Plasmon dispersions in ultrathin metallic films

2014 ◽  
Vol 28 (27) ◽  
pp. 1450189
Author(s):  
Reng-Lai Wu ◽  
Ye-Jun Long ◽  
Hong-Jie Xue ◽  
Yabin Yu ◽  
Hui-Fang Hu
Keyword(s):  
Ultrathin Films ◽  
Metallic Films ◽  
Surface Electron ◽  
Plasmon Energy ◽  
Multilayer Systems ◽  
Long Wave ◽  
2D System ◽  
The One ◽  
Wave Limit ◽  
Plasmon Spectrum

We present an eigen-equation for plasmon of ultrathin films based on the self-consistent linear response approximation (SCLRA). The calculations for plasmon dispersion in both single and multilayer systems are reported. There are two types of plasmon in the plasmon spectrum, two-dimensional (2D) and bulk-like (BL) modes. The plasmon energy of the 2D mode is zero in the long wave limit, while the one of BL mode is nonzero in the long-wave limit. Given a surface electron density, with the decrease of the wave vector the dispersions of the 2D plasmon of different layer systems become equal to each other, and approach results of the pure 2D system.

On the soliton solutions of the Davey-Stewartson equation for long waves

1978 ◽  
Vol 360 (1703) ◽  
pp. 529-540 ◽  
Keyword(s):  
Scattering Theory ◽  
Soliton Solutions ◽  
Finite Depth ◽  
Operator Equations ◽  
One Dimensional ◽  
Linear System Of Equations ◽  
Long Wave ◽  
The One ◽  
Wave Limit ◽  
Dimensional Surface

The Davey-Stewartson equations describe two-dimensional surface waves on water of finite depth. In the long wave limit, it is shown that these equations belong to the class derivable from operator equations in the manner of Zakharov & Shabat. The basic underlying linear system of equations is obtained and solutions to the original nonlinear system sought from the Gelfand-Levitan equations of Inverse Scattering Theory. Single soliton and multi-soliton solutions are deduced corresponding to the one-dimensional solutions already available. The solitons so obtained are pseudo one dimensional in that they have the same form as onedimensional solitons but move at an angle to the main direction of propagation. The multi-soliton solution describes the interaction of many such solitons each propagating in different directions. For two solitons, it is shown that resonance occurs and a triple soliton structure is produced.

On periodic water-waves and their convergence to solitary waves in the long-wave limit

1981 ◽  
Vol 303 (1481) ◽  
pp. 633-669 ◽  
Keyword(s):  
Integral Equation ◽  
Solitary Waves ◽  
Water Waves ◽  
Periodic Problem ◽  
Existence Theory ◽  
Periodic Waves ◽  
Equation Formulation ◽  
Long Wave ◽  
Integral Equation Formulation ◽  
Wave Limit

A detailed discussion of Nekrasov’s approach to the steady water-wave problems leads to a new integral equation formulation of the periodic problem. This development allows the adaptation of the methods of Amick & Toland (1981) to show the convergence of periodic waves to solitary waves in the long-wave limit. In addition, it is shown how the classical integral equation formulation due to Nekrasov leads, via the Maximum Principle, to new results about qualitative features of periodic waves for which there has long been a global existence theory (Krasovskii 1961, Keady & Norbury 1978).

On the modulation of water waves on shear flows

1976 ◽  
Vol 347 (1651) ◽  
pp. 537-546 ◽  
Keyword(s):  
Water Waves ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Vries Equation ◽  
Harmonic Wave ◽  
Short Wave ◽  
Long Wave ◽  
Stokes Waves ◽  
The Stability ◽  
Wave Limit

The method of multiple scales is used to examine the slow modulation of a harmonic wave moving over the surface of a two dimensional channel. The flow is assumed inviscid and incompressible, but the basic flow takes the form of an arbitrary shear. The appropriate nonlinear Schrödinger equation is derived with coefficients that depend, in a complicated way, on the shear. It is shown that this equation agrees with previous work for the case of no shear; it also agrees in the long wave limit with the appropriate short wave limit of the Korteweg-de Vries equation, the shear being arbitrary. Finally, it is remarked that the stability of Stokes waves over any shear can be examined by using the results derived here.

