Stability considerations associated with the meniscoid particle band at advancing interfaces in hele-shaw suspension flows

We present a new convergent strong-coupling expansion for two-level atoms in external periodic fields, free of secular terms. As a first application, we show that the coherent destruction of tunneling is a third-order effect. We also present an exact treatment of the high-frequency region, and compare it with the theory of averaging. The qualitative frequency spectrum of the transition probability amplitude contains an effective Rabi frequency.     

Viscous scattering of a pressure wave: calculation of the fluid tractions on a biomimetic acoustic velocity sensor

In the paper we give a method for calculating the tractions (local forces) of the fluid motion determined by an incoming plane pressure wave on an artificial hair cell transducer structure. The sensing element of the transducer is a standing high aspect ratio cilium in the shape of a narrow thin curved beam (tape-like), which can be easily fabricated in micro-/nanotechnology. The method is based on considering the system of partial differential equations describing the motion of the compressible viscous fluid in an acoustic linearized approximation, and representation of the velocity field as a viscous acoustic single-layer potential. The boundary conditions, stating the cancellation of the velocity components on the solid beam, yield a two-dimensional (2-D) system of three integral equations over the beam's surface for the traction components. In the case of a narrow cilium, the system of integral equations furnishes a system of two 1-D integral equations over the symmetry curve of the structure for obtaining the tangential and normal components of the traction. This system is solved numerically by a finite (boundary) element method. The numerical code written for solving the problem was applied to some particular structures. The last structure is similar to the trichobothrium of a spider Cupiennius salei. The results obtained show that the curvature of the hair is enhancing sensitivity to flows directed normal to the main shaft of the hair confirming the assertion of Barth et al. [Philos. Trans. R. Soc. London, Ser. B 340, 445-461 (1993)].     

Conformal mapping of multiply connected domains exterior to thin regions

Summary This paper gives the formal asymptotic expansion of the functionZ=F(z, ) which maps conformally the multiple connected domain exterior to some symmetrical thin regions inz plane into the complex planeZ with aligned cuts on the real axis.The functionF(z, ) is represented as a superposition of singularities on segments inside the thin regions. The resulting integral equation is integrated asymptotically by using the method developed in [1].In the last section of the paper the given theory is applied to the conformal mapping of the domain exterior to two aligned thin ellipses.

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Résumé Cet ouvrage donne le développement asymptotique formel de la fonctionZ=F(z, ) qui transforme conformément le domaine multiplement connexe, exterieur de certaines régions symétriques minces du planz dans le plan complexeZ avec coupures alignées sur l'axe réele.La fonctionZ=F(z, ) est representée comme une superposition des singularités sur des segments à l'interieur des régions minces. L'équation intégrale qui en résulte est intégrée asymptotiquement à l'aide de la méthode developée en [1].Dans la dernière section du cet article la théorie donnée est appliquée à la transformation conforme du domaine extérieur à deux ellipses minces alignées.

     

On the mixed boundary-value problem for harmonic functions in plane domains

This paper considers the problem of the determination of a harmonic function in a simply connected plane domain when the values of the function are known on some arcs of the boundary and the values of the normal derivative are known on the remaining boundary. We first present the solution in theoretical form and then show how to compute the solution with the aid of rapidly convergent series. The coefficients of these series are Fourier coefficients of certain functions and can be estimated by using the Fast Fourier Transform. The examples considered in the last part of the paper emphasize the advantages of the method presented in this paper for solving the mixed boundary-value problem as compared to other methods used for this purpose.

