Dynamical Properties and Assembly of Galaxies in the Epoch of Reionization

In a quest for understanding the nature of the furthest galaxies in the Universe, a large amount of effort has been expended to build large telescopes as well as to perform sophisticated cosmological simulations. Despite these achievements, we still know little about the structural and dynamical properties of star-forming galaxies belonging to the epoch when the age of the Universe was less than a Giga year i.e. the Epoch of Reionization (EoR). Indeed, galaxy dynamics in such a distant universe is an uncharted field and we do not have solid answers to several fundamental questions about the structure of EoR galaxies: 1- What are the dynamical and morphological properties of EoR galaxies? 2- Do we expect galaxies to form their disk structure as early as the EoR? 3- Are there any signatures of galaxy-galaxy mergers in such early epochs? 4- Are EoR galaxies rotationally supported or dispersion-dominated systems? 5- What is the energy source powering the gas velocity dispersion in EoR galaxies? Atacama Large Millimeter/submillimeter Array (ALMA), being the most powerful millimeter/ sub-millimeter interferometer on Earth, has been playing a revolutionary role in the field of high-z galaxy dynamics by providing spatially-resolved emission-line observations. However, as we aim at studying the first galaxies that appeared in the Universe, the limiting angular resolutions and signal-to-noise ratio of the observations significantly limit such studies. These limitations can be overcome either by performing deeper observations or targeting lensed galaxies. While waiting for such high-quality data to be available for EoR galaxies, we can address the problem theoretically. This Thesis focuses on the study of structural and dynamical properties of EoR galaxies by utilizing analytical modelings (when possible) as well as state-of-the-art hydrodynamical simulations of galaxies. Since our aim is to provide a solid comparison and/or prediction for the upcoming observations, we develop a framework in which a common cross-talk among observations and pure theoretical works becomes possible. The Thesis is structured as follows: 1- In Chapter 1, we give the reader the necessary theoretical and observational background information to follow the whole Thesis. A brief review of the conventional galaxy formation in the context of the standard model of cosmology is followed by explaining the current status of observations of distant galaxies with particular attention to the EoR. 2- In Chapter 2, we introduce the ISM physics including far-infrared (FIR) line emissions, then we introduce semi-analytical models of galaxies that we have developed to get the first insights on the properties of [C II] emission line coming from high-z galaxies either as the kinematics or star formation tracer. We end this Chapter by explaining the modeling features of a suite of hydrodynamical simulations used in the rest of the Thesis. 3- In Chapter 3, we explore different kinematical features of EoR galaxies and their connection with the assembly process as imprinted in the FIR line emission profiles. This is achieved by tracing the evolution of a simulated galaxy from z = 7 to z = 6 through the FIR [C II] emission. 4- In Chapter 4, we study the structure of spatially resolved, line-of-sight velocity dispersion in EoR galaxies traced by [C II] line emission in the redshift range of 6 < z < 8. We also quantify the contribution of the different energy sources powering such velocity dispersions in EoR galaxies. 5- In Chapter 5, we address one of the recent puzzling issues in high-z galaxy dynamics studies, which is related to the observations of surprisingly cold galactic disks at high redshift universe. This problem is addressed by studying the dynamical properties of a large sample of simulated EoR galaxies in the redshift range of 6 ≤ z < 9 probed by [C II] and nebular Hα emission. 6- Finally in Chapter 6, we present the conclusions and the future prospects

Stochastic Model for Tumor Control Probability: Effects of Cell Cycle and (A)symmetric Proliferation

Estimating the required dose in radiotherapy is of crucial importance since the administrated dose should be sufficient to eradicate the tumor and at the same time should inflict minimal damage on normal cells. The probability that a given dose and schedule of ionizing radiation eradicates all the tumor cells in a given tissue is called the tumor control probability (TCP), and is often used to compare various treatment strategies used in radiation therapy. In this paper, we aim to investigate the effects of including cell-cycle phase on the TCP by analyzing a stochastic model of a tumor comprised of actively dividing cells and quiescent cells with different radiation sensitivities. We derive an exact phase-diagram for the steady-state TCP of the model and show that at high, clinically-relevant doses of radiation, the distinction between active and quiescent tumor cells (i.e. accounting for cell-cycle effects) becomes of negligible importance in terms of its effect on the TCP curve. However, for very low doses of radiation, these proportions become significant determinants of the TCP. Moreover, we use a novel numerical approach based on the method of characteristics for partial differential equations, validated by the Gillespie algorithm, to compute the TCP as a function of time. We observe that our results differ from the results in the literature using similar existing models, even though similar parameters values are used, and the reasons for this are discussed.Comment: 12 pages, 5 figure

Phenotypic heterogeneity in modeling cancer evolution

The unwelcome evolution of malignancy during cancer progression emerges through a selection process in a complex heterogeneous population structure. In the present work, we investigate evolutionary dynamics in a phenotypically heterogeneous population of stem cells (SCs) and their associated progenitors. The fate of a malignant mutation is determined not only by overall stem cell and differentiated cell growth rates but also differentiation and dedifferentiation rates. We investigate the effect of such a complex population structure on the evolution of malignant mutations. We derive exact analytic results for the fixation probability of a mutant arising in each of the subpopulations. The analytic results are in almost perfect agreement with the numerical simulations. Moreover, a condition for evolutionary advantage of a mutant cell versus the wild type population is given in the present study. We also show that microenvironment-induced plasticity in invading mutants leads to more aggressive mutants with higher fixation probability. Our model predicts that decreasing polarity between stem and differentiated cells turnover would raise the survivability of non-plastic mutants; while it would suppress the development of malignancy for plastic mutants. We discuss our model in the context of colorectal/intestinal cancer (at the epithelium). This novel mathematical framework can be applied more generally to a variety of problems concerning selection in heterogeneous populations, in other contexts such as population genetics, and ecology.Comment: 28 pages, 7 figures, 2 table

On the Newtonian Anisotropic Configurations

In this paper we are concerned with the effects of anisotropic pressure on the boundary conditions of anisotropic Lane-Emden equation and homology theorem. Some new exact solutions of this equation are derived. Then some of the theorems governing the Newtonian perfect fluid star are extended taking the anisotropic pressure into account

Mathematical Model of the Effect of Interstitial Fluid Pressure on Angiogenic Behavior in Solid Tumors

We present a mathematical model for the concentrations of proangiogenic and antiangiogenic growth factors, and their resulting balance/imbalance, in host and tumor tissue. In addition to production, diffusion, and degradation of these angiogenic growth factors (AGFs), we include interstitial convection to study the locally destabilizing effects of interstitial fluid pressure (IFP) on the activity of these factors. The molecular sizes of representative AGFs and the outward flow of interstitial fluid in tumors suggest that convection is a significant mode of transport for these molecules. The results of our modeling approach suggest that changes in the physiological parameters that determine interstitial fluid pressure have as profound an impact on tumor angiogenesis as those parameters controlling production, diffusion, and degradation of AGFs. This model has predictive potential for determining the angiogenic behavior of solid tumors and the effects of cytotoxic and antiangiogenic therapies on tumor angiogenesis