Effect of tangential interface motion on the viscous instability in fluid flow past flexible surfaces

The stability of linear shear flow of a Newtonian fluid past a flexible membrane is analysed in the limit of low Reynolds number as well as in the intermediate Reynolds number regime for two different membrane models. The objective of this paper is to demonstrate the importance of tangential motion in the membrane on the stability characteristics of the shear flow. The first model assumes the wall to be a “spring-backed” plate membrane, and the displacement of the wall is phenomenologically related in a linear manner to the change in the fluid stresses at the wall. In the second model, the membrane is assumed to be a two-dimensional compressible viscoelastic sheet of infinitesimal thickness, in which the constitutive relation for the shear stress contains an elastic part that depends on the local displacement field and a viscous component that depends on the local velocity in the membrane. The stability characteristics of the laminar flow in the limit of low are crucially dependent on the tangential motion in the membrane wall. In both cases, the flow is stable in the low Reynolds number limit in the absence of tangential motion in the membrane. However, the presence of tangential motion in the membrane destabilises the shear flow even in the absence of fluid inertia. In this case, the non-dimensional velocity (Λ_t) required for unstable fluctuations is proportional to the wavenumber k ( Λ _t∼k) in the plate membrane type of wall while it scales as k² in the viscoelastic membrane type of wall ( Λ _t∼k ²) in the limit k→ 0. The results of the low Reynolds number analysis are extended numerically to the intermediate Reynolds number regime for the case of a viscoelastic membrane. The numerical results show that for a given set of wall parameters, the flow is unstable only in a finite range of Reynolds number, and it is stable in the limit of large Reynolds number. Received 8 November 2000 and Received in final form 20 March 2001     

Generation of CdS clusters using laser ablation: the role of wavelength and fluence

The formation of cationic clusters in the laser ablation of CdS targets has been investigated as a function of wavelength and fluence by mass spectrometric analysis of the plume. Ablation was carried out at the laser wavelengths of 1064, 532, 355, and 266 nm in order to scan the interaction regimes below and above the energy band gap of the material. In all cases, the mass spectra showed stoichiometric Cd _n S _n ⁺ and nonstoichiometric Cd _n S _n−1⁺, Cd _n S _n+1⁺, and Cd _n S _n+2⁺ clusters up to 4900 amu. Cluster size distributions were well represented by a log-normal function, although larger relative abundance for clusters with n=13, 16, 19, 34 was observed (magic numbers). The laser threshold fluence for cluster observation was strongly dependent on wavelength, ranging from around 16 mJ/cm² at 266 nm to more than 300 mJ/cm² at 532 and 1064 nm. According to the behavior of the detected species as a function of fluence, two distinct families were identified: the “light” family containing S₂⁺ and Cd⁺ and the “heavy” clusterized family grouping Cd₂⁺ and Cd _n S _m ⁺. In terms of fluence, it has been determined that the best ratio for clusterization is achieved close to the threshold of appearance of clusters at all wavelengths. At 1064, 532, and 355 nm, the production of “heavy” cations as a function of fluence showed a maximum, indicating the participation of competitive effects, whereas saturation is observed at 266 nm. In terms of relative production, the contribution of the “heavy” family to the total cation signal was significantly lower for 266 nm than for the longer wavelengths. Irradiation at 355 nm in the fluence region of 200 mJ/cm² has been identified as the optimum for the generation of large clusters in CdS.     

STM-study of triangular defect structures induced on WSe2

With short voltage pulses, applied between sample and tip of a scanning tunnelling microscope, it is possible to generate a variety of defects on the surface of layered transition metal dichalcogenides. In the case of WSe₂ triangular holes can be induced with a depth of a single Se-W-Se layer that grow in lateral size during scanning. We present measurements of the time evolution of the growth and its dependence on parameters of the scanning process. Furthermore, we draw attention to the peculiar shape of the edges of such triangles where several distinct rims are found. As a possible interpretation we suggest that these are caused by an oscillating workfunction or density of states due to electron interference.     

