共查询到20条相似文献，搜索用时 38 毫秒
1.
《New Astronomy》2022
In this paper, we study chaos control of a class of fractional-order chaotic systems where the dynamic control system depends on the Caputo fractional derivatives. We first propose an infinite horizon optimal control problem related to the given fractional chaotic system. With the help of an approximation, we replace the Caputo derivative to integer order derivative. We then convert the obtained infinite horizon optimal control problem into an equivalent finite horizon one. Based on the Pontryagin minimum principle (PMP) for optimal control problems and by constructing an error function, we define an unconstrained minimization problem. In the optimization problem, we use trial solutions for state, costate and control functions where these trial solutions are constructed by using a two-layered perceptron neural network. A learning procedure of the proposed neural network with convergence properties are also given. Some numerical results are introduced to explain our main results. Three applicable examples on chaos control of Malkus waterwheel, finance fractional chaotic models and fractional-order Geomagnetic Field models are finally considered. 相似文献
2.
The authors investigate the solution of a nonlinear reaction-diffusion equation connected with nonlinear waves. The equation discussed is more general than the one discussed recently by Manne et al. (2000). The results are presented in a compact and elegant form in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for numerical computation. The importance of the derived results lies in the fact that numerous results on fractional reaction, fractional diffusion, anomalous diffusion problems, and fractional telegraph equations scattered in the literature can be derived, as special cases, of the results investigated in this article. 相似文献
3.
In a series of papers, Saxena et al. (2002, 2004a, 2004b) derived solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which provide the extension of the work of Haubold and Mathai (1995, 2000). The subject of the present paper is to investigate the solution of a fractional reaction-diffusion equation. The results derived are of general nature and include the results reported earlier by many authors, notably by Jespersen et al. (1999) for anomalous diffusion and del-Castillo-Negrete et al. (2003) for reaction-diffusion systems with Lévy flights. The solution has been developed in terms of the H-function in a compact form with the help of Laplace and Fourier transforms. Most of the results obtained are in a form suitable for numerical computation. 相似文献
4.
This paper deals with the investigation of a closed form solution of a generalized fractional reaction-diffusion equation. The solution of the proposed problem is developed in a compact form in terms of the H-function by the application of direct and inverse Laplace and Fourier transforms. Fractional order moments and the asymptotic expansion of the solution are also obtained. 相似文献
5.
The infinite medium Green’s function is used to solve the half-space albedo, slab albedo and Milne problems for the unpolarized Rayleigh scattering case; these problems are the most classical problems of radiative transfer theory. The numerical results are obtained and are compared with previous ones. 相似文献
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7.
In view of the usefulness and a great importance of the kinetic equation in certain astrophysical problems the authors develop a new and further generalized form of the fractional kinetic equation involving the G-function, a generalized function for the fractional calculus. This new generalization can be used for the computation of the change of chemical composition in stars like the Sun. The Mellin-Barnes contour integral representation of the G-function is also established. The manifold generality of the G-function is discussed in terms of the solution of the above fractional kinetic equation. A compact and easily computable solution is established. Special cases, involving the generalized Mittag-leffler function and the R-function, are considered. The obtained results imply more precisely the known results. 相似文献
8.
A generalized Langevin equation driven by fractional Brownian motion is used to describe the vertical oscillations of general relativistic disks. By means of numerical calculation method, the displacements, velocities and luminosities of oscillating disks are explicitly obtained for different Hurst exponent H. The results show that as H increases, the energies and luminosities of oscillating disk are enhanced, and the spectral slope at high frequencies of the power spectrum density of disk luminosity is also increased. This could explain the observational features related to the Intra Day Variability of the BL Lac objects. 相似文献
9.
In this paper we have presented a method of obtaining varieties of new parametric classes of spherically symmetric analytic
solutions of the general relativistic field equations in canonical coordinates. A number of previously known classes of solutions
has been rediscovered which describe perfect fluid balls with infinite central pressure and infinite central density though
their ratio is positively finite and less then one. From the solutions of one of the class we have constructed a causal model
of polytrope with constant sound speed Corresponding to the polytrope model we have maximized the Neutron star mass 3.26 M⊙ with the linear dimensions 32.27 kms with surface red shift 0.7355 and for other class we have constructed a causal model
in which outmarch of pressure and density is monotonically decreasing and pressure–density ratio is positive and less than
1 throughout with in the ball. Corresponding to this model we have maximized the Neutron star mass 3.09 M⊙ with the linear dimensions 30.55 kms with surface red shifts 0.5811. 相似文献
10.
Neeraj Pant 《Astrophysics and Space Science》1996,240(2):187-193
We present a new class of spherically symmetric exact solutions of the general relativistic field equations. These solutions describe perfect fluid balls with infinite central pressure and central density though their ratio is finite. A member of the class has been studied in detail from which we have constructed a model of causal fluid ball with constant sound speed. 相似文献
11.
Hiroto Kawamoto 《Planetary and Space Science》1986,34(12):1229-1239
A chemical model of negative ions in the troposhere (0–15 km) is presented. This model is an extension of the negative ion composition model in the lower stratosphere (Kawamoto and Ogawa, 1984, Planet. Space Sci. 32, 1223) with some modifications. The computed result shows that the predominant ions are NO3−HNO3H2O below 10km and NO−3(HNO3)2 above 10km, and that the fractional abundance of cluster ions having a HSO−4 core increases with height below 12km and decreases with height above it. The ions having CO−3 cores are at most 2% in fractional abundance. The other kinds of negative ions are far smaller in fractional abundance than the NO−3, HSO−4 and CO−3 core ions. The result is compared with the two mass spectrometric observed results (Heitmann and Arnold, 1983, Nature, Lond. 306, 747; Perkins and Eisele, 1984, J. geophys. Res. 89, 9649). The problems on the tropospheric negative ions which arose are discussed. 相似文献
12.
