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Comparison theorems on H-type sub-Riemannian manifolds
No full textOn H-type sub-Riemannian manifolds we establish sub-Hessian and sub-Laplacian comparison theorems which are uniform for a family of approximating Riemannian metrics converging to the sub-Riemannian one. We also prove a sharp sub-Riemannian Bonnet–Myers theorem that extends to this general setting results previously proved on contact and quaternionic contact manifolds
Il piano di comunicazione per l'emergenza bradisismo dei Campi Flegrei. Un'analisi dell'efficacia informativa nel contesto della comunicazione del rischio
No full textElastic bodies with kinematic constraints on many small regions
No full textWe study the equilibrium of hyperelastic solids subjected to kinematic constraints on many small regions, which we call perforations. Such constraints on the displacement u are given in the quite general form u(x)∈Fx, where Fx is a closed set, and thus comprise confinement conditions, unilateral constraints, controlled displacement conditions, etc., both in the bulk and on the boundary of the body. The regions in which such conditions are active are assumed to be so small that they do not produce an overall rigid constraint, but still large enough so as to produce a non-trivial effect on the behaviour of the body. Mathematically, this is translated in an asymptotic analysis by introducing two small parameters: ɛ, describing the distance between the elements of the perforation, and δ, the size of the element of the perforation. We find the critical scale at which the effect of the perforation is non-trivial and express it in terms of a Γ-limit in which the constraints are relaxed so that, in their place, a penalization term appears in the form of an integral of a function φ(x,u). This function is determined by a blow-up procedure close to the perforation and depends on the shape of the perforation, the constraint Fx, and the asymptotic behaviour at infinity of the strain energy density σ. We give a concise proof of the mathematical result and numerical studies for some simple yet meaningful geometries
A hybrid reduced order model to enforce outflow pressure boundary conditions in computational hemodynamics
No full text: This paper deals with the development of a reduced order model (ROM) which could be used as an efficient tool for the reconstruction of the unsteady blood flow patterns in cardiovascular applications. The methodology relies on proper orthogonal decomposition to compute basis functions, combined with a Galerkin projection to compute the reduced coefficients. The main novelty of this work lies in the extension of the lifting function method, which typically is adopted for treating nonhomogeneous inlet velocity boundary conditions, to the handling of nonhomogeneous outlet boundary conditions for pressure, representing a very delicate point in numerical simulations of cardiovascular systems. Moreover, we incorporate a properly trained neural network in the ROM framework to approximate the mapping from time parameter to outflow pressure, which in the most general case is not available in closed form. We define our approach as "hybrid", because it merges equation-based elements with purely data-driven ones. The full order model (FOM) is related to a finite volume method which is employed for the discretization of unsteady Navier-Stokes equations while a two-element Windkessel model is adopted to enforce a reliable estimation of outflow pressure. Numerical results, firstly related to a 3D idealized blood vessel and then to a 3D patient-specific aortic arch, demonstrate that our ROM is able to accurately approximate the FOM with a significant reduction in computational cost
Environmental effects in the LISA stochastic signal from stellar-mass black hole binaries
No full textThe population of unresolved stellar-mass black hole binaries (sBBHs) is expected to produce a stochastic gravitational-wave background (SGWB) potentially detectable by the Laser Interferometer Space Antenna (LISA). In this work, we compute the imprint of astrophysical environmental effects—such as gas dynamical friction and accretion—on this background. Using the sBBH population constraints obtained by the LIGO-Virgo-KAGRA Collaboration, we compute the expected SGWB and develop a phenomenological parametric model that can accurately capture the effect of dynamical friction and accretion. Using our model, we perform Bayesian inference on simulated signals to assess the detectability of these environmental effects. We find that, even for large injected values of the Eddington ratio, the effect of accretion in the SGWB is undetectable by LISA. However, LISA will be able to constrain the effect of dynamical friction with an upper bound on the gas density ofρ ≲ 7.6 × 10−10 g cm−3, thus probing the sBBH environment forming in typical thin accretion disks around active galactic nuclei. For injected densities of ρ ∼ 10−10–10−9 g cm−3, dynamical friction effects can be well measured and clearly distinguished from vacuum, with Bayes factors reaching up to ∼60, even when the Galactic foreground is included
