20,689 research outputs found

    Heat kernel-based p-energy norms on metric measure spaces

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    We focus on heat kernel-based p-energy norms (1<p<\infty) on bounded and unbounded metric measure spaces, in particular, weak-monotonicity properties for different types of energies. Such properties are key to related studies, under which we generalise the convergence result of Bourgain-Brezis-Mironescu (BBM) for p\neq2. We establish the equivalence of various p-energy norms and weak-monotonicity properties when there admits a heat kernel satisfying the two-sided estimates. Using these equivalences, we verify various weak-monotonicity properties on nested fractals and their blowups. Immediate consequences are that, many classical results on p-energy norms hold for such bounded and unbounded fractals, including the BBM convergence and Gagliardo-Nirenberg inequality.Comment: 39 pages with 1 figur

    Atypical developmental trajectories of white matter microstructure in prenatal alcohol exposure: Preliminary evidence from neurite orientation dispersion and density imaging

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    IntroductionFetal alcohol spectrum disorder (FASD), a life-long condition resulting from prenatal alcohol exposure (PAE), is associated with structural brain anomalies and neurobehavioral differences. Evidence from longitudinal neuroimaging suggest trajectories of white matter microstructure maturation are atypical in PAE. We aimed to further characterize longitudinal trajectories of developmental white matter microstructure change in children and adolescents with PAE compared to typically-developing Controls using diffusion-weighted Neurite Orientation Dispersion and Density Imaging (NODDI).Materials and methodsParticipants: Youth with PAE (n = 34) and typically-developing Controls (n = 31) ages 8–17 years at enrollment. Participants underwent formal evaluation of growth and facial dysmorphology. Participants also completed two study visits (17 months apart on average), both of which involved cognitive testing and an MRI scan (data collected on a Siemens Prisma 3 T scanner). Age-related changes in the orientation dispersion index (ODI) and the neurite density index (NDI) were examined across five corpus callosum (CC) regions defined by tractography.ResultsWhile linear trajectories suggested similar overall microstructural integrity in PAE and Controls, analyses of symmetrized percent change (SPC) indicated group differences in the timing and magnitude of age-related increases in ODI (indexing the bending and fanning of axons) in the central region of the CC, with PAE participants demonstrating atypically steep increases in dispersion with age compared to Controls. Participants with PAE also demonstrated greater increases in ODI in the mid posterior CC (trend-level group difference). In addition, SPC in ODI and NDI was differentially correlated with executive function performance for PAE participants and Controls, suggesting an atypical relationship between white matter microstructure maturation and cognitive function in PAE.DiscussionPreliminary findings suggest subtle atypicality in the timing and magnitude of age-related white matter microstructure maturation in PAE compared to typically-developing Controls. These findings add to the existing literature on neurodevelopmental trajectories in PAE and suggest that advanced biophysical diffusion modeling (NODDI) may be sensitive to biologically-meaningful microstructural changes in the CC that are disrupted by PAE. Findings of atypical brain maturation-behavior relationships in PAE highlight the need for further study. Further longitudinal research aimed at characterizing white matter neurodevelopmental trajectories in PAE will be important

    Full trajectory optimizing operator inference for reduced-order modeling using differentiable programming

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    Accurate and inexpensive Reduced Order Models (ROMs) for forecasting turbulent flows can facilitate rapid design iterations and thus prove critical for predictive control in engineering problems. Galerkin projection based Reduced Order Models (GP-ROMs), derived by projecting the Navier-Stokes equations on a truncated Proper Orthogonal Decomposition (POD) basis, are popular because of their low computational costs and theoretical foundations. However, the accuracy of traditional GP-ROMs degrades over long time prediction horizons. To address this issue, we extend the recently proposed Neural Galerkin Projection (NeuralGP) data driven framework to compressibility-dominated transonic flow, considering a prototypical problem of a buffeting NACA0012 airfoil governed by the full Navier-Stokes equations. The algorithm maintains the form of the ROM-ODE obtained from the Galerkin projection; however coefficients are learned directly from the data using gradient descent facilitated by differentiable programming. This blends the strengths of the physics driven GP-ROM and purely data driven neural network-based techniques, resulting in a computationally cheaper model that is easier to interpret. We show that the NeuralGP method minimizes a more rigorous full trajectory error norm compared to a linearized error definition optimized by the calibration procedure. We also find that while both procedures stabilize the ROM by displacing the eigenvalues of the linear dynamics matrix of the ROM-ODE to the complex left half-plane, the NeuralGP algorithm adds more dissipation to the trailing POD modes resulting in its better long-term performance. The results presented highlight the superior accuracy of the NeuralGP technique compared to the traditional calibrated GP-ROM method

