Dynamics spatio-temporal

Radiation probes such as neutrons, x-rays and visible light are used to see the structure of physical systems tlirough elastic scattering experunents. Inelastic scattering experiments measure both the structural and dynamical correlations that exist in a physical system. For a system which is in thennodynamic equilibrium, the molecular dynamics create spatio-temporal correlations which are the manifestation of themial fluctuations around the equilibrium state. For a condensed phase system, dynamical correlations are intimately linked to its structure. For systems in equilibrium, linear response tiieory is an appropriate framework to use to inquire on the spatio-temporal correlations resulting from thennodynamic fluctuations. Appropriate response and correlation functions emerge naturally in this framework, and the role of theory is to understand these correlation fiinctions from first principles. This is the subject of section A3.3.2. 

The local dynamics of tire systems considered tluis far has been eitlier steady or oscillatory. However, we may consider reaction-diffusion media where tire local reaction rates give rise to chaotic temporal behaviour of tire sort discussed earlier. Diffusional coupling of such local chaotic elements can lead to new types of spatio-temporal periodic and chaotic states. It is possible to find phase-synchronized states in such systems where tire amplitude varies chaotically from site to site in tire medium whilst a suitably defined phase is synclironized tliroughout tire medium 51. Such phase synclironization may play a role in layered neural networks and perceptive processes in mammals. Somewhat suriDrisingly, even when tire local dynamics is chaotic, tire system may support spiral waves... 

Dynamical Entropy In order to capture the dynamics of a CML pattern, Kaneko has constructed what amounts to it mutual information between two successive patterns at a given time interval [kaneko93]. It is defined by first obtaining an estimate, through spatio-temporal samplings, of the probability transition matrix Td,d = transition horn domain of size D to a domain of size D. The dynamical entropy, Sd, is then given by... 

We recall from our earlier discussion of chaos in one-dimensional continuous systems (see section 4.1) that period-doubling is not the only mechanism by which chaos can be generated. Another frequently occurring route to chaos is intermittency. But while intermittency in low dimensional dynamical systems appears to be constrained to purely temporal behavior [pomeau80], CMLs exhibit a spatio-temporal intermittency in which laminar eddies are intermixed with turbulent regions in a complex pattern in space-time. 

Mutabari I., Weslreid J. E. and Guyon E.(eds) (2004) Dynamics of Spatio-temporal Cellular Structures Henri Benard Centenary Review Springer Tracts in Modem Physics, Springer, New York. 

Parlitz U, Mettin R, Luther S, Akhatov I, Voss M, Lauterbom W (1999) Spatio-temporal dynamics of acoustic cavitation bubble cloud. Philos Trans R Soc London A 357 313-334... 

Picard V, Lair N (2005) Spatio-temporal investigations on the planktonic organisms of the Middle Loire (France), during the low water period biodiversity and community dynamics. Hydrobiologia 551 69-86... 

Hirose K, Kadowaki S, Tanabe M, Takeshima H, lino M 1999 Spatio-temporal dynamics of inositol 1,4,5-trisphosphate that underlies complex Ca2+ mobilization patterns. Science 284 1527-1530... 

Recently there has been an increasing interest in self-oscillatory phenomena and also in formation of spatio-temporal structure, accompanied by the rapid development of theory concerning dynamics of such systems under nonlinear, nonequilibrium conditions. The discovery of model chemical reactions to produce self-oscillations and spatio-temporal structures has accelerated the studies on nonlinear dynamics in chemistry. The Belousov-Zhabotinskii(B-Z) reaction is the most famous among such types of oscillatory chemical reactions, and has been studied most frequently during the past couple of decades [1,2]. The B-Z reaction has attracted much interest from scientists with various discipline, because in this reaction, the rhythmic change between oxidation and reduction states can be easily observed in a test tube. As the reproducibility of the amplitude, period and some other experimental measures is rather high under a found condition, the mechanism of the B-Z reaction has been almost fully understood until now. The most important step in the induction of oscillations is the existence of auto-catalytic process in the reaction network. 

Contreras A, Hale TK, Stenoien DL, Rosen JM, Mancini MA, Herrera RE (2003) The dynamic mobility of histone HI is regulated by cyclin/CDK phosphorylation. Mol Cell Biol 23(23) 8626-8636 Crosio C, Fimia GM, Loury R, Kimura M, Okano Y, Zhou H, Sen S, Allis CD, Sassone-Corsi P (2002) Mitotic phosphorylation of histone H3 spatio-temporal regulation by mammalian Aurora kinases. Mol Cell Biol 22(3) 874-885... 

Spatio-temporal geochemical dynamics of an acid rock drainage stream in the Yukon Territory implications for mineral exploration... 

