Contractive probability metrics and asymptotic behavior of dissipative kinetic equations

The present notes are intended to present a detailed review of the existing results in dissipative kinetic theory which make use of the contraction properties of two main families of probability metrics: optimal mass transport and Fourier-based metrics. The first part of the notes is devoted to a self-consistent summary and presentation of the properties of both probability metrics, including new aspects on the relationships between them and other metrics of wide use in probability theory. These results are of independent interest with potential use in other contexts in Partial Differential Equations and Probability Theory. The second part of the notes makes a different presentation of the asymptotic behavior of Inelastic Maxwell Models than the one presented in the literature and it shows a new example of application: particle's bath heating. We show how starting from the contraction properties in probability metrics, one can deduce the existence, uniqueness and asymptotic stability in classical spaces. A global strategy with this aim is set up and applied in two dissipative models.

Pozzolanic behavior of bamboo leaf ash: Characterization and determination of the kinetic parameters

The paper presents a characterization and study of the pozzolanic behavior between calcium hydroxide (CH) and bamboo leaf ash (BLAsh), which was obtained by calcining bamboo leaves at 600 degrees C for 2 h in a laboratory electric furnace. To evaluate the pozzolanic behavior the conductometric method was used, which is based on the measurement of the electrical conductivity in a BLAsh/CH solution with the reaction time. Later, the kinetic parameters are quantified by applying a kinetic-diffusive model. The kinetic parameters that characterize the process (in particular, the reaction rate constant and free energy of activation) were determined with relative accuracy in the fitting process of the model. The pozzolanic activity is quantitatively evaluated according to the values obtained of the kinetic parameters. Other experimental techniques, such as X-ray diffraction (XRD) and scanning electron microscopy (SEM), were also employed. The results show that this kind of ash is formed by silica with a completely amorphous nature and a high pozzolanic activity. The correlation between the values of free energy of activation (Delta G(#)) and the reaction rate constants (K) are in correspondence with the theoretical studies about the rate processes reported in the literature. (C) 2010 Elsevier Ltd. All rights reserved.

Thermal Study in Solid State of Zn(II)-Diclofenac Complex: Behavior Kinetic of the Dehydration, Transition Phase and Thermal Decomposition

The dehydration, thermal decomposition and transition phase stage of Zn(II)-diclofenac compound were studied by simultaneous TG-DTA and DSC techniques. The TG and DSC curves of this compound were obtained with the mass of sample of 2 and 5 mg. Additionally, DSC curves were carried out in opened and closed alpha-alumina pans under static and nitrogen atmosphere. The DTA and DSC curves show that this compound possesses exothermic transition phase between 170-180 degrees C, which it is irreversible (monotropic reaction) The kinetics study of this transition phase stage was evaluated by DSC under non-isothermal conditions. The obtained data were evaluated with the isoconversional method, where the values of activation energy (E(a) / kJ mol(-1)) was plotted in function of the conversion degree (alpha). The results show that due to mass sample, different activation energies were obtained From these curves a tendency can be seen where the plots maintain the same profile for closed lids and almost run parallel to each other.

Thermal study in solid state of Zn(II)-diclofenac complex: Behavior kinetic of dehydration, transition phase and thermal decomposition

The dehydration, thermal decomposition and transition phase stage of Zn(II)-diclofenac compoundwere studied by simultaneous TG-DTA and DSC techniques. The TG and DSC curves of this compoundwere obtained with the mass of sample of 2 and 5 mg. Additionally, DSC curves were carried out inopened and closed a-alumina pans under static and nitrogen atmosphere. The DTA and DSC curves showthat this compound possesses exothermic transition phase between 170-180 ºC, which it is irreversible(monotropic reaction). The kinetics study of this transition phase stage was evaluated by DSC undernon-isothermal conditions. The obtained data were evaluated with the isoconversional method, where thevalues of activation energy (Ea/kJmol-1) was plotted in function of the conversion degree (a). The resultsshow that due to mass sample, different activation energies were obtained. From these curves a tendencycan be seen where the plots maintain the same profile for closed lids and almost run parallel to each other.

