Local Energy Decay in Even Dimensions for the Wave Equation with a Time-Periodic Non-Trapping Metric and Applications to Strichartz Estimates

2000 Mathematics Subject Classification: 35B40, 35L15.

Element characteristic tolerance for semi-batch fixed bed biomass pyrolysis

Biomass pyrolysis to bio-oil is one of the promising sustainable fuels. In this work, relation between biomass feedstock element characteristic and crude bio-oil production yield and lower heating value was explored. The element characteristics considered in this study include moisture, ash, fix carbon, volatile matter, C, H, N, O, S, cellulose, hemicellulose, and lignin content. A semi-batch fixed bed reactor was used for biomass pyrolysis with heating rate of 30 °C/min from room temperature to 600 °C and the reactor was held at 600 °C for 1 h before cooling down. Constant nitrogen flow (1bar) was provided for anaerobic condition. Sago and Napier glass were used in the study to create different element characteristic of feedstock by altering mixing ratio. Comparison between each element characteristic to crude bio-oil yield and low heating value was conducted. The result suggested potential key element characteristic for pyrolysis and provide a platform to access the feedstock element acceptance range.

Green's function for paraxial equation

The theory and experimental applications of optical Airy beams are in active development recently. The Airy beams are characterised by very special properties: they are non-diffractive and propagate along parabolic trajectories. Among the striking applications of the optical Airy beams are optical micro-manipulation implemented as the transport of small particles along the parabolic trajectory, Airy-Bessel linear light bullets, electron acceleration by the Airy beams, plasmonic energy routing. The detailed analysis of the mathematical aspects as well as physical interpretation of the electromagnetic Airy beams was done by considering the wave as a function of spatial coordinates only, related by the parabolic dependence between the transverse and the longitudinal coordinates. Their time dependence is assumed to be harmonic. Only a few papers consider a more general temporal dependence where such a relationship exists between the temporal and the spatial variables. This relationship is derived mostly by applying the Fourier transform to the expressions obtained for the harmonic time dependence or by a Fourier synthesis using the specific modulated spectrum near some central frequency. Spatial-temporal Airy pulses in the form of contour integrals is analysed near the caustic and the numerical solution of the nonlinear paraxial equation in time domain shows soliton shedding from the Airy pulse in Kerr medium. In this paper the explicitly time dependent solutions of the electromagnetic problem in the form of time-spatial pulses are derived in paraxial approximation through the Green's function for the paraxial equation. It is shown that a Gaussian and an Airy pulse can be obtained by applying the Green's function to a proper source current. We emphasize that the processes in time domain are directional, which leads to unexpected conclusions especially for the paraxial approximation.

Unveiling temporal correlations characteristic of a phase transition in the output intensity of a fiber laser

We use advanced statistical tools of time-series analysis to characterize the dynamical complexity of the transition to optical wave turbulence in a fiber laser. Ordinal analysis and the horizontal visibility graph applied to the experimentally measured laser output intensity reveal the presence of temporal correlations during the transition from the laminar to the turbulent lasing regimes. Both methods unveil coherent structures with well-defined time scales and strong correlations both, in the timing of the laser pulses and in their peak intensities. Our approach is generic and may be used in other complex systems that undergo similar transitions involving the generation of extreme fluctuations.

Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations

A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.

Inverse space-dependent force problems for the wave equation

The determination of the displacement and the space-dependent force acting on a vibrating structure from measured final or time-average displacement observation is thoroughly investigated. Several aspects related to the existence and uniqueness of a solution of the linear but ill-posed inverse force problems are highlighted. After that, in order to capture the solution a variational formulation is proposed and the gradient of the least-squares functional that is minimized is rigorously and explicitly derived. Numerical results obtained using the Landweber method and the conjugate gradient method are presented and discussed illustrating the convergence of the iterative procedures for exact input data. Furthermore, for noisy data the semi-convergence phenomenon appears, as expected, and stability is restored by stopping the iterations according to the discrepancy principle criterion once the residual becomes close to the amount of noise. The present investigation will be significant to researchers concerned with wave propagation and control of vibrating structures.

