2,059 research outputs found
Effects of Geometrical Symmetry on the Vortex Nucleation and Penetration in Mesoscopic Superconductors
We investigate how the geometrical symmetry affects the penetration and
arrangement of vortices in mesoscopic superconductors using self-consistent
Bogoliubov-de Gennes equations. We find that the entrance of the vortex happens
when the current density at the hot spots reaches the depairing current
density. Through determining the spatial distribution of hot spots, the
geometrical symmetry of the superconducting sample influences the nucleation
and entrance of vortices. Our results propose one possible experimental
approach to control and manipulate the quantum states of mesoscopic
superconductors with their topological geometries, and they can be easily
generalized to the confined superfluids and Bose-Einstein condensates
Dynamical Creation of Fractionalized Vortices and Vortex Lattices
We investigate dynamic creation of fractionalized half-quantum vortices in
Bose-Einstein condensates of sodium atoms. Our simulations show that both
individual half-quantum vortices and vortex lattices can be created in rotating
optical traps when additional pulsed magnetic trapping potentials are applied.
We also find that a distinct periodically modulated spin-density-wave spatial
structure is always embedded in square half-quantum vortex lattices; this
structure can be conveniently probed by taking absorption images of
ballistically expanding cold atoms in a Stern-Gerlach field.Comment: 4 pages, 3 figures; published versio
Finite Difference Approximation with ADI Scheme for Two-dimensional Keller-Segel Equations
Keller-Segel systems are a set of nonlinear partial differential equations
used to model chemotaxis in biology. In this paper, we propose two alternating
direction implicit (ADI) schemes to solve the 2D Keller-Segel systems directly
with minimal computational cost, while preserving positivity, energy
dissipation law and mass conservation. One scheme unconditionally preserves
positivity, while the other does so conditionally. Both schemes achieve
second-order accuracy in space, with the former being first-order accuracy in
time and the latter second-order accuracy in time. Besides, the former scheme
preserves the energy dissipation law asymptotically. We validate these results
through numerical experiments, and also compare the efficiency of our schemes
with the standard five-point scheme, demonstrating that our approaches
effectively reduce computational costs.Comment: 29 page
Multiobjective imperialist competitive algorithm for solving nonlinear constrained optimization problems
Nonlinear constrained optimization problem (NCOP) has been arisen in a diverse range of sciences such as portfolio, economic management, airspace engineering and intelligence system etc. In this paper, a new multiobjective imperialist competitive algorithm for solving NCOP is proposed. First, we review some existing excellent algorithms for solving NOCP; then, the nonlinear constrained optimization problem is transformed into a biobjective optimization problem. Second, in order to improve the diversity of evolution country swarm, and help the evolution country swarm to approach or land into the feasible region of the search space, three kinds of different methods of colony moving toward their relevant imperialist are given. Thirdly, the new operator for exchanging position of the imperialist and colony is given similar as a recombination operator in genetic algorithm to enrich the exploration and exploitation abilities of the proposed algorithm. Fourth, a local search method is also presented in order to accelerate the convergence speed. At last, the new approach is tested on thirteen well-known NP-hard nonlinear constrained optimization functions, and the experiment evidences suggest that the proposed method is robust, efficient, and generic when solving nonlinear constrained optimization problem. Compared with some other state-of-the-art algorithms, the proposed algorithm has remarkable advantages in terms of the best, mean, and worst objective function value and the standard deviations
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