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We show that the unique solution to a semilinear stochastic differential equation with almost periodic coefficients driven by a fractional Brownian motion is almost periodic in a sense related to random dynamical systems. This type of…
A new mechanism for toroidal momentum transport in a tokamak is investigated using the gyro-kinetic model. First, an analytic model is developed through the use of the ballooning transform. The terms that generate the momentum transport are…
We investigate the dynamical motion of particles on a two-dimensional symmetric periodic substrate in the presence of both a dc drive along a symmetry direction of the periodic substrate and an additional circular ac drive. For large enough…
A charged particle in a suitably strong magnetic field spirals along the field lines while slowly drifting transversely. This note provides a brief derivation of an effective Lagrangian formulation for the guiding-centre approximation that…
The problem of the charged-particle motion in crossed electric and magnetic fields is investigated, and the validity of the guiding-center representation is assessed in comparison with the exact particle dynamics. While the magnetic field…
We analyze the spatial dynamics of polarized atom vapor and present a mathematical method to eliminate the diffusion effect partially. It is found that the diffusion effect of polarized atoms can be regarded as a low pass filter in spatial…
Dynamic graph algorithms have seen significant theoretical advancements, but practical evaluations often lag behind. This work bridges the gap between theory and practice by engineering and empirically evaluating recently developed…
We present the applications of methods from nonlinear local harmonic analysis in variational framework to calculations of nonlinear motions in polynomial/rational approximations (up to any order) of arbitrary n-pole fields. Our approach is…
We describe an exact simulation algorithm for the increments of Brownian motion on a sphere of arbitrary dimension, based on the skew-product decomposition of the process with respect to the standard geodesic distance. The radial process is…
Gyrokinetic field theory is addressed in the context of a general Hamiltonian. The background magnetic geometry is static and axisymmetric, and all dependence of the Lagrangian upon dynamical variables is in the Hamiltonian or in free field…
We introduce a Monte-Carlo algorithm for the simulation of charged particles moving in the continuum. Electrostatic interactions are not instantaneous as in conventional approaches, but are mediated by a constrained, diffusing electric…
Efficient molecular dynamics (MD) simulation is vital for understanding atomic-scale processes in materials science and biophysics. Traditional density functional theory (DFT) methods are computationally expensive, which limits the…
Previous work shows that a net directed motion arises from a system of individual particles undergoing run-and-tumble dynamics in the presence of an array of asymmetric barriers. Here, we show that when the individual particle is replaced…
We develop an approach of Grad-Shafranov (GS) reconstruction for toroidal structures in space plasmas, based on in-situ spacecraft measurements. The underlying theory is the GS equation that describes two-dimensional magnetohydrostatic…
We consider the long time evolution of a population of charged particles, under strong magnetic fields and collision mechanisms. We derive a fluid model and justify the asymptotic behavior toward smooth solutions of this regime. In three…
We derive the zero order approximation of a charged particle under the influence of a strong magnetic field in a mathematically rigorous manner and clarify in which sense this approximation is valid. We use this to further rigorously derive…
Diffeomorphic matching (only one of several names for this technique) is a technique for non-rigid registration of curves and surfaces in which the curve or surface is embedded in the flow of a time-series of vector fields. One seeks the…
The dynamics of anisotropic particles are dictated by forces and torques that can be challenging to mathematically represent in computer simulations. Several data-driven approaches have been developed to approximate these interactions, but…
In this paper, exponential energy-preserving methods are formulated and analysed for solving charged-particle dynamics in a strong and constant magnetic field. The resulting method can exactly preserve the energy of the dynamics. Moreover,…
We present the implementation of a three-dimensional, second order accurate Godunov-type algorithm for magneto-hydrodynamic (MHD), in the adaptive-mesh-refinement (AMR) cosmological code {\tt CHARM}. The algorithm is based on the full…