915 resultados para Second Order Parabolic Heat Equation
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This study is focused on the synthesis and application of glycerol-based carbon materials (GBCM200, GBCM300 and GBCM350) as adsorbents for the removal of the antibiotic compounds flumequine and tetracycline from aqueous solution. The synthesis enrolled the partial carbonization of a glycerol-sulfuric acid mixture, followed by thermal treatments under inert conditions and further thermal activation under oxidative atmosphere. The textural properties were investigated through N2 adsorption–desorption isotherms, and the presence of oxygenated groups was discussed based on zeta potential and Fourier transform infrared (FTIR) data. The kinetic data revealed that the equilibrium time for flumequine adsorption was achieved within 96 h, while for tetracycline, it was reached after 120 h. Several kinetic models, i.e., pseudo-first order, pseudo-second order, fractional power, Elovich and Weber–Morris models, were applied, finding that the pseudo-second order model was the most suitable for the fitting of the experimental kinetic data. The estimated surface diffusion coefficient values, Ds, of 3.88 and 5.06 10 14 m2 s 1, suggests that the pore diffusion is the rate limiting step of the adsorption process. Finally, as it is based on SSE values, Sips model well-fitted the experimental FLQ and TCN adsorption isotherm data, followed by Freundlich equation. The maximum adsorption capacities for flumequine and tetracycline was of 41.5 and 58.2 mg g 1 by GBCM350 activated carbon.
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Sediment cores collected from the Eastern Equatorial Pacific Ocean display a clear positive second-order relationship between wet bulk density (WBD) and carbonate content. This has long interested the paleoceanography community because detailed Gamma Ray Attenuation Porosity Evaluator (GRAPE) measurements, which approximate WBD, might be used to determine records of carbonate content at very high temporal resolution. Although general causes for the relationship are known, they have not been presented and discussed systematically on the basis of first principles. In this study, we measure the mass and carbonate content of 50 sediment samples with known WBD from Site U1338, before and after rinsing with de-ionized water; we also determine the mass related proportion of coarse (> 63 µm) material. Samples exhibit clear relationships between WBD, carbonate content, mass loss upon rinsing, and grain size. We develop a series of mathematical expressions to describe these relationships, and solve them numerically. As noted by previous workers, the second-order relationship between WBD and carbonate content results from the mixing of biogenic carbonate and biogenic silica, which have different grain densities and different porosities. However, at high carbonate content, a wide range in WBD occurs because samples with greater amounts of coarse carbonate have higher porosity. Moreover compaction impacts carbonate particles more than biogenic silica particles. As such, a single two-component equation cannot be used to determine carbonate content accurately across depth intervals where both the porosity and type of carbonate vary. Instead, the WBD-carbonate relationship is described by an infinite series of curves, each which represents mixing of multiple sediment components with different densities and porosities. Dissolved ions also precipitate from pore space during sample drying, which adds mass to the sediment. Without rinsing samples, simple empirical relationships between WBD and carbonate content are further skewed by salt dilution.
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Adsorption of a basic dye, methylene blue, from aqueous solutions onto as-received activated carbons and acid-treated carbons was investigated. The physical and surface chemical properties of the activated carbons were characterized using BET-N-2 adsorption, X-ray photoelectron spectroscopy (XPS), and mass titration. It was found that acid treatment had little effect on carbon textural characteristics but significantly changed the surface chemical properties, resulting in an adverse effect on dye adsorption. The physical properties of activated carbon, such as surface area and pore volume, have little effect on dye adsorption, while the pore size distribution and the surface chemical characteristics play important roles in dye adsorption. The pH value of the solution also influences the adsorption capacity significantly. For methylene blue, a higher pH of solution favors the adsorption capacity. The kinetic adsorption of methylene blue on all carbons follows a pseudo-second-order equation. (c) 2004 Elsevier Inc. All rights reserved.
