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The great expansion in offshore power plants is raising the concern regarding the cumulative effect of the electromagnetic field emissions caused by submarine power cables. In this sense, owners are required to predict these emissions during the permitting and consenting process of new power plants. This is a challenging task, especially in the case of HVAC three-core armored cables due to their complex geometry. Customarily, 2D approaches based on the finite element method (FEM) have been employed for evaluating the magnetic field emissions caused by these cables. However, inaccurate results are obtained since the phase conductors and armor twisting is omitted. This work develops, for the first time in the literature, an in-depth analysis of the magnetic field caused by this type of cable through an ultra-shortened 3D-FEM model, which is also faced to experimental measurements taken on an actual 132 kV, 800 mm2 three-core armored cable. Relevant conclusions are derived regarding the impact of the cable design on the magnetic field emissions, including material properties, as well as single and double-layer armors, presenting the proposed model not only as a valuable tool for predicting purposes, but also for optimizing cable design in terms of magnetic field emissions.

Loss allocation of the three different components (conductor, sheaths and armor) of solidly bonded three-core separated lead-sheathed armored cables, frequently employed in offshore wind farms, is challenging due to the lack of accurate enough analytical expressions in the IEC standard. Also, loss allocation through experimental tests leads to inaccurate results since it is based on questionable assumptions. This paper improves both the IEC formulae and experimental methods by means of different analytical corrections in the conductor and sheath loss expressions. To this aim, an ad hoc application interface (Virtual Lab) based on 3D numerical simulations (finite element method) has been developed. This tool virtualizes and automates different test setups to emulate, in few seconds, the most employed experimental procedures in this type of cable. The analytical corrections have been derived from an in-depth analysis of a first set of 368 cables, ranging from 30 to 275 kV. The new loss expressions were successfully applied to a second set of 645 armored cables of quite diverse features (voltages from 10 to 275 kV, sections and dimensional parameters), hence bringing a general framework for any kind of three-core armored cable.

Due to recent advances, the numerical analysis of submarine three-core armored cables can nowadays be developed through the finite element method (FEM) in a small slice of the cable. This strongly reduces the computational burden and simulation time. However, the performance of this ultra-shortened 3D-FEM model is still to be fully assessed with experimental measurements. This paper focuses on this validation for an extensive variety of situations through the experimental measurements available in the specialized literature for up to 10 actual cables. In particular, it deals not only with relevant calculations at power frequency, like the series resistance and inductive reactance or the induced sheath current, but also with other aspects never analyzed before through 3D-FEM simulations, such as the zero sequence impedance, the magnetic field distribution around the power cable, as well as side effects due to the nonlinear properties of the armor wires. All this considering different armoring and sheath bonding configurations. Results show a very good agreement between measured and computed values, presenting the ultra-shortened 3D-FEM model as a suitable tool for the analysis and design of three-core armored cables, and opening the possibility to reduce the need of extensive experimental tests in the design stage of new cables.

Recently, large offshore wind power plants have been installed far from the shore, using long HVAC three-core armored cables to export power. Its high capacitance may contribute to the appearance of unwanted phenomena, such as overvoltages or resonances at low frequencies. To adequately assess these problems, detailed and reliable cable models are required to develop time-domain/frequency-domain analyses on this type of cables. This paper presents, for the first time in the literature, an assessment on the performance of 3D finite element method-based (3D-FEM) models for developing frequency-domain analyses on three-core armored cables, confronting simulation results with experimental measurements found in the literature for three real cables. To this aim, a simplified ultra-shortened 3D-FEM model is proposed to reduce the simulation time during frequency sweeps, through which relevant aspects never analyzed before with frequency-domain 3D-FEM simulations are addressed, such as total losses, induced sheath current, magnetic field around the power cable, positive and zero sequence harmonic impedances, as well as resonant frequencies. Also, a time-domain example derived from the frequency-domain analysis is provided. Remarkable results are obtained when comparing computed values and measurements, presenting the simplified ultra-shortened 3DFEM model as a valuable tool for the frequency-domain analysis of these cables.

