arXiv subjects

A. Nobile

Publications and source records attributed to A. Nobile.

12 recordsLinked to original sources

arXiv2024

Notes on Nash modification

The Nash blowing-up (or modification) of an algebraic variety $X$ is a canonical process that produces a proper, birational morphism $π: X' \to X$ of varieties. It is expected that the singularities of $X'$ will be better than those of $X$. In the mid-1970's, it was proved that in characteristic zero, $π$ is an isomorphism if and only if $X$ is nonsingular, which is false in positive characteristic. The focus of this article is on several subsequent studies on this subject. Topics covered include: (a) the extension of the mentioned theorem to the case where $X$ is normal, in any characteristic, (b) the introduction and study of Nash modifications of higher order, (c) the case where the variety $X$ is toric, where more precise results can be obtained and (d) desingularization properties of the Nash process.

math.AG↗

arXiv2014

Nucleon axial charge and pion decay constant from two-flavor lattice QCD

The axial charge of the nucleon $g_A$ and the pion decay constant $f_π$ are computed in two-flavor lattice QCD. The simulations are carried out on lattices of various volumes and lattice spacings. Results are reported for pion masses as low as $m_π=130\,\mbox{MeV}$. Both quantities, $g_A$ and $f_π$, suffer from large finite size effects, which to leading order ChEFT and ChPT turn out to be identical. By considering the naturally renormalized ratio $g_A/f_π$, we observe a universal behavior as a function of decreasing quark mass. From extrapolating the ratio to the physical point, we find $g_A^R=1.29(5)(3)$, using the physical value of $f_π$ as input and $r_0=0.50(1)$ to set the scale. In a subsequent calculation we attempt to extrapolate $g_A$ and $f_π$ separately to the infinite volume. Both volume and quark mass dependencies of $g_A$ and $f_π$ are found to be well decribed by ChEFT and ChPT. We find at the physical point $g_A^R=1.24(4)$ and $f_π^R=89.6(1.1)(1.8)\,\mbox{MeV}$. Both sets of results are in good agreement with experiment. As a by-product we obtain the low-energy constant $\bar{l}_4=4.2(1)$.

hep-lat↗

arXiv2012

Nucleon mass and sigma term from lattice QCD with two light fermion flavors

We analyze Nf=2 nucleon mass data with respect to their dependence on the pion mass down to mpi = 157 MeV and compare it with predictions from covariant baryon chiral perturbation theory (BChPT). A novel feature of our approach is that we fit the nucleon mass data simultaneously with the directly obtained pion-nucleon sigma-term. Our lattice data below mpi = 435 MeV is well described by O(p^4) BChPT and we find sigma=37(8)(6) MeV for the sigma-term at the physical point. Using the nucleon mass to set the scale we obtain a Sommer parameter of r_0=0.501(10)(11) fm.

hep-lat↗

arXiv2012

First moments of the nucleon generalized parton distributions from lattice QCD

We report on our lattice calculations of the nucleon's generalized parton distributions (GPDs), concentrating on their first moments for the case of N_f=2. Due to recent progress on the numerical side we are able to present results for the generalized form factors at pion masses as low as 260 MeV. We perform a fit to one-loop covariant baryon chiral perturbation theory with encouraging results.

hep-lat↗

arXiv2011

A lattice study of the strangeness content of the nucleon

We determine the quark contributions to the nucleon spin Delta s, Delta u and Delta d as well as their contributions to the nucleon mass, the sigma-terms. This is done by computing both, the quark line connected and disconnected contributions to the respective matrix elements, using the non-perturbatively improved Sheikholeslami-Wohlert Wilson Fermionic action. We simulate n_F=2 mass degenerate sea quarks with a pion mass of about 285 MeV and a lattice spacing a = 0.073 fm. The renormalization of the matrix elements involves mixing between contributions from different quark flavours. The pion-nucleon sigma-term is extrapolated to physical quark masses exploiting the sea quark mass dependence of the nucleon mass. We obtain the renormalized value sigma_{piN}=38(12) MeV at the physical point and the strangeness fraction f_{Ts}=sigma_s/m_N=0.012(14)(+10-3) at our larger than physical sea quark mass. For the strangeness contribution to the nucleon spin we obtain in the MSbar scheme at the renormalization scale of 2.71 GeV Delta s = -0.020(10)(2).

