Higher modes of the Orr-Sommerfeld problem for boundary layer flows

The discrete spectrum of the Orr-Sommerfeld problem of hydrodynamic stability for boundary layer flows in semi-infinite regions is examined. Related questions concerning the continuous spectrum are also addressed. Emphasis is placed on the stability problem for the Blasius boundary layer profile. A general theoretical result is given which proves that the discrete spectrum of the Orr-Sommerfeld problem for boundary layer profiles (U(y), 0,0) has only a finite number of discrete modes when U(y) has derivatives of all orders. Details are given of a highly accurate numerical technique based on collocation with splines for the calculation of stability characteristics. The technique includes replacement of 'outer' boundary conditions by asymptotic forms based on the proper large parameter in the stability problem. Implementation of the asymptotic boundary conditions is such that there is no need to make apriori distinctions between subcases of the discrete spectrum or between the discrete and continuous spectrums. Typical calculations for the usual Blasius problem are presented

Quantitative measurement of combustion gases in harsh environments using NDIR spectroscopy

The global climate change calls for a more environmental friendly use of energy and has led to stricter limits and regulations for the emissions of various greenhouse gases. Consequently, there is nowadays an increasing need for the detection of exhaust and natural gases. This need leads to an ever-growing market for gas sensors, which, at the moment, is dominated by chemical sensors. Yet, the increasing demands to also measure under harsh environmental conditions pave the way for non-invasive measurements and thus to optical detection techniques. Here, we present the development of a non-dispersive infrared absorption spectroscopy (NDIR) method for application to optical detection systems operating under harsh environments.Comment: 10 pages, 8 figure

Absolute and convective instabilities in an inviscid compressible mixing layer

We consider the stability of a compressible shear flow separating two streams of different speeds and temperatures. The velocity and temperature profiles in this mixing layer are hyperbolic tangents. The normal mode analysis of the flow stability reduces to an eigenvalue problem for the pressure perturbation. We briefly describe the numerical method that we used to solve this problem. Then, we introduce the notions of the absolute and convective instabilities and examine the effects of Mach number, and the velocity and temperature ratios of each stream on the transition between convective and absolute instabilities. Finally, we discuss the implication of the results presented in this paper for the heliopause stability.Comment: 5 pages, 6 figures, accepted by Astronomical Notes (Astron. Nachrichten

Grosch's law: a statistical illusion?.

In this paper a central law on economies of scale in computer hardware pricing, Grosch's law is discussed. The history and various validation efforts are examined in detail. It is shown how the last set of validations during the eighties may be interpreted as a statistical misinterpretation, although this effect may have been present in all validation attempts, including the earliest ones. Simulation experiments reveal that constant returns to scale in combination with decreasing computer prices may give the illusion of Grosch's law when performing regression models against computer prices over many years. The paper also shows how the appropriate definition of computer capacity, and in particular Kleinrock's power definition, plays a central role in economies of scale for computer prices.Law;

Absolute/convective instabilities and the convective Mach number in a compressible mixing layer

Two aspects of the stability of a compressible mixing layer: Absolute/Convective instability and the convective Mach number were considered. It was shown that, for Mach numbers less than one, the compressible mixing layer is convectively unstable unless there is an appreciable amount of backflow. Also presented was a rigorous derivation of a convective Mach number based on linear stability theory for the flow of a multi-species gas in a mixing layer. The result is compared with the heuristic definitions of others and to selected experimental results

Geometric path planning without maneuvers for nonholonomic parallel orienting robots

Current geometric path planners for nonholonomic parallel orienting robots generate maneuvers consisting of a sequence of moves connected by zero-velocity points. The need for these maneuvers restrains the use of this kind of parallel robots to few applications. Based on a rather old result on linear time-varying systems, this letter shows that there are infinitely differentiable paths connecting two arbitrary points in SO(3) such that the instantaneous axis of rotation along the path rest on a fixed plane. This theoretical result leads to a practical path planner for nonholonomic parallel orienting robots that generates single-move maneuvers. To present this result, we start with a path planner based on three-move maneuvers, and then we proceed by progressively reducing the number of moves to one, thus providing a unified treatment with respect to previous geometric path planners.Peer ReviewedPostprint (author's final draft

Aroma-active secondary oxidation products of butter

Butter contains vitamins, minerals and unsaturated lipids, such as polyunsaturated fatty acids (PUFA) and conjugated linoleic acids (CLAs). However the oxidative stability and consequently the shelf-life of milk products are inversely correlated with their PUFA and CLA content. The objective of this study is the evaluation of the oxidative stability and sensory quality of PUFA/CLA-enriched butter versus conventional butter, with both types of butter being produced at ALP. For this purpose, new chemical and sensory-based methods will be developed, as well holistic complementary methods. This paper focuses on a preliminary study achieved using conventional butter, subjected to a long storage and to oxygen and light exposure, to develop a gas chromatography olfactometry (GC-O) method able to detect the aroma-active compounds originated from oxidation. This will be one of the methods used for the evaluation of the oxidative stability of PUFA/CLA-enriched butter

State, rate and temperature-dependent sliding friction of elastomers

We present an experimental investigation of the non stationary frictional properties of multicontact interfaces between rough elastomers and rough hard glass at low velocities (<= 200 mu m s^{-1}). These systems, for which the deformation contribution to friction is negligible, are shown to exhibit a phenomenology which is similar to what is observed for non elastomeric materials in the same multi-contact configuration, and which are quantitatively described by the state- and rate-dependent friction laws. This permits to identify clearly the two contributions to adhesive friction which are mixed in steady sliding: the interfacial shear stress which appears as thermally activated formation and breaking of molecular bonds, and the real area of contact which evolves through viscoelastic creep of the load bearing asperities

Rubber friction on smooth surfaces

We study the sliding friction for viscoelastic solids, e.g., rubber, on hard flat substrate surfaces. We consider first the fluctuating shear stress inside a viscoelastic solid which results from the thermal motion of the atoms or molecules in the solid. At the nanoscale the thermal fluctuations are very strong and give rise to stress fluctuations in the MPa-range, which is similar to the depinning stresses which typically occur at solid-rubber interfaces, indicating the crucial importance of thermal fluctuations for rubber friction on smooth surfaces. We develop a detailed model which takes into account the influence of thermal fluctuations on the depinning of small contact patches (stress domains) at the rubber-substrate interface. The theory predicts that the velocity dependence of the macroscopic shear stress has a bell-shaped f orm, and that the low-velocity side exhibits the same temperature dependence as the bulk viscoelastic modulus, in qualitative agreement with experimental data. Finally, we discuss the influence of small-amplitude substrate roughness on rubber sliding friction.Comment: 14 pages, 16 figure