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We consider the evolution of a spatially periodic, perturbed vortex sheet for small times after the formation of a curvature singularity at time $t=t_c$ as demonstrated by Moore (Proc. R. Soc. Lond. A, vol. 365, issue 1720, 1979, pp. 105–119). The Moore analysis is extended to provide the small-amplitude, full-sheet structure at $t=t_c$ for a general single-mode initial condition in terms of polylogarithmic functions, from which its asymptotic form near the singular point is determined. This defines an intermediate evolution problem for which the leading-order, and most singular, approximation is solved as a Taylor-series expansion in $\tau = t-t_c$, where coefficients are calculated by repeated differentiation of the defining Birkhoff–Rott (BR) equation. The first few terms are in good agreement with numerical calculation based on the full-sheet solution. The series is summed, providing an analytic continuation which shows sheet rupture at circulation $\varGamma =0^+$, $\tau >0^+$, but with non-physical features owing to the absence of end-tip sheet roll up. This is corrected by constructing an inner solution with $\varGamma < \tau$, as a perturbed similarity form with small parameter $\tau ^{1/2}$. Numerical solutions of both the inner, nonlinear zeroth-order and first-order linear BR equations are obtained whose outer limits match the intermediate solution. The composite solution shows sheet tearing at $\tau =0^+$ into two separate, rolled up algebraic spirals near the central singular point. Branch separation distance scales as $\tau$ with a non-local, $\tau ^{3/2}$ correction. Properties of the intermediate and inner solutions are discussed.
This research work presents an implantable antenna that operates at 5.8 GHz. By using a radiator with a loop-based design, the antenna can be made smaller. Radiator is made up of three connected rectangular loops. On the substrate’s back side, an I-shaped ground plane is used. As substrate and superstrate, polydimethylsiloxane (PDMS) with dimensions of 7 mm × 5 mm × 0.3 mm is used. The conducting sections are made using copper foil that is 30 µm thick. The suggested antenna is examined by the implantable medical device using realistic human scalp phantom models and a homogenous skin box. Simulated study revealed that it operates around 5.8 GHz with a bandwidth from 5.69 to 5.92 GHz. The specific absorption rate was 0.28 and 0.26 W/kg for skin box and human scalp phantoms, respectively, at 1 mW input power across 1 g volume tissue.
An ultra-wideband (UWB) and compact-size four-port multiple input multiple output (MIMO) antenna with a footprint of 34 mm × 34 mm fed by an asymmetric coplanar strip (ACS) is investigated. The proposed antenna is composed of four orthogonally placed identical modified elliptical-shaped radiators and achieves an impedance bandwidth of 3.4–12.2 GHz. By etching two inverted L-shaped slots in the radiator element, WLAN band and X-band are rejected in the operating communication range. Because of the usage of a meander line decoupler, the isolation enhancement at the 8–12 GHz band is achieved and the isolation is more than 18 dB for most of the UWB range. The performance of the proposed antenna is studied in terms of isolation between each port, radiation pattern, current distribution, gain, envelope correlation coefficient, diversity gain, and total active reflection coefficient. The compact size and reduced complexity make the proposed design highly suitable for portable devices.
In this chapter we first describe the experiments of Grangier et al., which gave clear evidence of anti-correlation effects and of the interference effects where only a single photon is involved. We then provide a fully quantum mechanical treatment of a lossless beam splitter. Interferometry with single photons is then treated fully quantum mechanically. Interaction-free measurement is then discussed, followed by interferometry with coherent states of light. Next, the SU(2) formulation of beam splitters and interferometers is discussed.
The increase in global population and urbanization is presenting significant challenges to society: space is becoming increasingly scarce, demand is exceeding capacity for deteriorating infrastructure, transportation is fraught with congestion, and environmental impacts are accelerating. Underground space, and particularly tunnels, has a key role to play in tackling these challenges. However, the cost, risk, uncertainty, and complexity of the tunneling process have impeded its growth. In this paper, we envision several technological advancements that can potentially innovate and transform the mechanized tunneling industry, including artificial intelligence (AI), autonomous, and bio-inspired systems. The proliferation of AI may assist human engineers and operators in making informed decisions systematically and quantitatively based on massive real-time data during tunneling. Autonomous tunneling systems may enable precise and predictable tunneling operations with minimal human intervention and facilitate the construction of massive and large-scale underground infrastructure projects that were previously challenging or unfeasible using conventional methods. Bio-inspired systems may provide valuable references and strategies for more efficient tunneling design and construction concepts. While these technological advancements can offer great promise, they also face considerable challenges, such as improving accessibility to and shareability of tunneling data, developing robust, reliable, and explainable machine learning systems, as well as scaling the mechanics and ensuring the applicability of bio-inspired systems from the prototype level to real-world applications. Addressing these challenges is imperative to ensure the successful implementation of these innovations for future tunneling.
