Notes

O-Net: A general Convolutional System pertaining to Segmentation Tasks.
Analytical solutions to two axisymmetric problems of a penny-shaped crack when an annulus-shaped (model 1) or a disc-shaped (model 2) rigid inclusion of arbitrary profile are embedded into the crack are derived. The problems are governed by integral equations with the Weber-Sonine kernel on two segments. By the Mellin convolution theorem, the integral equations associated with models 1 and 2 reduce to vector Riemann-Hilbert problems with 3 × 3 and 2 × 2 triangular matrix coefficients whose entries consist of meromorphic and plus or minus infinite indices exponential functions. Canonical matrices of factorization are derived and the partial indices are computed. Exact representation formulae for the normal stress, the stress intensity factors (SIFs) at the crack and inclusion edges, and the normal displacement are obtained and the results of numerical tests are reported. In addition, simple asymptotic formulae for the SIFs are derived.This study presents a generalized elastodynamic theory, based on fractional-order operators, capable of modelling the propagation of elastic waves in non-local attenuating solids and across complex non-local interfaces. Classical elastodynamics cannot capture hybrid field transport processes that are characterized by simultaneous propagation and diffusion. The proposed continuum mechanics formulation, which combines fractional operators in both time and space, offers unparalleled capabilities to predict the most diverse combinations of multiscale, non-local, dissipative and attenuating elastic energy transport mechanisms. Despite the many features of this theory and the broad range of applications, this work focuses on the behaviour and modelling capabilities of the space-fractional term and on its effect on the elastodynamics of solids. We also derive a generalized fractional-order version of Snell's Law of refraction and of the corresponding Fresnel's coefficients. This formulation allows predicting the behaviour of fully coupled elastic waves interacting with non-local interfaces. The theoretical results are validated via direct numerical simulations.We investigate the occurrence of anomalous transport phenomena associated with tracer particles propagating through arrays of steady vortices. The mechanism responsible for the occurrence of anomalous transport is identified in the particle dynamic, which is characterized by long collision-less trajectories (Lévy flights) interrupted by chaotic interactions with vortices. The process is studied via stochastic molecular models that are able to capture the underlying non-local nature of the transport mechanism. These models, however, are not well suited for problems where computational efficiency is an enabling factor. We show that fractional-order continuum models provide an excellent alternative that is able to capture the non-local nature of anomalous transport processes in turbulent environments. The equivalence between stochastic molecular and fractional continuum models is demonstrated both theoretically and numerically. In particular, the onset and the temporal evolution of heavy-tailed diffused fields are shown to be accurately captured, from a macroscopic perspective, by a fractional diffusion equation. The resulting anomalous transport mechanism, for the selected ranges of density of the vortices, shows a superdiffusive nature.The fifth-generation (5G) wireless cellular network is expected to be ready for commercialization within this year. The huge spectrum enabled by the millimetre-wave (mm-Wave) technology is expected to introduce a hype in data usage per user. The 5G is also expected to concurrently support a wide variety of services; however, the practical trade-offs associated with concurrent services require further investigations. In this work, a physical layer (PHY) design to support visible light communications is considered to efficiently support concurrent services that are essential to serve the needs of the sixth-generation (6G) network. A novel communication technique, i.e. mixed-carrier communication (MCC), is proposed. MCC enables simultaneous wireless services such as broadband access, low-rate internet-of-things connectivity, device-free sensing, and device-based localization. This study presents, firstly, a thorough investigation of the design procedure of the novel MCC PHY, secondly, the spectral profile of MCC towards proper spectrum management and interference analysis, and thirdly, performance evaluation based on modelling, simulation and an experimental proof-of-concept. The design steps recommend that the system performance degrades beyond a signal-to-noise ratio (SNR) threshold. For instance, SNR of 25.1 dB and 2.6652 optical power ratio between the communications signal and the driving envelope, for 64-quadrature amplitude modulation (64-QAM), are recommended to avoid performance degradation due to clipping. Simulation results show an interference-immune performance of a properly managed spectrum. For a bit-error-rate (BER) of 10-3, an SNR penalty of 2-5 dB is observed for different interference scenarios. The experimental measurements illustrate a high-quality signal of 21 dB SNR at 50 cm and 10-3 BER using 64-QAM.In this paper, we have studied the impact created by the introduction of up to 5% dust particles in enhancing the decay of blast waves produced by a nuclear explosion. CDK inhibitor A mathematical model is designed and modified using appropriate assumptions, the most important being treating a nuclear explosion as a point source of energy. A system of partial differential equations describing the one-dimensional, adiabatic, unsteady flow of a relaxing gas with dust particles and radiation effects is considered. The symmetric nature of an explosion is captured using the Lie group invariance and self-similar solutions obtained for the gas undergoing strong shocks. The enhancements in decay caused by varying the quantity of dust are studied. The energy released and the damage radius are found to decrease with time with an increase in the dust parameters.In many applications, it is important to reconstruct a fluid flow field, or some other high-dimensional state, from limited measurements and limited data. In this work, we propose a shallow neural network-based learning methodology for such fluid flow reconstruction. Our approach learns an end-to-end mapping between the sensor measurements and the high-dimensional fluid flow field, without any heavy preprocessing on the raw data. No prior knowledge is assumed to be available, and the estimation method is purely data-driven. We demonstrate the performance on three examples in fluid mechanics and oceanography, showing that this modern data-driven approach outperforms traditional modal approximation techniques which are commonly used for flow reconstruction. Not only does the proposed method show superior performance characteristics, it can also produce a comparable level of performance to traditional methods in the area, using significantly fewer sensors. Thus, the mathematical architecture is ideal for emerging global monitoring technologies where measurement data are often limited.
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