This paper analyzes different ways to simulate electromagnetically three-core armored cables in 3D by means of the finite element method. Full periodic models, as lengthy as 36 m, are developed to evaluate the accuracy when simulating only a small portion of the cable, as commonly employed in the literature. The adequate length and boundary conditions for having the same accuracy of full periodic models are also studied. To this aim, five medium voltage and high voltage armored cables are analyzed, obtaining the minimum length of the cable that may be simulated for having accurate results in shorter time and with less computational burden. This also results in the proposal of a new method comprising the advantages of short geometries and the applicability of periodic boundary conditions. Its accuracy is compared with experimental measurements and the IEC standard for 145 kV and 245 kV cables. The results show a very good agreement between simulations and measurements (errors below 4 %), obtaining a reduction in the computation time of about 90 %. This new method brings a more effective tool for saving time and computational resources in cable design and the development of new analytical expressions for improving the IEC standard.

We present a non-reactive force field for molecular dynamics simulations of interfaces between passivated amorphous surfaces and their interaction with water. The force field enables large-scale dynamic simulations of dry and lubricated tribological contacts and is tailored to surfaces with hydrogen, hydroxyl and aromatic surface passivation. To favour its compatibility with existing force-field parameterizations for liquids and allow a straightforward extension to other types of surface passivation species, we adopt the commonly used OPLS functional form. The optimisation of the force-field parameters is systematic and follows a protocol that can be reused for other surface-molecule combinations. Reference data are calculated with gradient- and dispersion-corrected density functional theory and include the bonding structure and elastic deformation of bulk and surface structures as well as surface adhesion and water adsorption energy landscapes. The conventions adopted to define the different force-field atom types are based on the hybridisation of carbon orbitals and enable a simple and efficient parameter optimisation strategy based on quantum-mechanical calculations performed only on crystalline reference structures. Transferability tests on amorphous interfaces demonstrate the effectiveness of this approach. After testing the force field, we present two examples of application to tribological problems. Namely, we investigate relationships between dry friction and the corrugation of the contact potential energy surface and the dependency of friction on the thickness of interface water films. We finally discuss the limitations of the force field and propose strategies for its improvement and extension.

A crucial task to obtain optimal and reliable quantum devices is to quantify their overall performance. The average fidelity of quantum gates is a particular figure of merit that can be estimated efficiently by Randomized Benchmarking (RB). However, the concept of gate-fidelity itself relies on the crucial assumption that noise behaves in a predictable, time-local, or so-called Markovian manner, whose breakdown can naturally become the leading source of errors as quantum devices scale in size and depth. We analytically show that error suppression techniques such as Dynamical Decoupling (DD) and Randomized Compiling (RC) can operationally Markovianize RB: i) fast DD reduces non-Markovian RB to an exponential decay plus longer-time corrections, while on the other hand, ii) RC generally does not affect the average, but iii) it always suppresses the variance of such RB outputs. We demonstrate these effects numerically with a qubit noise model. Our results show that simple and efficient error suppression methods can simultaneously tame non-Markovian noise and allow for standard and reliable gate quality estimation, a fundamentally important task in the path toward fully functional quantum devices., Comment: 12+19 pages, 10 figures

In situ observations of interplanetary (IP) coronal mass ejections (ICMEs) and IP shocks are important to study as they are the main components of the solar activity. Hundreds of IP shocks have been detected by various space missions at different times and heliocentric distances. Some of these are followed by clearly identified drivers, while some others are not. In this study, we carry out a statistical analysis of the distributions of plasma and magnetic parameters of the IP shocks recorded at various distances to the Sun. We classify the shocks according to the heliocentric distance, namely from 0.29 to 0.99 AU (Helios-1/2); near 1 AU (Wind, ACE and STEREO-A/B); and from 1.35 to 5.4 AU (Ulysses). We also differentiate the IP shocks into two populations, those with a detected ICME and those without one. We find, as expected, that there are no significant differences in the results from spacecraft positioned at 1 AU. Moreover, the distributions of shock parameters, as well as the shock normal have no significant variations with the heliocentric distance. Additionally, we investigate how the number of shocks associated to stream-interaction regions (SIRs) increases with distance in proportion of ICME/shocks. From 1 to 5 AU, SIRs/ shock occurrence increases slightly from 21% to 34%, in contrast ICME/shocks occurrence decreases from 47% to 17%. We find also indication of an asymmetry induced by the Parker spiral for SIRs and none for ICMEs., Comment: 29 Pages, 11 Figures. Accepted for Publication in Solar Physics

