Double behavior

A natural question is how does the local period-doubling behavior cf the logistic map translate to its CML-version incarnation Without loss of generality, let us consider the Laplacian-coupled version of the logistic-driven CML ... 

On the other hand, the complex phenomenon of gas-liquid bubbling has been recently analyzed via experimental velocity prohles measured from hot-hlm anemometry [45] or light rehection [10], [29], [48]. Several oscillatory patterns (periodic and nonperiodic oscillations, including chaos and period doubling behavior) were reported by Tritton and Edgeh in [45]. The authors... 

Fig. 35. The CO/O, reaction on Pdf 110). Slight variation of the conditions caused a transition from harmonic to period-doubling behavior. (From Ref. 147.)...

J. Masere, F. Stewart, T. Meehan, and J. Pojman, Period-doubling behavior in frontal polymerization of multifunctional acrylates. Chaos, 9 (1999), pp. 315-322. 

It should be noticed however that the period-doubling behavior is only observed for elastomer substrates without pre-strain. When the compression is achieved through a pre-stretching of the elastomer slab prior deposition of the thin sheet, the nonlinear elasticity of the PDMS mbber comes into play and other morphology characterized by periodic cusps is observed [21]. 

By contrary to someone expecting the first order of Koopmans theorem being more systematic, only in this order 2C result is practically doubled respecting SLR counterpart such double behavior becomes convergent when superior Koopmans orders of valence orbitals are considered either in simpler or complex forms of 2C and SLR, respectively. 

Asphalt binder is a thermoplastic material that behaves as an elastic solid at low service temperatures or during rapid loading and as a viscous liquid at high temperatures or slow loading. This double behavior creates a need to improve the performance of the asphalt binder to minimize stress cracking, which occurs at low temperatures, and permanent deformation, which occurs at high service temperatures addition of crumb rubber to sulfur asphalt enhanced the temperature resistance of the binder. Utilization of waste crumb rubber and sulfur in asphalt modification proved to enhance asphalt pavement [129]. 

Relaxations in the double layers between two interacting particles can retard aggregation rates and cause them to be independent of particle size [101-103]. Discrepancies between theoretical predictions and experimental observations of heterocoagulation between polymer latices, silica particles, and ceria particles [104] have promptetl Mati-jevic and co-workers to propose that the charge on these particles may not be uniformly distributed over the surface [105, 106]. Similar behavior has been seen in the heterocoagulation of cationic and anionic polymer latices [107]. 

Stem layer adsorption was involved in the discussion of the effect of ions on f potentials (Section V-6), electrocapillary behavior (Section V-7), and electrode potentials (Section V-8) and enters into the effect of electrolytes on charged monolayers (Section XV-6). More speciflcally, this type of behavior occurs in the adsorption of electrolytes by ionic crystals. A large amount of wotk of this type has been done, partly because of the importance of such effects on the purity of precipitates of analytical interest and partly because of the role of such adsorption in coagulation and other colloid chemical processes. Early studies include those by Weiser [157], by Paneth, Hahn, and Fajans [158], and by Kolthoff and co-workers [159], A recent calorimetric study of proton adsorption by Lyklema and co-workers [160] supports a new thermodynamic analysis of double-layer formation. A recent example of this is found in a study... 

Not all the properties of alkenes are revealed by focusing exclusively on the func tional group behavior of the double bond A double bond can affect the proper ties of a second functional unit to which it is directly attached It can be a sub stituent for example on a positively charged carbon in an allylic carbocation, or on a carbon that bears an unpaired electron in an allylic free radical, or it can be a substituent on a second double bond in a conjugated diene... 

A common example of the Peieds distortion is the linear polyene, polyacetylene. A simple molecular orbital approach would predict S hybddization at each carbon and metallic behavior as a result of a half-filled delocalized TT-orbital along the chain. Uniform bond lengths would be expected (as in benzene) as a result of the delocalization. However, a Peieds distortion leads to alternating single and double bonds (Fig. 3) and the opening up of a band gap. As a result, undoped polyacetylene is a semiconductor. 

