Surface Mode Frequencies Research Articles

New mathematical model to analysis fluid sloshing in 3D tanks with slotted middle baffle

This work studies the natural frequencies and modes of liquid sloshing in a rectangular 3D tank with the slotted baffles in middle. A new vibrational model incorporating the pressure difference between the two sides of the baffle, using a transmission function in Laplace space is presented. To this end, a part of the baffle that includes the wall and the slot is modeled in Fluent software, to express this pressure difference as a function of the fluid velocity passing through the baffle. Then, using the boundary element method, and boundary conditions, the equations of the fluid domain are developed. In this research, the rigid baffle is surrounded by a three-dimensional irrotational velocity field of an ideal liquid, and the potential flow conditions are considered. So, the equations from the boundary element method are coupled with the equations of potential flow and other boundary conditions, and then the fluid free surface mode shapes and frequencies are extracted. In the following, after validating the proposed model, the effects of different slot sizes on the liquid sloshing parameters are analyzed. Also, the effects of parameters of the mentioned new vibrational method on the frequencies and damping of the system are investigated.

First-order Bose-Einstein condensation with three-body interacting bosons

Bose-Einstein condensation, observed in either strongly interacting liquid helium or weakly interacting atomic Bose gases, is widely known to be a second-order phase transition. Here, we predict a first-order Bose-Einstein condensation in a cloud of harmonically trapped bosons interacting with both attractive two-body interaction and repulsive three-body interaction, characterized respectively by an $s$-wave scattering length $a<0$ and a three-body scattering hypervolume $D>0$. It happens when the harmonic trapping potential is weak, so with increasing temperature the system changes from a low-temperature liquid-like quantum droplet to a normal gas, and therefore experiences a first-order liquid-to-gas transition. At large trapping potential, however, the quantum droplet can first turn into a superfluid gas, rendering the condensation transition occurred later from a superfluid gas to a normal gas smooth. We determine a rich phase diagram and show the existence of a tri-critical point, where the three phases - quantum droplet, superfluid gas and normal gas - meet together. We argue that an ensemble of spin-polarized tritium atoms could be a promising candidate to observe the predicted first-order Bose-Einstein condensation, across which the condensate fraction or central condensate density jumps to zero and the surface-mode frequencies diverge.

Collective excitations of spherical semiconductor nanoparticles

In this article, we study the dispersion properties of bulk and surface electrostatic oscillations of a spherical quantum electron-hole semiconductor plasma as a simple model of a semiconductor nanoparticle. We derive general dispersion relation for both bulk and surface modes, using quantum hydrodynamic theory (including the electrons and holes quantum recoil effects, quantum statistical pressures of the plasma species, as well as exchange and correlation effects) in conjunction with Poisson’s equation and appropriate boundary conditions. We show that for the arbitrary value of angular quantum number there are only two surface plasmon modes, but two infinite series of bulk modes for that owe their existence to the curvature of the interface. We use the typical values of GaAs semiconductor to compute the bulk and surface mode frequencies for different value of .

Properties of surface modes in one dimensional plasma photonic crystals

Properties of surface modes supported at the interface of air and a semi-infinite one dimensional plasma photonic crystal are analyzed. The surface mode equation is obtained by using transfer matrix method and applying continuity conditions of electric fields and its derivatives at the interface. It is observed that with increase in the width of cap layer, frequencies of surface modes are shifted towards lower frequency side, whereas increase in tangential component of wave-vector increases the mode frequency and total energy carried by the surface modes. With increase in plasma frequency, surface modes are found to shift towards higher frequency side. The group velocity along interface is found to control by cap layer thickness.

Vortex dynamics in cubic-quintic Bose-Einstein condensates

We study vortex dynamics in a trapped Bose-Einstein condensate with tunable two- and three-body interactions. The dynamics is governed by two-dimensional cubic-quintic Gross-Pitaevskii equation. A time-dependent variational method has been used to obtain critical rotational frequency and surface mode frequency analytically and are compared with numerical simulation results. An imaginary time propagation method and Crank-Nicolson scheme for discretization have been used for numerical simulation. The numerically calculated average value of the angular momentum per particle shows very clearly its dynamical relation with the time development of the vortex formation. The rotational frequency dependence of the variation of average value of the angular momentum per particle with time shows that vortices form much faster in time for higher rotational frequency. Similarly, the vortex forms much faster in time with an increase of the strength of the repulsive three-body interaction. The simulation of the vortex lattice formation in the condensate shows that the presence of the three-body interactions does not alter the vortex lattice pattern but it helps in the shape deformations of the condensate thereby leading to vortex lattice formation. Likewise, the three-body interactions enable the vortex lattice formation in Bose-Einstein condensates even with attractive two-body interactions and in purely quintic BEC.

