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The finite element method is widely used in simulations of various fields. However, when considering domains whose extent differs strongly in different spatial directions a finite element simulation becomes computationally very expensive due to the large number of degrees of freedom. An example of such a domain are the cables inside of the magnets of particle accelerators. For translationally invariant domains, this work proposes a quasi-3-D method. Thereby, a 2-D finite element method with a nodal basis in the cross-section is combined with a spectral method with a wavelet basis in the longitudinal direction. Furthermore, a spectral method with a wavelet basis and an adaptive and time-dependent resolution is presented. All methods are verified. As an example the hot-spot propagation due to a quench in Rutherford cables is simulated successfully.

Temporal patterns of cardiac motion provide important information for cardiac disease diagnosis. This pattern could be obtained by three-directional CINE multi-slice left ventricular myocardial velocity mapping (3Dir MVM), which is a cardiac MR technique providing magnitude and phase information of the myocardial motion simultaneously. However, long acquisition time limits the usage of this technique by causing breathing artifacts, while shortening the time causes low temporal resolution and may provide an inaccurate assessment of cardiac motion. In this study, we proposed a frame synthesis algorithm to increase the temporal resolution of 3Dir MVM data. Our algorithm is featured by 1) three attention-based encoders which accept magnitude images, phase images, and myocardium segmentation masks respectively as inputs; 2) three decoders that output the interpolated frames and corresponding myocardium segmentation results; and 3) loss functions highlighting myocardium pixels. Our algorithm can not only increase the temporal resolution 3Dir MVMs, but can also generates the myocardium segmentation results at the same time.

The Poisson equation is critical to get a self-consistent solution in plasma fluid simulations used for Hall effect thrusters and streamers discharges. Solving the 2D Poisson equation with zero Dirichlet boundary conditions using a deep neural network is investigated using multiple-scale architectures, defined in terms of number of branches, depth and receptive field. The latter is found critical to correctly capture large topological structures of the field. The investigation of multiple architectures, losses, and hyperparameters provides an optimum network to solve accurately the steady Poisson problem. Generalization to new resolutions and domain sizes is then proposed using a proper scaling of the network. Finally, found neural network solver, called PlasmaNet, is coupled with an unsteady Euler plasma fluid equations solver. The test case corresponds to electron plasma oscillations which is used to assess the accuracy of the neural network solution in a time-dependent simulation. In this time-evolving problem, a physical loss is necessary to produce a stable simulation. PlasmaNet is then benchmarked on meshes with increasing number of nodes, and compared with an existing solver based on a standard linear system algorithm for the Poisson equation. It outperforms the classical plasma solver, up to speedups 700 times faster on large meshes. PlasmaNet is finally tested on a more complex case of discharge propagation involving chemistry and advection. The guidelines established in previous sections are applied to build the CNN to solve the same Poisson equation but in cylindrical coordinates. Results reveal good CNN predictions with significant speedup. These results pave the way to new computational strategies to predict unsteady problems involving a Poisson equation, including configurations with coupled multiphysics interactions such as in plasma flows.

Many robots move through the world by composing locomotion primitives like steps and turns. To do so well, robots need not have primitives that make intuitive sense to humans. This becomes of paramount importance when robots are damaged and no longer move as designed. Here we propose a goal function we call "coverage", that represents the usefulness of a library of locomotion primitives in a manner agnostic to the particulars of the primitives themselves. We demonstrate the ability to optimize coverage on both simulated and physical robots, and show that coverage can be rapidly recovered after injury. This suggests that by optimizing for coverage, robots can sustain their ability to navigate through the world even in the face of significant mechanical failures. The benefits of this approach are enhanced by sample-efficient, data-driven approaches to system identification that can rapidly inform the optimization of primitives. We found that the number of degrees of freedom improved the rate of recovery of our simulated robots, a rare result in the fields of gait optimization and reinforcement learning. We showed that a robot with limbs made of tree branches (for which no CAD model or first principles model was available) is able to quickly find an effective high-coverage library of motion primitives. The optimized primitives are entirely non-obvious to a human observer, and thus are unlikely to be attainable through manual tuning.

