Dissipation time

Table (b) shows charge dissipation times to reduce the charge density to 5% of the initial values for a series of initial charge densities (Qg) and for... 

TABLE (b). Charge Dissipation Times for Hyperbolic Relaxation (e, = 2-4)... 

Owing to the change from exponential to hyperbolic relaxation, a nominal dissipation time of 100 s is assigned in Appendix B to all liquids whose conductivities are below 2 pS/m. The 2 pS/m demarcation is convenient... 

Once soil samples have been analyzed and it is certain that the corresponding results reflect the proper depths and time intervals, the selection of a method to calculate dissipation times may begin. Many equations and approaches have been used to help describe dissipation kinetics of organic compounds in soil. Selection of the equation or model is important, but it is equally important to be sure that the selected model is appropriate for the dataset that is being described. To determine if the selected model properly described the data, it is necessary to examine the statistical assumptions for valid regression analysis. 

Beguier, C., I. Dekeyser, and B. E. Launder (1978). Ratio of scalar and velocity dissipation time scales in shear flow turbulence. The Physics of Fluids 21, 307-310. 

Hereafter we put /ig = 1. Below we express our results in terms of the statistical properties (correlators) of the environment s noise, X(t). Depending on the physical situation at hand, one can choose to model the environment via a bath of harmonic oscillators [6, 3]. In this case the generalized coordinate of the reservoir is defined as X = ]T)Awhere xi are the coordinate operators of the oscillators and Aj are the respective couplings. Eq. 2 is then referred to as the spin-boson Hamiltonian [8]. Another example of a reservoir could be a spin bath [11] 5. However, in our analysis below we do not specify the type of the environment. We will only assume that the reservoir gives rise to markovian evolution on the time scales of interest. More specifically, the evolution is markovian at time scales longer than a certain characteristic time rc, determined by the environment 6. We assume that rc is shorter than the dissipative time scales introduced by the environment, such as the dephasing or relaxation times and the inverse Lamb shift (the scale of the shortest of which we denote as Tdiss, tc [Pg.14]

Figures 1A, 2A and 3A give representative dissipation curves for parathion, azinphosmethyl and methidathion on orange trees in California (6). Parathion dissipates with the formation of considerable amounts of paraoxon. Low volume application (100 gal/acre) of these insecticides results in high levels of OP residues and thus longer dissipation times to safe levels. Azinphosmethyl does not dissipate as rapidly as parathion under field conditions. Azinphosmethyl oxon is formed during the process and dissipates slowly with time. Azinphosmethyl oxon levels were determined only for azinphosmethyl at 6.0 lb AI per 100 gal/acre. Methidathion dissipates on citrus also with the formation of its oxon.

In the mesoscale model, setting Tf = 0 forces the fluid velocity seen by the particles to be equal to the mass-average fluid velocity. This would be appropriate, for example, for one-way coupling wherein the particles do not disturb the fluid. In general, fluctuations in the fluid generated by the presence of other particles or microscale turbulence could be modeled by adding a phase-space diffusion term for Vf, similar to those used for macroscale turbulence (Minier Peirano, 2001). The time scale Tf would then correspond to the dissipation time scale of the microscale turbulence. 

The dissipation of metolachlor in the soil is three times slower than that of alachlor. Gerber et al. (1974) found, at 22°C and a 50% soil moisture content in sandy loam of 3.8% organic content, a 50% dissipation time of 26 days. Under identical laboratory conditions this value was 60 days for atrazine, 100 days for trifluralin and 80 days for diuron. Under field conditions, metolachlor is completely degraded in a growing season, and thus does not interfere, with crop rotation. 

Figure 10. Comparison of dissipation times for sand and silt...

The electrical conductivity of liquid hydrocarbons can be measured by a precision meter. The method is used to evaluate aviation fuels and oflier low-conductivity hydrocarbons. The generation and dissipation of electrostatic charges in liquids during handling depends on ionic species which may be characterized by electrical conductivity at rest. The dissipation time of the charges is inversely proportional to the conductivity. The measurement is done by a conductivity meter. 

The following treatment applies to homogeneous systems with constant mass. The dissipative, time-dependent effects are caused in such homogeneous systems by disturbance of the equilibrium of the internal, molecular degrees of freedom. The... 

Experience shows that objects in motion tend to slow down and stop. This is attributed to the force of friction. Ultimately, this force results from the collisions between molecules however, friction is usually manifested in the atmosphere by the turbulence resulting from large wind shears on very small spatial scales. There are common mathematical expressions for the frictional force in terms of the gradient of the wind and coefficients of viscosity, but often it suffices to refer to friction by a dissipative time scale (Rayleigh friction) or to neglect it entirely. 

Lee and Park [263] derived a more general constitutive equation for immiscible blends. which compared well with the dynamic shear data of PS/ LLD P E blends over a full range of frequency and composition. Their model included the dissipative time evolution of Qand qjj, written as functions of (i) the degree of total relaxation, (ii) the size relaxation strongly dependent on concentration, viz. a and (iii) the breakup and shape relaxation, assumed dependent on (1— )- The parameters contain adjustable constants and depend on concentration as well as on the deformation mode. The interfacial tension coefficient was assumed to be constant, independent of As before [249, 264], the constitutive equation was written in form of three functions dq /dt, and Oy. The model predicts well the dynamic moduli of... 

Armero, F. Sc Romero, I. 2001. On the formulation of high-frequency dissipative time-stepping algorithms for nonlinear dynamics. Part II Second order methods, Computer Methods in Applied Mechanics and Engineering, 190, 6783-6824. 

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