Search results for "linear equations"
showing 10 items of 64 documents
One pendulum to run them all
2013
The analytical solution for the three-dimensional linear pendulum in a rotating frame of reference is obtained, including Coriolis and centrifugal accelerations, and expressed in terms of initial conditions. This result offers the possibility of treating Foucault and Bravais pendula as trajectories of the same system of equations, each of them with particular initial conditions. We compare them with the common two-dimensional approximations in textbooks. A previously unnoticed pattern in the three-dimensional Foucault pendulum attractor is presented.
Physical model, theoretical aspects and applications of the flight of a ball in the atmosphere. Part I: Modelling of forces and torque, and theoretic…
1991
A model of the forces and the torque operating on a ball that is flying with rotation in the atmosphere of the Earth, and the resulting system of ordinary differential equations, are derived from mechanics and aerodynamics. The system of equations allows the theoretical aspects of the flight of a ball, such as the boundedness of its kinetic energy, the curvature of the orbit or the velocity function, to be investigated using certain transformations of the variables. The solutions of the corresponding ordinary or boundary value problems, computed numerically, are used to treat certain tasks in international ball games, for example, the maximum and minimum velocities of a volleyball service.
Numerical relativistic hydrodynamics: Local characteristic approach.
1991
We extend some recent Ishock capturing methodsR designed to solve nonlinear hyperbolic systems of conservation laws and which avoid the use of artifical viscosity for treating strong discontinuities to a relativistic hydrodynamics system of equations. Some standard shock-tube problems and radial accretion onto a Schwarzschild black hole are used to calibrate our code.
Numerical study of a multiscale expansion of the Korteweg de Vries equation and Painlev\'e-II equation
2007
The Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order $\e^2$, $\e\ll 1$, is characterized by the appearance of a zone of rapid modulated oscillations. These oscillations are approximately described by the elliptic solution of KdV where the amplitude, wave-number and frequency are not constant but evolve according to the Whitham equations. Whereas the difference between the KdV and the asymptotic solution decreases as $\epsilon$ in the interior of the Whitham oscillatory zone, it is known to be only of order $\epsilon^{1/3}$ near the leading edge of this zone. To obtain a more accurate description near the leading edge of the oscillatory zone we present a…
Gravitational waves in dynamical spacetimes with matter content in the fully constrained formulation
2012
The Fully Constrained Formulation (FCF) of General Relativity is a novel framework introduced as an alternative to the hyperbolic formulations traditionally used in numerical relativity. The FCF equations form a hybrid elliptic-hyperbolic system of equations including explicitly the constraints. We present an implicit-explicit numerical algorithm to solve the hyperbolic part, whereas the elliptic sector shares the form and properties with the well known Conformally Flat Condition (CFC) approximation. We show the stability andconvergence properties of the numerical scheme with numerical simulations of vacuum solutions. We have performed the first numerical evolutions of the coupled system of…
Real-time calibration of the A4 electromagnetic lead fluoride (PbF2) calorimeter
2011
Abstract Sufficient energy resolution is the key issue for the calorimetry in particle and nuclear physics. The calorimeter of the A4 parity violation experiment at MAMI is a segmented calorimeter where the energy of an event is determined by summing the signals of neighboring channels. In this case, the precise matching of the individual modules is crucial to obtain a good energy resolution. We have developed a calibration procedure for our total absorbing electromagnetic calorimeter which consists of 1022 lead fluoride (PbF 2 ) crystals. This procedure reconstructs the single-module contributions to the events by solving a linear system of equations, involving the inversion of a 1022×1022…
A model study of Hartree-Fock and Linear Response in coordinate space
1979
A fast procedure for spherical Hartree-Fock is obtained by coordinate space representation and a modification of gradient iteration. Along similar lines, the corresponding Linear Response equations are derived and solved, in order to achieve a fully consistent treatment. The Linear Response equations are applied to a change in particle numbers, i.e. to the description of isotopic differences. In a model study we look for their physical and numerical properties, i.e. linearity of the response, numerical stability and consistency requirements for the Hartree-Fock basis.
Translationally-Invariant Coupled-Cluster Method for Finite Systems
1997
The translational invariant formulation of the coupled-cluster method is presented here at the complete SUB(2) level for a system of nucleons treated as bosons. The correlation amplitudes are solution of a non-linear coupled system of equations. These equations have been solved for light and medium systems, considering the central but still semi-realistic nucleon-nucleon S3 interaction.
Combining spectral and shock-capturing methods: A new numerical approach for 3D relativistic core collapse simulations
2005
We present a new three-dimensional general relativistic hydrodynamics code which is intended for simulations of stellar core collapse to a neutron star, as well as pulsations and instabilities of rotating relativistic stars. Contrary to the common approach followed in most existing three-dimensional numerical relativity codes which are based in Cartesian coordinates, in this code both the metric and the hydrodynamics equations are formulated and solved numerically using spherical polar coordinates. A distinctive feature of this new code is the combination of two types of accurate numerical schemes specifically designed to solve each system of equations. More precisely, the code uses spectra…
Linear response theory in asymmetric nuclear matter for Skyrme functionals including spin-orbit and tensor terms
2014
The formalism of linear response theory for a Skyrme functional including spin-orbit and tensor terms is generalized to the case of infinite nuclear matter with arbitrary isospin asymmetry. Response functions are obtained by solving an algebraic system of equations, which is explicitly given. Spin-isospin strength functions are analyzed varying the conditions of density, momentum transfer, asymmetry, and temperature. The presence of instabilities, including the spinodal one, is studied by means of the static susceptibility.