword(s):  
Inelastic Collisions ◽  
Water Molecules ◽  
Vibrationally Excited

ON THE COMPLEX BIFURCATION SET FOR A SYSTEM WITH SIMPLE DYNAMICS

1996 ◽  
Vol 06 (05) ◽  
pp. 949-968 ◽  
Author(s):  
MIKHAIL V. SHASHKOV ◽  
DMITRY V. TURAEV
Keyword(s):  
Periodic Orbit ◽  
Dynamic Behavior ◽  
Bifurcation Analysis ◽  
General Position ◽  
Equilibrium Points ◽  
Small Neighborhood ◽  
Heteroclinic Orbits ◽  
Bifurcation Set ◽  
Focus Type

Bifurcations of a heteroclinic contour composed of two equilibrium points of saddle-focus type and two heteroclinic orbits are considered. The case is selected where dynamics of the system is simple, i.e., no more than one periodic orbit is born at bifurcations in a small neighborhood of the contour. In spite of the simplicity of dynamic behavior, the structure of the bifurcation set corresponding to multi-round heteroclinic orbits is shown to be rather complicated. The complete bifurcation analysis is done under some conditions of a general position.

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