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An existing capillarity correction for free surface groundwater flow as modelled by the Boussinesq equation is re-investigated. Existing solutions, based on the shallow flow expansion, have considered only the zeroth-order approximation. Here, a second-order capillarity correction to tide-induced watertable fluctuations in a coastal aquifer adjacent to a sloping beach is derived. A new definition of the capillarity correction is proposed for small capillary fringes, and a simplified solution is derived. Comparisons of the two models show that the simplified model can be used in most cases. The significant effects of higher-order capillarity corrections on tidal fluctuations in a sloping beach are also demonstrated. (c) 2004 Elsevier Ltd. All rights reserved.
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We present phase-space techniques for the modelling of spontaneous emission in two-level bosonic atoms. The positive-P representation is shown to give a full and complete description within the limits of our model. The Wigner representation, even when truncated at second order, is shown to need a doubling of the phase-space to allow for a positive-definite diffusion matrix in the appropriate Fokker-Planck equation and still fails to agree with the full quantum results of the positive-P representation. We show that quantum statistics and correlations between the ground and excited states affect the dynamics of the emission process, so that it is in general non-exponential. (c) 2005 Elsevier B.V. All rights reserved.
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To investigate the control mechanisms used in adapting to position-dependent forces, subjects performed 150 horizontal reaching movements over 25 cm in the presence of a position-dependent parabolic force field (PF). The PF acted only over the first 10 cm of the movement. On every fifth trial, a virtual mechanical guide (double wall) constrained subjects to move along a straight-line path between the start and target positions. Its purpose was to register lateral force to track formation of an internal model of the force field, and to look for evidence of possible alternative adaptive strategies. The force field produced a force to the right, which initially caused subjects to deviate in that direction. They reacted by producing deviations to the left, into the force field, as early as the second trial. Further adaptation resulted in rapid exponential reduction of kinematic error in the latter portion of the movement, where the greatest perturbation to the handpath was initially observed, whereas there was little modification of the handpath in the region where the PF was active. Significant force directed to counteract the PF was measured on the first guided trial, and was modified during the first half of the learning set. The total force impulse in the region of the PF increased throughout the learning trials, but it always remained less than that produced by the PF. The force profile did not resemble a mirror image of the PF in that it tended to be more trapezoidal than parabolic in shape. As in previous studies of force-field adaptation, we found that changes in muscle activation involved a general increase in the activity of all muscles, which increased arm stiffness, and selectively-greater increases in the activation of muscles which counteracted the PF. With training, activation was exponentially reduced, albeit more slowly than kinematic error. Progressive changes in kinematics and EMG occurred predominantly in the region of the workspace beyond the force field. We suggest that constraints on muscle mechanics limit the ability of the central nervous system to employ an inverse dynamics model to nullify impulse-like forces by generating mirror-image forces. Consequently, subjects adopted a strategy of slightly overcompensating for the first half of the force field, then allowing the force field to push them in the opposite direction. Muscle activity patterns in the region beyond the boundary of the force field were subsequently adjusted because of the relatively-slow response of the second-order mechanics of muscle impedance to the force impulse.
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What is the minimal size quantum circuit required to exactly implement a specified n-qubit unitary operation, U, without the use of ancilla qubits? We show that a lower bound on the minimal size is provided by the length of the minimal geodesic between U and the identity, I, where length is defined by a suitable Finsler metric on the manifold SU(2(n)). The geodesic curves on these manifolds have the striking property that once an initial position and velocity are set, the remainder of the geodesic is completely determined by a second order differential equation known as the geodesic equation. This is in contrast with the usual case in circuit design, either classical or quantum, where being given part of an optimal circuit does not obviously assist in the design of the rest of the circuit. Geodesic analysis thus offers a potentially powerful approach to the problem of proving quantum circuit lower bounds. In this paper we construct several Finsler metrics whose minimal length geodesics provide lower bounds on quantum circuit size. For each Finsler metric we give a procedure to compute the corresponding geodesic equation. We also construct a large class of solutions to the geodesic equation, which we call Pauli geodesics, since they arise from isometries generated by the Pauli group. For any unitary U diagonal in the computational basis, we show that: (a) provided the minimal length geodesic is unique, it must be a Pauli geodesic; (b) finding the length of the minimal Pauli geodesic passing from I to U is equivalent to solving an exponential size instance of the closest vector in a lattice problem (CVP); and (c) all but a doubly exponentially small fraction of such unitaries have minimal Pauli geodesics of exponential length.