Kinetic study and thermal decomposition behavior of viscoelastic memory foam

A systematic investigation of the thermal decomposition of viscoelastic memory foam (VMF) was performed using thermogravimetric analysis (TGA) to obtain the kinetic parameters, and thermogravimetric analysis coupled to Fourier Transformed Infrared Spectrometry (TGA-FTIR) and thermogravimetric analysis coupled to Mass Spectrometry (TGA-MS) to obtain detailed information of evolved products on pyrolysis and oxidative degradations. Two consecutive nth-order reactions were employed to correlate the experimental data from dynamic and isothermal runs performed at three different heating rates (5, 10 and 20 K/min) under an inert atmosphere. On the other hand, for the kinetic study of the oxidative decomposition, the data from combustion (synthetic air) and poor oxygen combustion (N2:O2 = 9:1) runs, at three heating rates and under dynamic and isothermal conditions, were correlated simultaneously. A kinetic model consisting of three consecutive reactions presented a really good correlation in all runs. TGA-FTIR analysis showed that the main gases released during the pyrolysis of VMF were determined as ether and aliphatic hydrocarbons, whereas in combustion apart from the previous gases, aldehydes, amines and CO2 have also been detected as the main gases. These results were confirmed by the TGA-MS.

Thermal behavior and decomposition kinetics of rifampicin polymorphs under isothermal and non-isothermal conditions

The thermal behavior of two polymorphic forms of rifampicin was studied by DSC and TG/DTG. The thermoanalytical results clearly showed the differences between the two crystalline forms. Polymorph I was the most thermally stable form, the DSC curve showed no fusion for this species and the thermal decomposition process occurred around 245 ºC. The DSC curve of polymorph II showed two consecutive events, an endothermic event (Tpeak = 193.9 ºC) and one exothermic event (Tpeak = 209.4 ºC), due to a melting process followed by recrystallization, which was attributed to the conversion of form II to form I. Isothermal and non-isothermal thermogravimetric methods were used to determine the kinetic parameters of the thermal decomposition process. For non-isothermal experiments, the activation energy (Ea) was derived from the plot of Log β vs 1/T, yielding values for polymorph form I and II of 154 and 123 kJ mol-1, respectively. In the isothermal experiments, the Ea was obtained from the plot of lnt vs 1/T at a constant conversion level. The mean values found for form I and form II were 137 and 144 kJ mol-1, respectively.

Fermentative behavior of Saccharomyces strains during microvinification of raspberry juice (Rubus idaeus L.)

Sixteen different strains of Saccharomyces cerevisiae and Saccharomyces bayanus were evaluated in the production of raspberry fruit wine. Raspberry juice sugar concentrations were adjusted to 16 degrees Brix with a sucrose solution, and batch fermentations were performed at 22 degrees C. Various kinetic parameters, such as the conversion factors of the substrates into ethanol (Y(p/s)), biomass (Y(x/s)), glycerol (Y(g/s)) and acetic acid (Y(ac/s)), the volumetric productivity of ethanol (Q(p)), the biomass productivity (P(x)), and the fermentation efficiency (E(f)) were calculated. Volatile compounds (alcohols, ethyl esters, acetates of higher alcohols and volatile fatty acids) were determined by gas chromatography (GC-FID). The highest values for the E(f), Y(p/s), Y(g/s), and Y(x/s) parameters were obtained when strains commonly used in the fuel ethanol industry (S. cerevisiae PE-2, BG, SA, CAT-1, and VR-1) were used to ferment raspberry juice. S. cerevisiae strain UFLA FW 15, isolated from fruit, displayed similar results. Twenty-one volatile compounds were identified in raspberry wines. The highest concentrations of total volatile compounds were found in wines produced with S. cerevisiae strains UFLA FW 15 (87,435 mu g/L), CAT-1 (80,317.01 mu g/L), VR-1 (67,573.99 mu g/L) and S. bayanus CBS 1505 (71,660.32 mu g/L). The highest concentrations of ethyl esters were 454.33 mu g/L, 440.33 mu g/L and 438 mu g/L for S. cerevisiae strains UFLA FW 15, VR-1 and BG, respectively. Similar to concentrations of ethyl esters, the highest concentrations of acetates (1927.67 mu g/L) and higher alcohols (83,996.33 mu g/L) were produced in raspberry wine from S. cerevisiae UFLA FW 15. The maximum concentration of volatile fatty acids was found in raspberry wine produced by S. cerevisiae strain VR-1. We conclude that S. cerevisiae strain UFLA FW 15 fermented raspberry juice and produced a fruit wine with low concentrations of acids and high concentrations of acetates, higher alcohols and ethyl esters. (c) 2010 Elsevier B.V. All rights reserved.

