Search results for " Mathematica"
showing 10 items of 689 documents
Nilpotence of orbits under monodromy and the length of Melnikov functions
2021
Abstract Let F ∈ ℂ [ x , y ] be a polynomial, γ ( z ) ∈ π 1 ( F − 1 ( z ) ) a non-trivial cycle in a generic fiber of F and let ω be a polynomial 1-form, thus defining a polynomial deformation d F + e ω = 0 of the integrable foliation given by F . We study different invariants: the orbit depth k , the nilpotence class n , the derivative length d associated with the couple ( F , γ ) . These invariants bind the length l of the first nonzero Melnikov function of the deformation d F + e ω along γ . We analyze the variation of the aforementioned invariants in a simple but informative example, in which the polynomial F is defined by a product of four lines. We study as well the relation of this b…
QCD condensates from tau-decay data: A functional approach
2004
We study a functional method to extract the V − A condensate of dimension 6 from a comparison of τ -decay data with the asymptotic space-like QCD prediction. Our result is in agreement within errors with that from conventional analyses based on finite energy sum rules.
A calorimeter for the precise determination of the activity of the 144Ce-144Pr anti-neutrino source in the SOX experiment
2018
We describe the design and the performance of a high precision thermal calorimeter, whose purpose was the measurement of the total activity of the 144Ce-144Pr anti-neutrino source of the SOX (Short distance neutrino Oscillation with BoreXino) experiment. SOX aimed at the search for eV-scale sterile neutrinos by means of the Borexino detector at the Laboratori Nazionali del Gran Sasso in Italy and of a very powerful artificial anti-neutrino source located at 8.51 m from the detector center. In order to obtain the required sensitivity, the activity of the source (approximately 150 kCi) had to be known at 1% precision. In this work we report the design of the experimental apparatus and the res…
Scattering on Riemannian Symmetric Spaces and Huygens Principle
2018
International audience; The famous paper by L. D. Faddeev and B. S. Pavlov (1972) on automorphic wave equation explored a highly romantic link between Scattering Theory (in the sense of Lax and Phillips) and Riemann hypothesis. An attempt to generalize this approach to general semisimple Lie groups leads to an interesting evolution system with multidimensional time explored by the author in 1976. In the present paper, we compare this system with a simpler one defined for zero curvature symmetric spaces and show that the Huygens principle for this system in the curved space holds if and only if it holds in the zero curvature limit.
Three-state quantum systems: A procedure for the solution
1989
An iterative method to obtain a solution of the differential equation $$i\dot a = \hat H(t)a$$ , with Ĥ a 3×3 Hermitian matrix anda the unknown vector, is proposed. The procedure is particularly suitable for computer implementation and, as an example, has been applied to find the excitation probability of a three-level atom after the synchronous passage of two laser pulses each almost resonant with a pair of atomic levels.
Apparent remote synchronization of amplitudes: A demodulation and interference effect
2018
A form of "remote synchronization" was recently described, wherein amplitude fluctuations across a ring of non-identical, non-linear electronic oscillators become entrained into spatially-structured patterns. According to linear models and mutual information, synchronization and causality dip at a certain distance, then recover before eventually fading. Here, the underlying mechanism is finally elucidated through novel experiments and simulations. The system non-linearity is found to have a dual role: it supports chaotic dynamics, and it enables the energy exchange between the lower and higher sidebands of a predominant frequency. This frequency acts as carrier signal in an arrangement rese…
Computing absolute free energies of disordered structures by molecular simulation
2009
We present a Monte Carlo simulation technique by which the free energy of disordered systems can be computed directly. It is based on thermodynamic integration. The central idea is to construct an analytically solvable reference system from a configuration which is representative for the state of interest. The method can be applied to lattice models (e.g., the Ising model) as well as off-lattice molecular models. We focus mainly on the more challenging off-lattice case. We propose a Monte Carlo algorithm, by which the thermodynamic integration path can be sampled efficiently. At the examples of the hard sphere liquid and a hard disk solid with a defect, we discuss several properties of the …
Characterisation and mitigation of beam-induced backgrounds observed in the ATLAS detector during the 2011 proton-proton run
2013
This paper presents a summary of beam-induced backgrounds observed in the ATLAS detector and discusses methods to tag and remove background contaminated events in data. Triggerrate based monitoring of beam-related backgrounds is presented. The correlations of backgrounds with machine conditions, such as residual pressure in the beam-pipe, are discussed. Results from dedicated beam-background simulations are shown, and their qualitative agreement with data is evaluated. Data taken during the passage of unpaired, i.e. non-colliding, proton bunches is used to obtain background-enriched data samples. These are used to identify characteristic features of beam-induced backgrounds, which then are …
A neural network clustering algorithm for the ATLAS silicon pixel detector
2014
A novel technique to identify and split clusters created by multiple charged particles in the ATLAS pixel detector using a set of artificial neural networks is presented. Such merged clusters are a common feature of tracks originating from highly energetic objects, such as jets. Neural networks are trained using Monte Carlo samples produced with a detailed detector simulation. This technique replaces the former clustering approach based on a connected component analysis and charge interpolation. The performance of the neural network splitting technique is quantified using data from proton-proton collisions at the LHC collected by the ATLAS detector in 2011 and from Monte Carlo simulations. …
Pointwise Inequalities for Sobolev Functions on Outward Cuspidal Domains
2019
Abstract We show that the 1st-order Sobolev spaces $W^{1,p}(\Omega _\psi ),$$1<p\leq \infty ,$ on cuspidal symmetric domains $\Omega _\psi $ can be characterized via pointwise inequalities. In particular, they coincide with the Hajłasz–Sobolev spaces $M^{1,p}(\Omega _\psi )$.