    Chiral active fluids: Odd viscosity, active turbulence, and directed flows of hydrodynamic microrotors

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    While the number of publications on rotating active matter has rapidly increased in recent years, studies on purely hydrodynamically interacting rotors on the microscale are still rare, especially from the perspective of particle based hydrodynamic simulations. The work presented here targets to fill this gap. By means of high-performance computer simulations, performed in a highly parallelised fashion on graphics processing units, the dynamics of ensembles of up to 70,000 rotating colloids immersed in an explicit mesoscopic solvent consisting out of up to 30 million fluid particles, are investigated. Some of the results presented in this thesis have been worked out in collaboration with experimentalists, such that the theoretical considerations developed in this thesis are supported by experiments, and vice versa. The studied system, modelled in order to resemble the essential physics of the experimentally realisable system, consists out of rotating magnetic colloidal particles, i.e., (micro-)rotors, rotating in sync to an externally applied magnetic field, where the rotors solely interact via hydrodynamic and steric interactions. Overall, the agreement between simulations and experiments is very good, proving that hydrodynamic interactions play a key role in this and related systems. While already an isolated rotating colloid is driven out of equilibrium, only collections of two or more rotors have experimentally shown to be able to convert the rotational energy input into translational dynamics in an orbital rotating fashion. The rotating colloids inject circular flows into the fluid, such that detailed balance is broken, and it is not a priori known whether equilibrium properties of colloids can be extended to isolated rotating colloids. A joint theoretical and experimental analysis of isolated, pairs, and small groups of hydrodynamically interacting rotors is given in chapter 2. While the translational dynamics of isolated rotors effectively resemble the dynamics of non-rotating colloids, the orbital rotation of pairs of rotors can be described with leading order hydrodynamics and a two-dimensional analogy of Faxén’s law is derived. In chapter 3, a homogeneously distributed ensemble of rotors (bulk) as a realisation of a chiral active fluid is studied and it is explicitly shown computationally and experimentally that it carries odd viscosity. The mutual orbital translation of rotors and an increase of the effective solvent viscosity with rotor density lead to a non-monotonous behaviour of the average translational velocity. Meanwhile, the rotor suspension bears a finite osmotic compressibility resulting from the long-ranged nature of hydrody- namic interactions such that rotational and odd stresses are transmitted through the solvent also at small and intermediate rotor densities. Consequently, density inhomogeneities predicted for chiral active fluids with odd viscosity can be found and allow for an explicit measurement of odd viscosity in simulations and experiments. At intermediate densities, the collective dynamics shows the emergence of multi-scale vortices and chaotic motion which is identified as active turbulence with a self-similar power-law decay in the energy spectrum, showing that the injected energy on the rotor scale is transported to larger scales, similar to the inverse energy cascade of clas- sical two-dimensional turbulence. While either odd viscosity or active turbulence have been reported in chiral active matter previously, the system studied here shows that the emergence of both simultaneously is possible resulting from the osmotic compressibility and hydrodynamic mediation of odd and active stresses. The collective dynamics of colloids rotating out of phase, i.e., where a constant torque instead of a constant angular velocity is applied, is shown to be qualitatively very similar. However, at smaller densities, local density inhomogeneities imply position dependent angular velocities of the rotors resulting from inter-rotor friction. While the friction of a quasi-2D layer of active colloids with the substrate is often not easily modifiable in experiments, the incorporation of substrate friction into the simulation models typically implies a considerable increase in computational effort. In chapter 4, a very efficient way of incorporating the friction with a substrate into a two-dimensional multiparticle collision dynamics solvent is introduced, allowing for an explicit investigation of the influences of substrate on active dynamics. For the rotor fluid, it is explicitly shown that the influence of the substrate friction results in a cutoff of the hydrodynamic interaction length, such that the maximum size of the formed vortices is controlled by the substrate friction, also resulting in a cutoff in the energy spectrum, because energy is taken