Spatiotemporal theory

In this context, time, speed and distances (space) are important parameters to be kept in mind, leading to the so-called "spatiotemporal" or "proximity theory". This theory states that "the reaction rate (speed) is a sensitive inverse function of distance and time". 

The problem of spatiotemporal recovery of monitoring data can be solved using the inductive method of model self-organization developed in Ivachnenko et al. (1984). The idea behind this approach is the traditional function approximation theory. 

Determination of the statistical characteristics of natural catastrophes in their historical aspect, selecting categories and determining spatiotemporal scales of catastrophic changes in habitats. Analysis of the history of disasters is important for understanding the present dependences of crises both in nature and in society. The statistical characteristics of the dynamics of natural disasters enable formulation of the basis for the mathematical theory of catastrophes and to determine top-priority directions of studies. 

Hebert B, Costantino S, Wiseman PW. Spatiotemporal image correlation spectroscopy (STICS) theory, verification, and application to protein velocity mapping in living CHO cells. Biophys. J. 2005 88 3601-3614. 

In microscale models the explicit chain nature has generally been integrated out completely. Polymers are often described by variants of models, which were primarily developed for small molecular weight materials. Examples include the Avrami model of crystallization,- and the director model for liquid crystal polymer texture. Polymeric characteristics appear via the values of certain constants, i.e. different Frank elastic constant for liquid crystal polymers rather than via explicit chain simulations. While models such as the liquid crystal director model are based on continuum theory, they typically capture spatiotemporal interactions, which demand modelling on a very fine scale to capture the essential effects. It is not always clearly defined over which range of scales this approach can be applied. 

Poff, N.L. and 3.V. Ward. 1990. Physical habitat template of lotic systems recovery in the context of historical pattern of spatiotemporal heterogeneity. In Recovery of Lotic Communities and Ecosystems Following Disturbance Theory and Application, J.D. Yount and G.J. Niemi, Eds. Environ. Manage. 14(5) 629-646. 

In the modern theory of fluid dynamic systems the term turbulence is accepted to mean a state of spatiotemporal chaos (e.g., [155], chap 5). That is, the fluid exhibits chaos on all scales in both space and time. Chaos theory involves the behavior of non-linear dynamical systems and their response to initial and boundary conditions. Using such methods it can be shown that although the solution of the Navier-Stokes is apparently random for turbulent flows, its behavior presents some orderly structures. In addition, the numerical solution of the Navier-Stokes equations is sometimes strongly dependent on the initial conditions, thus even very small inaccuracies in the initial conditions may be fatal providing completely erroneous results. ... 

One final point with regard to comparing the critical-distance and entropy theories is the following. Words like true and false , correct and incorrect , and valid and invalid have been avoided. Such descriptives have no place in discussions of chemical models that are, above all, fictitious. Models—one must never forget—are to be used, not believed. Thus, I do not claim the spatiotemporal hypothesis represents the truth I merely claim that it is a valuable aid for thinking, especially in cases where entropic arguments fail to help. 

Note that nowhere in the spatiotemporal postulate is the term transition state used. This term is not used because the transition state, for reasons just mentioned, is considered peripheral to time and distance. Perhaps the love affair that physical organic chemists are having with transition structure is overly passionate. Diffusion theory, not quantum mechanics, may be the key to future progress. 

Similarly, the characteristic equation of the linear spatial stability theory for semi-infinite inviscid jets found in [36] based on (1.49)-(1.51) coincides with the long-wave limit of the exact result found in [13] based on flie three-dimensional equations of fluid mechanics (cf. section Spatiotemporal Instability of a Jet ). 

This is the most well-known Einstein s energy equation in the special theory of relativity. According to special relativity hght travels at the same speed for all inertial observers, which implies that one can select units such that spatial distances are specified by units of time (space-time concept). In such units energy and mass have the same units and they are equal numerically, which implies that mass and energy are not two distinct properties. In a way the perception of mass and energy as distinct units is due to the fact that spatiotemporal intervals are overlooked. 

Oscillations and chaos are observed frequently in chemical systems. Most of the experimental investigations of these phenomena have been carried out for well-stirred systems where spatial degrees of freedom are assumed to play no role. If this is the case the system may be described in terms of chemical rate equations for a small number of macroscopic chemical concentrations. The periodic or chaotic attractors typically have low dimensions and can be characterized using the tools of dynamical systems theory [20]. Chemical systems may also display spatiotemporal oscillations and chaos. If spatial degrees of freedom are important the appropriate macroscopic model is the reaction-diffusion equation. The attractors may have high dimension and the theoretical description of such spatiotemporal states is less well developed. 

Among the characteristic physical properties of liquid crystals, what are of critical importance to display devices (LCDs) are those of macroscopic spatiotemporal scale there, the theories of liquid crystals as continuous media play essential roles. The basis of static continuum mechanics of nematic liquid crystals was established by... 

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