The complex spatio-temporal mosaic of habitats in alpine river systems relates to the interaction of a range of physicochemical processes, with different processes dominating the river environment at different scales. Our new approach to alpine stream classification provides a basis to conceptualise this dynamic habitat template. The contributions from the different water sources have an important influence on the aquatic habitat template for the establishment of biotic communities, particularly through the effect on physicochemical variables outlined above. These include channel stability, water temperature and sediment regimes. Where alpine streams... 

The ionization of focal volume, or formation of plasma, is expected to alter the usual photochemical material modihcation pathway, as has been recently demonstrated in photopolymerization of SU-8 resist by femtosecond pulses [57]. In addition, nanometric-sized plasma regions created by the ionization, e.g., at defect sites, have spatio-temporal dynamics of their own. Recently, a model of nanosheet formation from plasma nanospheres in glass has been proposed [60]. Similar conditions are expected in polymers as well. Let us discuss here held enhancement by a metalhc nanoparticle (similar arguments are also valid for surfaces containing nanometric features). 

By C. Denz, M. Schwab, and C. Weilnau 2003. 143 figs., XVIII, 331 pages 1S9 Spatio-Temporal Dynamics and Quantum Fluctuations in Semiconductor Lasers By O. Hess, E. Gehrig 2003. 91 figs., XIV, 232 pages... 

Dynamics of Spatio-Temporal Cellular Structures Henri Benard Centenary Review... 

The high temporal resolution of SFM imaging uncovered elementary dynamic processes of structural rearrangements. We observed short-term interfacial undulations [111], fast repetitive transitions between distinct defect configurations [112], their spatio-temporal correlations on a length scale of several microdomains [112], and unexpected defect annihilation pathways via formation of temporal excited states [51, 111]. 

The studies of Ertl and co-workers showed that the reason for self-oscillations [142, 145, 185-187] and hysteresis effects [143] in CO oxidation over Pt(100) in high vacuum ( 10 4 Torr) is the existence of spatio-temporal waves of the reversible surface phase transition hex - (1 x 1). The mathematical model [188] suggests that in each of the phases an adsorption mechanism with various parameters of CO and 02 adsorption/desorption and their interaction is realized, and the phase transition is modelled by a semi-empirical method via the introduction of discontinuous non-linearity. Later, an imitation model based on the stochastic automat was used [189] to study the qualitative characteristics for the dynamic behaviour of the surface. 

Richter, O., P. Zwerger, and U. Bottcher (2002). Modeling spatio-temporal dynamics of herbicide resistance. Weed Res., 42 52-64. 

Dynamic odor maps 24.4.2.3.1 Spatio-temporal representations... 

Fig. 53. (a) Cyclic voltammogram during the formic acid oxidation on a Bi-modified Pt ring electrode scan rate 5mV s-1. The change in the oscillation form close to t = 73.7 s (i.e. U = 0.16 V) indicates a qualitative change in the dynamics, (b) Spatio-temporal profile of the interfacial potential in the transition region of the oscillation form in (a). For the experimental set-up, see Fig. 49b. (Reproduced from J. Lee, J. Christoph, P. Strasser, M. Eiswrith and G. Ertl, J. Chem. Phys. (2001) 115, 1485 by permission of the American Institute of Physics.)...

The question then arises as to how the cell organizes these specific events to create a spatio-temporal order to maintain its life. Cells have hierarchical dynamic structure from the nanometer to the micrometer scale. Therefore, to answer this question, it is necessary to explore the mesoscopic level of description, given the molecular knowledge in the nanometer scale. 

Example 9.15 Long-term asymptotic solution of reversible reaction diffusion systems The formation of dynamic reaction-diffusion fronts occurs when two species A and B are uniformly distributed on opposite sides of an impenetrable barrier, which is removed at time t 0 at isothermal conditions. The species A and B start to diffuse and react upon mixing, and produce species C. This creates a dynamic reaction front, and the spatio-temporal evolution of this front may exhibit some unique features, which may be valuable in understanding many phenomena in physical, chemical, biological, and geological systems. The long-term behavior of this reversible reaction-diffusion system was studied by Koza (2003). 

The essential difference between these and the cases shown in Fig. 4.3 is that the latter have three modes, while C possesses a single mode and D possesses two modes. The frontrunner in Fig. 4.3 is due to interactions of multiple stable modes. In the absence of multiple modes- as for the point C- no such forerunner is seen in Fig. 4.4. Again for the point D, there are only two stable modes that create spatio-temporally growing wave front. Thus, for fluid dynamic systems presence of a minimum of two stable modes is necessary to produce a spatio-temporally growing wave front, when the least stable mode is spatially damped. 

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