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We propose and analyze two convection quasi-robust and pressure robust finite element methods for a fully nonlinear time-dependent magnetohydrodynamics problem. The schemes make use of suitable upwind and CIP stabilizations to handle the fluid and magnetic convective terms. The developed error estimates are uniform in both diffusion parameters and optimal with respect to the diffusive norm; furthermore, for the second (more complex) method we are able to show a quicker error reduction rate in convection dominated regimes. A set of numerical tests support our theoretical findings.

In this paper, we design and analyze a Virtual Element discretization for the steady motion of non-Newtonian, incompressible fluids. A specific stabilization, tailored to mimic the monotonicity and boundedness properties of the continuous operator, is introduced and theoretically investigated. The proposed method has several appealing features, including the exact enforcement of the divergence free condition and the possibility of making use of fully general polygonal meshes. A complete well-posedness and convergence analysis of the proposed method is presented under mild assumptions on the non-linear laws, encompassing common examples such as the Carreau--Yasuda model. Numerical experiments validating the theoretical bounds as well as demonstrating the practical capabilities of the proposed formulation are presented.

We introduce a pressure robust Finite Element Method for the linearized Magnetohydrodynamics equations in three space dimensions, which is provably quasi-robust also in the presence of high fluid and magnetic Reynolds numbers. The proposed scheme uses a non-conforming BDM approach with suitable DG terms for the fluid part, combined with an $H^1$-conforming choice for the magnetic fluxes. The method introduces also a specific CIP-type stabilization associated to the coupling terms. Finally, the theoretical result are further validated by numerical experiments.

In the present contribution we propose a novel conforming Finite Element scheme for the time-dependent Navier-Stokes equation, which is proven to be both convection quasi-robust and pressure robust. The method is built combining a "divergence-free" velocity/pressure couple (such as the Scott-Vogelius element), a Discontinuous Galerkin in time approximation, and a suitable SUPG-curl stabilization. A set of numerical tests, in accordance with the theoretical results, is included.

We design an adaptive virtual element method (AVEM) of lowest order over triangular meshes with hanging nodes in 2d, which are treated as polygons. AVEM hinges on the stabilization-free a posteriori error estimators recently derived in [8]. The crucial property, that also plays a central role in this paper, is that the stabilization term can be made arbitrarily small relative to the a posteriori error estimators upon increasing the stabilization parameter. Our AVEM concatenates two modules, GALERKIN and DATA. The former deals with piecewise constant data and is shown in [8] to be a contraction between consecutive iterates. The latter approximates general data by piecewise constants to a desired accuracy. AVEM is shown to be convergent and quasi-optimal, in terms of error decay versus degrees of freedom, for solutions and data belonging to appropriate approximation classes. Numerical experiments illustrate the interplay between these two modules and provide computational evidence of optimality.

Since its launch, the Alpha Magnetic Spectrometer-02 (AMS-02) has delivered outstanding quality measurements of the spectra of cosmic-ray (CR) species, $\bar{p}$, $e^{\pm}$, and nuclei (H-Si, Fe), which resulted in a number of breakthroughs. The most recent AMS-02 result is the measurement of the spectra of CR sodium and aluminum up to $\sim$2 TV. Given their low solar system abundances, a significant fraction of each element is produced in fragmentations of heavier species, predominantly Ne, Mg, and Si. In this paper, we use precise measurements of the sodium and aluminum spectra by AMS-02 together with ACE-CRIS and Voyager 1 data to test their origin. We show that the sodium spectrum agrees well with the predictions made with the GalProp-HelMod framework, while aluminum spectrum shows a significant excess in the rigidity range from 2-7 GV. In this context, we discuss the origin of other low-energy excesses in Li, F, and Fe found earlier. The observed excesses in Li, F, and Al appear to be consistent with the local Wolf-Rayet (WR) stars hypothesis, invoked to reproduce anomalous $^{22}$Ne/$^{20}$Ne, $^{12}$C/$^{16}$O, and $^{58}$Fe/$^{56}$Fe ratios in CRs, while excess in Fe is likely connected with a past SN activity in the solar neighborhood. We also provide updated local interstellar spectra (LIS) of sodium and aluminum in the rigidity range from few MV to $\sim$2 TV. Our calculations employ the self-consistent GalProp-HelMod framework that has proved to be a reliable tool in deriving the LIS of CR $\bar{p}$, $e^{-}$, and nuclei $Z\le28$., Comment: 19 pages, 16 figures, 11 tables; ApJ in press

