The existence of periodic solutions of a two dimensional Lattice

We consider a two dimensional lattice coupled with nearest neighbor interaction potential of power type. The existence of infinite many periodic solutions is shown by using minimax methods.

Effective one-dimensional square well for two-dimensional quantum wires

The symmetrical two-dimensional quantum wire with two straight leads joined to an arbitrarily shaped interior cavity is studied with emphasis on the single-mode approximation. It is found that for both transmission and bound-state problems the solution is equivalent to that for an energy-dependent one-dimensional square well. Quantum wires with a circular bend, and with single and double right-angle bends, are examined as examples. We also indicate a possible way to detect bound states in a double bend based on the experimental setup of Wu et al.

Pairing in two-dimensional boson-fermion mixtures

The possibilities of pairing in two-dimensional boson-fermion mixtures are carefully analyzed. It is shown that the boson-induced attraction between two identical fermions dominates the p wave pairing at low density. For a given fermion density, the pairing gap becomes maximal at a certain optimal boson concentration. The conditions for observing pairing in current experiments are discussed.

On the zeta-function regularization of a two-dimensional series of epsten-Hurwitz type

For a few years now, the study of quantum field theories in partially compactified space-time manifolds has acquired increasing importance in several domains of quantum physics. Let me just mention the issues of dimensional reduction and spontaneous compactification, and the multiple questions associated with the study of quantum field theories in the presence of boundaries (like the Casimir effect) and on curved space-time (manifolds with curvature and nontrivial topology), a step towards quantum gravity.

Structural disorder in two-dimensional random magnets: Very thin films of rare earths and transition metals

The low-temperature isothermal magnetization curves, M(H), of SmCo4 and Fe3Tb thin films are studied according to the two-dimensional correlated spin-glass model of Chudnovsky. We have calculated the magnetization law in approach to saturation and shown that the M(H) data fit well the theory at high and low fields. In our fit procedure we have used three different correlation functions. The Gaussian decay correlation function fits well the experimental data for both samples.

Methods for the analysis of two dimensional measurement data of paper web

This work is devoted to the problem of reconstructing the basis weight structure at paper web with black{box techniques. The data that is analyzed comes from a real paper machine and is collected by an o®-line scanner. The principal mathematical tool used in this work is Autoregressive Moving Average (ARMA) modelling. When coupled with the Discrete Fourier Transform (DFT), it gives a very flexible and interesting tool for analyzing properties of the paper web. Both ARMA and DFT are independently used to represent the given signal in a simplified version of our algorithm, but the final goal is to combine the two together. Ljung-Box Q-statistic lack-of-fit test combined with the Root Mean Squared Error coefficient gives a tool to separate significant signals from noise.

Cosmic censorship in two-dimensional gravity

A weak version of the cosmic censorship hypothesis is implemented as a set of boundary conditions on exact semiclassical solutions of two-dimensional dilaton gravity. These boundary conditions reflect low-energy matter from the strong coupling region and they also serve to stabilize the vacuum of the theory against decay into negative energy states. Information about low-energy incoming matter can be recovered in the final state but at high energy black holes are formed and inevitably lead to information loss at the semiclassical level.

Speed of travelling fronts: Two-dimensional and ballistic dispersal probability distributions

The speed of traveling fronts for a two-dimensional model of a delayed reactiondispersal process is derived analytically and from simulations of molecular dynamics. We show that the one-dimensional (1D) and two-dimensional (2D) versions of a given kernel do not yield always the same speed. It is also shown that the speeds of time-delayed fronts may be higher than those predicted by the corresponding non-delayed models. This result is shown for systems with peaked dispersal kernels which lead to ballistic transport

Performance of two-dimensional Doppler echocardiography for the assessment of infarct size and left ventricular function in rats

Although echocardiography has been used in rats, few studies have determined its efficacy for estimating myocardial infarct size. Our objective was to estimate the myocardial infarct size, and to evaluate anatomic and functional variables of the left ventricle. Myocardial infarction was produced in 43 female Wistar rats by ligature of the left coronary artery. Echocardiography was performed 5 weeks later to measure left ventricular diameter and transverse area (mean of 3 transverse planes), infarct size (percentage of the arc with infarct on 3 transverse planes), systolic function by the change in fractional area, and diastolic function by mitral inflow parameters. The histologic measurement of myocardial infarction size was similar to the echocardiographic method. Myocardial infarct size ranged from 4.8 to 66.6% when determined by histology and from 5 to 69.8% when determined by echocardiography, with good correlation (r = 0.88; P < 0.05; Pearson correlation coefficient). Left ventricular diameter and mean diastolic transverse area correlated with myocardial infarct size by histology (r = 0.57 and r = 0.78; P < 0.0005). The fractional area change ranged from 28.5 ± 5.6 (large-size myocardial infarction) to 53.1 ± 1.5% (control) and correlated with myocardial infarct size by echocardiography (r = -0.87; P < 0.00001) and histology (r = -0.78; P < 00001). The E/A wave ratio of mitral inflow velocity for animals with large-size myocardial infarction (5.6 ± 2.7) was significantly higher than for all others (control: 1.9 ± 0.1; small-size myocardial infarction: 1.9 ± 0.4; moderate-size myocardial infarction: 2.8 ± 2.3). There was good agreement between echocardiographic and histologic estimates of myocardial infarct size in rats.

