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This study identifies two previously unrecognised screech modes in non-axisymmetric jets. Spectral proper orthogonal decomposition (SPOD) of ultra-high-speed schlieren images reveals a bi-axial flapping mode in a rectangular jet and a quasi-helical mode in an elliptical jet. To educe the complex three-dimensional structure of these new modes, SPOD is performed on datasets from different viewing perspectives, produced by rotating the nozzle with respect to the schlieren path to an azimuthal angle $\theta$. The bi-axial flapping mode is strongly antisymmetric from any perspective. However, the SPOD eigenvalue at the screech frequency ($\lambda _s$) varies with $\theta$ and the axial distance of the SPOD domain from the nozzle lip. This mode most closely resembles a flapping mode in the minor-axis plane close to the nozzle lip and a wagging mode in the major-axis plane further downstream. This transition from flapping to wagging at the same frequency correlates with the axis switching defined by the shock-cell structure in the mean flow. The quasi-helical mode in the elliptical jet is characterised by an antisymmetric structure present in the SPOD spatial modes whose eigenvalue $\lambda _s$ is insensitive to both $\theta$ and the axial domain. These findings indicate that the spatial evolution of the mean flow in non-axisymmetric jets may allow them to support a range of additional screech modes that differ significantly from those supported by the original three-dimensional shape of the jet.
Real-time systems need to be built out of tasks for which the worst-case execution time is known. To enable accurate estimates of worst-case execution time, some researchers propose to build processors that simplify that analysis. These architectures are called precision-timed machines or time-predictable architectures. However, what does this term mean? This paper explores the meaning of time predictability and how it can be quantified. We show that time predictability is hard to quantify. Rather, the worst-case performance as the combination of a processor, a compiler, and a worst-case execution time analysis tool is an important property in the context of real-time systems. Note that the actual software has implications as well on the worst-case performance. We propose to define a standard set of benchmark programs that can be used to evaluate a time-predictable processor, a compiler, and a worst-case execution time analysis tool. We define worst-case performance as the geometric mean of worst-case execution time bounds on a standard set of benchmark programs.
This, then, was the final culmination of a succession of dreams that had emerged progressively in 11 steps or stages that had begun in antiquity. In logical order, the several steps were from: (1) the birth of ancient Greek and other myths of flight, to (2) proposals for machines that would make flight possible by mimicking the flapping wings of birds, to (3) actual attempts at human flight, to (4) successful human flight through the air by means of balloons, to (5) powered, controlled, sustained human flight through the atmosphere by winged vehicles, to (6) fictional accounts of flying to the Moon, to (7) the invention of rockets leading to an understanding of the principles of space flight, to (8) the Apollo Project Moon landings, to (9) fictional accounts of traveling to Mars, to (10) actual landings on Mars by rockets and robotic rovers, to (11) the idea of leaving Earth and colonizing the universe.
DARPA and NASA had jointly realized that nobody in their right mind formulated plans and undertook projects on anything like the 100-year time horizon that they thought was needed to design, build, outfit, and launch a crewed interstellar vehicle. So they wanted to seed-fund some private organization to do so, and for an essentially backdoor reason: namely to reap whatever possible spinoff technologies might accrue from such an endeavor. “DARPA also anticipates that the advancements achieved by such technologies will have substantial relevance to Department of Defense (DoD) mission areas including propulsion, energy storage, biology/life support, computing, structures, navigation, and others.”
The techniques of celestial dynamics are useful within the solar system and other planetary systems. However, techniques that are useful in a system containing a few mutually gravitating objects are not as useful in a system containing a hundred thousand million objects.
The three-dimensional flow field past an I-shaped dual-step cylinder has been obtained by numerical integration of the Navier–Stokes equations at Reynolds number ($Re_D$) 150. The I-shaped cylinder consisted of two large-diameter (D) cylinders with a small-diameter (d) cylinder in between. With a view to exploring the vortex dynamics and structural loads, simulations were performed for eight different lengths $l$ of the small cylinder, varied from $l/D=10$ to 0.2 for a fixed diameter ratio $D/d=2$. When the length of the small cylinder is sufficiently large, the wake behind the I-shaped cylinder is similar to the wake behind the single-step cylinder (Tian et al., J. Fluid Mech., vol. 891, 2020, A24). As the small cylinder length decreases, the enhanced interactions between the two steps make the present wake deviate from the wake of the single-step cylinder, leading to four different wake modes distinguished by different combinations of vortex cells. The physical formation mechanisms were analysed in terms of the vortex dynamics. Besides the wake flow, the streamwise vortices around the I-shaped step cylinder were also investigated. A pair of edge vortices and a junction vortex were identified for $l/D \geq ~1$. When the gap between the two steps becomes too small, $l/D \leq ~0.2$, the junction vortex disappears, and only a pair of edge vortices exists. Varying the distance between the two steps strongly affects the structural loads (drag and lift) along the I-shaped cylinder. The dependence of the loads on $l/D$ was readily explained by the different wake modes.
