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We consider a system of two coupled parallel queues with infinite waiting rooms. The time setting is discrete. In either queue, the service of a customer requires exactly one discrete time slot. Arrivals of new customers occur independently from slot to slot, but the numbers of arrivals into both queues within a slot may be mutually dependent. Their joint probability generating function (pgf) is indicated as A (z 1 , z 2) and characterizes the whole model. In general, determining the steady-state joint probability mass function (pmf) u (m , n) , m , n ≥ 0 or the corresponding joint pgf U (z 1 , z 2) of the numbers of customers present in both queues is a formidable task. Only for very specific choices of the arrival pgf A (z 1 , z 2) are explicit results known. In this paper, we identify a multi-parameter, generic class of arrival pgfs A (z 1 , z 2) , for which we can explicitly determine the system-content pgf U (z 1 , z 2) . We find that, for arrival pgfs of this class, U (z 1 , z 2) has a denominator that is a product, say r 1 (z 1) r 2 (z 2) , of two univariate functions. This property allows a straightforward inversion of U (z 1 , z 2) , resulting in a pmf u (m , n) which can be expressed as a finite linear combination of bivariate geometric terms. We observe that our generic model encompasses most of the previously known results as special cases. [ABSTRACT FROM AUTHOR]

We consider a system of two parallel discrete-time single-server queues, queue 1 and queue 2. The service time of any customer in either queue is equal to 1 time slot. Arrivals during consecutive slots occur independently from slot to slot. However, the arrival streams into both queues are possibly mutually interdependent, i.e., during any slot, the numbers of arrivals in queue 1 and queue 2 need not be statistically independent. Their joint probability generating function (pgf) A(x, y) fully characterizes the queueing model. As a consequence of the possible intra-slot correlation in the arrival process, the numbers of customers present ("system contents") in queues 1 and 2, at any given slot boundary, are not necessarily independent either. In a previous paper, we have already discussed the mathematical difficulty of computing their steady-state joint pgf U (z 1 , z 2) ; explicit closed-form results can only be obtained for specific choices of A(x, y). In this paper, we therefore look at the problem from an other angle. Specifically, we study the (asymptotic) conditional steady-state behavior of the system under the condition that the content of queue 1 is (temporarily) very high (goes to infinity). For ease of terminology, we refer to the system as the "asymptotic system" in these circumstances. We prove that the asymptotic system is nearly identical to the original (unconditional) system, but with a modified joint arrival pgf A ∗ (x , y) that can be computed explicitly from A(x, y). This fundamental result allows us to determine the stability condition of queue 2 in the asymptotic system, and explicitly compute the classical queueing performance metrics of queue 2, such as the pgf, the moments and the approximate tail distribution of its system content, when this condition is fulfilled. It also leads to accurate approximative closed-form expressions for the joint tail distribution of the system contents in both queues, in the original (unconditional) system. We extensively illustrate our methodology by means of various specific (popular) choices of A(x, y). In some examples, where an explicit solution for U (z 1 , z 2) or for the (approximative) joint tail distribution is known, we retrieve the known results easily. In other cases, new results are found for arrival pgfs A(x, y) for which no explicit results were known until now. [ABSTRACT FROM AUTHOR]

We consider a discrete-time queueing system with two queues and one server. The server is allocated in each slot to the first queue with probability α and to the second queue with probability 1 - α . The service times are equal to one time slot. The queues have exponentially bounded, but general, arrival distributions. The mathematical description of this system leads to a single functional equation for the joint probability generating function of the stationary system contents. As the joint stochastic process of the system contents is not amenable for exact analysis, we focus on an efficient approximation of the joint probability generating function. In particular, first we prove that the partial probability generating functions, present in the functional equation, have a unique dominant pole. Secondly, we use this information to approximate these partial probability generating functions by truncating an infinite sum. The remaining finite number of unknowns are estimated from a noise perturbed linear system. We illustrate our approach by various numerical examples and verify the accuracy by means of simulation. [ABSTRACT FROM AUTHOR]

