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We present a novel scheme for rapid quantitative analysis of debris generated during experiments with solid targets following relativistic laser–plasma interaction at high-power laser facilities. Results are supported by standard analysis techniques. Experimental data indicate that predictions by available modelling for non-mass-limited targets are reasonable, with debris of the order of hundreds of μg per shot. We detect for the first time two clearly distinct types of debris emitted from the same interaction. A fraction of the debris is ejected directionally, following the target normal (rear and interaction side). The directional debris ejection towards the interaction side is larger than on the side of the target rear. The second type of debris is characterized by a more spherically uniform ejection, albeit with a small asymmetry that favours ejection towards the target rear side.
In this article, a coupled line diplexer (operating at 2.4 GHz and 3.5 GHz) which can be used as single-band filter with tunable attenuation characteristics in the pass band has been designed. Multilayer graphene (MLG) pads are used to achieve tunable features in this circuit. The graphene pads are placed at each branch of the diplexer. Single-band tunable attenuation characteristics are achieved by applying bias to graphene pads placed at optimum locations on the filter. The proposed tunable coupled line attenuating diplexer is realized on FR-4 glass epoxy substrate of thickness 1.58 mm with a total size of 45 × 75 mm2. By varying the bias voltage (0 V –6 V) of MLG pads the resistance of graphene pad placed in the circuit gets decreases thereby attenuating/controlling the transmission power to the other port in the required band. In lower pass band (2.28–2.55 GHz) the signal is attenuated from 3 to 10.8 dB and in higher pass band (3.2–3.58 GHz) signal is attenuated from 5 to 13 dB. Simulations of the structure with and without graphene pads have been carried out and are in good agreement with measured results.
We live in a turbulent world observed through coarse grained lenses. Coarse graining (CG), however, is not only a limit but also a need imposed by the enormous amount of data produced by modern simulations. Target audiences for our survey are graduate students, basic research scientists, and professionals involved in the design and analysis of complex turbulent flows. The ideal readers of this book are researchers with a basic knowledge of fluid mechanics, turbulence, computing, and statistical methods, who are disposed to enlarging their understanding of the fundamentals of CG and are interested in examining different methods applied to managing a chaotic world observed through coarse-grained lenses.
Hydrodynamic consequences of using simpler geometric shapes to represent coral canopies are examined through a laboratory study. A canopy composed of cylinders is compared with a canopy composed of 3-D-printed, scaled down coral heads in a recirculating flume. Vertical velocity profiles are measured at four horizontal locations for each canopy type, and mean velocity and turbulence statistics are compared both within and above the canopy. A narrow, defined wake on the scale of the canopy element is present behind the cylinder canopy elements that is absent in the coral canopy. There is also a peak in shear stress at the top of the cylinder canopy, likely due to the sharp edge at the top of the cylinder. Above the canopy, however, turbulence statistics and friction velocities behave similarly for both canopy types. Therefore, the results indicate we may reasonably get coral reef drag estimates from canopies with simpler geometric surrogates, especially when the mean free-stream and within-canopy flow speeds are matched to environmental conditions.
This chapter covers the basics from real analysis to linear algebra and the theory of computation that is foundational for the rest of the book. A careful discussion of different models of computation is taken up, which discusses several issues that are often ignored in other presentations of optimization theory and algorithms.
A careful exposition of the conceptual underpinnings of algorithmic or computational optimization is presented. Computation in continuous optimization has its origins in the traditions of scientific computing and numerical analysis, whereas discrete optimization broadly views computation via the Turing machine model. The different views lead to some friction. In the continuous world, one often designs algorithms assuming one can perform exact operations with real numbers (consider, for example, Newton’s method), which is impossible in the Turing machine model. In the discrete world, the “input" to a Turing machine becomes a tricky question when dealing with general nonlinear functions and sets. The question of “complexity" of an optimization algorithm is also treated in somewhat different ways in the two communities. This chapter, combined with the careful discussion of computation models in Chapter 1, shows how all these issues can be handled in a unified, coherent way making no distinction whatsoever between "continuous" and "discrete" optimization.
This chapter deals with the important question of certifying optimality of a solution to a mixed-integer convex optimization problem. The classical duality theory for continuous optimization, including Lagrangian relaxations, KKT and general optimality conditions, and Slater type conditions for strong duality, is rigorously covered in complete detail. Recent work on duality for mixed-integer convex optimization is succinctly summarized.