In the present paper we initiate the challenging task of building a mathematically sound theory for Adaptive Virtual Element Methods (AVEMs). Among the realm of polygonal meshes, we restrict our analysis to triangular meshes with hanging nodes in 2d -- the simplest meshes with a systematic refinement procedure that preserves shape regularity and optimal complexity. A major challenge in the a posteriori error analysis of AVEMs is the presence of the stabilization term, which is of the same order as the residual-type error estimator but prevents the equivalence of the latter with the energy error. Under the assumption that any chain of recursively created hanging nodes has uniformly bounded length, we show that the stabilization term can be made arbitrarily small relative to the error estimator provided the stabilization parameter of the scheme is sufficiently large. This quantitative estimate leads to stabilization-free upper and lower a posteriori bounds for the energy error. This novel and crucial property of VEMs hinges on the largest subspace of continuous piecewise linear functions and the delicate interplay between its coarser scales and the finer ones of the VEM space. An important consequence for piecewise constant data is a contraction property between consecutive loops of AVEMs, which we also prove. Our results apply to $H^1$-conforming (lowest order) VEMs of any kind, including the classical and enhanced VEMs.

Since its launch, the Alpha Magnetic Spectrometer-02 (AMS-02) has delivered outstanding quality measurements of the spectra of cosmic-ray (CR) species, $\bar{p}$, $e^{\pm}$, and nuclei (H--O, Ne, Mg, Si, Fe), which resulted in a number of breakthroughs. The most recent AMS-02 result is the measurement of the spectrum of CR fluorine up to $\sim$2 TV. Given its very low solar system abundance, fluorine in CRs is thought to be mostly secondary, produced in fragmentations of heavier species, predominantly Ne, Mg, and Si. Similar to the best-measured secondary-to-primary boron to carbon nuclei ratio that is widely used to study the origin and propagation of CR species, the precise fluorine data would allow the origin of Si-group nuclei to be studied independently. Meanwhile, the secondary origin of CR fluorine has never been tested in a wide energy range due to the lack of accurate CR data. In this paper, we use the first ever precise measurements of the fluorine spectrum by AMS-02 together with ACE-CRIS and Voyager 1 data to actually test this paradigm. Our detailed modeling shows an excess below 10 GV in the fluorine spectrum that may hint at a primary fluorine component. We also provide an updated local interstellar spectrum (LIS) of fluorine in the rigidity range from few MV to $\sim$2 TV. Our calculations employ the self-consistent GalProp-HelMod framework that has proved to be a reliable tool in deriving the LIS of CR $\bar{p}$, $e^{-}$, and nuclei $Z\le28$., Comment: 14 pages, 10 figures, 8 tables; ApJ in press

Since its launch, the Alpha Magnetic Spectrometer - 02 (AMS-02) has delivered outstanding quality measurements of the spectra of cosmic-ray (CR) species, $\bar{p}$, $e^{\pm}$, and nuclei, $_1$H-$_8$O, $_{10}$Ne, $_{12}$Mg, $_{14}$Si, which resulted in a number of breakthroughs. One of the latest long awaited surprises is the spectrum of $_{26}$Fe just published by AMS-02. Because of the large fragmentation cross section and large ionization energy losses, most of CR iron at low energies is local, and may harbor some features associated with relatively recent supernova (SN) activity in the solar neighborhood. Our analysis of new iron spectrum together with Voyager 1 and ACE-CRIS data reveals an unexpected bump in the iron spectrum and in the Fe/He, Fe/O, and Fe/Si ratios at 1-2 GV, while a similar feature in the spectra of He, O, Si, and in their ratios is absent, hinting at a local source of low-energy CRs. The found excess fits well with recent discoveries of radioactive $^{60}$Fe deposits in terrestrial and lunar samples, and in CRs. We provide an updated local interstellar spectrum (LIS) of iron in the energy range from 1 MeV nucleon$^{-1}$ to $\sim$10 TeV nucleon$^{-1}$. Our calculations employ the GalProp-HelMod framework that is proved to be a reliable tool in deriving the LIS of CR $\bar{p}$, $e^{-}$, and nuclei $Z\le28$., Comment: 12 pages, 9 figures, 5 tables; Accepted for publication in the Astrophysical Journal. arXiv admin note: text overlap with arXiv:2006.01337

