Search results for "numerical methods"

A New Approach to the Modeling of Anisotropic Media with the Transmission Line Matrix Method

2021

A reformulation of the Transmission Line Matrix (TLM) method is presented to model non-dispersive anisotropic media. Two TLM-based solutions to solve this problem can already be found in the literature, each one with an interesting feature. One can be considered a more conceptual approach, close to the TLM fundamentals, which identifies each TLM in Maxwell’s equations with a specific line. But this simplicity is achieved at the expense of an increase in the memory storage requirements of a general situation. The second existing solution is a more powerful and general formulation that avoids this increase in memory storage. However, it is based on signal processing techniques and considerabl…

Fast simulation of muons produced at the SHiP experiment using Generative Adversarial Networks

2019

This paper presents a fast approach to simulating muons produced in interactions of the SPS proton beams with the target of the SHiP experiment. The SHiP experiment will be able to search for new long-lived particles produced in a 400~GeV$/c$ SPS proton beam dump and which travel distances between fifty metres and tens of kilometers. The SHiP detector needs to operate under ultra-low background conditions and requires large simulated samples of muon induced background processes. Through the use of Generative Adversarial Networks it is possible to emulate the simulation of the interaction of 400~GeV$/c$ proton beams with the SHiP target, an otherwise computationally intensive process. For th…

Computational approach to compact Riemann surfaces

2017

International audience; A purely numerical approach to compact Riemann surfaces starting from plane algebraic curves is presented. The critical points of the algebraic curve are computed via a two-dimensional Newton iteration. The starting values for this iteration are obtained from the resultants with respect to both coordinates of the algebraic curve and a suitable pairing of their zeros. A set of generators of the fundamental group for the complement of these critical points in the complex plane is constructed from circles around these points and connecting lines obtained from a minimal spanning tree. The monodromies are computed by solving the defining equation of the algebraic curve on…

New Indicators of Approximation Errors for Problems in Continuum Mechanics

2010

In this paper we present a new error indicator for approximate solutions of elliptic problems. We discuss error indication with the paradigm of the diffusion problem, however the techniques are easily adaptable to more complicated elliptic problems, for example to linear elasticity, viscous flow models and electromagnetic models. The proposed indicator does not contain mesh dependent constants and it admits parallelization. nonPeerReviewed

Computational Techniques for the Analysis of Small Signals in High-Statistics Neutrino Oscillation Experiments

2020

The current and upcoming generation of Very Large Volume Neutrino Telescopes – collecting unprecedented quantities of neutrino events – can be used to explore subtle effects in oscillation physics, such as (but not restricted to) the neutrino mass ordering. The sensitivity of an experiment to these effects can be estimated from Monte Carlo simulations. With the high number of events that will be collected, there is a trade-off between the computational expense of running such simulations and the inherent statistical uncertainty in the determined values. In such a scenario, it becomes impractical to produce and use adequately-sized sets of simulated events with traditional methods, such as M…

Time-domain effective-one-body gravitational waveforms for coalescing compact binaries with nonprecessing spins, tides and self-spin effects

2018

We present TEOBResumS, a new effective-one-body (EOB) waveform model for nonprecessing (spin-aligned) and tidally interacting compact binaries.Spin-orbit and spin-spin effects are blended together by making use of the concept of centrifugal EOB radius. The point-mass sector through merger and ringdown is informed by numerical relativity (NR) simulations of binary black holes (BBH) computed with the SpEC and BAM codes. An improved, NR-based phenomenological description of the postmerger waveform is developed.The tidal sector of TEOBResumS describes the dynamics of neutron star binaries up to merger and incorporates a resummed attractive potential motivated by recent advances in the post-Newt…

Convergence of dynamic programming principles for the $p$-Laplacian

2018

We provide a unified strategy to show that solutions of dynamic programming principles associated to the $p$-Laplacian converge to the solution of the corresponding Dirichlet problem. Our approach includes all previously known cases for continuous and discrete dynamic programming principles, provides new results, and gives a convergence proof free of probability arguments.

Global sensitivity analysis in environmental water quality modelling: Where do we stand?

2014

Global sensitivity analysis (GSA) is a valuable tool to support the use of mathematical models for environmental systems. During the last years the water quality modelling field has embraced the use of GSA. Environmental water quality modellers have tried to transfer the knowledge and experience acquired in other disciplines. The main objective of this paper is to provide an informed problem statement of the issues surrounding GSA applications in the environmental water quality modelling field. Specifically, this paper aims at identifying, for each GSA method, the potential use, the critical issues to be solved and the limits identified in a comprehensive literature review. The paper shows …

Numerical methods for pricing options under jump-diffusion processes

2013

Numerical treatment of radiation processes in the internal shocks of magnetized relativistic outflows

2017

Los blázares son un tipo de núcleo activo de galaxia (AGN, por sus siglas en inglés) que se encuentran entre los objetos astrofísicos más energéticos y violentos, a la par de los brotes de rayos gamma (GRB por sus siglas en inglés). Los procesos físicos y, en particular, el escenario del chorro relativista en el que se genera la radiación ultraenergética detectada por observatorios terrestres y en órbita, han conseguido atraer la atención e interés de los astrónomos y astrofísicos desde su descubrimiento. En la presente tesis investigamos el modelo de choques internos (IS) cuya hipótesis consta del choque de dos capas de plasma con geometría cilíndrica, formando dos ondas de choque que atra…