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Kinetic Theory (kinetic + theory)
Selected AbstractsProbability Density Function (PDF) Simulation of Turbulent Reactive Gas-Solid Flow in a RiserCHEMICAL ENGINEERING & TECHNOLOGY (CET), Issue 3 2009S. N. P. Vegendla Abstract A hybrid Lagrangian-Eulerian methodology is developed for the numerical simulation of turbulent reactive gas-solid flow. The SO2 -NOx Adsorption Process (SNAP) in a riser reactor with dilute gas-solid flow is taken as a test case. A three-dimensional time-dependent simulation is performed. By using the transported composition PDF method [1], modeling of the mean chemical source term and mass transfer terms in the gas-solid flow model equations is no longer needed. A notional particle-based Monte-Carlo algorithm is used to solve the transported composition PDF equations. A Finite-Volume technique is used to calculate the hydrodynamic fields from the Reynolds Averaged Navier Stokes (RANS) equations combined with the k -, turbulence model for the gas phase and the Kinetic Theory of Granular Flow (KTGF) for the solid phase [2]. The newly developed hybrid solution technique is tested with the SNAP chemistry that has a total of 13 scalars (i.e., 5 gas phase components and 8 solid phase species) for which the composition fields of the reactive species are calculated. A good agreement between simulated and experimental gas-outlet composition of a demonstration unit is obtained. [source] Temperature sensitivity and substrate quality in soil organic matter decomposition: results of an incubation study with three substratesGLOBAL CHANGE BIOLOGY, Issue 6 2010J. Å. MARTIN WETTERSTEDT Abstract Kinetic theory suggests that the temperature sensitivity of decomposition of soil organic matter should increase with increasing recalcitrance. This ,temperature,quality hypothesis' was tested in a laboratory experiment. Microcosms with wheat straw, spruce needle litter and mor humus were initially placed at 5, 15 and 25 °C until the same cumulative amount of CO2 had been respired. Thereafter, microcosms from each single temperature were moved to a final set of incubation temperatures of 5, 15 and 25 °C. Straw decomposed faster than needle litter at 25 and 15 °C, but slower than needle litter at 5 °C, and showed a higher temperature sensitivity (expressed as Q10) than needle litter at low temperatures. When moved to the same temperature, needle litter initially incubated at 5 and 15 °C had significantly higher respiration rates in the final incubation than litters initially placed at 25 °C. Mor humus placed at equal temperatures during the initial and final incubations had higher cumulative respiration during the final incubation than humus experiencing a shift in temperature, both up- and downwards. These results indicate that other factors than substrate quality are needed to fully explain the temperature dependence. In agreement with the hypothesis, Q10 was always higher for the temperature step between 5 and 15 °C than between 15 and 25 °C. Also in agreement with the temperature,quality hypothesis, Q10 significantly increased with increasing degree of decomposition in five out of the six constant temperature treatments with needle litter and mor humus. Q10s for substrates moved between temperatures tended to be higher than for substrates remaining at the initial temperature and an upward shift in temperature increased Q10 more than a downward shift. This study largely supports the temperature,quality hypothesis. However, other factors like acclimation and synthesis of recalcitrant compounds can modify the temperature response. [source] A brief overview of theories of PVC plasticization and methods used to evaluate PVC-plasticizer interaction,JOURNAL OF VINYL & ADDITIVE TECHNOLOGY, Issue 4 2009Paul H. Daniels This paper reviews the most widely used models for explaining how plasticizers render PVC flexible. These models include the gel, lubricity, and free volume theories; kinetic theories; and mathematical models which predict on the basis of plasticizer structure how much a plasticizer will lower the polymer glass transition in a flexible PVC compound. Since plasticization results from interactions between plasticizer and polymer, methods which have been used to study either the strength or the permanence (or both) of those interactions are also briefly discussed. Tools which have often been used to study plasticizer-PVC interactions include infrared and nuclear magnetic resonance spectroscopy, compression and humid-aging tests, dynamic mechanical analysis, torque rheometer tests, plasticizer-resin clear point temperature measurements, plastisol gelation/fusion by hot stage measurements, and others. J. VINYL ADDIT. TECHNOL., 2009. © 2009 Society of Plastics Engineers [source] General Gyrokinetic Equations for Edge PlasmasCONTRIBUTIONS TO PLASMA PHYSICS, Issue 7-9 2006H. Qin Abstract During the pedestal cycle of H-mode edge plasmas