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Critical systems represent a valuable resource in quantum sensing and metrology. Critical quantum sensing (CQS) protocols can be realized using finite-component phase transitions, where criticality is not due to the thermodynamic limit but rather to the rescaling of the system parameters. In particular, the second-order phase transitions of parametric Kerr resonators are of high experimental relevance, as they can be implemented and controlled with various quantum technologies currently available. Here, we show that collective quantum advantage can be achieved with a multipartite critical quantum sensor based on a parametrically coupled Kerr resonators chain in the weak-nonlinearity limit. We derive analytical solutions for the low-energy spectrum of this unconventional quantum many-body system, which is composed of \emph{locally} critical elements. We then assess the performance of an adiabatic CQS protocol, comparing the coupled-resonator chain with an equivalent ensemble of independent critical sensors. We evaluate the scaling of the quantum Fisher information with respect to fundamental resources, and find that the critical chain achieves a quadratic enhancement in the number of resonators. Beyond the advantage found in the case of zero Kerr, we find that there is a collective enhancement even in the scenario of finite Kerr nonlinearity., Comment: 15 pages, 4 figures

Van der Waals assembly allows for the creation of Josephson junctions in an atomically sharp interface between two exfoliated Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212) flakes that are twisted relative to each other. In a narrow range of angles close to $45^\circ$, the junction exhibits a regime where time-reversal symmetry can be spontaneously broken and it can be used to encode an inherently protected qubit called flowermon. In this work we investigate the physics emerging when two such junctions are integrated in a SQuID circuit threaded by a magnetic flux. We show that the flowermon qubit regime is maintained up to a finite critical value of the magnetic field and, under appropriate conditions, it is protected against both charge and flux noise. For larger external fluxes, the interplay between the inherent twisted d-wave nature of the order parameter and the external magnetic flux enables the implementation of different artificial atoms, including a flux-biased protected qubit and a supersymmetric quantum circuit.

We present an implementation of a recently proposed procedure for defining time, based on the description of the evolving system and its clock as non-interacting, entangled systems, according to the Page and Wootters approach. We study how the quantum dynamics transforms into a classical-like behaviour when conditions related with macroscopicity are met by the clock alone, or by both the clock and the evolving system. In the description of this emerging behaviour finds its place the classical notion of time, as well as that of phase-space and trajectories on it. This allows us to analyze and discuss the relations that must hold between quantities that characterize system and clock separately, in order for the resulting overall picture be that of a physical dynamics as we mean it.

Nuclear power is a significant source of electricity in the United States, but the average U.S. nuclear power plant is around 40 years old. Safe management of spent nuclear fuel (SNF) is a crucial aspect of the back end of the nuclear fuel cycle. SNF dry storage systems are increasingly popular as they represent an effective solution in this area, given the absence of a final disposal system. In particular, the spent fuel cask system (dry cask method) provides a feasible solution for maintaining SNF ($\sim$60 years) prior to the final disposal. The HI-STORM overpack and MPC-32 canister are the primary components of the HI-STORM 100 dry cask storage system. They remove heat from the system via natural circulation with no human intervention required. This characteristic provides passive heat removal while requiring little maintenance in dry cask storage systems. This project aims to validate and compare the capabilities of a thermal model of HI-STORM overpack developed using the Multiphysics Object-Oriented Simulation Environment (MOOSE) based on the author's previous study. MOOSE is an open-source framework developed by Idaho National Laboratory for multiscale, multiphysics simulations. This study will improve the capabilities of the thermal-hydraulic model of the HI-STORM dry cask storage system by producing high-fidelity results for the air circulation in the overpack. Large Eddy Simulations (LES) are performed using the open-source spectral element code NekRS, developed by Argonne National Laboratory (ANL), for simulating transitional and turbulent flows in complex geometries. NekRS will produce high-fidelity results for the HI-STORM overpack to assess the validity of the current thermal-hydraulic model., Comment: 12 pages, 9 figures, Proceedings of NURETH-20 Conference

The modelling and analysis of biological systems has deep roots in Mathematics, specifically in the field of Ordinary Differential Equations. Alternative approaches based on formal calculi, often derived from process algebras or term rewriting systems, provide a quite complementary way to analyse the behaviour of biological systems. These calculi allow to cope in a natural way with notions like compartments and membranes, which are not easy (sometimes impossible) to handle with purely numerical approaches, and are often based on stochastic simulation methods. The Calculus of Wrapped Compartments is a framework based on stochastic multiset rewriting in a compartmentalised setting used for the description of biological and ecological systems. We provide an extended presentation of the Calculus of Wrapped Compartments, sketch a few modelling guidelines to encode biological and ecological interactions, show how spatial properties can be handled within the framework and define a hybrid simulation algorithm. Several applications in Biology and Ecology are proposed as modelling case studies., Comment: arXiv admin note: text overlap with arXiv:1505.01985

