Search results for "Numerical"
showing 10 items of 2002 documents
A walk on sunset boulevard
2016
A walk on sunset boulevard can teach us about transcendental functions associated to Feynman diagrams. On this guided tour we will see multiple polylogarithms, differential equations and elliptic curves. A highlight of the tour will be the generalisation of the polylogarithms to the elliptic setting and the all-order solution for the sunset integral in the equal mass case.
Pseudospectrum and Black Hole Quasinormal Mode Instability
2020
We study the stability of quasinormal modes (QNM) in asymptotically flat black hole spacetimes by means of a pseudospectrum analysis. The construction of the Schwarzschild QNM pseudospectrum reveals the following: (i) the stability of the slowest-decaying QNM under perturbations respecting the asymptotic structure, reassessing the instability of the fundamental QNM discussed by Nollert [H. P. Nollert, About the Significance of Quasinormal Modes of Black Holes, Phys. Rev. D 53, 4397 (1996)] as an "infrared" effect; (ii) the instability of all overtones under small-scale ("ultraviolet") perturbations of sufficiently high frequency, which migrate towards universal QNM branches along pseudospec…
Wick Theorem for General Initial States
2012
We present a compact and simplified proof of a generalized Wick theorem to calculate the Green's function of bosonic and fermionic systems in an arbitrary initial state. It is shown that the decomposition of the non-interacting $n$-particle Green's function is equivalent to solving a boundary problem for the Martin-Schwinger hierarchy; for non-correlated initial states a one-line proof of the standard Wick theorem is given. Our result leads to new self-energy diagrams and an elegant relation with those of the imaginary-time formalism is derived. The theorem is easy to use and can be combined with any ground-state numerical technique to calculate time-dependent properties.
Multi-boson block factorization of fermions
2017
The numerical computations of many quantities of theoretical and phenomenological interest are plagued by statistical errors which increase exponentially with the distance of the sources in the relevant correlators. Notable examples are baryon masses and matrix elements, the hadronic vacuum polarization and the light-by-light scattering contributions to the muon g-2, and the form factors of semileptonic B decays. Reliable and precise determinations of these quantities are very difficult if not impractical with state-of-the-art standard Monte Carlo integration schemes. I will review a recent proposal for factorizing the fermion determinant in lattice QCD that leads to a local action in the g…
Mechanical properties of carbon nanotube fibres: St Venant’s principle at the limit and the role of imperfections
2015
Abstract Carbon nanotube (CNT) fibres, especially if perfect in terms of their purity and alignment, are extremely anisotropic. With their high axial strength but ready slippage between the CNTs, there is utmost difficulty in transferring uniformly any applied force. Finite element analysis is used to predict the stress distribution in CNT fibres loaded by grips attached to their surface, along with the resulting tensile stress–strain curves. This study demonstrates that, in accordance with St Venant’s principle, very considerable length-to-diameter ratios (∼103) are required before the stress becomes uniform across the fibre, even at low strains. It is proposed that lack of perfect orienta…
On the graded identities and cocharacters of the algebra of 3×3 matrices
2004
Abstract Let M2,1(F) be the algebra of 3×3 matrices over an algebraically closed field F of characteristic zero with non-trivial Z 2 -grading. We study the graded identities of this algebra through the representation theory of the hyperoctahedral group Z 2 ∼S n . After splitting the space of multilinear polynomial identities into the sum of irreducibles under the Z 2 ∼S n -action, we determine all the irreducible Z 2 ∼S n -characters appearing in this decomposition with non-zero multiplicity. We then apply this result in order to study the graded cocharacter of the Grassmann envelope of M2,1(F). Finally, using the representation theory of the general linear group, we determine all the grade…
On the optimum form of an aperture for a confinement of the optically excited electric near field.
2008
Summary A triangular nanoaperture in an aluminium film was used previously as a probe in a scanning near-field optical microscope to image single fluorescent molecules with an optical resolution down to 30 nm. The high-resolution capability of the triangular aperture probe is because of a highly confined spot of the electric near field which emerges at an edge of the aperture, when the incident light is polarized perpendicular to this edge. Previous numerical calculations of the near-field distribution of a triangular aperture in a planar metal film using the field susceptibility technique yielded a nearly quantitative agreement with the experimental results. Using the same numerical techni…
Understanding the detector behavior through Montecarlo and calibration studies in view of the SOX measurement
2015
International audience; Borexino is an unsegmented neutrino detector operating at LNGS in central Italy. The experiment has shown its performances through its unprecedented accomplishments in the solar and geoneutrino detection. These performances make it an ideal tool to accomplish a state- of-the-art experiment able to test the existence of sterile neutrinos (SOX experiment). For both the solar and the SOX analysis, a good understanding of the detector response is fundamental. Consequently, calibration campaigns with radioactive sources have been performed over the years. The calibration data are of extreme importance to develop an accurate Monte Carlo code. This code is used in all the n…
A new calculation procedure for non-uniform residual stress analysis by the hole-drilling method
1998
The hole-drilling method is one of the most used semi-destructive techniques for residual stress analysis in mechanical parts. In the presence of non-uniform residual stress, the stress field can be determined from the measured relaxed strains using several calculation methods, but the most used one is the so-called integral method. This method is characterized by some simplifications that lead to approximate results, especially when the residual stress varies abruptly. In this paper a new calculation procedure called the spline methods is proposed, which allows these drawbacks to be overcome. Numerical simulations and an experimental test have corroborated the best performance of the prop…
Optimal calculation steps for the evaluation of residual stress by the incremental hole-drilling method
1999
The integral method is a suitable calculation procedure for the determination of nonuniform residual stresses by semidestructive mechanical methods such as the hole-drilling method and the ring-core method. However, the high sensitivity to strain measurement errors due to the ill conditioning of the equations has hindered its practical use. the analysis of the influence of the strain measurment error on the computed stresses carried out in the present work has showed that, given both maximum hole depth and number of total steps, the error sensitivity depends on the particular depth increment distribution used. By means of the matrix formulation, the depth increment distribution that optimiz…