Geometric Phase and Modulo Relations for Probability Amplitudes as Functions on Complex Parameter Spaces

We investigate general differential relations connecting the respective behavior s of the phase and modulo of probability amplitudes of the form \amp{\psi_f}{\psi}, where $\ket{\psi_f}$ is a fixed state in Hilbert space and $\ket{\psi}$ is a section of a holomorphic line bundle over some complex parameter space. Amplitude functions on such bundles, while not strictly holomorphic, nevertheless satisfy generalized Cauchy-Riemann conditions involving the U(1) Berry-Simon connection on the parameter space. These conditions entail invertible relations between the gradients of the phase and modulo, therefore allowing for the reconstruction of the phase from the modulo (or vice-versa) and other conditions on the behavior of either polar component of the amplitude. As a special case, we consider amplitude functions valued on the space of pure states, the ray space ${\cal R} = {\mathbb C}P^n$, where transition probabilities have a geometric interpretation in terms of geodesic distances as measured with the Fubini-Study metric. In conjunction with the generalized Cauchy-Riemann conditions, this geodesic interpretation leads to additional relations, in particular a novel connection between the modulus of the amplitude and the phase gradient, somewhat reminiscent of the WKB formula. Finally, a connection with geometric phases is established.Comment: 11 pages, 1 figure, revtex

HOSM State Estimation and Robust PID Control of a Chemical Process

This paper presents some results of the authors’ studies on robust estimation and control for chemical processes. Here, an observer-based controller is designed for a chemical process. A High Order Sliding Mode Observer (HOSMO) for state and parameter estimation is synthesized and, a Multi-Variable PID (MV-PID) controller is calculated using the estimated variables. The HOSMO presents insensitivity and robustness against a class of uncertainties in the system, and the MV-PID allows the tracking of slow-varying and piecewise constant references, which are often proposed to drive chemical processes. Numerical simulations show that the observer-based controller presents a good performance in presence of parametric variations, which often are presented in chemical processes; the proposed structure is compared with a First Order Sliding Mode Observer (FOSMO) coupled with a MV-PID.CinvestavUniversidad Nacional de Colombi

Estrategias de control y estimación de estado por modos deslizantes para un horno eléctrico

Este artículo presenta el diseño de un observador por modos deslizantes de segundo orden para una planta con modelo lineal, asumiendo ruido en la variable medida. Adicionalmente se propone un controlador de alto orden por modos deslizantes para una de las variables de estado asociadas al proceso. Para finalizar, se realiza un ejemplo con las respectivas simulaciones. This paper presents the design of a sliding mode observer for a second order linear plant model, assuming noise in the measured variable. Additionally, high order controller for sliding for state variables associated with the process modes is proposed. Finally, an example is made with the respective simulations.Universidad Nacional de ColombiaCINVESTAVColciencia

Influence of MWCNT/surfactant dispersions on the mechanical properties of Portland cement pastes

This work studies the reinforcing effect of Multi Walled Carbon Nanotubes (MWCNT) on cement pastes. A 0.35% solid concentration of MWCNT in powder was dispersed in deionized water with sodium dodecyl sulfate (cationic surfactant), cetylpyridinium chloride (anionic surfactant) and triton X-100 (amphoteric surfactant) using an ultrasonic tip processor. Three concentrations of each surfactant (1mM, 10mM and 100mM) were tested, and all samples were sonicated until an adequate dispersion degree was obtained. Cement pastes with additions of carbon nanotubes of 0.15% by mass of cement were produced in two steps; first the dispersions of MWCNT were combined with the mixing water using an ultrasonic tip processor to guarantee homogeneity, and then cement was added and mixed until a homogeneous paste was obtained. Direct tensile strength, apparent density and open porosity of the pastes were measured after 7 days of curing. It was found that the MWCNT/surfactants dispersions decrease the mechanical properties of the cement based matrix due to an increased porosity caused by the presence of surfactants. © Published under licence by IOP Publishing Ltd

State and Parameter Estimation of a CSTR

In the continuation of authors’ studies on estimation and control for Continuous Stirred-Tank Reactors (CSTR), a new structure to estimate the concentration of reactive state, the global heat transfer coefficient, and the heat of reaction parameters is proposed here. This scheme consist of an Observer Based Estimator (OBE) connected in cascade with a High Order Sliding Mode Observer (HOSMO). The OBE estimates the global heat transfer coefficient, and the HOSMO estimates the heat of reaction, and the concentration of reactive. Numerical simulations show that the whole structure presents a good performance in presence of parametric variations, which often are presented in chemical processes.Universidad Nacional de ColombiaCINVESTA

State and unknown input estimation in a CSTR using higher-order sliding mode observer

The aim of this paper is to design and analyze an observer based on high-order sliding mode to estimate states and unknown inputs in a continuous stirred tank reactor (CSTR). Additionally, the designed HOSM allows to reduce the chattering. The performance of HOSM observer is compared with a 1-order sliding mode observer.ColcienciasUniversidad Nacional de ColombiaCinvesta

Diseño un controlador robusto basado en observador para el modelo lineal de un helicóptero de un grado de libertad (VTOL)

Este artículo propone un controlador basado en observador para un modelo de helicóptero tipo VTOL de un grado de libertad. El objetivo de control es mantener la posición del VTOL en un punto de operación, a pesar de las incertidumbres ocasionadas por inexactitud en el modelo y ruido en las mediciones. El controlador y el observador son diseñados con base en algoritmos que inducen modos deslizantes en el sistema en lazo cerrado, ofreciendo características de robustez y convergencia en tiempo finito. Los resultados de simulación muestran un buen desempeño del esquema propuesto tanto en condiciones de ausencia de ruido como cuando se consideran mediciones ruidosas.Universidad Nacional de ColombiaCinvestavColcienciasBanco Mundia

Predicted Optimum Composition for the Glass-Forming Ability of Bulk Amorphous Alloys: Application to Cu−Zr−Al

Metallic glasses have been established to have unique properties such as ductility, toughness, and soft magnetism with promising engineering applications. However, the glass-forming ability (GFA) has not been sufficient to synthesize the bulk metallic glasses (BMGs) required for many engineering applications. Attempts to develop the understanding of the GFA required to predict the optimum alloys have not yet been proven successful. We develop here a computational model based on molecular dynamics simulations that explains the dramatic change of GFA with alloying small amounts of Al into Cu−Zr. We find that the high GFA to form BMGs depends on a combination of three factors, (a) a low thermodynamic driving force for crystallization, (b) a high melt viscosity, and (c) large ratios of icosahedral structures in the liquid phase. These computational methods to predict these factors that suppress formation of crystal nuclei and slow the dynamic motions in the liquids are practical for in silico prediction of new alloys with optimal GFA