Temporal variations of the

The spatio-temporal variations of the concentration field in turbulent mixing processes are associated wdth very different conditions for chemical reactions in different parts of a reactor. This scenario usually has a detrimental effect on the selectivity of reactions when the reaction time-scale is small compared with the mixing time-scale. Under the same conditions (slow mixing), the process times are increased considerably. Due to mass transfer inhibitions, the true kinetics of a reaction does not show up instead, the mixing determines the time-scale of a process. This effect is known as mixing masking of reactions [126]. 

Fig.4.9. Oscilloscope traces of temporal variation of the electric conductivity of a ZnO sensor for different initial pressures of the isopropyl alcohol vapor 5-2-t0-2 Torr (0, 3-6.10-2 (2), 1.65-10-1 0 and 3.25 10- Torr. The temperature of the ZnO film is 390 C.

In 1958, Forrester started studies on an effect which is nowadays often referred to as the bullwhip effect. The bullwhip effect describes the amplification of temporal variations of the orders in a supply chain the more one moves away from the retail customer. Forrester showed that small changes in consumer demand result in large variations of orders placed upstream [4, 5]. It is interesting that this effect occurs even if the demand of final products is almost stable. For his studies, he assumed that some time delay exists between placing an order and the realization of this order (production). Furthermore, he assumed that each part of the supply chain plans its production and places its orders upstream taking into account only the information about the demands of its direct customer. 

The vertical distribution of LAS in the sediment column has been characterised in various lakes [21,22], where evidence has been found of its degradation in the top 5 cm, but not at greater depths where the conditions usually are anoxic. Amano et al. [23,24] have simulated the temporal variation of the concentration of LAS in the surface layer of sediments and have estimated the flux across the water-sediment... 

The time scale for describing the temporal variations of the pollutant species, T, is large when compared with the time scale characterizing the turbulent processes in the atmosphere (i.e., the Lagrangian time scale, Tl). Thus, T > Tl-... 

When the limiting conditions of the friction approximation are not valid, e.g., there is strong non-adiabatic coupling or rapid temporal variation of the coupling, there is at present no well-defined first principles method to calculate the breakdown in the BOA. The fundamental problem is that DFT cannot calculate excited states of adsorbates and quantum chemistry techniques, that can in principle calculate excited states, are not possible for extended systems. 

In contrast, in dynamic light scattering (DLS) the temporal variation of the intensity is measured and is represented usually through what is known as the intensity autocorrelation function. The diffusion coefficients of the particles, particle size, and size distribution can be deduced from such measurements. There are many variations of dynamic light scattering, and... 

Arbitrary input variation. We have now developed recipes with which we can estimate the influence of temporal variations of the external force in general. One can always separate the trend of a function J(t) from its oscillatory variation. The former can be analyzed with Eq. 21-14, the latter with 21-18, Since the system is linear we could make a frequency analysis of J(t) and then treat the influences of the different frequencies on C(t) separately. 

The second input scenario, simpler from a mathematical viewpoint but less probable to occur, is a generalization of the instantaneous (5-)input. It is assumed that the temporal variation of the input is Gaussian and leads to an initial longitudinal variation of the concentration cloud with standard deviation ... 

Friedrich AB, Fischer I, Proksch P, Hacker J, Hentschel U (2001) Temporal Variation of the Microbial Community Associated with the Mediterranean Sponge Aplysina aerophoba. FEMS Microbiol Ecol 38 105... 

The results obtained by the model are the temporal variation of the emitted mass and of the mass flux as well as the... 

Fig. 2.7 (a) Temporal variation of the membrane potential V and the intracellular calcium concentration S in the considered simple model of a bursting pancreatic cell, (b) Bifurcation diagram forthe fast subsystem the black square denotes a Hopf bifurcation, the open circles are saddle-node bifurcations, and the filled circle represents a global bifurcation, (c) Trajectory plotted on top of the bifurcation diagram. The null-cline forthe slow subsystem is shown dashed. 

Figure 12.2c shows the temporal variation of the instantaneous frequencies for the two modes. It is interesting to observe how the frequency of the fast mode is modulated in a fairly regular manner. With about 17 modulation cycles for fjast during the 500 s of observation time, we conclude that the frequency of the fast mode is modulated by the presence of the slow mode, indicating that the two modes interact with one another. If one compares the phase of the tubular pressure variations in Fig. 12.2a with the phase of the frequency modulation in Fig. 12.2c it appears that the maximum of ffast occurs about 60° after the maximum of Pt. It is important to note, however, that the various steps of our wavelet analysis may have introduced a certain phase lag. We are presently trying to correct for such effects in order to obtain a better understanding of the instantaneous relation between the two variables. 

