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This work aims to construct and analyze a discontinuous Galerkin method on polytopal grids (PolydG) to solve the pseudo-stress formulation of the unsteady Stokes problem. The pseudo-stress variable is introduced due to the growing interest in non-Newtonian flows and coupled interface problems, where stress assumes a fundamental role. The space-time discretization of the problem is achieved by combining the PolydG approach with the implicit theta-method time integration scheme. For both the semi- and fully-discrete problems we present a detailed stability analysis. Moreover, we derive convergence estimates for the fully discrete space-time discretization. A set of verification tests is presented to verify the theoretical estimates and the application of the method to cases of engineering interest.

The emergence of Centralized-RAN (C-RAN) has revolutionized mobile network infrastructure, offering streamlined cell-site engineering and enhanced network management capabilities. As C-RAN gains momentum, the focus shifts to optimizing fronthaul links. While fiber fronthaul guarantees performance, wireless alternatives provide cost efficiency and scalability, making them preferable in densely urbanized areas. However, wireless fronthaul often requires expensive over-dimensioning to overcome the challenging atmospheric attenuation typical of high frequencies. We propose a framework designed to continuously align radio access capacity with fronthaul link quality to overcome this rigidity. By gradually adapting radio access capacity to available fronthaul capacity, the framework ensures smooth degradation rather than complete service loss. Various strategies are proposed, considering factors like functional split and beamforming technology and exploring the tradeoff between adaptation strategy complexity and end-to-end system performance. Numerical evaluations using experimental rain attenuation data illustrate the framework's effectiveness in optimizing radio access capacity under realistically variable fronthaul link quality, ultimately proving the importance of adaptive capacity management in maximizing C-RAN efficiency.

Parameterized quantum circuits play a key role for the development of quantum variational algorithms in the realm of the NISQ era. Knowing their actual capability of performing different kinds of tasks is then of the utmost importance. By comparing them with a prototypical class of universal random circuits we have found that their approach to the asymptotic complexity defined by the Haar measure is faster, needing less gates to reach it. Topology has been revealed crucial for this. The majorization criterion has proven as a relevant complementary tool to the expressibility and the mean entanglement., Comment: 8 pages, 4 figures

While scalable error correction schemes and fault tolerant quantum computing seem not to be universally accessible in the near sight, the efforts of many researchers have been directed to the exploration of the contemporary available quantum hardware. Due to these limitations, the depth and dimension of the possible quantum circuits are restricted. This motivates the study of circuits with parameterized operations that can be classically optimized in hybrid methods as variational quantum algorithms (VQAs), enabling the reduction of circuit depth and size. The characteristics of these Parameterized Quantum Circuits (PQCs) are still not fully understood outside the scope of their principal application, motivating the study of their intrinsic properties. In this work, we analyse the generation of random states in PQCs under restrictions on the qubits connectivities, justified by different quantum computer architectures. We apply the expressibility quantifier and the average entanglement as diagnostics for the characteristics of the generated states and classify the circuits depending on the topology of the quantum computer where they can be implemented. As a function of the number of layers and qubits, circuits following a Ring topology will have the highest entanglement and expressibility values, followed by Linear/All-to-all almost together and the Star topology. In addition to the characterization of the differences between the entanglement and expressibility of these circuits, we also place a connection between how steep is the increase on the uniformity of the distribution of the generated states and the generation of entanglement. Circuits generating average and standard deviation for entanglement closer to values obtained with the truly uniformly random ensemble of unitaries present a steeper evolution when compared to others., Comment: 14 pages, 13 figures

The spectrum crunch challenge poses a vital threat to the progress of cellular networks and recently prompted the inclusion of millimeter wave (mmWave) and Upper 6GHz (U6G) in the 3GPP standards. These two bands promise to unlock a large portion of untapped spectrum, but the harsh propagation due to the increased carrier frequency might negatively impact the performance of urban Radio Access Network (RAN) deployments. Within the span of a year, two co-located 5G networks operating in these frequency bands were deployed at Politecnico di Milano, Milan, Italy, entirely dedicated to the dense urban performance assessment of the two systems. This paper presents an in-depth analysis of the measurement campaigns conducted on them, with the U6G campaign representing the first of its kind. A benchmark is provided by ray-tracing simulations. The results suggest that networks operating in these frequency bands provide good indoor and outdoor coverage and throughput in urban scenarios, even when deployed in the macro base station setup common to lower frequencies. In addition, a comparative performance analysis of these two key technologies is provided, offering insights on their relative strengths, weaknesses and improvement margins and informing on which bands is better suited for urban macro coverage.