Information geometry is concerned with the application of differential geometry concepts in the study of the parametric spaces of statistical models. When the random variables are independent and identically distributed, the underlying parametric space exhibit constant curvature, which makes the geometry hyperbolic (negative) or spherical (positive). In this paper, we derive closed-form expressions for the components of the first and second fundamental forms regarding pairwise isotropic Gaussian-Markov random field manifolds, allowing the computation of the Gaussian, mean and principal curvatures. Computational simulations using Markov Chain Monte Carlo dynamics indicate that a change in the sign of the Gaussian curvature is related to the emergence of phase transitions in the field. Moreover, the curvatures are highly asymmetrical for positive and negative displacements in the inverse temperature parameter, suggesting the existence of irreversible geometric properties in the parametric space along the dynamics. Furthermore, these asymmetric changes in the curvature of the space induces an intrinsic notion of time in the evolution of the random field.

A reconfigurable intelligent surface (RIS) is a planar structure that is engineered to dynamically control the electromagnetic waves. In wireless communications, RISs have recently emerged as a promising technology for realizing programmable and reconfigurable wireless propagation environments through nearly passive signal transformations. With the aid of RISs, a wireless environment becomes part of the network design parameters that are subject to optimization. In this tutorial paper, we focus our attention on communication models for RISs. First, we review the communication models that are most often employed in wireless communications and networks for analyzing and optimizing RISs, and elaborate on their advantages and limitations. Then, we concentrate on models for RISs that are based on inhomogeneous sheets of surface impedance, and offer a step-by-step tutorial on formulating electromagnetically-consistent analytical models for optimizing the surface impedance. The differences between local and global designs are discussed and analytically formulated in terms of surface power efficiency and reradiated power flux through the Poynting vector. Finally, with the aid of numerical results, we discuss how approximate global designs can be realized by using locally passive RISs with zero electrical resistance (i.e., inhomogeneous reactance boundaries with no local power amplification), even for large angles of reflection and at high power efficiency.

In this paper, derivation of different forms of dynamic formulation of spherical parallel robots (SPRs) is investigated. These formulations include the explicit dynamic forms, linear regressor, and Slotine-Li (SL) regressor, which are required for the design and implementation of the vast majority of model-based controllers and dynamic parameters identification schemes. To this end, the implicit dynamic of SPRs is first formulated using the principle of virtual work in task-space, and then by using an extension, their explicit dynamic formulation is derived. The dynamic equation is then analytically reformulated into linear and S-L regression form with respect to the inertial parameters, and by using the Gauss-Jordan procedure, it is reduced to a unique and closed-form structure. Finally, to illustrate the effectiveness of the proposed method, two different SPRs, namely, the ARAS-Diamond, and the 3-RRR, are examined as the case studies. The obtained results are verified by using the MSC-ADAMS software, and are shared to interested audience for public access.

Jittering effects significantly degrade the performance of UAV millimeter-wave (mmWave) communications. To investigate the impacts of UAV jitter on mmWave communications, we firstly model UAV mmWave channel based on the geometric relationship between element antennas of the uniform planar arrays (UPAs). Then, we extract the relationship between (I) UAV attitude angles & position coordinates and (II) angle of arrival (AoA) & angle of departure (AoD) of mmWave channel, and we also derive the distribution of AoA/AoD at UAV side from the random fluctuations of UAV attitude angles, i.e., UAV jitter. In beam training design, with the relationship between attitude angles and AoA/AoD, we propose to generate a rough estimate of AoA and AoD from UAV navigation information. Finally, with the rough AoA/AoD estimate, we develop a compressed sensing (CS) based beam training scheme with constrained sensing range as the fine AoA/AoD estimation. Particularly, we construct a partially random sensing matrix to narrow down the sensing range of CS-based beam training. Numerical results show that our proposed UAV beam training scheme assisted by navigation information can achieve better accuracy with reduced training length in AoA/AoD estimation and is thus more suitable for UAV mmWave communications under jittering effects.

The potential diagnostic applications of magnet-actuated capsules have been greatly increased in recent years. For most of these potential applications, accurate position control of the capsule have been highly demanding. However, the friction between the robot and the environment as well as the drag force from the tether play a significant role during the motion control of the capsule. Moreover, these forces especially the friction force are typically hard to model beforehand. In this paper, we first designed a magnet-actuated tethered capsule robot, where the driving magnet is mounted on the end of a robotic arm. Then, we proposed a learning-based approach to model the friction force between the capsule and the environment, with the goal of increasing the control accuracy of the whole system. Finally, several real robot experiments are demonstrated to showcase the effectiveness of our proposed approach.