O câncer (neoplasia) é uma das principais causas de mortalidade no mundo. Apesar dos grandes avanços no diagnóstico e nas formas de tratamento, ele ainda representa um enorme desafio para os pesquisadores de muitas áreas. Recentemente houve uma importante descoberta que poderá fornecer um paradigma completamente diferente no entendimento de como o câncer se inicia e cresce, com eventualmente profundas consequências nas formas de tratamento. Essa descoberta diz respeito a presença de células tronco adultas em tumores e seu possível papel no surgimento e crescimento destes. Propomos nesse trabalho um modelo matemático que considera a presença de células com propriedades de (a) auto renovação , (b) diferenciação e (c) mobilidade , características das células tronco. O modelo proposto é um autômato celular probabilístico com atualização assíncrona em uma rede. Cada elemento da rede pode estar vazio ou conter uma célula tumoral. Há dois tipos de células: as células rotuladas como do tipo 2 que são aquelas associadas com as células tronco tumorais e aquelas rotuladas como do tipo 1 que são as células diferenciadas, somente com capacidade de reprodução. A taxa de reprodução de cada célula é definida como uma função de sua vizinhança e tipo. Diferentes taxas de reprodução foram usadas nas simulações e as células do tipo 2 podem diferenciar-se ou mover-se. Os resultados das simulações mostram como a motilidade das células 2 e as taxas de reprodução de ambos os tipos de células influenciam os padrões morfológicos do tumor. Também investigamos uma possível transição de fase que pode estar relacionada a metástase. Essa transição de fase representa algo de grande interesse biológico, uma vez que a metástase é o mecanismo mais importante que leva o organismo a óbito. Compararemos nossos resultados com dados experimentais dos colaboradores Nascimento TL et al [1] da UNIFESP- Escola Paulista de Medicina. / Cancer (neoplasia) is one of the most dangerous diseases and one of the main cause of mortality around the world. Despite the great advances in diagnosis and treatment, it still represents a huge challenge to researchers of many areas. Recently there was a strinking discovery that may give rise to a complete different paradigm in the understanding of how cancer starts and grows, with eventually profound consequences in the forms of treatment. It is related to the ending of adult stem cells in tumors, and its possible role in the birth and growth of them. We propose in this work a mathematical model that takes into account the presence of cells with the properties of (a) self renewal, (b) differentiation and (c) mobility, characteristics of stem cells. The model developed is a probabilistic cellular automaton with asynchronous update set in a grid. Each element of the grid may be empty or contain a tumor cell. There are two types of cells: the cells labeled as type 2 are those associated with cancer stem cells and those labeled as type 1 are differentiated cells only capable of reproducing. The reproduction rate of each cell is defined as a function of its neighborhood and its type. Different rates of reproduction have been used in the simulations, and type 2 cells may differentiate and some motility. Our simulation results show how the motility of cells 2 and the reproduction rates of both types of cells influence the morphological patterns of tumor. We have also investigated a possible phase transition that may be related to metastasis. This phase transition represents something of great biological interest because metastasis is the most important mechanism that leads to death. We will compare our results with experimental data from collaborators Nascimento TL et al [1] in UNIFESP-Escola Paulista de Medicina.