We present the library lymph for the finite element numerical discretization of coupled multi-physics problems. lymph is a Matlab library for the discretization of partial differential equations based on high-order discontinuous Galerkin methods on polytopal grids (PolyDG) for spatial discretization coupled with suitable finite-difference time marching schemes. The objective of the paper is to introduce the library by describing it in terms of installation, input/output data, and code structure, highlighting - when necessary - key implementation aspects related to the method. A user guide, proceeding step-by-step in the implementation and solution of a Poisson problem, is also provided. In the last part of the paper, we show the results obtained for several differential problems, namely the Poisson problem, the heat equation, the elastodynamics system, and a multiphysics problem coupling poroelasticity and acoustic equations. Through these examples, we show the convergence properties and highlight some of the main features of the proposed method, i.e. geometric flexibility, high-order accuracy, and robustness with respect to heterogeneous physical parameters.

This work is concerned with the analysis of a space-time finite element discontinuous Galerkin method on polytopal meshes (XT-PolydG) for the numerical discretization of wave propagation in coupled poroelastic-elastic media. The mathematical model consists of the low-frequency Biot's equations in the poroelastic medium and the elastodynamics equation for the elastic one. To realize the coupling, suitable transmission conditions on the interface between the two domains are (weakly) embedded in the formulation. The proposed PolydG discretization in space is then coupled with a dG time integration scheme, resulting in a full space-time dG discretization. We present the stability analysis for both the continuous and the semidiscrete formulations, and we derive error estimates for the semidiscrete formulation in a suitable energy norm. The method is applied to a wide set of numerical test cases to verify the theoretical bounds. Examples of physical interest are also presented to investigate the capability of the proposed method in relevant geophysical scenarios.

Millimeter-Wave (mm-Wave) Radio Access Networks (RANs) are a promising solution to tackle the overcrowding of the sub-6 GHz spectrum, offering wider and underutilized bands. However, they are characterized by inherent technical challenges, such as a limited propagation range and blockage losses caused by obstacles. Integrated Access and Backhaul (IAB) and Reconfigurable Intelligent Surfaces (RIS) are two technologies devised to face these challenges. This work analyzes the optimal network layout of RANs equipped with IAB and RIS in real urban scenarios using MILP formulations to derive practical design guidelines. In particular, it shows how optimizing the peak user throughput of such networks improves the achievable peak throughput, compared to the traditional mean-throughput maximization approaches, without actually sacrificing mean throughputs. In addition, it indicates star-like topologies as the best network layout to achieve the highest peak throughputs.

We propose AeroSPEED, a solver based on the Spectral Element Method (SEM) that solves the aeroacoustic Lighthill's wave equation. First, the fluid solution is computed employing a cell centered Finite Volume method. Then, AeroSPEED maps the sound source coming from the flow solution onto the acoustic grid, where finally the Lighthill's wave equation is solved. An ad-hoc projection strategy is adopted to apply the flow source term in the acoustic solver. A model problem with a manufactured solution and the Noise Box test case are used as benchmark for the acoustic problem. We studied the noise generated by the complex flow field around tandem cylinders as a relevant aeroacoustic application. AeroSPEED is an effective and accurate solver for both acoustics and aeroacoustic problems.

