Integration time interval

In addition to measuring shock wave and bubble energies, underwater tests also can measure the shock wave impulse, another indicator of explosive strength. The shock wave impulse is derived by measuring the area under the pressure-time curve for a selected integration time interval at a known distance from the explosion... 

In practice. Ax will be normally be set in advance by the modeller by his choice of the number of cells, while the integration routine may well seek to vary the integration timestep. The resulting restriction on the integration time interval is ... 

In Eqs. (19.1), (19.2), (19.3) and (19.4) and are the linear and the non-linear stiffness matrices, M and C are the mass and viscous damping matrices, d and d are the predictor and corrector displacement vectors, v and a are the velocity and acceleration vectors, and At is the integration time interval, respectively. The main characteristic of this method is the division of the stiffness of the whole structure into a linear and a non-linear stiffness. For the non-linear tested part, the explicit predictor-corrector method is used. 

The most simple balance of the system in a certain (usually integral) time interval means the complete information about... 

The integral time interval is about 1 fs and the equation of motion is integrated by fifth-order Gear predictor-corrector method [8]. 

The distance covered by a fluid particle in this flow field in a time interval of -- t can be found by integrating Equation (3.78) as... 

Relative to CO2 on a volume basis. A more useful way to compare the relative warming potentials is to consider the lifetimes of the species and integrate the efficiencies over a fixed time interval, usually 100 years (see Ref. 8). 

The input is continued until 200 lb mol of A have been added, which is for 50 min. Eq. (3) is integrated for this time interval. After input is discontinued the rate equation is... 

For, suppose that this inequality is not true, and that becomes negative at t = t. The smoothness assumptions that have been made imply that the integrand must continue to be negative for at least a short finite-time interval Ar. Now a second cycle may be chosen which is identical with tj) over the time interval (tf, tf + At), but in which elastic unloading commences at time t f + At. Since is zero during elastic portions of the cycle, the integral of is negative for this second cycle, which contradicts (5.50). 

Other timing switch gear works with electronic digital clocks. The 1-s time interval derived from the mains frequency is counted in an integrating counter. The... 

Solving Newton s equation of motion requires a numerical procedure for integrating the differential equation. A standard method for solving ordinary differential equations, such as Newton s equation of motion, is the finite-difference approach. In this approach, the molecular coordinates and velocities at a time it + Ait are obtained (to a sufficient degree of accuracy) from the molecular coordinates and velocities at an earlier time t. The equations are solved on a step-by-step basis. The choice of time interval Ait depends on the properties of the molecular system simulated, and Ait must be significantly smaller than the characteristic time of the motion studied (Section V.B). 

In equation (4.68), T is called the integral action time, and is formally defined as The time interval in which the part of the control signal due to integral action increases by an amount equal to the part of the control signal due to proportional action when the error is unchanging . (BS 1523). 

The vane anemometer is an old invention. It can be likened to a small wind turbine with 4-10 rotating blades and a handle, as in Fig. 12.20. Earlier constructions were fully mechanical, where the spindle rotation was transmitted to a pointer through a series of gears. In modern vane anemometers, an electrical sensor records the spindle rotation and the signal is processed, giving the velocity on a digital display. Such an instrument usually is able to integrate the mean velocity over a time interval. 

The power required for pumping will be given by the product of the volumetric flowrate and the pressure difference between the pump outlet and the discharge end of the pipeline. Taking note of the fluctuating nature of the flow, it is necessary to consider the energy transferred to the fluid over a small time interval and to integrate over the cycle to obtain the mean value of the power. 

As we are particularly interested in surface reactions and catalysis, we will calculate the rate of collisions between a gas and a surface. For a surface of area A (see Fig. 3.8) the molecules that will be able to hit this surface must have a velocity component orthogonal to the surface v. All molecules with velocity Vx, given by the Max-well-Boltzmann distribution f(v ) in Cartesian coordinates, at a distance v At orthogonal to the surface will collide with the surface. The product VxAtA = V defines a volume and the number of molecules therein with velocity Vx is J vx) V Vx)p where p is the density of molecules. By integrating over all Vx from 0 to infinity we obtain the total number of collisions in time interval At on the area A. Since we are interested in the collision number per time and per area, we calculate... 

The function 7(f) can be chosen for the whole reaction time interval, or two or three subsequent temperature-time data points 7(fi-i), 7(fi), and 7(fi+i) can be approximated by polynomials of second or third order 7,(f), respectively. These polynomials will then be used in a procedure for numerical integration in each integration step i. This method has been successfully applied in a kinetic study of the partial oxidation of hydrocarbons (Skrzypek et al., 1975, Krajewski etai, 1975, 1976, 1977). 

The procedure for the selection of the most appropriate time interval requires the integration of the state and sensitivity equations and the computation of lj(t), j=l,...,p at each grid point of the operability region. Next by plotting I/t), j=l,...,p versus time (preferably on a log scale) the time interval [t, tNp] where the information indices are excited and become large in magnitude is determined. This is the time period over which measurements of the output vector should be obtained. 

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