The objective of this contribution is to develop a convergence analysis for SUPG-stabilized Virtual Element Methods in diffusion-convection problems that is robust also in the convection dominated regime. For the original method introduced in [Benedetto et al, CMAME 2016] we are able to show an "almost uniform" error bound (in the sense that the unique term that depends in an unfavorable way on the parameters is damped by a higher order mesh-size multiplicative factor). We also introduce a novel discretization of the convection term that allows us to develop error estimates that are fully robust in the convection dominated cases. We finally present some numerical result.

We study, both theoretically and numerically, the equilibrium of a hinged rigid leaflet with an attached rotational spring, immersed in a stationary incompressible fluid within a rigid channel. Through a careful investigation of the properties of the functional describing the angular momentum exerted by the fluid on the leaflet (which depends on both the leaflet angular position and its thickness), we identify sufficient conditions on the spring stiffness function for the existence (and uniqueness) of equilibrium positions. We propose a numerical technique that exploits the mesh flexibility of the Virtual Element Method (VEM). A (polygonal) computational mesh is generated by cutting a fixed background grid with the leaflet geometry, and the problem is then solved with stable VEM Stokes elements of degrees $1$ and $2$ combined with a bisection algorithm. We present a large array of numerical experiments to document the accuracy and robustness with respect to degenerate geometry of the proposed methodology.

Composition and spectra of Galactic cosmic rays (CRs) are vital for studies of high-energy processes in a variety of environments and on different scales, for interpretation of gamma-ray and microwave observations, disentangling possible signatures of new phenomena, and for understanding of our local Galactic neighborhood. Since its launch, AMS-02 has delivered outstanding quality measurements of the spectra of antiprotons, electrons, positrons, and nuclei: H-O, Ne, Mg, Si. These measurements resulted in a number of breakthroughs, however, spectra of heavier nuclei and especially low-abundance nuclei are not expected until later in the mission. Meanwhile, a comparison of published AMS-02 results with earlier data from HEAO-3-C2 indicate that HEAO-3-C2 data may be affected by undocumented systematic errors. Utilizing such data to compensate for the lack of AMS-02 measurements could result in significant errors. In this paper we show that a fraction of HEAO-3-C2 data match available AMS-02 measurements quite well and can be used together with Voyager 1 and ACE-CRIS data to make predictions for the local interstellar spectra (LIS) of nuclei that are not yet released by AMS-02. We are also updating our already published LIS to provide a complete set from H-Ni in the energy range from 1 MeV/nucleon to ~100-500 TeV/nucleon thus covering 8-9 orders of magnitude in energy. Our calculations employ the GalProp-HelMod framework that is proved to be a reliable tool in deriving the LIS of CR antiprotons, electrons, and nuclei H-O., Comment: 90 pages, 36 figures, 60 tables, ApJS; Fixed typos in Eqs.(C2) and (C32)

In the present contribution we develop a sharper error analysis for the Virtual Element Method, applied to a model elliptic problem, that separates the element boundary and element interior contributions to the error. As a consequence we are able to propose a variant of the scheme that allows to take advantage of polygons with many edges (such as those composing Voronoi meshes or generated by agglomeration procedures) in order to yield a more accurate discrete solution. The theoretical results are supported by numerical experiments., Comment: 22 pages, 6 figures

