Instantaneous pressure distributions

The assumption of independence of the desired solution from the concrete form of tv(t) suggests that the solution, for example, the instantaneous pressure distribution p(x, t) at t > r, should be sought in a self-similar form,... 

Figure 8.12(b) shows the instantaneous pressure distribution and velocity profile for the top half of the geometry. 

Figure 11. A comparison of numerical results with theory and experiment for instantaneous pressure distributions on a half-cylinder (ka — 2.5 and kh = 5) with...

Ehara, Shiro Instantaneous pressure distributions of orchestra sounds, /. Acoust. Soc. Japan, vol. 22, pp. 276-289,1966. 

Together with the questions of ignition and the feasibility (limit) of combustion, the concepts developed here are important for the combustion of EM or powder under variable conditions, in particular, at non-constant pressure. Variable pressure is accompanied by a variable combustion velocity, and to each value of the combustion velocity corresponds a particular value of the gradient ip which is established in the steady regime. It is at precisely this value combustion velocity occurs. Meanwhile, for rapid pressure variation the temperature distribution in the c-phase is not able to keep up with the change in pressure for a non-steady value of

combustion velocity will also prove different from the steady value. For rapid pressure variation the combustion velocity turns out to depend not only on the instantaneous pressure, but also on its variation curve, which distorts the classical law of combustion. 

Fig. 8.7 We plot the results of an NPT simulation of 64 atoms of Lennard-Jonesium using the given discretization where yr = yp = y, with y set to zero (blue), y = 0.1 [green) or y = 1 [red). Although the distribution of instantaneous pressure 77 (centered on the target pressure P) looks similar for all three cases, we can see that without any stochasticity the simulation exhibits artificial periodic fluctuations in the temperature and volume...

The instantaneous pressure and velocity distributions along the resonance tube are monitored by piezoelectric transducers and hot-wire thermal anemometer that are connected to the oscilloscope and photo film recorder. These make possible the tuning of the generator to the acoustic resonance by varying the rotational speed of the crankshaft. Also, there is a provision to attach resonance tubes of various lengths and diameters to obtain required amplitudes of pressure and velocity pulsations. 

Streeter DD, Vaishnav RN, Patel DJ, Spotnitz HM, Ross J Jr, Sonnenblick EH (1970). Stress distribution in the canine left ventricle during diastole and systole. Biophysical J 10 345-363 Suga H, Sagawa K (1974) Instantaneous pressure-volume relationships and their ratio in the excised, supported canine left ventricle. Circ Res 35 117-126 Tozeren A (1983) Static analysis of the left ventricle. J Biomech Eng 105 39-46 Yin FCP (1981) Ventricular wall stress. Circ Res 49 829-842... 

In (Pao and Ritman, 1978), the 3-layer analysis was adopted in the investigation of the transmural pressure distributions in the left ventricular wall before and after the coronary artery ligation. The stress-dependent E equation such as Eq. (3) enables the fiber stiffness to be adjusted from one element to another in accordance with the instantaneous stress level in each element calculated during the incremental-loading finite element analysis. 

In the deformed state, the variables in the Hamiltonian change from ( R , r ) to ( R , Ar ). However, the distribution p( r ) of finding the topology r depends solely on how the material is made instantaneously at thermal equilibrium (i.e., at constant temperature T, pressure p, etc.) i.e., p( r ) does not depend on the external deformation tensor A. Then, the final answer for the free energy of the deformed network is... 

The blast load is modeled as a triangular-shaped overpressure time curve. The blast overpressure rises instantaneously to the peak overpressure, B, then decays linearly with a blast pressure duration, T. The pressure is uniformly distributed over the surface of the plate and is applied perpendicular to the pane. 

The mechanism of the polymerization of this monomer has been studied in far greater detail than any other. It is clear from the outset that a much more complex mechanism is involved than is the case for olefins. A large proportion of the initiator is used to form polymer whose molecular weight is only a few hundreds and the overall molecular weight distribution is so broad as to be rivalled only by those found in polyethylene produced by the high pressure process (19, 39). The initiator disappears almost instantaneously on mixing the reactants (19, 38). Under these conditions, an almost monodisperse polymer would be expected if chain transfer or termination processes are absent. 

Flow processes inevitably result from pressure gradients witliin tire fluid. Moreover, temperature, velocity, and even concentration gradients may exist witliin the flowing fluid. This contrasts witlr tire uniform conditions tlrat prevail at equilibrium in closed systems. The distribution of conditions in flow systems requires tlrat properties be attributed to point masses of fluid. Thus we assume tlrat intensive properties, such as density, specific enthalpy, specific entropy, etc., at a point are determined solely by the temperature, pressure, and composition at tire point, uirinfluenced by gradients tlrat may exist at tire point. Moreover, we assume that the fluid exlribits tire same set of intensive properties at the point as tlrough it existed at equilibrium at tire same temperature, pressure, and composition. The implication is tlrat an equation of state applies locally and instantaneously at any point in a fluid system, and tlrat one may invoke a concept of local state, independent of tire concept of equilibrium. Experience shows tlrat tlris leads for practical purposes to results in accord with observation. 

The opportunity to measure the dilute polymer solution viscosity in GPC came with the continuous capillary-type viscometers (single capillary or differential multicapillary detectors) coupled to the traditional chromatographic system before or after a concentration detector in series (see the entry Viscometric Detection in GPC-SEC). Because liquid continuously flows through the capillary tube, the detected pressure drop across the capillary provides the measure for the fluid viscosity according to the Poiseuille s equation for laminar flow of incompressible liquids [1], Most commercial on-line viscometers provide either relative or specific viscosities measured continuously across the entire polymer peak. These measurements produce a viscometry elution profile (chromatogram). Combined with a concentration-detector chromatogram (the concentration versus retention volume elution curve), this profile allows one to calculate the instantaneous intrinsic viscosity [17] of a polymer solution at each data point i (time slice) of a polymer distribution. Thus, if the differential refractometer is used as a concentration detector, then for each sample slice i. 

The liquid-side resistance can be eliminated and the rate of absorption can be made independent of the liquid-side residence-time distribution by using a solution that reacts instantaneously and irreversibly with the dissolved gas and thus eliminates the back pressure. Therefore (Section II,B,4,b)... 

Both the absolute- and local Maxwellians are termed equilibrium distributions. This result relates to the local and instantaneous equilibrium assumption in continuum mechanics as discussed in chap. 1, showing that the assumption has a probabilistic fundament. It also follows directly from the local equilibrium assumption that the pressure tensor is related to the thermodynamic pressure, as mentioned in sect. 2.3.3. 

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