Doctor of Philosophy / Department of Physics / Talat S. Rahman / This dissertation is an extensive study of several issues related to post deposition morphological evolution of fcc metal surfaces. These studies were carried out by probing the energetics and the dynamics of underlying atomistic mechanisms responsible for surface diffusion. An important aspect is the determination of relative probability of competing atomistic mechanisms and their contribution to controlling shapes and step edge patterns of nano structures on surfaces. In this scenario, the descent of adatoms from Ag islands on Ag(111) surface is examined. It shows an exchange mechanism to dominate over hopping and the process to favor the formation of (100)-microfacetted steps (A-type) over the (111)-microfacetted ones (B-type). Molecular dynamics simulations support these results at low temperature while at high temperature B-type step formation dominates. This change in the trend could happen if these processes leading to the formation of the A and B type steps have different values of their diffusion prefactors. This difference is confirmed on the basis of our calculations of the diffusion coefficients. Further, to understand the macroscopic properties of a system on the basis of its atomic scale information, spatial and temporal fluctuations of step edges on vicinal Cu(1 1 13) and Cu(1 1 19) surfaces is studied using kinetic Monte Carlo (KMC) simulations. These results show excellent agreement with experimental data, highlighting the role of mass transport along step edges, and also showing the validity of tools like KMC which aims at bridging the gap in length and time scales at which a range of interesting phenomena take place. To facilitate unbiased modeling of material properties, a novel way of performing KMC simulations is presented. In this approach the lists of diffusion processes are automatically collected during the simulation using a saddle-point search method in the potential energy landscape. The speed of the simulations is thus enhanced along with a substantial gain in reliability. Using this method the diffusion and coalescence of two-dimensional Cu and Ag adatom-island on Cu(111) and Ag(111) is studied. Together with input from molecular dynamics simulations, new processes involving the concerted motion of smaller islands are revealed. A significant difference in the scaling of the effective diffusion barriers with island size is observed for the sets of smaller (less than 10 atoms) and larger islands. In particular, the presence of concerted island motion leads to an almost linear increase in the effective diffusion barrier with size, while its absence accounts for strong size-dependent oscillations and anomalous behavior for trimers and heptamers. A crossover from diffusion due to the collective motion of the smaller island to a regime in which the island diffuses through the periphery dominated mass transport (large islands, 19 to 100 atoms) is predicted. For islands containing 19 to 100 atoms the scaling exponent is found to be in good agreement with that found in previous studies.

This thesis is devoted to the study of excitations in atomic and polariton Bose-Einstein condensates (BEC). These two specimens are prime examples for equilibrium and non equilibrium BEC. The corresponding condensate wave function of each system satisfies a particular partial differential equation (PDE). These PDEs are discussed in the beginning of this thesis and justified in the context of the quantum many-body problem. For high occupation numbers and when neglecting quantum fluctuations the quantum field operator simplifies to a semiclassical wave. It turns out that the interparticle interactions can be simplified to a single parameter, the scattering length, which gives rise to an effective potential and introduces a nonlinearity to the PDE. In both cases, i.e. equilibrium and non equilibrium, the main model corresponding to the semiclassical wave is the Gross-Pitaevskii equation (GPE), which includes certain mathematical adaptions depending on the physical context of the consideration and the nature of particles/quasiparticles, such as additional complex pumping and growth terms or terms due to motion. In the course of this work I apply a variety of state-of-the-art analytical and numerical tools to gain information about these semiclassical waves. The analytical tools allow e.g. to determine the position of the maximum density of the condensate wave function or to find the critical velocities at which excitations are expected to be generated within the condensate. In addition to analytical considerations I approximate the GPE numerically. This allows to gain the condensate wave function explicitly and is often a convenient tool to study the emergence of excitations in BEC. It is in particular shown that the form of the possible excitations significantly depends on the dimensionality of the considered system. The generated excitations within the BEC include quantum vortices, quantum vortex rings or solitons. In addition multicomponent systems are considered, which enable more complex dynamical scenarios. Under certain conditions imposed on the condensate one obtains dark-bright soliton trains within the condensate wave function. This is shown numerically and analytical expressions are found as well. In the end of this thesis I present results as part of an collaborative effort with a group of experimenters. Here it is shown that the wave function due to a complex GPE fits well with experiments made on polariton condensates, statically and dynamically.

Orientador: Maurice de Koning / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-18T18:05:04Z (GMT). No. of bitstreams: 1 Barrozo_AlexandreHernandes_M.pdf: 4359405 bytes, checksum: c11339c45a35270724d3ee11084432af (MD5) Previous issue date: 2011 / Resumo: Fizemos estudos de uma nova técnica proposta para amostrar o ensemble canônico [H. Dammak et al., Phys. Rev. Lett. 103,190601 (2009)], capaz de amostrar flutuações quânticas através de Dinâmica Molecular(DM) clássica. Esta técnica é baseada nos termostatos estocásticos clássicos, que se baseiam nas equações de Langevin, com a diferença de usar um ruído com correlação temporal, ao invés de ruído branco. Aplicamos esta técnica para o cálculo de grandezas termodinâmicas de sistemas cuja solução analítica (ou numérica) é conhecida. Mais especificamente, focamos o estudo no cálculo de energias livres através de integração termodinâmica fora do equilíbrio. Neste trabalho também desenvolvemos um método que nos permite alterar a temperatura do termostato ao longo da simulação. Este método é baseado no reescalonamento do ruído aleatório que constitui este termostato quântico. Mostramos aqui que, apesar de termos excelentes resultados para o caso do oscilador harmônico, esta técnica apresenta falhas no que se diz respeito a potenciais anarmônicos, amostrando distribuições fundamentalmente incorretas / Abstract: We study a new method devised to sample the canonical ensemble [H. Dammak et al., Phys. Rev. Lett. 103,190601 (2009)], which includes quantum uctuations by means of classical Molecular Dynamics. This method is based on classical stochastic thermostats, except that it uses colored noise, instead of a white one. We apply this method to compute thermodynamical properties of systems whose analytical (or numerical) solution for the Schr odinger equation is known. Specifically, we focus on free-energy calculations using non-equilibrium thermodynamics integration. In this work, we also develop a technique that allows one to change the thermostat's temperature during the simulation. This technique is based on rescaling the random noise sequence that constitutes the thermostat. We show that, although we have excelent results for the harmonic oscillator case, problems arise while studying anharmonic potentials, in which the method sample distributions that are fundamentally incorrect / Mestrado / Física Estatistica e Termodinamica / Mestre em Física