We discuss the odderon in the QCD and analyze the effects of running coupling introduced in a particular way to preserve the reggeization of the gluon within the leading logarithmic description. This idea is also applied to a family of BKP states with arbitrarily number of gluons in the planar limit. The numerical analysis shows that contrary to the pomeron case where the leading states become discretized, the odderon states still remain a continuous family starting at intercept one. The following rapidity dependence of the amplitude is studied. For the pomeron-odderon system the relation between the descriptions in the reggeized gluon (BFKL) framework and the color dipole/CGC one is investigated., Comment: 41 pages, 8 figures; a chapter for the memorial volume "From the past to the future - the legacy of Lev Lipatov"

We discuss the possibility to define exact RG equations for a UV regulated Wilsonian action based on a proper time (PT) regulator function. We start from a functional mapping which shows how each particular flow equation (and RG scheme) is associated to infinitely many scale dependent field redefinitions, which are related to specific coarse-graining procedures. On specializing to a sub-family of one parameter PT regulators we briefly analyze few results for the Ising Universality class in three dimensions, obtained within a second order truncation in the derivative expansion of the Wilsonian action., Comment: 18 pages, 1 figure, revtex, few clarifying comments and references added

Local interstellar spectra (LIS) of secondary cosmic ray (CR) nuclei, lithium, beryllium, boron, and partially secondary nitrogen, are derived in the rigidity range from 10 MV to ~200 TV using the most recent experimental results combined with the state-of-the-art models for CR propagation in the Galaxy and in the heliosphere. The lithium spectrum appears somewhat flatter at high energies compared to other secondary species that may imply a primary lithium component. Two propagation packages, GALPROP and HelMod, are combined to provide a single framework that is run to reproduce direct measurements of CR species at different modulation levels, and at both polarities of the solar magnetic field. An iterative maximum-likelihood method is developed that uses GALPROP-predicted LIS as input to HelMod, which provides the modulated spectra for specific time periods of the selected experiments for the model-data comparison. The proposed LIS accommodate the low-energy interstellar spectra measured by Voyager 1, HEAO-3, and ACE/CRIS as well as the high-energy observations by PAMELA, AMS-02, and earlier experiments that are made deep in the heliosphere. The interstellar and heliospheric propagation parameters derived in this study are consistent with our earlier results for propagation of CR protons, helium, carbon, oxygen, antiprotons, and electrons., Comment: 17 pages, 10 figures, 6 tables, ApJ accepted

A measurement of the dipole anisotropy in galactic coordinates for different charged cosmic rays has been performed with the Alpha Magnetic Spectrometer (AMS) onboard the International Space Station (ISS). Results are presented for the first 7.5 years of data taking for protons, Helium, Carbon and Oxygen, and 6.5 years for positrons and electrons. All the species are found to be consistent with isotropy and upper limits to the dipole amplitude have been computed. In particular, for energies above 16 GeV a limit of delta < 1.9% and delta < 0.5% at the 95% C.I. is found for positrons and electrons respectively. For rigidities above 200 GV a limit of delta < 0.38%, delta < 0.36%, delta < 1.9% and delta < 1.7% is obtained for protons, Helium, Carbon and Oxygen., Comment: "Talk presented at the 2019 Meeting of the Division of Particles and Fields of the American Physical Society (DPF2019), July 29 - August 2, 2019, Northeastern University, Boston, C1907293."

The present paper has two objectives. On one side, we develop and test numerically divergence free Virtual Elements in three dimensions, for variable ``polynomial'' order. These are the natural extension of the two-dimensional divergence free VEM elements, with some modification that allows for a better computational efficiency. We test the element's performance both for the Stokes and (diffusion dominated) Navier-Stokes equation. The second, and perhaps main, motivation is to show that our scheme, also in three dimensions, enjoys an underlying discrete Stokes complex structure. We build a pair of virtual discrete spaces based on general polytopal partitions, the first one being scalar and the second one being vector valued, such that when coupled with our velocity and pressure spaces, yield a discrete Stokes complex.

