Dissipative effects

Internal surfactant antistats ate physically mixed with the plastic resin prior to processing. When the resin is melted, the antistat distributes evenly in the polymer matrix. The antistat usually has some degree of solubiUty in the molten polymer. However, when the polymer is processed (extmded, molded, etc) into its final form and allowed to cool, the antistat migrates to the surface of the finished article due to its limited solubiUty in the solidified resin. The molecule of a surface-active agent is composed of a polar hydrophilic portion and a nonpolar hydrophobic portion. The hydrophilic portion of the surfactant at the surface attracts moisture from the atmosphere it is the moisture that has the static dissipative effect. 

The shock wave is subject to other dissipative effects, however, such as viscosity and heat transport. It is these dissipative mechanisms that are responsible for preventing the shock from becoming a true, infinitesimally thin discontinuity. In reality, the velocity gradient can only increase until... 

At temperatures above there is no instanton, and escape out of the initial well is accounted for by the static solution Q = Q with the action S ff = PVo (where Vq is the adiabatic barrier height here) which does not depend on friction. This follows from the fact that the zero Fourier component of K x) equals zero and hence the dissipative term in (5.38) vanishes if Q = constant. The dissipative effects come about only through the prefactor which arises from small fluctuations around the static solution. Decomposing the trajectory into Fourier series. 

Celata et al. (2005) evaluated the effect of viscous heating on friction factor for flow of an incompressible fluid in a micro-channel. By integrating the energy equation over the micro-channel length, a criterion that determines conditions when viscous dissipation effect is signiflcant was obtained ... 

Judy J, Maynes D, Webb BW (2002) Characterization of frictional pressure drop for liquid flows through micro-channels. Int J Heat Mass Transfer 45 3477-3489 Kandlikar SG, Joshi S, Tian S (2003) Effect of surface roughness on heat transfer and fluid flow characteristics at low Reynolds numbers in small diameter tubes. Heat Transfer Eng 24 4-16 Koo J, Kleinstreuer C (2004) Viscous dissipation effects in microtubes and microchannels. Int J Heat Mass Transfer 47 3159-3169... 

Experimental and numerical analyses were performed on the heat transfer characteristics of water flowing through triangular silicon micro-channels with hydraulic diameter of 160 pm in the range of Reynolds number Re = 3.2—84 (Tiselj et al. 2004). It was shown that dissipation effects can be neglected and the heat transfer may be described by conventional Navier-Stokes and energy equations as a common basis. Experiments carried out by Hetsroni et al. (2004) in a pipe of inner diameter of 1.07 mm also did not show effect of the Brinkman number on the Nusselt number in the range Re = 10—100. 

Koo J, Kleinstreuer C (2004) Viscous dissipation effects in micro-tubes and micro-channels. Int J Heat Mass Transfer 47 3159-3169... 

This contribution considers systems which can be described with just the Hamiltonian, and do not need a dissipative term so that TZd = 0- This would be the case for an isolated system, or in phenomena where the dissipation effects can be represented by an additional operator to form a new effective non-Hermitian Hamiltonian. These will be called here Hamiltonian systems. For isolated systems with a Hermitian Hamiltonian, the normalization is constant over time and the density operator may be constructed in a simpler way. In effect, the initial operator may be expanded in its orthonormal eigenstates (density amplitudes) and eigenvalues Wn (positive populations), where n labels the states, in the form... 

Colour and line-strength gradients are also observed across elliptical galaxies, as is to be expected from dissipative effects (see Appendix 5). However, the detailed... 

General Remarks. The wavefront analysis as presented here, is limited only to the chemical relaxations and excludes any dissipation effects. The space relaxation, manifested as the change of the propagating primary wavefront itself, is met with and corresponds to the initial steady state or an equilibrium state of the system. On the other hand, the time relaxation manifests the changes in the system, caused by the primary wavefront. 