Figure 12.6a shows the temporal variation of the proximal tubular pressure Pt as obtained from the single-nephron model for a = 12 and T = 16 s. All other parameters attain their standard values as listed in Table 12.1. Under these conditions the system operates slightly beyond the Hopf bifurcation point, and the depicted pressure variations represent the steady-state limit cycle oscillations reached after the initial transient has died out For physiologically realistic parameter values the model reproduces the observed self-sustained oscillations with characteristic periods of 30-40 s. The amplitudes in the pressure variation also correspond to experimentally observed values. Figure 12.6b shows the phase plot Here, we have displayed the normalized arteriolar radius r against the proximal intratubular pressure. Again, the amplitude in the variations of r appears reasonable. The motion... 

Fig. 12.6 (a) Temporal variation of the proximal tubular pressure Pt as obtained from the single-nephron model fora = 12 and T = 16 s. (b) Corresponding phase plot. With the assumed parameters the model displays self-sustained oscillations in good agreement with the behavior observed for normotensive rats. The unstable equilibrium point falls in the middle of the limit cycle, and the motion along the cycle proceeds in the clockwise direction. 

Fig. 12.15 (a) Phase plot for one of the nephrons and (b) temporal variation of the tubular pressures for both nephrons in a pair of coupled chaotically oscillating units, a = 32, T = 16 s, and e = y = 0.2. The figure illustrates the phenomenon of chaotic phase synchronization. By virtue of their mutual coupling the two chaotic oscillators adjust their (average) periods to be identical. The amplitudes, however, vary incoherently and in a chaotic manner [27],... 

Equation (5) was modified in order to take into account the different oxygen sticking coefficients on the 1 x 1 and 1 x 2 patches. If their ratio is denoted by a [which was taken to be 1.5 from the experimental estimates (66)], the temporal variation of the oxygen coverage now reads... 

Formulation of the temporal variations of the coverages of CO, NO, and O in terms of three coupled differential equations (the recombination of 2Nad and desorption of N, is much faster than the other processes and can hence be left without explicit consideration) leads indeed to oscillatory solutions without the need for additional inclusion of a surface-phase transition step. The physical reason lies in the fact that dissociation of adsorbed NO (step g) needs another free adsorption site and is inhibited if the total coverage exceeds a critical value [The adsorptive properties of... 

A second improvement was that we measured the cyclotron frequency in the precision trap simultaneously with the Larmor frequency. This reduces to a large extent possible errors induced by a temporal variation of the magnetic field which occurs in superconducting solenoids typically at a level of 10-8 per hour. In the final experiment we measure the rate of spin Hips at different ratios of the Larmor- and cyclotron field frequencies. An example is shown in Fig. 10. The linewidth is of the order of 10-8 and the g factor can be determined with a statistical uncertainty below 1 ppb [19]. 

This mechanism is denoted as an EC mechanism (Testa and Reinmuth, 1961 Bott, 1997). Thus homogeneous kinetic terms may be combined with the expressions for diffusion and convection [i.e. a modified version of (18)] to give the temporal variation of the concentration of a species in an electrode reaction mechanism. In order to model the voltammetric response associated with this mechanism, a knowledge of , a, ko and k is required, or deduced from a theoretical-experimental comparison, and the set of concentrationtime equations for species A, B and C must be solved subject to the constraints of the Butler-Volmer equation and the experimental design. Considerable simplification of the theory is achieved if the kinetics for the forward and reverse processes associated with the E step are fast, which is a good approximation for many organic reactions. Section 7 describes the approaches used to solve the equations associated with electrode reaction mechanisms, thus enabling theoretical simulation of voltammetric responses to be achieved. 

In conclusion, the present intense research effort triggered by the El Chichon eruption should have a significant impact on aerosol science and on dynamic climatology. It is fair to expect that a detailed description of the spatial and temporal variation of the radiative field, of the fluxes... 

Figure 2. Temporal variations of the droplet temperature profiles for single-component droplet vaporization (45)...

The only convection-free experiments are those of Kumagai and his co-workers (47,48), in which a free droplet undergoes combustion in a freely falling chamber. The observed behavior on the temporal variations of the droplet and flame sizes agreed very well with predictions from the transient analyses (36,45),... 

Figure 5. Temporal variations of the droplet heptane composition for a heptane-octane droplet, with extreme internal heat and mass transport rates...

Figure 3 shows the temporal variations of the normalized droplet surface area and the rate of droplet vaporization for the three modes of gas-phase heat and mass transfer. Surprisingly there is very little influence... 

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