We present some general results for the multi-critical multi-field models in d>2 recently obtained using CFT and Schwinger-Dyson methods at perturbative level without assuming any symmetry. Results in the leading non trivial order are derived consistently for several conformal data in full agreement with functional perturbative RG methods. Mechanisms like emergent (possibly approximate) symmetries can be naturally investigated in this framework., Comment: 12 pages, 1 figure, Contribution to the Conference QFT2018, Quantum Fields From Fundamental Concepts to Phenomenological Questions, Mainz 26-28 September 2018

We discuss the $p$- and the $hp$-versions of the virtual element method for the approximation of eigenpairs of elliptic operators with a potential term on polygonal meshes. An application of this model is provided by the Schr\"odinger equation with a pseudo-potential term. We present in details the analysis of the p-version of the method, proving exponential convergence in the case of analytic eigenfunctions. The theoretical results are supplied with a wide set of experiments. We also show numerically that, in the case of eigenfunctions with finite Sobolev regularity, an exponential approximation of the eigenvalues in terms of the cubic root of the number of degrees of freedom can be obtained by employing $hp$-refinements. Importantly, the geometric flexibility of polygonal meshes is exploited in the construction of the $hp$-spaces., Comment: 25 pages, 7 figures

In this paper we encode the perturbative BFKL leading logarithmic resummation, relevant for the Regge limit behavior of QCD scattering amplitudes, in the IR-regulated effective action which satisfies exact functional renormalization group equations. This is obtained using a truncation with a specific infinite set of non local vertices describing the multi-Regge kinematics (MRK). The goal is to use this framework to study, in the high energy limit and at larger transverse distances the transition to a much simpler effective local reggeon field theory, whose critical properties were recently investigated in the same framework. We perform a numerical analysis of the spectrum of the BFKL Pomeron deformed by the introduction of a Wilsonian infrared regulator to understand the properties of the leading poles (states) contributing to the high energy scattering., Comment: 46 pages, 27 figures, latex (one figure added, a reference corrected)

In the present paper, we investigate the underlying Stokes complex structure of the Virtual Element Method for Stokes and Navier--Stokes introduced in previous papers by the same authors, restricting our attention to the two dimensional case. We introduce a Virtual Element space $\Phi_h \subset H^2(\Omega)$ and prove that the triad $\{\Phi_h, V_h, Q_h\}$ (with $V_h$ and $Q_h$ denoting the discrete velocity and pressure spaces) is an exact Stokes complex. Furthermore, we show the computability of the associated differential operators in terms of the adopted degrees of freedom and explore also a different discretization of the convective trilinear form. The theoretical findings are supported by numerical tests.

Local interstellar spectra (LIS) of primary cosmic ray (CR) nuclei, such as helium, oxygen, and mostly primary carbon are derived for the rigidity range from 10 MV to ~200 TV using the most recent experimental results combined with the state-of-the-art models for CR propagation in the Galaxy and in the heliosphere. Two propagation packages, GALPROP and HelMod, are combined into a single framework that is used to reproduce direct measurements of CR species at different modulation levels, and at both polarities of the solar magnetic field. The developed iterative maximum-likelihood method uses GALPROP-predicted LIS as input to HelMod, which provides the modulated spectra for specific time periods of the selected experiments for model-data comparison. The interstellar and heliospheric propagation parameters derived in this study are consistent with our prior analyses using the same methodology for propagation of CR protons, helium, antiprotons, and electrons. The resulting LIS accommodate a variety of measurements made in the local interstellar space (Voyager 1) and deep inside the heliosphere at low (ACE/CRIS, HEAO-3) and high energies (PAMELA, AMS-02)., Comment: 13 pages, 13 figures, 6 tables, ApJ in press. arXiv admin note: text overlap with arXiv:1704.06337

The local interstellar spectrum (LIS) of cosmic-ray (CR) electrons for the energy range 1 MeV to 1 TeV is derived using the most recent experimental results combined with the state-of-the-art models for CR propagation in the Galaxy and in the heliosphere. Two propagation packages, GALPROP and HelMod, are combined to provide a single framework that is run to reproduce direct measurements of CR species at different modulation levels, and at both polarities of the solar magnetic field. An iterative maximum-likelihood method is developed that uses GALPROP-predicted LIS as input to HelMod, which provides the modulated spectra for specific time periods of the selected experiments for model-data comparison. The optimized HelMod parameters are then used to adjust GALPROP parameters to predict a refined LIS with the procedure repeated subject to a convergence criterion. The parameter optimization uses an extensive data set of proton spectra from 1997-2015. The proposed CR electron LIS accommodates both the low-energy interstellar spectra measured by Voyager 1 as well as the high-energy observations by PAMELA and AMS-02 that are made deep in the heliosphere; it also accounts for Ulysses counting rate features measured out of the ecliptic plane. The interstellar and heliospheric propagation parameters derived in this study agree well with our earlier results for CR protons, helium nuclei, and anti-protons propagation and LIS obtained in the same framework., Comment: 11 pages, 14 figures, 4 tables; ApJ, in press

