Dynamic history

Samuelson, L. and Wolfson, M. (1986) Expository Marxism and comparative economic dynamics , History of Political Economy, 18 65-85. 

The dynamical history of stress-relaxation in a star-linear blend begins life in just the same way as a star-star blend,because when t r gp the linear chain relaxation is dominated by pathlength fluctuation and behaves as a two-arm star with M =Mii /2. So very early Rouse fluctuation (Eq. 25) crosses over to activated fluctuation in self-consistent potentials. These are calculated via the coordinate transformation used in the star-star case above. For example, the effective potential for the star component in this regime is... 

For a pulse-type NMR experiment, the assumption has a straightforward interpretation, since the pulse applied at the moment zero breaks down the dynamic history of the spin system involved. The reasoning presented here, which leads to the equation of motion in the form of equation (72), bears some resemblance to Kaplan and Fraenkel s approach to the quantum-mechanical description of continuous-wave NMR. (39) The crucial point in our treatment is the introduction of the probabilities izUa which are expressed in terms of pseudo-first-order rate constants. This makes possible a definition of the mean density matrix pf of a molecule at the moment of its creation, even for complicated multi-reaction systems. The definition of the pf matrix makes unnecessary the distinction between intra- and inter-molecular spin exchange which has so far been employed in the literature. 

Observations show that protoplanetary disks are dynamic, evolving objects, whose density and temperature structures change with time due to the transport of mass and angular momentum. Chondritic meteorites and comets record a dynamic history of our own solar nebula as they contain materials that formed in a wide variety... 

There are several technical details in a rigorous definition of the autocorrelation function for velocity. First, one has to remember the vectorial character of velocity, because clearly the direction in which the particle is knocked is important to its subsequent dynamic history. Then, according to the way it is defined, one has to take the product of the velocity at f = 0, Vg, and that at the later chosen time, v,. However, it is not as simple as just multiplying together the two veetors, Vg and v,. One has to allow for the distribution of positions and momenta of the particle in the system at the beginning, that is, at i = 0. To allow for this, one can introduce symbolically a probability distribution coefficient, g. Therefore, the expression for the autocorrelation function will involve the product gVgV,. 

A postulated fast reactor accident that has been extant for many years is the collapse of the core following partial melting of the fuel, hidependently of the cause or probability of such a situation, certain cases can be defined and some facets of the dynamic history of these cases can be described with more than enough accuracy for safety considerations.. The situation considered is that during which a fair fraction of the fuel has become molten and has reassembled in a nearly critical state somewhere in or below the customary location of the core. 

You can detect hydroxyl group transitions by plotting dihedral angles versus time over the course of the simulation. This is the distance history. Brady investigated the distance history of water 19. Brady, J.W. Molecular dynamics simulations of a-d-glucose in aqueous solution. 

Relaxations of a-PVDF have been investigated by various methods including dielectric, dynamic mechanical, nmr, dilatometric, and piezoelectric and reviewed (3). Significant relaxation ranges are seen in the loss-modulus curve of the dynamic mechanical spectmm for a-PVDF at about 100°C (a ), 50°C (a ), —38° C (P), and —70° C (y). PVDF relaxation temperatures are rather complex because the behavior of PVDF varies with thermal or mechanical history and with the testing methodology (131). 

Floor acceleration This is the time history of acceleration of a partictilar floor nr structure caused by a given ground acceleration (Figure 14.16). It may have an amplified narrow band spectrum due to structural filtration, where single frequency excitation and resonance may predominate, depending upon the dynamic characteristics of the structure. A floor response spectrum (FR.S). as shown in Figure 14.18, can be derived from this history. Consideration of GRS or FRS will depend upon the location of the object under test. 

The structure/property relationships in materials subjected to shock-wave deformation is physically very difficult to conduct and complex to interpret due to the dynamic nature of the shock process and the very short time of the test. Due to these imposed constraints, most real-time shock-process measurements are limited to studying the interactions of the transmitted waves arrival at the free surface. To augment these in situ wave-profile measurements, shock-recovery techniques were developed in the late 1950s to assess experimentally the residual effects of shock-wave compression on materials. The object of soft-recovery experiments is to examine the terminal structure/property relationships of a material that has been subjected to a known uniaxial shock history, then returned to an ambient pressure... 

The energy which drives the fragmentation process (elastic plus kinetic) is determined by the dynamic loading conditions and does not directly depend on the properties of the material at issue. The fragmentation energy, on the other hand, is an intimate property of the material and can depend in a complex way on the thermal and dynamic conditions at spall, as well as on the deformation history of the material leading to spall. 

Among these three polybibenzoates, PTEB has a smectic mesophase stable during several days at any temperature below its isotropization point, although the transformation into a three-dimensional crystal can be attained by annealing at the appropriate temperatures, thus making it possible to analyze the effect of the thermal history on the dynamic mechanical relaxations of PTEB [27]. 

In conclusion, the different thermal histories imposed to PTEB have a minor effect on the /3 and y relaxations, while the a. transition is greatly dependent on the annealing of the samples, being considerably more intense and narrower for the specimen freshly quenched from the melt, which exhibits only a liquid crystalline order. The increase of the storage modulus produced by the aging process confirms the dynamic mechanical results obtained for PDEB [24], a polyester of the same series, as well as the micro-hardness increase [22] (a direct consequence of the modulus rise) with the aging time. 

Geld C (2004) Prediction of dynamic contact angle histories of a bubble growing at a wall. Int J Heat Fluid Flow 25 74—80... 

It is now widely accepted that the compositions of the atmosphere and world ocean are dynamically controlled. The atmosphere and the ocean are nearly homogeneous with respect to most major chemical constituents. Each can be viewed as a reservoir for which processes add material, remove material, and alter the compositions of substances internally. The history of the relative rates of these processes determines the concentrations of substances within a reservoir and the rate at which concentrations change. Commonly, only a few processes predominate in determining the flux of a substance between reservoirs. In turn, particular features of a predominant process are often critical in controlling the flux of a phase through that process. These are rate-controlling steps. 

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