Related papers: Symplectic integrator for $s$-dependent static mag…
A spin angular gradient approximation for the exchange correlation magnetic field in the density functional formalism is proposed. The usage of such corrections leads to a consistent spin dynamical approach beyond the local approximation.…
We propose a family of reliable symplectic integrators adapted to the Discrete Non-Linear Schr\"odinger equation; based on an idea of Yoshida (H. Yoshida, Construction of higher order symplectic integrators, Physics Letters A, 150, 5,6,7,…
In this paper we study the performance of a symplectic numerical integrator based on the splitting method. This method is applied to a subtle problem i.e. higher order resonance of the elastic pendulum. In order to numerically study the…
This paper gives a method that maps the static magnetic field due to a system of parallel current-carrying wires to a complex function. Using this function simplifies the calculation of the magnetic field energy density and inductance per…
Fringe fields in multipole magnets can have a variety of effects on the linear and nonlinear dynamics of particles moving along an accelerator beamline. An accurate model of an accelerator must include realistic models of the magnet fringe…
In recent decades, there have been many attempts to construct symplectic integrators with variable time steps, with rather disappointing results. In this paper we identify the causes for this lack of performance, and find that they fall…
We propose Electrostatic Field Matching (EFM), a novel method that is suitable for both generative modeling and distribution transfer tasks. Our approach is inspired by the physics of an electrical capacitor. We place source and target…
In this paper, we study the itinerant ferromagnetic phase in multi-component fermionic systems with symplectic (Sp(4), or isomorphically SO(5)) symmetry. Two different microscopic models have been considered and an effective field theory…
It has previously been shown that varying the numerical timestep during a symplectic orbital integration leads to a random walk in energy and angular momentum, destroying the phase space-conserving property of symplectic integrators. Here…
Let M be a compact oriented even-dimensional manifold. This note constructs a compact symplectic manifold S of the same dimension and a map f from S to M of strictly positive degree. The construction relies on two deep results: the first is…
We study the motion of a charged particle under the action of a magnetic field with cylindrical symmetry. In particular we consider magnetic fields with constant direction and with magnitude depending on the distance $r$ from the symmetry…
Most numerical integration algorithms are not designed specifically for Hamiltonian systems and do not respect their characteristic properties, which include the preservation of phase space volume with time. This can lead to spurious…
Symplectic integrators can be excellent for Hamiltonian initial value problems. Reasons for this include their preservation of invariant sets like tori, good energy behaviour, nonexistence of attractors, and good behaviour of statistical…
Symplectic integrators offer many advantages for the numerical solution of Hamiltonian differential equations, including bounded energy error and the preservation of invariant sets. Two of the central Hamiltonian systems encountered in…
In magnetically confined plasma, it is possible to qualitatively describe the magnetic field configuration via phase spaces of suitable symplectic maps. These phase spaces are of mixed type, where chaos coexists with regular motion, and the…
Brain-inspired computing architectures attempt to emulate the computations performed in the neurons and the synapses in human brain. Memristors with continuously tunable resistances are ideal building blocks for artificial synapses. Through…
Magnetic translation symmetry on a finite periodic square lattice is investigated for an arbitrary uniform magnetic field in arbitrary dimensions. It can be used to classify eigenvectors of the Hamiltonian. The system can be converted to…
Invariant theory provides more efficient tools, such as Molien generating functions and integrity bases, than basic group theory, that relies on projector techniques for the construction of symmetry--adapted polynomials in the symmetry…
We show that symplectic Runge-Kutta methods provide effective symplectic integrators for Hamiltonian systems with index one constraints. These include the Hamiltonian description of variational problems subject to position and velocity…
We develop a powerful yet simple method that generates multifractal fields with fully controlled scaling properties. Adopting the Multifractal Random Walk (MRW) model of Bacry et al. (2001), synthetic multifractal fields are obtained from…