The presence of correlations in noisy quantum circuits will be an inevitable side effect as quantum devices continue to grow in size and depth. Randomized Benchmarking (RB) is arguably the simplest method to initially assess the overall performance of a quantum device, as well as to pinpoint the presence of temporal-correlations, so-called non-Markovianity; however, when such presence is detected, it hitherto remains a challenge to operationally quantify its features. Here, we demonstrate a method exploiting the power of machine learning with matrix product operators to deduce the minimal average non-Markovianity displayed by the data of a RB experiment, arguing that this can be achieved for any suitable gate set, as well as tailored for most specific-purpose RB techniques., Comment: 5+10 pages, 5 figures

The rapid progress in the development of quantum devices is in large part due to the availability of a wide range of characterization techniques allowing to probe, test and adjust them. Nevertheless, these methods often make use of approximations that hold in rather simplistic circumstances. In particular, assuming that error mechanisms stay constant in time and have no dependence in the past, is something that will be impossible to do as quantum processors continue scaling up in depth and size. We establish a theoretical framework for the Randomized Benchmarking protocol encompassing temporally-correlated, so-called non-Markovian noise, at the gate level, for any gate set belonging to a wide class of finite groups. We obtain a general expression for the Average Sequence Fidelity (ASF) and propose a way to obtain average gate fidelities of full non-Markovian noise processes. Moreover, we obtain conditions that are fulfilled when an ASF displays authentic non-Markovian deviations. Finally, we show that even though gate-dependence does not translate into a perturbative term within the ASF, as in the Markovian case, the non-Markovian sequence fidelity nevertheless remains stable under small gate-dependent perturbations., Comment: 12 + 24 pages, no figures. Journal version (acceptance date corrected)

A generic non-integrable (unitary) out-of-equilibrium quantum process, when interrogated across many times, is shown to yield the same statistics as an (non-unitary) equilibrated process. In particular, using the tools of quantum stochastic processes, we prove that under loose assumptions, quantum processes equilibrate within finite time intervals. Sufficient conditions for this to occur are that multitime observables are coarse grained in both space and time, and that the initial state overlaps with many different energy eigenstates. These results help bridge the gap between (unitary) quantum and (non-unitary) statistical physics, i.e., when all multitime properties and correlations are well approximated by stationary quantities, which includes non-Markovianity and temporal entanglement. We discuss implications of this result for the emergence of classical stochastic processes from multitime measurements of an underlying genuinely quantum system., Comment: 12+6 pages, 3 figures

Equilibrium statistical mechanics provides powerful tools to understand physics at the macroscale. Yet, the question remains how this can be justified based on a microscopic quantum description. Here, we extend the ideas of pure state quantum statistical mechanics, which focus on single time statistics, to show the equilibration of isolated quantum processes. Namely, we show that most multitime observables for sufficiently large times cannot distinguish a nonequilibrium process from an equilibrium one, unless the system is probed for an extremely large number of times or the observable is particularly fine-grained. A corollary of our results is that the size of non-Markovianity and other multitime characteristics of a nonequilibrium process also equilibrate., Comment: 7+13 pages, 2+2 figures