in tokamak experiments, large-amplitude pedestal build-up and destruction coexist with small-amplitude drift wave turbulence. The pedestal dynamics simultaneously includes fast time-scale electromagnetic instabilities, long time-scale turbulence-induced transport processes, and more interestingly the interaction between them. To numerically simulate the pedestal dynamics from first principles, it is desirable to develop an effective algorithm based on the gyrokinetic theory. However, existing gyrokinetic theories cannot treat fully nonlinear electromagnetic perturbations with multi-scale-length structures in spacetime, and therefore do not apply to edge plasmas. A set of generalized gyrokinetic equations valid for the edge plasmas has been derived. This formalism allows large-amplitude, time-dependent background electromagnetic fields to be developed fully nonlinearly in addition to small-amplitude, short-wavelength electromagnetic perturbations. It turns out that the most general gyrokinetic theory can be geometrically formulated. The Poincaré-Cartan-Einstein 1-form on the 7D phase space determines particles' worldlines in the phase space, and realizes the momentum integrals in kinetic theory as fiber integrals. The infinitesimal generator of the gyro-symmetry is then asymptotically constructed as the base for the gyrophase coordinate of the gyrocenter coordinate system. This is accomplished by applying the Lie coordinate perturbation method to the Poincaré-Cartan-Einstein 1-form. General gyrokinetic Vlasov-Maxwell equations are then developed as the Vlasov-Maxwell equations in the gyrocenter coordinate system, rather than a set of new equations. Because the general gyrokinetic system developed is geometrically the same as the Vlasov-Maxwell equations, all the coordinate-independent properties of the Vlasov-Maxwell equations, such as energy conservation, momentum conservation, and phase space volume conservation, are automatically carried over to the general gyrokinetic system. The pullback transformation associated with the coordinate transformation is shown to be an indispensable part of the general gyrokinetic Vlasov-Maxwell equations. As an example, the pullback transformation in the gyrokinetic Poisson equation is explicitly expressed in terms of moments of the gyrocenter distribution function, with the important gyro-orbit squeezing effect due to the large electric field shearing in the edge and the full finite Larmour radius effect for short wavelength fluctuations. The familiar "polarization drift density" in the gyrocenter Poisson equation is replaced by a more general expression. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Contributions of Yuri L. Klimontovich to the kinetic theory of nonideal plasmasCONTRIBUTIONS TO PLASMA PHYSICS, Issue 5-6 2003M. Bonitz Abstract We give a short summary of live and work of Yuri L. Klimontovich (1924,2002), in particular we discuss his work on nonideal plasma physics. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Sum rules and exact relations for quantal Coulomb systemsCONTRIBUTIONS TO PLASMA PHYSICS, Issue 5-6 2003V.M. Adamyan Abstract A complex response function describing a reaction of a multi-particle system to a weak alternating external field is the boundary value of a Nevanlinna class function (i.e. a holomorphic function with non-negative imaginary part in the upper half-plane). Attempts of direct calculations of response functions based on standard approximations of the kinetic theory for real Coulomb condensed systems often result in considerable discrepancies with experiments and computer simulations. At the same time a relatively simple approach using only the exact values of leading asymptotic terms of the response function permits to restrict essentially a subset of Nevanlinna class functions containing this response function, and in this way to obtain sufficient data to explain and predict experimental results. Mathematical details of this approach are demonstrated on an example with the response function being the (external) dynamic electrical conductivity of cold dense hydrogen-like plasmas. In particular, the exact values of the leading terms of asymptotic expansions of the conductivity are calculated. