SEMICLASSICAL THEORY OF MAGNETIZATION FOR A 2-DIMENSIONAL NONINTERACTING ELECTRON-GAS

We compute the semiclassical magnetization and susceptibility of non-interacting electrons, confined by a smooth two-dimensional potential and subjected to a uniform perpendicular magnetic field, in the general case when their classical motion is chaotic. It is demonstrated that the magnetization per particle m(B) is directly related to the staircase function N(E), which counts the single-particle levels up to energy E. Using Gutzwiller's trace formula for N, we derive a semiclassical expression for m. Our results show that the magnetization has a non-zero average, which arises from quantum corrections to the leading-order Weyl approximation to the mean staircase and which is independent of whether the classical motion is chaotic or not. Fluctuations about the average are due to classical periodic orbits and do represent a signature of chaos. This behaviour is confirmed by numerical computations for a specific system.

STOCHASTIC ADDING MACHINE AND 2-DIMENSIONAL JULIA SETS

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A 2-dimensional computational model to analyze the effects of cellular heterogeinity on cardiac pacemaking

The mechanical action of the heart is made possible in response to electrical events that involve the cardiac cells, a property that classifies the heart tissue between the excitable tissues. At the cellular level, the electrical event is the signal that triggers the mechanical contraction, inducing a transient increase in intracellular calcium which, in turn, carries the message of contraction to the contractile proteins of the cell. The primary goal of my project was to implement in CUDA (Compute Unified Device Architecture, an hardware architecture for parallel processing created by NVIDIA) a tissue model of the rabbit sinoatrial node to evaluate the heterogeneity of its structure and how that variability influences the behavior of the cells. In particular, each cell has an intrinsic discharge frequency, thus different from that of every other cell of the tissue and it is interesting to study the process of synchronization of the cells and look at the value of the last discharge frequency if they synchronized.

A critical evaluation of secondary cancer risk models applied to Monte Carlo dose distributions of 2-dimensional, 3-dimensional conformal and hybrid intensity-modulated radiation therapy for breast cancer

The comparison of radiotherapy techniques regarding secondary cancer risk has yielded contradictory results possibly stemming from the many different approaches used to estimate risk. The purpose of this study was to make a comprehensive evaluation of different available risk models applied to detailed whole-body dose distributions computed by Monte Carlo for various breast radiotherapy techniques including conventional open tangents, 3D conformal wedged tangents and hybrid intensity modulated radiation therapy (IMRT). First, organ-specific linear risk models developed by the International Commission on Radiological Protection (ICRP) and the Biological Effects of Ionizing Radiation (BEIR) VII committee were applied to mean doses for remote organs only and all solid organs. Then, different general non-linear risk models were applied to the whole body dose distribution. Finally, organ-specific non-linear risk models for the lung and breast were used to assess the secondary cancer risk for these two specific organs. A total of 32 different calculated absolute risks resulted in a broad range of values (between 0.1% and 48.5%) underlying the large uncertainties in absolute risk calculation. The ratio of risk between two techniques has often been proposed as a more robust assessment of risk than the absolute risk. We found that the ratio of risk between two techniques could also vary substantially considering the different approaches to risk estimation. Sometimes the ratio of risk between two techniques would range between values smaller and larger than one, which then translates into inconsistent results on the potential higher risk of one technique compared to another. We found however that the hybrid IMRT technique resulted in a systematic reduction of risk compared to the other techniques investigated even though the magnitude of this reduction varied substantially with the different approaches investigated. Based on the epidemiological data available, a reasonable approach to risk estimation would be to use organ-specific non-linear risk models applied to the dose distributions of organs within or near the treatment fields (lungs and contralateral breast in the case of breast radiotherapy) as the majority of radiation-induced secondary cancers are found in the beam-bordering regions.

Comparison between Radiographic (2-dimensional and 3-dimensional) and Histologic Findings of Periapical Lesions Treated with Apical Surgery.