RENORMALIZATION OF FERMI VELOCITY IN A COMPOSITE TWO DIMENSIONAL ELECTRON GAS

1993 ◽  
Vol 07 (01n03) ◽  
pp. 87-94 ◽  
Author(s):  
M. WEGER ◽  
L. BURLACHKOV
Keyword(s):  
Electron Gas ◽  
Fermi Velocity ◽  
Bohr Radius ◽  
Dimensional Electron ◽  
Temperature Dependent ◽  
Two Dimensional Electron Gas ◽  
Self Energy ◽  
2D System ◽  
Dimensional Electron Gas ◽  
The One

We calculate the self-energy Σ(k, ω) of an electron gas with a Coulomb interaction in a composite 2D system, consisting of metallic layers of thickness d ≳ a 0, where a 0 = ħ2∊1/ me 2 is the Bohr radius, separated by layers with a dielectric constant ∊2 and a lattice constant c perpendicular to the planes. The behavior of the electron gas is determined by the dimensionless parameters k F a 0 and k F c ∊2/∊1. We find that when ∊2/∊1 is large (≈5 or more), the velocity v(k) becomes strongly k-dependent near k F , and v ( k F ) is enhanced by a factor of 5-10. This behavior is similar to the one found by Lindhard in 1954 for an unscreened electron gas; however here we take screening into account. The peak in v(k) is very sharp (δ k/k F is a few percent) and becomes sharper as ∊2/∊1 increases. This velocity renormalization has dramatic effects on the transport properties; the conductivity at low T increases like the square of the velocity renormalization and the resistivity due to elastic scattering becomes temperature dependent, increasing approximately linearly with T. For scattering by phonons, ρ ∝ T 2. Preliminary measurements suggest an increase in v k in YBCO very close to k F .

Lumps, breathers, rogue waves and interaction solutions to a (3+1)-dimensional Kudryashov–Sinelshchikov equation

2020 ◽  
Vol 34 (12) ◽  
pp. 2050117 ◽  
Author(s):  
Xianglong Tang ◽  
Yong Chen
Keyword(s):  
Rogue Waves ◽  
Hirota Bilinear Method ◽  
Bilinear Method ◽  
Lump Solutions ◽  
Interaction Solutions ◽  
Long Wave ◽  
Wave Limit ◽  
Hirota Bilinear

Utilizing the Hirota bilinear method, the lump solutions, the interaction solutions with the lump and the stripe solitons, the breathers and the rogue waves for a (3[Formula: see text]+[Formula: see text]1)-dimensional Kudryashov–Sinelshchikov equation are constructed. Two types of interaction solutions between the lumps and the stripe solitons are exhibited. Some different breathers are given by choosing special parameters in the expressions of the solitons. Through a long wave limit of breathers, the lumps and rogue waves are derived.

Families of exact solutions of the generalized (3+1)-dimensional nonlinear-wave equation

2018 ◽  
Vol 32 (29) ◽  
pp. 1850359 ◽  
Author(s):  
Wenhao Liu ◽  
Yufeng Zhang
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Soliton Solutions ◽  
Rogue Waves ◽  
Lump Solution ◽  
Rational Solutions ◽  
Bilinear Method ◽  
The One ◽  
Wave Limit

In this paper, the traveling wave method is employed to investigate the one-soliton solutions to two different types of bright solutions for the generalized (3[Formula: see text]+[Formula: see text]1)-dimensional nonlinear-wave equation, primarily. In the following parts, we derive the breathers and rational solutions by using the Hirota bilinear method and long-wave limit. More specifically, we discuss the lump solution and rogue wave solution, in which their trajectory will be changed by varying the corresponding coefficient or coordinate axis. On the one hand, the breathers express the form of periodic line waves in different planes, on the other hand, rogue waves are localized in time.

Lump and interactional solutions of the (2+1)-dimensional generalized breaking soliton equation

2019 ◽  
Vol 34 (03) ◽  
pp. 2050037
Author(s):  
Yu-Pei Fan ◽  
Ai-Hua Chen
Keyword(s):  
Solitary Wave ◽  
Asymptotic Analysis ◽  
Bilinear Form ◽  
Lump Solution ◽  
Soliton Equation ◽  
Long Wave ◽  
Wave Limit

In this paper, by using the long wave limit method, we study lump solution and interactional solution of the (2[Formula: see text]+[Formula: see text]1)-dimensional generalized breaking soliton equation without using bilinear form. The moving properties of the lump solution, and the interactional properties of a lump and a solitary wave, are analyzed theoretically and graphically with asymptotic analysis.