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Experimental evidence for the attenuating effect of SOM protection on temperature sensitivity of SOM decompositionGLOBAL CHANGE BIOLOGY, Issue 10 2010JEROEN GILLABEL Abstract The ability to predict C cycle responses to temperature changes depends on the accurate representation of temperature sensitivity (Q10) of soil organic matter (SOM) decomposition in C models for different C pools and soil depths. Theoretically, Q10 of SOM decomposition is determined by SOM quality and availability (referred to here as SOM protection). Here, we focus on the role of SOM protection in attenuating the intrinsic, SOM quality dependent Q10. To assess the separate effects of SOM quality and protection, we incubated topsoil and subsoil samples characterized by differences in SOM protection under optimum moisture conditions at 25 °C and 35 °C. Although lower SOM quality in the subsoil should lead to a higher Q10 according to kinetic theory, we observed a much lower overall temperature response in subsoil compared with the topsoil. Q10 values determined for respired SOM fractions of decreasing lability within the topsoil increased from 1.9 for the most labile to 3.8 for the least labile respired SOM, whereas corresponding Q10 values for the subsoil did not show this trend (Q10 between 1.4 and 0.9). These results indicate the existence of a limiting factor that attenuates the intrinsic effect of SOM quality on Q10 in the subsoil. A parallel incubation experiment of 13C-labeled plant material added to top- and subsoil showed that decomposition of an unprotected C substrate of equal quality responds similarly to temperature changes in top- and subsoil. This further confirms that the attenuating effect on Q10 in the subsoil originates from SOM protection rather than from microbial properties or other nutrient limitations. In conclusion, we found experimental evidence that SOM protection can attenuate the intrinsic Q10 of SOM decomposition. [source] Flow of particles suspended in a sheared viscous fluid: Effects of finite inertia and inelastic collisionsAICHE JOURNAL, Issue 10 2010Micheline Abbas Abstract We investigate in this article the macroscopic behavior of sheared suspensions of spherical particles. The effects of the fluid inertia, the Brownian diffusion, and the gravity are neglected. We highlight the influence of the solid-phase inertia on the macroscopic behavior of the suspension, considering moderate to high Stokes numbers. Typically, this study is concerned with solid particles O (100 ,m) suspended in a gas with a concentration varying from 5% to 30%. A hard-sphere collision model (with elastic or inelasic rebounds) coupled with the particle Lagrangian tracking is used to simulate the suspension dynamics in an unbounded periodic domain. We first consider the behavior of the suspension with perfect elastic collisions. The suspension properties reveal a strong dependence on the particle inertia and concentration. Increasing the Stokes number from 1 to 10 induces an enhancement of the particle agitation by three orders of magnitude and an evolution of the probability density function of the fluctuating velocity from a highly peaked (close to the Dirac function) to a Maxwellian shape. This sharp transition in the velocity distribution function is related to the time scale which controls the overall dynamics of the suspension flow. The particle relaxation (resp. collision) time scale dominates the particulate phase behavior in the weakly (resp. highly) agitated suspensions. The numerical results are compared with the prediction of two statistical models based on the kinetic theory for granular flows adapted to moderately inertial regimes. The suspensions have a Newtonian behavior when they are highly agitated similarly to rapid granular flows. However, the stress tensors are highly anisotropic in weakly agitated suspensions as a difference of normal stresses arises. Finally, we discuss the effect of energy dissipation due to inelastic collisions on the statistical quantities. We also tested the influence of a simple modeling of local hydrodynamic interactions during the collision by using a restitution coefficient which depends on the local impact velocities. © 2010 American Institute of Chemical Engineers AIChE J, 2010 [source] Extension of PIV for measuring granular temperature field in dense fluidized bedsAICHE JOURNAL, Issue 1 2007W. Dijkhuizen Abstract In this work a particle image velocimetry (PIV) technique has been extended to enable the simultaneous measurement of the instantaneous velocity and granular temperature fields. The PIV algorithm has been specifically optimized for dense granular systems and has been thoroughly tested with artificially generated images. The new PIV technique has been successfully applied to a fluidized bed at incipient fluidization conditions in which a single bubble is injected by a jet and to a freely bubbling fluidized bed. The instantaneous spatial distribution of the solids-phase velocity and granular temperature that can be measured with this new technique can be used to validate CFD models for dense granular systems, such as multifluid continuum models using the KTGF (kinetic theory of granular flow) to describe the internal momentum transport in the particulate phase. © 2006 American Institute of Chemical Engineers AIChE J, 2007 [source] Crystallization of Silicate Magmas Deciphered Using Crystal Size DistributionsJOURNAL OF THE AMERICAN CERAMIC SOCIETY, Issue 3 2007Bruce D. Marsh The remoteness and inhospitable nature of natural silicate magma make it exceedingly difficult to study in its natural setting