In this paper we initiate the investigation of Virtual Elements with curved faces. We consider the case of a fixed curved boundary in two dimensions, as it happens in the approximation of problems posed on a curved domain or with a curved interface. While an approximation of the domain with polygons leads, for degree of accuracy $k \geq 2$, to a sub-optimal rate of convergence, we show (both theoretically and numerically) that the proposed curved VEM lead to an optimal rate of convergence.

Local interstellar spectra (LIS) for protons, helium and antiprotons are built using the most recent experimental results combined with the state-of-the-art models for propagation in the Galaxy and heliosphere. Two propagation packages, GALPROP and HelMod, are combined to provide a single framework that is run to reproduce direct measurements of cosmic ray (CR) species at different modulation levels and at both polarities of the solar magnetic field. To do so in a self-consistent way, an iterative procedure was developed, where the GALPROP LIS output is fed into HelMod that provides modulated spectra for specific time periods of selected experiments to compare with the data; the HelMod parameters optimization is performed at this stage and looped back to adjust the LIS using the new GALPROP run. The parameters were tuned with the maximum likelihood procedure using an extensive data set of proton spectra from 1997-2015. The proposed LIS accommodate both the low energy interstellar CR spectra measured by Voyager 1 and the high energy observations by BESS, Pamela, AMS-01, and AMS-02 made from the balloons and near-Earth payloads; it also accounts for Ulysses counting rate features measured out of the ecliptic plane. The found solution is in a good agreement with proton, helium, and antiproton data by AMS-02, BESS, and PAMELA in the whole energy range., Comment: 22 pages, 23 figures, 8 tables, and 3 machine-readable tables; ApJ, in press

The heliospheric modulation model \helmod{} is a two dimensional treatment dealing with the helio-colatitude and radial distance from Sun and is employed to solve the transport-equation for the GCR propagation through the heliosphere down to Earth. This work presents the current version 3 of the \helmod{} model and reviews how main processes involved in GCR propagation were implemented.~The treatment includes the so-called particle drift effects --~e.g., those resulting, for instance, from the extension of the neutral current sheet inside the heliosphere and from the curvature and gradient of the IMF --, which affect the transport of particles entering the solar cavity as a function of their charge sign.~The \helmod{} model is capable to provide modulated spectra which well agree within the experimental errors with those measured by AMS-01, BESS, PAMELA and AMS-02 during the solar cycles 23 and 24.~Furthermore, the counting rate measured by Ulysses at +/- 80degree of solar latitude and 1 to 5\,AU was also found in agreement with that expected by \helmod{} code version 3.

A family of Virtual Element Methods for the 2D Navier-Stokes equations is proposed and analysed. The schemes provide a discrete velocity field which is point-wise divergence-free. A rigorous error analysis is developed, showing that the methods are stable and optimally convergent. Several numerical tests are presented, confirming the theoretical predictions. A comparison with some mixed finite elements is also performed.

