We collect and describe the observed geometrical and dynamical properties of turbulence in quantum fluids, particularly superfluid helium and atomic condensates for which more information about turbulence is available. Considering the spectral features, the temporal decay, and the comparison with relevant turbulent classical flows, we identify three main limiting types of quantum turbulence: Kolmogorov quantum turbulence, Vinen quantum turbulence, and strong quantum turbulence. This classification will be useful to analyze and interpret new results in these and other quantum fluids.

When the intensity of turbulence is increased (by increasing the Reynolds number, e.g., by reducing the viscosity of the fluid), the rate of the dissipation of kinetic energy decreases but does not tend asymptotically to zero: it levels off to a nonzero constant as smaller and smaller vortical flow structures are generated. This fundamental property, called the dissipation anomaly, is sometimes referred to as the zeroth law of turbulence. The question of what happens in the limit of vanishing viscosity (purely hypothetical in classical fluids) acquires a particular physical significance in the context of liquid helium, a quantum fluid which becomes effectively inviscid at low temperatures achievable in the laboratory. By performing numerical simulations and identifying the superfluid Reynolds number, here we show evidence for a superfluid analog to the classical dissipation anomaly. Our numerics indeed show that as the superfluid Reynolds number increases, smaller and smaller structures are generated on the quantized vortex lines on which the superfluid vorticity is confined, balancing the effect of weaker and weaker dissipation.

We show that a toroidal bundle of quantized vortex rings in superfluid helium generates a large-scale wake in the normal fluid which reduces the overall friction experienced by the bundle, thus greatly enhancing its lifetime, as observed in experiments. This collective effect is similar to the drag reduction observed in systems of active, hydrodynamically cooperative agents such as bacteria in aqueous suspensions, fungal spores in the atmosphere, and cyclists in pelotons.

This Letter proposes a solution of the Vacuum Energy and the Cosmological Constant (CC)paradox based on the Zel'dovich's ansatz, which states that the observable contribution to thevacuum energy density is given by the gravitational energy of virtual particle-antiparticle pairs,continually generated and annihilated in the vacuum state. The novelty of this work is the use of anultraviolet cut-off length based on the Holographic Principle, which is shown to yield current valuesof the CC in good agreement with experimental observations.

We compute to high post-Newtonian accuracy the 4-momentum (linear momentum and energy), radiatedas gravitational waves in a two-body system undergoing gravitational scattering. We include, for the firsttime, all the relevant time-asymmetric effects that arise when consistently going three post-Newtonianorders beyond the leading post-Newtonian order. We find that the inclusion of time-asymmetric radiativeeffects (both in tails and in the radiation-reacted hyperbolic motion) is crucial to ensure the masspolynomiality of the post-Minkowskian expansion (G expansion) of the radiated 4-momentum. Imposingthe mass polynomiality of the corresponding individual impulses determines the conservativelikeradiative contributions at the fourth post-Minkowskian order and strongly constrains them at the fifthpost-Minkowskian order.

We compute the leading order contribution to radiative losses in the case of spinning binaries with alignedspins due to their spin-orbit interaction. The orbital average along hyperboliclike orbits is taken through anappropriate spin-orbit modification to the quasi-Keplerian parametrization for nonspinning bodies, whichmaintains the same functional form, but with spin-dependent orbital elements. We perform consistencychecks with existing post-Newtonian-based and post-Minkowskian (PM)-based results. In the former case,we compare our expressions for both radiated energy and angular momentum with those obtained in [G. Choet al., From boundary data to bound states. Part III. Radiative effects,J. High Energy Phys. 04 (2022) 154] byapplying the boundary-to-bound correspondence to known results for ellipticlike orbits, finding agreement.The linear momentum loss is instead newly computed here. In the latter case, we also find agreement with thelow-velocity limit of recent calculations of the total radiated energy, angular momentum and linearmomentum in the framework of an extension of the worldline quantum field theory approach to the classicalscattering of spinning bodies at the leading PM order [G. U. Jakobsen et al., Gravitational Bremsstrahlungand Hidden Supersymmetry of Spinning Bodies, Phys. Rev. Lett. 128, 011101 (2022), M. M. Riva et al.,Gravitational bremsstrahlung from spinning binaries in the post-Minkowskian expansion, Phys. Rev. D 106,044013 (2022)]. We get exact expressions of the radiative losses in terms of the orbital elements, even if theyare at the leading post-Newtonian order, so that their expansion for large values of the eccentricity parameter(or equivalently of the impact parameter) provides higher-order terms in the corresponding PM expansion,which can be useful for future crosschecks of other approaches.

