Kinetic modeling for the synthesis of ethyl levulinate

This work is focused on studying the kinetics of esterification of levulinic acid in an isothermal batch reactor using ethanol as a reactant and as a protic polar solvent at the same time and in the presence of an acid catalyst (sulfuric acid). The choice of solvent is important as it affects the kinetics and thermodynamics of the reaction system moreover, the knowledge of the reaction kinetics plays an important role in the design of the process. This work is divided into two stages; The first stage is the experimental part in which the experimental matrix was developed by changing the process variables one at a time (temperature, molar ratio between reactants, and catalyst concentration) in order to study their influence on the kinetics; the second stage is using the obtained data from the experiments to build the modeling part in order to estimate the thermodynamics parameters.

Mathematical Modeling to Investigate Antiarrhythmic Drug Side Effects: Rate-Dependence Role in Ionic Currents and Action Potentials Shape in the O’Hara Model

Sudden cardiac death due to ventricular arrhythmia is one of the leading causes of mortality in the world. In the last decades, it has proven that anti-arrhythmic drugs, which prolong the refractory period by means of prolongation of the cardiac action potential duration (APD), play a good role in preventing of relevant human arrhythmias. However, it has long been observed that the “class III antiarrhythmic effect” diminish at faster heart rates and that this phenomenon represent a big weakness, since it is the precise situation when arrhythmias are most prone to occur. It is well known that mathematical modeling is a useful tool for investigating cardiac cell behavior. In the last 60 years, a multitude of cardiac models has been created; from the pioneering work of Hodgkin and Huxley (1952), who first described the ionic currents of the squid giant axon quantitatively, mathematical modeling has made great strides. The O’Hara model, that I employed in this research work, is one of the modern computational models of ventricular myocyte, a new generation began in 1991 with ventricular cell model by Noble et al. Successful of these models is that you can generate novel predictions, suggest experiments and provide a quantitative understanding of underlying mechanism. Obviously, the drawback is that they remain simple models, they don’t represent the real system. The overall goal of this research is to give an additional tool, through mathematical modeling, to understand the behavior of the main ionic currents involved during the action potential (AP), especially underlining the differences between slower and faster heart rates. In particular to evaluate the rate-dependence role on the action potential duration, to implement a new method for interpreting ionic currents behavior after a perturbation effect and to verify the validity of the work proposed by Antonio Zaza using an injected current as a perturbing effect.

A Phase Space Box-counting based Method for Arrhythmia Prediction from Electrocardiogram Time Series

Arrhythmia is one kind of cardiovascular diseases that give rise to the number of deaths and potentially yields immedicable danger. Arrhythmia is a life threatening condition originating from disorganized propagation of electrical signals in heart resulting in desynchronization among different chambers of the heart. Fundamentally, the synchronization process means that the phase relationship of electrical activities between the chambers remains coherent, maintaining a constant phase difference over time. If desynchronization occurs due to arrhythmia, the coherent phase relationship breaks down resulting in chaotic rhythm affecting the regular pumping mechanism of heart. This phenomenon was explored by using the phase space reconstruction technique which is a standard analysis technique of time series data generated from nonlinear dynamical system. In this project a novel index is presented for predicting the onset of ventricular arrhythmias. Analysis of continuously captured long-term ECG data recordings was conducted up to the onset of arrhythmia by the phase space reconstruction method, obtaining 2-dimensional images, analysed by the box counting method. The method was tested using the ECG data set of three different kinds including normal (NR), Ventricular Tachycardia (VT), Ventricular Fibrillation (VF), extracted from the Physionet ECG database. Statistical measures like mean (μ), standard deviation (σ) and coefficient of variation (σ/μ) for the box-counting in phase space diagrams are derived for a sliding window of 10 beats of ECG signal. From the results of these statistical analyses, a threshold was derived as an upper bound of Coefficient of Variation (CV) for box-counting of ECG phase portraits which is capable of reliably predicting the impeding arrhythmia long before its actual occurrence. As future work of research, it was planned to validate this prediction tool over a wider population of patients affected by different kind of arrhythmia, like atrial fibrillation, bundle and brunch block, and set different thresholds for them, in order to confirm its clinical applicability.

Pricing in stochastic-local volatility models with default

In recent years is becoming increasingly important to handle credit risk. Credit risk is the risk associated with the possibility of bankruptcy. More precisely, if a derivative provides for a payment at cert time T but before that time the counterparty defaults, at maturity the payment cannot be effectively performed, so the owner of the contract loses it entirely or a part of it. It means that the payoff of the derivative, and consequently its price, depends on the underlying of the basic derivative and on the risk of bankruptcy of the counterparty. To value and to hedge credit risk in a consistent way, one needs to develop a quantitative model. We have studied analytical approximation formulas and numerical methods such as Monte Carlo method in order to calculate the price of a bond. We have illustrated how to obtain fast and accurate pricing approximations by expanding the drift and diffusion as a Taylor series and we have compared the second and third order approximation of the Bond and Call price with an accurate Monte Carlo simulation. We have analysed JDCEV model with constant or stochastic interest rate. We have provided numerical examples that illustrate the effectiveness and versatility of our methods. We have used Wolfram Mathematica and Matlab.