Indeterminate stability

The indeterminate-stability region, shown in Figure 12.6, was obtained by relating observations of sustained perturbations in water-fluidized beds to predictions of amplitude growth rates a, eqn (10.3), for a... 

Figure 12.6 Indeterminate-stability region for fluidization by ambient water.

Local inhomogeneities may be measured by means of two probes spaced a short axial distance apart in the bed and connected across a differential pressure transducer (Figure 13.3). In contrast to the previously described method, measurements obtained in this way are effectively uninfluenced by bed surface eruptions, reflecting instead the passage of inhomogeneities between the probes. This was the arrangement employed in the indeterminate stability study referred to in Chapter 12 (Gibilaro et ai, 1988). The probes in that case consisted of 3 mm diameter tubes spaced 10 mm apart. 

This group covers polymeric peroxides of indeterminate stmcture rather than polyfunctional macromolecules of known stmcture. These usually arise from autoxidation of susceptible monomers and are of very limited stability or... 

This group covers polymeric peroxides of indeterminate structure rather than polyfunctional macromolecules of known structure. These usually arise from autoxidation of susceptible monomers and are of very limited stability or explosive. Polymeric peroxide species described as hazardous include those derived from butadiene (highly explosive) isoprene, dimethylbutadiene (both strongly explosive) 1,5-p-menthadiene, 1,3-cyclohexadiene (both explode at 110°C) methyl methacrylate, vinyl acetate, styrene (all explode above 40°C) diethyl ether (extremely explosive even below 100°C ) and 1,1-diphenylethylene, cyclo-pentadiene (both explode on heating). 

Acceleration of a reaction, 418.—308. Comparison of the fundamental principle of chemical dynamics and the principle of dynamics properly so called, 418.—309. Influence of the composition of the system on the velodty of reaction, 416.—310. Every isothermal reaction is a moderated reaction, 416.— 3x1. The acceleration of a mod- erated reaction is negative, 416. 31 a. Influence of temperature on the velocity of reaction, 416.-—3x3. Example Phenomena of etherlfl-cation, 416.-3x4. Variation of the velocity due to a small change of composition and temperature, 418.-3x5. Return to isothermal reactions, 418.— 3x6. Adiabatic reactions, 418.—3x7. An adiabatic reaction may have a positive acceleration, 430.-3x8. Reactions with positive acceleration and explosive reactions, 430.-3x9. Conditions In order that an adiabatic reaction be explosive, 421.—320. Indetermination of the temperature which renders a reaction explosive, 421.—3ax. Stability and instability of limiting false equilibria, 421.—32a. Eveiy state of false equilibrium which is not limited is indifferent, 428.—... 

Linear stability analysis is carried out on dynamical equations linearized about the steady-state solution (Mj,Vj). The steady-state solution is stable if the eigenvalues of the system of linearized equations are negative, unstable if those are positive, and indeterminate otherwise. 

Indeterminate teleology results from a mixture of stochastic and deterministic events. Vernadsky (1997, p. 55) wrote that the biosphere will transform (in one way or another, sooner or later) into the noosphere". That is the way the noosphere created and the final form of the noosphere is not predetermined. The only thing which is determined is the direction of the evolution of the biosphere. The biosphere evolves in the direction of increasing stability, increasing degree of self-regulation and ultimately transfoims into the noosphere. 

To enhance our understanding of spinal loads, mathematical models are helpful. These models require the concepts of equilibrium and mechanical stability to be addressed. An early equilibrium model to predict the loading in the spine was developed by Schultz et al. (1982). These investigators used an indeterminate analysis with optimization to predict the loading in the spine in a variety of muscle groups at the L3 level of the lumbar spine. The concept of mechanical stability has been adopted in more recent mathematical models since it was realized that the osteoligamentous spine is inherently unstable (Lucas 1961 Crisco 1992). These mathematical models predict co-activation of the spinal musculature which increases compressive forces and anterior shear forces in the lumbar spine (Mirka 1993 Mar-ras 1997). 

With the higher members of the thioether series, VCl forms rather indeterminate compounds, the thermal decomposition of which indicates (for the VCl -SPr systems) some stability for the composition VCl (SPr ). ... 

Fe(II) solutions in water are stable in absence of oxygen. But if oxygen is present and no acid has been added, one moves up in the diagram into the Fe(OH)3 region. The Fe ion is weakly acidic, so that the original solution may have pH about 5. The E value of, say, 0.1 M FeS04 is indeterminate. Equation (12-7) shows that some Fe(III) must form (by reaction with water), so that the E is not — 00, as a value of zero for (Fe ) produces in the Nernst equation. If one part per 10 forms Fe(III), the E is about 0.2 V, which lies in the Fe stability area at pH 5. 

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