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In this work, we studied the broadband temporal and spectral properties of the flat-spectrum radio quasar Ton 599. We collected the long-term data from January 2019 to August 2024 when the source was in a long flaring episode. We used the Bayesian block methodology to identify the various flux states, including three flares. The broadband fractional variability is estimated during two flaring states. The F$_{\text{var}}$ variation with respect to frequency shows a nearly double hump structure similar to broadband SED. The power spectral density shows a pink-noise kind of stochastic variability in the light curve, and we do not see any break in the power spectrum, suggesting a much longer characteristic timescale is involved in gamma-ray variability. The flux distribution is well-fitted with a double log-normal flux distribution, suggesting the variability of non-linear in nature. The gamma-ray, optical, and X-ray emissions were found to be highly correlated with a zero time lag, suggesting a co-spatial origin of their emissions. We used the one-zone leptonic model to reproduce the broadband spectrum in the energy range from the IR to very high-energy gamma rays. The increase in the magnetic field and the Doppler factor were found to be the main causes for high flux states. The XMM-Newton spectra taken during one of the flaring durations exhibit a signature of thermal black body emission from the accretion disc, suggesting a possible disc-jet coupling. This has also been indicated by the gamma-ray flux distribution, which shows the distribution as non-linear in nature, which is mostly seen in galactic X-ray binaries or active galactic nuclei, where the accretion disc dominates the emission.
This study explores an interesting fluid–structure interaction scenario: the flow past a flexible filament fixed at two ends. The dynamic performance of the filament under various inclination angles ($\theta$) was numerically investigated using the immersed boundary method. The motion of the filament in the $\theta$–$Lr$ space was categorised into three flapping modes and two stationary modes, where $Lr$ is the ratio of filament length to the distance between its two ends. The flow fields for each mode and their transitions were introduced. A more in-depth analysis was carried out for flapping at a large angle (FLA mode), which is widely present in the $\theta$–$Lr$ space. The maximum width $W$ of the time-averaged shape of the filament has been shown to strongly correlate with the flapping frequency. After non-dimensionalising based on $W$, the flapping frequency shows little variation across different $Lr$ and $\theta$. Moreover, two types of lift variation process were also identified. Finally, the total lift, drag and lift-to-drag ratio of the system were studied. Short filaments, such as those with $Lr\leqslant 1.5$, were shown to significantly increase lift and the lift-to-drag ratio over a wide range of $\theta$ compared with a rigid plate. Flow field analysis concluded that the increases in pressure difference on both sides of the filament, along with the upper part of the flexible filament having a normal direction closer to the $y$ direction, were the primary reasons for the increase in lift and lift-to-drag ratio. This study can provide some guidance for the potential applications of flexible structures.
This chapter presents the classical Penrose singularity theorem. The main ingredients of the proof concern, on the one hand, the caussal structure of a globally hyperbolic spacetime, and on the other, differential geometry techniques involving Jacobi fields together with the Riccati and Raychaudhuri equations.
The stability characteristics of a Mach $5.35$ boundary-layer flow over a flat plate with parametrised two-dimensional sinusoidal surface roughness are investigated. The investigation involves varying the roughness height from $10\,\%$ to $44\,\%$ of the boundary-layer thickness and exploring wavelengths ranging between $0.44$ and $3.56$ times the dominant second-mode wavelength in the region. The introduction of surface roughness leads to notable variations in the mean flow, resulting in separation behind the roughness elements and the propagation of local compression and expansion waves into the free stream. Stability investigations involved the utilisation of wave packet tracking in a linear disturbance simulation (LDS) framework and linear stability theory. The findings revealed significant effects on Mack modes including a reduction in frequency corresponding to maximum amplification with increased roughness height. Proper scaling of the dominant wavelength facilitates a collapse of the growth rate data. In contrast to the commonly reported stabilisation effects for roughness wavelengths significantly larger than the instability mode’s wavelength, the findings primarily revealed destabilisation compared with the smooth-wall case, except for cases with very small roughness wavelengths and large amplitudes approaching the threshold of being classified as porous media. The LDS findings depicted lobed wall pressure amplitude plots, indicating potential undiscovered instability mechanisms or differences compared with the smooth wall. A detailed stability analysis elucidates these LDS findings, establishing a connection between the lobed amplitude structures and substantial changes in local stability characteristics, along with the emergence of Mack’s first, second and third modes.