out of the system at the respective length. These findings are in agreement with the experiments. Since active particles in confinement are known to organise in states of collective dynamics, ensembles of rotationally actuated colloids are studied in circular confinement and in the presence of periodic obstacle lattices in chapters 5 and 6, respectively. The results show that the chaotic active turbulent transport of rotors in suspension can be enhanced and guided resulting from edge flows generated at the boundaries, as has recently been reported for a related chiral active system. The consequent collective rotor dynamics can be regarded as a superposition of active turbulent and imposed flows, leading to on average stationary flows. In contrast to the bulk dynamics, the imposed flows inject additional energy into the system on the long length scales, and the same scaling behaviour of the energy spectrum as in bulk is only obtained if the energy injection scales, due to the mutual generation of rotor translational dynamics throughout the system and the edge flows, are well separated. The combination of edge flow and entropic layering at the boundaries leads to oscillating hydrodynamic stresses and consequently to an oscillating vorticity profile. In the presence of odd viscosity, this consequently leads to non-trivial steady-state density modulations at the boundary, resulting from a balance of osmotic pressure and odd stresses. Relevant for the efficient dispersion and mixing of inert particles on the mesoscale by means of active turbulent mixing powered by rotors, a study of the dynamics of a binary mixture consisting out of rotors and passive particles is presented in chapter 7. Because the rotors are not self-propelled, but the translational dynamics is induced by the surrounding rotors, the passive particles, which do not inject further energy into the system, are transported according to the same mechanism as the rotors. The collective dynamics thus resembles the pure rotor bulk dynamics at the respective density of only rotors. However, since no odd stresses act between the passive particles, only mutual rotor interactions lead to odd stresses leading to the accumulation of rotors in the regions of positive vorticity. This density increase is associated with a pressure increase, which balances the odd stresses acting on the rotors. However, the passive particles are only subject to the accumulation induced pressure increase such that these particles are transported into the areas of low rotor concentration, i.e., the regions of negative vorticity. Under conditions of sustained vortex flow, this results in segregation of both particle types. Since local symmetry breaking can convert injected rotational into translational energy, microswimmers can be constructed out of rotor materials when a suitable breaking of symmetry is kept in the vicinity of a rotor. One hypothetical realisation, i.e., a coupled rotor pair consisting out of two rotors of opposite angular velocity and of fixed distance, termed a birotor, are studied in chapter 8. The birotor pumps the fluid into one direction and consequently translates into the opposite direction, and creates a flow field reminiscent of a source doublet, or sliplet flow field. Fixed in space the birotor might be an interesting realisation of a microfluidic pump. The trans- lational dynamics of a birotor can be mapped onto the active Brownian particle model for single swimmers. However, due to the hydrodynamic interactions among the rotors, the birotor ensemble dynamics do not show the emergence of stable motility induced clustering. The reason for this is the flow created by birotor in small aggregates which effectively pushes further arriving birotors away from small aggregates, which eventually are all dispersed by thermal fluctuations

    Global Convergence of SGD On Two Layer Neural Nets

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    In this note we demonstrate provable convergence of SGD to the global minima of appropriately regularized 2\ell_2-empirical risk of depth 22 nets -- for arbitrary data and with any number of gates, if they are using adequately smooth and bounded activations like sigmoid and tanh. We build on the results in [1] and leverage a constant amount of Frobenius norm regularization on the weights, along with sampling of the initial weights from an appropriate distribution. We also give a continuous time SGD convergence result that also applies to smooth unbounded activations like SoftPlus. Our key idea is to show the existence loss functions on constant sized neural nets which are "Villani Functions". [1] Bin Shi, Weijie J. Su, and Michael I. Jordan. On learning rates and schr\"odinger operators, 2020. arXiv:2004.06977Comment: 23 pages, 6 figures. Extended abstract accepted at DeepMath 2022. v2 update: New experiments added in Section 3.2 to study the effect of the regularization value. Statement of Theorem 3.4 about SoftPlus nets has been improve

