scholarly journals Complete Determination of Relaxation Parameters From Two-Dimensional Raman Spectroscopy

1999 ◽  
Vol 19 (1-4) ◽  
pp. 109-116 ◽  
Author(s):  
Vladimir Chernyak ◽  
Andrei Piryatinski ◽  
Shaul Mukamel
Keyword(s):  
Equations Of Motion ◽  
Raman Signal ◽  
Two Dimensional ◽  
Echo Signal ◽  
Time Resolved ◽  
Vibrational Coherence ◽  
Relaxation Parameters ◽  
Complete Determination ◽  
Population Relaxation

Using the model of a weakly-anharmonic, underdamped oscillator coupled to a bath, we demonstrate that the 2D time-resolved Raman signal carries information about the population decay T1, the homogeneous dephasing T2, and the inhomogeneous dephasing T1 relaxation timescales. We distinguish between two projections of the 2D signal: first, the echo signal, which is stretched in the diagonal direction decays with T2, and the second which is stretched along one axis is related to the population relaxation and decays with T1. The width of both signals reflects T1. Equations of motion for vibrational coherence and population variables are employed in these calculations.

A Perturbation Approach for Analyzing Dispersion and Group Velocities in Two-Dimensional Nonlinear Periodic Lattices

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
R. K. Narisetti ◽  
M. Ruzzene ◽  
M. J. Leamy
Keyword(s):  
Perturbation Technique ◽  
Equations Of Motion ◽  
Wave Dispersion ◽  
Perturbation Approach ◽  
Two Dimensional ◽  
Weakly Nonlinear ◽  
Nonlinear Lattices ◽  
Directivity Patterns ◽  
Group Velocities

The paper investigates wave dispersion in two-dimensional, weakly nonlinear periodic lattices. A perturbation approach, originally developed for one-dimensional systems and extended herein, allows for closed-form determination of the effects nonlinearities have on dispersion and group velocity. These expressions are used to identify amplitude-dependent bandgaps, and wave directivity in the anisotropic setting. The predictions from the perturbation technique are verified by numerically integrating the lattice equations of motion. For small amplitude waves, excellent agreement is documented for dispersion relationships and directivity patterns. Further, numerical simulations demonstrate that the response in anisotropic nonlinear lattices is characterized by amplitude-dependent “dead zones.”

Two-dimensional leaps in near-critical flow over isolated orography

2005 ◽  
Vol 461 (2064) ◽  
pp. 3747-3763 ◽  
Author(s):  
E.R Johnson ◽  
G.G Vilenski
Keyword(s):  
Unsteady Flow ◽  
Equations Of Motion ◽  
Fold Increase ◽  
Flow Speed ◽  
Two Dimensional ◽  
Subcritical Flow ◽  
One Dimensional ◽  
Petviashvili Equation ◽  
Lee Wave ◽  
Supercritical Flows

This paper describes steady two-dimensional disturbances forced on the interface of a two-layer fluid by flow over an isolated obstacle. The oncoming flow speed is close to the linear longwave speed and the layer densities, layer depths and obstacle height are chosen so that the equations of motion reduce to the forced two-dimensional Korteweg–de Vries equation with cubic nonlinearity, i.e. the forced extended Kadomtsev–Petviashvili equation. The distinctive feature noted here is the appearance in the far lee-wave wake behind obstacles in subcritical flow of a ‘table-top’ wave extending almost one-dimensionally for many obstacles widths across the flow. Numerical integrations show that the most important parameter determining whether this wave appears is the departure from criticality, with the wave appearing in slightly subcritical flows but being destroyed by two-dimensional effects behind even quite long ridges in even moderately subcritical flow. The wave appears after the flow has passed through a transition from subcritical to supercritical over the obstacle and its leading and trailing edges resemble dissipationless leaps standing in supercritical flow. Two-dimensional steady supercritical flows are related to one-dimensional unsteady flows with time in the unsteady flow associated with a slow cross-stream variable in the two-dimensional flows. Thus the wide cross-stream extent of the table-top wave appears to derive from the combination of its occurrence in a supercritical region embedded in the subcritical flow and the propagation without change of form of table-top waves in one-dimensional unsteady flow. The table-top wave here is associated with a resonant steepening of the transition above the obstacle and a consequent twelve-fold increase in drag. Remarkably, the table-top wave is generated equally strongly and extends laterally equally as far behind an axisymmetric obstacle as behind a ridge and so leads to subcritical flows differing significantly from linear predictions.

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