Solution Polymerization of N-vinylcaprolactam in 1,4-dioxane. Kinetic Dependence on Temperature, Monomer, and Initiator Concentrations

The kinetics of the solution free radical polymerization of N-vinylcaprolactam, in 1,4-dioxane and under various polymerization conditions was studied. Azobisisobutyronitrile and 3-mercaptopropionic acid were used as initiator and as chain transfer agent (CTA), respectively. The influence of monomer and initiator concentrations and polymerization temperature on the rate of polymerizations (R(p)) was investigated. In general, high conversions were obtained. The order with respect to initiator was consistent with the classical kinetic rate equation, while the order with respect to the monomer was greater than unity. The overall activation energy of 53.6 kJ mol(-1) was obtained in the temperature range 60-80 degrees C. The decreasing of the absolute molecular weights when increasing the CIA concentration was confirmed by GPC/SEC/LALS analyses. It was confirmed by UV-visible analyses the effect of molecular weights on the lower critical solution temperature of the polymers. It was also verified that the addition of the CTA influenced the kinetic of the polymerizations. (C) 2010 Wiley Periodicals, Inc. J Appl Polym Sci 118: 229-240, 2010

Loss of Ergodicity in the Transition from Annealed to Quenched Disorder in a Finite Kinetic Ising Model

We consider a kinetic Ising model which represents a generic agent-based model for various types of socio-economic systems. We study the case of a finite (and not necessarily large) number of agents N as well as the asymptotic case when the number of agents tends to infinity. The main ingredient are individual decision thresholds which are either fixed over time (corresponding to quenched disorder in the Ising model, leading to nonlinear deterministic dynamics which are generically non-ergodic) or which may change randomly over time (corresponding to annealed disorder, leading to ergodic dynamics). We address the question how increasing the strength of annealed disorder relative to quenched disorder drives the system from non-ergodic behavior to ergodicity. Mathematically rigorous analysis provides an explicit and detailed picture for arbitrary realizations of the quenched initial thresholds, revealing an intriguing ""jumpy"" transition from non-ergodicity with many absorbing sets to ergodicity. For large N we find a critical strength of annealed randomness, above which the system becomes asymptotically ergodic. Our theoretical results suggests how to drive a system from an undesired socio-economic equilibrium (e. g. high level of corruption) to a desirable one (low level of corruption).

Extracting kinetic information from literature with KineticRE

To better understand the dynamic behavior of metabolic networks in a wide variety of conditions, the field of Systems Biology has increased its interest in the use of kinetic models. The different databases, available these days, do not contain enough data regarding this topic. Given that a significant part of the relevant information for the development of such models is still wide spread in the literature, it becomes essential to develop specific and powerful text mining tools to collect these data. In this context, this work has as main objective the development of a text mining tool to extract, from scientific literature, kinetic parameters, their respective values and their relations with enzymes and metabolites. The approach proposed integrates the development of a novel plug-in over the text mining framework @Note2. In the end, the pipeline developed was validated with a case study on Kluyveromyces lactis, spanning the analysis and results of 20 full text documents.

A well-posedness theory in measures for some kinetic models of collective motion

We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the behavior of large groups of animals, such as flocks of birds, swarms, or schools of fish. Our aim is to give a well-posedness theory for general models which possibly include a variety of effects: an interaction through a potential, such as a short-range repulsion and long-range attraction; a velocity-averaging effect where individuals try to adapt their own velocity to that of other individuals in their surroundings; and self-propulsion effects, which take into account effects on one individual that are independent of the others. We develop our theory in a space of measures, using mass transportation distances. As consequences of our theory we show also the convergence of particle systems to their corresponding kinetic equations, and the local-in-time convergence to the hydrodynamic limit for one of the models.

Asymptotic flocking dynamics for the kinetic Cucker-Smale model

In this paper, we analyse the asymptotic behavior of solutions of the continuous kinetic version of flocking by Cucker and Smale [16], which describes the collective behavior of an ensemble of organisms, animals or devices. This kinetic version introduced in [24] is here obtained starting from a Boltzmann-type equation. The large-time behavior of the distribution in phase space is subsequently studied by means of particle approximations and a stability property in distances between measures. A continuous analogue of the theorems of [16] is shown to hold for the solutions on the kinetic model. More precisely, the solutions will concentrate exponentially fast their velocity to their mean while in space they will converge towards a translational flocking solution.