We present and analyze a high-order discontinuous Galerkin method for the space discretization of the wave propagation model in thermo-poroelastic media. The proposed scheme supports general polytopal grids. Stability analysis and $hp$-version error estimates in suitable energy norms are derived for the semi-discrete problem. The fully-discrete scheme is then obtained based on employing an implicit Newmark-$\beta$ time integration scheme. A wide set of numerical simulations is reported, both for the verification of the theoretical estimates and for examples of physical interest. A comparison with the results of the poroelastic model is provided too, highlighting the differences between the predictive capabilities of the two models.

We propose a hybrid Finite Volume (FV) - Spectral Element Method (SEM) for modelling aeroacoustic phenomena based on the Lighthill's acoustic analogy. First the fluid solution is computed employing a FV method. Then, the sound source term is projected onto the acoustic grid and the inhomogeneous Lighthill's wave equation is solved employing the SEM. The novel projection method computes offline the intersections between the acoustic and the fluid grids in order to preserve the accuracy. The proposed intersection algorithm is shown to be robust, scalable and able to efficiently compute the geometric intersection of arbitrary polyhedral elements. We then analyse the properties of the projection error, showing that if the fluid grid is fine enough we are able to exploit the accuracy of the acoustic solver and we numerically assess the obtained theoretical estimates. Finally, we address two relevant aeroacoustic benchmarks, namely the corotating vortex pair and the noise induced by a laminar flow around a squared cylinder, to demonstrate in practice the effectiveness of the projection method when dealing with high order solvers. The flow computations are performed with OpenFOAM [46], an open-source finite volume library, while the inhomogeneous Lighthill's wave equation is solved with SPEED [31], an opensource spectral element library.

We design a Mixed Virtual Element Method for the approximated solution to the first-order form of the acoustic wave equation. In absence of external load, the semi-discrete method exactly conserves the system energy. To integrate in time the semi-discrete problem we consider a classical theta-method scheme. We carry out the stability and convergence analysis in the energy norm for the semi-discrete problem showing optimal rate of convergence with respect to the mesh size. We further study the property of energy conservation for the fully-discrete system. Finally, we present some verification tests as well as engineering application of the method.

MmWaves have been envisioned as a promising direction to provide Gbps wireless access. However, they are susceptible to high path losses and blockages, which directional antennas can only partially mitigate. That makes mmWave networks coverage-limited, thus requiring dense deployments. Integrated access and backhaul (IAB) architectures have emerged as a cost-effective solution for network densification. Resource allocation in mmWave IAB networks must face big challenges to cope with heavy temporal dynamics, such as intermittent links caused by user mobility and blockages from moving obstacles. This makes it extremely difficult to find optimal and adaptive solutions. In this article, exploiting the distributed structure of the problem, we propose a Multi-Agent Reinforcement Learning (MARL) framework to optimize user throughput via flow routing and link scheduling in mmWave IAB networks characterized by user mobility and link outages generated by moving obstacles. The proposed approach implicitly captures the environment dynamics, coordinates the interference, and manages the buffer levels of IAB relay nodes. We design different MARL components, considering full-duplex and half-duplex IAB-nodes. In addition, we provide a communication and coordination scheme for RL agents in an online training framework, addressing the feasibility issues of practical systems. Numerical results show the effectiveness of the proposed approach., Comment: B. Zhang, I. Filippini, "Mobility-Aware Resource Allocation for mmWave IAB Networks: A Multi-Agent Reinforcement Learning Approach", to appear on IEEE/ACM Transactions on Networking

Electric fields arising from the distribution of charge in metal halide perovskite solar cells are critical for understanding the many weird and wonderful optoelectronic properties displayed by these devices. Mobile ionic defects are thought to accumulate at interfaces to screen electric fields within the bulk of the perovskite semiconductor on application of external bias, but tools are needed to directly probe the dynamics of the electric field in this process. Here we show that electroabsorption measurements allow the electric field within the active layer to be tracked as a function of frequency or time. The magnitude of the electroabsorption signal, corresponding to the strength of the electric field in the perovskite layer, falls off for externally applied low frequency voltages or at long times following voltage steps. Our observations are consistent with drift-diffusion simulations, impedance spectroscopy, and transient photocurrent measurements. They indicate charge screening/redistribution on time-scales ranging from 10 ms to 100 s depending on the device interlayer material, perovskite composition, dominant charged defect, and illumination conditions. The method can be performed on typical solar cell structures and has potential to become a routine characterization tool for optimizing hybrid perovskite devices., Comment: 65 pages, 41 figures