When a system involves dissipative effects such as friction caused by molecular collisions or turbulence caused by a non-uniform molecular distribution, even under adiabahc conditions, ds becomes a positive value, and then Eqs. (1.13) and (1.14) are no longer valid. However, when these physical effects are very small and heat loss from the system or heat gain by the system are also small, the system is considered to undergo an isentropic change. 

If one can assume that the process in the flow field is adiabatic and that dissipative effects are negligibly small, the flow in the system is isentropic (ds = 0), and then Eq. (1.21) becomes... 

The above iterative method provides a means of estimating shock effects of spherical underwater charges, but the method is cumbersome and the approximations involved (particularly the neglect of dissipation effects) are not completely justifiable... 

The first term on the right-hand side corresponds to Eq. (2), whereas the second term describes dissipative effects that are induced in the system due to its coupling to the environment. The latter is modeled, as usual [32, 33], as the thermal (temperature T) ensemble of harmonic oscillators, with nonlinear coupling A Qiq) F( thermal bath, expressed in terms of nonlinear molecular and linear environment coupling operators Q(q) and F( qk )- As shown in Ref. 15, it is important to describe the dissipative term in Eq. (10) by making use of the non-Markovian expression... 

The quantity 17(f) is the time-dependent friction kernel. It characterizes the dissipation effects of the solvent motion along the reaction coordinate. The dynamic solute-solvent interactions in the case of charge transfer are analogous to the transient solvation effects manifested in C(t) (see Section II). We assume that the underlying dynamics of the dielectric function for BA and other molecules are similar to the dynamics for the coumarins. Thus we quantify t](t) from the experimental C(t) values using the relationship discussed elsewhere [139], The solution to the GLE is in the form of p(z, t), the probability distribution function. 

P. N. Kaloyerou and J. P. Vigier, Derivation of a non-linear Schrodinger equation describing possible vacuum dissipative effects, Phys. Lett. A 130(4—5), 260-266 (1988). 

Finally, we address the inclusion of dissipative effects in accordance with the discussion of Sec. 4.3. Dissipation is not expected to induce major changes in the dynamics, but its effect could be important in view of the fact that the finite-dimensional model under consideration tends to overemphasize coherent features on intermediate and long time scales. Fig. 8 (panel (b)) illustrates the effects of dissipation included at the level of the Markovian closure addressed in Sec. 4.3. We consider the approximation according to Eq. (16), i.e.,... 

To simplify the problem, we can assume that the polymer bar moves at a constant speed Usy, and that a film of constant thickness, 5, exists between the bar and the heated plate. In addition, we assume that the polymer melt is Newtonian and that the viscosity is independent of temperature. The Newtonian assumption is justified by low rates of deformation that develop in this relatively slow flow problem. Furthermore, due to these low rates of deformation we can assume that the convective and viscous dissipation effects are negligible. 

Determine what the viscous dissipation effects are in a melting with pressure removal problem. Use the notation of Fig. 6.65. 

Omar Estrada, Ivan Lopez, Carlos Roldan, Maria del Pilar Noriega, and Whady Florez. Solution of steady and transient 2D-energy equation including convection and viscous dissipation effects using radial basis function interpolation. Journal of Applied Numerical Mathematics, 2005. 

The dilational rheology behavior of polymer monolayers is a very interesting aspect. If a polymer film is viewed as a macroscopy continuum medium, several types of motion are possible [96], As it has been explained by Monroy et al. [59], it is possible to distinguish two main types capillary (or out of plane) and dilational (or in plane) [59,60,97], The first one is a shear deformation, while for the second one there are both a compression - dilatation motion and a shear motion. Since dissipative effects do exist within the film, each of the motions consists of elastic and viscous components. The elastic constant for the capillary motion is the surface tension y, while for the second it is the dilatation elasticity e. The latter modulus depends upon the stress applied to the monolayer. For a uniaxial stress (as it is the case for capillary waves or for compression in a single barrier Langmuir trough) the dilatational modulus is the sum of the compression and shear moduli [98]... 

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