50 resultados para Second Order Parabolic Heat Equation


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The present paper focuses on improving chromium (III) uptake capacity of sugarcane bagasse through its chemical modification with citric acid and/or sodium hydroxide. The chemical modifications were confirmed by infrared spectroscopy, with an evident peak observed at 1730 cm-1, attributed to carbonyl groups. Equilibrium was reached after 24 h, and the kinetics followed the pseudo-second-order model. The highest chromium (III) maximum adsorption capacity (MAC) value was found when using sugarcane bagasse modified with sodium hydroxide and citric acid (58.00 mg g-1) giving a MAC value about three times greater (20.34 mg g-1) than for raw sugarcane bagasse.

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This work describes the synthesis of hydrogels of cellulose acetate (AC) crosslinked with 1,2,4,5-benzenotetracarboxylic dianhydride (PMDA). The crosslinking reaction was monitored by FTIR. Analysis of aromatic fragments from the alkaline hydrolysis of the gels by UV spectroscopy indicated that an increase in the stoichiometric ratio of dianhydride resulted in higher degrees of crosslinking. The non-porous nature of the gels was confirmed by analysis of nitrogen adsorption. Water absorption isotherms showed that as the temperature and degree of crosslinking increased, the percentage of water absorbed at equilibrium (%Seq) also increased. The hydrogels presented second order swelling kinetics.

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Adsorption of Reactive Blue 19 dye onto activated red mud was investigated. Red mud was treated with hydrogen peroxide (LVQ) and heated at both 400 ºC (LVQ400) and 500 ºC (LVQ500). These samples were characterized by pH, specific surface area, point of zero charge and mineralogical composition. Adsorption was found to be significantly dependent on solution pH, with acidic conditions proving to be the most favorable. The adsorption followed pseudo-second-order kinetics. The Langmuir isotherm was the most appropriate to describe the phenomenon of dye removal using LVQ, LVQ400 and LVQ500, with maximum adsorption capacity of 384.62, 357.14 and 454.54 mg g-1, respectively.

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This work presents the use of potentiometric measurements for kinetic studies of biosorption of Cd2+ ions from aqueous solutions on Eichhornia crassipes roots. The open circuit potential of the Cd/Cd2+ electrode of the first kind was measured during the bioadsorption process. The amount of Cd2+ ions accumulated was determined in real time. The data were fit to different models, with the pseudo-second-order model proving to be the best in describing the data. The advantages and limitations of the methodology proposed relative to the traditional method are discussed.

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The nonlinear analysis of a general mixed second order reaction was performed, aiming to explore some basic tools concerning the mathematics of nonlinear differential equations. Concepts of stability around fixed points based on linear stability analysis are introduced, together with phase plane and integral curves. The main focus is the chemical relationship between changes of limiting reagent and transcritical bifurcation, and the investigation underlying the conclusion.

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In the present study, a high-surface area activated carbon was prepared by chemical activation of lemon peel with H3PO4 as the active agent. Then, the adsorption behavior of Malachite green dye and Pb(II) ions on the produced activated carbon was studied. Batch process was employed for sorption kinetics and equilibrium studies. Experimental data were fitted to various isotherm models. According to the Langmuir model, the maximum adsorption capacities of Malachite green dye and Pb(II) ions were found to be 66.67 and 90.91 mg g-1, respectively, at room temperature. Kinetic studies showed the adsorption process followed a pseudo second-order rate model. The sorption kinetics were controlled by intra-particle diffusion. The results indicated that the produced activated carbon can be economically and effectively used as an adsorbent for the removal of Malachite green dye and Pb(II) ions from wastewaters.

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On the basis of theoretical B3LYP calculations, Yáñez and co-workers (J. Chem. Theory Comput. 2012, 8, 2293) illustrated that beryllium ions are capable of significantly modulating (changing) the electronic structures of imidazole. In this computational organic chemistry study, the interaction of this β-amino acid and five model Lewis acids (BeF1+, Be2+, AlF2(1+), AlF2+, and Al3+) were investigated. Several aspects were addressed: natural bond orbitals, including second order perturbation analysis of intra-molecular charge delocalization and the natural population analysis atomic charges; molecular geometries; selected infrared stretching frequencies (C-N, C-O, and N-H), and selected ¹H-NMR chemical shifts. The data illustrate that this interaction can weaken the H-O bond and goes beyond strengthening the intra-molecular hydrogen bond (N...H-O) to cause a spontaneous transfer of the proton to the nitrogen atom in five cases generating zwitterion structures. Many new features are observed. Most importantly, the zwitterion structures include a stabilizing hydrogen bond (N-H...O) that varies in relative strength according to the Lewis acid. These findings explain the experimental observations of α-amino acids (for example: J. Am. Chem. Soc. 2001, 123, 3577) and are the first reported fundamental electronic structure characterization of β-amino acids in zwitterion form.

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Multivariate Curve Resolution with Alternating Least Squares (MCR-ALS) is a resolution method that has been efficiently applied in many different fields, such as process analysis, environmental data and, more recently, hyperspectral image analysis. When applied to second order data (or to three-way data) arrays, recovery of the underlying basis vectors in both measurement orders (i.e. signal and concentration orders) from the data matrix can be achieved without ambiguities if the trilinear model constraint is considered during the ALS optimization. This work summarizes different protocols of MCR-ALS application, presenting a case study: near-infrared image spectroscopy.