deep beneath volcanoes. Although laboratory experiments involving molten rock are routinely performed, it is the style and nature of crystallization under natural conditions that is important to understand. This is where the crystal size distributions (CSD) method becomes fundamentally valuable. Just as chemical thermodynamics offers a quantitative macroscopic means of investigating chemical processes that occur at the atomic level, crystal size distribution theory quantitatively relates the overall observed spectrum of crystal sizes to both the kinetics of crystallization and the physical processes affecting the population of crystals themselves. Petrography, which is the qualitative study of rock textures, is the oldest, most comprehensively developed, and perhaps most beautiful aspect of studying magmatic rocks. It is the ultimate link to the kinetics of crystallization and the integrated space,time history of evolution of every magma. CSD analysis offers a quantitative inroad to unlocking and quantifying the observed textures of magmatic rocks. Perhaps the most stunning feature of crystal-rich magmatic rocks is that the constituent crystal populations show smooth and often quasi-linear log-normal distributions of negative slope when plotted as population density against crystal size. These patterns are decipherable using CSD theory, and this method has proven uniquely valuable in deciphering the kinetics of crystallization of magma. The CSD method has been largely developed in chemical engineering by Randolph and Larson,1,2 among many others, for use in understanding industrial crystallization processes, and its introduction to natural magmatic systems began in 1988. The CSD approach is particularly valuable in its ease of application to complex systems. It is an aid to classical kinetic theory by being, in its purest form, free of any atomistic assumptions regarding crystal nucleation and growth. Yet the CSD method provides kinetic information valuable to understanding the connection between crystal nucleation and growth and the overall cooling and dynamics of magma. It offers a means of investigating crystallization in dynamic systems, involving both physical and chemical processes, independent of an exact kinetic theory. The CSD method applied to rocks shows a systematic and detailed history of crystal nucleation and growth that forms the foundation of a comprehensive and general model of magma solidification. [source] Use of the Rotation Vector in Brownian Dynamics Simulation of Transient Electro-Optical PropertiesMACROMOLECULAR THEORY AND SIMULATIONS, Issue 1 2009Tom Richard Evensen Abstract We have recently developed a new singularity-free algorithm for Brownian dynamics simulation of free rotational diffusion. The algorithm is rigorously derived from kinetic theory and makes use of the Cartesian components of the rotation vector as the generalized coordinates describing angular orientation. Here, we report on the application of this new algorithm in Brownian dynamics simulations of transient electro-optical properties. This work serves two main purposes. Firstly, it demonstrates the integrity of the new algorithm for BD-simulations of the most common transient electro-optic experiments. Secondly, it provides new insight into the performance of the new algorithm compared to algorithms that make use of the Euler angles. We study the transient electrically induced birefringence in dilute solutions of rigid particles with anisotropic polarization tensor in response to external electric field pulses. The use of both one single electric pulse and two electric pulses with opposite polarity are being analyzed. We document that the new singularity-free algorithm performs flawlessly. We find that, for these types of systems, the new singularity-free algorithm, in general, outperforms similar algorithms based on the Euler angles. In a wider perspective, the most important aspect of this work is that it serves as an important reference for future development of efficient BD-algorithms for studies of more complex systems. These systems include polymers consisting of rigid segments with single-segment translational,rotational coupling, segment,segment fluid-dynamic interactions and holonomic constraints. [source] Singularity-Free Brownian Dynamics Analyses of Rotational Dynamics: Non-Spherical Nanoparticles in SolutionMACROMOLECULAR THEORY AND SIMULATIONS, Issue 5 2005Stine Nalum Naess Abstract Summary: From kinetic theory we have rigorously derived singularity-free Brownian dynamics analyses of nanoparticle rotational dynamics. The rigid non-spherical nanoparticles incorporate all three rotational degrees of freedom. This was achieved by using the components of Cartesian rotation vectors as the generalized coordinates describing angular orientation. The new results constitute an important advance compared to the situation when Eulerian angles specify angular orientation. Our finding