    Rotational and Dilational Reconstruction in Transition Metal Dichalcogenide Moir\'e Bilayers

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    Lattice reconstruction and corresponding strain accumulation play a key role in defining the electronic structure of two-dimensional moir\'e superlattices, including those of transition metal dichalcogenides (TMDs). Imaging of TMD moir\'es has so far provided a qualitative understanding of this relaxation process in terms of interlayer stacking energy, while models of the underlying deformation mechanisms have relied on simulations. Here, we use interferometric four-dimensional scanning transmission electron microscopy to quantitatively map the mechanical deformations through which reconstruction occurs in small-angle twisted bilayer MoS2 and WSe2/MoS2 heterobilayers. We provide direct evidence that local rotations govern relaxation for twisted homobilayers, while local dilations are prominent in heterobilayers possessing a sufficiently large lattice mismatch. Encapsulation of the moir\'e layers in hBN further localizes and enhances these in-plane reconstruction pathways, suppressing out-of-plane corrugation. We also find that extrinsic uniaxial heterostrain, which introduces a lattice constant difference in twisted homobilayers, leads to accumulation and redistribution of reconstruction strain, demonstrating another route to modify the moir\'e potential.Comment: 27 pages, 5 figure

    Effect of Pulse Shapes on the Weldability of High Conductivity Copper ‎C101 by Nd-YAG Laser

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    يتضمن هذا البحث دراسة تجريبية&nbsp; لتأثير درجة الحرارة لجريان مائعين (الهواء والماء)&nbsp; على الضغط خلال انبوب&nbsp; ( ذو أنحناء&nbsp;&nbsp; ͦ90) على جانبي المنحنى&nbsp;&nbsp; و في المنحنى نفسه. أن هذه&nbsp; الدراسة&nbsp; ذات أهمية لفهم وتحسين العمليات الصناعية التي تنطوي على جريان مائعين. أن التجربة الحالية تتألف&nbsp; من&nbsp; ثلاث&nbsp; اجزاء:&nbsp; أفقي, عمودى, والمسار&nbsp; المنحنى&nbsp; للجريان خلال&nbsp; انبوب&nbsp; مصنوع&nbsp; من مادة (البولي فينيل كلورايد ) ويبلغ قطره الداخلي 68 مم ؛ وأما القسم المنحني من الأنبوب يحتوي على نسبة انحناء نصف القطر الى القطر بمقدار&nbsp; ( R/D) 8.&nbsp; وقد تم&nbsp; أستخدام مجموعة متنوعة من معدلات تدفق المياه التي تراوحت من 18 إلى 42 متر مكعب في الساعة وأما معدلات جريان الهواء فقد تراوحت&nbsp; بين 4 إلى 18 متر مكعب في درجات الحرارة&nbsp; مختلفة ، وقد تم استخدام&nbsp; ستة مجسات ضغط لمراقبة الضغط خلال مدة&nbsp; التجربة . وقد تمت مقارنة النتائج التجريبية&nbsp; لهبوط الضغط&nbsp; التي تم الحصول عليها&nbsp; من التجربة ومقارنتها مع النماذج المنشورة مسبقًا لتقييم نتائج أدائها في التنبؤ بانخفاض الضغط في ظروف انتقال الحرارة ولكن بدون الغليان .بناءً على النتيجة التجريبية ، يزداد الضغط عبر أجزاء&nbsp; التجربة&nbsp; مع زيادة درجة حرارة في الحالة التي لا تهيمن فيها لزوجة السائل على لزوجة الخليط نظرًا لارتفاع معدل تدفق السائل أيضًا ، يكون انخفاض الضغط&nbsp; عبر المنحنى عالياً&nbsp; عندما يكون&nbsp; معدل تدفق الهواء قليلاً مقارنة بمعدل تدفق هواء ألعالي&nbsp; عند ثبوت معدل تدفق الماء و عند درجة حرارة الغرفة ، و تنعكس الحالة بزيادة درجة حرارة الخليط&nbsp; حيث أن أنخفاض الضغط&nbsp; عند معدل تدفق الهواء العالي . تكون أعلى&nbsp; بالمقارنة مع معدل&nbsp;&nbsp; تدفق الهواء المنخفض .وكشفت الدراسة بان الحرارة تزيد الضغط و هبوط&nbsp; الضغط عند المنحنى لجريان مائعين عند معدلات تدفق الهواء العالية بثبوت معدل جريان الماء .The current work presents an experimental demonstration of the impact of two-phase flow mixture (water and air) temperature on the pressure across the bend's upstream and downstream sides as well as the bend itself, as it is crucial for understanding and optimizing industrial processes. The test section in this study comprises a horizontal section, a vertical section, and a bend section, all made of PVC-U material with an inner diameter of 68 mm. The bend section has a curvature radius to diameter ratio (R/D) of 8. Pressure was monitored using six sensors over the test length for a range of water flow rates 18 to 42 and air flow rates 4 to 18 &nbsp;at various mixture temperatures. The obtained experimental pressure drop results were also compared to already previously published models to evaluate their performance in predicting pressure drop in conditions with heat transfer but no boiling. Based on the experimental result, the pressure across the test section increases with increasing temperature in a situation in which mixture viscosity is not dominated by liquid viscosity due to its high volume flow rate. Also, the pressure drop across the bend is higher at a lower air flow rate compared to a higher air flow rate at the same water flow rate and mixture temperature at room temperature, but as the mixture temperature increases, the pressure drop at a high air flow rate will be higher compared to a low air flow rate