We compare recent one-loop-level, scattering-amplitude-based, computations of the classical partof the gravitational bremsstrahlung waveform to the frequency-domain version of the corresponding Multipolar-Post-Minkowskianwaveform result. When referring the one-loop result to the classical averaged momenta $\bar p_a = \frac12 (p_a+p'_a)$,the two waveforms are found to agree at the Newtonian and first post-Newtonian levels,as well as at the first-and-a-half post-Newtonian level, i.e. for the leading-order quadrupolar tail.However, we find that there are significant differences at the second-and-a-half post-Newtonian level,$O\left( \frac{G^2}{c^5} \right)$, i.e.when reaching: (i) the first post-Newtonian correction to the linear quadrupole tail; (ii) Newtonian-level linear tailsof higher multipolarity (odd octupole and even hexadecapole); (iii) radiation-reaction effects on the worldlines;and (iv) various contributions of cubically nonlinear origin (notably linked tothe quadrupole$\times$ quadrupole$\times$ quadrupole coupling in the wavezone).These differences are reflected at the sub-sub-sub-leading level in the soft expansion, $ \sim \om \ln \om $, i.e. $O\left(\frac{1}{t^2} \right)$in the time domain.Finally, we computed the first four terms of the low-frequency expansion of the Multipolar-Post-Minkowskian waveform and checkedthat they agree with the corresponding existing classical soft graviton results.

Based on a previous ansatz by Zel'dovich for the gravitational energy of virtualparticle-antiparticle pairs, supplemented with the Holographic Principle, we estimate the vacuumenergy in a fairly reasonable agreement with the experimental values of the Cosmological Constant.We further highlight a connection between Wheeler's quantum foam and graviton condensation,as contemplated in the quantum N-portrait paradigm, and show that such connection also leads toa satisfactory prediction of the value of the cosmological constant. The above results suggest thatthe "unnaturally" small value of the cosmological constant may find a quite "natural" explanationonce the nonlocal perspective of the large N-portrait gravitational condensation is endorsed.

The class of Petrov type I curvature tensors is further divided into those for whichthe span of the set of distinct principal null directions has dimension four (maximallyspanning type I) or dimension three (nonmaximally spanning type I). Explicit examplesare provided for both vacuum and nonvacuum spacetimes.

Taking wedge products of the p distinct principal null directions (PNDs) associated with the eigen-bivectors of the Weyl tensor associated with the Petrov classification, when linearly independent, one is able to express them in terms of the eigenvalues governing this decomposition. We study here algebraic and differential properties of such p-forms by completing previous geometrical results concerning type I spacetimes and extending that analysis to algebraically special spacetimes with at least two distinct PNDs. A number of vacuum and nonvacuum spacetimes are examined to illustrate the general treatment.

Regular physical exercise and appropriate nutrition affect metabolic and hormonal responses and may reduce the risk of developing chronic non-communicable diseases such as high blood pressure, ischemic stroke, coronary heart disease, some types of cancer, and type 2 diabetes mellitus. Computational models describing the metabolic and hormonal changes due to the synergistic action of exercise and meal intake are, to date, scarce and mostly focussed on glucose absorption, ignoring the contribution of the other macronutrients. We here describe a model of nutrient intake, stomach emptying, and absorption of macronutrients in the gastrointestinal tract during and after the ingestion of a mixed meal, including the contribution of proteins and fats. We integrated this effort to our previous work in which we modeled the effects of a bout of physical exercise on metabolic homeostasis. We validated the computational model with reliable data from the literature. The simulations are overall physiologically consistent and helpful in describing the metabolic changes due to everyday life stimuli such as multiple mixed meals and variable periods of physical exercise over prolonged periods of time. This computational model may be used to design virtual cohorts of subjects differing in sex, age, height, weight, and fitness status, for specialized in silico challenge studies aimed at designing exercise and nutrition schemes to support health.

