Formulação lagrangiana para sistemas dissipativos através do cálculo fracionário

Neste trabalho, generalizamos o Princípio da Mínima Ação proposto por Riewe para sistemas não conservativos, contendo forças dissipativas lineares dependentes de derivadas temporais de qualquer ordem. A Ação generalizada é construída a partir de funções Lagrangianas dependentes de derivadas de ordem inteira e fracionária. Diferente de outras formulações, o uso de derivadas fracionárias permite a construção de Lagrangianas físicas para sistemas não conservativos. Uma Lagrangiana é dita física se fornece relações fisicamente consistentes para o momentum e o Hamiltoniano do sistema. Neste Princípio da Mínima Ação generalizado, as equações de movimento são obtidas a partir da equação de Euler-Lagrange e, tomando-se o limite indo à zero para o intervalo de tempo definindo a Ação. Finalmente, como exemplo de aplicação, formulamos pela primeira vez uma Lagrangiana física para o problema da carga pontual acelerada.

Discrete breathers in a two-dimensional Fermi-Pasta-Ulam lattice

Using asymptotic methods, we investigate whether discrete breathers are supported by a two-dimensional Fermi-Pasta-Ulam lattice. A scalar (one-component) two-dimensional Fermi-Pasta-Ulam lattice is shown to model the charge stored within an electrical transmission lattice. A third-order multiple-scale analysis in the semi-discrete limit fails, since at this order, the lattice equations reduce to the (2+1)-dimensional cubic nonlinear Schrödinger (NLS) equation which does not support stable soliton solutions for the breather envelope. We therefore extend the analysis to higher order and find a generalised $(2+1)$-dimensional NLS equation which incorporates higher order dispersive and nonlinear terms as perturbations. We find an ellipticity criterion for the wave numbers of the carrier wave. Numerical simulations suggest that both stationary and moving breathers are supported by the system. Calculations of the energy show the expected threshold behaviour whereby the energy of breathers does {\em not} go to zero with the amplitude; we find that the energy threshold is maximised by stationary breathers, and becomes arbitrarily small as the boundary of the domain of ellipticity is approached.

The Becker-Döring equations with monomer input, competition and inhibition

We investigate the Becker-Döring model of nucleation with three generalisations; an input of monomer, an input of inhibitor and finally, we allow the monomers to form two morphologies of cluster. We assume size-independent aggregation and fragmentation rates. Initially we consider the problem of constant monomer input and determine the steady-state solution approached in the large-time limit, and the manner in which it is approached. Secondly, in addition to a constant input of monomer we allow a constant input of inhibitor, which prevents clusters growing any larger and this removes them from the kinetics of the process; the inhibitor is consumed in the action of poisoning a cluster. We determine a critical ratio of poison to monomer input below which the cluster concentrations tend to a non-zero steady-state solution and the poison concentration tends to a finite value. Above the critical input ratio, the concentrations of all cluster sizes tend to zero and the poison concentration grows without limit. In both cases the solution in the large-time limit is determined. Finally we consider a model where monomers form two morphologies, but the inhibitor only acts on one morphology. Four cases are identified, depending on the relative poison to monomer input rates and the relative thermodynamic stability. In each case we determine the final cluster distribution and poison concentration. We find that poisoning the less stable cluster type can have a significant impact on the structure of the more stable cluster distribution; a counter-intuitive result. All results are shown to agree with numerical simulation.

Estudo sobre a influência do massará no processo de formação de salitre em rebocos na região de Teresina - PI

This work had to verify the influence of massará, while mortar component, in the process of formation of saltpeter in cementitious plaster walls of buildings. The massará is a ceramic material, texture areno usually found in large volumes argillaceous sediments in Teresina, Piaui State capital, which is associated with the Portland cement mortar form for fixing and finishing in construction. Saltpeter or flowering is a pathology that happens in gypsum wallboard, which invariably reaction between soluble salts present in materials, water and oxygen. This pathology, supposedly credited to massará caused its use to suffer significant reduction in the market of the buildings. Verify this situation with particular scientific rigor is part of the proposal of this work. Grading tests Were performed, consistency limits (LL, LP and IP), determination of potential hydrogen, capacity Exchange (CTC), electrical conductivity (EC), x-ray fluorescence (FRX) and x-ray diffraction (DRX). Massará analysed samples in number six, including sample plastering salitrado presented potential hydrogen medium 5.7 in water and 5.2 on KCl n and electrical conductivity (EC), equal to zero. These results pointed to the affirmative that massará is a material that does not provide salinity content that can be taken into consideration. It is therefore concluded that the material analyzed not competing, at least with respect to the presence of soluble salts, for the formation of saltpeter

On the duration of negative surplus

Doutoramento em Matemática

Avaliação de produtos naturais no controle de biofilmes formados em sistema dinâmico

