Search results for "equation"
showing 10 items of 4219 documents
A Sequential Quadratic Programming Method for Volatility Estimation in Option Pricing
2006
Our goal is to identify the volatility function in Dupire's equation from given option prices. Following an optimal control approach in a Lagrangian framework, we propose a globalized sequential quadratic programming (SQP) algorithm with a modified Hessian - to ensure that every SQP step is a descent direction - and implement a line search strategy. In each level of the SQP method a linear-quadratic optimal control problem with box constraints is solved by a primal-dual active set strategy. This guarantees L^1 constraints for the volatility, in particular assuring its positivity. The proposed algorithm is founded on a thorough first- and second-order optimality analysis. We prove the existe…
A note on Sobolev isometric immersions below W2,2 regularity
2017
Abstract This paper aims to investigate the Hessian of second order Sobolev isometric immersions below the natural W 2 , 2 setting. We show that the Hessian of each coordinate function of a W 2 , p , p 2 , isometric immersion satisfies a low rank property in the almost everywhere sense, in particular, its Gaussian curvature vanishes almost everywhere. Meanwhile, we provide an example of a W 2 , p , p 2 , isometric immersion from a bounded domain of R 2 into R 3 that has multiple singularities.
Reconsidering TOF calculation in the transformation of epoxides and CO2 into cyclic carbonates
2020
Abstract The combination of Lewis acids and Lewis bases, currently defined as catalysts and co-catalysts (or promoter) respectively, in the reaction between epoxides and CO2 to give cyclic carbonates, is discussed, starting from examples in which the Lewis base was used in larger amount with respect to the Lewis acid. In these cases, turnover frequency (TOF) values have been usually calculated taking into account solely the amount of the Lewis acid employed. The occurrence of two distinct reaction pathways, one catalysed by the sole Lewis base and the other one catalysed by the Lewis acid/Lewis base couple, in which the Lewis acid alone does not play a catalytic role, should bring researche…
Numerically solving the relativistic Grad–Shafranov equation in Kerr spacetimes: numerical techniques
2018
The study of the electrodynamics of static, axisymmetric and force-free Kerr magnetospheres relies vastly on solutions of the so called relativistic Grad-Shafranov equation (GSE). Different numerical approaches to the solution of the GSE have been introduced in the literature, but none of them has been fully assessed from the numerical point of view in terms of efficiency and quality of the solutions found. We present a generalization of these algorithms and give detailed background on the algorithmic implementation. We assess the numerical stability of the implemented algorithms and quantify the convergence of the presented methodology for the most established setups (split-monopole, parab…
Jet launching from binary black hole-neutron star mergers: Dependence on black hole spin, binary mass ratio and magnetic field orientation
2018
Black hole-neutron star (BHNS) mergers are one of the most promising targets for multimessenger astronomy. Using general relativistic magnetohydrodynamic simulations of BHNS undergoing merger we showed that a magnetically--driven jet can be launched by the remnant if the NS is endowed with a dipole B field extending from the interior into the exterior as in a radio pulsar. These self-consistent studies considered a BHNS system with mass ratio $q=3:1$, BH spin $a/M_{BH}=0.75$ aligned with the total orbital angular momentum (OAM), and a NS that is irrotational, threaded by an aligned B field, and modeled by an $\Gamma$--law equation of state with $\Gamma=2$. Here, as a crucial step in establi…
Numerical-relativity simulations of long-lived remnants of binary neutron star mergers
2019
We analyze the properties of the gravitational wave signal emitted after the merger of a binary neutron star system when the remnant survives for more than a 80 ms (and up to 140ms). We employ four different piecewise polytropic equations of state supplemented by an ideal fluid thermal component. We find that the post-merger phase can be subdivided into three phases: an early post-merger phase (where the quadrupole mode and a few subdominant features are active), the intermediate post-merger phase (where only the quadrupole mode is active) and the late post-merger phase (where convective instabilities trigger inertial modes). The inertial modes have frequencies somewhat smaller than the qua…
Beyond second-order convergence in simulations of binary neutron stars in full general relativity
2014
Despite the recent rapid progress in numerical relativity, a convergence order less than the second has so far plagued codes solving the Einstein-Euler system of equations. We report simulations of the inspiral of binary neutron stars in quasi-circular orbits computed with a new code employing high-order, high-resolution shock-capturing, finite-differencing schemes that, for the first time, go beyond the second-order barrier. In particular, without any tuning or alignment, we measure a convergence order above three both in the phase and in the amplitude of the gravitational waves. Because the new code is able to calculate waveforms with very small phase errors already at modest resolutions,…
On the deceleration of Fanaroff-Riley Class I jets: mass loading of magnetized jets by stellar winds.
2020
In this paper we present steady-state RMHD simulations that include a mass-load term to study the process of jet deceleration. The mass-load mimics the injection of a proton-electron plasma from stellar winds within the host galaxy into initially pair plasma jets, with mean stellar mass-losses ranging from $10^{-14}$ to $10^{-9}\,{M_\odot\,yr^{-1}}$. The spatial jet evolution covers $\sim 500\,{\rm pc}$ from jet injection in the grid at 10~pc from the jet nozzle. Our simulations use a relativistic gas equation of state and a pressure profile for the ambient medium. We compare these simulations with previous dynamical simulations of relativistic, non-magnetised jets. Our results show that to…
An HLLC Riemann solver for resistive relativistic magnetohydrodynamics
2017
We present a new approximate Riemann solver for the augmented system of equations of resistive relativistic magnetohydrodynamics (RRMHD) that belongs to the family of Harten-Lax-van Leer contact wave (HLLC) solvers. In HLLC solvers, the solution is approximated by two constant states flanked by two shocks separated by a contact wave. The accuracy of the new approximate solver is calibrated through one- and two-dimensional test problems.
The force-free twisted magnetosphere of a neutron star – II. Degeneracies of the Grad–Shafranov equation
2017
We extend our previous study of equilibrium solutions of non-rotating force-free magnetospheres of neutron stars. We show that multiple solutions exist for the same sets of parameters, implying that the solutions are degenerate. We are able to obtain configurations with disconnected field lines, however, in nearly all cases these correspond to degenerate higher energy solutions. We carry out a wide parametric search in order to understand the properties of the solutions. We confirm our previous results that the lower energy solutions have up to $\sim 25\%$ more energy than the vacuum case, helicity of the order of $\sim 5$ (in some defined units), maximum twist of $\sim 1.5$ rad, and a dipo…