Numerical Simulations for Optimal Control of a Cancer Cell Model With Delay

Mathematical models are often created to analyze the complicated behavior of many physical systems. One such system is that of the interaction between cancer cells, the immune system, and various treatments such as chemotherapy, radiation, and immunotherapy. Using models that depict these relationships gives researchers insight on the dynamics of this complicated system and possibly ideas for improved treatment schedules. The model presented here gives the relationship of cancer cells in development phases with immune cells and cycle-specific chemotherapy treatment. This model includes a constant delay term in the mitotic phase. Optimal control theory is used to minimize the cost of the chemotherapy and the number of cancer cells. Numerical methods, such as a forward-backward sweep method and adjusted methods to evaluate delays, are used to show qualitative treatment options

Evaluation of VOC Degradation in Photo-Catalytic Air Reactors: TiO2 Immobilization, Energy Efficiency and Kinetic Modeling

The high VOC emissions from anthropogenic sources are detrimental to both the environment and humans, contributing with ground-level ozone and particle matter formation. Heterogeneous photocatalysis provides significant potential for VOC degradation. However, the approaches to be used for photocatalyst immobilization in scaled and highly efficient photoreactors are still not well established. Furthermore, there is a lack of reported photonic efficiencies and a shortage of required methods to establish these efficiencies. To address these issues, this PhD Dissertation reports the study of photonic efficiencies, TiO2 immobilization on a stainless steel mesh and kinetic models in a scaled-up Photo-CREC-Air Reactor. Acetone and acetaldehyde are considered with a 25-320 initial concentration range. The irradiation field is experimentally evaluated in order to estimate the photon absorption on the TiO2 film through macroscopic balances. Quantum Yields (QYs) and Photochemical Thermodynamic Efficiency Factors (PTEFs) are also established. TiO2 coatings are prepared using two methods: an Air Assisted Spray with an Automatized Spinning Coating (TiO2-AAS-ASC) and a Spread Coating (TiO2-SCM). TiO2-AAS-ASC shows a more efficient use of the photocatalyst than the TiO2-SCM, and also displays homogeneity, limited particle agglomeration and stability under flow. Moreover, the TiO2-AAS-ASC shows a high degree of photonic energy utilization. A series-parallel Langmuir-Hinshelwood based kinetic model describes the photodegradation of acetone and acetaldehyde data well with a 0.97-0.98 range correlation coefficient. It is believed that altogether the approach reported in the present PhD Dissertation contributes to clarify key engineering issues of significant value for the scale-up of photocatalytic reactors for air treatment

Exact monopole instantons and cosmological solutions in string theory from abelian dimensional reduction

We compute the exact string vacuum backgrounds corresponding to the non-compact coset theory $SU(2,1)/SU(2)$. The conformal field theory defined by the level $k= 4$ results in a five dimensional singular solution that factorizes in an asymptotic region as the linear dilaton solution and a $S^3$ model. It presents two abelian compact isometries that allow to reinterpreting it from a four dimensional point of view as a stationary and magnetically charged space-time resembling in some aspects the Kerr-Newman solution of general relativity. The $k=\frac{13}{7}$ theory on the other hand describes a cosmological solution that interpolates between a singular phase at short times and a $S^1 \times S^2$ universe after some planckian times.Comment: 18 pages, section 5 replaced by 5 and 6, references added; to appear in Phys. Rev.

SO(3) \times U(1) isometric instantons with non abelian hair in four dimensional string theory

We compute the exact effective string vacuum backgrounds of the level $k = 81/19 SU(2,1)/U(1)$ coset model. A compact SU(2) isometry present in this seven dimensional solution allows to interpreting it after compactification as a four dimensional non-abelian SU(2) charged instanton with a singular submanifold and an $SO(3) \times U(1)$ isometry. The semiclassical backgrounds, solutions of the type II strings, present similar characteristics.Comment: 12 pages, latex fil

Principios matem?ticos de los hiperreales.