The biofilms microbial forms of association are responsible for generating, accelerating and / or induce the process of corrosion. The damage generated in the petroleum industry for this type of corrosion is significatives, representing major investment for your control. The aim of this study was to evaluate such tests antibiograms the effects of extracts of Jatropha curcas and essential oil of Lippia gracilis Schauer on microrganisms isolated from water samples and, thereafter, select the most effective natural product for further evaluation of biofilms formed in dynamic system. Extracts of J. curcas were not efficient on the complete inhibition of microbial growth in tests type antibiogram, and essential oil of L. gracilis Schauer most effective and determined for the other tests. A standard concentration of essential oil of 20 μL was chosen and established for the evaluation of the biofilms and the rate of corrosion. The biocide effect was determined by microbial counts of five types of microorganisms: aerobic bacteria, precipitating iron, total anaerobic, sulphate reducers (BRS) and fungi. The rate of corrosion was measured by loss of mass. Molecular identification and scanning electron microscopy (SEM) were performed. The data showed reduction to zero of the most probable number (MPN) of bacteria precipitating iron and BRS from 115 and 113 minutes of contact, respectively. There was also inhibited in fungi, reducing to zero the rate of colony-forming units (CFU) from 74 minutes of exposure. However, for aerobic and anaerobic bacteria there was no significant difference in the time of exposure to the essential oil, remaining constant. The rate of corrosion was also influenced by the presence of oil. The essential oil of L. gracilis was shown to be potentially effective

On the optimaL response of q-vortex

Wingtip vortices represent a hazard for the stability of the following airplane in airport highways. These flows have been usually modeled as swirling jets/wakes, which are known to be highly unstable and susceptible to breakdown at high Reynolds numbers for certain flow conditions, but different to the ones present in real flying airplanes. A very recent study based on Direct Numerical Simulations (DNS) shows that a large variety of helical responses can be excited and amplified when a harmonic inlet forcing is imposed. In this work, the optimal response of q-vortex (both axial vorticity and axial velocity can be modeled by a Gaussian profile) is studied by considering the time-harmonically forced problem with a certain frequency ω. We first reproduce Guo and Sun’s results for the Lamb-Oseen vortex (no axial flow) to validate our numerical code. In the axisymmetric case m = 0, the system response is the largest when the input frequency is null. The axial flow has a weak influence in the response for any axial velocity intensity. We also consider helical perturbations |m| = 1. These perturbations are excited through a resonance mechanism at moderate and large wavelengths as it is shown in Figure 1. In addition, Figure 2 shows that the frequency at which the optimal gain is obtained is not a continuous function of the axial wavenumber k. At smaller wavelengths, large response is excited by steady forcing. Regarding the axial flow, the unstable response is the largest when the axial velocity intensity, 1/q, is near to zero. For perturbations with higher azimuthal wavenumbers |m| > 1, the magnitudes of the response are smaller than those for helical modes. In order to establish an alternative validation, DNS has been carried out by using a pseudospectral Fourier formulation finding a very good agreement.

MULTI-WAVELENGTH SPECKLE REDUCTION FOR LASER PICO-PROJECTORS USING DIFFRACTIVE OPTICS

Personal electronic devices, such as cell phones and tablets, continue to decrease in size while the number of features and add-ons keep increasing. One particular feature of great interest is an integrated projector system. Laser pico-projectors have been considered, but the technology has not been developed enough to warrant integration. With new advancements in diode technology and MEMS devices, laser-based projection is currently being advanced for pico-projectors. A primary problem encountered when using a pico-projector is coherent interference known as speckle. Laser speckle can lead to eye irritation and headaches after prolonged viewing. Diffractive optical elements known as diffusers have been examined as a means to lower speckle contrast. Diffusers are often rotated to achieve temporal averaging of the spatial phase pattern provided by diffuser surface. While diffusers are unable to completely eliminate speckle, they can be utilized to decrease the resultant contrast to provide a more visually acceptable image. This dissertation measures the reduction in speckle contrast achievable through the use of diffractive diffusers. A theoretical Fourier optics model is used to provide the diffuser’s stationary and in-motion performance in terms of the resultant contrast level. Contrast measurements of two diffractive diffusers are calculated theoretically and compared with experimental results. In addition, a novel binary diffuser design based on Hadamard matrices will be presented. Using two static in-line Hadamard diffusers eliminates the need for rotation or vibration of the diffuser for temporal averaging. Two Hadamard diffusers were fabricated and contrast values were subsequently measured, showing good agreement with theory and simulated values. Monochromatic speckle contrast values of 0.40 were achieved using the Hadamard diffusers. Finally, color laser projection devices require the use of red, green, and blue laser sources; therefore, using a monochromatic diffractive diffuser may not optimal for color speckle contrast reduction. A simulation of the Hadamard diffusers is conducted to determine the optimum spacing between the two diffusers for polychromatic speckle reduction. Experimental measured results are presented using the optimal spacing of Hadamard diffusers for RGB color speckle reduction, showing 60% reduction in contrast.