Graphene-based photovoltaic cells for near-field thermal energy conversion

Thermophotovoltaic devices are energy-conversion systems generating an electric current from the thermal photons radiated by a hot body. While their efficiency is limited in far field by the Schockley-Queisser limit, in near field the heat flux transferred to a photovoltaic cell can be largely enhanced because of the contribution of evanescent photons, in particular for a source supporting a surface mode. Unfortunately, in the infrared where these systems operate, the mismatch between the surface-mode frequency and the semiconductor gap reduces drastically the potential of this technology. In this paper we propose a modified thermophotovoltaic device in which the cell is covered by a graphene sheet. By discussing the transmission coefficient and the spectral properties of the flux, we show that both the cell efficiency and the produced current can be enhanced, paving the way to promising developments for the production of electricity from waste heat.

Asymptotic behavior of trapped modes in two-layer fluids

We investigate the trapping of oblique water-waves by horizontal cylinders in a two-layer liquid. Two cases depending on a small parameter are studied: first, the liquid densities are close to each other, and second, the density of the upper layer is small in comparison with that of the lower layer. We give sufficient conditions for wave trapping for appropriate limit problems. The main results involve asymptotic formulas for the surface and interfacial trapped mode frequencies. In addition, we prove comparison principles and sufficient conditions for the existence of trapped modes in various situations.

Critical rotation of an anharmonically trapped Bose–Einstein condensate

We consider rotational motion of an interacting atomic Bose–Einstein condensate (BEC) with both two- and three-body interactions in a quadratic-plus-quartic and harmonic-plus-Gaussian trap. By using the variational method, the influence of the three-body interaction and the anharmonicity of the trap on the lowest energy surface mode excitation and the spontaneous shape deformation (responsible for the vortex formation) in a rotating BEC is discussed in detail. It is found that the repulsive three-body interaction helps the formation of the vortex and reduces the lowest energy surface mode frequency and the critical rotational frequency of the system. Moreover, the critical rotational frequency for the vortex formation in the harmonic-plus-Gaussian potential is lower than that in the quadratic-plus-quartic potential.

Surface mode absorption and infrared optical properties of gallium phosphide nanoparticles

The surface optical (SO) mode of ellipsoidal gallium phosphide (GaP) nanoparticles is investigated by infrared transmission spectroscopy. The surface mode theory of diatomic cubic particles is generalized and applied to GaP nanoparticles in a systematic treatment. The Frohlich mode of GaP nanoparticles has been observed in our experiment. As far as surface mode frequency is concerned, the result of the experiment agrees with that of the theoretical calculation. The characteristics of the SO mode peak, including frequency shift, broadening and line shape, are analyzed. The frequency shift is attributed to the surrounding medium effect, surface oxidation and the aggregation effect as well as intrinsic point defects; the broadening is mainly due to the non-spherical particle shape, aggregation and quantum confinement effect; and the line shape is related to the particle shape and the damping function.

Retarded modes of lateral ferromagnetic/ferromagnetic superlattice

In this paper，we calculated the retarded modes of semi-infinite lateral ferromagnetic/ ferromagnetic superlattice with the effective-medium theory. We took the Co/Ni system surface modes and bulk modes as the examples for the superlattice and found some interesting properties different from that of the lateral ferromagnetic/nonmagnetic superlattice. Lateral magnetic/magnetic superlattice have some complex retarded modes which are very common in the systems. Changing the ratio of the thicknesses of the ferromagnetic layers, the two branches of surface mode frequency and bulk mode frequency band can be adjusted consequently. This tailoring effect is related to the two ferromagnetic layers' saturation magnetization values, and it is quite pronounced when the two saturation magnetization values are quite different from each other. If the difference between the tow values is large，the tailoring effect of f1 is more obvious. When the saturation magnetization value of the second ferromangtic medium approaches to zero，this system will become the magnetic/nonmagnetic superlattice. If in Maxwell equation ε=0，the retarded modes will transit to the ferromangtic/ferromangnetic superlattice magnetostatic modes.

