Conservation Laws in Cellular Automata

Conservation laws in physics are numerical invariants of the dynamics of a system. In cellular automata (CA), a similar concept has already been defined and studied. To each local pattern of cell states a real value is associated, interpreted as the “energy” (or “mass”, or . . . ) of that pattern.The overall “energy” of a configuration is simply the sum of the energy of the local patterns appearing on different positions in the configuration. We have a conservation law for that energy, if the total energy of each configuration remains constant during the evolution of the CA. For a given conservation law, it is desirable to find microscopic explanations for the dynamics of the conserved energy in terms of flows of energy from one region toward another. Often, it happens that the energy values are from non-negative integers, and are interpreted as the number of “particles” distributed on a configuration. In such cases, it is conjectured that one can always provide a microscopic explanation for the conservation laws by prescribing rules for the local movement of the particles. The onedimensional case has already been solved by Fuk´s and Pivato. We extend this to two-dimensional cellular automata with radius-0,5 neighborhood on the square lattice. We then consider conservation laws in which the energy values are chosen from a commutative group or semigroup. In this case, the class of all conservation laws for a CA form a partially ordered hierarchy. We study the structure of this hierarchy and prove some basic facts about it. Although the local properties of this hierarchy (at least in the group-valued case) are tractable, its global properties turn out to be algorithmically inaccessible. In particular, we prove that it is undecidable whether this hierarchy is trivial (i.e., if the CA has any non-trivial conservation law at all) or unbounded. We point out some interconnections between the structure of this hierarchy and the dynamical properties of the CA. We show that positively expansive CA do not have non-trivial conservation laws. We also investigate a curious relationship between conservation laws and invariant Gibbs measures in reversible and surjective CA. Gibbs measures are known to coincide with the equilibrium states of a lattice system defined in terms of a Hamiltonian. For reversible cellular automata, each conserved quantity may play the role of a Hamiltonian, and provides a Gibbs measure (or a set of Gibbs measures, in case of phase multiplicity) that is invariant. Conversely, every invariant Gibbs measure provides a conservation law for the CA. For surjective CA, the former statement also follows (in a slightly different form) from the variational characterization of the Gibbs measures. For one-dimensional surjective CA, we show that each invariant Gibbs measure provides a conservation law. We also prove that surjective CA almost surely preserve the average information content per cell with respect to any probability measure.

Análises seqüenciais de agrupamentos aplicadas ao estudo de partículas atmosféricas

The present paper has as objective to apply a sequential Cluster Analysis to the atmospheric particles: Hierarchical Cluster Analysis followed by Nonhierarchical Cluster Analysis. The hierarchical cluster analysis results were used as start point for the nonhierarchical cluster analysis as an agglomerative technique. These particles were taken from two areas of the metropolitan region of Porto Alegre, Charqueadas and Sapucaia do Sul., from may /97 to may/98, using a High Volume Sampler (Hi-Vol). Around 10,000 particles were analysed by Scanning Electron Microscope with Energy-Dispersive X-Ray microanalysis (SEM-EDS). The Hierarchical Cluster Analysis allowed the identification of five groups of particles, whose amounts were differentiated according to the summer and the winter campaigns. The abundance of each type of particles inside each group according to the different sections was verified by the Nonhierarchical Cluster Analysis, resulting in information about the emissions sources. The groups of particles of Si/Al and Si and of Fe/Zn and Fe for Charqueadas were more significant in section 2 and 3 (NW and W wind directions) and in section 1 (SE wind direction), evidencing the influence of the coal power plant and steel industry, respectively located in these quadrants. In Sapucaia do Sul the data were more heterogeneous, causing a certain difficulty to identify the source as anthropogenic. Nevertheless the group of particles containing Fe was found in sectors of NW/W wind directions which shows the influence of the steel plant.

Aplicação da CLAE para determinação do ácido 10-Hidróxi-2-decenóico (10-HDA) em geléia real pura e adicionada a mel brasileiro

The aim of this paper was to determine the 10-HDA in pure royal jelly and products containing royal jelly, using HPLC methodology. 10-HDA is the natural indicator of the presence of royal jelly in products and also gives the authenticity of pure royal jelly. The chromatographic conditions used were: isocratic system, C18-H column, auto sampler, diode array UV-VIS detector (225 nm), mobile phase with methanol/water (45:55), pH= 2.5 and a-naphtol as internal standard. The results obtained using laboratory samples for pure royal jelly were 2.37%, varying from 0.15% for honey with 10% of royal jelly to 2.10% for honey with 90% of royal jelly respectivelly. For commercial products, the 10-HDA content varied from no detectable to 0.026%. The recovery test presented a minumum of 100.44% The detection limit was 45.92 ng/mL and the quantification limit was 76.53 ng/mL.