13.
Steady plane flows of an incompressible rotating viscous fluid with infinite electrical conductivity are studied. Certain results of physical importance have been deduced for orthogonal flows. Lastly, the solutions to vortex and source flow problems are obtained. 相似文献
14.
We present the optical spectroscopic study of two classical Be stars, 59 Cyg and OT Gem obtained over a period of few months in 2009. We detected a rare triple-peak H α emission phase in 59 Cyg and a rapid decrease in the emission strength of H α in OT Gem, which are used to understand their circumstellar disks. We find that 59 Cyg is likely to be rapid rotator, rotating at a fractional critical rotation of ～0.80. The radius of the H α emission region for 59 Cyg is estimated to be R d/R ? ～ 10.0, assuming a Keplerian disk, suggesting that it has a large disk. We classify stars which have shown triple-peaks into two groups and find that the triple-peak emission in 59 Cyg is similar to ζ Tau. OT Gem is found to have a fractional critical rotation of ～0.30, suggesting that it is either a slow rotator or viewed in low inclination. In OT Gem, we observed a large reduction in the radius of the H α emission region from ～6.9 to ～1.7 in a period of three months, along with the reduction in the emission strength. Our observations suggest that the disk is lost from outside to inside during this disk loss phase in OT Gem. 相似文献
15.
Irom Ablu Meitei K. Yugindro Singh T. Ibungochouba Singh N. Ibohal 《Astrophysics and Space Science》2010,327(1):67-69
The thermodynamics of the Reissner–Nordström black hole at the charge-to-mass ratio of \(\sqrt{3}/2\) is studied. We show that there exists infinite discontinuity not only in the heat capacity but also in the electromagnetic potential and hence in the Gibbs free energy. Despite the existence of an infinite discontinuity in the heat capacity, it is shown that there exists no phase transition in the Reissner–Nordström black hole. The discontinuity may be merely an artefact of the change in the slope of the |Q| vs. M curve when the charge-to-mass ratio crosses \(\sqrt{3}/2\). This may signify that the horizon temperature is not a well-behaved thermodynamic parameter in the black hole thermodynamics. 相似文献
16.
Melchiorri A Ade PA de Bernardis P Bock JJ Borrill J Boscaleri A Crill BP De Troia G Farese P Ferreira PG Ganga K de Gasperis G Giacometti M Hristov VV Jaffe AH Lange AE Masi S Mauskopf PD Miglio L Netterfield CB Pascale E Piacentini F Romeo G Ruhl JE Vittorio N 《The Astrophysical journal》2000,536(2):L63-L66
We use the angular power spectrum of the cosmic microwave background, measured during the North American test flight of the Boomerang experiment, to constrain the geometry of the universe. Within the class of cold dark matter models, we find that the overall fractional energy density of the universe Omega is constrained to be 0.85相似文献
17.
A non-singular exact solution with an infinite central density is obtained for the interior of spherically symmetric and static
structures. Both the energy density and the pressure are infinite at the center but we have e
λ(0)=1 and e
ν(0)≠0. The solution admits the possibility of receiving signals from the region of infinite pressure. 相似文献
18.
We present radio observations made with the Australia Telescope Compact Array to study the jets and lobes of three Fanaroff–Riley class I (FR I) radio galaxies: PKS B1234−723, 1452−517 and B2148−555. The total intensity and polarization radio images of the FR I jets are used to determine jet brightness and width variations, magnetic field structure and fractional polarization. The equipartition pressure is determined as a function of distance from the galaxies to probe the intergalactic medium. 相似文献
19.
The existence of life in the Universe is interpreted in terms of the `Weak Anthropic Principle'. It is shown that cosmological
models are constrained to a class that involves an open timescale and access to infinite quantities of carbonaceous material.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
20.
Frank N. Edmonds Jr. 《Solar physics》1974,38(1):33-41
The fractional convective flux πF c (x c /πF) is computed for the effective level x c = logτ c = 0.125, using bi-dimensional co-spectra for relative continuum-brightness fluctuations ΔI and radial velocity fluctuations ΔV measured for the C i 5052.16 spectral line. A more uncertain flux for x Fe ≈ - 0.9 is obtained for the Fe i 5049.83 line. Since the results (Figure 1) incorporate current uncertainties in RMS ΔI , RMS ΔV and RMS ΔT (x), where ΔT are photospheric temperature fluctuations, they must be considered qualitative until these uncertainties are appreciably reduced. The requirement that the fractional convective flux < 1, places restrictions on these uncertainties which suggest that current RMS ΔT (x)'s are too large. The results confirm the importance of overshoot at the top of the solar hydrogen convection zone and suggest a non-negligible fractional convective flux throughout the lower photosphere. Qualitatively, they do not agree with the predictions of the generally-used, local, mixing-length theory or those of Parsons' (1969) modified mixing-length theory. However, qualitative agreement with the predictions of the non-local, generalized mixing-length theory of Spiegel (1963) and with the non-local theory of Ulrich (1970) cannot be considered as observational confirmation of these theories. 相似文献