eliminates one of the main longstanding obstacles to detailed studies of nanoparticle rotational dynamics in the diffusion time domain. The described formalism is applicable to a wide range of nanoparticle systems including liquid crystals, biopolymers, and colloids. [source] A mathematical model of immune competition related to cancer dynamicsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2010Ilaria Brazzoli Abstract This paper deals with the qualitative analysis of a model describing the competition among cell populations, each of them expressing a peculiar cooperating and organizing behavior. The mathematical framework in which the model has been developed is the kinetic theory for active particles. The main result of this paper is concerned with the analysis of the asymptotic behavior of the solutions. We prove that, if we are in the case when the only equilibrium solution if the trivial one, the system evolves in such a way that the immune system, after being activated, goes back toward a physiological situation while the tumor cells evolve as a sort of progressing travelling waves characterizing a typical equilibrium/latent situation. Copyright © 2009 John Wiley & Sons, Ltd. [source] Non-local thermodynamic equilibrium dust nucleation in subsaturated vapoursMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 1 2008Davide Lazzati ABSTRACT We use the kinetic theory of nucleation to explore the properties of dust nucleation in subsaturated vapours. Due to radiation losses, the subcritical clusters have a smaller temperature compared to their vapour. This alters the dynamical balance between the attachment and detachment of monomers, allowing for stable nucleation of grains in vapours that are subsaturated for their temperature. We find this effect particularly important at low densities and in the absence of a strong background radiation field. We find new conditions for stable nucleation in the n,T phase diagram. The nucleation in the non-local thermodynamic equilibrium (non-LTE) regions is likely to be at much slower rate than in the supersaturated vapours. We evaluate the nucleation rate, warning the reader that it does depend on poorly substantiated properties of the macro-molecules assumed in the computation. On the other hand, the conditions for nucleation depend only on the properties of the large stable grains and are more robust. We finally point out that this mechanism may be relevant in the early Universe as an initial dust pollution mechanism, since once the interstellar medium is polluted with dust, mantle growth is likely to be dominant over non-LTE nucleation in the diffuse medium. [source] Experimental and computational study of the bed dynamics of semi-cylindrical gas,solid fluidized bedTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 1 2009A. Sahoo Abstract With computational fluid dynamics (CFD) it is possible to get a detailed view of the flow behaviour of the fluidized beds. A profound and fundamental understanding of bed dynamics such as bed pressure drop, bed expansion ratio, bed fluctuation ratio, and minimum fluidization velocity of homogeneous binary mixtures has been made in a semi-cylindrical fluidized column for gas,solid systems, resulting in a predictive model for fluidized beds. In the present work attempt has been made to study the effect of different system parameters (viz., size and density of the bed materials and initial static bed height) on the bed dynamics. The correlations for the bed expansion and bed fluctuations have been developed on the basis of dimensional analysis using these system parameters. Computational study has also been carried out using a commercial CFD package Fluent (Fluent, Inc.). A multifluid Eulerian model incorporating the kinetic theory for solid particles was applied in order to simulate the gas,solid flow. CFD simulated bed pressure drop has been compared with the experimental bed pressure drops under different conditions for which the results show good agreements. La simulation par ordinateur de la dynamique des fluides (CFD) permet de décrire le comportement des écoulements dans les lits fluidisés. Une étude fondamentale et approfondie de la dynamique de lit, tels la perte de charge de lit, le taux d'expansion de lit, le taux de fluctuation de lit et la vitesse de fluidisation minimale de mélanges binaires homogènes, a été réalisée dans une colonne fluidisée semi-cylindrique pour des systèmes solides de gaz, permettant d'obtenir un modèle prédictif pour les lits fluidisés. Dans le présent travail, on a tenté d'étudier l'effet de différents paramètres de système (à savoir, la taille et la masse volumique des matériaux de lit et la hauteur statique initiale de lit) sur la dynamique de lit. Des corrélations ont été établies pour l'expansion de lit et les fluctuations de lit en s'appuyant sur l'analyse dimensionnelle de ces paramètres de système. Une étude par ordinateur a également été menée à l'aide