Engineering design of an integrated sustainable process system for cassava biobased materials

Cassava contributes significantly to biobased material development. Conventional approaches for its bio-derivative-production and application cause significant wastes, tailored material development challenges, with negative environmental impact and application limitations. Transforming cassava into sustainable value-added resources requires redesigning new approaches. Harnessing unexplored material source, and downstream process innovations can mitigate challenges. The ultimate goal proposed an integrated sustainable process system for cassava biomaterial development and potential application. An improved simultaneous release recovery cyanogenesis (SRRC) methodology, incorporating intact bitter cassava, was developed and standardized. Films were formulated, characterised, their mass transport behaviour, simulating real-distribution-chain conditions quantified, and optimised for desirable properties. Integrated process design system, for sustainable waste-elimination and biomaterial development, was developed. Films and bioderivatives for desired MAP, fast-delivery nutraceutical excipients and antifungal active coating applications were demonstrated. SRRC-processed intact bitter cassava produced significantly higher yield safe bio-derivatives than peeled, guaranteeing 16% waste-elimination. Process standardization transformed entire root into higher yield and clarified colour bio-derivatives and efficient material balance at optimal global desirability. Solvent mass through temperature-humidity-stressed films induced structural changes, and influenced water vapour and oxygen permeability. Sevenunit integrated-process design led to cost-effectiveness, energy-efficient and green cassava processing and biomaterials with zero-environment footprints. Desirable optimised bio-derivatives and films demonstrated application in desirable in-package O2/CO2, mouldgrowth inhibition, faster tablet excipient nutraceutical dissolutions and releases, and thymolencapsulated smooth antifungal coatings. Novel material resources, non-root peeling, zero-waste-elimination, and desirable standardised methodology present promising process integration tools for sustainable cassava biobased system development. Emerging design outcomes have potential applications to mitigate cyanide challenges and provide bio-derivative development pathways. Process system leads to zero-waste, with potential to reshape current style one-way processes into circular designs modelled on nature's effective approaches. Indigenous cassava components as natural material reinforcements, and SRRC processing approach has initiated a process with potential wider deployment in broad product research development. This research contributes to scientific knowledge in material science and engineering process design.

Measure-valued mass evolution problems with flux boundary conditions and solution-dependent velocities

In this paper we prove well-posedness for a measure-valued continuity equation with solution-dependent velocity and flux boundary conditions, posed on a bounded one-dimensional domain. We generalize the results of an earlier paper [J. Differential Equations, 259 (2015), pp. 10681097] to settings where the dynamics are driven by interactions. In a forward-Euler-like approach, we construct a time-discretized version of the original problem and employ those results as a building block within each subinterval. A limit solution is obtained as the mesh size of the time discretization goes to zero. Moreover, the limit is independent of the specific way of partitioning the time interval [0, T]. This paper is partially based on results presented in Chapter 5 of [Evolution Equations for Systems Governed by Social Interactions, Ph.D. thesis, Eindhoven University of Technology, 2015], while a number of issues that were still open there are now resolved.

Equilibrium existence in the circle model with linear quadratic transport costÂ

We treat the problem of existence of a location-then-price equilibrium in the circle model with a linear quadratic type of transportation cost function which can be either convex or concave. We show the existence of a unique perfect equilibrium for the concave case when the linear and quadratic terms are equal and of a unique perfect equilibrium for the convex case when the linear term is equal to zero. Aside from these two cases, there are feasible locations by the firms for which no equilibrium in the price subgame exists. Finally, we provide a full taxonomy of the price equilibrium regions in terms of weights of the linear and quadratic terms in the cost function.

Matlab simulink modeling of photovoltaic cells for understanding shadow effect

Irradiation is the main component for producing the electricity from solar energy. When obstacles come in between the sun and the PV cell then it doesn’t get sufficient irradiance to produce enough electricity. Shadowing has a great impact on photovoltaic cell. The main fuel of PV cell is solar radiation. Using solar radiation, a photovoltaic cell produces electricity. The shadow on a PV cell decreases the output of the photovoltaic cell. It has been already shown in different papers that shadow effect decreases the output of the PV cell. There are different kinds of shadow effects which are observed, some minimize the PV cell output and some reduce the output to zero. There are different types of shadow based on their effects on the photovoltaic cell. The shadow has also effects depending on whether the PV cells are connected in series connection or in parallel connection. In series when one cell is out of order then the whole series of the PV cells will not work but in parallel connection if one cell is damaged, the others will work because they work independently. According to the output requirement the arrangement of the PV cells are made in series or parallel. Simulink modeling is made for series and parallel connection between two PV cells and the shadow effect is analyzed on one of the PV cells. Using SIMULINK, the shadowing is simulated on the two PV cells, where in one system they are in series and in another system they are in parallel. Slowly the irradiance is decreased to simulate the shadow effect. Simulation of the shadow effect gives an idea about the output of the PV cell system when system has shadow on the PV cells. Here the shadow effect on the two PV cells using series and parallel combinations are simulated and analyzed for understanding the effects on output.