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The adsorption of Cr(VI) in aqueous solution by magnetic particles of crosslinked chitosan-ethylenediamine-Fe(III) (MPCh-EDA-FeCL) was studied in a batch system. Fe3+ in the MPCh-EDA-FeCL permitted that adsorption of Cr(VI) occurred with maximum efficiency between pH 3 and 11. The maximum adsorption capacity at pH 7.0 was 81.04 mg g-1 at 25 ºC. The adsorption kinetic process was described by the pseudo-second-order model. Thermodynamic parameters indicated spontaneous, exothermic and chemical adsorption nature. The adsorbent was successively regenerated using a 0.1 mol L-1 NaOH solution. Results were satisfactory for treatment of wastewater from the electroplating industry.

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This paper describes a comparative study between the procedures of deconvolution and the second-order derivative of square wave voltammograms to achieve separation of the voltammetric peaks of levofloxacin (LEVO) and norfloxacin (NOR), for their simultaneous quantification in urine samples. The obtained results indicate that the use of second-derivative voltammograms coupled with carbon screen-printed electrodes is the most efficient approach for completely separating the voltammetric peaks of LEVO and NOR. In addition, this approach has produced detection limits lower than 1.0 µmol L-1 and a wide linear range for both drugs. The proposed method was successfully used to simultaneously determine LEVO and NOR in spiked human and bovine urine samples with recovery percentages close to 100% for all analyzed samples.

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The pollution and toxicity problems posed by arsenic in the environment have long been established. Hence, the removal and recovery remedies have been sought, bearing in mind the efficiency, cost effectiveness and environmental friendliness of the methods employed. The sorption kinetics and intraparticulate diffusivity of As (III) bioremediation from aqueous solution using modified and unmodified coconut fiber was investigated. The amount adsorbed increased as time increased, reaching equilibrium at about 60 minutes. The kinetic studies showed that the sorption rates could be described by both pseudo-first order and pseudo-second order process with the later showing a better fit with a value of rate constant of 1.16 x 10-4 min-1 for the three adsorbent types. The mechanism of sorption was found to be particle diffusion controlled. The diffusion and boundary layer effects were also investigation. Therefore, the results show that coconut fiber, both modified and unmodified is an efficient sorbent for the removal of As (III) from industrial effluents with particle diffusion as the predominant mechanism.

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This paper aims at clarifying the nature of Frege's system of logic, as presented in the first volume of the Grundgesetze . We undertake a rational reconstruction of this system, by distinguishing its propositional and predicate fragments. This allows us to emphasise the differences and similarities between this system and a modern system of classical second-order logic.

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The unsteady, viscous, supersonic flow over a spike-nosed body of revolution is numerically investigated by solving the Navier-Stokes equations. The time-accurate computations are performed employing an implicit algorithm based on the second-order time-accurate LU-SGS scheme with the incorporation of a subiteration procedure to maintain time accuracy. The characteristics of the flow field for a Mach number of 3.0, Reynolds number of 7.87 x 10(6)/m, and angles of attack of 5 and 10 degrees are described. Self-sustained asymmetric shock wave oscillations were observed in the numerical computations for these angles of attack. The main characteristic of the flow field, as well as its influence on drag coefficient is discussed.

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A system is said to be "instantaneous" when for a given constant input an equilibrium output is obtained after a while. In the meantime, the output is changing from its initial value towards the equilibrium one. This is the transient period of the system and transients are important features of open-respirometry systems. During transients, one cannot compute the input amplitude directly from the output. The existing models (e.g., first or second order dynamics) cannot account for many of the features observed in real open-respirometry systems, such as time lag. Also, these models do not explain what should be expected when a system is speeded up or slowed down. The purpose of the present study was to develop a mechanistic approach to the dynamics of open-respirometry systems, employing basic thermodynamic concepts. It is demonstrated that all the main relevant features of the output dynamics are due to and can be adequately explained by a distribution of apparent velocities within the set of molecules travelling along the system. The importance of the rate at which the molecules leave the sensor is explored for the first time. The study approaches the difference in calibrating a system with a continuous input and with a "unit impulse": the former truly reveals the dynamics of the system while the latter represents the first derivative (in time) of the former and, thus, cannot adequately be employed in the apparent time-constant determination. Also, we demonstrate why the apparent order of the output changes with volume or flow.

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In this paper, the topology of cortical visuotopic maps in adult primates is reviewed, with emphasis on recent studies. The observed visuotopic organisation can be summarised with reference to two basic rules. First, adjacent radial columns in the cortex represent partially overlapping regions of the visual field, irrespective of whether these columns are part of the same or different cortical areas. This primary rule is seldom, if ever, violated. Second, adjacent regions of the visual field tend to be represented in adjacent radial columns of a same area. This rule is not as rigid as the first, as many cortical areas form discontinuous, second-order representations of the visual field. A developmental model based on these physiological observations, and on comparative studies of cortical organisation, is then proposed, in order to explain how a combination of molecular specification steps and activity-driven processes can generate the variety of visuotopic organisations observed in adult cortex.