du logiciel commercial de CFD Fluent (Fluent, Inc.). Un modèle eulérien multifluide faisant appel à la théorie cinétique pour les particules solides a été utilisé afin de simuler l'écoulement gaz-solides. La perte de charge de lit simulée par la CFD a été comparée à la perte de charge de lit expérimentale dans différentes conditions et les résultats montrent un bon accord. [source] An Improved LES on Dense Particle-Liquid Turbulent Flows Using Integrated Boltzmann EquationsTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 2 2007Xuelin Tang Abstract An improved large eddy simulation (LES) using a dynamic second-order subgrid stress (SGS) model has been developed for simulating dense particle-liquid two-phase turbulent flows. The governing equations of each phase are obtained from a microscopic point of view, using the kinetic theory of molecular gas. They are derived by multiplying the Boltzmann equation of each phase by property parameters and integrating over the velocity space. An inter-particle collision term is included in the governing equation of the particle phase. Assuming a Maxwellian distribution of the velocity for particle-phase, an inter-particle collision term is derived. On a amélioré la simulation des grands tourbillons (LES) à l'aide d'un modèle de contraintes dans les mailles inférieures (SGS) de second ordre dynamique afin de simuler des écoulements turbulents diphasiques particules-liquide. Les équations gouvernantes de chaque phase sont obtenues d'un point de vue microscopique, au moyen de la théorie cinétique du gaz moléculaire. Elles sont calculées en multipliant l'équation de Boltzmann de chaque phase par des paramètres de propriétés et en intégrant sur l'intervalle des vitesses. Un terme de collision inter-particulaire est inclus dans l'équation gouvernante de la phase des particules. [source] Wärme- und Feuchtetransport in VakuumisolationspaneelenBAUPHYSIK, Issue 6 2008Andreas Beck Prof. Dr. Wegen ihrer extrem niedrigen Wärmeleitfähigkeit und der damit verbundenen Möglichkeiten, mit geringen Bauteildicken hochwertig zu dämmen, haben Vakuumisolationspaneele (VIP) innerhalb kurzer Zeit Verbreitung im Bauwesen gefunden , insbesondere in Situationen, in denen andere Dämmstoffe aus Platzgründen nicht in Frage kommen. Da noch keine Langzeiterfahrungen über die Alterung der Paneele vorhanden sind, muss beim Bemessungswert der Wärmeleitfähigkeit im Moment allerdings noch mit hohen Sicherheitszuschlägen gerechnet werden, vor allem wegen des über die Nutzungsdauer stattfindenden Gaseintrags. Besonders von Interesse ist hierbei das Verhalten von aus der Umgebung eindiffundierendem Wasserdampf. Während die Auswirkungen von trockenen Gasen genau bezifferbar sind, überlagern sich beim Stoff- und Wärmetransport durch Wasser verschiedene Vorgänge, die die Wärmeleitung im VIP deutlich erhöhen, aber messtechnisch nur schwer erfassbar sind. Daher wurde ein theoretisches Modell entwickelt, das den Wärmestrom auf Grundlage der kinetischen Gastheorie für Molekularströmung und Oberflächendiffusion beschreibt und darüber hinaus Rückschlüsse auf die Diffusionseigenschaften des Kernmaterials zulässt. Heat and Moisture Transport in Vacuum Insulation Panels. Due to their extremely low thermal conductivity, vacuum insulation panels (VIP) allow for high standard thermal insulation with slim building components. Within few years, this led to widespread use especially in building situations where space is limited. As there are no long-term experiences concerning the thermal characteristics of VIPs, however, their rated values of thermal conductivity are notably higher than the actual measured values at present, which primarily represents effects of degradation caused by gases infiltrating the panel. Most significant is the influence of water vapour diffusing into the VIP. Whereas the effects of dry gases are well known and can be exactly quantified, water vapour causes different processes of heat and matter transfer which increase thermal conduction within the VIP considerably, but which cannot be separated accurately by means of measuring. Thus a theoretical model was developed which describes heat flux basing on the kinetic theory of gases for molecular diffusion and surface diffusion. It moreover provides information about the diffusion characteristics of the core material. [source] Anomalous energy transport in the FPU-, chainCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 12 2008Jani Lukkarinen We consider the energy current correlation function for the FPU-, lattice. For small nonlinearity one can rely on kinetic theory. The issue reduces then to a spectral analysis of the linearized collision operator. We prove thereby that, on the basis of kinetic theory, the energy current correlations decay in time as t,3/5. It follows that the thermal conductivity is anomalous, increasing as N2/5 with the system size N. © 2008 Wiley Periodicals, Inc. [source] | |||||||||||||||||||