Problems, stability

One way to avoid the stabilization problem just mentioned is to propagate the log derivative matrix Y(R) [43]. This is defined by... 

The construction of an aberration-corrected TEM proved to be teclmically more demanding the point resolution of a conventional TEM today is of the order of 1-2 A. Therefore, the aim of a corrected TEM must be to increase the resolution beyond the 1 A barrier. This unplies a great number of additional stability problems, which can only be solved by the most modem technologies. The first corrected TEM prototype was presented by Flaider and coworkers [M]- Eigure BE 17.9 shows the unprovement in image quality and interpretability gained from the correction of the spherical aberration in the case of a materials science sample. 

Assuming that an equilibrium is now well established, the simulation may be restarted (not newly started) to begin with the sampling of structural and thermodynamic data. In our model case, data acquisition was performed for 3 ns (trajectory data plot not shown). For the production phase, also, the time evolution of the variables mentioned above should be monitored to detect stability problems or con-... 

In unsteady states the situation is less satisfactory, since stoichiometric constraints need no longer be satisfied by the flux vectors. Consequently differential equations representing material balances can be constructed only for binary mixtures, where the flux relations can be solved explicitly for the flux vectors. This severely limits the scope of work on the dynamical equations and their principal field of applicacion--Che theory of stability of steady states. The formulation of unsteady material and enthalpy balances is discussed in Chapter 12, which also includes a brief digression on stability problems. 

Aris (1969) pointed out that the mathematical definition of the CSTR stability problem and the catalyst particle problem cooled by the feed flow were essentially identical. 

Squeeze film dampers have long been used to combat rotor dynamic and stability problems that conventional bearings cannot solve on turbomachinery rotor systems. The use of squeeze film dampers in problem process machinery has tainted it as a treat-the-symptom solution, and many users shy away from using squeeze film dampers for this reason. Also, their limited use is explained by the difficulty in accurately predicting performance, particularly with o-ring supported dampers. 

In the 1990s this approach became more common in order to ensure sufficient compressive strength with the trend to lower bulk densities. Furthermore the proportion of SAN to polyol has been increased to about 40%. This may lead to serious stability problems and care must be taken to control the size and distribution of the particles and prevent agglomeration. Polymer polyols using polystyrene as the polymer component have recently become available (Postech-Shell) and are claimed to exhibit good stability, low viscosity and less discolouration as well as providing price advantages. 

This sulfonate is cleaved with Bu4N 1 or ammonia. The group has been reported to suffer from stability problems upon storage and use. ... 

Sulfonio. Incorporation of this group in azines may present synthetic and stability problems. In benzene derivatives, dimethyl-sulfonio is substantially better as a leaving group than is a nitro or trimethylammonio group. 

Importantly, all biological procedures are operating at a temperature of 310 Kelvin, not at 0 Kelvin as the potential energy is calculated by the force fields. The kinetic energy must also be considered. Molecules and proteins at room temperature change the conformation at least at the surface and in loop region. Molecular dynamics simulation (MD) is an approach to tackle these kinetic and stability problems. 

To avoid these stability problems, it is necessary to minimize the proportion of chains that terminate by radical-radical reaction. One way of achieving this is to conduct the polymerization in the presence of an appropriate chain transfer agent. For example, if polymerization is performed in the presence of a H-donor chain transfer agent, conditions can be chosen such that most chains terminate by hydrogen-atom transfer. Bagby et al.iA examined the thermal stability of PMMA formed with dodecanethiol. These polymer chains will then possess, more... 

For a systematic account, see A. M. Liapounov, General Problem of Stability of Motion, Charkov, 1892 W. Hahn, Theorie und Anwendungen der directen Methode von Liapounov, Springer, Berlin, 1959 L. Cesari, Asymptotic Behavior and Stability Problems, Springer, Berlin, 1959. 

Storage stability problems were encountered with all of these expls... 

In addition to the above chemical reactivity and dimensional stability problems, Minol 11 exhibits borderline initiatability at —65°F with small boosters, but initiates reliably at low temps with standard larger boosters (Ref 43)... 