We analyze a discrete-time two-class queueing system with a single server which is alternately available for only one customer class. The server is each time allocated to a customer class for a geometrically distributed amount of time. Service times of the customers are deterministically equal to 1 time slot each. During each time slot, both classes can have at most one arrival. The bivariate process of the number of customers of both classes can be considered as a two-dimensional nearest-neighbor random walk. The generating function of this random walk has to be obtained from a functional equation. This type of functional equation is known to be difficult to solve. In this paper, we obtain closed-form expressions for the joint probability distribution for the number of customers of both classes, in steady state. [ABSTRACT FROM AUTHOR]

The aim of this paper is to review the various laser-wavelength effects reported in the field of ultrafast acoustics (UA). First observed by chance in 1999, a wavelength change can indeed have a strong effect on the signal detected in UA. After the physical origin of the effect was clarified and from a systematic exploration we established that all the opto-acoustic mechanisms acting in UA are influenced by the laser-wavelength. From that we suggested original applications of UA to fundamental and applied physics. So emerged a new field, now referred as Colored Picosecond Acoustics or APiC. [ABSTRACT FROM AUTHOR]

Recently, an alternative way of measuring hypersound attenuation in silica thin films using ultrafast acoustics was proposed. The attenuation of longitudinal acoustic phonons around 250 GHz has been measured in vitreous silica deposited on a silicon substrate. This method is based on the emission of a short-acoustic pulse from a thin-metallic layer on top of the sample. The high frequency content of the pulse is optically detected in the silicon substrate after propagation in silica. By comparing the signal obtained for various film thicknesses, we can precisely extract sound attenuation in silica in the sub-terahertz range. In order to reach higher and higher frequencies, it is needed to improve both acoustic emission and detection. Concerning emission, it is governed by the thin metallic layer deposited on top which converts the ultrashort optical pulse in an acoustic pulse. Usually, Al is preferred due to its efficiency in light-sound conversion. In this work, the high frequency content of the acoustic emission was improved by studying the influence of the chemical nature, the thickness, and the deposition parameters of the transducer on the detection of ultra-high frequencies in the substrate. As a result of this optimization, it is expected that the hypersound attenuation can be measured in silica up to 350 GHz. A second conclusion of this work is an alternative way of emitting the acoustic pulse based on a resonance effect. [ABSTRACT FROM AUTHOR]

This paper deals with the propagation of waves along a one-dimensional chain made up of welded spheres. First, a theoretical analysis allows the vibration modes of the chain to be quantitatively described. It has been validated by a comparison between numerical results, using the finite element method and experimental results, restricted to sets of two or three coupled spheres. It is numerically and experimentally verified that the peaks associated with the Rayleigh modes broaden out as the mode number increases and that the passband structure is strongly influenced by the characteristics of the welding between the cells of the periodic structure. The interest of such an approach is then illustrated by the examination of an inverse problem, in which the analytical model is used to deduce the characteristics of the welding. [ABSTRACT FROM AUTHOR]

This paper compares two discrete-time single-server queueing models with two queues. In both models, the server is available to a queue with probability 1/2 at each service opportunity. Since obtaining easy-to-evaluate expressions for the joint moments is not feasible, we rely on a heavy-traffic limit approach. The correlation coefficient of the queue-contents is computed via the solution of a two-dimensional functional equation obtained by reducing it to a boundary value problem on a hyperbola. In most server-sharing models, it is assumed that the system is work-conserving in the sense that if one of the queues is empty, a customer of the other queue is served with probability 1. In our second model, we omit this work-conserving rule such that the server can be idle in case of a non-empty queue. Contrary to what we would expect, the resulting heavy-traffic approximations reveal that both models remain different for critically loaded queues. [ABSTRACT FROM AUTHOR]