Chapter 11 delves into the manipulation of quantum resources, the core aspect of quantum resource theories that explore the transformation and conversion of quantum states within a given resource theory framework. The chapter introduces the generalized asymptotic equipartition property and the generalized quantum Stein’s lemma, both foundational to understanding the asymptotic behavior of quantum resources. These concepts pave the way for discussing the uniqueness of the Umegaki relative entropy in quantifying the efficiency of resource conversion processes. Furthermore, the text explores asymptotic interconversions, detailing the conditions and limits for converting one resource into another when multiple copies of quantum states are considered. This analysis is pivotal for establishing the reversible exchange rates between different resources in the asymptotic limit. By providing a comprehensive overview of resource manipulation strategies, the chapter equips readers with the theoretical tools needed for advanced study and research in quantum resource theories, emphasizing both the single-shot and asymptotic domains.
Minkowskian geometry provides a mathematical model of spacetime that resolves a number of perplexing issues that had arisen in physics by the dawn of the twentieth century. The model leads to surprising predictions for physics, which have been confirmed experimentally. In the chapter we review several well-known features of Minkowski spacetime, including Lorentz transformations, time dilation and Lorentz contraction, as well as its conformal compactification.
Chapter 10 delves into the quantification of quantum resources, an essential aspect of quantum resource theories that determines the value of quantum states for specific applications. It begins by defining resource measures and investigating their fundamental properties such as monotonicity under free operations and convexity. The chapter discusses distance-based resource measures, which quantify how far a given quantum state is from the set of free states. Such measures often utilize divergences and metrics explored in earlier chapters. Techniques to compute the relative entropy of a resource are also covered.
To refine resource measures, the chapter introduces the concept of smoothing, which considers small deviations from the ideal state to make the measures more robust against perturbations. This approach is crucial in single-shot scenarios where finite resources are available. Furthermore, the chapter examines resource monotones and support functions, offering a comprehensive framework for the theoretical and practical assessment of quantum resources.
Parametric oscillations of an interface separating two fluid phases create nonlinear surface waves, called Faraday waves, which organise into simple patterns, such as squares and hexagons, as well as complex structures, such as double hexagonal and superlattice patterns. In this work, we study the influence of surfactant-induced Marangoni stresses on the formation and transition of Faraday-wave patterns. We use a control parameter, $B$, that assesses the relative importance of Marangoni stresses as compared with the surface-wave dynamics. Our results show that the threshold acceleration required to destabilise a surfactant-covered interface through vibration increases with increasing $B$. For a surfactant-free interface, a square-wave pattern is observed. As $B$ is incremented, we report transitions from squares to asymmetric squares, weakly wavy stripes and ultimately to ridges and hills. These hills are a consequence of the bidirectional Marangoni stresses at the neck of the ridges. The mechanisms underlying the pattern transitions and the formation of exotic ridges and hills are discussed.
Chapter 7 discusses quantum conditional entropy, extending the concept of conditional majorization and introducing the notion of negative quantum conditional entropy. The chapter starts with the basic definition of conditional entropy, exploring its key properties like monotonicity and additivity. It further delves into the concepts of conditional min- and max-entropies, emphasizing their roles in quantifying uncertainty in quantum states and their operational significance in quantum information theory.
The text presents conditional entropy as a measure sensitive to the effects of entanglement, showing that negative conditional entropy is a distinctive feature of quantum systems, contrasting with the classical domain where entropy values are nonnegative. This negativity is particularly pronounced in the context of maximally entangled states and is connected to the fundamental differences between classical and quantum information processing. Moreover, the chapter includes theorems and exercises to solidify understanding, like the invariance of conditional entropy under local isometric channels and its reduction to entropy for product states. It concludes by underscoring the inevitability of negative conditional entropy in quantum systems, a topic of both theoretical and practical importance in the quantum domain.
