Strange

There are many examples in nature where a system is not in equilibrium and is evolving in time towards a thennodynamic equilibrium state. (There are also instances where non-equilibrium and time variation appear to be a persistent feature. These include chaos, oscillations and strange attractors. Such phenomena are not considered here.)... 

Anet F A L and O Leary D J 1992 The shielding tensor. Part II. Understanding its strange effects on relaxation Concepts Magn. Reson. 4 35-52... 

Similarly strange tilings happen to other materials. Above 5 GPa, CO spontaneously polymerizes the... 

Deverell C, Morgan R E and Strange J FI 1970 Studies of ohemioal exohange by nuolear magnetio relaxation in the rotating frame Mol. Phys. 18 553-9... 

Shaw R 1981 Strange attractors, chaotic behaviour, and information flow Z. Naturf. a 36 80-112... 

We shall now analyse the stmcture of a chemical strange attractor and describe why the dynamics may be classified as chaotic. 

At the th period doubling the period of the oscillation is In the limit —> co we arrive at the strange attractor where the time variation of the concentrations is no longer periodic. This is the period-doubling route to chaos. 

Several important topics have been omitted in this survey. We have described only a few of the routes by which chaos can arise in chemical systems and have made no attempt to describe in detail the features of the different kinds of chemical strange attractor seen in experiments. A wide variety of chemical patterns have been observed and while the many aspects of the mechanisms for their appearance are understood, some features like nonlinear... 

Before the limit is taken, the properties of the probability distribution appear to be strange in at least five ways. 

As shown in [16], the two corresponding flow maps, exp(rLH,) and exp(rLHj), can be represented analytically. Using the second order Strang... 

G. Strang On the construction and comparison of difference schemes. SIAM J. Numer. Anal. 5 (1968) 506-517... 

All numerical computations inevitably involve round-off errors. This error increases as the number of calculations in the solution procedure is increased. Therefore, in practice, successive mesh refinements that increase the number of finite element calculations do not necessarily lead to more accurate solutions. However, one may assume a theoretical situation where the rounding error is eliminated. In this case successive reduction in size of elements in the mesh should improve the accuracy of the finite element solution. Therefore, using a P C" element with sufficient orders of interpolation and continuity, at the limit (i.e. when element dimensions tend to zero), an exact solution should be obtaiiied. This has been shown to be true for linear elliptic problems (Strang and Fix, 1973) where an optimal convergence is achieved if the following conditions are satisfied ... 

Strang, G. and Fix, G. J., 1973. An Analysis of the Finite Element Method, Prentice Hall, Englewood Cliffs, NJ. 

Strangely enough, the universe appears to be eomprised of only two kinds of paitieles, bosons and fermions. Bosons are symmetrical under exehange, and fermions are antisymmetrieal under exehange. This bit of abstiaet physies relates to our quantum moleeular problems beeause eleetions are femiions. 

Analogously, water is extremely efficient in weakening hard Lewis add - hard Lewis base interactions. Consequently, when aiming at catalysis by hard Lewis adds, the inefficiency of the interaction between the catalyst and the substrate is a serious problem. Strangely enough, this characteristic of water is not recognised by many researchers working with hard Lewis acids in... 

Strangely enough, cyanide ion is also involved in one special reaction giving an a-hydroxy-ketone. Can you show how the adduct A of benzaldehyde and cyanide ion can give a stable carbanion ... 

This really crazy looking method is one of them. There are a lot of things about it that make it very attractive. The first is the author of the article Rajender S. Varma. You will see in the Nitropropene section of this book (and in references from many other parts of the book) that this guy has been making a lot of strangely applicable advances in catalysis, amination, and reduction of amphetamines and related compounds. It is uncanny how often Strike has come across this person s work. It is like he is the Shulgin of basic precursor and amphetamine progress. Go figure ... 

Additional notes - Nitromethane is found in high performance RC model fuel, usually as a mixture with methanol and various strange lubricants. One particular brand, found at a local hobby shop, was 55% nitromethane. 

The point was made earlier (Section 5 9) that alcohols require acid catalysis in order to undergo dehydration to alkenes Thus it may seem strange that aldol addition products can be dehydrated in base This is another example of the way in which the enhanced acidity of protons at the a carbon atom affects the reactions of carbonyl com pounds Elimination may take place in a concerted E2 fashion or it may be stepwise and proceed through an enolate ion... 

Strange reports the following information for a 2 factorial design used to investigate the yield of a chemical process. ... 

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