Reference time

Here r(t) is the stress at a fluid particle given by an integral of deformation history along the fluid particle trajectory between a deformed configuration at time f and the current reference time t. 

Adding time-dependent terms to the equations the simulation is treated as an initial value problem in which at a given reference time all stresses are zero the steady-state solution can be found iteratively. 

If the reference time f and the current time t coincide then the reference and current positions will also coincide and the right-hand side of Equation (3.77) can be replaced by the reference position defined as x in Equation (3.76). In a velocity field given as = u x,t ) the motion of a material point can be described... 

The idea behind OELs is to identify the highest level of exposure concentration and the corresponding reference time period for which we can be confident that there will be no adverse effects on health. However, the concentrations and lengths of exposure at which the presence of airborne chemical agents could damage health have not been clear for many years, and even today there are many questions to be answered. 

In this example we will repeat the previous study but now slow down the action by reducing the free-moving probability of the ingredient to Pm = 0.5. Repeat the same calculations as in Study 2.1a, but now using 100 iterations as the reference time. In this case plot d) against for = 0, 10, 20, 30,..., 100. Again, comment on your results. How does d) after 60 iterations compare with the corresponding result from Study 2.1a above Explain any difference. 

These solutions of the idealized problem are a good approximation for the behavior within a time window Xx < t < Xu or the corresponding frequency window 1/2U < co < l/X. Truncation effects can be seen near the edges Xx and Xu. X0 is some material-specific reference time, which has to be specified in each choice of material, and H0r(n) = G0 is the corresponding modulus value. 

Cerenkov radiation accounts for a very minor part of the energy loss of fast electrons. Its main importance is for monitoring purposes and establishment of a reference time, since it is produced almost instantaneously with the passage of the particle. Katsumura et al. (1985) have observed a very fast rise of solute fluorescence attributable to the Cerenkov effect the G value for this process is estimated to be -0.02. 

Vibration Diagram Method. In actuality the last cases above are not described accurately by this dipole array model because actual phases of the electric fields are significantly altered from those of linear waves. (A more realistic, but complex model is to consider amplitude and phase characteristics of the oscillating vertically polarized component of electric field resulting from rotation of a line of transverse dipoles of equal magnitude but rotated relative to each other along the line such that their vertical components at some reference time are depicted by Figure 2.) For this reason and to handle details of focused laser beams one must resort to a more mathematically based description. Fortunately, numerical... 

Some BOMs have validities start and end of validity interval and the reference time used to determine if the product flow is valid or not earliest start, due date, start or end of production. 

Finally, if a Markov process is in some state 5 at some (reference) time t0, and if 6 is the random time required for the process to leave state s to go to some other state, then the probability that 6 is larger than some arbitrary time t is given by... 

To elucidate the possible causes of the decrease in suppression potential, the effects of flow residence time and relative pulsating fuel amount were examined. One possible explanation for the above trend is the reduction in flow residence time as the flow rate was increased. At these conditions some of the larger fuel droplets that persisted in the downstream may not have had enough time to react completely if the residence time became very short. When the residence time was estimated by the reference time scale which is the combustor length divided by inlet velocity (Fig. 21.12), the general trend appears to be consistent with the expectation. The scatter in the plot reflects the crudeness of the estimation larger droplets do not follow the carrier flow very well. 

Correlation functions are powerful tools in statistical physics, and in the above example they permit one to examine the behavior of a fluctuating system from a reference time back to previous times. Such fluctuations can occur in the concentration of two (or more) interconverting chemical species in dynamic equilibrium, and the technique of concentration correlation analysis permits one to determine the forward and reverse rate constants for their interconversion. See Concentration Correlation Analysis... 

Time derivative of a strain tensor for a viscoelastic liquid or solid in homogeneous deformation at reference time, t. 

Rivlin-Ericksen tensor of order n, for a viscoelastic liquid or solid in homogeneous deformation, is the nth time derivative of the Cauchy strain tensor at reference time, t. Note 1 For an inhomogeneous deformation the material derivatives have to be used. 

Qualitative analysis of bile samples is performed using retention time of nor-DCA (internal standard) as relative reference time. 

The first tank ( M = 3.9 x 105 kg) ruptured at 2 40 p.m. (Note This time is chosen as reference time, t = 0.) All the chloroform was lost within a very short time. 

Although the partial differential equation Eq. 25-10 is linear and looks rather simple, explicit analytical solutions can be derived only for special cases. They are characterized by the size of certain nondimensional numbers that completely determine the shape of the solutions in space and time. A reference distance x0 and a reference time f0 are chosen that are linked by ... 

Since we do not weigh these streaks, we assumed that the Ag + Cu + Zn + As + Sb + Au = 100%. By comparing the radioactivity levels in the streaks with those in the standard alloy streaks (each corrected for decay to a common reference time) we can then calculate the percent ratios Cu/Ag, Au/Ag, Zn/Ag, Sb/Ag, and As/Ag. The combination of these ratio data and the above equation allows us to calculate the individual percent values. Various chemical analyses reported in the literature for silver coins and art objects indicate that other elements such as lead and tin (which we do not detect) are usually present at less than 2%. There are notable exceptions however. Some types of coins from certain periods contain up to 10-15% Pb + Bi. As a result, we have always performed direct neutron Howitzer silver analysis on at least a few coins of each general type that are analyzed by streak analysis. The silver data for the Howitzer analysis are invariably lower than those for the streak analysis, but this is to be expected for two reasons the... 

The reference time x0 in Equation 13.14 represents the resource depletion time at which the abundance factor a, is at the value of exactly one half (i.e., 50%). This reference time x0 must be given an appropriate value at which the factors a, adequately reflect the differences in the abundance of real resources. For example, a reference time x0 of 1000 years will give fossil fuels abundance factors roughly ranging from 0.1 to 0.5, while sunlight, probably available for billions of years, will have an abundance factor approaching unity. 

Note the close resemblance between the reference time of the internal rotary diffusion of the magnetic moment and the Debye time... 

In the opposite limit, a —> 0, all the decrements, including A], tend to the sequence A/ 1(1 I lj and thus become of the same order of magnitude. This regime corresponds to a vanishing anisotropy so that the difference between the inter- and intrawell motions disappear, and the magnetic moment diffuses almost freely over all the 4n radians with the reference time xD given by Eq. (4.91). 

In this section we study the arbitrary relationship between the external and internal orientational relaxation reference times. 

---