We consider the problem of interpolating a given function on arbitrary configurations of nodes in a compact interval, with a special focus on the case of equidistant or quasi-equidistant nodes. In this case, instead of polynomial interpolation, a family of rational interpolants introduced by Floater and Hormann in [2] turns out to be very useful . Such interpolants (briefly FH interpolants) generalize Berrut's rational interpolation [1] introducing a fixed integer parameter d >= 1 to speed up the convergence getting, in theory, arbitrarily high approximation orders. In this talk we will further generalize by presenting a whole new family of rational interpolants that depend on an additional parameter ? ? N. When ? = 1 we get the original FH interpolants. For ? > 1 we will see that the new interpolants share a lot of the interesting properties of the original FH interpolants (no real poles, baryentric-type representation, high rates of approximation). But, in addition, we get uniformly bounded Lebesgue constants and a more localized approximation of less smooth functions, compared to the original FH interpolation.

As known, polynomial interpolation is not advisable in the case of equidistant nodes, given the exponential growth of the Lebesgue constants and the consequent stability problems. In [1] Floater and Hormann introduce a family of rational interpolants (briefly FH interpolants) depending on a fixed integer parameter d >= 1. They are based on any configuration of the nodes in [a, b], have no real poles and approximation order O(h^{d+1}) for functions in C^{d+2}[a, b], where h denotes the maximum distance between two consecutive nodes. FH interpolants turn out to be very useful for equidistant or quasi-equidistant configurations of nodes when the Lebesgue constants present only a logarithmic growth as the number of nodes increases [2, 3]. In this talk, we introduce a generalization of FH interpolants depending on an additional parameter ? ? N. If ? = 1 we get the classical FH interpolants, but taking ? > 1 we succeed in getting uniformly bounded Lebesgue constants for quasi-equidistant configurations of nodes. Moreover, in comparison with the original FH interpolants, we show that the new interpolants present a much better error prole when the function is less smooth.

Homophily is the principle whereby "similarity breeds connections."We give a quantitative formulation of this principle within networks. Given a network and a labeled partition of its vertices, the vector indexed by each class of the partition, whose entries are the number of edges of the subgraphs induced by the corresponding classes, is viewed as the observed outcome of the random vector described by picking labeled partitions at random among labeled partitions whose classes have the same cardinalities as the given one. This is the recently introduced random coloring model for network homophily. In this perspective, the value of any homophily score ?, namely, a nondecreasing real-valued function in the sizes of subgraphs induced by the classes of the partition, evaluated at the observed outcome, can be thought of as the observed value of a random variable. Consequently, according to the score ?, the input network is homophillic at the significance level ? whenever the one-sided tail probability of observing a value of ? at least as extreme as the observed one is smaller than ?. Since, as we show, even approximating ? is an NP-hard problem, we resort to classical tails inequality to bound ? from above. These upper bounds, obtained by specializing ?, yield a class of quantifiers of network homophily. Computing the upper bounds requires the knowledge of the covariance matrix of the random vector, which was not previously known within the random coloring model. In this paper we close this gap. Interestingly, the matrix depends on the input partition only through the cardinalities of its classes and depends on the network only through its degrees. Furthermore all the covariances have the same sign, and this sign is a graph invariant. Plugging this structure into the bounds yields a meaningful, easy to compute class of indices for measuring network homophily. As demonstrated in real-world network applications, these indices are effective and reliable, and may lead to discoveries that cannot be captured by the current state of the art.

Path graphs are intersection graphs of paths in a tree. We start from the characterization of path graphs by Monma and Wei (1986) [14] and we reduce it to some 2-coloring subproblems, obtaining the first characterization that directly leads to a polynomial recognition algorithm. Then we introduce the collection of the attachedness graphs of a graph and we exhibit a list of minimal forbidden 2-edge colored subgraphs in each of the attachedness graph.