In the early part of the 20th century, Hermann Minkowski developed a novel geometric approach to several questions in number theory. This approach developed into a field called the geometry of numbers and it had an influence on fields outside number theory as well, particularly functional analysis and the study of Banach spaces, and more recently on cryptography and discrete optimization. This chapter covers those aspects of the geometry of numbers that are most relevant for the second part of the book on optimization. Topics include the basic theory of lattices (including Minkowski’s convex body theorem), packing and covering radii, shortest and closest lattice vector problems (SVPs and CVPs), Dirichlet-Voronoi cells, Khinchine’s flatness theorem, and maximal lattice-free convex sets. Several topics like lattice basis reduction and SVP/CVP algorithms are presented without making a rationality assumption as is common in other expositions. This presents a slightly more general perspective on these topics that contains the rational setting as a special case.
A compact microstrip eight-channel diplexer based on quad-mode stepped impedance resonator (QMSIR) is proposed in this paper. The proposed diplexer is composed by two second-order quad-band bandpass filters (BPFs) and common-port distributed coupling matching circuit. Each quad-band BPF is formed by two coupled-QMSIRs controlling the passband characteristics. By introducing multiple coupling paths between input and output ports, the isolation between the eight channels is performed. For demonstration, an eight-channel diplexer based on QMSIR is designed and fabricated with microstrip technology. The use of the QMSIR can lead to significant size reduction for the multiplexer, this is because the required resonator number is reduced. As a result, the diplexer occupies a compact size of 0.083λ2, which is smaller than most of the eight-channel diplexers that have been proposed. And the 3 dB fractional bandwidth is 97% (2.5–7.2 GHz). Measurement results correlate well with the simulated predictions, showing that a good isolation of better than 20 dB and upper stopband of better than 10 dB.
Understanding the mechanisms behind the remote triggering of landslides by seismic waves at micro-strain amplitude is essential for quantifying seismic hazards. Granular materials provide a relevant model system to investigate landslides within the unjamming transition framework, from solid to liquid states. Furthermore, recent laboratory experiments have revealed that ultrasound-induced granular avalanches can be related to a reduction in the interparticle friction through shear acoustic lubrication of the contacts. However, investigating slip at the scale of grain contacts within an optically opaque granular medium remains a challenging issue. Here, we propose an original coupling model and numerically investigate two-dimensional dense granular flows triggered by basal acoustic waves. We model the triggering dynamics at two separated time scales – one for grain motion (milliseconds) and the other for ultrasound (10 ${\rm \mu} {\rm s}$) – relying on the computation of vibrational modes with a discrete element method through the reduction of the local friction. We show that ultrasound predominantly propagates through the strong-force chains, while the ultrasound-induced decrease of interparticle friction occurs in the weak contact forces perpendicular to the strong-force chains. This interparticle friction reduction initiates local rearrangements at the grain scale that eventually lead to a continuous flow through a percolation process at the macroscopic scale – with a delay depending on the proximity to the failure. Consistent with experiments, we show that ultrasound-induced flow appears more uniform in space than pure gravity-driven flow, indicating the role of an effective temperature by ultrasonic vibration.
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.
This chapter introduces the concept of a convex function and develops the basic theory of convex functions. Standard continuity and differentiability properties are established. Fundamental notions like subgradients and subdifferentials are introduced and their properties are investigated in detail. Sublinear functions get particular focus, given their recent importance in optimization theory and practice. Some new results on sublinear functions that have never before appeared outside specialized research articles are presented with clean, textbook-style proofs. Elementary Brunn-Minkowski theory is covered, including important consequences like the concavity principle and the Rogers-Shepard inequality.
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.
Assessment of occupational exoskeletons should ideally include longitudinal and multistage studies in real working scenarios to prove their effectiveness and sustainability in real in-field contexts and to help generalize the findings for specific scenarios. This work presents a comprehensive assessment methodology implemented as a multistage experimental campaign for rail industry workers using a back-support exoskeleton (StreamEXO). This work demonstrates that a sector/task-specific exoskeleton developed to address work task-specific requirements generates beneficial performance and user experience results. The experimental work in this paper involves collecting data from nine workers over multiple days of testing. During this testing, workers did not report hindrances to their work operations, with an acceptance rate of 86%. In addition, worker fatigue was reduced by 16.9% as measured through metabolic consumption, and 51% when assessed by perceived effort. This work supports the hypothesis that sector/task-specific exoskeletons when tailored to meet the needs of workers and the work tasks can produce demonstrable benefits in real industrial sectors.