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11.
In this work we consider computing and continuing connecting orbits in parameter dependent dynamical systems. We give details
of algorithms for computing connections between equilibria and periodic orbits, and between periodic orbits. The theoretical
foundation for these techniques is given by the seminal work of Beyn in 1994, “On well-posed problems for connecting orbits
in dynamical systems”, where a numerical technique is also proposed. Our algorithms consist of splitting the computation of
the connection from that of the periodic orbit(s). To set up appropriate boundary conditions, we follow the algorithmic approach
used by Demmel, Dieci, and Friedman, for the case of connecting orbits between equilibria, and we construct and exploit the
smooth block Schur decomposition of the monodromy matrices associated to the periodic orbits. Numerical examples illustrate
the performance of the algorithms.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
12.
Chelo Ferreira 《Journal of Mathematical Analysis and Applications》2004,298(1):210-224
The Hurwitz-Lerch zeta function Φ(z,s,a) is considered for large and small values of a∈C, and for large values of z∈C, with |Arg(a)|<π, z∉[1,∞) and s∈C. This function is originally defined as a power series in z, convergent for |z|<1, s∈C and 1−a∉N. An integral representation is obtained for Φ(z,s,a) which define the analytical continuation of the Hurwitz-Lerch zeta function to the cut complex z-plane C?[1,∞). From this integral we derive three complete asymptotic expansions for either large or small a and large z. These expansions are accompanied by error bounds at any order of the approximation. Numerical experiments show that these bounds are very accurate for real values of the asymptotic variables. 相似文献
13.
O. Penrose 《Journal of statistical physics》1995,78(1-2):267-283
The grand potentialP(z)/kT of the cluster model at fugacityz, neglecting interactions between clusters, is defined by a power series
n
Q
n
z
n
, whereQ
n
, which depends on the temperatureT, is the partition function of a cluster of sizen. At low temperatures this series has a finite radius of convergencez
s
. Some theorems are proved showing that ifQ
n
, considered as a function ofn, is the Laplace transform of a function with suitable properties, thenP(z) can be analytically continued into the complexz plane cut along the real axis fromz
s
to + and that (a) the imaginary part ofP(z) on the cut is (apart from a relatively unimportant prefactor) equal to the rate of nucleation of the corresponding metastable state, as given by Becker-Döring theory, and (b) the real part ofP(z) on the cut is approximately equal to the metastable grand potential as calculated by truncating the divergent power series at its smallest term. 相似文献
14.
The root count developed by Bernshtein, Kushnirenko and Khovanskii only counts the number of isolated zeros of a polynomial system in the algebraic torus . In this paper, we modify this bound slightly so that it counts the number of isolated zeros in . Our bound is, apparently, significantly sharper than the recent root counts found by Rojas and in many cases easier to compute. As a consequence of our result, the Huber-Sturmfels homotopy for finding all the isolated zeros of a polynomial system in can be slightly modified to obtain all the isolated zeros in .
15.
Bendazzoli Gianni L. Raimondi Mario Garetz Bruce A. George Thomas F. Morokuma Keiji 《Theoretical chemistry accounts》1977,44(4):341-350
Semiclassical calculations are carried out by two methods for the problem of collision-induced predissociation of electronically excited I2. The first method is that of surface-hopping with the Landau-Zener model. The second method is similar to surface-hopping, except that analytic continuation of the adiabatic potential energy surfaces replaces the Landau-Zener model. Results of the calculations by the two methods compare favorably with each other and with experiment. The possible advantages of the second method are discussed.Camille and Henry Dreyfus Teacher-Scholar, Alfred P. Sloan Research Fellow. 相似文献
16.
We study the analytic structure of thermodynamic functions at first-order phase transitions in systems with short-range interactions and in particular in the two-dimensional Ising model. We analyze the nature of the approximation of the d=2 system by anN × strip. Investigation of the structure of the eigenvalues of the transfer matrix in the vicinity of H=0 in the complexH plane allows us to define a new function which provides rapidly convergent approximations to the stable free energyf and its derivatives for allH 0. This new function is used for numerical calculation of the coefficients Cn in the power series expansions of the magnetizationm in the form m(H)=1 + Cn(H-H
0
)n for various H0 0. The resulting series are studied by conventional methods. We confirm recent series analysis results on the existence of the droplet model type essential singularity at H=0. Evidence is found for a spinodal at H=Hsp(Ti < 0. 相似文献
17.
Hanwen Ning 《Applicable analysis》2013,92(4):563-577
In this article, we consider dynamic behaviours of a class of non-linear delay stochastic evolution equations. Local existence and uniqueness of the solutions are obtained with the aid of proper iterative scheme and moment estimations. We also propose a continuation result and our results generalize the known results. 相似文献
18.
Yongsheng Song 《Stochastic Processes and their Applications》2019,129(6):2066-2085
As is known, if is a -Brownian motion, a process of form , , is a non-increasing -martingale. In this paper, we shall show that a non-increasing -martingale cannot be form of or , , which implies that the decomposition for generalized -Itô processes is unique: For arbitrary , and non-increasing -martingales , if then we have , and. As an application, we give a characterization to the -Sobolev spaces introduced in Peng and Song (2015). 相似文献
19.
20.