A method of fundamental solutions for theaxisymmetric backward heat equation

We propose and investigate an application of the method of fundamental solutions (MFS) to the radially symmetric and axisymmetric backward heat conduction problem (BHCP) in a solid or hollow cylinder. In the BHCP, the initial temperature is to be determined from the temperature measurements at a later time. This is an inverse and ill-posed problem, and we employ and generalize the MFS regularization approach [B.T. Johansson and D. Lesnic, A method of fundamental solutions for transient heat conduction, Eng. Anal. Boundary Elements 32 (2008), pp. 697–703] for the time-dependent heat equation to obtain a stable and accurate numerical approximation with small computational cost.

Numerical solution of a Cauchy problem for Laplace equation in 3-dimensional domains by integral equations

A numerical method based on integral equations is proposed and investigated for the Cauchy problem for the Laplace equation in 3-dimensional smooth bounded doubly connected domains. To numerically reconstruct a harmonic function from knowledge of the function and its normal derivative on the outer of two closed boundary surfaces, the harmonic function is represented as a single-layer potential. Matching this representation against the given data, a system of boundary integral equations is obtained to be solved for two unknown densities. This system is rewritten over the unit sphere under the assumption that each of the two boundary surfaces can be mapped smoothly and one-to-one to the unit sphere. For the discretization of this system, Weinert’s method (PhD, Göttingen, 1990) is employed, which generates a Galerkin type procedure for the numerical solution, and the densities in the system of integral equations are expressed in terms of spherical harmonics. Tikhonov regularization is incorporated, and numerical results are included showing the efficiency of the proposed procedure.

A coherent master equation for active mode locking in lasers

We present the derivation of a new master equation for active mode locking in lasers that fully takes into account the coherent effects of the light matter interaction through a peculiar adiabatic elimination technique. The coherent effects included in our model could be relevant to describe properly mode-locked semiconductor lasers where the standard Haus' Master Equation predictions show some discrepancy with respect to the experimental results and can be included in the modelling of other mode locking techniques too.

Exact solution for the energy spectrum of Kelvin-wave turbulence in superfluids

We study the statistical and dynamical behavior of turbulent Kelvin waves propagating on quantized vortices in superfluids and address the controversy concerning the energy spectrum that is associated with these excitations. Finding the correct energy spectrum is important because Kelvin waves play a major role in the dissipation of energy in superfluid turbulence at near-zero temperatures. In this paper, we show analytically that the solution proposed by [L’vov and Nazarenko, JETP Lett. 91, 428 (2010)] enjoys existence, uniqueness, and regularity of the prefactor. Furthermore, we present numerical results of the dynamical equation that describes to leading order the nonlocal regime of the Kelvin-wave dynamics. We compare our findings with the analytical results from the proposed local and nonlocal theories for Kelvin-wave dynamics and show an agreement with the nonlocal predictions. Accordingly, the spectrum proposed by L’vov and Nazarenko should be used in future theories of quantum turbulence. Finally, for weaker wave forcing we observe an intermittent behavior of the wave spectrum with a fluctuating dissipative scale, which we interpreted as a finite-size effect characteristic of mesoscopic wave turbulence.

Pyrolysis of Napier grass in a fixed bed reactor:effect of operating conditions on product yields and characteristic

This study presents a report on pyrolysis of Napier grass stem in a fixed bed reactor. The effects of nitrogen flow (20 to 60 mL/min), and reaction temperature (450 to 650 degrees C) were investigated. Increasing the nitrogen flow from 20 to 30 mL/min increased the bio-oil yield and decreased both bio-char and non-condensable gas. 30 mL/min nitrogen flow resulted in optimum bio-oil yield and was used in the subsequent experiments. Reaction temperatures between 450 and 600 degrees C increased the bio-oil yield, with maximum yield of 32.26 wt% at 600 degrees C and a decrease in the corresponding bio-char and non-condensable gas. At 650 degrees C, reductions in the bio-oil and bio-char yields were recorded while the non-condensable gas increased. Water content of the bio-oil decreased with increasing reaction temperature, while density and viscosity increased. The observed pH and higher heating values were between 2.43 to 2.97, and 25.25 to 28.88 MJ/kg, respectively. GC-MS analysis revealed that the oil was made up of highly oxygenated compounds and requires upgrading. The bio-char and non-condensable gas were characterized, and the effect of reaction temperature on the properties was evaluated. Napier grass represents a good source of renewable energy when all pyrolysis products are efficiently utilized.