In this work we design a procedure to estimate the minimum size beyond which a system is amenable to a classical-like description, i.e. a description based on representative points in classical phase-spaces. This is obtained by relating quantum states to representative points via Generalized Coherent States (GCS), and designing a POVM for GCS discrimination. Conditions upon this discrimination are defined, such that the POVM results convey enough information to meet our needs for reliability and precision, as gauged by two parameters $\epsilon$, of our arbitrary choice, and $\delta$, set by the experimental apparatus, respectively. The procedure implies a definition of what is meant by "size" of the system, in terms of the number $N$ of elementary constituents that provide the global algebra leading to the phase-space for the emergent classical-like description. The above conditions on GCS discrimination can be thus turned into $N>N_{\rm t}(\epsilon,\delta)$, where $N_{\rm t}(\epsilon,\delta)$ is the threshold size mentioned in the title. The specific case of a magnetic system is considered, with details of a gedanken experiment presented and thoroughly commented. Results for pseudo-spin and bosonic systems are also given.

Traditional 1D system thermal hydraulic analysis has been widely applied in nuclear industry for licensing purposes due to its numerical efficiency. However, such codes are inherently deficient for modeling of multiscale multidimensional flows. For such scenarios coarse-grid 3D simulations are useful due to the balance between the cost and the amount of information a modeler can extract from the results. At the same time, coarse grids do not allow to accurately resolve and capture turbulent mixing in reactor enclosures, while existing turbulence models (closures for the Reynolds stresses or turbulent viscosity) have large model form uncertainties. Thus, there is an interest in the improvement of such solvers. In this work two data-driven high-to-low methodologies to reduce mesh and model-induced errors are explored using a case study based on the Texas A&M upper plenum of high-temperature gas-cooled reactor facility. The first approach relies on the usage of turbulence closure for eddy viscosity with higher resolution/fidelity in a coarse grid solver. The second methodology employs artificial neural networks to map low-fidelity input features with errors in quantities of interest (velocity fields). Both methods have shown potential to improve the coarse grid simulation results by using data with higher fidelity (Reynolds-averaged Navier-Stokes and large eddy simulations), though, influence of the mesh-induced (discretization) error is quite complex and requires further investigations.

In the present study, the capabilities of a new Convolutional Neural Network (CNN) model are explored with the paramount objective of reconstructing the temperature field of wall-bounded flows based on a limited set of measurement points taken at the boundaries of the fluid domain. For that, we employ an algorithm that leverages the CNN capabilities provided with additional information about the governing equations of the physical problem. Great progress has been made in recent years towards reconstructing and characterizing the spatial distribution of physical variables of interest using CNNs. In principle, CNNs can represent any continuous mathematical function with a relatively reduced number of parameters. However, depending on the complexity imposed by the physical problem, this technique becomes unfeasible. The present study employs a Physics Informed Neuron Network technique featuring a data-efficient function approximator. As a proof of concept, the CNN is trained to retrieve the temperature of a heated channel based on a limited number of sensors placed at the boundaries of the domain. In this context, the training data are the temperature fields solutions considering various flows conditions at steady state, e.g varying the Reynolds and the Prandtl numbers. Additionally, a demonstration case considering the more complex geometry of a MSR is also provided. Assessment on the performance of the CNN is done by the mean L2 and the maximum Linf Euclidean norms stemmed from the difference between the actual solutions and the predictions made by the CNN. Finally, a sensitivity analysis is carried out such that the robustness of the CNN is tested considering a potential real application scenario where noise is inevitable. For that, the original test inputs are overlaid with a normal distribution of random numbers targeting to mimic different levels of noise in the measurement points., Comment: This paper has been submitted and accepted to be published in the 19th International Conference on Nuclear Reactor Thermal Hydraulics (NURETH-19) The paper number in that conference is 35774

It has previously been shown that by increasing the Reynolds number across a channel by spatially varying the viscosity does not cause an immediate change in the size of turbulent structures and a delay is in fact observed in both wall shear and friction Reynolds number (Coppo Leite, V. & Merzari, E., Proceedings of the ASME 2020 FEDSM, p. V003T05A019). Furthermore, it is also shown that depending on the length in which the flow condition changes, turbulence bursts are observed in the turbulence field. For the present work we propose a new version of the standard Reynolds Averaged Navier Stokes (RANS) k-tau model that includes some modifications in the production term in order to account for these effects. The new proposed model may be useful for many engineering applications as turbulent flows featuring temperature gradients and high heat transfer rates are often seen in heat exchangers, combustion chambers and nuclear reactors. In these applications, thermal and viscous properties f the working fluid are important design parameters that depende on temperature; hence it is likely to observe strong gradients on these scalars' fields. To accomplish our goal, the modifications for the k-tau model are implemented and tested for a channel flow with spatial varying viscosity in the streamwise direction. The numerical simulations are performed using Nek5000, a spectral-element code developed at Argonne National Laboratory (ANL). Finally, the results considering a turbulence channel using the proposed model are compared against data obtained using Direct Numerical Simulations from the earlier work.