abstract: Autonomic closure is a recently-proposed subgrid closure methodology for large eddy simulation (LES) that replaces the prescribed subgrid models used in traditional LES closure with highly generalized representations of subgrid terms and solution of a local system identification problem that allows the simulation itself to determine the local relation between each subgrid term and the resolved variables at every point and time. The present study demonstrates, for the first time, practical LES based on fully dynamic implementation of autonomic closure for the subgrid stress and the subgrid scalar flux. It leverages the inherent computational efficiency of tensorally-correct generalized representations in terms of parametric quantities, and uses the fundamental representation theory of Smith (1971) to develop complete and minimal tensorally-correct representations for the subgrid stress and scalar flux. It then assesses the accuracy of these representations via a priori tests, and compares with the corresponding accuracy from nonparametric representations and from traditional prescribed subgrid models. It then assesses the computational stability of autonomic closure with these tensorally-correct parametric representations, via forward simulations with a high-order pseudo-spectral code, including the extent to which any added stabilization is needed to ensure computational stability, and compares with the added stabilization needed in traditional closure with prescribed subgrid models. Further, it conducts a posteriori tests based on forward simulations of turbulent conserved scalar mixing with the same pseudo-spectral code, in which velocity and scalar statistics from autonomic closure with these representations are compared with corresponding statistics from traditional closure using prescribed models, and with corresponding statistics of filtered fields from direct numerical simulation (DNS). These comparisons show substantially greater accuracy from autonomic closure than from traditional closure. This study demonstrates that fully dynamic autonomic closure is a practical approach for LES that requires accuracy even at the smallest resolved scales. / Dissertation/Thesis / Doctoral Dissertation Aerospace Engineering 2020

abstract: The quest to find efficient algorithms to numerically solve differential equations isubiquitous in all branches of computational science. A natural approach to address this problem is to try all possible algorithms to solve the differential equation and choose the one that is satisfactory to one's needs. However, the vast variety of algorithms in place makes this an extremely time consuming task. Additionally, even after choosing the algorithm to be used, the style of programming is not guaranteed to result in the most efficient algorithm. This thesis attempts to address the same problem but pertinent to the field of computational nanoelectronics, by using PETSc linear solver and SLEPc eigenvalue solver packages to efficiently solve Schrödinger and Poisson equations self-consistently. In this work, quasi 1D nanowire fabricated in the GaN material system is considered as a prototypical example. Special attention is placed on the proper description of the heterostructure device, the polarization charges and accurate treatment of the free surfaces. Simulation results are presented for the conduction band profiles, the electron density and the energy eigenvalues/eigenvectors of the occupied sub-bands for this quasi 1D nanowire. The simulation results suggest that the solver is very efficient and can be successfully used for the analysis of any device with two dimensional confinement. The tool is ported on www.nanoHUB.org and as such is freely available. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2020

No description available.