In an effort to overcome the dimensional stability problem, recent work has been directed toward substituting a solid soln of K nitrate (KN) in AN (AN—KN or KN—AN form III) for the AN in Minol II. Charges containing 40% TNT,... 

Recent trends in rocket propint development and most of the recent developments in SP are for rocket and not gun proplnts, were directed toward the attainment of higher energy systems (actually higher specific impulse). Unfortunately, the use of exotic components presents grave stability problems which are yet to be overcome. Some energetic plasticizers have been developed and in some applications specific impulse has been increased substantially by substituting Be for Al. Much of this subject remains classified... 

There arc stability problems with most of the metal additives other than aluminum, although... 

N.J. Blay I. Duns tan, USNatTechlnform-Serv, AD 744871 (1970) CA 78, 6069 (1973) Compatibility and stability problems encountered in the design and development of weapon systems containing expls and solid proplnts are discussed. Safety during storage and reliability in service are emphasized. The effects of materials used near or in contact with the expls and proplnts are considered... 

Compatibility and Stability Problems Associated with Pyrotechnic Progress 1970—1973 , Ref 155 61) Yu.N. Sukhushin et al, De-... 

The well-known traditional detergent basic material soap often causes problems because of its sensitivity to water hardness, i.e., poor lime dispersibility we encounter stability problems, reduced detergent power, and inferior foaming properties in hard water. 

The state of the synthetic art in this area, in 1979, is much more satisfactory. During the past decade, several new synthetic developments have occurred such that we are closer to the point where the limitations upon synthesis of trifluoromethyl compounds are related more to stability problems in isolated cases, and are not nearly so much due to lack of widely applicable synthetic techniques. We find ourselves, for example, in a position in 1979 where the germanium compound, Ge(CF3)4, which in the past decade, was considered by many workers to be of insufficient stability to permit isolation, has been prepared by four independent methods and is known to be stable to over 100°C. Many of these new synthetic techniques have emerged from studies conducted in our laboratory at the University of Texas and previously... 

Will the feed distribute itself evenly between the tubes This is a concern when there is a large change in viscosity due to reaction. The resulting stability problem is discussed in Chapter 13. Feed distribution can also be a concern with very large tube bundles when the pressure drop down the tube is small. 

Reacting to low conversions avoids most problems. The polyethylene example uses a single, small-diameter tube. This avoids thermal runaway and mitigates the velocity elongation problem. The polystyrene reactor avoids the multitubular stability problem by using a substantially polymerized, high-viscosity feed. 

These equations can be solved numerically with a computer, without making any approximations. Naturally all the involved kinetic parameters need to be either known or estimated to give a complete solution capable of describing the transient (time dependent) kinetic behavior of the reaction. However, as with any numerical solution we should anticipate that stability problems may arise and, if we are only interested in steady state situations (i.e. time independent), the complete solution is not the route to pursue. 

With respect to CO oxidation an activity order similar to that described above for CH4 combustion has been obtained. A specific activity enhancement is observed for Lai Co 1-973 that has provided a 10% conversion of CO already at 393 K, 60 K below the temperature required by LalMnl-973. This behavior is in line with literature reports on CO oxidation over lanthanum metallates with perovskite structures [17] indicating LaCoOs as the most active system. As in the case of CH4 combustion, calcination at 1373 K of LalMnl has resulted in a significant decrease of the catalytic activity. Indeed the activity of LalMnl-1373 is similar to those of Mn-substituted hexaaluminates calcined at 1573 K. Dififerently from the results of CH4 combustion tests no stability problems have been evidenced under reaction conditions for LalMnl-1373 possibly due to the low temperature range of CO oxidation experiments. Similar apparent activation energies have been calculated for all the investigated systems, ranging from 13 to 15 Kcal/mole, i.e almost 10 Kcal/mole lower than those calculated for CH4 oxidation. 

It can easily be shown that for the upwind scheme all coefficients a appearing in Eq. (37) are positive [81]. Thus, no unphysical oscillatory solutions are foimd and stability problems with iterative equation solvers are usually avoided. The disadvantage of the upwind scheme is its low approximation order. The convective fluxes at the cell faces are only approximated up to corrections of order h, which leaves room for large errors on course grids. 

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