Thermal boundary layer for non-Newtonian fluid

Summary Analytical and numerical solutions for the momentum and thermal boundary layer equations of a non-Newtonian power law fluid are presented. The flow is assumed to be under the influence of an external magnetic fieldB (x) applied perpendicular to the surface and an electric fieldE(x) perpendicular toB(x) and the direction of the longitudinal velocity in the boundary layer. For the power law fluid it is assumed that the shear stress is proportional to then-th power of the velocity gradient andn is called the flow index. The variations of the velocity fieldf′, the temperature field θ, the shear stress on the surfaceτ _W , the displacement thicknessδ ₁ and the momentum thicknessδ ₂ with the magnetic-field parameter γ, the flow indexn, the heat transfer indexS and the Prandtl number Pr are studied. It is found that, if the outer flow velocityU(x) (potential flow) is proportional to the arc lengthx raised to a powerm, then the similarity solution for the thermal boundary layer equation is possible only whenm=1/3, which represents flow past a wedge of included angle π/2. It is established that the temperature of the wedge increases with the increase of γ, Pr,S and the decrease ofn. In general the magnetic field can be used as a heater for the surface of the wedge.     

Comparison of Cut Path Deviation Between CO2 and Diode Lasers in Float-Glass Cutting

Laser cutting of glass using the controlled fracture technique leads to cut path deviation at the leading and trailing edges of the float glass sheet. In this technique, thermal stresses are used to induce the crack, and the material is separated along the cutting path by extending the crack. We show that the cut path deviation is partly due to high magnitudes of thermal stresses generated near the sheet edges. The absorption of intense radiation from the CO₂ and diode laser beams in the glass causes local temperature increases and consequently generates different thermal fields and stress distributions due to surface and volumetric heat absorption. In this paper, we report the effect of the CO₂ and diode laser wavelength interaction with the float glass and its effect on the magnitudes of thermal stresses generated near the edges of the glass sheet. We simulate the distribution of the thermal stress and temperature using finite-element analysis software Abaqus and validate it against the experimental data. We show that the CO₂ laser produces a lower surface quality and a larger cut path deviation at the leading and trailing edges of the glass sheet as compared to the diode laser.     

CdS plume composition and dynamics of neutral species upon ablation with 532 nm laser light

The neutral species present in CdS ablation plumes upon nanosecond 532 nm laser irradiation at a moderate fluence of 0.5–0.75 J cm⁻² have been studied. Neutral Cd _n S _m clusters have been identified, some as large as (CdS)₃₃₋₃₄ (1–2 nm in diameter). The analysis of the dynamics of neutral species shows an expansion with two components that differ both in composition and dynamics. A fast, high kinetic energy component, dominated by S₂ which acquires free-flow conditions at short distances from the target, is followed by a slower component characterized by similar speeds for all species. This slower component shows dynamic features that are expected to favor aggregation processes leading to effective cluster formation.     

Cylindrical spike model for the formation of diamondlike thin films by ion deposition

T /n_S of n_T rearrangements and n_S atoms in the spike volume as the crucial parameter characterizing the ability of a given ion–target combination to achieve complete rearrangement of the spike volume. n_T/n_S>1 is the optimum condition for diamondlike film growth. For aC films the ion energy dependence of n_T/n_S agrees well with the measured sp³ bond fraction. For Ar⁺-ion-assisted deposition of aC we find n_T/n_S>1 above 50 eV with no pronounced ion energy dependence. Furthermore, our model predicts optimum conditions for the formation of cubic boron nitride between 50 eV and 3 keV. Accepted: 14 October 1997     

Asymptotic behavior of orbits of C 0-semigroups and solutions of linear and semilinear abstract differential equations