hep-lat↗

arXiv2011

Dirac and Pauli form factors from lattice QCD

We present a comprehensive analysis of the electromagnetic form factors of the nucleon from a lattice simulation with two flavors of dynamical O(a)-improved Wilson fermions. A key feature of our calculation is that we make use of an extensive ensemble of lattice gauge field configurations with four different lattice spacings, multiple volumes, and pion masses down to m_π~ 180 MeV. We find that by employing Kelly-inspired parametrizations for the Q^2-dependence of the form factors, we are able to obtain stable fits over our complete ensemble. Dirac and Pauli radii and the anomalous magnetic moments of the nucleon are extracted and results at light quark masses provide evidence for chiral non-analytic behavior in these fundamental observables.

hep-lat↗

arXiv2011

Lattice QCD Applications on QPACE

QPACE is a novel massively parallel architecture optimized for lattice QCD simulations. A single QPACE node is based on the IBM PowerXCell 8i processor. The nodes are interconnected by a custom 3-dimensional torus network implemented on an FPGA. The compute power of the processor is provided by 8 Synergistic Processing Units. Making efficient use of these accelerator cores in scientific applications is challenging. In this paper we describe our strategies for porting applications to the QPACE architecture and report on performance numbers.

hep-lat↗

arXiv2011

Nucleon form factors and structure functions

We give an update on our ongoing efforts to compute the nucleon's form factors and moments of structure functions using Nf=2 flavours of non-perturbatively improved Clover fermions. We focus on new results obtained on gauge configurations where the pseudo-scalar meson mass is in the range of 170-270 MeV. We will compare our results with various estimates obtained from chiral effective theories since we have some overlap with the quark mass region where results from such theories are believed to be applicable.

hep-lat↗

arXiv2009

QPACE -- a QCD parallel computer based on Cell processors

QPACE is a novel parallel computer which has been developed to be primarily used for lattice QCD simulations. The compute power is provided by the IBM PowerXCell 8i processor, an enhanced version of the Cell processor that is used in the Playstation 3. The QPACE nodes are interconnected by a custom, application optimized 3-dimensional torus network implemented on an FPGA. To achieve the very high packaging density of 26 TFlops per rack a new water cooling concept has been developed and successfully realized. In this paper we give an overview of the architecture and highlight some important technical details of the system. Furthermore, we provide initial performance results and report on the installation of 8 QPACE racks providing an aggregate peak performance of 200 TFlops.

hep-lat↗

arXiv2008

Status of the QPACE Project

We give an overview of the QPACE project, which is pursuing the development of a massively parallel, scalable supercomputer for LQCD. The machine is a three-dimensional torus of identical processing nodes, based on the PowerXCell 8i processor. The nodes are connected by an FPGA-based, application-optimized network processor attached to the PowerXCell 8i processor. We present a performance analysis of lattice QCD codes on QPACE and corresponding hardware benchmarks.

hep-lat↗

arXiv2007

QCD on the Cell Broadband Engine

We evaluate IBM's Enhanced Cell Broadband Engine (BE) as a possible building block of a new generation of lattice QCD machines. The Enhanced Cell BE will provide full support of double-precision floating-point arithmetics, including IEEE-compliant rounding. We have developed a performance model and applied it to relevant lattice QCD kernels. The performance estimates are supported by micro- and application-benchmarks that have been obtained on currently available Cell BE-based computers, such as IBM QS20 blades and PlayStation 3. The results are encouraging and show that this processor is an interesting option for lattice QCD applications. For a massively parallel machine on the basis of the Cell BE, an application-optimized network needs to be developed.

hep-lat↗

arXiv2000

On Algorithmic Equiresolution and Stratification of Hilbert Schemes

Given an algorithm of resolution of singularities satisfying certain conditions (``good algorithms''), natural notions of simultaneous algorithmic resolution, or equiresolution, for families of embedded schemes (parametrized by a reduced scheme $T$) are proposed. It is proved that these conditions are equivalent. Something similar is done for families of sheaves of ideals, here the goal is algorithmic simultaneous principalization. A consequence is that given a family of embedded schemes over a reduced $T$, this parameter scheme can be naturally expressed as a disjoint union of locally closed sets $T_{j}$, such that the induced family on each part $T_{j}$ is equisolvable. In particular, this can be applied to the Hilbert scheme of a smooth projective variety; in fact, our result shows that, in characteristic zero, the underlying topological space of any Hilbert scheme parametrizing embedded schemes can be naturally stratified in equiresolvable families.

math.AG↗