Négy jellegzetesség. A magyar fejlődés politikai gazdaságtani megközelítésben. 1. rész = Four characteristic features. Development in Hungary from the aspect of political economy. First Part

A két részből álló cikk a magyarországi reformfolyamat és posztszocialista átalakulás négy olyan jellegzetességét emeli ki, amelyek megszakítás nélkül, a politikai szférában bekövetkezett rendszerváltást követően is, folyamatosan jellemezték az elmúlt harminc év fejlődését: a lakosság anyagi jólétének prioritása, erős paternalista jóléti állam, a reformfolyamat és átmenet fokozatossága és a politikai nyugalom. Az 1995. március 12­én bejelentett stabilizációs program - amennyiben megvalósul - jelenthet elmozdulást ezektől a jellegzetességektől. A cikk politikai gazdaságtani megközelítésben vizsgálja, hogy miért alakult ki ez a négy jellegzetesség, miképpen hatottak azok egymásra, milyen kedvező és kedvezőtlen hatásokat fejtettek ki. Az első rész az 1956­os forradalom hatásából kiindulva politikatörténeti áttekintést ad, majd a mai jólét, biztonság és nyugalom prioritását és a társadalmi adósság felhalmozódását, végül a stabilizációs program gazdasági és politikai hatásait elemzi. / === / The article, consisting of two parts, emphasizes four characteristic features of the Hungarian reform process and the post­socialist transformation, which, uninterruptedly, characterized the development over the last thirty years, even after the systemic change in the political sphere. These were: priority of the material welfare of the population, a strong, paternalistic welfare state, the gradual progress of the reform process and the transition, as well as political calmness. The stabilization programme, announced on March 12,1995, may imply - if it materializes - a shift away from these characteristics. The article investigates, from the aspect of political economy, why the four characteristic features had developed, how they affected each other and what were their advantageous and disadvantageous impacts. Setting out from the impacts of the 1956 revolution, the first part gives an overview of political history and then analyses the priority of today's welfare, security and calm as well as the accumulation of societal debt and, finally, the economic and political impacts of the stabilization programme.

Négy jellegzetesség. A magyar fejlődés politikai gazdaságtani megközelítésben. 2. rész = Four characteristic features. Development in Hungary from the aspect of political economy - II.

A tulajdonviszonyok és intézmények átalakulását is a fokozatosság, a szerves fejlődés jellemzi; Magyarországon a hosszú reformszocialista fázist a politikai fordulat után sem követte ugrás a piacgazdaság felé, bár az átalakulás felgyorsult. A cikk a fokozatosság érvényesülését az értékesítési stratégia sokféle változatát alkalmazó, burjánzó privatizációban, az új vállalkozások keletkezésének folyamatában, a liberalizálás menetében és a jogi infrastruktúra változásában mutatja be. Elemzi az átmenet során megerősödő korporatista elemek hatását a magyar gazdaságpolitikára. Végül néhány összefoglaló megjegyzést fűz a magyar fejlődéshez a politikai gazdaságtan és a politikai filozófia szemszögéből. Az elmúlt harminc évben a mindenkori kormánynak jól érzékelhető preferenciája volt a radikális intézkedések elodázása, a társadalmi adósság felhalmozódásának vállalása a konfliktusok elkerülése érdekében. A szerző felhívja a figyelmet a különböző nemzedékek eltérő időpreferenciájára és az ezzel kapcsolatos etikai problémákra. Befejezésül a népszerűtlen intézkedéseket az állampolgárok nagy hányadának véleményével szemben is felvállaló kormányzás és a demokrácia viszonyáról szól. / === / Gradualism and organic development also distinguish the transformation of property relations and institutions. Hungary's long reform­socialist phase was not followed, after the political change, by a leap towards a market economy, although the transformation became faster. The article shows how gradualism applies to the proliferating of privatization, with its wide variety of selling strategies, to the foundation process of new firms, to the course of liberalization, and to change in the legal infrastructure. It analyses the effect on Hungarian economic policy of corporatist elements which strengthen during the transition. Finally, it makes some comments summing up Hungarian development in terms of political economy and political philosophy. The government at any time in the last thirty years showed an obvious preference for putting off radical measures and accepting an accumulation of social debt as a way of averting conflict. The article notes differences of time preference between generations and the ethical problems these raise. Finally, it makes remarks on the relationship between democracy and an administration intent on unpopular measures opposed by a high proportion of citizens.