abstract: I describe the first continuous space nuclear path integral quantum Monte Carlo method, and calculate the ground state properties of light nuclei including Deuteron, Triton, Helium-3 and Helium-4, using both local chiral interaction up to next-to-next-to-leading-order and the Argonne $v_6'$ interaction. Compared with diffusion based quantum Monte Carlo methods such as Green's function Monte Carlo and auxiliary field diffusion Monte Carlo, path integral quantum Monte Carlo has the advantage that it can directly calculate the expectation value of operators without tradeoff, whether they commute with the Hamiltonian or not. For operators that commute with the Hamiltonian, e.g., the Hamiltonian itself, the path integral quantum Monte Carlo light-nuclei results agree with Green's function Monte Carlo and auxiliary field diffusion Monte Carlo results. For other operator expectations which are important to understand nuclear measurements but do not commute with the Hamiltonian and therefore cannot be accurately calculated by diffusion based quantum Monte Carlo methods without tradeoff, the path integral quantum Monte Carlo method gives reliable results. I show root-mean-square radii, one-particle number density distributions, and Euclidean response functions for single-nucleon couplings. I also systematically describe all the sampling algorithms used in this work, the strategies to make the computation efficient, the error estimations, and the details of the implementation of the code to perform calculations. This work can serve as a benchmark test for future calculations of larger nuclei or finite temperature nuclear matter using path integral quantum Monte Carlo. / Dissertation/Thesis / Doctoral Dissertation Physics 2020

In soil, where trees and crops grow, heavy vehicles shear and compact the soil, leading to reduced plant growth and diminished nutrient recycling. Computer simulations offer the possibility to improve the understanding of these undesired phenomena. In this thesis, soils were modelled as large collections of contacting spherical particles using the Discrete Element Method (DEM) and the physics engine AGX Dynamics, and these entities were analyzed. In the first part of the thesis, soils, which were considered to be continua, were subjected to various controlled deformations and fields for quantities such as stress and strain were visualized using coarse graining (CG). These fields were then compared against analytical solutions. The main goal of the thesis was to evaluate the usefulness, accuracy, and precision of this plotting technique when applied to DEM-soils. The general behaviour of most fields agreed well with analytical or expected behaviour. Moreover, the fields presented valuable information about phenomena in the soils. Relative errors varied from 1.2 to 27 %. The errors were believed to arise chiefly from non-uniform displacement (due to the inherent granularity in the technique), and unintended uneven particle distribution. The most prominent drawback with the technique was found to be the unreliability of the plots near the boundaries. This is significant, since the behaviour of a soil at the surface where it is in contact with e.g. a vehicle tyre is of interest. In the second part of the thesis, a vehicle traversed a soil and fields were visualized using the same technique. Following a limited analysis, it was found that the stress in the soil can be crudely approximated as the stress in a linear elastic solid.

Strongly correlated low-dimensional quantum spin models provide a well-established frame- work to study magnetic properties of insulators, and are of great theoretical interest and experimental relevance in condensed-matter physics. In this thesis, I use quantum Monte Carlo methods to numerically study quantum critical behavior in low-dimensional quantum spin models and wavefunctions. First, I study spinons &ndash emergent spin-1/2 bosonic excitations &ndash at certain one- and two-dimensional quantum phase transitions (QPTs) in spin models, by characterizing their size and confinement length quantitatively. In particular, I focus on the QPT from an antiferromagnetic (AFM) phase into a valence-bond solid (VBS) phase, which is an example of a violation of the standard Landau-Ginzburg-Wilson paradigm for phase transitions. This transition in two dimensions (2D) is instead likely described by a novel theory called "deconfined quantum criticality" (DQC). According to the theory, spinons should be deconfined. The degree of deconfinement is quantified in my calculations. Second, I present a comprehensive study of so-called short-bond resonating-valence-bond (RVB) spin liquids in 2D, which have been suggested as a good starting point for understanding the spin physics of high-temperature cuprates. I find that these RVB states can also be classified as quantum-critical VBS states, which indicates that RVB is less disordered than expected. This work suggests a possible mapping from the quantum RVB states to classical dimer models via a classical continuum field theory--the height model. This map explicitly bridges well-established classical results to future quantum studies. Third, I consider 1D amplitude product (AP) states, which are generalized versions of RVB states, with different wavefunction weightings of bonds according to their lengths. AP states constitute a good ansatz for certain Hamiltonians and are of broad interest in quantum magnetism. I study phase transitions from AFM-VBS phases in AP states by tuning their amplitudes, and obtain continuously varying critical exponents. In addition, I classify the 1D AP states through entanglement entropy calculations of the central charge in (1+1)D conformal field theory. This new classification could serve as guide for AP states as trial wavefunctions to search for ground states of corresponding quantum spin models.