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31.
We give a geometric analysis of relaxation oscillations and canard cycles in a singularly perturbed predator–prey system of Holling and Leslie types. We discuss how the canard cycles are found near the Hopf bifurcation points. The transition from small Hopf-type cycles to large relaxation cycles is also discussed. Moreover, we outline one possibility for the global dynamics. Numerical simulations are also carried out to verify the theoretical results. 相似文献
32.
Paul Bracken 《Central European Journal of Physics》2008,6(1):135-140
An effective Hamiltonian for the generalized harmonic oscillator is determined by using squeezed state wavefunctions. The
equations of motion over an extended phase space are determined and then solved perturbatively for a specific choice of the
oscillator parameters. These results are used to calculate the dynamic and geometric phases for the generalized oscillator
with this choice of parameters.
相似文献
33.
M.J. Kaiser 《Applied Mathematics Letters》1996,9(6):67-70
Based on Gage's notion of a “positive center” of a planar convex set, an ε-positive center figure is defined, constructed, and illustrated through example. The existence of an ε-positive center point, and the convexity of the ε-positive center figure, is conjectured. 相似文献
34.
Das R Kumar SK Kumar A 《Journal of magnetic resonance (San Diego, Calif. : 1997)》2005,177(2):318-328
Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled dynamics of qubits. In controlled dynamics, one qubit undergoes coherent evolution and acquires appropriate phase, depending on the state of other qubits. If the evolution is geometric, then the phase acquired depend only on the geometry of the path executed, and is robust against certain types of error. This phenomenon leads to an inherently fault-tolerant quantum computation. Here we suggest a technique of using non-adiabatic geometric phase for quantum computation, using selective excitation. In a two-qubit system, we selectively evolve a suitable subsystem where the control qubit is in state |1, through a closed circuit. By this evolution, the target qubit gains a phase controlled by the state of the control qubit. Using the non-adiabatic geometric phase we demonstrate implementation of Deutsch-Jozsa algorithm and Grover's search algorithm in a two-qubit system. 相似文献
35.
We consider a space of Chebyshev splines whose left and right derivatives
satisfy linear constraints that are given by arbitrary nonsingular connection matrices.
We show that for almost all knot sequences such spline spaces have basis functions
whose support is equal to the support of the ordinary B-splines with the same knots.
Consequently, there are knot insertion and evaluation algorithms analogous to de Boors
algorithm for ordinary splines. 相似文献
36.
Yeh Lam 《应用数学学报(英文版)》2003,19(3):405-416
Geometric process (GP) was introduced by Lam[4,5], it is defined as a stochastic process {Xn, n = 1, 2,…} for which there exists a real number a > 0, such that {an-1 Xn, n = 1,2, …} forms a renewal process (RP). In this paper, we study some limit theorems in GP. We first derive the Wald equation for GP and then obtain the limit theorems of the age, residual life and the total life at t for a GP. A general limit theorem for Sn with a > 1 is also studied. Furthermore, we make a comparison between GP and RP, including the comparison of their limit distributions of the age, residual life and the total life at t. 相似文献
37.
A. Chaudhury R. Khatirkar N.N. Viswanathan V. Singal A. Ingle S. Joshi I. Samajdar 《Journal of magnetism and magnetic materials》2007
Commercial supply, from several steel manufacturers, of low-silicon non-grain-oriented electrical steel was monitored over a span of several years. A total of 51 samples were selected—selected from many hundreds on the basis of large differences in magnetic properties, but absence of significant variations in chemistry (other than differences in silicon percentage). The selected samples were analyzed for crystallographic texture and for grain size. 相似文献
38.
For the Landau–Lifshitz equation on a domain with three space dimensions, we consider energy concentration phenomena arising in the context of weakly convergent sequences of solutions. The concentration measure can be interpreted as a family of generalized curves. We establish a connection to a geometric flow. 相似文献
39.
The displacement field of an edge dislocation in aluminum was experimentally investigated. Three typical theoretical models were discussed. High-resolution transmission electron microscopy (HRTEM) and geometric phase analysis (GPA) were used to map the displacement field of an edge dislocation. The displacement field near the dislocation core was determined. The experimental show that Peierls-Nabarro model is the most appropriate theoretical model for displacement field of dislocation in aluminum. 相似文献
40.
The geometric characterization identifies the sets of nodes such that the Lagrange polynomials are products of factors of
first degree. We offer a detailed classification of all known sets satisfying the geometric characterization in the plane.
The defect, which takes into account the number of lines containing more nodes than the degree, plays a fundamental role in
this classification.
Partially supported by the Spanish Research Grant MTM2006-03388, by Gobierno de Aragón and Fondo Social Europeo. 相似文献