General high-order breather, lump, and semi-rational solutions to the (2+1)-dimensional generalized Bogoyavlensky–Konopelchenko equation

2020 ◽  
pp. 2150057
Author(s):  
Xin-Mei Zhou ◽  
Shou-Fu Tian ◽  
Ling-Di Zhang ◽  
Tian-Tian Zhang
Keyword(s):  
Bilinear Form ◽  
Soliton Solutions ◽  
High Order ◽  
Rational Solutions ◽  
Lump Solutions ◽  
Long Wave ◽  
Wave Limit

In this work, we investigate the (2+1)-dimensional generalized Bogoyavlensky–Konopelchenko (gBK) equation. Based on its bilinear form, the [Formula: see text]th-order breather solutions of the gBK equation are successful given by taking appropriate parameters. Furthermore, the [Formula: see text]th-order lump solutions of the gBK equation are obtained via the long-wave limit method. In addition, the semi-rational solutions are generated to reveal the interaction between lump solutions, soliton solutions, and breather solutions.

scholarly journals Absorption spectra of the alkyl halides: energies of the C-I and C-Br bonds

1931 ◽  
Vol 133 (822) ◽  
pp. 430-439 ◽  
Keyword(s):  
Excitation Energy ◽  
Absorption Spectra ◽  
Satisfactory Agreement ◽  
Halogen Atom ◽  
Alkyl Halides ◽  
Thermochemical Data ◽  
Long Wave ◽  
Absorption Of Light ◽  
Wave Limit

It is to be expected that the alkyl halides will dissociate on absorption of light into alkyl residues and excited halogen atoms. Their absorption spectra are continuous, as is also the case with phenyl iodide, which liberates iodine under identical conditions. The C-I and C-Br linkages are certainly homopolar in the gas state. On Franck’s theory the long-wave limit of the absorption continuum should correspond to the heat of binding of C-I together with the excitation energy of the halogen atom. We would expect the alkyl halides to resemble the halogen hydrides in their behaviour, although with HI and HBr the long-wave limits are not very happily situated. The limit for HI is at 3320 Å., corresponding to a heat of dissocia­tion of 65,000 calories (the thermochemical heat is 69,000 calories) and the limit for HBr at 2640 Å. (97,000 calories, the thermochemical being 85,000). It is doubtful if these disagreements are entirely due to inaccuracy in the thermochemical data. The determination of these absorption limits seems to be a difficult matter. However, in the case of some of the alkyl halides we have been successful in obtaining very satisfactory agreement between the two sets of data, and have thought it worth while to give a brief account of our experi­mental method, and to reproduce at least one of our photometric records.

Dissipative effects on the resonant flow of a stratified fluid over topography

1988 ◽  
Vol 192 ◽  
pp. 287-312 ◽  
Author(s):  
N. F. Smyth
Keyword(s):  
Bottom Topography ◽  
Stratified Fluid ◽  
Flow Speed ◽  
Resonant Condition ◽  
Weakly Nonlinear ◽  
Dissipative Effects ◽  
Long Wave ◽  
Near Resonance ◽  
Wave Limit ◽  
Wave Modes

The effect of dissipation on the flow of a stratified fluid over topography is considered in the weakly nonlinear, long-wave limit for the case when the flow is near resonance, i.e. the basic flow speed is close to a linear long-wave speed for one of the long-wave modes. The two types of dissipation considered are the dissipation due to viscosity acting in boundary layers and/or interfaces and the dissipation due to viscosity acting in the fluid as a whole. The effect of changing bottom topography on the flow produced by a force moving at a resonant velocity is also considered. In this case, the resonant condition is that the force velocity is close to a linear long-wave velocity for one of the long-wave modes. It is found that in most cases, these extra effects result in the formation of a steady state, in contrast to the flow without these effects, which remains unsteady for all time. The flow resulting under the action of boundary-layer dissipation is compared with recent experimental results.

Sign in / Sign up

Export Citation Format

Share Document