Influence of bottom topography on the propagation of linear shallow water waves: an exact approach based on the invariant imbedding method

The wave equation for linear shallow water waves propagating over a varying bottom topography has the same form as that for p-polarized electromagnetic waves in inhomogeneous dielectric media. The role played by the dielectric permittivity in the case of electromagnetic waves is played by the inverse water depth. We apply the invariant imbedding theory of wave propagation, which has been developed mainly to study the electromagnetic wave propagation, to linear shallow water waves in the special case where the depth depends on only one coordinate. By comparing the numerical result obtained using our method, when the depth profile is linear, with an exact analytical formula, we demonstrate that our method is numerically reliable. The invariant imbedding method can be used in studying the influence of complicated bottom topography on the propagation of shallow water waves, in a numerically exact manner. We illustrate this by considering the case where a periodic modulation is added to a linear depth profile. Bragg scattering due to the periodic component competes with the tsunami effect due to the linear depth variation. This competition is seen to generate interesting physical effects. We also consider a ridge-type bottom topography and examine the resonant transmission phenomenon associated with the Fabry–Perot effect.     

Anomalous lateral beam shift and total absorption due to excitation of surface waves in materials with negative refraction

We studied electromagnetic beam reflection from layered structures that include materials with negative refraction. Excitation of leaky surface waves leads to the formation of anomalous lateral shifts in the reflected beams with single or double peak structures. The presence of reasonable losses within material with negative refraction, besides significant influence on manifestation of the giant lateral shifts, can lead to their total suppression and anomalously high absorption of the incident radiation. If, in addition to the resonant excitation of leaky surface waves, radiation inflow exactly compensates their irreversible damping, total absorption of the incoming radiation can be achieved for moderately wide beams.     

Mechanical properties of silicon nanobeams with undercut evaluated by combining dynamic resonance test and finite element analysis

Mechanical properties of silicon nanobeams are of prime importance in nanoelectromechanical system applications. A numerical experimental method of determining resonant frequencies and Young's modulus of nanobeams by combining finite element analysis and frequency response tests based on an electrostatic excitation and visual detection by laser Doppler vibrometer is presented in this paper. Silicon nanobeams test structures are fabricated from silicon-on-insulator wafers by using a standard lithography and anisotropic wet etching release process, which inevitably generates the undercut of the nanobeam clamping. In conjunction with three-dimensional finite element numerical simulations incorporating the geometric undercut, dynamic resonance tests reveal that the undercut significantly reduces resonant frequencies of nanobeams due to the fact that it effectively increases the nanobeam length by a correct value Δ L, which is a key parameter that is correlated with deviations in the resonant frequencies predicted from the ideal Euler-Bernoulli beam theory and experimentally measured data. By using a least-square fit expression including Δ L, we finally extract Young's modulus from the measured resonance frequency versus effective length dependency and find that Young's modulus of silicon nanobeam with 200-nm thickness is close to that of bulk silicon. This result supports that the finite size effect due to surface effect does not play a role in mechanical elastic behaviour of silicon nanobeams with the thickness larger than 200 nm.     

Effective Range Expansion for Electron-Neutrino and Electron-Antineutrino Scattering

Weak interactions from a pure S-matrix point of view are considered in order to get an idea about the high-energy behaviour. To have the weak interaction as undisturbed as possible by electromagnetic and strong interactions we study only the leptonic processes eν → νe, eν → ν e and eē → ν ν. We calculate the corresponding partial wave amplitudes for s and p waves and constrain them by low energy behaviour coming from the lowest order approximation, analyticity and unitarity. Several examples of partial wave cross sections for the three reactions with resonant behaviour in the eν or eν channel are calculated numerically.     

Assessment of interface deformation and fracture in metal matrix composites under transverse loading conditions

The transverse properties of unidirectional metal matrix composites (MMCs) are dominated by the fiber/matrix interfacial properties, residual stresses and matrix mechanical response. In order to monitor and study, in situ, the failure of interfaces in titanium-based composites subjected to transverse loading conditions, an ultrasonic imaging technique has been developed. The interface was imaged ultrasonically and the change in ultrasonic amplitude with the transverse loading was monitored, indicating the sensitivity of the technique to fracture and deformation of interfaces. This change in amplitude has been explained in terms of the multiple reflection theory of ultrasonic waves. The multiple reflection theory enabled estimation of the interfacial deformation and debonding as a function of loading. The ultrasonic technique was also used in conjunction with finite element modeling in order to quantify the fiber/matrix interfacial transverse strength in situ in MMCs.     

