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Variational symplectic algorithms have recently been developed for carrying out long-time simulation of charged particles in magnetic fields. As a direct consequence of their derivation from a discrete variational principle, these…
We study the dynamics of particles in a multi-component 2d Lennard-Jones (LJ) fluid in the limiting case where {\it all the particles are different} (APD). The equilibrium properties of this APD system were studied in our earlier work…
Electric power distribution systems will encounter fluctuations in supply due to the introduction of renewable sources with high variability in generation capacity. It is therefore necessary to provide algorithms that are capable of…
Standard approximations for the exchange-correlation functional have been found to give big errors for the linearity condition of fractional charges, leading to delocalization error, and the constancy condition of fractional spins, leading…
Wave propagation problems for heterogeneous media are known to have many applications in physics and engineering. Recently, there has been an increasing interest in stochastic effects due to the uncertainty, which may arise from impurities…
The discrete dipole approximation (DDA) is a widely used and versatile numerical method for solving electromagnetic scattering by arbitrarily shaped objects. Despite its popularity, quantitative comparisons between independent…
The alternating gradient descent (AGD) is a simple but popular algorithm which has been applied to problems in optimization, machine learning, data ming, and signal processing, etc. The algorithm updates two blocks of variables in an…
We review current status of the study of parity and time invariance phenomena in atoms, nuclei and molecules. We focus on three most promising areas of research: (i) parity non-conservation in a chain of isotopes, (ii) search for nuclear…
We study a force-based hybrid method that couples atomistic model with Cauchy-Born elasticity model with sharp transition interface. We identify stability conditions that guarantee the convergence of the hybrid scheme to the solution of the…
In this paper, we rigorously analyze the energy, momentum and magnetic moment behaviours of two splitting methods for solving charged-particle dynamics. The near-conservations of these invariants are given for the system under constant…
Many applications involve partial differential equations which admits nontrivial steady state solutions. The design of schemes which are able to describe correctly these equilibrium states may be challenging for numerical methods, in…
We propose a new method for computing Dynamic Mode Decomposition (DMD) evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of…
We present and discuss three discontinuous Galerkin (dG) discretizations for the anisotropic heat conduction equation on non-aligned cylindrical grids. Our most favourable scheme relies on a self-adjoint local dG (LDG) discretization of the…
We consider structure-preserving methods for conservative systems, which rigorously replicate the conservation property yielding better numerical solutions. There, corresponding to the skew-symmetry of the differential operator, that of…
This paper develops necessary and sufficient conditions for the preservation of asymptotic convergence rates of deterministically and stochastically perturbed ordinary differential equations with regularly varying nonlinearity close to…
This paper develops a charge-conservative mixed finite element method with optimal convergence rates for the stationary incompressible inductionless MHD equations on three-dimensional curved domains. The discretization employs the…
A few electron double electrostatic lateral quantum dot can be transformed into a few electron triple quantum dot by applying a different combination of gate voltages. Quadruple points have been achieved at which all three dots are…
We present an approach to electronic polarization in molecular solids treated as a set of quantum systems interacting classically. Individual molecules are dealt with rigorously as quantum-mechanical systems subject to classical external…
The dynamics of a metallic particle confined between charged walls is studied. One wall is fixed and the other moves smoothly and periodically in time. Dissipation is considered by assuming a friction produced by the contact between the…
The Parareal algorithm allows to solve evolution problems exploiting parallelization in time. Its convergence and stability have been proved under the assumption of regular (smooth) inputs. We present and analyze here a new Parareal…