We study the asymptotic behavior, as the lattice spacing ? tends to zero, of the discrete elastic energy induced by topological singularities in an inhomogeneous ? periodic medium within a two-dimensional model for screw dislocations in the square lattice. We focus on the |log?| regime which, as ?->0 allows the emergence of a finite number of limiting topological singularities. We prove that the ?-limit of the |log?| scaled functionals as ?->0 is equal to the total variation of the so-called "limiting vorticity measure" times a factor depending on the homogenized energy density of the unscaled functionals.

This paper deals with the limit cases for s-fractional heat flows in a cylindrical domain, with homogeneous Dirichlet boundary conditions, as s-> 0+ and s-> 1-. We describe the fractional heat flows as minimizing move-ments of the corresponding Gagliardo seminorms, with re-spect to the L2 metric. To this end, we first provide a Gamma-convergence analysis for the s-Gagliardo seminorms as s-+ 0+ and s-+ 1-; then, we exploit an abstract stability result for minimizing movements in Hilbert spaces, with respect to a sequence of Gamma-converging uniformly lambda-convex energy function-als. We prove that s-fractional heat flows (suitably scaled in time) converge to the standard heat flow as s-+ 1-, and to a de-generate ODE type flow as s-+ 0+. Moreover, looking at the next order term in the asymptotic expansion of the s -fractional Gagliardo seminorm, we show that suitably forced s-fractional heat flows converge, as s-+ 0+, to the parabolic flow of an energy functional that can be seen as a sort of renormalized 0-Gagliardo seminorm: the resulting parabolic equation involves the first variation of such an energy, that can be understood as a zero (or logarithmic) Laplacian.(c) 2023 Elsevier Inc. All rights reserved.

We present and release in open source format a sparse linear solver which efficiently exploits heterogeneous parallel computers. The solver can be easily integrated into scientific applications that need to solve large and sparse linear systems on modern parallel computers made of hybrid nodes hosting Nvidia Graphics Processing Unit (GPU) accelerators. The work extends previous efforts of some of the authors in the exploitation of a single GPU accelerator and proposes an implementation, based on the hybrid MPI-CUDA software environment, of a Krylov-type linear solver relying on an efficient Algebraic MultiGrid (AMG) preconditioner already available in the BootCMatchG library. Our design for the hybrid implementation has been driven by the best practices for minimizing data communication overhead when multiple GPUs are employed, yet preserving the efficiency of the GPU kernels. Strong and weak scalability results of the new version of the library on well-known benchmark test cases are discussed. Comparisons with the Nvidia AmgX solution show a speedup, in the solve phase, up to 2.0x.

In this paper, a complete picture of the different plastic failure modes that can be predicted by the strain gradient plasticity model proposed in Del Piero et al. (J. Mech. Mater. Struct. 8:109-151, 2013) is drawn. The evolution problem of the elasto-plastic strain is formulated in Del Piero et al. (J. Mech. Mater. Struct. 8:109-151, 2013) as an incremental minimization problem acting on an energy functional which includes a local plastic term and a non-local gradient contribution. Here, an approximate analytical solution of the evolution problem is determined in the one-dimensional case of a tensile bar. Different solutions are found describing specific plastic strain processes, and correlations between the different evolution modes and the convexity/concavity properties of the plastic energy density are established. The variety of solutions demonstrates the large versatility of the model in describing many failure mechanisms, ranging from brittle to ductile. Indeed, for a convex plastic energy, the plastic strain diffuses in the body, while, for a concave plastic energy, it localizes in regions whose amplitude depends on the internal length parameter included into the non-local energy term, and, depending on the convexity properties of the first derivative of the plastic energy, the localization band expands or contracts. Complex failure processes combining different modes can be reproduced by assuming plastic energy functionals with specific convex and concave branches. The quasi-brittle failure of geomaterials in simple tension tests was reproduced by assuming a convex-concave plastic energy, and the accuracy of the analytical predictions was checked by comparing them with the numerical results of finite element simulations.

We investigate rare semileptonic B -> K* l(+) l(-) by looking at a specific long distance contribution. Our analysis is limited to the very small values of physical accessible range of invariant mass of the leptonic couple q(2). We show that the light quarks loop has to be accounted for, along with the charming penguin contribution, in order to accurately compute the q(2)-spectrum in the Standard Model. Such a long distance contribution may also play a role in the analysis of the lepton flavor universality violation in this process. (c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).