Retrieving nonstabilizerness with neural networks
No full textQuantum computing's promise lies in its intrinsic complexity, with entanglement initially heralded as its hallmark. However, the quest for quantum advantage extends beyond entanglement, encompassing the realm of nonstabilizer (magic) states. Despite their significance, quantifying and characterizing these states pose formidable challenges. Here, we introduce a different approach leveraging convolutional neural networks (CNNs) to classify quantum states based on their nonstabilizerness content. Without relying on a complete knowledge of the state, we utilize partial information acquired from measurement snapshots to train the CNN in distinguishing between stabilizer and nonstabilizer states. Importantly, our methodology circumvents the limitations of full state tomography, offering a practical solution for real-world quantum experiments. In addition, we unveil a theoretical connection between stabilizer Rényi entropies and the expectation value of Pauli matrices for pure quantum states. Our findings pave the way for experimental applications, providing a robust and accessible tool for deciphering the intricate landscape of quantum resources
The EFT of large spin mesons
No full textWe use effective string theory to study mesons with large spin J in large Nc QCD as rotating open strings. In the first part of this work, we formulate a consistent effective field theory (EFT) for open spinning strings with light quarks. Our EFT provides a consistent treatment of the endpoints’ singularities that arise in the massless limit. We obtain results, in a systematic 1/J expansion, for the spectrum of the leading and daughter Regge trajectories. Interestingly, we find that the redshift factor associated with the quarks’ acceleration implies that the applicability regime of the EFT is narrower compared to that of static flux tubes. In the second part of this work, we discuss several extensions of phenomenological interests, including mesons with heavy quarks, the quarks’ spin and the daughter Regge trajectories associated with the worldsheet axion, a massive string mode identified in lattice simulations of 4d flux tubes. We compare our predictions with 4d QCD spectroscopy data, and suggest potential stringy interpretations of the observed mesons. We finally comment on the relation between the EFT spectrum and the Axionic String Ansatz, a recently proposed characterization of the spectrum of Yang-Mills glueballs
Thermodynamic properties of fcc lead: A scalar and fully relativistic first principle study
No full textThis study investigates the thermodynamic properties of face-centered cubic lead (fcc-Pb) using ab-initio methods within the quasi-harmonic approximation (QHA), examining the influence of spin-orbit coupling (SOC) and the exchange-correlation functionals. Two types of ultrasoft pseudopotential (US-PP) are considered: one that excludes (scalar relativistic PP) and one that includes the SOC effects (fully relativistic PP). Further, for each PP, we test the performance of three popular exchange-correlation functionals: Perdew-Burke-Ernzerhof generalized gradient approximation (PBE) (Perdew et al. Phys. Rev. Lett. 77, 3865 (1996)), PBE modified for dense solids (PBEsol) (Perdew et al. Phys. Rev. Lett. 100, 136,406 (2008)), and local density approximation (LDA) (Perdew et al. Phys. Rev. B 23, 5048 (1981)). We calculate the Helmholtz free energy, incorporating lattice vibrations (phonons) and electronic excitation contributions. The estimated equation of state (at 4 K and 301 K), phonon dispersions (at 100 K and 300 K), mode-Gr & uuml;neisen parameters (gamma q eta) (at 100 K), volume thermal expansion coefficient (beta), isobaric heat capacity (CP), bulk modulus (BS), and thermodynamic average Gr & uuml;neisen parameter (gamma) are compared with the available experimental and theoretical studies. Moreover, the 0 K pressure- dependent elastic constant-coefficient (Cij) of fcc lead and Pugh ratio, Debye temperature, and longitudinal and transverse sound velocities for polycrystalline lead are presented. The contributions of electronic excitations in all the thermodynamic properties are found to be negligible. With increasing pressure, the role of spin-orbit effects decreases but does not vanish. Our findings demonstrate that SOC leads to results distinct from the SR approach, but agreement with the experiment is not consistently improved by including SOC