We draw a picture of physical systems that allows us to recognize what is this thing called "time" by requiring consistency not only with our notion of time but also with the way time enters the fundamental laws of Physics, independently of one using a classical or a quantum description. Elements of the picture are two non-interacting and yet entangled quantum systems, one of which acting as a clock, and the other one doomed to evolve. The setting is based on the so called "Page and Wootters (PaW) mechanism", and updates, with tools from Lie-Group and large-$N$ quantum approaches. The overall scheme is quantum, but the theoretical framework allows us to take the classical limit, either of the clock only, or of the clock and the evolving system altogether; we thus derive the Schr\"odinger equation in the first case, and the Hamilton equations of motion in the second one. Suggestions about possible links with general relativity and gravity are also put forward.

In this article we examine channel flow subject to spatially varying viscosity in the streamwise direction. The Reynolds number is imposed locally with three different ramps. The setup is reminiscent of transient channel flow, but with a space dependent viscosity rather than a time dependent viscosity. It is also relevant to various applications in nuclear engineering and in particular in test reactors, where the viscosity changes significantly in the streamwise direction, and there is a severe lack of Direct Numerical Simulation (DNS) data to benchmark turbulence models in these conditions. As part of this work we set up a novel benchmark case: the channel is extended in the stream-wise direction up to 20p. The viscosity is kept constant in the first 4p region. This inlet region is used as a cyclic region to obtain a fully developed flow profile at the beginning of the ramping region. In the ramping region the Reynolds number is linearly increased along the channel. The flow is homogenous in the spanwise direction, while it is nonhomogenous in the stream-wise and wall-normal direction. We perform here Direct Numerical Simulation (DNS) with Nek5000, a spectral-element computational fluid dynamics (CFD) code developed at Argonne National Laboratory. In this study, specific focus is given to the investigation of turbulence properties and structures in the near-wall region along the flow direction. Turbulent statistics are collected and investigated. Similarly to transient channel flow, the results show that a variation in the Reynolds across a channel does not cause an immediate change in the size of turbulent structures in the ramp region and a delay is in fact observed in both wall shear and friction Reynolds number. The results from the present study are compared with a correlation available in the literature for the friction velocity and as a function of the Reynolds number.

We present and discuss a formal approach for describing the quantum to classical crossover based on the group-theoretic construction of generalized coherent states. The method was originally introduced by L. Yaffe in 1982 for tackling large-$N$ quantum field theories, and has been recently used for studying open quantum systems whose environment, while becoming macroscopic, may or may not display a classical behaviour. Referring to these recent developments, in this paper we provide the essential elements of Yaffes's approach in the framework of standard quantum mechanics, so as to clarify how the approach can be used without referring to quantum field theory. Moreover, we address the role played by a possible global symmetry in making the large-$N$ limit of the original quantum theory to flow into a formally well defined classical theory, and we specifically consider the quantum-to-classical crossover of angular momentum. We also give details of a paradigmatic example, namely that of $N$ free one-dimensional spinless particles. Finally, we discuss upon the foundational requirement that any classical description should ultimately be derived from an underlying quantum theory, that however is not, and should never be confused with, the one obtained via some quantization procedure of the classical description itself., Comment: 13 pages. Accepted for publication in Soft Computing

Within the frame of the ANR-funded CANTARE-Alsace project, we have undertaken a multi-scale and multidisciplinary approach to increase our knowledge of the transition zone between the sedimentary cover and the basement and provide fundamental knowledge for the assessment of its geothermal potential. In this paper, we report out the results of a study performed on an exhumed transition zone in the Ringelbach area in the Vosges Mountains, on the flank of the Rhine graben. In this analogue of a deeply buried transition zone of the Rhine Graben, a thin layer of Triassic sandstones is still present on the top of the fractured and altered granitic basement providing the opportunity to study in-situ the physical properties of this transition zone. In this paper, we focused on electrical and acoustic properties of the transition zone as they are the main physical parameters usually assessed with the help of geophysical methods during the exploration phase of a geothermal project.

We have investigated the benefits and drawbacks of active EM surveying (Controlled-Source EM or CSEM) for monitoring geothermal reservoirs in the presence of strong industrial noise with an actual time-lapse survey over the Reykjanes geothermal field in Iceland before and after the thermal stimulation of the supercritical RN-15/IDDP-2 geothermal well. It showed that a high CSEM survey repeatability can be achieved with electric field measurements (within a few percent) but that time-lapse MT survey is a challenging task because of the high level of cultural noise in this industrialized environment. To assess the quality of our CSEM dataset, we inverted the data and confronted the resulting resistivity model with the resistivity logged in the RN-15/IDDP-2 well. We obtained a good match up to 2-3km depth, i.e. enough to image the caprock and the liquid-dominated reservoir but not deep enough to image the reservoir in supercritical conditions. To obtain such an image, we had to jointly invert legacy MT data with our CSEM data. On the monitoring aspects, the analysis of changes in electric fields did not allow to identify any CSEM signal related to the thermal stimulation of the RN-15/IDDP-2 well. One possible explanation is the weakness of the time-lapse CSEM signal compared the achieved CSEM survey repeatability as a result of a limited resistivity change over a limited volume within the reservoir.