The focusing of weak shock waves

This paper reports an experimental investigation, using shadowgraphs and pressure measurements, of the detailed behaviour of converging weak shock waves near three different kinds of focus. Shocks are brought to a focus by reflecting initially plane fronts from concave end walls in a large shock tube. The reflectors are shaped to generate perfect foci, arêtes and caustics. It is found that, near the focus of a shock discontinuity, a complex wave field develops, which always has the same basic character, and which is always essentially nonlinear. A diffracted wave field forms behind the non-uniform converging shock; its compressive portions steepen to form diffraction shocks, while diffracted expansion waves overtake and weaken the diffraction shocks. The diffraction shocks participate in a Mach reflexion process near the focus, whose development is determined by competition between the convergence of the sides of the focusing front and acceleration of its central portion. In fact, depending on the aperture of the convergence and the strength of the initial wave, the three-shock intersections of the Mach reflexions either cross on a surface of symmetry or remain uncrossed. In the former case, which is observed if the shock wave is relatively weak, the wavefronts emerge from focus crossed and folded, in accordance with the predictions of geometrical acoustics theory. In the latter, the strong-shock case, the fronts beyond focus are uncrossed, as predicted by the theory of shock dynamics. It is emphasized that in both cases the behaviour at the focus is nonlinear. The overtaking of the diffraction shocks by the diffracted expansions limits the amplitude of the converging wave near focus, and is the mechanism by which the maximum amplification factor observed at focus is determined. In all cases, maximum pressures are limited to rather low values

Computational Design of Nucleic Acid Feedback Control Circuits

The design of synthetic circuits for controlling molecular-scale processes is an important goal of synthetic biology, with potential applications in future in vitro and in vivo biotechnology. In this paper, we present a computational approach for designing feedback control circuits constructed from nucleic acids. Our approach relies on an existing methodology for expressing signal processing and control circuits as biomolecular reactions. We first extend the methodology so that circuits can be expressed using just two classes of reactions: catalysis and annihilation. We then propose implementations of these reactions in three distinct classes of nucleic acid circuits, which rely on DNA strand displacement, DNA enzyme and RNA enzyme mechanisms, respectively. We use these implementations to design a Proportional Integral controller, capable of regulating the output of a system according to a given reference signal, and discuss the trade-offs between the different approaches. As a proof of principle, we implement our methodology as an extension to a DNA strand displacement software tool, thus allowing a broad range of nucleic acid circuits to be designed and analyzed within a common modeling framework

An experimental investigation on focussing of weak shock waves in air

The behavior of focussing weak shock waves is experimentally investigated with a view to observe and understand the processes occurring near the focus, especially the processes that control the maximum amplitude. Concave reflectors are used against the endwall of a large 17" diameter shock tube, to focus the plane incident shock. Reflectors producing line and point foci, and cusped and smooth caustics are examined for incident shock Mach numbers ranging between 1.005 to 1.5. The flowfield is observed with spark shadowgraphs to visualize the motion of various wavefronts. Pressure histories measured at various points in the flow with miniature piezoelectric gauges provide additional information about the various processes occurring near the focus. Shadowgraphs show that for weak shocks, the observed foci are predominantly nonlinear, even though away from the focus, the shockfronts appear to be almost acoustic. Thus a weak shockfront, after the focus, crosses itself and forms a loop, which is an essential feature of acoustic wavefronts. Nonetheless, at the focus, distortion in the geometry of the fronts due to nonlinear effects is very prominent. Inherently nonlinear phenomena, such as formation of three-shock intersections, lead to foci of finite size, in which, as the pressure measurements show, the amplitudes are finite. The amplitude dependence of these phenomena confirms that they are basically nonlinear. The geometrical distortion and the focus are larger for stronger shock waves, and the maximum amplification is smaller. Further, when the distortion becomes significant compared to the size of the initial shockfront, a transition occurs in the geometry of the focussed shockfront. In this case, the focussed front does not cross and remains "unlooped", which is consistent with the nonlinear behavior predicted by shock dynamics. The transition in the geometry of the wavefronts is related to the behavior of the three-shock intersections formed near the focus. In fact, it is shown that the occurrence of crossed or uncrossed shockfronts is very parallel to the occurrence of regular or Mach reflection, respectively, in the case of a shock diffracted by a wedge. (The reflecting wedge surface corresponds to the axis of symmetry in a focussing process.) The dependence on the steepness of the approaching waves is also similar in the two cases; rapid convergence of waves suppresses nonlinear effects, whereas in a slow convergence, nonlinear effects gain prominence. The pressure histories at various locations, when correlated with the waves occurring there, show that nonlinear diffraction processes are very important. In fact, it is shown that the formation of the three-shock intersection occurs due to nonlinear distortion and breaking of a compressive diffraction, and that, in the focus, the limiting and reduction of the peak amplitude occurs by a diffracted expansion overtaking the shock due to nonlinear effects

Incidence of Mango Flower Galls in Bombay Karnatak

Volume: 53Start Page: 147End Page: 14