In this paper, we study the asymptotic behavior of solutions of semilinear abstract differential equations (*) u′(t) = Au(t) + t ⁿ f(t, u(t)), where A is the generator of a C ₀-semigroup (or group) T(·), f(·, x) ∈ A for each x ∈ X, A is the class of almost periodic, almost automorphic or Levitan almost periodic Banach space valued functions ϕ: ℝ → X and n ∈ {0, 1, 2, ...}. We investigate the linear case when T(·)x is almost periodic for each x ∈ X; and the semilinear case when T(·) is an asymptotically stable C ₀-semigroup, n = 0 and f(·, x) satisfies a Lipschitz condition. Also, in the linear case, we investigate (*) when ϕ belongs to a Stepanov class S ^p-A defined similarly to the case of S ^p-almost periodic functions. Under certain conditions, we show that the solutions of (*) belong to A _u:= A ∩ BUC(ℝ, X) if n = 0 and to t ⁿ A _u ⊕ w _n C ₀ (ℝ, X) if n ∈ ℕ, where w _n(t) = (1 + |t|)ⁿ. The results are new for the case n ∈ ℕ and extend many recent ones in the case n = 0. Dedicated to the memory of B. M. Levitan     

Calorimetric studies of the crystallization process in a-Se75S25−xAgx chalcogenide glasses

Calorimetric studies of amorphous Se₇₅S_25−xAg_x (x = 2, 4, 6 and 8) chalcogenide glasses are made at different heating rates (5, 10, 15 and 20 K/min) under non-isothermal condition using Differential scanning calorimetry. The values of glass transition temperature and crystallization temperature are observed to be composition and heating rate dependence. From the heating rate dependence of glass transition temperature and crystallization temperature, the activation energy for structural relaxation (ΔE_t), the activation energy of crystallization (ΔE_c) and the order parameter (n) have been calculated. It is observed that Se₇₅S₁₉Ag₆ has a minimum value of activation energy for structural relaxation (ΔE_t), which indicates that this particular glass has a larger probability to jump to a state of lower configurational energy and higher stability in the glassy region. On the basis of the obtained experimental data the temperature difference (T_c − T_g) is found to be maximum for Se₇₅S₁₉Ag₆, which further indicate that this glass is the thermally most stable in the entire composition range of investigation.     

A narrow linewidth and frequency-stable probe laser source for the <Superscript>88</Superscript>Sr<Superscript>+</Superscript> single ion optical frequency standard

In this paper, we describe in detail a narrow linewidth and frequency-stable laser source used to probe the 5s ² S _1/2–4d ² D _5/2 clock transition of the ⁸⁸Sr⁺ optical frequency standard. The performance of the laser system is investigated with studies of its frequency drift rates and with high resolution spectra of the ⁸⁸Sr⁺ clock transition. The observed short-term drift rates are typically in the range of 10 to 23 mHz/s, and the current long-term drift rate is 13.9(3) mHz/s. The laser stability, after subtraction of linear drifts, reaches 5×10⁻¹⁶ at an averaging time of 3000 s. This high level of stability is attributed for the most part to stabilization of the reference cavity at the temperature where the coefficient of linear thermal expansion crosses zero. An upper bound for the laser linewidth is given by the observation of a Fourier-transform limited resonance of 4.3 Hz (Δν/ν=1×10⁻¹⁴) on the ⁸⁸Sr⁺ clock transition. The effective averaging time during the linewidth measurements was about 100 s.     

Influence of oxygen depletion layer on the properties of tin oxide gas-sensing films fabricated by atomic layer deposition

In this paper we report on the influence of film thickness on the electrical and gas-sensing properties of tin oxide thin films grown by atomic layer deposition (ALD) technique. The nature of the carrier and post-flow gases used in ALD was found to have a dramatic influence on the electrical conductance of the deposited films. Up to a film thickness of 50 nm the sheet conductance of the films increased with the thickness, and above 50 nm the sheet conductance was not significantly influenced by the film thickness. This effect was attributed to oxygen depletion at the film surface. When the depth of oxygen depletion (d _dep) was greater than or equal to the film thickness (t), the sheet conductance was thickness dependant. On the other hand, when d _dep≤t, the sheet conductance was independent of the film thickness but depended on the depth of the oxygen depletion. This proposed explanation was verified by subjecting the films to different lengths of post-annealing in an oxygen depleted atmosphere. Gas-sensing functionality of the films with various thicknesses was examined. It was observed that the film thickness had a significant influence on the gas-sensing property of the films. When the thickness was greater than 40 nm, the sensitivity of the films to ethanol was found to follow the widely reported trend, i.e., the sensitivity decreases when the film thickness increases. Below the film thickness of 40 nm the sensitivity decreases as film thickness decreases, and we propose a model to explain this observation based on the increase in resistance due to multiple grain boundaries.     