Direct nitrous oxide (N2O) fluxes from soils under different land use in Brazil: a critical review.

Brazil typifies the land use changes happening in South America, where natural vegetation is continuously converted into agriculturally used lands, such as cattle pastures and croplands. Such changes in land use are always associated with changes in the soil nutrient cycles and result in altered greenhouse gas fluxes from the soil to the atmosphere. In this study, we analyzed literature values to extract patterns of direct nitrous oxide (N2O) emissions from soils of different ecosystems in Brazil. Fluxes from natural ecosystems exhibited a wide range: whereas median annual flux rates were highest in Amazonian and Atlantic rainforests (2.42 and 0.88 kg N ha-1), emissions from cerrado soils were close to zero. The decrease in emissions from pastures with increasing time after conversion was associated with pasture degradation. We found comparatively low N2O-N fluxes from croplands (-0.07 to 4.26 kg N ha-1 yr-1 , median 0.80 kg N ha-1 yr-1) and a low response to N fertilization. Contrary to the assumptions, soil parameters, such as pH, Corg, and clay content emerged as poor predictors for N2O fluxes. This could be a result of the formation of micro-aggregates, which strongly affect the hydraulic properties of the soil, and consequently define nitrification and denitrification potentials. Since data from croplands mainly derived from areas that had been under natural cerrado vegetation before, it could explain the low emissions under agriculture. Measurements must be more frequent and regionally spread in order to enable sound national estimates.

Universal zero-bias conductance through a quantum wire side-coupled to a quantum dot

A numerical renormalization-group study of the conductance through a quantum wire containing noninteracting electrons side-coupled to a quantum dot is reported. The temperature and the dot-energy dependence of the conductance are examined in the light of a recently derived linear mapping between the temperature-dependent conductance and the universal function describing the conductance for the symmetric Anderson model of a quantum wire with an embedded quantum dot. Two conduction paths, one traversing the wire, the other a bypass through the quantum dot, are identified. A gate potential applied to the quantum wire is shown to control the current through the bypass. When the potential favors transport through the wire, the conductance in the Kondo regime rises from nearly zero at low temperatures to nearly ballistic at high temperatures. When it favors the dot, the pattern is reversed: the conductance decays from nearly ballistic to nearly zero. When comparable currents flow through the two channels, the conductance is nearly temperature independent in the Kondo regime, and Fano antiresonances in the fixed-temperature plots of the conductance as a function of the dot-energy signal interference between them. Throughout the Kondo regime and, at low temperatures, even in the mixed-valence regime, the numerical data are in excellent agreement with the universal mapping.

Analytical solution to the zero-inertia problem for surge flow phenomena in nonprismatic channels

Surge flow phenomena. e.g.. as a consequence of a dam failure or a flash flood, represent free boundary problems. ne extending computational domain together with the discontinuities involved renders their numerical solution a cumbersome procedure. This contribution proposes an analytical solution to the problem, It is based on the slightly modified zero-inertia (ZI) differential equations for nonprismatic channels and uses exclusively physical parameters. Employing the concept of a momentum-representative cross section of the moving water body together with a specific relationship for describing the cross sectional geometry leads, after considerable mathematical calculus. to the analytical solution. The hydrodynamic analytical model is free of numerical troubles, easy to run, computationally efficient. and fully satisfies the law of volume conservation. In a first test series, the hydrodynamic analytical ZI model compares very favorably with a full hydrodynamic numerical model in respect to published results of surge flow simulations in different types of prismatic channels. In order to extend these considerations to natural rivers, the accuracy of the analytical model in describing an irregular cross section is investigated and tested successfully. A sensitivity and error analysis reveals the important impact of the hydraulic radius on the velocity of the surge, and this underlines the importance of an adequate description of the topography, The new approach is finally applied to simulate a surge propagating down the irregularly shaped Isar Valley in the Bavarian Alps after a hypothetical dam failure. The straightforward and fully stable computation of the flood hydrograph along the Isar Valley clearly reflects the impact of the strongly varying topographic characteristics on the How phenomenon. Apart from treating surge flow phenomena as a whole, the analytical solution also offers a rigorous alternative to both (a) the approximate Whitham solution, for generating initial values, and (b) the rough volume balance techniques used to model the wave tip in numerical surge flow computations.