The Role of Time

When a process is time dependent, one speaks of unsteady, unsteady-state, or d5mamic systems and balances. If, on the other hand, there are no variations with time, the process is said to be at steady state. There are several categories of unsteady balances depending on the balance space and time framework we use. They are summarized below. 

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Figure Al.6.7. Schematic diagram illustrating the different possibilities of interference between a pair of wavepackets, as described in the text. The diagram illustrates the role of phase ((a) and (c)), as well as the role of time delay (b). These cases provide the interpretation for the experimental results shown in figure Al.6.8. Reprinted from [22],...

Sohnel, O. and Mullin, J.W., 1988. The role of time in metastable zone width determinations. Chemical Engineering Research and Design, 66, 537-540. 

This is Bloch s equation. We note that this equation is essentially of the same form as Schrbdinger s equation, with playing the role of wave function, and ]8 playing the role of time, j8 (i]E)t, and the operator H — E representing deviation of the hamiltonian from the ensemble average. 

Langhans SD, Tockner K (2006) The role of timing, duration, and frequency of inundation in controlling leaf-litter decomposition in a river-floodplain ecosystem (Tagliamento, NE Italy). Oecologia 147 501-509... 

For the case of interest, copolymerization dynamics is described by nonlinear equations (Eq. 62) where variable plays the role of time, supplemented by the thermodynamic relationship (Eq. 63). The instantaneous state of the system characterized by vector X may be represented by a point inside the unit interval X + X2 = 1. The evolution of composition X in the course of... 

Muller WA, Luz A, Schaffer EH, et al. 1983. The role of time-factor and RBE for the induction of osteosarcomas by incorporated short-lived bone-seekers. Health Phys44(Suppl 1) 203-212. 

One way to visualize the three-sphere S is to think of a movie, with u playing the role of time. For times before — 1 or after 1 there is nothing on the three-dimensional screen at time n = — 1 exactly there is one point visible at the spatial point (0, 0, 0) more generally, for u e [—1,1] there is a two-sphere of radius Vl — visible on the three-dimensional screen. (One can also interpret the fourth dimension as color. See Exercise 1.10.) We can write... 

This is nothing but the continuous chain version of Eq. (A 5-18). except that the endpoints r,r are held fixed. Equation (A 7.10) is the standard path integral representation of the Greensfunetion of a diffusion equation, where plays the role of time ... 

Many variables used and phenomena described by fracture mechanics concepts depend on the history of loading (its rate, form and/or duration) and on the (physical and chemical) environment. Especially time-sensitive are the level of stored and dissipated energy, also in the region away from the crack tip (far held), the stress distribution in a cracked visco-elastic body, the development of a sub-critical defect into a stress-concentrating crack and the assessment of the effective size of it, especially in the presence of microyield. The role of time in the execution and analysis of impact and fatigue experiments as well as in dynamic fracture is rather evident. To take care of the specihcities of time-dependent, non-linearly deforming materials and of the evident effects of sample plasticity different criteria for crack instability and/or toughness characterization have been developed and appropriate corrections introduced into Eq. 3, which will be discussed in most contributions of this special Double Volume (Vol. 187 and 188). 

Grodstein F, Manson JE, Stampfer MJ. Hormone therapy and coronary heart disease the role of time since menopause and age at hormone initiation. J Womens Health. 2006 I 5 35M4. 

Butlerov s prophecy has been taken as heralding the first step toward the creation of molecular representations with which all chemical properties of a substance could be rationalized. Some imagine these to be iconic formulas of a "photographic" fidelity. Others assert that the ultimate representation of a chemical substance is a mathematical equation—the molecular wavefunction—that would permit not only the rationalization but even the prediction of the material s chemical behavior (Mosini, 1994). One of my theses is that no such single "rational formula" exists or could exist. However, exploring why Butlerov s vision is unrealizable can shed light on what entities chemists see as "fundamental" and the role of time within chemistry. 

It goes beyond the scope of this chapter to discuss the matter of time scale where such a density function appears justified nevertheless, one should recognize that the effects of zero-point energy and the associated vibrations modify the role of the effective external potential experienced by the actual electron density, which also involves the role of time. Whereas electron density changes and fluctuations can carry information, all such effects on the molecular information are also dependent on the ground-state electron density. 

By considering the role of timing of odorant delivery in biological olfaction (Rubin Cleland 2006), we have recently built a novel machine olfaction technology, termed an artificial olfactory mucosa , which demonstrates clearly a third principle of odour discrimination in artificial olfactory systems ... 

In our previous work we have discussed how to calculate in practice this quantity when the temporal patterns of the responses of the individual sensors are not taken into account (corresponding to the first mechanism for discrimination identified in Section 1). Here we extend and calculate the Fisher Information for the spatio-temporal case which includes the role of time in the responses. The first step is to model the noise in the sensors, which will determine p (Yj I c). 

The role of time-sharing in gas chromatography has been recently reviewed by Gill several customers have published their experience... 

Constitutive principles of memory give more detailed description of the influence of the past on the response. Section 2.3 describes the role of time scales (cf. Sect. 1.1) for this description and the expression of the influence of the past (or history) through internal variables. The influence of the past frequently expected from the experience is contained in the constitutive principle of fading memory the more the past is remote, the less influence it has on the response. Mathematical formulation of this principle need not be unique [24-29] (for introduction see [2, 4, 6, 30]). In limit of equilibrium there is some time interval (natural time scale or relaxation time, cf. Rem. 11 in Chap. 1 Sects. 2.4, 3.8, 4.7) after which the (practical) influence of the past is negligible. 

In both cases, (4.2) can be viewed as Newton s equation for a particle moving in one dimension under the action of the force —F p) — vp the variable z plays the role of time. The force —F p) is conservative and derives from the potential Vip) = F s)ds. 

G. E. Cossali, M. Marengo, A. Coghe, S. Zhdanov The role of time in single droplet splash on thin film, Exp. Fluids, 36(6), 888-900 (2004). 

Notwithstanding the inherent advantages of the controlled-stress technique in yield studies, it should be borne in mind that an interpretation of the results of creep-compliance measurements in terms of a real yield stress (i.e. a stress below which the sample exhibits Hookean elastic behaviour) is subject to the usual experimental limitations of machine resolution (i.e. of angular displacement) and the role of time-scale in the sample s response to applied stress. 

Good engineers recognize the role of time in their lives and in calculating speed, acceleration, and flow of traffic, as well as flow of materials and substances. They know what is meant by frequency and period and understand the difference between a steady and a transient process. Good engineers have a comfortable grasp of rotational motion and understand how it differs from translational motion. 

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