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The authors study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. They prove that for sufficiently regular initial data of size $\\epsilon \\leq c_0\\mathbf {Re}^-1$ for some universal $c_0 > 0$, the solution is global, remains within $O(c_0)$ of the Couette flow in $L^2$, and returns to the Couette flow as $t \\rightarrow \\infty $. For times $t \\gtrsim \\mathbf {Re}^1/3$, the streamwise dependence is damped by a mixing-enhanced dissipation effect and the solution is rapidly attracted to the class of \"2.5 dimensional\" streamwise-independent solutions referred to as streaks.

The authors prove the existence and the linear stability of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable x) of a 2-dimensional ocean with infinite depth under the action of gravity and surface tension. Such an existence result is obtained for all the values of the surface tension belonging to a Borel set of asymptotically full Lebesgue measure.

Resonances and continuum states of super(4)He are studied using correlated Gaussians. Applicability of the square-integrable functions is tested with use of a complex scaling method. All the known levels of super(4)He up to the excitation energy of 26 MeV are well understood with a realistic nucleon-nucleon potential. The importance of the tensor force is stressed. Strength functions for isoscalar monopole and spin-dipole tensor operators are investigated.

In this paper, we show that, for each p > 1, there are continuum many Borel equivalence relations between a,, super( omega ) sub(1) and a,, super( omega ) sub( )pordered by less than or equal to B which are pairwise Borel incomparable.

Aerial manipulators have seen a rapid uptake for multiple applications, including inspection tasks and aerial robot–human interaction in building and construction. Whilst single degree of freedom (DoF) and multiple DoF rigid link manipulators (RLMs) have been extensively discussed in the aerial manipulation literature, continuum manipulators (CMs), often referred to as continuum robots (CRs), have not received the same attention. This survey seeks to summarise the existing works on continuum manipulator-based aerial manipulation research and the most prevalent designs of continuous backbone tendon-driven continuum robots (TDCRs) and multi-link backbone TDCRs, thereby providing a structured set of guidelines for fabricating continuum robots for aerial manipulation. With a history spanning over three decades, dominated by medical applications, CRs are now increasingly being used in other domains like industrial machinery and system inspection, also gaining popularity in aerial manipulation. Fuelled by diverse applications and their associated challenges, researchers have proposed a plethora of design solutions, primarily falling within the realms of concentric tube (CT) designs or tendon-driven designs. Leveraging research works published in the past decade, we place emphasis on the preparation of backbones, support structures, tendons, stiffness control, test procedures, and error considerations. We also present our perspectives and recommendations addressing essential design and fabrication aspects of TDCRs in the context of aerial manipulation, and provide valuable guidance for future research and development endeavours in this dynamic field.

It is known that graphene exhibits natural ripples with characteristic lengths of around 10 nm. But when it is stretched across nanometre-scale trenches that form in a reconstructed copper surface, it develops even tighter corrugations that cannot be explained by continuum theory. Understanding how the mechanical behaviour of materials deviates at the nanoscale from the macroscopically established concepts is a key challenge of particular importance for graphene, given the complex interplay between its nanoscale morphology and electronic properties 1 , 2 , 3 , 4 , 5 . In this work, the (sub)nanometre-wavelength periodic rippling of suspended graphene nanomembranes has been realized by thermal strain engineering and investigated using scanning tunnelling microscopy. This allows us to explore the rippling of a crystalline membrane with wavelengths comparable to its lattice constant. The observed nanorippling mode violates the predictions of the continuum model 6 , and evidences the breakdown of the plate idealization 7 of the graphene monolayer. Nevertheless, microscopic simulations based on a quantum mechanical description of the chemical binding accurately describe the observed rippling mode and elucidate the origin of the continuum model breakdown. Spatially resolved tunnelling spectroscopy measurements indicate a substantial influence of the nanoripples on the local electronic structure of graphene and reveal the formation of one-dimensional electronic superlattices.

In this paper, we show the existence of the first non trivial family of classical global solutions of the inviscid surface quasi-geostrophic equation.

AbstractAnalysis of the mechanical behavior of nanostructures has been very challenging. Surface energy and nonlocal elasticity of materials have been incorporated into the traditional continuum analysis to create modified continuum mechanics models. This paper reviews recent advancements in the applications of such modified continuum models in nanostructures such as nanotubes, nanowires, nanobeams, graphenes, and nanoplates. A variety of models for these nanostructures under static and dynamic loadings are mentioned and reviewed. Applications of surface energy and nonlocal elasticity in analysis of piezoelectric nanomaterials are also mentioned. This paper provides a comprehensive introduction of the development of this area and inspires further applications of modified continuum models in modeling nanomaterials and nanostructures.Graphic abstract

The Reionization Era Bright Emission Line Survey (REBELS) is a cycle-7 ALMA Large Program (LP) that is identifying and performing a first characterization of many of the most luminous star-forming galaxies known in the z > 6.5 universe. REBELS is providing this probe by systematically scanning 40 of the brightest UV-selected galaxies identified over a 7 deg2 area for bright [C ii]158 μm and [O iii]88 μm lines and dust-continuum emission. Selection of the 40 REBELS targets was done by combining our own and other photometric selections, each of which is subject to extensive vetting using three completely independent sets of photometry and template-fitting codes. Building on the observational strategy deployed in two pilot programs, we are increasing the number of massive interstellar medium (ISM) reservoirs known at z > 6.5 by ∼4–5× to >30. In this manuscript, we motivate the observational strategy deployed in the REBELS program and present initial results. Based on the first-year observations, 18 highly significant ≥ 7σ [C ii]158 μm lines have already been discovered, the bulk of which (13/18) also show ≥3.3σ dust-continuum emission. These newly discovered lines more than triple the number of bright ISM-cooling lines known in the z > 6.5 universe, such that the number of ALMA-derived redshifts at z > 6.5 rival Lyα discoveries. An analysis of the completeness of our search results versus star formation rate (SFR) suggests an ∼79% efficiency in scanning for [C ii]158 μm when the SFRUV+IR is >28 M ⊙ yr−1. These new LP results further demonstrate ALMA’s efficiency as a “redshift machine,” particularly in the Epoch of Reionization.

A superconducting artificial atom coupled to a 1D waveguide tests the limits of light–matter interaction in an unexplored coupling regime, which may enable new perspectives for quantum technologies. The study of light–matter interaction has led to important advances in quantum optics and enabled numerous technologies. Over recent decades, progress has been made in increasing the strength of this interaction at the single-photon level. More recently, a major achievement has been the demonstration of the so-called strong coupling regime 1 , 2 , a key advancement enabling progress in quantum information science. Here, we demonstrate light–matter interaction over an order of magnitude stronger than previously reported, reaching the nonperturbative regime of ultrastrong coupling (USC). We achieve this using a superconducting artificial atom tunably coupled to the electromagnetic continuum of a one-dimensional waveguide. For the largest coupling, the spontaneous emission rate of the atom exceeds its transition frequency. In this USC regime, the description of atom and light as distinct entities breaks down, and a new description in terms of hybrid states is required 3 , 4 . Beyond light–matter interaction itself, the tunability of our system makes it a promising tool to study a number of important physical systems, such as the well-known spin-boson 5 and Kondo models 6 .