A fleet of aircraft can be seen as a set of degrading systems that undergo variable loads as they fly missions and require maintenance throughout their lifetime. Optimal fleet management aims to maximise fleet availability while minimising overall maintenance costs. To achieve this goal, individual aircraft, with variable age and degradation paths, need to operate cooperatively to maintain high fleet availability while avoiding mechanical failure by scheduling preventive maintenance actions. In recent years, reinforcement learning (RL) has emerged as an effective method to optimise complex sequential decision-making problems. In this paper, an RL framework to optimise the operation and maintenance of a fleet of aircraft is developed. Three cases studies, with varying number of aircraft in the fleet, are used to demonstrate the ability of the RL policies to outperform traditional operation/maintenance strategies. As more aircraft are added to the fleet, the combinatorial explosion of the number of possible actions is identified as a main computational limitation. We conclude that the RL policy has potential to support fleet management operators and call for greater research on the application of multi-agent RL for fleet availability optimisation.
The current paper is focused on the conceptual design of a thermal management system with a liquid working medium for a commuter hybrid-electric aircraft, featuring a series propulsion configuration. Regarding the system’s architecture, parametric analyses are conducted, by altering the number of heat exchangers. To clarify, a centralised and a decentralised thermal management system architecture are examined. Furthermore, a computational model calculates the temperatures during the system’s operation and the required coolant mass flows to sufficiently cool all the compartments. Subsequently, the required heat exchanger surface is determined and the weight of each compartment that comprises the thermal management system can be calculated. It is worth noting, that the compartments’ cold plate weight is integrated. The results indicate that the decentralised configuration results in lower temperature fields for all components compared to the centralised configuration. However, the latter weighs 32.2% lower at 158.22kg while the decentralised configuration weighs 233.48kg.
This research paper presents an application of the integrated process and product design (IPPD) approach for selecting the best joint configuration for dissimilar material joining in the early product design phase. The proposed methodology integrates the multi-criteria decision making (MCDM) approach with quality function deployment (QFD) to identify the key criteria for joint selection, including load-carrying capacity, size, cost per joint, ease of manufacturing, time consumption and deformation. Three types of joints (rivet, weld and adhesive) and two hybrid joints (adhesive-weld and adhesive-rivet) are considered for three dissimilar material configurations: carbon fiber-reinforced plastic (CFRP) aluminum, CFRP steel, and aluminum-steel. QFD is utilised to transform job requirements into design criteria, and in the second phase, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is employed to choose the optimal joint configuration based on the weighted criteria acquired in the previous phase. The selected joint configuration is then validated through experimental study. The findings demonstrate that the proposed IPPD approach with QFD-TOPSIS techniques is highly effective for selecting mechanical joints for dissimilar material joining in the early design phase. The study concludes that the adhesive-rivet hybrid joint is the optimal solution among all alternatives. The proposed methodology can ultimately lead to improved product reliability and performance, as well as reduced development time and cost.
High-intensity vortex beams with tunable topological charges and low coherence are highly demanded in applications such as inertial confinement fusion (ICF) and optical communication. However, traditional optical vortices featuring nonuniform intensity distributions are dramatically restricted in application scenarios that require a high-intensity vortex beam owing to their ineffective amplification resulting from the intensity-dependent nonlinear effect. Here, a low-coherence perfect vortex beam (PVB) with a topological charge as high as 140 is realized based on the super-pixel wavefront-shaping technique. More importantly, a globally adaptive feedback algorithm (GAFA) is proposed to efficiently suppress the original intensity fluctuation and achieve a flat-top PVB with dramatically reduced beam speckle contrast. The GAFA-based flat-top PVB generation method can pave the way for high-intensity vortex beam generation, which is crucial for potential applications in ICF, laser processing, optical communication and optical trapping.
Mid-spatial frequency wavefront deformation can be deleterious for the operation of high-energy laser systems. When fluid cooled high-repetition-rate amplifiers are used, the coolant flow is likely to induce such detrimental mid-spatial frequency wavefront deformations. Here, we describe the design and performance of a 90 mm × 90 mm aperture, liquid-cooled Nd:phosphate split-slab laser amplifier pumped by flash-lamps. The performance of the system is evaluated in terms of wavefront aberration and gain at repetition rates down to 1 shot per minute. The results show that this single cooled split-slab system exhibits low wavefront distortions in the medium to large period range, compatible with a focus on target, and despite the use of liquid coolant traversed by both pump and amplified wavelengths. This makes it a potential candidate for applications in large high-energy laser facilities.
This paper presents the development and experimental utilization of a synchronized off-harmonic laser system designed as a probe for ultra-intense laser–plasma interaction experiments. The system exhibits a novel seed-generation design, allowing for a variable pulse duration spanning over more than three orders of magnitude, from 3.45 picoseconds to 10 nanoseconds. This makes it suitable for various plasma diagnostics and visualization techniques. In a side-view configuration, the laser was employed for interferometry and streaked shadowgraphy of a laser-induced plasma while successfully suppressing the self-emission background of the laser–plasma interaction, resulting in a signal-to-self-emission ratio of 110 for this setup. These properties enable the probe to yield valuable insights into the plasma dynamics and interactions at the PHELIX facility and to be deployed at various laser facilities due to its easy-to-implement design.