Recent fluid deformation closure for velocity gradient tensor dynamics in turbulence: Timescale effects and expansions

In order to model pressure and viscous terms in the equation for the Lagrangian dynamics of the velocity gradient tensor in turbulent flows, Chevillard & Meneveau [L. Chevillard, C. Meneveau, Lagrangian dynamics and geometric structure of turbulence, Phys. Rev. Lett. 97 (174501) (2006) 1-4] introduced the Recent Fluid Deformation closure. Using matrix exponentials, the closure allows us to overcome the unphysical finite-time blow-up of the well-known Restricted Euler model. However, it also requires the specification of a decorrelation timescale of the velocity gradient along the Lagrangian evolution, and when the latter is chosen too short (or, equivalently, the Reynolds number is too high), the model leads to unphysical statistics. In the present paper, we explore the limitations of this closure by means of numerical experiments and analytical considerations. We also study the possible effects of using time-correlated stochastic forcing instead of the previously employed white-noise forcing. Numerical experiments show that reducing the correlation timescale specified in the closure and in the forcing does not lead to a commensurate reduction of the autocorrelation timescale of the predicted evolution of the velocity gradient tensor. This observed inconsistency could explain the unrealistic predictions at increasing Reynolds numbers. We perform a series expansion of the matrix exponentials in powers of the decorrelation timescale, and we compare the full original model with a linearized version. The latter is not able to extend the limits of applicability of the former but allows the model to be cast in terms of a damping term whose sign gives additional information about the stability of the model as a function of the second invariant of the velocity gradient tensor.     

Exact solutions for a forced Burgers equation with a linear external force

We investigate the solutions of the Burgers equation , where F(x,t) is an external force and Φ(x,t) represents a forcing term. This equation is first analyzed in the absence of the forcing term by taking F(x,t)=k₁(t)−k₂(t)x into account. For this case, the solution obtained extends the usual one present in the Ornstein-Uhlenbeck process and depending on the choice of k₁(t) and k₂(t) it can present a stationary state or an anomalous spreading. Afterwards, the forcing terms Φ(x,t)=Φ₁(t)+Φ₂(t)x and Φ(x,t)=Φ₃x−Φ₄/x³ are incorporated in the previous analysis and exact solutions are obtained for both cases.     

Lattice Dislocations in a 1-Dimensional Model

The spectral properties of the Schr?dinger operator T(t)=−d ²/dx ²+q(x,t) in L ²(ℝ) are studied, where the potential q is defined by q=p(x+t), x>0, and q=p(x), x<0; p is a 1-periodic potential and t∈ℝ is the dislocation parameter. For each t the absolutely continuous spectrum σ _ac (T(t))=σ _ac (T(0)) consists of intervals, which are separated by the gaps γ _n (T(t))=γ _n (T(0))=(α _n ⁻,α _n ⁺), n≥1. We prove: in each gap γ _n ≠?, n≥ 1 there exist two unique “states” (an eigenvalue and a resonance) λ _n ^±(t) of the dislocation operator, such that λ _n ^±(0)=α _n ^± and the point λ _n ^±(t) runs clockwise around the gap γ _n changing the energy sheet whenever it hits α _n ^±, making n/2 complete revolutions in unit time. On the first sheet λ _n ^±(t) is an eigenvalue and on the second sheet λ _n ^±(t) is a resonance. In general, these motions are not monotonic. There exists a unique state λ₀(t) in the basic gap γ₀(T(t))=γ₀(T(0))=(−∞ ,α₀ ⁺). The asymptotics of λ _n ^±(t) as n→∞ is determined. Received: 5 April 1999 / Accepted: 3 March 2000     

Influence of Thomson effect on the resultant local Seebeck coefficient in thermoelectric composite materials