66 P?ginasRecurso Electr?nicoSe introducen los hiperreales por medio de la llamada construcci?n del ultrafiltro. Se parte del concepto conjuntista de hiperextensi?n, para mostrar luego las ventajas que la l?gica proporciona al estudio de los hiperreales. Se realiza, as? mismo, una aplicaci?n de la teor?a obtenida al estudio de la continuidad y la diferenciabilidad de las funciones univariadas reales. Tambi?n se trata brevemente la convergencia de las sucesiones de n?meros reales con ayuda de los infinitesimales.Abstract. We present a construction of the hyperreals by means of ultrafilters. We depart from the set-theoretic concept of hyperextension and then show the benefits provided by Logic to the study of hyperreals. Furthermore, we perform an application of the theory to the study of continuity and differentiability of real univariate functions. In this framework, we briefly discuss the convergence of sequences of real numbers.Introducci?n 8 1. Hiperextensiones 11 1.1. Definici?n11 1.2. Consecuencias para los subconjuntos 13 1.3. Consecuencias para las funciones16 1.4. Una consecuencia para las relaciones 22 2. Existencia 24 2.1. Definici?n 24 2.2. Ultrafiltros 25 2.3. Ultraproductos 27 2.4. Teorema fundamental 27 3. Transferencia 33 3.1. F?rmulas l?gicas 33 3.2. Principio de transferencia 35 4. Hiperreales 41 4.1. ?R es un cuerpo ordenado 41 4.1.1. Axiomas de cuerpo 42 4.1.2. Axiomas de orden y de compatibilidad 42 4.2. Par?ntesis sobre ultrafiltros 43 4.3. Infinitesimales e infinitos 44 5. An?lisis infinitesimal 48 5.1. Algunas propiedades algebraicas 48 5.2. Algunas propiedades topol?gicas 49 5.3. Diferenciaci?n 54 5.4. Sucesiones 59 Conclusiones 62 Bibliograf?a 6

Gravitating sphalerons and sphaleron black holes in asymptotically anti-de Sitter spacetime

Numerical arguments are presented for the existence of spherically symmetric regular and black hole solutions of the EYMH equations with a negative cosmological constant. These solutions approach asymptotically the anti-de Sitter spacetime. The main properties of the solutions and the differences with respect to the asymptotically flat case are discussed. The instability of the gravitating sphaleron solutions is also proven.Comment: 30 pages, LaTeX, 8 Encapsulated PostScript figure

Aerodynamic Shape Multi-Objective Optimization for SAE Aero Design Competition Aircraft

The SAE Regular Class Aero Design Competition requires students to design a radio-controlled aircraft with limits to the aircraft power consumption, take-off distance, and wingspan, while maximizing the amount of payload it can carry. As a result, the aircraft should be designed subject to these simultaneous and contradicting objectives: 1) minimize the aerodynamic drag force, 2) minimize the aerodynamic pitching moment, and 3) maximize the aerodynamic lift force. In this study, we optimized the geometric design variables of a biplane configuration using 3D aerodynamic analysis using the ANSYS Fluent. Coefficients of lift, drag, and pitching moment were determined from the completed 3D CFD simulations. Extracted coefficients were used in modeFRONTIER multi-objective optimization software to find a set of non-dominated (Pareto-optimal or best trade-off) optimized 3D aircraft shapes from which the winner was selected based to the desired plane performance

Gauge invariant perturbation theory and non-critical string models of Yang-Mills theories

We carry out a gauge invariant analysis of certain perturbations of $D-2$-branes solutions of low energy string theories. We get generically a system of second order coupled differential equations, and show that only in very particular cases it is possible to reduce it to just one differential equation. Later, we apply it to a multi-parameter, generically singular family of constant dilaton solutions of non-critical string theories in $D$ dimensions, a generalization of that recently found in arXiv:0709.0471[hep-th]. According to arguments coming from the holographic gauge theory-gravity correspondence, and at least in some region of the parameters space, we obtain glue-ball spectra of Yang-Mills theories in diverse dimensions, putting special emphasis in the scalar metric perturbations not considered previously in the literature in the non critical setup. We compare our numerical results to those studied previously and to lattice results, finding qualitative and in some cases, tuning properly the parameters, quantitative agreement. These results seem to show some kind of universality of the models, as well as an irrelevance of the singular character of the solutions. We also develop the analysis for the T-dual, non trivial dilaton family of solutions, showing perfect agreement between them.Comment: A new reference added