INTRODUCTION The aim of this study was to evaluate the concordance of 2- and 3-dimensional radiography and histopathology in the diagnosis of periapical lesions. METHODS Patients were consecutively enrolled in this study provided that preoperative periapical radiography (PR) and cone-beam computed tomographic imaging of the tooth to be treated with apical surgery were performed. The periapical lesional tissue was histologically analyzed by 2 blinded examiners. The final histologic diagnosis was compared with the radiographic assessments of 4 blinded observers. The initial study material included 62 teeth in the same number of patients. RESULTS Four lesions had to be excluded during processing, resulting in a final number of 58 evaluated cases (31 women and 27 men, mean age = 55 years). The final histologic diagnosis of the periapical lesions included 55 granulomas (94.8%) and 3 cysts (5.2%). Histologic analysis of the tissue samples from the apical lesions exhibited an almost perfect agreement between the 2 experienced investigators with an overall agreement of 94.83% (kappa = 0.8011). Radiographic assessment overestimated cysts by 28.4% (cone-beam computed tomographic imaging) and 20.7% (periapical radiography), respectively. Comparing the correlation of the radiographic diagnosis of 4 observers with the final histologic diagnosis, 2-dimensional (kappa = 0.104) and 3-dimensional imaging (kappa = 0.111) provided only minimum agreement. CONCLUSIONS To establish a final diagnosis of an apical radiolucency, the tissue specimen should be evaluated histologically and specified as a granuloma (with/without epithelium) or a cyst. Analysis of 2-dimensional and 3-dimensional radiographic images alike results only in a tentative diagnosis that should be confirmed with biopsy.

Boston, Massachusetts, 2-Dimensional Building Footprints with Height Data (from LIDAR data), 2002

This dataset consists of 2D footprints of the buildings in the metropolitan Boston area, based on tiles in the orthoimage index (orthophoto quad ID: 229890, 229894, 229898, 229902, 233886, 233890, 233894, 233898, 233902, 237890, 237894, 237898, 237902, 241890, 241894, 241898, 241902, 245898, 245902). This data set was collected using 3Di's Digital Airborne Topographic Imaging System II (DATIS II). Roof height and footprint elevation attributes (derived from 1-meter resolution LIDAR (LIght Detection And Ranging) data) are included as part of each building feature. This data can be combined with other datasets to create 3D representations of buildings and the surrounding environment.

pl/2d--a programming language for generating 2-dimensional patterns /

Thesis (M.S.)--University of Illinois at Urbana-Champaign.

The structure and dynamics of 2-dimensional fluids in swelling clays

The interlayer pores of swelling 2:1 clays provide an ideal 2-dimensional environment in which to study confined fluids. In this paper we discuss our understanding of the structure and dynamics of interlayer fluid species in expanded clays, based primarily on the outcome of recent molecular modelling and neutron scattering studies. Counterion solvation is compared with that measured in bulk solutions, and at a local level the cation-oxygen coordination is found to be remarkably similar in these two environments. However, for the monovalent ions the contribution to the first coordination shell from the clay surfaces increases with counterion radius. This gives rise to inner-sphere (surface) complexes in the case of potassium and caesium. In this context, the location of the negative clay surface charge (i.e. arising from octahedral or tetrahedral substitution) is also found to be of major importance. Divalent cations, such as calcium, eagerly solvate to form outer-sphere complexes. These complexes are able to pin adjacent clay layers together, and thereby prevent colloidal swelling. Confined water molecules form hydrogen bonds to each other and to the clays' surfaces. In this way their local environment relaxes to close to the bulk water structure within two molecular layers of the clay surface. Finally, we discuss the way in which the simple organic molecules methane, methanol and ethylene glycol behave in the interlayer region of hydrated clays. Quasi-elastic neutron scattering of isotopically labelled interlayer CH 3OD and (CH2OD)2 in deuterated clay allows us to measure the diffusion of the CH3- and CH2-groups in both clay and liquid environments. We find that in both the one-layer methanol solvates and the two-layer glycol solvates the diffusion of the most mobile organic molecules is close to that in the bulk solution.

Geometric properties of 2-dimensional minimal surfaces in a sub-Riemannian manifold which models the Visual Cortex

In this paper we study the notion of degree forsubmanifolds embedded in an equiregular sub-Riemannian manifold and we provide the definition of their associated area functional. In this setting we prove that the Hausdorff dimension of a submanifold coincides with its degree, as stated by Gromov. Using these general definitions we compute the first variation for surfaces embedded in low dimensional manifolds and we obtain the partial differential equation associated to minimal surfaces. These minimal surfaces have several applications in the neurogeometry of the visual cortex.