Accurate and efficient numerical methods for computing ground states and dynamics of dipolar Bose-Einstein condensates via the nonuniform FFT

In this paper, we propose efficient and accurate numerical methods for computing the ground state and dynamics of the dipolar Bose-Einstein condensates utilising a newly developed dipole-dipole interaction (DDI) solver that is implemented with the non-uniform fast Fourier transform (NUFFT) algorithm. We begin with the three-dimensional (3D) Gross-Pitaevskii equation (GPE) with a DDI term and present the corresponding two-dimensional (2D) model under a strongly anisotropic confining potential. Different from existing methods, the NUFFT based DDI solver removes the singularity by adopting the spherical/polar coordinates in Fourier space in 3D/2D, respectively, thus it can achieve spectral accuracy in space and simultaneously maintain high efficiency by making full use of FFT and NUFFT whenever it is necessary and/or needed. Then, we incorporate this solver into existing successful methods for computing the ground state and dynamics of GPE with a DDI for dipolar BEC. Extensive numerical comparisons with existing methods are carried out for computing the DDI, ground states and dynamics of the dipolar BEC. Numerical results show that our new methods outperform existing methods in terms of both accuracy and efficiency.Comment: 26 pages, 5 figure

Compact graphene mode-locked wavelength-tunable erbium-doped fiber lasers: from all anomalous dispersion towards all normal dispersion

Soliton operation and soliton wavelength tuning of erbium-doped fiber lasers mode locked with atomic layer graphene was experimentally investigated under various cavity dispersion conditions. It was shown that not only wide range soliton wavelength tuning but also soltion pulse width variation could be obtained in the fiber lasers. Our results show that the graphene mode locked erbium-doped fiber lasers provide a compact, user friendly and low cost wavelength tunable ultrahsort pulse source

Large energy soliton erbium-doped fiber laser with a graphene-polymer composite mode locker

Due to its unique electronic property and the Pauli Blocking Principle, atomic layer graphene possesses wavelength-independent ultrafast saturable absorption, which can be exploited for the ultrafast photonics application. Through chemical functionalization, a graphene-polymer nanocomposite membrane was fabricated and firstly used to mode lock a fiber laser. Stable mode locked solitons with 3 nJ pulse energy, 700 fs pulse width at the 1590 nm wavelength have been directly generated from the laser. We show that graphene-polymer nanocomposites could be an attractive saturable absorber for high power fiber laser mode locking.Comment: Large energy soliton erbium-doped fiber laser with a graphene-polymer composite mode locker. Applied Physics Letters, Accepte

Vector Dissipative Solitons in Graphene Mode Locked Fiber Lasers

Vector soliton operation of erbium-doped fiber lasers mode locked with atomic layer graphene was experimentally investigated. Either the polarization rotation or polarization locked vector dissipative solitons were experimentally obtained in a dispersion-managed cavity fiber laser with large net cavity dispersion, while in the anomalous dispersion cavity fiber laser, the phase locked NLSE solitons and induced NLSE soliton were experimentally observed. The vector soliton operation of the fiber lasers unambiguously confirms the polarization insensitive saturable absorption of the atomic layer graphene when the light is incident perpendicular to its 2D atomic layer

Ideal strengths and bonding properties of PuO2 under tension

We perform a first-principles computational tensile test on PuO$_{2}$ based on density-functional theory within local density approximation (LDA)+\emph{U} formalism to investigate its structural, mechanical, magnetic, and intrinsic bonding properties in the four representative directions: [001], [100], [110], and [111]. The stress-strain relations show that the ideal tensile strengths in the four directions are 81.2, 80.5, 28.3, and 16.8 GPa at strains of 0.36, 0.36, 0.22, and 0.18, respectively. The [001] and [100] directions are prominently stronger than other two directions since that more Pu$-$O bonds participate in the pulling process. Through charge and density of states analysis along the [001] direction, we find that the strong mixed ionic/covalent character of Pu$-$O bond is weakened by tensile strain and PuO$_{2}$ will exhibit an insulator-to-metal transition after tensile stress exceeds about 79 GPa.Comment: 11 pages, 6 figure

Graphene mode locked, wavelength-tunable, dissipative soliton fiber laser

Atomic layer graphene possesses wavelength-insensitive ultrafast saturable absorption, which can be exploited as a full-band mode locker. Taking advantage of the wide band saturable absorption of the graphene, we demonstrate experimentally that wide range (1570 nm - 1600nm) continuous wavelength tunable dissipative solitons could be formed in an erbium doped fiber laser mode locked with few layer graphene

Computing the ground state and dynamics of the nonlinear Schrödinger equation with nonlocal interactions via the nonuniform FFT

International audienceWe present efficient and accurate numerical methods for computing the ground state and dynamics of the nonlinear Schrödinger equation (NLSE) with nonlocal interactions based on a fast and accurate evaluation of the long-range interactions via the nonuniform fast Fourier transform (NUFFT). We begin with a review of the fast and accurate NUFFT based method in [29] for nonlocal interactions where the singularity of the Fourier symbol of the interaction kernel at the origin can be canceled by switching to spherical or polar coordinates. We then extend the method to compute other nonlocal interactions whose Fourier symbols have stronger singularity at the origin that cannot be canceled by the coordinate transform. Many of these interactions do not decay at infinity in the physical space, which adds another layer of complexity since it is more difficult to impose the correct artificial boundary conditions for the truncated bounded computational domain. The performance of our method against other existing methods is illustrated numerically, with particular attention on the effect of the size of the computational domain in the physical space. Finally, to study the ground state and dynamics of the NLSE, we propose efficient and accurate numerical methods by combining the NUFFT method for potential evaluation with the normalized gradient flow using backward Euler Fourier pseudospectral discretization and time-splitting Fourier pseudospectral method, respectively. Extensive numerical comparisons are carried out between these methods and other existing methods for computing the ground state and dynamics of the NLSE with various nonlocal interactions. Numerical results show that our scheme performs much better than those existing methods in terms of both accuracy and efficiency

On a Class of Variational-Hemivariational Inequalities Involving Upper Semicontinuous Set-Valued Mappings

This paper is devoted to the various coercivity conditions in order to guarantee existence of solutions and boundedness of the solution set for the variational-hemivariational inequalities involving upper semicontinuous operators. The results presented in this paper generalize and improve some known results