Chapter 8 explores the asymptotic regime of quantum information processing, beginning with quantum typicality, which illustrates the convergence of quantum states toward a typical form with increasing copies. This leads to the asymptotic equipartition property (AEP), indicating that with a high number of copies, probability vectors become uniformly distributed. The method of types is introduced next, a tool from classical information theory that classifies sequences based on their statistical properties. This is crucial for understanding the behavior of large quantum systems and has implications for quantum data compression. Advancing to quantum hypothesis testing, the chapter outlines efficient strategies for distinguishing between two quantum states through repeated measurements. Central to this is the Quantum Stein’s lemma, which asserts the exponential decline in the error probability of hypothesis testing as the sample size of quantum systems increases. The chapter highlights the deep interplay between typicality, statistical methods, and hypothesis testing, laying the groundwork for asymptotic interconversion of quantum resources.
Chapter 16, centered on the resource theory of nonuniformity, serves as an essential precursor to discussions on thermodynamics as a resource theory. It presents nonuniformity as a fundamental quantum resource, using it as a toy model to prepare for more complex thermodynamic concepts. In this model, free states are considered to be maximally mixed states, analogous to Gibbs states with a trivial Hamiltonian, providing a simplified context for exploring quantum thermodynamics. The chapter carefully outlines how nonuniformity is quantified, offering closed formulas for the conversion distance, nonuniformity cost, and distillable nonuniformity. These measures are explored both in the single-shot and the asymptotic domains. The availability of closed formulas makes this model particularly insightful, demonstrating clear, quantifiable relationships between various measures of nonuniformity.
We present numerical analysis of the lateral movement of a spherical capsule in the steady and pulsatile channel flow of a Newtonian fluid for a wide range of oscillatory frequencies. Each capsule membrane satisfying strain-hardening characteristics is simulated for different Reynolds numbers $Re$ and capillary numbers $Ca$. Our numerical results showed that capsules with high $Ca$ exhibit axial focusing at finite $Re$ similarly to the inertialess case. We observe that the speed of the axial focusing can be substantially accelerated by making the driving pressure gradient oscillate in time. We also confirm the existence of an optimal frequency that maximises the speed of axial focusing, which remains the same found in the absence of inertia. For relatively low $Ca$, however, the capsule exhibits off-centre focusing, resulting in various equilibrium radial positions depending on $Re$. Our numerical results further clarify the existence of a specific $Re$ for which the effect of the flow pulsation to the equilibrium radial position is maximum. The roles of channel size on the lateral movements of the capsule are also addressed. Throughout our analyses, we have quantified the radial position of the capsule in a tube based on an empirical expression. Given that the speed of inertial focusing can be controlled by the oscillatory frequency, the results obtained here can be used for label-free cell alignment/sorting/separation techniques, e.g. for circulating tumour cells in cancer patients or precious haematopoietic cells such as colony-forming cells.
We simulate the dynamics, including laser cooling, of three-dimensional (3-D) ion crystals confined in a Penning trap using a newly developed molecular dynamics-like code. The numerical integration of the ions’ equations of motion is accelerated using the fast multipole method to calculate the Coulomb interaction between ions, which allows us to efficiently study large ion crystals with thousands of ions. In particular, we show that the simulation time scales linearly with ion number, rather than with the square of the ion number. By treating the ions’ absorption of photons as a Poisson process, we simulate individual photon scattering events to study laser cooling of 3-D ellipsoidal ion crystals. Initial simulations suggest that these crystals can be efficiently cooled to ultracold temperatures, aided by the mixing of the easily cooled axial motional modes with the low frequency planar modes. In our simulations of a spherical crystal of 1000 ions, the planar kinetic energy is cooled to several millikelvin in a few milliseconds while the axial kinetic energy and total potential energy are cooled even further. This suggests that 3-D ion crystals could be well suited as platforms for future quantum science experiments.
Coherent combining of several low-energy few-cycle beams offers a reliable and feasible approach to producing few-cycle laser pulses with energies exceeding the multi-joule level. However, time synchronization and carrier-envelope phase difference (ΔCEP) between pulses significantly affect the temporal waveform and intensity of the combined pulse, requiring precise measurement and control. Here, we propose a concise optical method based on the phase retrieval of spectral interference and quadratic function symmetry axis fitting to simultaneously measure the time synchronization and ΔCEP between few-cycle pulses. The control precision of our coherent beam combining system can achieve a time delay stability within 42 as and ΔCEP measurement precision of 40 mrad, enabling a maximum combining efficiency of 98.5%. This method can effectively improve the performance and stability of coherent beam combining systems for few-cycle lasers, which will facilitate the obtaining of high-quality few-cycle lasers with high energy.