Improved SPR technique for determination of the thickness and optical constants of thin metal films

A novel method with single-wavelength light is developed to determine the optical constants and the thickness of a thin metal film. It bases on a new geometry that consists of a coupling prism, a transparent coating layer directly deposited onto the prism base, a thin metal film to be detected, and the air. The attenuated total reflection technique is employed in our configuration to excite two different kinds of surface plasmon waves simultaneously. As a result, the reflection curve shows two obvious surface plasmon resonant dips. Using the Chen's et al. (Opt. Soc. Am. 71 189, 1981) method, we can obtain two sets of () and thickness of the thin metal film through one resonant dip (surface plasmon), then the real value can be determined through the other resonant dip (modified long-range surface plasmon). Compared to conventional double wavelength method and the double-medium technique (Yang et al. Appl. Opt. 27 11, 1988), the present single-scan method avoids both the ambiguity of different conditions caused by two-scan technique, and the dispersion problem with different light wavelength.     

The SRS line-shaped nonlinear resonance in consideration of flight effects

We investigate the problem of nonlinear interaction of a gas of three-level atoms with the field of standing waves in the situation where the atomic free path length at the initial and final metastable levels is comparable with the transverse dimensions of the field. The standing waves are resonant to adjacent Doppler-broadened transitions. The case of fields of Gaussian profile is analysed. It has been shown that in the limiting case of large free path length the nonlinear resonance width is of the order of the inverse time of flight of an atom in the field. The first and second derivatives of resonance with respect to frequency are considered. It has been shown that in the situation of flight they contain narrow resonant structures with a width of the order of a homogeneous width of the forbidden transition between metastable levels.     

Above-barrier reflection of cold atoms by resonant laser light within the Gross-Pitaevskii approximation

Above-barrier reflection of cold alkali atoms by resonant laser light was considered analytically within the Gross-Pitaevskii approximation. Correction for the reflection coefficient because of a weak nonlinearity of the stationary Schrödinger equation has been derived using multiscale analysis as a form of perturbation theory. The nonlinearity adds spatial harmonics to linear incident and reflecting waves. It was shown that the role of nonlinearity increases when the kinetic energy of an atom is nearly to the height of the potential barrier. Results are compared to the known numerical derivations for wave functions of the Gross-Pitaevskii equation with the step potential.     

Macroscopic and mesoscopic matter waves

It has been shown earlier [3,6] that matter waves which are known to lie typically in the range of a few angstrom, can also manifest in the macrodomain with a wave length of a few centimeters, for electrons propagating along a magnetic field. This followed from the predictions of a probability amplitude theory by the author [1,2] in the classical macrodomain of the dynamics of charged particles in a magnetic field. It is shown in this paper that this case constitutes only a special case of a generic situation whereby composite systems such as atoms and molecules in their highly excited internal states, can exhibit matter wave manifestation in macro and mesodomains, in one-dimensional scattering. The wave length of these waves is determined, not by the mass of the particle as in the case of the de Broglie wave, but by the frequency ω, of the classical orbital motion of the internal state in the correspondence limit, and is given by a nonquantal expression, λ = 2πv/ω, v being the velocity of the particle. For the electrons in a magnetic field the frequency corresponds to the gyrofrequency, Ω and the nonquantal wave length is given by λ = 2πv _|| /Ω; v _|| being the velocity of electrons along the magnetic field. Received 29 September 2001 / Received in final form 23 May 2002 Published online 19 July 2002     

Rarefactive ion-acoustic electrostatic solitary structures in nonthermal plasmas

An investigation has been made of ion-acoustic solitary waves in an unmagnetized nonthermal plasma whose constituents are an inertial ion fluid and nonthermally distributed electrons. The properties of stationary solitary structures are briefly studied by the pseudo-potential approach, which is valid for arbitrary amplitude waves, and by the reductive perturbation method which is valid for small but finite amplitude limit. The time evolution of both compressive and rarefactive solitary waves, which are found to coexist in this nonthermal plasma model, is also examined by solving numerically the full set of fluid equations. The temporal behaviour of positive (compressive) solitary waves is found to be typical, i.e., the positive initial disturbance breaks up into a series of solitary waves with the largest in front. However, the behaviour of negative (rarefactive) solitary waves is quite different. These waves appear to be unstable and produce positive solitary waves at a later time. The relevancy of this investigation to observations in the magnetosphere of density depressions is briefly pointed out. Received 12 October 1999     

