Global convergence of the nonmonotone MBFGS method for nonconvex unconstrained minimization

AbstractIn this paper, we propose a new nonmonotone Armijo type line search and prove that the MBFGS method proposed by Li and Fukushima with this new line search converges globally for nonconvex minimization. Some numerical experiments show that this nonmonotone MBFGS method is efficient for the given test problems

Some remarks on the Navier-Stokes equations with regularity in one direction

summary:We review the developments of the regularity criteria for the Navier-Stokes equations, and make some further improvements

Approche thermodynamique pour la commande d’un système non linéaire de dimension infinie : application aux réacteurs tubulaires

The main objective of this thesis consists to investigate the problem of modelling and control of a nonlinear parameter distributed thermodynamic system : the tubular reactor. We address the control problem of this non linear system relying on the thermodynamic properties of the process. This approach requires to use the classical extensive variables as the state variables. We use the thermodynamic availability as well as the reduced thermodynamic availability (this function is formed from some terms of the thermodynamic availabilty) as Lyapunov functions in order to asymptotically stabilize the tubular reactor aroud a steady profile. The distributed temperature of the jacket is the control variable. Some simulations illustrate these results as well as the eficiency of the control in presence of perturbations. Next we study the Port Hamiltonian representation of irreversible infinite dimensional systems. We propose a Stokes-Dirac structure of a reaction-diffusion system by means of the extension of the vectors of the flux and effort variables. We illustrate this approach on the example of the reaction-diffusion system. For this latter we use the internal energy as well as the opposite of the entropy to obtain Stokes-Dirac structures. We propose also a pseudo-Hamiltonian representation for the two Hamiltonians. Finally we tackle the boundary control problem. The objective is to study the existence of solutions associated to a linearized model of the tubular reactor controlled to the boundaryLe travail présenté dans cette thèse porte sur la modélisation et la commande d'un système thermodynamique non linéaire de dimension infinie, le réacteur tubulaire. Nous abordons le problème de commande sur ce système non linéaire en nous appuyant sur les propriétés thermodynamiques du procédé. Cette approche nécessite l'utilisation d'un modèle ayant comme variables d'état les variables extensives thermodynamiques classiques. Nous utilisons la fonction de disponibilité thermodynamique ainsi qu'une autre fonction déduite de la précédente, la disponibilité réduite, comme fonction de Lyapunov candidate pour résoudre le problème de stabilisation du réacteur autour d'un profil d'équilibre en utilisant comme commande distribuée la température de la double enveloppe. Des simulations illustrent ces résultats ainsi que l'efficacité des commandes en présence de perturbations. Nous nous intéressons aussi à la représentation hamiltonienne à port des systèmes irréversibles de dimension infinie. La structure de Stokes-Dirac pour un modèle réaction diffusion est obtenue en étendant les vecteurs de variables de flux et d'effort. Nous présentons cette démarche pour les équations du système réaction-diffusion en prenant premièrement l'énergie interne comme Hamiltonien puis deuxièmement l'opposé de l'entropie. Nous montrons dans les deux cas qu'en utilisant une extension des couples de variables effort-flux thermodynamiques classiques nous obtenons une structure de Stokes-Dirac. Enfin nous donnons quelques résultats aboutissant à une représentation pseudo hamiltonienne. Enfin nous abordons le problème de commande à la frontière. L'objectif est d'étudier l'existence de solutions associées à un modèle linéarisé de réacteur tubulaire complet commandé à la frontièr

Quantifying the short-term dynamics of soil organic carbon decomposition using a power function model

Introduction Soil heterotrophic respiration (R h, an indicator of soil organic carbon decomposition) is an important carbon efflux of terrestrial ecosystems. However, the dynamics of soil R h and its empirical relations with climatic factors have not been well understood. Methods We incubated soils of three subtropical forests at five temperatures (10, 17, 24, 31, and 38 °C) and five moistures (20, 40, 60, 80, and 100% water holding capacity (WHC)) over 90 days. R h was measured throughout the course of the incubation. Three types of models (log-linear, exponential, and power model) were fitted to the measurements and evaluated based on the coefficient of determination (r 2) and Akaike Information Criterion (AIC) of the model. Further regression analysis was used to derive the empirical relations between model parameters and the two climatic factors. Results Among the three models, the power function model (R h = R 1 t −k) performed the best in fitting the descending trend of soil R h with incubation time (r 2 \u3e 0.69 for 26 of 30 models). Both R 1 and k generally increased linearly with soil temperature but varied quadratically with soil moisture in the three forest soils. Conclusions This study demonstrated that the power function model was much more accurate than the exponential decay model in describing the decomposition dynamics of soil organic carbon (SOC) in mineral soils of subtropical forests. The empirical relations and parameter values derived from this incubation study may be incorporated into process-based ecosystem models to simulate R h responses to climate changes

Towards Efficient and Accurate Approximation: Tensor Decomposition Based on Randomized Block Krylov Iteration

Efficient and accurate low-rank approximation (LRA) methods are of great significance for large-scale data analysis. Randomized tensor decompositions have emerged as powerful tools to meet this need, but most existing methods perform poorly in the presence of noise interference. Inspired by the remarkable performance of randomized block Krylov iteration (rBKI) in reducing the effect of tail singular values, this work designs an rBKI-based Tucker decomposition (rBKI-TK) for accurate approximation, together with a hierarchical tensor ring decomposition based on rBKI-TK for efficient compression of large-scale data. Besides, the error bound between the deterministic LRA and the randomized LRA is studied. Numerical experiences demonstrate the efficiency, accuracy and scalability of the proposed methods in both data compression and denoising

Infinite Dimensional Port Hamiltonian Representation of Chemical Reactors

International audienceInfinite dimensional Port Hamiltonian representation of non isothermal chemical reactors is proposed in the case of mass transport diffusion and chemical reaction without convection. The proposed approach uses thermodynamic variables. The presentation is given for one dimensional spatial domain by using the internal energy and the opposite of the entropy as hamiltonian functions

Cosmic-ray-mediated Formation of Benzene on the Surface of Saturn's Moon Titan

The aromatic benzene molecule (C_6H_6)—a central building block of polycyclic aromatic hydrocarbon molecules—is of crucial importance for the understanding of the organic chemistry of Saturn's largest moon, Titan. Here, we show via laboratory experiments and electronic structure calculations that the benzene molecule can be formed on Titan's surface in situ via non-equilibrium chemistry by cosmic-ray processing of low-temperature acetylene (C_2H_2) ices. The actual yield of benzene depends strongly on the surface coverage. We suggest that the cosmic-ray-mediated chemistry on Titan's surface could be the dominant source of benzene, i.e., a factor of at least two orders of magnitude higher compared to previously modeled precipitation rates, in those regions of the surface which have a high surface coverage of acetylene