Review of the synthesis of layered double hydroxides: a thermodynamic approach

The synthesis of layered double hydroxides (LDHs) by hydrothermal-LDH reconstruction and coprecipitation methods is reviewed using a thermodynamic approach. A mixture model was used for the estimation of the thermodynamics of formation of LDHs. The synthesis and solubility of LDHs are discussed in terms of standard molar Gibbs free energy change of reaction. Data for numerous divalent and trivalent metals as well as for some monovalent and tetravalent metals that may be part of the LDH structure have been compiled. Good agreement is found between theoretical and experimental data. Diagrams and tables for the prediction of possible new LDH materials are provided.

Comparação de duas metodologias de amostragem atmosférica com ferramenta estatística não paramétrica

In atmospheric aerosol sampling, it is inevitable that the air that carries particles is in motion, as a result of both externally driven wind and the sucking action of the sampler itself. High or low air flow sampling speeds may lead to significant particle size bias. The objective of this work is the validation of measurements enabling the comparison of species concentration from both air flow sampling techniques. The presence of several outliers and increase of residuals with concentration becomes obvious, requiring non-parametric methods, recommended for the handling of data which may not be normally distributed. This way, conversion factors are obtained for each of the various species under study using Kendall regression.

Construção de amostrador passivo de baixo custo para determinação de dióxido de nitrogênio

A new passive sampling system for monitoring NO2 in air has been developed to measure gas concentrations in indoor and outdoor air. The sampler is inexpensive, and easy to construct and operate. Nitrogen dioxide forms a derivative after reaction with a filter coated with triethanolamine and ethyleneglycol. The nitrogen dioxide derivative is extracted from the filter, and the concentration is determined by colorimetry. To test the sampler for measuring ambient level nitrogen dioxide, measurements were carried out inside homes and in a range of workplace environments.

O emprego de quitosana quimicamente modificada com anidrido succínico na adsorção de azul de metileno

The adsorption capacity of alpha-chitosan and its modified form with succinic anhydride was compared with the traditional adsorbent active carbon by using the dye methylene blue, employed in the textile industry. The isotherms for both biopolymers were classified as SSA systems in the Giles model, more specifically in L class and subgroup 3. The dye concentration in the supernatant in the adsorption assay was determined through electronic spectroscopy. By calorimetric titration thermodynamic data of the interaction between methyene blue and the chemically modified chitosan at the solid/liquid interface were obtained. The enthalpy of the dye/chitosan interaction gave 2.47 ± 0.02 kJ mol-1 with an equilibrium constant of 7350 ± 10 and for the carbon/dye interaction this constant gave 5951 ± 8. The spontaneity of these adsorptions are reflected by the free Gibbs energies of -22.1 ± 0.4 and -21.5 ± 0.2 kJ mol-1, respectively, found for these systems. This new adsorbent derived from a natural polysaccharide is as efficient as activated carbon. However 97% of the bonded dye can be eluted by sodium chloride solution, while this same operation elutes only 42% from carbon. Chitosan is efficient in dye removal with the additional advantage of being cheap, non-toxic, biocompatible and biodegradable.

Diagramas de Ellingham e de Van't Hoff: algumas considerações

The main subject of this article is to show the parallelism betwen the Ellingham and Van't Hoff diagrams. The first one is a graphic representation of the changes in the standard Gibbs free energy (deltarGtheta) as a function of T and was introduced by Ellingham in 1944, in order to study metallurgic processes involving oxides and sulphides. On the other hand, the Van't Hoff diagram is a representation of the function ln K versus (1/T). The equivalence between both diagrams is easily demonstrated, making simple mathematical manipulations. In order to show the parallelism between both diagrams, they are presented briefly and two examples are discussed. The comparison of the both diagrams surely will be helpful to students and teachers in their learning and teaching activities, and will certainly enrich important aspects of chemical thermodynamics.