In this work, we present a new high order Discontinuous Galerkin time integration scheme for second-order (in time) differential systems that typically arise from the space discretization of the elastodynamics equation. By rewriting the original equation as a system of first order differential equations we introduce the method and show that the resulting discrete formulation is well-posed, stable and retains super-optimal rate of convergence with respect to the discretization parameters, namely the time step and the polynomial approximation degree. A set of two- and three-dimensional numerical experiments confirm the theoretical bounds. Finally, the method is applied to real geophysical applications.

In this work we review discontinuous Galerkin finite element methods on polytopal grids (PolydG) for the numerical simulation of multiphysics wave propagation phenomena in heterogeneous media. In particular, we address wave phenomena in elastic, poro-elastic, and poro-elasto-acoustic materials. Wave propagation is modeled by using either the elastodynamics equation in the elastic domain, the acoustics equations in the acoustic domain and the low-frequency Biot's equations in the poro-elastic one. The coupling between different models is realized by means of (physically consistent) transmission conditions, weakly imposed at the interface between the subdomains. For all models configuration, we introduce and analyse the PolydG semi-discrete formulation, which is then coupled with suitable time marching schemes. For the semi-discrete problem, we present the stability analysis and derive a-priori error estimates in a suitable energy norm. A wide set of verification tests with manufactured solutions are presented in order to validate the error analysis. Examples of physical interest are also shown to demonstrate the capability of the proposed methods., Comment: 28 pages, 21 figures

As a mean to assess the risk dam structures are exposed to during earthquakes, we employ an abstract mathematical, three dimensional, elasto-acoustic coupled wave-propagation model taking into account (i) the dam structure itself, embedded into (ii) its surrounding topography, (iii) different material soil layers, (iv) the seismic source as well as (v) the reservoir lake filled with water treated as an acoustic medium. As a case study for extensive numerical simulations we consider the magnitude 7 seismic event of the 30$^{\rm th}$ of October 2020 taking place in the Icarian Sea (Greece) and the Tahtali dam around 30 km from there (Turkey). A challenging task is to resolve the multiple length scales that are present due to the huge differences in size between the dam building structure and the area of interest, considered for the propagation of the earthquake. Interfaces between structures and highly non-conforming meshes on different scales are resolved by means of a discontinuous Galerkin approach. The seismic source is modeled using inversion data about the real fault plane. Ultimately, we perform a real data driven, multi-scale, full source-to-site, physics based simulation based on the discontinuous Galerkin spectral element method, which allows to precisely validate the ground motion experienced along the Tahtali dam, comparing the synthetic seismograms against actually observed ones. A comparison with a more classical computational method, using a plane wave with data from a deconvolved seismogram reading as an input, is discussed., Comment: 26 pages, 16 figures

This work deals with the problem of localizing a victim buried by an avalanche by means of a drone equipped with an ARVA (Appareil de Recherche de Victimes d'Avalanche) sensor. The proposed control solution is based on a "model-free" extremum seeking strategy which is shown to succeed in steering the drone in a neighborhood of the victim position. The effectiveness and robustness of the proposed algorithm is tested in Gazebo simulation environment, where a new flight mode and a new controller module have been implemented as an extension of the well-known PX4 open source flight stack. Finally, to test usability, we present hardware-in-the-loop simulations on a Pixhawk 2 Cube board.

