Long-range memory elementary 1D cellular automata: Dynamics and nonextensivity

We numerically study the dynamics of elementary 1D cellular automata (CA), where the binary state _σi(t)∈{0,1}${\sigma }_i(t)\in \{0,1\}$ of a cell i   does not only depend on the states in its local neighborhood at time t-1$t-1$, but also on the memory of its own past states _σi(t-2),_σi(t-3),…,_σi(t-τ),…${\sigma }_i(t-2),{\sigma }_i(t-3),\dots ,{\sigma }_i(t-\tau ),\dots$ . We assume that the weight of this memory decays proportionally to τ^-α${\tau }^{-\alpha }$, with α?0$\alpha ?0$ (the limit α→∞$\alpha \to \infty$ corresponds to the usual CA). Since the memory function is summable for α>1$\alpha >1$ and nonsummable for 0?α?1$0?\alpha ?1$, we expect pronounced changes of the dynamical behavior near α=1$\alpha =1$. This is precisely what our simulations exhibit, particularly for the time evolution of the Hamming distance H   of initially close trajectories. We typically expect the asymptotic behavior H(t)∝t^1/(1-q)$H(t)\propto t^{1/(1-q)}$, where q   is the entropic index associated with nonextensive statistical mechanics. In all cases, the function q(α)$q(\alpha )$ exhibits a sensible change at α?1$\alpha ?1$. We focus on the class II rules 61, 99 and 111. For rule 61, q=0$q=0$ for 0?α?_αc?1.3$0?\alpha ?{\alpha }_c?1.3$, and q<0$q<0$ for α>_αc$\alpha >{\alpha }_c$, whereas the opposite behavior is found for rule 111. For rule 99, the effect of the long-range memory on the spread of damage is quite dramatic. These facts point at a rich dynamics intimately linked to the interplay of local lookup rules and the range of the memory. Finite size scaling studies varying system size N   indicate that the range of the power-law regime for H(t)$H(t)$ typically diverges ∝N^z$\propto N^z$ with 0?z?1$0?z?1$.     

Detailed 1H and 13C NMR structural assignment and relative stereochemistry determination for three closely related sesquiterpene lactones

A complete analysis of (1)H and (13)C NMR spectra of the trypanocidal sesquiterpene lactone eremantholide C and two of its analogues is described. These structurally similar sesquiterpene lactones were submitted to (1)H NMR, (13)C {(1)H} NMR, gCOSY, gHSQC, gHMBC, J-resolved and DPFGSE-NOE NMR techniques. The detailed analysis of those results, correlated to some computational calculations (molecular mechanics), led to the total and unequivocal assignment of all (1)H and (13)C NMR data. The determination of all (1)H/(1)H coupling constants and all signal multiplicities, together with the elimination of previous ambiguities were also achieved.     

Distribution of deoxynivalenol in wheat,wheat flour,bran, and gluten,and variability associated with the test procedure

Analytical data obtained on deoxynivalenol (DON) concentration in naturally contaminated wheat during processing in an industrial mill were statistically analyzed, and the distribution functions of DON concentration in lots of wheat, bran, wheat flour, and gluten were estimated. The analytical method had acceptable precision (HORRAT 0.25-0.32) for each test sample. The total variance combined sampling, sample preparation, and analytical variances were 0.188, 0.033, 0.42, and 0.0014 ppm2 for wheat, 1.93; flour, 0.99; bran, 4.68; and gluten, 0.29, respectively. The distribution function of DON contamination presented an asymmetric tail for high values of concentration in wheat grains and wheat flour; in bran it seemed to be bimodal with 2 separated peaks of different concentrations; in gluten the normal distribution function gave a reasonably good fit to empirical data. The function eta(c) = -In(-Inp), where p (c) is the cumulative distribution function was linear with c in the so-called extreme-value type I distribution and could be fitted by a cubic polynomial in c in the distributions determined for all the products. This variability and distributional information contributes to the design of better sampling plans in order to reduce the total variability and to estimate errors in the evaluation of DON concentration in lots of wheat and wheat products.     

Bionanocomposites of Cassava Starch and Synthetic Clay

Starch-based biofilms containing synthetic Laponite clay and glycerol were prepared using a solvent casting technique. Electron microscopy images showed predominance of the exfoliated type of nanocomposite. Dynamic mechanical analysis revealed a larger influence of glycerol content on the polymer β relaxation and T _g than the clay content. Gas barrier properties were influenced by clay particles and plasticizer content. An increase of clay content led to lower gas permeability values. Although both glycerol and Laponite are hydrophilic, no significant changes were observed on the water sorption by starch films at different relative humidity values. Mechanical properties are kept similar after the inorganic filler incorporation.     

