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11.
N.C.A. da Costa 《Applied mathematics and computation》2009,215(4):1361-1367
We claim that the theoretical hypercomputation problem has already been solved, and that what remains is an engineering problem. We review our construction of the Halting Function (the function that settles the Halting Problem) and then sketch possible blueprints for an actual hypercomputer. 相似文献
12.
Valeriy K. Bulitko 《Mathematical Logic Quarterly》1999,45(4):561-571
We apply complexity concepts to define a new sort of sub-Turing reducibilities ≤ ?? make the degree hierarchy thinner and to obtain some new specifications of the well known jump inversion theorem of Friedberg. We show that this theorem doesn't hold when ≤ T is replaced with ≤ ??, where ?? is any countable subset of the class ?? of all total increasing functions f : ? → ?. 相似文献
13.
We have studied the effect of advection on reaction–diffusion equations by using toroidal velocity fields. Turing patterns formation in diffusion–advection–reaction problems was studied specifically, considering the Schnackenberg and glycolysis reaction kinetics models. Four cases were analyzed and solved numerically using finite elements. For glycolysis models, the advective effect modified the form of Turing patterns obtained with diffusion–reaction; whereas for Schnackenberg problems, the original patterns distorted themselves slightly, making them rotate in direction of the velocity field. We have also determined that the advective effect surpassed the diffusive one for high values of velocity and instability driven by diffusion was eliminated. On the other hand the advective effect is not considerable for very low values in the velocity field, and there was no modification in the original Turing pattern. 相似文献
14.
四则运算图灵机的构造 总被引:3,自引:0,他引:3
王强 《内蒙古师范大学学报(自然科学版)》2004,33(3):275-277
著名的丘奇(A.Church)命题指出,任何算法都可以用一个图灵机来描述.对自然数的四则运算给出了相应的图灵机. 相似文献
15.
A.G. Nikitin 《Journal of Mathematical Analysis and Applications》2007,332(1):666-690
Group classification of systems of two coupled non-linear reaction-diffusion equation with a diagonal diffusion matrix is carried out. Symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms are described. 相似文献
16.
Anotida Madzvamuse Andrew J. Wathen Philip K. Maini 《Journal of computational physics》2003,190(2):478-500
Many problems in biology involve growth. In numerical simulations it can therefore be very convenient to employ a moving computational grid on a continuously deforming domain. In this paper we present a novel application of the moving grid finite element method to compute solutions of reaction–diffusion systems in two-dimensional continuously deforming Euclidean domains. A numerical software package has been developed as a result of this research that is capable of solving generalised Turing models for morphogenesis. 相似文献
17.
Spontaneous Formation of Microgroove Arrays on the Surface of p‐Type Porous Silicon Induced by a Turing Instability in Electrochemical Dissolution
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Prof. Dr. Kazuhiro Fukami Tomoko Urata Prof. Dr. Katharina Krischer Prof. Dr. Naoya Nishi Prof. Dr. Tetsuo Sakka Dr. Atsushi Kitada Prof. Dr. Kuniaki Murase 《Chemphyschem》2015,16(8):1613-1618
Self‐organization plays an imperative role in recent materials science. Highly tunable, periodic structures based on dynamic self‐organization at micrometer scales have proven difficult to design, but are desired for the further development of micropatterning. In the present study, we report a microgroove array that spontaneously forms on a p‐type silicon surface during its electrodissolution. Our detailed experimental results suggest that the instability can be classified as Turing instability. The characteristic scale of the Turing‐type pattern is small compared to self‐organized patterns caused by the Turing instabilities reported so far. The mechanism for the miniaturization of self‐organized patterns is strongly related to the semiconducting property of silicon electrodes as well as the dynamics of their surface chemistry. 相似文献
18.
Inside Cover: Spontaneous Formation of Microgroove Arrays on the Surface of p‐Type Porous Silicon Induced by a Turing Instability in Electrochemical Dissolution (ChemPhysChem 8/2015)
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19.
In this paper, we concentrate on the spatiotemporal patterns of a delayed reaction‐diffusion Holling‐Tanner model with Neumann boundary conditions. In particular, the time delay that is incorporated in the negative feedback of the predator density is considered as one of the principal factors to affect the dynamic behavior. Firstly, a global Turing bifurcation theorem for τ = 0 and a local Turing bifurcation theorem for τ > 0 are given. Then, further considering the degenerated situation, we derive the existence of Bogdanov‐Takens bifurcation and Turing‐Hopf bifurcation. The normal form method is used to study the explicit dynamics near the Turing‐Hopf singularity. It is shown that a pair of stable nonconstant steady states (stripe patterns) and a pair of stable spatially inhomogeneous periodic solutions (spot patterns) could be bifurcated from a positive equilibrium. Moreover, the Turing‐Turing‐Hopf–type spatiotemporal patterns, that is, a subharmonic phenomenon with two spatial wave numbers and one temporal frequency, are also found and explained theoretically. Our results imply that the interaction of Turing and Hopf instabilities can be considered as the simplest mechanism for the appearance of complex spatiotemporal dynamics. 相似文献
20.
Guiquan Sun Shumin Liu Li Li Jing Li Zhen Jin 《Journal of Nonlinear Modeling and Analysis》2021,3(4):617-646
Mussel beds are important habitats and food sources for biodiversity in coastal ecosystems. The predation of mussel on algae depends not only on the current time and location, but also on the quantity of algae at other spatial location and time. To know the impacts of such predation behavior on the dynamics of mussel beds well, we pose a reaction-diffusion mussel-algae model coupling nonlocal interaction with kernel function. By calculating the critical conditions of Hopf bifurcation and Turing bifurcation, the conditions for the generation of Turing pattern are obtained. We find that the diffusion rate and predation rate of mussels have effect on the structure and density of spatial pattern of mussels under the nonlocal interaction, and the predation rate of mussels can produce different pattern types, while the diffusion rate plays a more important role on the pattern density. Moreover, the nonlocal interaction promotes the stability of the mussel beds. These results suggest that the nonlocal interaction between mussels and algaes is one of the important mechanisms for the formation of the spatial structure of mussel beds. 相似文献