Canonical Formalism for Lagrangians of Maximal Nonlocality

A canonical formalism for Lagrangians of maximal nonlocality is established. The method is based on the familiar Legendre transformation to a new function which can be derived from the maximally nonlocal Lagrangian. The corresponding canonical equations are derived through the standard procedure in local theory and appear much like those local ones, though the implication of the equations is largely expanded.Comment: 17 pages with 1 eps figur

N-person differential games. Part 1: Duality-finite element methods

The duality approach, which is motivated by computational needs and is done by introducing N + 1 Language multipliers is addressed. For N-person linear quadratic games, the primal min-max problem is shown to be equivalent to the dual min-max problem

Study on Actuator Line Modeling of Two NREL 5-MW Wind Turbine Wakes

The wind turbine wakes impact the efficiency and lifespan of the wind farm. Therefore, to improve the wind plant performance, research on wind plant control is essential. The actuator line model (ALM) is proposed to simulate the wind turbine efficiently. This research investigates the National Renewable Energy Laboratory 5 Million Watts (NREL 5-MW) wind turbine wakes with Open Field Operation and Manipulation (OpenFOAM) using ALM. Firstly, a single NREL 5-MW turbine is simulated. The comparison of the power and thrust with Fatigue, Aerodynamics, Structures, and Turbulence (FAST) shows a good agreement below the rated wind speed. The information relating to wind turbine wakes is given in detail. The top working status is proved at the wind speed of 8 m/s and the downstream distance of more than 5 rotor diameters (5D). Secondly, another case with two NREL 5-MW wind turbines aligned is also carried out, in which 7D is validated as the optimum distance between the two turbines. The result also shows that the upstream wind turbine has an obvious influence on the downstream one

Controllable Persistent Atom Current of Bose-Einstein Condensates in an Optical Lattice Ring

In this paper the macroscopic quantum states of Bose-Einstein condensates in optical lattices is studied by solving the periodic Gross-Pitaevskii equation in one-dimensional geometry. It is shown that an exact solution seen to be a travelling wave of excited macroscopic quantum states resultes in a persistent atom current which can be controlled by adjusting of the barrier height of the optical periodic potential. A critical condition to generate the travelling wave is demonstrated and we moreover propose a practical experiment to realize the persistent atom current in a toroidal atom waveguide.Comment: 9 pages, 1 figure

Study on SPH Viscosity Term Formulations

For viscosity-dominated flows, the viscous effect plays a much more important role. Since the viscosity term in SPH-governing (Smoothed Particle Hydrodynamics) equations involves the discretization of a second-order derivative, its treatment could be much more challenging than that of a first-order derivative, such as the pressure gradient. The present paper summarizes a series of improved methods for modeling the second-order viscosity force term. By using a benchmark patch test, the numerical accuracy and efficiency of different approaches are evaluated under both uniform and non-uniform particle configurations. Then these viscosity force models are used to compute a documented lid-driven cavity flow and its interaction with a cylinder, from which the most recommended viscosity term formulation has been identified

The effects of the model errors generated by discretization of 'on-off'' processes on VDA

Through an idealized model of a partial differential equation with discontinuous 'on-off'' switches in the forcing term, we investigate the effect of the model error generated by the traditional discretization of discontinuous physical 'on-off'' processes on the variational data assimilation (VDA) in detail. Meanwhile, the validity of the adjoint approach in the VDA with 'on-off'' switches is also examined. The theoretical analyses illustrate that in the analytic case, the gradient of the associated cost function (CF) with respect to an initial condition (IC) exists provided that the IC does not trigger the threshold condition. But in the discrete case, if the on switches (or off switches) in the forward model are straightforwardly assigned the nearest time level after the threshold condition is (or is not) exceeded as the usual treatment, the discrete CF gradients (even the one-sided gradient of CF) with respect to some ICs do not exist due to the model error, which is the difference between the analytic and numerical solutions to the governing equation. Besides, the solution of the corresponding tangent linear model (TLM) obtained by the conventional approach would not be a good first-order linear approximation to the nonlinear perturbation solution of the governing equation. Consequently, the validity of the adjoint approach in VDA with parameterized physical processes could not be guaranteed. Identical twin numerical experiments are conducted to illustrate the influences of these problems on VDA when using adjoint method. The results show that the VDA outcome is quite sensitive to the first guess of the IC, and the minimization processes in the optimization algorithm often fail to converge and poor optimization retrievals would be generated as well. Furthermore, the intermediate interpolation treatment at the switch times of the forward model, which reduces greatly the model error brought by the traditional discretization of 'on-off'' processes, is employed in this study to demonstrate that when the 'on-off'' switches in governing equations are properly numerically treated, the validity of the adjoint approach in VDA with discontinuous physical 'on-off'' processes can still be guaranteed

Hidden force opposing ice compression

Coulomb repulsion between the unevenly-bound bonding and nonbonding electron pairs in the O:H-O hydrogen-bond is shown to originate the anomalies of ice under compression. Consistency between experimental observations, density functional theory and molecular dynamics calculations confirmed that the resultant force of the compression, the repulsion, and the recovery of electron-pair dislocations differentiates ice from other materials in response to pressure. The compression shortens and strengthens the longer-and-softer intermolecular O:H lone-pair virtual-bond; the repulsion pushes the bonding electron pair away from the H+/p and hence lengthens and weakens the intramolecular H-O real-bond. The virtual-bond compression and the real-bond elongation symmetrize the O:H-O as observed at ~60 GPa and result in the abnormally low compressibility of ice. The virtual-bond stretching phonons (< 400 cm-1) are thus stiffened and the real-bond stretching phonons (> 3000 cm-1) softened upon compression. The cohesive energy of the real-bond dominates and its loss lowers the critical temperature for the VIII-VII phase transition. The polarization of the lone electron pairs and the entrapment of the bonding electron pairs by compression expand the band gap consequently. Findings should form striking impact to understanding the physical anomalies of H2O.Comment: arXiv admin note: text overlap with arXiv:1110.007

Phase diagram of two-species Bose-Einstein condensates in an optical lattice

The exact macroscopic wave functions of two-species Bose-Einstein condensates in an optical lattice beyond the tight-binding approximation are studied by solving the coupled nonlinear Schrodinger equations. The phase diagram for superfluid and insulator phases of the condensates is determined analytically according to the macroscopic wave functions of the condensates, which are seen to be traveling matter waves.Comment: 13 pages, 2 figure