Desviaciones al modelo logarítmico-lineal en la solubilidad de ibuprofén y naproxén en mezclas cosolventes propilenoglicol-agua

The deviations observed in the solubility of ibuprofen (IBP) and naproxen (NAP) in propylene glycol (PG) + water (W) cosolvent mixtures with respect to the logarithmic-linear model proposed by Yalkowsky have been analyzed at 25.00 ± 0.05 ºC. Negative deviations were obtained in all cosolvent compositions for both drugs; they were greater for IBP. Another treatment, based on Gibbs free energy relationships, was also employed showing an apparent hydrophobicity chameleonic effect, because at low PG proportions NAP is more hydrophobic, whereas at high PG proportions IBP is more hydrophobic. The results are discussed in terms of solute-solvent and solvent-solvent interactions.

Adsorción física sobre sólidos: aspectos termodinámicos

A thermodynamic formalism based on the Gibbs Dividing Surface (GDS) for the description of a solid-fluid interface is presented, so that the adsorption layer is understand as a phase and the adsorption process as the transference of components between a 3-dimensional phase and a 2-dimensional one. Using a state equation derived from the Henry's Law, we shall show how the Langmuir isotherm is deduced from de Gibbs isotherm. The GDS is useful also for understanding the release of heat by a system as the adsorption occurs.

Desenvolvimento e aplicação de sistema passivo de coleta de poluentes atmosféricos para monitoramento de Cd, Cr, Pb, Cu, Fe, Mn, Zn e particulados totais

The objective of this study was to assess a new monitoring technique of particulate and trace metals in the atmosphere via the use of a passive sampler of air pollutants in the city of Goiânia. The average particulate weight and average concentrations of metals Fe, Cr, Zn, Pb, Cu, Mn, and Cd were 0.1104 g and 257.5; 23.4; 17.8; 6.7; 1.9; 0.8; 0.2 μg/m²/day, respectively. Higher Pb and Cr concentrations were obtained in areas with intense traffic. This study revealed that it is possible to monitor trace metals with passive sampling, developed at a low cost and operational facility.

Desenvolvimento e avaliação de um porta-amostra de baixo custo para caracterização elétrica de materiais cerâmicos

Conventional sample holder cells used to the electric characterization of ceramics at high temperature consists of an alumina tube and platinum wires and plates using a complex design. The high cost materials used in the conventional sampler holder cell were replaced by stainless steel and conventional ceramics. The sample holder was validated by characterizing yttria-stabilized-zirconia in a temperature range of 25 to 700 ºC. The results do not present variations, discontinuity or unusual noise in the electric signals. Several samples were characterized without maintenance, which demonstrates that the sample holder is electric and mechanic adequate to be used to electrical characterization of ceramics up to 700 ºC.

Thermodynamic study of the solubility of sodium naproxen in some ethanol + water mixtures

By using the van't Hoff and Gibbs equations the apparent thermodynamic functions Gibbs energy, enthalpy, and entropy of solution for sodium naproxen in ethanol + water cosolvent mixtures, were evaluated from solubility data determined at temperatures from (278.15 to 308.15) K. The drug solubility was greatest in neat water and lowest in neat ethanol at all the temperatures studied. By means of non-linear enthalpy-entropy compensation analysis, it follows that the dissolution process of this drug in ethanol-rich mixtures is entropy-driven, whereas, in water-rich mixtures the process is enthalpy-driven.

Remoção dos corantes azul brilhante, amarelo crepúsculo e amarelo tartrazina de soluções aquosas utilizando carvão ativado, terra ativada, terra diatomácea, quitina e quitosana: estudos de equilíbrio e termodinâmica

This work compared activated carbon, activated earth, diatomaceous earth, chitin and chitosan to removal acid blue 9, food yellow 3 and FD&C yellow nº 5 dyes from aqueous solutions with different pH values (2-10). In the best process condition for each dye, equilibrium studies were carried out at different temperatures (from 298 to 328 K) and Langmuir, Freundlich, Redlich-Peterson, Temkin and Dubinin-Radushkevich models were fitted with experimental data. In addition, entropy change, Gibbs free energy change and enthalpy change were obtained in order to verify the thermodynamic adsorption behavior.

Thermodynamic study of the solubility of triclocarban in ethanol + propylene glycol mixtures

By using the van't Hoff and Gibbs equations the apparent thermodynamic functions Gibbs energy, enthalpy, and entropy of solution for triclocarban in ethanol + propylene glycol mixtures were evaluated from solubility data determined at temperatures from (293.15 to 313.15) K. The drug solubility was greatest in the mixture with 0.60 in mass fraction of ethanol and lowest in neat propylene glycol at almost all the temperatures studied. Non-linear enthalpy-entropy compensation is found indicating apparently different mechanisms of the solution process according to the mixtures composition.