We presented an attosecond-precision timing detector based on linear optics. The minimum measurement floor is 1×10–10 fs2/Hz with only 1 mW input optical power. With this novel technique, the residual dispersion of a 5.2 km fiber link is characterized and precisely compensated. Finally, a comprehensive feedback model has been developed to analyze the noise coupling in a long-distance link stabilization system. The simulation results demonstrate an out-of-loop jitter of merely 359 as, integrated at [1 Hz, 1 MHz], at 1 mW input power per photodetector of our timing detector. Remarkably, the system is capable of maintaining sub-femtosecond precision even at optical power levels as low as 240 nW (for a 5.2 km link length), or link lengths as long as 20 km (with 1 μW optical power), respectively.
Spectra have been obtained with the multi-fibre instrument 2dF on the Anglo-Australian Telescope of 89 candidate main sequence stars in the globular cluster M55 (NGC 6809). Radial velocities and Gaia proper motions confirm 72 candidates as cluster members. Among these stars one stands out as having a substantially stronger G-band (CH) than the rest of the member sample. The star is a dwarf carbon star that most likely acquired the high carbon abundance ([C/Fe] $\approx$ 1.2 $\pm$ 0.2) via mass transfer from a $\sim$1$-$3 M$_{\odot}$ binary companion (now a white dwarf) during its AGB phase of evolution. Interestingly, M55 also contains a CH-star that lies on the cluster red giant branch – the low central concentration/low density of this cluster presumably allows the survival of binaries that would otherwise be disrupted in denser systems. The existence of carbon stars in six other globular clusters is consistent with this hypothesis, while the origin of the carbon-enhanced star in M15 (NGC 7078) is attributed to a merger process similar to that proposed for the origin of the carbon-rich R stars.
Brown dwarfs are failed stars with very low mass (13–75 Jupiter mass) and an effective temperature lower than 2 500 K. Their mass range is between Jupiter and red dwarfs. Thus, they play a key role in understanding the gap in the mass function between stars and planets. However, due to their faint nature, previous searches are inevitably limited to the solar neighbourhood (20 pc). To improve our knowledge of the low mass part of the initial stellar mass function and the star formation history of the Milky Way, it is crucial to find more distant brown dwarfs. Using James Webb Space Telescope (JWST) COSMOS-Web data, this study seeks to enhance our comprehension of the physical characteristics of brown dwarfs situated at a distance of kpc scale. The exceptional sensitivity of the JWST enables the detection of brown dwarfs that are up to 100 times more distant than those discovered in the earlier all-sky infrared surveys. The large area coverage of the JWST COSMOS-Web survey allows us to find more distant brown dwarfs than earlier JWST studies with smaller area coverages. To capture prominent water absorption features around 2.7 ${\unicode{x03BC}}$m, we apply two colour criteria, $\text{F115W}-\text{F277W}+1\lt\text{F277W}-\text{F444W}$ and $\text{F277W}-\text{F444W}\gt\,0.9$. We then select point sources by CLASS_STAR, FLUX_RADIUS, and SPREAD_MODEL criteria. Faint sources are visually checked to exclude possibly extended sources. We conduct SED fitting and MCMC simulations to determine their physical properties and associated uncertainties. Our search reveals 25 T-dwarf candidates and 2 Y-dwarf candidates, more than any previous JWST brown dwarf searches. They are located from 0.3 to 4 kpc away from the Earth. The spatial number density of 900–1 050 K dwarf is $(2.0\pm0.9) \times10^{-6}\text{ pc}^{-3}$, 1 050–1 200 K dwarf is $(1.2\pm0.7) \times10^{-6}\text{ pc}^{-3}$, and 1 200–1 350 K dwarf is $(4.4\pm1.3) \times10^{-6}\text{ pc}^{-3}$. The cumulative number count of our brown dwarf candidates is consistent with the prediction from a standard double exponential model. Three of our brown dwarf candidates were detected by HST, with transverse velocities $12\pm5$, $12\pm4$, and $17\pm6$ km s$^{-1}$. Along with earlier studies, the JWST has opened a new window of brown dwarf research in the Milky Way thick disk and halo.