    Modelling uncertainties for measurements of the H → γγ Channel with the ATLAS Detector at the LHC

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    The Higgs boson to diphoton (H → γγ) branching ratio is only 0.227 %, but this final state has yielded some of the most precise measurements of the particle. As measurements of the Higgs boson become increasingly precise, greater import is placed on the factors that constitute the uncertainty. Reducing the effects of these uncertainties requires an understanding of their causes. The research presented in this thesis aims to illuminate how uncertainties on simulation modelling are determined and proffers novel techniques in deriving them. The upgrade of the FastCaloSim tool is described, used for simulating events in the ATLAS calorimeter at a rate far exceeding the nominal detector simulation, Geant4. The integration of a method that allows the toolbox to emulate the accordion geometry of the liquid argon calorimeters is detailed. This tool allows for the production of larger samples while using significantly fewer computing resources. A measurement of the total Higgs boson production cross-section multiplied by the diphoton branching ratio (σ × Bγγ) is presented, where this value was determined to be (σ × Bγγ)obs = 127 ± 7 (stat.) ± 7 (syst.) fb, within agreement with the Standard Model prediction. The signal and background shape modelling is described, and the contribution of the background modelling uncertainty to the total uncertainty ranges from 18–2.4 %, depending on the Higgs boson production mechanism. A method for estimating the number of events in a Monte Carlo background sample required to model the shape is detailed. It was found that the size of the nominal γγ background events sample required a multiplicative increase by a factor of 3.60 to adequately model the background with a confidence level of 68 %, or a factor of 7.20 for a confidence level of 95 %. Based on this estimate, 0.5 billion additional simulated events were produced, substantially reducing the background modelling uncertainty. A technique is detailed for emulating the effects of Monte Carlo event generator differences using multivariate reweighting. The technique is used to estimate the event generator uncertainty on the signal modelling of tHqb events, improving the reliability of estimating the tHqb production cross-section. Then this multivariate reweighting technique is used to estimate the generator modelling uncertainties on background V γγ samples for the first time. The estimated uncertainties were found to be covered by the currently assumed background modelling uncertainty

    Visualisation of Fundamental Movement Skills (FMS): An Iterative Process Using an Overarm Throw