The resultant local Seebeck coefficient α _R (=α _S−α _T) at the interface of a thermoelement has not yet been measured, although it is an important factor governing the thermoelectric efficiency, where α _S is the local Seebeck coefficient and α _T is the one caused by the Thomson effect. It is shown in this paper that α _S, α _T, and α _R of the p- and n-type Cu/Bi–Te/Cu composites are obtained analytically and experimentally on the assumption that the local temperature of the composite on which the temperature difference ΔT is imposed varies linearly with changes in position along the composite. They were indeed estimated as a function of position from the local experimental data of R,ΔI,ΔT, and V generated by applying an additional current of ±I to the composite, where R is the electrical resistance and ΔI is a current generated by the composite. As a result, it was found that the absolute values of α _S at the hot interface of the p- and n-type composites are approximately 1.5 and 1.4 times higher than their lowest values in the middle region of the composite, respectively, while those of α _T are less than 8% of α _S all over the composite and are so small that the relation α _R≈α _S can be held. We thus succeeded in measuring α _R at the interfaces of the composite.     

Investigation of the dielectric,optical and photorefractive properties of Sb-doped Sn<Subscript>2</Subscript>P<Subscript>2</Subscript>S<Subscript>6</Subscript> crystals

In this work we report results on electro-physical, optical and photorefractive investigations for Sb-doped Sn₂P₂S₆ crystals. The crystals are obtained by two methods: the vapour-transport technique and the Bridgman technique using stoichiometric Sn₂P₂S₆ composition with different amounts of antimony in the initial compound. The good optical quality of the crystals obtained with the Bridgman technique is underlined. The dependences of the photorefractive two-beam coupling coefficient and the grating build-up time are investigated at the wavelength of 633 nm. It is found that the sample doped with 1.5% of Sb is characterized by an optimal combination of the main photorefractive parameters exhibiting a fairly high two-beam coupling coefficient (up to 20 cm⁻¹) and a short response time (1.3 ms) that is the shortest among all the previously studied Sn₂P₂S₆ crystals in the red spectral region.     

Density functional theory study of AunMn(n=1-8) clusters

Equilibrium geometries, relative stabilities, and magnetic properties of small Au_nMn (n=1-8) clusters have been investigated using density functional theory at the PW91P86 level. It is found that Mn atoms in the ground state Au_nMn isomers tend to occupy the most highly coordinated position and the lowest energy structure of Au_nMn clusters with even n is similar to that of pure Au_n+1 clusters, except for n=2. The substitution of Au atom in Au_n+1 cluster by a Mn atom improves the stability of the host clusters. Maximum peaks are observed for Au_nMn clusters at n=2, 4 on the size dependence of second-order energy differences and fragmentation energies, implying that the two clusters possess relatively higher stability. The HOMO-LUMO energy gaps of the ground state Au_nMn clusters show a pronounced odd-even oscillation with the number of Au atoms, and the energy gap of Au₂Mn cluster is the biggest among all the clusters. The magnetism calculations indicate that the total magnetic moment of Au_nMn cluster, which has a very large magnetic moment in comparison to the pure Au_n+1 cluster, is mainly localized on Mn atom.     

Analysis of eta production using a generalized Lee model

We have investigated the processes N(π, π)N and N(π, η)N close to eta threshold using a simple, nonrelativistic Lee model which has the advantage of being analytically solvable. It is then possible to study the Riemann sheets of the S-matrix and the behavior of its resonance poles especially close to threshold. A theoretical simulation of the experimental cusp effect at eta threshold leads to a characteristic distribution of poles on the Riemann sheets. We find a pole located in the 4_th Riemann sheet that up to now has not been discussed. It belongs to the cusp peak at eta threshold. In addition we obtain the surprising result using the Lee model that the resonance S¹¹(1535) does not play a large role. The main features of the experimental data can be reproduced without explicitly introducing this resonance. Furthermore, we have also studied the reactions N(γ, π)N and N(γ, η)N and find reasonable agreement between the data and both models with and without the S¹¹(1535) resonance. Received: 5 March 1998 / Revised version: 23 June 1998