Radicals are employed widely in the polymer industry, where their chain-propagating behavior transforms vinyl monomers into polymers and copolymers. The mechanism of addition polymeri2ation involves all three types of reactions discussed above, ie, initiation, propagation by addition to carbon—carbon double bonds, and termination ... 

Acetyl-i-carnitine (4) is marketed in Italy for dementia as of this writing it is also in Phase III clinical trials in the United States and Europe. In a double-blind, placebo-controUed clinical trial over a one-year period involving 130 patients with clinically diagnosed AD, a slower rate of deterioration in 13 of the 14 outcome measures was observed in the dmg-treated group (28). Earfler smaller scale pilot studies in demented patients had also shown some improvement of various behavioral and cognitive functions (29). 

Under favorable conditions, low molecular weight organics may polymerize on surface of adsorbent (dialkenes, 1-alkenes, alkynes, conjugated double-bond systems, and epoxides are especially susceptible to this behavior). 

The properties and behavior of double phosphates such as — Y)3 (216), sodium—zirconium phosphate—siUcates (217), and... 

Electrically, the electrical double layer may be viewed as a capacitor with the charges separated by a distance of the order of molecular dimensions. The measured capacitance ranges from about two to several hundred microfarads per square centimeter depending on the stmcture of the double layer, the potential, and the composition of the electrode materials. Figure 4 illustrates the behavior of the capacitance and potential for a mercury electrode where the double layer capacitance is about 16 p.F/cm when cations occupy the OHP and about 38 p.F/cm when anions occupy the IHP. The behavior of other electrode materials is judged to be similar. 

Fig. 6. Discharge behavior of a battery where is the open circuit voltage (a) current—potential or power curve showing M activation, ohmic, and M concentration polarization regions where the double headed arrow represents polarization loss and (b) voltage—time profile.

Fig. 7. (a) Simple battery circuit diagram where represents the capacitance of the electrical double layer at the electrode—solution interface, W depicts the Warburg impedance for diffusion processes, and R is internal resistance and (b) the corresponding Argand diagram of the behavior of impedance with frequency, for an idealized battery system, where the characteristic behavior of A, ohmic B, activation and C, diffusion or concentration (Warburg... 

Miscellaneous Compounds. Among simple ionic salts cerium(III) acetate [17829-82-2] as commercially prepared, has lV2 H2O, has a moderate (- 100 g/L) aqueous solubiUty that decreases with increased temperature, and is an attractive precursor to the oxide. Cerous sulfate [13454-94-9] can be made in a wide range of hydrated forms and has solubiUty behavior comparable to that of the acetate. Many double sulfates having alkaU metal and/or ammonium cations, and varying degrees of aqueous solubiUty are known. Cerium(III) phosphate [13454-71 -2] being equivalent to mona2ite, is very stable. 

In Table 2, the computers ia the MOPAC benchmark are grouped as they are to reflect differing floatiag-poiat machine represeatatioas. AH these computers use 64 bits to represeat a double precisioa floatiag-poiat aumber. Differeat behavior arises from the slightly differeat ways ia which the bits are allocated. 

This equation is a reasonable model of electrokinetic behavior, although for theoretical studies many possible corrections must be considered. Correction must always be made for electrokinetic effects at the wall of the cell, since this wall also carries a double layer. There are corrections for the motion of solvated ions through the medium, surface and bulk conductivity of the particles, nonspherical shape of the particles, etc. The parameter zeta, determined by measuring the particle velocity and substituting in the above equation, is a measure of the potential at the so-called surface of shear, ie, the surface dividing the moving particle and its adherent layer of solution from the stationary bulk of the solution. This surface of shear ties at an indeterrninate distance from the tme particle surface. Thus, the measured zeta potential can be related only semiquantitatively to the curves of Figure 3. 

---