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We are concerned with the numerical study of a simple one-dimensional Schr\"odinger operator $-\frac 1 2 \Dxx + \alpha q(x)$ with $\alpha \in \Re$, $q(x)=\cos(x)+\eps \cos(kx)$, $\eps >0$ and $k$ being irrational. This governs the quantum wave function of an independent electron within a… |
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The problem is addressed of the maximal integrability of the gradient of solutions to quasilinear elliptic equations, with merely measurable coefficients, in two variables. Optimal results are obtained in the framework of Orlicz spaces, and in the more general setting of all rearrangement-invariant… |
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We give a decomposition for the dual space of some Banach Function Spaces as the Zygmund space EXP_alpha of the exponential integrable functions, the Marcinkiewicz spaceL^p,infty, and the Grand Lebesgue Space L^p),Theta |
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We have investigated systematically and statistically methanol-concentration effects on methane-hydrate nucleation using both experiment and restrained molecular-dynamics simulation, employing simple observables to achieve an initially homogeneous methane-supersaturated solution particularly… |
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Numericalmethods for Volterra integral equations with discontinuous kernel need to be tuned to their peculiar form. Here we propose a version of the trapezoidal direct quadrature method adapted to such a type of equations. In order to delineate its stability properties, we first investigate about… |
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In the current study, a direct-forcing immersed boundary-non-Newtonian lattice Boltzmann method (IB-NLBM) is developed to investigate the sedimentation and interaction of particles in shear-thinning and shear-thickening fluids. In the proposed IB-NLBM, the non-linear mechanics of non-Newtonian… |
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We focus on three different convexity principles for local and nonlocal variational integrals. We prove various generalizations of them, as well as their equivalences. Some applications to nonlinear eigenvalue problems and Hardy-type inequalities are given. We also prove a measure-theoretic minimum… |
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Significant improvements in the computational performance of the lattice-Boltzmann (LB) model, coded in FORTRAN90, were achieved through application of enhancement techniques. Applied techniques include optimization of array memory layouts, data structure simplification, random number generation… |
