Understanding the Different Exciton–Plasmon Coupling Regimes in Two-Dimensional Semiconductors Coupled with Plasmonic Lattices: A Combined Experimental and Unified Equation of Motion Approach

We have studied the behaviour of a charged particle in an axially symmetric magnetic field having a neutral point, so as to find a possibility of confining a charged particle in a thermonuclear device. In order to study the motion we have reduced a three-dimensional motion to a two-dimensional one by introducing a fictitious potential. Following Schmidt we have classified the motion, as an ‘off-axis motion’ and ‘encircling motion’ depending on the behaviour of this potential. We see that the particle performs a hybrid type of motion in the negative z-axis, i.e. at some instant it is in ‘off-axis motion’ while at another instant it is in ‘encircling motion’. We have also solved the equation of motion numerically and the graphs of the particle trajectory verify our analysis. We find that in most of the cases the particle is contained. The magnetic moment is found to be moderately adiabatic.

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Asymptotic behavior of velocity process in the Smoluchowski–Kramers approximation for stochastic differential equations

Advances in Applied Probability ◽

10.2307/1427751 ◽

1991 ◽

Vol 23 (2) ◽

pp. 317-326 ◽

Cited By ~ 1

Author(s):

Kiyomasa Narita

Keyword(s):

Mean Field ◽

Planck Equation ◽

Equation Of Motion ◽

Distribution Functions ◽

Two Dimensional ◽

Large Parameter ◽

Uhlenbeck Process ◽

One Dimensional ◽

Kramers Equation ◽

Non Linear Oscillator

Here a response of a non-linear oscillator of the Liénard type with a large parameter α ≥ 0 is formulated as a solution of a two-dimensional stochastic differential equation with mean-field of the McKean type. This solution is governed by a special form of the Fokker–Planck equation such as the Smoluchowski–Kramers equation, which is an equation of motion for distribution functions in position and velocity space describing the Brownian motion of particles in an external field. By a change of time and displacement we find that the velocity process converges to a one-dimensional Ornstein–Uhlenbeck process as α →∞.

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Enhanced dissipation for quasi-geostrophic motion over small-scale topography

Journal of Fluid Mechanics ◽

10.1017/s0022112099007430 ◽

2000 ◽

Vol 407 ◽

pp. 105-122 ◽

Cited By ~ 9

Author(s):

JACQUES VANNESTE

Keyword(s):

Large Scale ◽

Spatial Scales ◽

Additional Term ◽

Equation Of Motion ◽

Small Scale ◽

Two Dimensional ◽

Turbulent Dissipation ◽

Dissipative Term ◽

History Of ◽

Large Scale Flow

The effect of a small-scale topography on large-scale, small-amplitude oceanic motion is analysed using a two-dimensional quasi-geostrophic model that includes free-surface and β effects, Ekman friction and viscous (or turbulent) dissipation. The topography is two-dimensional and periodic; its slope is assumed to be much larger than the ratio of the ocean depth to the Earth's radius. An averaged equation of motion is derived for flows with spatial scales that are much larger than the scale of the topography and either (i) much larger than or (ii) comparable to the radius of deformation. Compared to the standard quasi-geostrophic equation, this averaged equation contains an additional dissipative term that results from the interaction between topography and dissipation. In case (i) this term simply represents an additional Ekman friction, whereas in case (ii) it is given by an integral over the history of the large-scale flow. The properties of the additional term are studied in detail. For case (i) in particular, numerical calculations are employed to analyse the dependence of the additional Ekman friction on the structure of the topography and on the strength of the original dissipation mechanisms.

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Two-dimensional electronic spectra investigated using hierarchical equation of motion and cumulant expansion

Journal of Modern Optics ◽

10.1080/09500340.2013.771754 ◽

2013 ◽

Vol 60 (4) ◽

pp. 301-308 ◽

Cited By ~ 1

Author(s):

Pan-Pan Zhang ◽

Zhi-Qiang Liu ◽

Xian-Ting Liang

Keyword(s):

Electronic Spectra ◽

Equation Of Motion ◽

Two Dimensional ◽

Cumulant Expansion

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Equation of motion approach to the two-dimensional Hubbard model

Physical Review B ◽

10.1103/physrevb.61.13418 ◽

2000 ◽

Vol 61 (20) ◽

pp. 13418-13423 ◽

Cited By ~ 1

Author(s):

Hong-Gang Luo ◽

Shun-Jin Wang

Keyword(s):

Hubbard Model ◽

Equation Of Motion ◽

Two Dimensional

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FERMION THRESHOLD ENERGY STATES

Modern Physics Letters B ◽

10.1142/s0217984992001241 ◽

1992 ◽

Vol 06 (24) ◽

pp. 1531-1534

Author(s):

CHANGHONG ZHU

Keyword(s):

Magnetic Field ◽

Magnetic Flux ◽

Three Dimensional ◽

Threshold Energy ◽

Index Theorem ◽

Equation Of Motion ◽

Field Configuration ◽

Two Dimensional ◽

Magnetic Field Configuration ◽

The Magnetic Field

We show that for a three-dimensional non-relativistic spinor confined on a plane, the spin-up component obeys the same equation of motion as a two-dimensional spinor. Threshold energy solution is investigated when the electron is moving in the vortex field. It can be proved from the index theorem that the existence of the threshold states depends on the magnetic flux only, not on the magnetic field configuration.

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Equation of motion for a string operator in two-dimensional massless lattice QCD

Physics Letters B ◽

10.1016/0370-2693(86)90553-8 ◽

1986 ◽

Vol 167 (1) ◽

pp. 94-98

Author(s):

Shijong Ryang

Keyword(s):

Lattice Qcd ◽

Equation Of Motion ◽

Two Dimensional ◽

String Operator

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An Inviscid Analysis in Polar Coordinates of Flow Between Two Flat Plates

Journal of Applied Mechanics ◽

10.1115/1.2900780 ◽

1993 ◽

Vol 60 (1) ◽

pp. 65-69

Author(s):

D. N. Contractor

Keyword(s):

Numerical Solution ◽

Flat Plate ◽

Equation Of Motion ◽

Polar Coordinates ◽

Two Dimensional ◽

Bernoulli Equation ◽

Simultaneous Solution ◽

Flat Plates ◽

External Point ◽

Two Dimensional Flow

An inviscid analysis is conducted of two-dimensional flow between a flat plate pivoting about an external point and falling onto another plate at rest. The motion of the fluid between the two plates is analyzed by the simultaneous solution of the unsteady Bernoulli equation, the equation of continuity, and the equation of motion for the plate. Numerical solution of the equations resulted in velocities and pressures along the plate as a function of time. The pressures were integrated to yield forces and moments on the falling plate. The results are compared with the motion of a horizontal flat plate falling vertically onto a rigid stationary flat plate. The two results are similar to one another.

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