Two-dimensional drift-diffusion simulation of organic solar cells

The aim of this master's thesis is to develop a two-dimensional drift-di usion model, which describes charge transport in organic solar cells. The main bene t of a two-dimensional model compared to a one-dimensional one is the inclusion of the nanoscale morphology of the active layer of a bulk heterojunction solar cell. The developed model was used to study recombination dynamics at the donor-acceptor interface. In some cases, it was possible to determine e ective parameters, which reproduce the results of the two-dimensional model in the one-dimensional case. A summary of the theory of charge transport in semiconductors was presented and discussed in the context of organic materials. Additionally, the normalization and discretization procedures required to nd a numerical solution to the charge transport problem were outlined. The charge transport problem was solved by implementing an iterative scheme called successive over-relaxation. The obtained solution is given as position-dependent electric potential, free charge carrier concentrations and current densities in the active layer. An interfacial layer, separating the pure phases, was introduced in order to describe charge dynamics occurring at the interface between the donor and acceptor. For simplicity, an e ective generation of free charge carriers in the interfacial layer was implemented. The pure phases simply act as transport layers for the photogenerated charges. Langevin recombination was assumed in the two-dimensional model and an analysis of the apparent recombination rate in the one-dimensional case is presented. The recombination rate in a two-dimensional model is seen to e ectively look like reduced Langevin recombination at open circuit. Replicating the J-U curves obtained in the two-dimensional model is, however, not possible by introducing a constant reduction factor in the Langevin recombination rate. The impact of an acceptor domain in the pure donor phase was investigated. Two cases were considered, one where the acceptor domain is isolated and another where it is connected to the bulk of the acceptor. A comparison to the case where no isolated domains exist was done in order to quantify the observed reduction in the photocurrent. The results show that all charges generated at the isolated domain are lost to recombination, but the domain does not have a major impact on charge transport. Trap-assisted recombination at interfacial trap states was investigated, as well as the surface dipole caused by the trapped charges. A theoretical expression for the ideality factor n_id as a function of generation was derived and shown to agree with simulation data. When the theoretical expression was fitted to simulation data, no interface dipole was observed.

Studies on collective excitations of quasi-two-dimensional Bose-Einstein condensate

Theory Division Department of Physics

The two-dimensional anharmonic oscillator I: vibration-rotation constants of fulminic acid, HCNO

The lowest-wavenumber vibration of HCNO and DCNO, ν5, is known to involve a largeamplitude low-frequency anharmonic bending of the CH bond against the CNO frame. In this paper the anomalous vibrational dependence of the observed rotational constants B(v5, l5), and of the observed l-doubling interactions, is interpreted according to a simple effective vibration-rotation Hamiltonian in which the appropriate vibrational operators are averaged in an anharmonic potential surface over the normal coordinates (Q5x, Q5y). All of the data on both isotopes are interpreted according to a single potential surface having a minimum energy at a slightly bent configuration of the HCN angle ( 170°) with a maximum at the linear configuration about 2 cm−1 higher. The other coefficients in the Hamiltonian are also interpreted in terms of the structure and the harmonic and anharmonic force fields; the substitution structure at the “hypothetical linear configuration” determined in this way gives a CH bond length of 1.060 Å, in contrast to the value 1.027 Å determined from the ground-state rotational constants. We also discuss the difficulties in rationalizing our effective Hamiltonian in terms of more fundamental theory, as well as the success and limitations of its use in practice.

An ‘ideal’ form of decaying two-dimensional turbulence

In decaying two-dimensional Navier-Stokes turbulence, Batchelor's similarity hypothesis fails due to the existence of coherent vortices. However, it is shown that decaying two-dimensional turbulence governed by the Harney-Hasegawa-Mima (CHM) equation ∂/∂t (V^2 φ-λ^2 φ)+J(φ,∇^2 φ)=D where D is a damping, is described well by Batchelor's similarity hypothesis for wave numbers k ≪ λ (the so-called AM regime). It is argued that CHM turbulence in the AM regime is a more `ideal' form of two-dimensional turbulence than is Navier-Stokes turbulence itself.