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    Fundamental Movement Skills (FMS) are precursor gross motor skills to more complex or specialised skills and are recognised as important indicators of physical competence, a key component of physical literacy. FMS are predominantly assessed using pre-defined manual methodologies, most commonly the various iterations of the Test of Gross Motor Development. However, such assessments are time-consuming and often require a minimum basic level of training to conduct. Therefore, the overall aim of this thesis was to utilise accelerometry to develop a visualisation concept as part of a feasibility study to support the learning and assessment of FMS, by reducing subjectivity and the overall time taken to conduct a gross motor skill assessment. The overarm throw, an important fundamental movement skill, was specifically selected for the visualisation development as it is an acyclic movement with a distinct initiation and conclusion. Thirteen children (14.8 ± 0.3 years; 9 boys) wore an ActiGraph GT9X Link Inertial Measurement Unit device on the dominant wrist whilst performing a series of overarm throws. This thesis illustrates how the visualisation concept was developed using raw accelerometer data, which was processed and manipulated using MATLAB 2019b software to obtain and depict key throw performance data, including the trajectory and velocity of the wrist during the throw. Overall, this thesis found that the developed visualisation concept can provide strong indicators of throw competency based on the shape of the throw trajectory. Future research should seek to utilise a larger, more diverse, population, and incorporate machine learning. Finally, further work is required to translate this concept to other gross motor skills

    The MeerKAT Galaxy Cluster Legacy Survey: Survey overview and highlights

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    MeerKAT’s large number (64) of 13.5 m diameter antennas, spanning 8 km with a densely packed 1 km core, create a powerful instrument for wide-area surveys, with high sensitivity over a wide range of angular scales. The MeerKAT Galaxy Cluster Legacy Survey (MGCLS) is a programme of long-track MeerKAT L-band (900−1670 MHz) observations of 115 galaxy clusters, observed for ∼6−10 h each in full polarisation. The first legacy product data release (DR1), made available with this paper, includes the MeerKAT visibilities, basic image cubes at ∼8″ resolution, and enhanced spectral and polarisation image cubes at ∼8″ and 15″ resolutions. Typical sensitivities for the full-resolution MGCLS image products range from ∼3−5 μJy beam−1. The basic cubes are full-field and span 2° × 2°. The enhanced products consist of the inner 1.2° × 1.2° field of view, corrected for the primary beam. The survey is fully sensitive to structures up to ∼10′ scales, and the wide bandwidth allows spectral and Faraday rotation mapping. Relatively narrow frequency channels (209 kHz) are also used to provide H I mapping in windows of 0 < z < 0.09 and 0.19 < z < 0.48. In this paper, we provide an overview of the survey and the DR1 products, including caveats for usage. We present some initial results from the survey, both for their intrinsic scientific value and to highlight the capabilities for further exploration with these data. These include a primary-beam-corrected compact source catalogue of ∼626 000 sources for the full survey and an optical and infrared cross-matched catalogue for compact sources in the primary-beam-corrected areas of Abell 209 and Abell S295. We examine dust unbiased star-formation rates as a function of cluster-centric radius in Abell 209, extending out to 3.5 R 200. We find no dependence of the star-formation rate on distance from the cluster centre, and we observe a small excess of the radio-to-100 μm flux ratio towards the centre of Abell 209 that may reflect a ram pressure enhancement in the denser environment. We detect diffuse cluster radio emission in 62 of the surveyed systems and present a catalogue of the 99 diffuse cluster emission structures, of which 56 are new. These include mini-halos, halos, relics, and other diffuse structures for which no suitable characterisation currently exists. We highlight some of the radio galaxies that challenge current paradigms, such as trident-shaped structures, jets that remain well collimated far beyond their bending radius, and filamentary features linked to radio galaxies that likely illuminate magnetic flux tubes in the intracluster medium. We also present early results from the H I analysis of four clusters, which show a wide variety of H I mass distributions that reflect both sensitivity and intrinsic cluster effects, and the serendipitous discovery of a group in the foreground of Abell 3365
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