Spatiotemporal

The search for Turing patterns led to the introduction of several new types of chemical reactor for studying reaction-diffusion events in feedback systems. Coupled with huge advances in imaging and data analysis capabilities, it is now possible to make detailed quantitative measurements on complex spatiotemporal behaviour. A few of the reactor configurations of interest will be mentioned here. 

Figure A3.14.16. Spatiotemporal complexity in a Couette reactor space-time plots showing the variation of...

Winquist, Engstrom R C, Meaney T, Tople R and Wightman R M 1987 Spatiotemporal desoription of the diffusion layer with a mioroeleotrode probe Anal. Chem. 59 2005... 

The same / lias also boon used as a model for spatiotemporal interniittency in Rayleigh-Benard convection ([cili88], [davl89]). 

Table 8.6 traces the evolution of the approximating CA rules as e increases from 0 to 1 for 2 < s < 3. We see that as e increases, only 7 of the 32 possible rules are actually visited. Nonetheless, even at this crude first order approximation, a remnant of the CML s transition to spatiotemporal intermittency remains. In particular, there is a threshold value of e, = 2 — 4/s, that acts as a boundary point below which the approximating CA-rule is simple-periodic (class 1 or 2) and above which it is complex (class 3 or 4). The surprising fact is not that the CML s transition appears to bo approximated by the CA-rule path - after all, allowing for finite-length computer words, the CML itself is essentially just a very-high order CA... 

Threshold Convergence to CML Values How close the value of c gets to the spatiotemporal iiitermittency threshold for the CML, c,CMi. 0.360 depends on the approximation method. Because /, does not converge to / when it is constructed using the pre-images of the laminar state (method I), remains close but does not converge to Method II, on the other hand, assures us that /y, -> / as p -> oo... 

Turbulence is generally understood to refer to a state of spatiotemporal chaos that is to say, a state in which chaos exists on all spatial and temporal scales. If the reader is unsatisfied with this description, it is perhaps because one of the many important open questions is how to rigorously define such a state. Much of our current understanding actually comes from hints obtained through the study of simpler dynamical systems, such as ordinary differential equations and discrete mappings (see chapter 4), which exhibit only temporal chaosJ The assumption has been that, at least for scenarios in which the velocity field fluctuates chaotically in time but remains relatively smooth in space, the underlying mechanisms for the onset of chaos in the simpler systems and the onset of the temporal turbulence in fluids are fundamentally the same. 

An altogether different behavior emerges for slightly larger values of 7 ( 40 -tSee also our discus.sion of spatiotemporal chaos in coupled-map lattices in section 8.2. 

Adaptor proteins are multi-domain proteins (Fig. 1) that interact with components of signaling pathways [1]. As a consequence of these interactions, adaptor proteins are able to regulate signaling events within the cell, providing spatiotemporal control and specificity, and influencing how a cell responds to a particular stimulus. 

Warrington NM, Woemer BM, Daginakatte GC, Dasgupta B, Perry A, Gutmaim DH, Rubin JB (2007) Spatiotemporal differences in CXCL12 expression and cyclic AMP underlie the unique pattern of optic glioma growth in neurofibromatosis type 1. Cancer Res 67 8588-8595... 

Masuda, A., Ushdia, K and Okamoto, T. (2005) New fluorescence correlation spectroscopy enabbng direct observation of spatiotemporal dependence of diffusion constants as an evidence of anomalous transport in extracellular matrices. Biophys.J., 88, 3584—3591. 

In the other type of self-organization (dynamic self-organization), spontaneous ordering of the systems occurs under thermodynamically non-equilibrium conditions, in which various ordered structures with wavelengths tens to hundreds of thousands times larger than the size of the system components are formed by spatiotemporal synchronization of various factors [10-12]. The spatiotemporal order... 

Cooper, D. L., Smith, G. E., Regan, M., Large, S., and Groenewegen, P. P. (2008). Tracking the spatial diffusion of influenza and norovirus using telehealth data A spatiotemporal analysis of syndromic data. BMC Med. 6,16. 

Clanis H. and Key B. (2001). Expression of glycoproteins in the vomero-nasal organ reveals a novel spatiotemporal pattern of sensory neurone maturation. J Neurobiol 46, 113-125. 

Abe and Choi [41] succeeded in the spatiotemporal separation of sodium atom emission from continuum emission in argon-saturated NaCl aqueous solution... 

Abe S, Choi P-K (2009) Spatiotemporal separation of Na-atom emission from continuum emission in sonoluminescence. Jpn J Appl Phys 48 07GH02... 

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