Dynamical phase transition in vibrational surface modes

We consider the dynamical properties of a simple model of vibrational surface modes. We obtain the exact spectrum of surface excitations and discuss their dynamical features. In addition to the usually discussed localized and oscillatory regimes we also find a second phase transition where surface mode frequency becomes purely imaginary and describes an overdamped regime. Noticeably, this transition has an exact correspondence to the oscillatory - overdamped transition of the standard oscillator with a frictional force proportional to velocity.

A note on the small oscillation regimes of rotating liquid bridges: Transition from surface to internal wave modes

An analysis of the small oscillation modes of rotating liquid bridges is carried out. The study is performed in the particular conditions when both surface and internal wave mode frequencies almost coincide for a certain meridional and azimuthal wave number. The critical values of the rotation speed and the natural frequencies for which this transitional condition takes place are obtained numerically as a function of the parameters characterizing the fluid configuration. The influence of both the outer bath and the liquid bridge equilibrium shape on the transition is analyzed. Analytical expressions providing the critical values of the rotation speed and the natural frequencies are obtained for cylindrical liquid bridges.

Vortex formation in a slowly rotating Bose-Einstein condensate confined in a harmonic-plus-Gaussian laser trap

Motivated by the recent experiment at ENS [ V. Bretin, S. Stock, Y. Seurin and, J. Dalibard, Phys. Rev. Lett. {\bf 92}, 050403 (2004)], we study a rotating (non-)interacting atomic Bose-Einstein condensate confined in a harmonic-plus-gaussian laser trap potential. By adjusting the amplitude of the laser potential, one can make quadratic-plus-quartic potential,purely quartic potential, and quartic-minus-quadratic potential. We show that an interacting Bose-Einstein condensate confined in a harmonic-plus-gaussian laser trap breaks the rotational symmetry of the Hamiltonian when rotational frequency is greater than one-half of the lowest energy surface mode frequency. We also show that by increasing the amplitude of the gaussian laser trap, a vortex appears in a slowly rotating Bose-Einstein condensate. Moreover, one can also create a vortex in non-interacting Bose-Einstein condensate confined in harmonic-plus-gaussian laser potential.

Vortex formation in a fast rotating Bose-Einstein condensate

We study rotational motion of an interacting atomic Bose-Einstein condensate confined in a quadratic-plus-quartic potential. We calculate the lowest energy surface mode frequency and show that a symmetric trapped (harmonic and quartic) Bose-Einstein condensate breaks the rotational symmetry of the Hamiltonian when rotational frequency is greater than one-half of the lowest energy surface mode frequency. We argue that the formation of a vortex is not possible in a noninteracting as well as in an attractive Bose-Einstein condensate confined in a harmonic trap due to the absence of the spontaneous shape deformation, but it can occur which leads to the vortex formation if we add an additional quartic potential. Moreover, the spontaneous shape deformation and consequently the formation of a vortex in an attractive system depends on the strengths of the two-body interaction and the quartic potential.

Effects of natural and electrochemical oxidation processes on acoustic waves in porous silicon films

Brillouin scattering has been performed to study the effects of natural and electrochemical oxidation on the surface and bulk acoustic mode properties of porous silicon films. The acoustic mode frequencies are observed to decrease with increasing oxidation time and this is attributed to the progressive transformation of silicon–silicon bonds on the inner pore walls into SiO2. The dependence of the surface and bulk acoustic mode frequencies on the natural oxidation time allows the evaluation of these wave frequencies for a porous-SiO2 glass film, and hence the estimation of its bulk modulus. Both Brillouin and Raman data confirm the expectation that oxidation leads to a reduction in silicon nanoparticle size, and provide a correlation between the redsifted acoustic mode frequency and the oxidation period.