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Résumé On considère le problème suivant: trouver une fonction harmonique dans un domaine simplement connexeDR ² dont la frontièreS est assez régulière, en connaissant les valeurs de la fonction sur une partieS ₁ de la frontière et les valeurs de la dérivée normale sur la complémentaire de366-1. La première partie présente des résultats théoriques liés à ce probléme. La deuxième partie s'appuie sur une représentation de la solution à l'aide de certaines séries de fonctions rapidement convergentes. Les coefficients des séries utilisées sont même les coefficients de Fourier de certaines fonctions, et leur calcul peut être effectué en utilisant la transformation de Fourier rapide (Fast Fourier Transform). Les exemples considérés dans la dernière partie de l'article mettent en évidence les avantages de la méthode présentée par rapport à d'autres méthodes employées pour la résolution du problème mixte.

     

Critical Considerations on the Isoconversional Methods. III. On the evaluation of the activation energy from non-isothermal data

The differential and integral isoconversional methods for evaluation the activation energy, described in the first note of this series, were applied for: a) simulated data for two successive reactions; b) dehydration of calcium oxalate monohydrate. It was shown that for these systems the activation energy depends on the conversion degree as well as on the method of evaluation. This revised version was published online in August 2006 with corrections to the Cover Date.     

On boundary value problems for the domain exterior to a thin or slender region

In this paper a method for obtaining uniformly valid asymptotic expansions of the solution of the boundary value problems in domains exterior to thin or slender regions is given. This approach combines the Tuck's method, based on the use of a suitable co-ordinates system with the method given by Handelsman and Keller yielding complete uniform asymptotic expansion of the solution for slender body problems. Our method avoids the determination of the extremities of the segment containing singularities; it is pointed out that this last problem is a pure geometrical one and independent of solving concrete boundary value problems in the given domain.     

Influence of viscosity on the diffraction of sound by a periodic array of screens

The paper contains an analysis of the transmission of a pressure wave through a periodic grating including the influence of the air viscosity. The system of equations in this case consists of the compressible Navier-Stokes equations associated with no-slip boundary conditions on solid surfaces. The problem is reduced to two hypersingular integral equations for determining the velocity components along the slits. These equations are solved by using Galerkin's method with some special trial functions. The results can be applied in designing protective screens for miniature microphones realized in the technology of micro-electro-mechanical systems (MEMS). In this case, the physical dimensions of the device are on the order of the viscous boundary layer so that the viscosity cannot be neglected. The microfluidic model of the screen consists of a periodic array of slits in a substrate. The analysis indicates that the openings in the screen should be on the order of 10 microm in order to avoid excessive attenuation of the signal.     

Re-expansion method for circular waveguide discontinuities: application to concentric expansion chambers

The paper applies the re-expansion method for analyzing planar discontinuities at the junction of two axi-symmetrical circular waveguides. The normal modes in the two waveguides are expanded at the junction plane into a system of functions accounting for velocity singularities at the corner points. As the new expansion has a high convergence order, only a few terms have to be considered for obtaining the solution of most practical problems. This paper gives the equivalent impedance accounting for nonplanar waves into a plane-wave analysis and also the scattering matrix describing the coupling of arbitrary modes at each side of the discontinuity valid in the case of many propagating modes in both sides of the duct. The last section applies the re-expansion technique to some concentric expansion chambers providing an explicit formula for the transmission loss coefficient.     

An analytical-numerical method for determining the mechanical response of a condenser microphone

The paper is based on determining the reaction pressure on the diaphragm of a condenser microphone by integrating numerically the frequency domain Stokes system describing the velocity and the pressure in the air domain beneath the diaphragm. Afterwards, the membrane displacement can be obtained analytically or numerically. The method is general and can be applied to any geometry of the backplate holes, slits, and backchamber. As examples, the method is applied to the Bruel & Kjaer (B&K) 4134 1/2-inch microphone determining the mechanical sensitivity and the mechano-thermal noise for a domain of frequencies and also the displacement field of the membrane for two specified frequencies. These elements compare well with the measured values published in the literature. Also a new design, completely micromachined (including the backvolume) of the B&K micro-electro-mechanical systems (MEM) 1/4-inch measurement microphone is proposed. It is shown that its mechanical performances are very similar to those of the B&K MEMS measurement microphone.