The scaling law for the horizontal length scale $\ell$ relative to the domain height $L$, originating from the linear theory of quasi-static magnetoconvection, $\ell /L \sim Q^{-1/6}$, has been verified through two-dimensional (2-D) direct numerical simulation (DNS), particularly at high values of the Chandrasekhar number ($Q$). This relationship remains valid within a specific flow regime characterized by columnar structures aligned with the magnetic field. Expanding upon the $Q$-dependence of the horizontal length scale, we have derived scaling laws for the Nusselt number ($Nu$) and the Reynolds number ($Re$) as functions of the driving forces (Rayleigh number ($Ra$) and $Q$) in quasi-static magnetoconvection influenced by a strong magnetic field. These scaling relations, $Nu \sim Ra/Q$ and $Re \sim Ra Q^{-5/6}$, have been successfully validated using 2-D DNS data spanning a wide range of five decades in $Q$, ranging from $10^5$ to $10^9$. The successful validation of the relations at large $Q$ values, combined with our theoretical analysis of dissipation rates and the incorporation of the horizontal length scale's influence on scaling behaviour, presents a valid approach for deriving scaling laws under various conditions.
We analytically derive an amplitude equation for the weakly nonlinear evolution of the linearly most amplified response of a non-normal dynamical system. The development generalizes the method proposed in Ducimetière et al. (J. Fluid Mech., vol. 947, 2022, A43), in that the base flow now arbitrarily depends on time, and the operator exponential formalism for the evolution of the perturbation is not used. Applied to the two-dimensional Lamb–Oseen vortex, the amplitude equation successfully predicts the nonlinearities to weaken or reinforce the transient gain in the weakly nonlinear regime. In particular, the minimum amplitude of the linear optimal initial perturbation required for the amplitude equation to lose a solution, interpreted as the flow experiencing a bypass (subcritical) transition, is found to decay as a power law with the Reynolds number. Although with a different exponent, this is recovered in direct numerical simulations, showing a transition towards a tripolar state. The simplicity of the amplitude equation and the link made with the sensitivity formula permits a physical interpretation of nonlinear effects, in light of existing work on Landau damping and on shear instabilities. The amplitude equation also quantifies the respective contributions of the second harmonic and the spatial mean flow distortion in the nonlinear modification of the gain.
The spatial relationship between turbulent and particle concentration structures is investigated based on the turbulent velocity and particle concentration data obtained synchronously at the Qingtu Lake Observation Array site. In addition to the observation of particle concentration structures that contain not only large-scale coherence but also significant energy in the high-Reynolds-number atmospheric surface layer (ASL), the scale of turbulent motions that have the most significant coherence with particle concentration is found to follow a 1/2 power scaling law with the local height and ASL thickness. Moreover, large-scale turbulent velocity fluctuations have a significant amplitude modulation effect on particle concentration fluctuations, but the modulating influence is different for small dust particles and large saltating particles. Based on the interphase amplitude modulation, there exists a particle–turbulence structure phase difference that varies with height, which further makes the structure inclination angle of the particle concentration larger than that of the turbulence. In this scenario, a conceptual model reflecting the relationship between the two is proposed, and a quantitative formulation is further derived and found to be in good agreement with the experimental results. These findings and the proposed model contribute insights into particle–turbulence interactions, thereby providing theoretical support for a unified model of turbulence dynamics and particle kinematics.
We develop a high-fidelity multi-physics model and, by using it, study the energy conversion process of a piezohydroelastic flag. Instead of a regular flag with a clamped upstream leading edge, we use an inverted flag so as to make the best of fluid elastic instability for energy harvesting. Moreover, different from many previous studies where a resistor–capacitor (RC) circuit is usually used, we adopt a resistor–inductor–capacitor (RLC) circuit for electricity generation. The influences of several key parameters associated with fluid, structure and electric dynamics are studied. Significantly different response modes are identified, among which the symmetric- and asymmetric-flutter modes are most suitable for sustainable energy harvesting, both emerging with moderate bending stiffness. If only deploying the RC circuit, increasing the resistance makes the flag more stable. By adding an inductor to turn the RC circuit into an RLC one, we observe the occurrence of ‘lock-in’ between the flag frequency and the circuit frequency as first reported on a regular flag by Xia et al. (Phys. Rev. Appl., vol. 3, 2015, 014009). This phenomenon can significantly enhance the energy output, but it only happens when the circuit resistance is sufficiently large. From a derivation based on dynamic mode decomposition analysis, we further identify an optimal condition for maximizing the energy output, which can serve as a guideline to determine whether deploying an inductor can boost the performance, and, if yes, the required inductance. The findings from this study can better guide the design of flow-induced-vibration-based piezoelectric energy harvesters for microelectronic devices.