In this work we present an extension of the Virtual Element Method with curved edges for the numerical approximation of the second order wave equation in a bidimensional setting. Curved elements are used to describe the domain boundary, as well as internal interfaces corresponding to the change of some mechanical parameters. As opposite to the classic and isoparametric Finite Element approaches, where the geometry of the domain is approximated respectively by piecewise straight lines and by higher order polynomial maps, in the proposed method the geometry is exactly represented, thus ensuring a highly accurate numerical solution. Indeed, if in the former approach the geometrical error might deteriorate the quality of the numerical solution, in the latter approach the curved interfaces/boundaries are approximated exactly guaranteeing the expected order of convergence for the numerical scheme. Theoretical results and numerical findings confirm the validity of the proposed approach.

The introduction of the mm-Wave spectrum into 5G NR promises to bring about unprecedented data throughput to future mobile wireless networks but comes with several challenges. Network densification has been proposed as a viable solution to increase RAN resilience, and the newly introduced Integrated-Access-and-Backhaul (IAB) is considered a key enabling technology with compelling cost-reducing opportunities for such dense deployments. Reconfigurable Intelligent Surfaces (RIS) have recently gained extreme popularity as they can create Smart Radio Environments by EM wave manipulation and behave as inexpensive passive relays. However, it is not yet clear what role this technology can play in a large RAN deployment. With the scope of filling this gap, we study the blockage resilience of realistic mm-Wave RAN deployments that use IAB and RIS. The RAN layouts have been optimised by means of a novel mm-Wave planning tool based on MILP formulation. Numerical results show how adding RISs to IAB deployments can provide high blockage resistance levels while significantly reducing the overall network planning cost., Comment: 2022 IEEE Wireless Communications and Networking Conference (WCNC) (IEEE WCNC 2022)

With the capability to support gigabit data rates, millimetre-wave (mm-Wave) communication is unanimously considered a key technology of future cellular networks. However, the harsh propagation at such high frequencies makes these networks quite susceptible to failures due to obstacle blockages. Recently introduced Reconfigurable Intelligent Surfaces (RISs) can enhance the coverage of mm-Wave communications by improving the received signal power and offering an alternative radio path when the direct link is interrupted. While several works have addressed this possibility from a communication standpoint, none of these has yet investigated the impact of RISs on large-scale mm-Wave networks. Aiming to fill this literature gap, we propose a new mathematical formulation of the coverage planning problem that includes RISs. Using well-established planning methods, we have developed a new optimization model where RISs can be installed alongside base stations to assist the communications, creating what we have defined as Smart Radio Connections. Our simulation campaigns show that RISs effectively increase both throughput and coverage of access networks, while further numerical results highlight additional benefits that the simplified scenarios analyzed by previous works could not reveal.

We numerically study by lattice Boltzmann simulations the rheological properties of an active emulsion made of a suspension of an active polar gel embedded in an isotropic passive background. We find that the hexatic equilibrium configuration of polar droplets is highly sensitive to both active injection and external forcing and may either lead to asymmetric unidirectional states which break top-bottom symmetry or symmetric ones. In this latter case, for large enough activity, the system develops a shear-thickening regime at low shear rates. Importantly, for larger external forcing a regime with stable negative effective viscosity is found. Moreover, at intermediate activity a region of multistability is encountered and we show that a maximum entropy production principle holds in selecting the most favorable state.

In this paper, we review recent results on the conforming virtual element approximation of polyharmonic and elastodynamics problems. The structure and the content of this review is motivated by three paradigmatic examples of applications: classical and anisotropic Cahn-Hilliard equation and phase field models for brittle fracture, that are briefly discussed in the first part of the paper. We present and discuss the mathematical details of the conforming virtual element approximation of linear polyharmonic problems, the classical Cahn-Hilliard equation and linear elastodynamics problems., Comment: 30 pages, 7 figures. arXiv admin note: text overlap with arXiv:1912.07122

We prove that for $k \ll \sqrt[4]{n}$ regular resolution requires length $n^{\Omega(k)}$ to establish that an Erd\H{o}s-R\'enyi graph with appropriately chosen edge density does not contain a $k$-clique. This lower bound is optimal up to the multiplicative constant in the exponent, and also implies unconditional $n^{\Omega(k)}$ lower bounds on running time for several state-of-the-art algorithms for finding maximum cliques in graphs.