Arrested kinetic Li isotope fractionation at the margin of the llimaussaq complex, South Greenland: Evidence for open-system processes during final cooling of peralkaline igneous rocks

Li contents [Li] and isotopic composition (delta Li-7) of mafic minerals (mainly amphibole and clinopyroxene) from the alkaline to peralkaline Ilimaussaq plutonic complex, South Greenland, track the behavior of Li and its isotopes during magmatic differentiation and final cooling of an alkaline igneous system. [Li] in amphibole increase from < 10 ppm in Caamphiboles of the least differentiated unit to >3000 ppm in Na-amphiboles of the highly evolved units. In contrast, [Li] in clinopyroxene are comparatively low (<85 ppm) and do not vary systematically with differentiation. The distribution of Li between amphibole and pyroxene is controlled by the major element composition of the minerals (Ca-rich and Na-rich, respectively) and changes in oxygen fugacity (due to Li incorporation via coupled substitution with ferric iron) during magmatic differentiation. delta(7) Li values of all minerals span a wide range from + 17 to - 8 parts per thousand, with the different intrusive units of the complex having distinct Li isotopic systematics. Amphiboles, which dominate the Li budget of whole-rocks from the inner part of the complex, have constant delta Li-7 of + 1.8 +/- 2.2 parts per thousand (2 sigma, n = 15). This value reflects a homogeneous melt reservoir and is consistent with their mantle derivation, in agreement with published O and Nd isotopic data. Clinopyroxenes of these samples are consistently lighter, with Delta Li-7(amph-cpx). as large as 8 parts per thousand and are thus not in Li isotope equilibrium. These low values probably reflect late-stage diffusion of Li into clinopyroxene during final cooling of the rocks, thus enriching the clinopyroxene in 6 Li. At the margin of the complex delta(7) Li in the syenites increases systematically, from +2 to high values of + 14 parts per thousand. This, coupled with the observed Li isotope systematics of the granitic country rocks, reflects post-magmatic open-system processes occurring during final cooling of the intrusion. Although the shape and magnitude of the Li isotope and elemental profiles through syenite and country rock are suggestive of diffusion-driven isotope fractionation, they cannot be modeled by one-dimensional diffusive transport and point to circulation of a fluid having a high 67 Li value (possibly seawater) along the chilled contact. In all, this study demonstrates that Li isotopes can be used to identify complex fluid- and diffusion-governed processes taking place during the final cooling of such rocks. (c) 2007 Elsevier B.V All rights reserved.

Solid phase crystallization under continuous heating: kinetic and microstructure scaling laws

The kinetics and microstructure of solid-phase crystallization under continuous heating conditions and random distribution of nuclei are analyzed. An Arrhenius temperature dependence is assumed for both nucleation and growth rates. Under these circumstances, the system has a scaling law such that the behavior of the scaled system is independent of the heating rate. Hence, the kinetics and microstructure obtained at different heating rates differ only in time and length scaling factors. Concerning the kinetics, it is shown that the extended volume evolves with time according to αex = [exp(κCt′)]m+1, where t′ is the dimensionless time. This scaled solution not only represents a significant simplification of the system description, it also provides new tools for its analysis. For instance, it has been possible to find an analytical dependence of the final average grain size on kinetic parameters. Concerning the microstructure, the existence of a length scaling factor has allowed the grain-size distribution to be numerically calculated as a function of the kinetic parameters

Monte Carlo study of a kinetic lattice model with random diffusion of disorder

We report Monte Carlo results for a nonequilibrium Ising-like model in two and three dimensions. Nearest-neighbor interactions J change sign randomly with time due to competing kinetics. There follows a fast and random, i.e., spin-configuration-independent diffusion of Js, of the kind that takes place in dilute metallic alloys when magnetic ions diffuse. The system exhibits steady states of the ferromagnetic (antiferromagnetic) type when the probability p that J>0 is large (small) enough. No counterpart to the freezing phenomena found in quenched spin glasses occurs. We compare our results with existing mean-field and exact ones, and obtain information about critical behavior.