Chemical Equilibrium, Free Energy, and Entropy of Mixing

In this paper we describe an approach for teaching the relation between chemical equilibrium and free energy that is, according to our experience, very efficient and enlightening. This approach has a strong visual appeal and can be used at different levels, from simple presentation of the results as graphs of free energy versus reaction mixture composition, up to full derivation of formulas to find the equations of the curves.     

Toward the optimization of an e-tongue system using information visualization: a case study with perylene tetracarboxylic derivative films in the sensing units

The wide variety of molecular architectures used in sensors and biosensors and the large amount of data generated with some principles of detection have motivated the use of computational methods, such as information visualization techniques, not only to handle the data but also to optimize sensing performance. In this study, we combine projection techniques with micro-Raman scattering and atomic force microscopy (AFM) to address critical issues related to practical applications of electronic tongues (e-tongues) based on impedance spectroscopy. Experimentally, we used sensing units made with thin films of a perylene derivative (AzoPTCD acronym), coating Pt interdigitated electrodes, to detect CuCl(2) (Cu(2+)), methylene blue (MB), and saccharose in aqueous solutions, which were selected due to their distinct molecular sizes and ionic character in solution. The AzoPTCD films were deposited from monolayers to 120 nm via Langmuir-Blodgett (LB) and physical vapor deposition (PVD) techniques. Because the main aspects investigated were how the interdigitated electrodes are coated by thin films (architecture on e-tongue) and the film thickness, we decided to employ the same material for all sensing units. The capacitance data were projected into a 2D plot using the force scheme method, from which we could infer that at low analyte concentrations the electrical response of the units was determined by the film thickness. Concentrations at 10 μM or higher could be distinguished with thinner films--tens of nanometers at most--which could withstand the impedance measurements, and without causing significant changes in the Raman signal for the AzoPTCD film-forming molecules. The sensitivity to the analytes appears to be related to adsorption on the film surface, as inferred from Raman spectroscopy data using MB as analyte and from the multidimensional projections. The analysis of the results presented may serve as a new route to select materials and molecular architectures for novel sensors and biosensors, in addition to suggesting ways to unravel the mechanisms behind the high sensitivity obtained in various sensors.     

Synthesis of 1-methyl-3-oxo-7-oxabicyclo[2.2.1]hept-5-ene-2-carboxylic acid methyl ester

A simple and efficient method for the preparation of 1-methyl-3-oxo-7- oxabicyclo[2.2.1]hept-5-en-2-carboxylic acid methyl ester (1) is described. The first step is a highly regioselective Diels-Alder reaction between 2-methylfuran and methyl-3-bromo- propiolate. A remarkably difficult ketal hydrolysis reaction was effected by treatment with HCl, a simple reagent that was shown to be more efficient, in this case, than commonly used more elaborate methods.     

Phase diagram of the Hubbard model with arbitrary band filling

The finite temperature phase diagram of the Hubbard model ind=2 andd=3 is calculated for arbitrary values of the parameterU/t and chemical potential using a quantum real space renormalization group. Evidence for a ferromagnetic phase at low temperatures is presented.     

Aromaticity and Homoaromaticity in Methano[10]annulenes

Aromaticity and neutral homoaromaticity have been evaluated in methano[10]annulenes systems, 1,4-methano[10]annulene (1), 1,5-methano[10]annulene (2), and 1,6-methano[10]annulene (3). C-C bond lengths indicate that 1 presents higher bond alternation than 2 and 3. The relative energies were determined at the B3LYP/6-311+G(d,p) level, and they pointed out that 3 is the most stable isomer. Strain energies, evaluated employing homodesmotic reactions, show the same order as the relative energies. Through a decomposition of strain energies, it could be concluded that the rings absorb more tension than the bridges. The changes in aromaticity were evaluated by magnetic susceptibilities, chiM, HOMA, NICS, and resonance energies, RE. HOMA, RE, and chiM indicate that 2 and 3 are strongly, and 1 is fairly, aromatic. NICS does not provide reliable results, due to interference of ring and bridge atoms. NBO analysis presents some interactions that suggest the existence of neutral homoaromaticity. GPA indices (evaluated at the B3LYP/6-31G* level) point out that homoaromaticity plays a relevant role only in 3. Moreover, this work is the first in the current literature that studies 1,4-methano[10]annulene (1).