A liquid drop impacting a rigid substrate undergoes deformation and spreading due to normal reaction forces, which are counteracted by surface tension. On a non-wetting substrate, the drop subsequently retracts and takes off. Our recent work (Zhang et al., Phys. Rev. Lett., vol. 129, 2022, 104501) revealed two peaks in the temporal evolution of the normal force $F(t)$ – one at impact and another at jump-off. The second peak coincides with a Worthington jet formation, which vanishes at high viscosities due to increased viscous dissipation affecting flow focusing. In this article, using experiments, direct numerical simulations and scaling arguments, we characterize both the peak amplitude $F_1$ at impact and the one at takeoff ($F_2$) and elucidate their dependency on the control parameters: the Weber number $We$ (dimensionless impact kinetic energy) and the Ohnesorge number $Oh$ (dimensionless viscosity). The first peak amplitude $F_1$ and the time $t_1$ to reach it depend on inertial time scales for low viscosity liquids, remaining nearly constant for viscosities up to 100 times that of water. For high viscosity liquids, we balance the rate of change in kinetic energy with viscous dissipation to obtain new scaling laws: $F_1/F_\rho \sim \sqrt {Oh}$ and $t_1/\tau _\rho \sim 1/\sqrt {Oh}$, where $F_\rho$ and $\tau _\rho$ are the inertial force and time scales, respectively, which are consistent with our data. The time $t_2$ at which the amplitude $F_2$ appears is set by the inertiocapillary time scale $\tau _\gamma$, independent of both the viscosity and the impact velocity of the drop. However, these properties dictate the magnitude of this amplitude.
The noun “dynamics” entered the English language in the eighteenth century, when natural philosophers, following the lead of Isaac Newton, began thinking of motion in terms of applied forces and the resulting accelerations. In 1788, the New Royal Encyclopaedia contained the definition, “Dynamics is the science of moving powers; more particularly of the motion of bodies that mutually act on one another.” This is still a useful definition. For the purposes of this book, we can define dynamics as the study of objects that move while interacting through mutual forces.
While the fate of a multigenerational interstellar population cannot be predicted with anything approaching certainty, the many dangers presented by the instantaneously lethal environment of space, plus the interpersonal pressures and conflicts that might result in social breakdown, make it doubtful that a successful transit to another star system with all the successive onboard generations remaining safe, healthy, and happy across time, is a realistic possibility. It is far more likely that the crew would suffer one or another kind of irremediable catastrophe en route than that everyone aboard would survive, and that the final, arriving generation would get there intact. But if that is true, then the question arises whether it would be morally justifiable to launch such an expedition to begin with, given its immense costs, high probability of failure, and lack of any benefit accruing to the sponsors back on Earth who had paid for it all.
A gravitationally bound two-body system (if the two bodies are spheres of constant mass) shows simple periodic motion. We have seen that a three-body system, even if we install restrictions for computational simplicity, can show a rich variety of behaviors. Tadpole orbits, horseshoe orbits, and ZLK oscillations are just a sampling of what can happen.
Beyond the task of developing a realistic and workable propulsion system that would make interstellar travel possible and practical, there is the prior challenge of identifying an extrasolar planet that would be suitable for long-term human habitation. Any planet that is a candidate for human colonization has to satisfy a surprisingly large number of requirements stemming from the fact that human biology has evolved on Earth and nowhere else, and is therefore fit to survive only in an environment that is substantially similar to our own. As Daniel Deudney has said in his book Dark Skies, “Humans are sprung from the Earth, have never lived anywhere but on Earth, and the features of this planet have shaped every aspect of human life .… Life is not on Earth, it is of Earth.” And for that reason, a planet fit for human colonization elsewhere must be earthlike in several important respects.
Researchers proposed ever larger and yet more implausible designs for interstellar vehicles. And so in 1996, writing in the journal Nanotechnology, one Thomas L. McKendree discussed what would be possible if materials provided by molecular nanotechnology were used to build spacecraft in place of then current structural building materials such as aluminum, steel, and titanium. Molecular nanotechnology was the theoretical ability to design and build products to atomic precision. Such a technology, which does not exist as yet and might never, would allow the use of diamondoid materials that had much higher strength-to-density ratios than those that are now used to build structures. In his paper “Implications of Molecular Nanotechnology Technical Performance Parameters on Previously Defined Space System Architectures,” McKendree argued that the use of diamondoid structural materials would make possible extremely large space colonies. The classic cylindrical colony, for example, if made of diamondoid structural elements could have a radius of 461 kilometers and a length of 4,610 kilometers, or 2,865 miles.
The prospect of human travel to the stars faces such an exceptionally wide and diverse assortment of obstacles, improbabilities, multiple risks, and inestimable costs, as to make any attempt to traverse the final frontier far more likely to end in tragedy than to succeed in getting human beings safely lodged on the surface of an extrasolar planet that is in all respects suitable for continued and sustained human life. There are, in general, seven separate categories of problems facing starflight: physical, biological, psychological, social, financial, ethical, and motivational. Starting with the physics of the enterprise, we have seen that none of the three icons of star travel embodies a realistic, practical, proven design that would be likely to work as advertised. Not the nuclear-powered Bernal sphere, nor the Bussard Interstellar Ramjet, nor the Project Daedalus rocket, which in any case was not even intended to carry passengers. Project Orion represented the high-watermark of deep space craziness, as many project members themselves realized afterward. As Freeman Dyson acknowledged much later, “We really were a bit insane, thinking that all these things would work.”