Picosecond ultrasonics, which studies laser-induced high-frequency strain waves, is a reliable and versatile method for nondestructive materials' characterization. Strain waves are generated through a light interaction with charges and their subsequent relaxation, and these waves conceal a wealth of information on the material. However, strain waves are detected through their convolution with a sensitivity function, which blurs much of this information. Here, we show that the reflection of strain waves at a free surface leads to the appearance of a Fano resonance in the reflectivity spectrum, accompanied by a drastic increase in the detection bandwidth. We take advantage of this feature to provide a method for the reconstruction of strain waves. We apply it to unambiguously highlight the exact origin of the generation of coherent acoustic phonons in Stranski–Krastanov grown quantum dots, revealing that both the wetting layer and quantum dots are responsible for the generation. Our results will offer the possibility to understand better the interaction of light with charges and their interactions with the lattice. [ABSTRACT FROM AUTHOR]

We demonstrate the ability to construct wide-area spatial mappings of buried interfaces in thin film stacks in a non-destructive manner using two color picosecond acoustics. Along with the extraction of layer thicknesses and sound velocities from acoustic signals, the morphological information presented is a powerful demonstration of phonon imaging as a metrological tool. For a series of heterogeneous (polymer, metal, and semiconductor) thin film stacks that have been treated with a chemical procedure known to alter layer properties, the spatial mappings reveal changes to interior thicknesses and chemically modified surface features without the need to remove uppermost layers. These results compare well to atomic force microscopy scans showing that the technique provides a significant advantage to current characterization methods for industrially important device stacks. [ABSTRACT FROM AUTHOR]

Abstract: The characterization of Young''s modulus, Poisson''s ratio, linear coefficient of thermal expansion and residual stress of thin films is a critical issue for the design and development of MEMS. As inconel thin films have a relatively large thermal expansion coefficient together with a high electrical resistivity, they are good candidates for thermal actuators in MEMS. This work focuses on the determination of the mechanical properties of inconel thin films ranging from 0.4 up to 1.2μm sputtered on a (100) silicon substrate. The atomic composition (6% Fe, 80% Ni, 14% Cr) of these films, close to that of inconel 600 alloys, has been determined by XRF analysis. A wafer curvature measurement technique is used to determine the residual stress and the linear thermal expansion coefficient. We measure residual stress between 152 and 342MPa. The value of the linear thermal expansion coefficient is discussed but is found to be around 10ppm/K−1. We perform bulge testing on micro machined square membranes to determine together the Young''s modulus and residual stress of 0.4μm films. Values of 166GPa and 296MPa are obtained, respectively. These results obtained by bulge testing are eventually compared with measurements made by nanoindentation. Good correspondence is found between the different methods. [Copyright &y& Elsevier]

This work describes the assessment of the acoustic properties of sputtered tantalum oxide films intended for use as high-impedance films of acoustic reflectors for solidly mounted resonators operating in the gigahertz frequency range. The films are grown by sputtering a metallic tantalum target under different oxygen and argon gas mixtures, total pressures, pulsed dc powers, and substrate biases. The structural properties of the films are assessed through infrared absorption spectroscopy and X-ray diffraction measurements. Their acoustic impedance is assessed by deriving the mass density from X-ray reflectometry measurements and the acoustic velocity from picosecond acoustic spectroscopy and the analysis of the frequency response of the test resonators. [ABSTRACT FROM PUBLISHER]

A phenomenological approach is developed to identify the physical parameters causing the dc-voltage-induced tunability of aluminum nitride (AlN) acoustic resonators, widely used for RF filters. The typical resonance frequency of these resonators varies from 2.038 GHz at -200 V to 2.062 GHz at +200 V. This indicates, based on these RF measurements versus dc bias and the model used, that the AlN stiffness variation versus dc bias is the prominent effect because both resonance and antiresonance experience a similar variation, respectively, 24 MHz and 19 MHz at 400 V. Picosecond ultrasonics were also used to prove independently that the acoustic velocity (and therefore AlN stiffness) is sensitive to dc bias and that the variation induced is comparable to that extracted from the resonance measurements. It turned out that the stiffness relative variation for an electric field of 1 V/?m extracted from picosecond ultrasonics is 54 ppm?μm/V. This is in good agreement with the value extracted from the RF measurements, namely 57.2 ppm?μm/V. The overall tunability of these AlN resonators reaches 1.1%, which is an interesting figure, although probably not high enough for genuine applications. [ABSTRACT FROM PUBLISHER]