A semi-Lagrangian scheme is applied for the first time to computations of charged particle motions along magnetic field lines, to numerically solve the δf gyrokinetic equations in a flux tube geometry. This new solver adopted in the gyrokinetic Vlasov simulations has an advantage over the conventional Eulerian codes in calculating the parallel dynamics, because semi-Lagrangian schemes are free ...

A novel semi-naive Bayesian classifier is introduced that is particularly suitable to data with many attributes. The naive Bayesian classifier is taken as a starting point and correlations are reduced through joining of highly correlated attributes. Our technique differs from related work in its use of kernel-functions that systematically include continuous attributes rather than relying on dis...

A new method is developed to solve the condensation equation as it relates to Air Quality Models using both semi-Lagrangian and Lagrangian fluxes to increase resolution and perform accurately under stringent conditions that occur in the atmosphere. The new method, Partitioned Flux Integrated Semi-Lagrangian Method (PFISLM), can be used with lower-order interpolators and they produce highly accu...

We propose a convex, lower semi-continuous, coercive approximation of Euler’s elastica energy for images, which is thus very well-suited as a regularizer in image processing. The approximation is not quite the convex relaxation, and we discuss its close relation to the exact convex relaxation as well as the difficulties associated with computing the latter. Interestingly, the convex relaxation ...

We introduce a new higher order scheme for computing a tangentially stabilized curve shortening flow with a driving force represented by an intrinsic partial differential equation for an evolving curve position vector. Our new scheme is a combination of the explicit forward Euler and the fully-implicit backward Euler schemes. At any discrete time step, the solution is found efficiently using a ...

We consider a class of evolutionary variational inequalities arising in quasistatic frictional contact problems for linear elastic materials. We indicate sufficient conditions in order to have the existence, the uniqueness and the Lipschitz continuous dependence of the solution with respect to the data, respectively. The existence of the solution is obtained using a time-discretization method, ...

We prove the existence of solutions for the differential inclusion ẋ(t) ∈ F (t, x(t)) + f(t, x(t)) for a multifunction F upper semicontinuous with compact values contained in the generalized Clarke gradient of a regular locally Lipschitz function and f a Carathéodory function.

When studying a metastable dynamical system, a prime concern is how to decompose the phase space into a set of metastable states. Unfortunately, the metastable state decomposition based on simulation or experimental data is still a challenge. The most popular and simplest approach is geometric clustering which is developed based on the classical clustering technique. However, the prerequisites ...

For a generator A of a C0 -semigroup T (·) on a Banach space X we consider the semi-norm Mk x := lim supt→0+ ‖t−1(T (t)− I)Ak−1x‖ on the Favard space Fk of order k associated with A . The use of this semi-norm is motivated by the functional analytic treatment of time-discretization methods of linear evolution equations. We show that sharp inequalities for bounded linear operators on D(Ak) can b...

We consider the Navier-Stokes-Alpha model as an approximation of turbulent flows under realistic, non-periodic, boundary conditions. We derive that the variational formulation of Navier-Stokes-Alpha model under non-periodic boundary conditions, and prove that it has a unique weak solution. Next we consider finite element approximation of the model. We give semi discretization of the model and p...