Search results for "Numerical integration"
showing 10 items of 43 documents
Efficient numerical integration of neutrino oscillations in matter
2016
A special purpose solver, based on the Magnus expansion, well suited for the integration of the linear three neutrino oscillations equations in matter is proposed. The computations are speeded up to two orders of magnitude with respect to a general numerical integrator, a fact that could smooth the way for massive numerical integration concomitant with experimental data analyses. Detailed illustrations about numerical procedure and computer time costs are provided.
Numerical integration of subtraction terms
2016
Numerical approaches to higher-order calculations often employ subtraction terms, both for the real emission and the virtual corrections. These subtraction terms have to be added back. In this paper we show that at NLO the real subtraction terms, the virtual subtraction terms, the integral representations of the field renormalisation constants and -- in the case of initial-state partons -- the integral representation for the collinear counterterm can be grouped together to give finite integrals, which can be evaluated numerically. This is useful for an extension towards NNLO.
Ultrasonic cavity solitons
2007
We report on a new type of localized structure, an ultrasonic cavity soliton, supported by large aspect-ratio acoustic resonators containing viscous media. These states of the acoustic and thermal fields are robust structures, existing whenever a spatially uniform solution and a periodic pattern coexist. Direct proof of their existence is given both through the numerical integration of the model and through the analysis and numerical integration of a generalized Swift-Hohenberg equation, derived from the microscopic equations under conditions close to nascent bistability. An analytical solution for the ultrasonic cavity soliton is given.
Symmetry breaking and singularity structure in Bose-Einstein condensates
2012
We determine the trajectories of vortex singularities that arise after a single vortex is broken by a discretely symmetric impulse in the context of Bose-Einstein condensates in a harmonic trap. The dynamics of these singularities are analyzed to determine the form of the imprinted motion. We find that the symmetry-breaking process introduces two effective forces: a repulsive harmonic force that causes the daughter trajectories to be ejected from the parent singularity, and a Magnus force that introduces a torque about the axis of symmetry. For the analytical non-interacting case we find that the parent singularity is reconstructed from the daughter singularities after one period of the tra…
Exponents of non-linear clustering in scale-free one-dimensional cosmological simulations
2012
One dimensional versions of cosmological N-body simulations have been shown to share many qualitative behaviours of the three dimensional problem. They can resolve a large range of time and length scales, and admit exact numerical integration. We use such models to study how non-linear clustering depends on initial conditions and cosmology. More specifically, we consider a family of models which, like the 3D EdS model, lead for power-law initial conditions to self-similar clustering characterized in the strongly non-linear regime by power-law behaviour of the two point correlation function. We study how the corresponding exponent \gamma depends on the initial conditions, characterized by th…
Relaxation, postponement, and features of the attractor in a driven varactor oscillator
1990
The driven varactor oscillator is investigated by numerical integration of its ODEs using the standard model of circuit theory. Attention is given to some properties of the basic relaxation mechanism. For time dependent amplitudes of the sinusoidal driving voltage the post-ponement of the bifurcations is characterized by transient Lyapunov numbers. The postponement of the first bifurcation shows the same dependence on the sweep velocity as in the case of the nonautonomous quadratic map. The shapes of the attractors are displayed in extended phase space. Generalized Renyi-dimensionsD 0 andD 1 have been determined in the chaotic region. A corresponding twodimensional Pioncare map indicates se…
The sunset diagram in SU(3) chiral perturbation theory
1996
A general procedure for the calculation of a class of two-loop Feynman diagrams is described. These are two-point functions containing three massive propagators, raised to integer powers, in the denominator, and arbitrary polynomials of the loop momenta in the numerator. The ultraviolet divergent parts are calculated analytically, while the remaining finite parts are obtained by a one-dimensional numerical integration, both below and above the threshold. Integrals of this type occur, for example, in chiral perturbation theory at order p^6.
Analytical solution for the solid angle subtended at any point by an ellipse via a point source radiation vector potential
2010
An axially symmetric radiation vector potential is derived for a spherically symmetric point source. This vector potential is used to derive a line integral for the solid angle subtended at a point source by a detector of arbitrary shape and location. An equivalent line integral given previously by Asvestas for optical applications is derived using this formulation. The line integral can be evaluated in closed form for important cases, and the analytical solution for the solid angle subtended by an ellipse at a general point is presented. The solution for the ellipse was obtained by considering sections of a right elliptic cone. The general solution for the ellipse requires the solution of …
Next-to-Leading-Order Results for Five, Six, and Seven Jets in Electron-Positron Annihilation
2012
We present next-to-leading order corrections in the leading color approximation for jet rates in electron-positron annihilation up to seven jets. The results for the two-, three-, and four-jet rates agree with known results. The NLO jet rates have been known previously only up to five jets. The results for the six- and seven-jet rate are new. The results are obtained by a new and efficient method based on subtraction and numerical integration.
Generalized Langevin dynamics: construction and numerical integration of non-Markovian particle-based models.
2018
We propose a generalized Langevin dynamics (GLD) technique to construct non-Markovian particle-based coarse-grained models from fine-grained reference simulations and to efficiently integrate them. The proposed GLD model has the form of a discretized generalized Langevin equation with distance-dependent two-particle contributions to the self- and pair-memory kernels. The memory kernels are iteratively reconstructed from the dynamical correlation functions of an underlying fine-grained system. We develop a simulation algorithm for this class of non-Markovian models that scales linearly with the number of coarse-grained particles. Our GLD method is suitable for coarse-grained studies of syste…