Lagrangian rings. Multiscale asymptotics of a spectrum near resonance

1987 ◽  
Vol 21 (1) ◽  
pp. 68-70 ◽  
Author(s):  
M. V. Karasev
Keyword(s):  
Multiscale Asymptotics ◽  
Near Resonance

scholarly journals Existence and multiplicity of solutions for class of Navier boundary $p$-biharmonic problem near resonance

2014 ◽  
Vol 32 (2) ◽  
pp. 83 ◽  
Author(s):  
Mohammed Massar ◽  
EL Miloud Hssini ◽  
Najib Tsouli
Keyword(s):  
Saddle Point ◽  
Point Theorem ◽  
Elliptic Problem ◽  
Weak Solutions ◽  
Mountain Pass Theorem ◽  
Mountain Pass ◽  
Saddle Point Theorem ◽  
Biharmonic Problem ◽  
Existence And Multiplicity ◽  
Near Resonance

This paper studies the existence and multiplicity of weak solutions for the following elliptic problem\\$\Delta(\rho|\Delta u|^{p-2}\Delta u)=\lambda m(x)|u|^{p-2}u+f(x,u)+h(x)$ in $\Omega,$\\$u=\Delta u=0$ on $\partial\Omega.$By using Ekeland's variationalprinciple, Mountain pass theorem and saddle point theorem, theexistence and multiplicity of weak solutions are established.

Evolution of solitary waves in a two-pycnocline system

2009 ◽  
Vol 642 ◽  
pp. 235-277 ◽  
Author(s):  
M. NITSCHE ◽  
P. D. WEIDMAN ◽  
R. GRIMSHAW ◽  
M. GHRIST ◽  
B. FORNBERG
Keyword(s):  
Solitary Waves ◽  
Initial Conditions ◽  
Oscillation Period ◽  
Resonance Phenomenon ◽  
Numerical Code ◽  
Asymptotic Model ◽  
Narrow Region ◽  
Near Resonance ◽  
Long Time ◽  
The Waves

Over two decades ago, some numerical studies and laboratory experiments identified the phenomenon of leapfrogging internal solitary waves located on separated pycnoclines. We revisit this problem to explore the behaviour of the near resonance phenomenon. We have developed a numerical code to follow the long-time inviscid evolution of isolated mode-two disturbances on two separated pycnoclines in a three-layer stratified fluid bounded by rigid horizontal top and bottom walls. We study the dependence of the solution on input system parameters, namely the three fluid densities and the two interface thicknesses, for fixed initial conditions describing isolated mode-two disturbances on each pycnocline. For most parameter values, the initial disturbances separate immediately and evolve into solitary waves, each with a distinct speed. However, in a narrow region of parameter space, the waves pair up and oscillate for some time in leapfrog fashion with a nearly equal average speed. The motion is only quasi-periodic, as each wave loses energy into its respective dispersive tail, which causes the spatial oscillation magnitude and period to increase until the waves eventually separate. We record the separation time, oscillation period and magnitude, and the final amplitudes and celerity of the separated waves as a function of the input parameters, and give evidence that no perfect periodic solutions occur. A simple asymptotic model is developed to aid in interpretation of the numerical results.

scholarly journals RESONANT RAMAN SCATTERING OF QUANTUM WIRE IN STRONG MAGNETIC FIELD

1999 ◽  
Vol 13 (17) ◽  
pp. 2275-2283 ◽  
Author(s):  
HYUN C. LEE
Keyword(s):  
Magnetic Field ◽  
Raman Scattering ◽  
Strong Magnetic Field ◽  
Coulomb Interaction ◽  
Quantum Wire ◽  
Spin Excitation ◽  
Momentum Dependence ◽  
Near Resonance ◽  
Resonant Raman ◽  
Resonant Raman Scattering

The resonant Raman scattering of a quantum wire in a strong magnetic field is studied, focused on the effect of long range Coulomb interaction and the spin–charge separation. The energy–momentum dispersions of charge and spin excitation obtained from Raman cross-section show the characteristc cross-over behaviour induced by inter-edge Coulomb interaction. The "SPE" peak near resonance in polarized spectra becomes broad due to the momentum dependence of charge velocity. The broad peak in the depolarized spectra is shown to originate from the disparity between charge and spin excitation velocity.

Wrinkle and Near Resonance Effect on the Vibrational and Electronic properties in Compressed Monolayer MoSe2

2021 ◽  
Author(s):  
Yan Liu ◽  
Qiang Zhou ◽  
Yalan Yan ◽  
Liang Li ◽  
Jian Zhu ◽  
...  
Keyword(s):  
High Pressure ◽  
Optical Properties ◽  
Transition Metal ◽  
Electronic Properties ◽  
Resonance Effect ◽  
Transition Metal Dichalcogenides ◽  
Effective Technique ◽  
Near Resonance ◽  
Metal Dichalcogenides

Pressure has been considered as an effective technique to modulate the structural, electronic, and optical properties of transition metal dichalcogenides (TMDs) materials. Here, by performing in situ high pressure Raman,...

Loss of atoms from a near-resonance hollow dipole trap

2021 ◽  
Vol 51 (6) ◽  
pp. 490-494
Author(s):  
V A Vinogradov ◽  
K A Karpov ◽  
Andrey Vadimovich Turlapov
Keyword(s):  
Dipole Trap ◽  
Near Resonance
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