Directive metamaterial-based subwavelength resonant cavity antennas – Applications for beam steering

This article presents the use of composite resonant metamaterials for the design of highly directive subwavelength cavity antennas. These metamaterials, composed of planar metallic patterns periodically organized on dielectric substrates, exhibit frequency dispersive phase characteristics. Different models of metamaterial-based surfaces (metasurfaces), introducing a zero degree reflection phase shift to incident waves, are firstly studied where the bandwidth and operation frequency are predicted. These surfaces are then applied in a resonant Fabry–Perot type cavity and a ray optics analysis is used to design different models of ultra-compact high-gain microstrip printed antennas. Another surface presenting a variable reflection phase by the use of a non-periodic metamaterial-based metallic strips array is designed for a passive low-profile steering beam antenna application. Finally, the incorporation of active electronic components on the metasurfaces, allowing an electronic control of the phase responses, is applied to an operation frequency reconfigurable cavity and a beam steering cavity. All these cavity antennas operate on subwavelength modes, the smallest cavity thickness being of the order of λ/60. To cite this article: A. Ourir et al., C. R. Physique 10 (2009).     

Angle-dependent infrared absorption spectroscopy at electrode/electrolyte interfaces

Angle-dependent internal reflection spectroscopy is performed in the attenuated total reflection setup for an electrochemical cell with a Fourier transform infrared spectrometer. The working electrode is a thin Pt film evaporated onto a hemispherical Si prism. The refractive index of the Pt film obtained from the experiment is found to differ from the value for bulk material. The difference is ascribed to the surface corrugation of the Pt surface and the film thickness in the nanometer range. The function of reflection intensity versus angle of incidence changes significantly when a resonant absorption occurs in the electrolyte medium. The angle-dependent absorption band intensity of CO adsorbed on the Pt film under potential control reveals changes in magnitude and an inversion of the band for different angles of incidence. This behaviour is explained by the excitation of resonant surface plasmon waves at the Pt/electrolyte interface and by multiple reflections occurring at the interfaces. A simulation for the three-layer system Si/Pt/electrolyte agrees with the experimental results.     

谐振腔反射器的模式匹配分析

 利用模式匹配方法对“冷”谐振腔反射器的反射特性进行了理论分析，推导出了谐振腔反射器的广义散射矩阵。对应用于X波段低磁场返波管的谐振腔反射器的反射特性进行了研究，并利用数值模拟软件分析了在全反射条件下谐振腔反射器中的电场分布。结果表明:当反射器的内外半径的选取合适时，反射器可以在较短的长度时获得较大的反射，而且反射系数对反射器长度的变化不敏感。     

X-ray circular dichroism under reflection from antiferromagnetically coupled multilayers

The fluorescence yield under the Bragg reflection of right and left circular polarized radiation with a wavelength in the vicinity of the FeL _{2, 3} absorption edges from the periodic multilayer [Fe(1.5 nm)/V(1.5 nm)]₁₀ that is characterized by the antiferromagnetic interlayer exchange coupling has been theoretically analyzed in L-MOKE geometry. It has been shown that the largest polarization asymmetry of reflectivity takes place at the ??magnetic?? Bragg reflection, which appears due to the doubling of the magnetic period. The expected occurrence of the dichronic signal in the fluorescence yield by its selective excitation in the layers with the same magnetization direction was confirmed, but the effect is suppressed by the specific behaviour of the standing waves in the strongly absorbing multilayers where the standing wave antinodes are situated in layers with low absorption.     

High frequency shear horizontal plate acoustic wave devices

It has been shown recently that shear horizontal acoustic waves propagating in piezoelectric plates whose thickness h is much less than the acoustic wavelength λ possess a number of attractive properties for use in sensor and signal processing applications. In order to exploit the potential benefits of these waves, however, one needs to fabricate devices on very thin plates. We have developed a suitable fabrication method which can be used to realize devices on such thin plates. In this method, the device is first fabricated on a plate of normal thickness (approximately 500 μm) and the substrate is then lapped from the back side to reduce the thickness. The technique has been utilized to realize devices on plates of thickness less than 70 μm. A shear horizontal plate acoustic wave (SH-PAW) delay line of fundamental resonant frequency greater than 25 MHz and insertion loss less than 7 dB has been realized on a 60 μm thick Y – cut, X – propagation lithium niobate substrate. The device also shows strong response near the third harmonic frequency of 75 MHz.     

