Finite strain Landau theory of high pressure phase transformations

The properties of materials near structural phase transitions are often successfully described in the framework of Landau theory. While the focus is usually on phase transitions, which are induced by temperature changes approaching a critical temperature T-c, here we will discuss structural phase transformations driven by high hydrostatic pressure, as they are of major importance for understanding processes in the interior of the earth. Since at very high pressures the deformations of a material are generally very large, one needs to apply a fully nonlinear description taking physical as well as geometrical nonlinearities (finite strains) into account. In particular it is necessary to retune conventional Landau theory to describe such phase transitions. In Troster et al (2002 Phys. Rev. Lett. 88 55503) we constructed a Landau-type free energy based on an order parameter part, an order parameter-(finite) strain coupling and a nonlinear elastic term. This model provides an excellent and efficient framework for the systematic study of phase transformations for a wide range of materials up to ultrahigh pressures

Dynamic optimization of a gas-liquid reactor

The final publication is available at Springer via http://dx.doi.org/10.1007/s10910-011-9941-1A dynamic gas-liquid transfer model without chemical reaction based on unsteady film theory is considered. In this case, the mathematical model presented for gas-liquid mass-transfer processes is based on mass balances of the transferred substance in both phases. The identificability property of this model is studied in order to confirm the possible identifiable parameters of the model from a given set of experimental data. For that, a different modeled of the system is given. A procedure for the identification is proposed. On the other hand, the aim of this work is to solve the quadratic optimal control problem, using an explicit representation of the model. The problem includes some results on controllability, observability and stability criteria and the relation between these properties and the parameters of the model. Using the optimal control problem we study the stability of the system and show how the choice of the weighting matrices can improve the behavior of the system but with an increase of the energy control cost. © 2011 Springer Science+Business Media, LLC.This work has been partially supported by PAID-05-10-003-295 and by MTM2010-18228.Cantó Colomina, B.; Cardona Navarrete, SC.; Coll, C.; Navarro-Laboulais, J.; Sánchez, E. (2012). Dynamic optimization of a gas-liquid reactor. Journal of Mathematical Chemistry. 50(2):381-393. https://doi.org/10.1007/s10910-011-9941-1S381393502Bayón L., Grau J.M., Ruiz M.M., Suárez P.M.: Initial guess of the solution of dynamic optimization of chemical processes. J. Math. Chem. Model. 48, 28–37 (2010)Ben-Zvi A., McLellan P.J., McAuley K.B.: Ind. Eng. Chem. Res. 42, 6607–6618 (2003)Cantó B., Coll C., Sánchez E.: Structural identifiability of a model of dialysis. Math. Comp. Model. 50, 733–737 (2009)Cantó B., Coll C., Sánchez E.: Identifiability of a class of discretized linear partial differential algebraic equations. Math. Probl. Eng. 2011, 1–12 (2011)Craciun G., Pantea C.: Identifiability of chemical reaction networks. J. Math. Chem. 44, 244–259 (2008)Dai L.: Descriptor Control Systems. Springer, New York (1989)Deckwer W.D.: Bubble Column Reactors. Wiley, Chichester (1992)Kantarci N., Borak F., Ulgen K.O.: Bubble column reactors. Proc. Biochem. 40(7), 2263–2283 (2005)Kawakernaak H., Sivan R.: Linear Optimal Control Systems. Wiley-Interscience, New York (1972)Kuo B.C.: Automatic Control Systems, 6th edn. Prentice-Hall, Englewood Cliffs (1991)Navarro-Laboulais J., Cardona S.C., Torregrosa J.I., Abad A., López F.: Practical identifiability analysis in dynamic gas-liquid reactors. Optimal experimental design for mass-transfer parameters determination. Comp. Chem. Eng. 32, 2382–2394 (2008)Navarro-Laboulais J., López F., Torregrosa J.I., Cardona S.C., Abad A.: Transient response, model structure and systematic errors in hybrid respirometers: structural identifiabilit analysis based on OUR and DO measurements. J. Math. Chem. 44(4), 969–990 (2007)Patel R., Munro N.: Multivariable Systen. Theory and Design. Pergamon Press, New York (1982)Sondergeld K.: A generalization of the Routh–Hurwitz stability criteria and a application to a problem in robust controller design. IEEE Trans. Automat. Contr. AC-28(10), 965–970 (1983