Estimating the features of noise is the first step in a chain of protocols that will someday lead to fault tolerant quantum computers. The randomized benchmarking (RB) protocol is designed with this exact mindset, estimating the average strength of noise in a quantum processor with relative ease in practice. However, RB, along with most other benchmarking and characterization methods, is limited in scope because it assumes that the noise is temporally uncorrelated (Markovian), which is increasingly evident not to be the case. Here, we combine the RB protocol with a recent framework describing non-Markovian quantum phenomena to derive a general analytical expression of the average sequence fidelity (ASF) for non-Markovian RB with the Clifford group. We show that one can identify non-Markovian features of the noise directly from the ASF through its deviations from the Markovian case, proposing a set of methods to collectively estimate these deviations, non-Markovian memory time-scales, and diagnose (in)coherence of non-Markovian noise in an RB experiment. Finally, we demonstrate the efficacy of our proposal by means of several proof-of-principle examples. Our methods are directly implementable and pave the pathway to better understanding correlated noise in quantum processors., Comment: Published version, results unchanged. 11 + 16 pages, 14 figures

Forgetfulness is a common feature of nature. Moreover, without forgetfulness, repeatability would be impossible. Despite this, small systems constantly leak information about their state to their surroundings, and quantum mechanics tells us that this information cannot be deleted, invariably returning to influence their future behaviour. How can physical nature be forgetful if it is forbidden to forget? The results within this thesis bridge this gap between what we see in the real world and what idealised physical theories say, explaining the emergence of forgetful processes from closed quantum dynamics and allowing to quantify the rate at which memory effects become relevant., Comment: PhD Thesis. Includes work related to three original papers: arXiv:1802.10344, arXiv:1905.08469 and arXiv:2004.07620; 116 pages + 14 pages appendix, 25 figures, 240 references

Memoryless processes are ubiquitous in nature, in contrast with the mathematics of open systems theory, which states that non-Markovian processes should be the norm. This discrepancy is usually addressed by subjectively making the environment forgetful. Here we prove that there are physical non-Markovian processes that with high probability look highly Markovian for all orders of correlations; we call this phenomenon Markovianization. Formally, we show that when a quantum process has dynamics given by an approximate unitary design, a large deviation bound on the size of non-Markovian memory is implied. We exemplify our result employing an efficient construction of an approximate unitary circuit design using two-qubit interactions only, showing how seemingly simple systems can speedily become forgetful. Conversely, since the process is closed, it should be possible to detect the underlying non-Markovian effects. However, for these processes, observing non-Markovian signatures would require highly entangling resources and hence be a difficult task., Comment: 6+9 pages, 5 figures. Published version, only presentation changes

We characterize the conditions under which a multi-time quantum process with a finite temporal resolution can be approximately described by an equilibrium one. By providing a generalization of the notion of equilibration on average, where a system remains closed to a fixed equilibrium for most times, to one which can be operationally assessed at multiple times, we place an upper-bound on a new observable distinguishability measure comparing a multi-time process with a finite temporal resolution against a fixed equilibrium one. While the same conditions on single-time equilibration, such as a large occupation of energy levels in the initial state remain necessary, we obtain genuine multi-time contributions depending on the temporal resolution of the process and the amount of disturbance of the observer's operations on it., Comment: 6+5 pages, 3 figures. Substantial changes and improvements. Published version

It is common, when dealing with quantum processes involving a subsystem of a much larger composite closed system, to treat them as effectively memory-less (Markovian). While open systems theory tells us that non-Markovian processes should be the norm, the ubiquity of Markovian processes is undeniable. Here, without resorting to the Born-Markov assumption of weak coupling or making any approximations, we formally prove that processes are close to Markovian ones, when the subsystem is sufficiently small compared to the remainder of the composite, with a probability that tends to unity exponentially in the size of the latter. We also show that, for a fixed global system size, it may not be possible to neglect non-Markovian effects when the process is allowed to continue for long enough. However, detecting non-Markovianity for such processes would usually require non-trivial entangling resources. Our results have foundational importance, as they give birth to almost Markovian processes from composite closed dynamics, and to obtain them we introduce a new notion of equilibration that is far stronger than the conventional one and show that this stronger equilibration is attained., Comment: 9 pages, 13 pages of appendices, 5 figures, numerical example. Replaced with journal version and fixed hyperlinks