Influence of bottom topography on the propagation of linear shallow water waves: an exact approach based on the invariant imbedding method

The wave equation for linear shallow water waves propagating over a varying bottom topography has the same form as that for p-polarized electromagnetic waves in inhomogeneous dielectric media. The role played by the dielectric permittivity in the case of electromagnetic waves is played by the inverse water depth. We apply the invariant imbedding theory of wave propagation, which has been developed mainly to study the electromagnetic wave propagation, to linear shallow water waves in the special case where the depth depends on only one coordinate. By comparing the numerical result obtained using our method, when the depth profile is linear, with an exact analytical formula, we demonstrate that our method is numerically reliable. The invariant imbedding method can be used in studying the influence of complicated bottom topography on the propagation of shallow water waves, in a numerically exact manner. We illustrate this by considering the case where a periodic modulation is added to a linear depth profile. Bragg scattering due to the periodic component competes with the tsunami effect due to the linear depth variation. This competition is seen to generate interesting physical effects. We also consider a ridge-type bottom topography and examine the resonant transmission phenomenon associated with the Fabry-Perot effect.     

Extension of the resonant scattering technique to liquid crystals without resonant element

We report X-ray resonant scattering experiments performed on the prototype liquid-crystalline compound MHPOBC doped with a chemical probe containing a resonant atom (selenium). We determined directly for the first time the microscopic 3- and 4-layer structure of the ferrielectric subphases ( SmC_FI1^* and SmC_FI2^*) present in MHPOBC. Despite the low fraction of the selenium probe, the resonant signal is strong enough to allow an unambiguous determination of the basic structure of the ferrielectric subphases. These experiments demonstrate that the resonant scattering technique can be extended to liquid crystalline materials without resonant element and may stimulate new studies. A non-resonant Bragg reflection was also found in the SmC_FI1^* phase in pure MHPOBC, consistent with the 3-layer distorted model, but never detected before.     

Viscous compressible hydrodynamics at planes,spheres and cylinders with finite surface slip

We consider the linearized time-dependent Navier-Stokes equation including finite compressibility and viscosity. We first constitute the Green's function, from which we derive the flow profiles and response functions for a plane, a sphere and a cylinder for arbitrary surface slip length. For high driving frequency the flow pattern is dominated by the diffusion of vorticity and compression, for low frequency compression propagates in the form of sound waves which are exponentially damped at a screening length larger than the sound wave length. The crossover between the diffusive and propagative compression regimes occurs at the fluid's intrinsic frequency w \omega ∼ c ² r₀ \rho_{0}^{}/h \eta , with c the speed of sound, r₀ \rho_{0}^{} the fluid density and h \eta the viscosity. In the propagative regime the hydrodynamic response function of spheres and cylinders exhibits a high-frequency resonance when the particle size is of the order of the sound wave length. A distinct low-frequency resonance occurs at the boundary between the propagative and diffusive regimes. Those resonant features should be detectable experimentally by tracking the diffusion of particles, as well as by measuring the fluctuation spectrum or the response spectrum of trapped particles. Since the response function depends sensitively on the slip length, in principle the slip length can be deduced from an experimentally measured response function.     

横波远探测测井换能器研究

为提高偶极子横波远探测反射波的信噪比和增加其探测距离,根据偶极子井孔模式波的激发特性及反射波传播特征分析,研制了基于三叠片的低频大功率偶极子的横波远探测换能器,以降低模式波的相对能量和增加反射波的相对能量。为了得到满足要求的低频大功率偶极换能器,采用有限元方法对现有三叠片进行了优化改进,得到一种符合设计要求的换能器结构,最后制作了样机并对其进行了测试。样机测试结果跟仿真吻合得很好,低频性能得到了极大改善：换能器在谐振频率1.2 kHz附近具有极好的偶极子指向性,谐振频率处的响应比X-MAC同频率段大19 dB。该换能器的研发成功将为偶极子远探测测井仪器性能及成像质量的提高奠定了坚实的基础。