Interlayer exchange coupling of epitaxial Fe/Al/Fe trilayer films: Dynamic and static measurements

This report deals with the interlayer exchange coupling of epitaxial Fe(3 nm)/Al(tAl=0.4–0.9 nm)/Fe(2 nm) trilayers studied by using ferromagnetic resonance (FMR), Brillouin light scattering (BLS) and magneto-optic Kerr effect (MOKE) measurement techniques. A very strong antiferromagnetic (AFM) interlayer exchange coupling (&amp;gt;3 erg/cm2) was observed at a spacer Al thickness of 0.7 nm. The bilinear (J1) and the biquadratic (J2) coupling constants were determined from (i) the fitting of angular variation (θH) of resonance field (Hres) from FMR, (ii) field variation of acoustic and optic surface mode frequencies from BLS and (iii) by fitting of longitudinal MOKE hysteresis loops. The samples with strong antiferromagnetic (AFM) coupling have a higher Hres along the easy axis than that along hard axis and their magnetizations are canted. The eightfold-like symmetry, of the acoustic Hres as a function of in-plane field angle at room temperature, is due to the strong competition between the fourfold anisotropy energy (HK) and the AFM interfacial coupling energy. This behavior vanished at low temperatures due to a strong increase of AFM coupling in comparison to HK. We distinguish the existence of canted magnetization states at resonance by fitting the experimental Hres(θH) data to the model calculation.

A comparative study of FMR and Brillouin light scattering on amorphous Fe 40Ni 40B 20

It is shown that magnetic surface mode frequencies in the amorphous ferromagnet Fe 40Ni 40B 20 measured using Brillouin light scattering depend upon the incident laser light intensity: presumably due to local heating of the specimen due to the concentration of the light flux into a focal spot only a few microns in diameter. Surface mode frequencies extrapolated to zero light intensity are shown to be consistent with magnetic parameters measured using ferromagnetic resonance at 35.731 GHz to within ±0.5 GHz for specimens of amorphous Fe 40Ni 40B 20. 0.5 GHz corresponds to a change of 0.17 kG in the saturation magnetization, 4π M s.

Surface and gap intrinsic localized modes in one-dimensional III-V semiconductors

A theoretical investigation has been made of intrinsic localized vibrational modes in an anharmonic one-dimensional diatomic lattice with alternating force constants coupling successive neighbours. This system simulates a row of atoms in the 111 direction of a III-V semiconductor. Specific calculations have been carried out for GaN, because it has a large gap between acoustic and optical branches. We study small-amplitude atom vibrations (up to 0.4 Å), accessible to experimental detection, in order to legitimize the expansion of the full potential to include cubic and quartic terms. We consider then nearest-neighbour interactions through harmonic as well as cubic and quartic anharmonic interactions to study the interplay between cubic and quartic terms in the frequencies of the localized modes. The force constants were determined empirically by fitting the longitudinal branches in the -L direction of GaN. We have studied both gap and surface intrinsic localized modes. Zinc-blende-structure chains are of particular interest, because the lack of inversion symmetry prevents the classification of the modes as even or odd parity. Nevertheless, modes were found that closely resemble the even- or odd-parity modes of an NaCl-structure chain. Their frequencies lie inside the gap for GaN. The absence of inversion symmetry permits a variety of surface modes to exist, depending on whether the bond at the surface is strong or weak and the atom at the surface is light or heavy. All surface mode frequencies for GaN lie inside the gap as found with the use of the full potential.

Nondestructive picosecond-ultrasonic characterization of Mo/Si extreme ultraviolet multilayer reflection coatings

We have used noncontact, nondestructive picosecond-ultrasonic techniques to characterize Mo/Si multilayer reflection coatings for extreme ultraviolet (EUV) lithography. Using our alternating-pump technique, we successfully excited and detected the two lowest frequency localized acoustic-phonon surface modes. By measuring their vibration frequencies simultaneously, we can extract the two key parameters for EUV reflector performance: d (bilayer thickness) and Γ (thickness ratio of Mo layer to the bilayer) of the Mo/Si multilayers. To demonstrate the utility of this technique, we measured the surface-mode frequencies and extracted the values of d and Γ for six mirrors. Good agreement with the results of at-wavelength EUV reflectometry was found. Damage to coatings caused by the pump and probe laser beams was also studied, and found to be negligible given our data-acquisition time.

Surface Wave Eigenmodes in a Finite-Area Plane Microwave Plasma

The resonance frequencies of electromagnetic surface modes propagating along a plane dielectric-plasma interface are computed, taking into account the finite area of the latter. The analysis results in simple analytical formulae for estimating the plasma density at which a given mode can be expected to occur for given geometry and wave frequency. Comparison with measurements in large-area circular plasmas is made.