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Optimal analog wavelet bases construction using hybrid optimization algorithm
An approach for the construction of optimal analog wavelet bases is presented. First, the definition of an analog wavelet is given. Based on the definition and the least-squares error criterion, a general framework for designing optimal analog wavelet bases is established, which is one of difficult nonlinear constrained optimization problems. Then, to solve this problem, a hybrid algorithm by combining chaotic map particle swarm optimization (CPSO) with local sequential quadratic programming (SQP) is proposed. CPSO is an improved PSO in which the saw tooth chaotic map is used to raise its global search ability. CPSO is a global optimizer to search the estimates of the global solution, while the SQP is employed for the local search and refining the estimates. Benefiting from good global search ability of CPSO and powerful local search ability of SQP, a high-precision global optimum in this problem can be gained. Finally, a series of optimal analog wavelet bases are constructed using the hybrid algorithm. The proposed method is tested for various wavelet bases and the improved performance is compared with previous works.Peer reviewedFinal Published versio
Enhancing Effective Instrument Resolution by an Analog Method Scientific Report No. 280
Analog computer using deconvolution to improve resolution of analytical instrument
Arnold Tongues and Feigenbaum Exponents of the Rational Mapping for Q-state Potts Model on Recursive Lattice: Q<2
We considered Q-state Potts model on Bethe lattice in presence of external
magnetic field for Q<2 by means of recursion relation technique. This allows to
study the phase transition mechanism in terms of the obtained one dimensional
rational mapping. The convergence of Feigenabaum and
exponents for the aforementioned mapping is investigated for the period
doubling and three cyclic window. We regarded the Lyapunov exponent as an order
parameter for the characterization of the model and discussed its dependence on
temperature and magnetic field. Arnold tongues analogs with winding numbers
w=1/2, w=2/4 and w=1/3 (in the three cyclic window) are constructed for Q<2.
The critical temperatures of the model are discussed and their dependence on Q
is investigated. We also proposed an approximate method for constructing Arnold
tongues via Feigenbaum exponent.Comment: 15 pages, 12 figure
Area preservation in computational fluid dynamics
Incompressible two-dimensional flows such as the advection (Liouville)
equation and the Euler equations have a large family of conservation laws
related to conservation of area. We present two Eulerian numerical methods
which preserve a discrete analog of area. The first is a fully discrete model
based on a rearrangement of cells; the second is more conventional, but still
preserves the area within each contour of the vorticity field. Initial tests
indicate that both methods suppress the formation of spurious oscillations in
the field.Comment: 14 pages incl. 3 figure
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