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Fly ash was modified by hydrothermal treatment using NaOH solutions under various conditions for zeolite synthesis. The XRD patterns are presented. The results indicated that the samples obtained after treatment are much different. The XRD profiles revealed a number of new reflexes, suggesting a phase transformation probably occurred. Both heat treatment and chemical treatment increased the surface area and pore volume. It was found that zeolite P would be formed at the conditions of higher NaOH concentration and temperature. The treated fly ash was tested for adsorption of heavy metal ions and dyes in aqueous solution. It was shown that fly ash and the modified forms could effectively absorb heavy metals and methylene blue but not effectively adsorb rhodamine B. Modifying fly ash with NaOH solution would significantly enhance the adsorption capacity depending on the treatment temperature, time, and base concentration. The adsorption capacity of methylene blue would increases with pH of the dye solution and the sorption capacity of FA-NaOH could reach 5 x 10(-5) mol/g. The adsorption isotherm could be described by the Langmuir and Freundlich isotherm equations. Removal of copper and nickel ions could also be achieved on those treated fly ash. The removal efficiency for copper and nickel ions could be from 30% to 90% depending on the initial concentrations. The increase in adsorption temperature will enhance the adsorption efficiency for both heavy metals. The pseudo second-order kinetics would be better for fitting the dynamic adsorption of Cu and Ni ions. (c) 2005 Elsevier B.V. All rights reserved.
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The purpose of this thesis is to conduct empirical research in corporate Thailand in order to (1) validate the Spirit at Work Scale (2) investigate the relationships between individual spirit at work and three employee work attitudinal variables (job satisfaction, organisational identification and psychological well-being) and three organisational outcomes (in-role performance, organisational citizenship behaviours (OCB), and turnover intentions) (3) further examine causal relations among these organisational behaviour variables with a longitudinal design (4) examine three employee work attitudes as mediator variables between individual spirit at work and three organisational outcomes and (5) explore the potential antecedents of organisational conditions that foster employee experienced individual spirit at work. The two pilot studies with 155 UK and 175, 715 Thai samples were conducted for validation testing of the main measure used in this study: Spirit at Work Scale (Kinjerski & Skrypnek, 2006a). The results of the two studies including discriminant validity analyses strongly provided supportive evidence that Spirit at Work Scale (SAWS) is a sound psychometric measure and also a distinct construct from the three work attitude constructs. The final model of SAWS contains a total of twelve items; a three factor structure (meaning in work, sense of community, and spiritual connection) in which the sub-factors loaded on higher order factors and also had very acceptable reliability. In line with these results it was decided to use the second-order of SAWS model for Thai samples in the main study and subsequent analysis. The 715 completed questionnaires were received from the first wave of data collection during July - August 2008 and the second wave was conducted again within the same organisations and 501 completed questionnaires were received during March - April 2009. Data were obtained through 49 organisations which were from three types of organisations within Thailand: public organisations, for-profit organisations, and notfor-profit organisations. Confirmatory factor analysis of all measures used in the study and hypothesised model were tested with structural equation modelling techniques. The results were greatly supportive for the direct structural model and partially supportive for the fully mediated model. Moreover, there were different findings across self report and supervisor rating on performance and OCB models. Additionally, the antecedent conditions that fostered employees experienced individual spirit at work and the implications of these findings for research and practice are discussed.