Propagation of cosmic rays (CRs) from their sources to the observer is described mainly as plain diffusion at high energies, while at lower energies there are other physical processes involved, both in the interstellar space and in the heliosphere. The latter was a subject of considerable uncertainty until recently. New data obtained by several CR missions can be used to and the local interstellar spectra (LIS) of CR species that would significantly reduce the uncertainties associated with the heliospheric propagation. In this paper we present the LIS of CR protons and helium outside the heliospheric boundary. The proposed LIS are tuned to accommodate both, the low energy CR spectra measured by Voyager 1, and the high energy observations publicly released by BESS, Pamela, AMS-01 and AMS-02. The proton and helium LIS are derived by combining CR propagation in the Galaxy, as described by GALPROP, with the heliospheric modulation computed using the HelMod Monte Carlo Tool. The proposed LIS are tuned to reproduce the modulated spectra for both, high and low, levels of solar activity., Comment: "XXV ECRS 2016 Proceedings - eConf C16-09-04.3"

The search for cosmic ray anisotropy has been performed using particles collected by the Alpha Magnetic Spectrometer after the first five years of operation. The positron to electron ratio is consistent with isotropy at all energies and angular scales. The limit on the dipole anisotropy at the 95% confidence level for energies above 16GeV is $\delta<0.020$ for positrons and $\delta<0.006$ for electrons. In the case of high rigidity protons the upper limit in the rigidity range from 80 to 1800GV is $\delta<0.003$. No indication of seasonal excess is observed for all particle species within the present statistics., Comment: XXV ECRS 2016 Proceedings - eConf C16-09-04.3

HelMod is a code evaluating the transport of Galactic cosmic rays through the inner heliosphere down to Earth. It is based on a 2-D Monte Carlo approach and includes a general description of the symmetric and antisymmetric parts of the diffusion tensor, thus, properly treating the particle drift effects. The model has been tuned in order to fit the data observed outside the ecliptic plane at several distances from the Earth and the spectra observed near the Earth for both, high and low solar activity levels. A stand-alone python module, fully compatible with GalProp, was developed for a comprehensive calculation of solar modulation effects, resulting in a newly suggested set of local interstellar spectra., Comment: XXV ECRS 2016 Proceedings - eConf C16-09-04.3

In this paper we extend our recent non perturbative functional renormalization group analysis of Reggeon Field Theory to the interactions of Pomeron and Odderon fields. We establish the existence of a fixed point and its universal properties, which exhibits a novel symmetry structure in the space of Odderon-Pomeron interactions. As in our previous analysis, this part of our program aims at the investigation of the IR limit of reggeon field theory (the limit of high energies and large transverse distances). It should be seen in the broader context of trying to connect the nonperturbative infrared region (large transverse distances) with the UV region of small transverse distances where the high energy limit of perturbative QCD applies., Comment: 26 pages, latex, 4 figures, version accepted for publication in PRD

In the present paper we develop a new family of Virtual Elements for the Stokes problem on polygonal meshes. By a proper choice of the Virtual space of velocities and the associated degrees of freedom, we can guarantee that the final discrete velocity is pointwise divergence-free, and not only in a relaxed (projected) sense, as it happens for more standard elements. Moreover, we show that the discrete problem is immediately equivalent to a reduced problem with less degrees of freedom, thus yielding a very efficient scheme. We provide a rigorous error analysis of the method and several numerical tests, including a comparison with a different Virtual Element choice.

The cosmic rays modulation inside the heliosphere is well described by a transport equation introduced by Parker in 1965. To solve this equation several approaches were followed in the past. Recently the Monte Carlo approach becomes widely used in force of his advantages with respect to other numerical methods. In the Monte Carlo approach, the transport equation is associated to a fully equivalent set of Stochastic Differential Equations. This set is used to describe the stochastic path of a quasi-particle from a source, e.g., the interstellar medium, to a specific target, e.g., a detector at Earth. In this work, we present both the Forward-in-Time and Backward-in-Time Monte Carlo solutions. We present an implementation of both algorithms in the framework of HelMod Code showing that the difference between the two approach is below 5\% that can be quoted as the systematic uncertain of the Method itself., Comment: presented at the The 34th International Cosmic Ray Conference, 30 July- 6 August, 2015, The Hague, The Netherlands

Can large distance high energy QCD be described by Reggeon Field Theory as an effective emergent theory? We start to investigate the issue employing functional renormalisation group techniques., Comment: 4 pages, 1 figure, To appear in the Proceedings of conference: Diffraction 2014 - International Workshop on Diffraction in High-Energy Physics

There have been some speculations about the existence of critical unitary O(N)-invariant scalar field theories in dimensions 4