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Blurring a pattern reversal stimulus increases the latency and decreases the amplitude of the visual evoked potential (VEP) P100 peak. Recording the visual evoked magnetic response (VEMR) is some subjects may therefore be difficult because their spectacles create excessive magnetic noise. Hence, the effect of varying degrees of blur (-5 to +5 D) on the VEMR was investigated in three subjects with 6/6 vision to determine whether refraction with non-magnetic frames and lenses was necessary before magnetic recording. Small (32') and larger (70') checks were studied since there is evidence that blurring small checks has a more significant effect on the VEP compared with large checks. The VEMR was recorded using a single channel dc-SQUID, second order gradiometer in an unshielded laboratory. The latency (ms) and amplitude (fT) of the most prominant positive peak within the first 130 ms (P100M) were measured. Blurring the 32' checks significantly increased latency aand reduced the amplitude of the P100M peak. The resulting response curves were parabolic with minimum latency and maximum amplitude recorded at 0 D. Blurring the 70' check had no significant effect on latency or amplitude. Hence, the magnetic P100M responds similarly to the electrical P100 in response to blur. It would be essential when recording the VEMR that vision is corrected with non-magnetic spectacles especially when small checks are used.
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The polymerization of isobutene initiated by 1-chloro-1-phenylethane has been investigated, and molecular weight studies conducted using size exclusion chromatography. Polymerizations carried out in a 40/60 (v/v) mixture of dichloromethaneIcyclohexane, using titanium (IV) chloride as a catalyst in the presence of pyridine at -30 °C were found to be controlled and living. The number average molecular weights of the polymers increased linearly with monomer conversion, and the molecular weight distributions were between 1.15 and 1.20. Efficiencies of initiation were between 80 and 100%, and evidence was found to suggest that backbiting to the initiator had occurred, resulting in the formation of cyclic oligomers during the early stages of polymerization. The kinetics of polymerization can be explained in terms of active species in. equilibrium with dormant species. The effects of temperature. and dielectric constant on this equilibrium were studied and a model based upon the Fuoss equation was developed. Pyridine was found to behave as proton trap in the system, and when it was used in excess the rate of polymerization was retarded. By assuming that the catalyst and pyridine formed a one to one complex, it was possible to show that the reaction was second order with respect to the catalyst. The synthesis of low molecular weight polyisobutenes was studied. When the concentration of initiator was increased relative to that of the isobutene, such that the theoretical degree of polymerization was 20 or less, the rate of initiation was slow compared to propagation. The efficiency of initiation in these polymerizations was typically between 30 and 40 %. Optimal conditions of temperature. and.catalyst concentration were established, leading to a 60 % efficiency of initiation. A one-pot synthesis of phenol end-capped polyisobutene was attempted by adding phenol at the end of a living polymerization. Evidence to substantiate the existence of capped polymer chains in the resultant product was inconclusive. Block copolymerizations of oxetane and isobutene were conducted using 1-chloro-1phenylethane/TiCl4, but no copolymer or oxetane homopolymer could be isolated.
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We extend a meshless method of fundamental solutions recently proposed by the authors for the one-dimensional two-phase inverse linear Stefan problem, to the nonlinear case. In this latter situation the free surface is also considered unknown which is more realistic from the practical point of view. Building on the earlier work, the solution is approximated in each phase by a linear combination of fundamental solutions to the heat equation. The implementation and analysis are more complicated in the present situation since one needs to deal with a nonlinear minimization problem to identify the free surface. Furthermore, the inverse problem is ill-posed since small errors in the input measured data can cause large deviations in the desired solution. Therefore, regularization needs to be incorporated in the objective function which is minimized in order to obtain a stable solution. Numerical results are presented and discussed. © 2014 IMACS.
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Experimental investigations of 10×118 Gbit/s DP-QPSK WDM transmission using three types of distributed Raman amplification techniques are presented. Novel ultra-long Raman fibre laser based amplification with second order counter-propagated pumping is compared with conventional first order and dual order counter-pumped Raman amplification. We demonstrate that URFL based amplification can extend the transmission reach up to a distance of 7520 km in comparison with 5010 km and 6180 km using first order and dual order Raman amplification respectively. © 2014 IEEE.
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2000 Mathematics Subject Classification: 34K15.
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AMS subject classification: Primary 34A60, Secondary 49K24.