On anomalous diffusion and the fractional generalized Langevin equation for a harmonic oscillator

The fractional generalized Langevin equation (FGLE) is proposed to discuss the anomalous diffusive behavior of a harmonic oscillator driven by a two-parameter Mittag-Leffler noise. The solution of this FGLE is discussed by means of the Laplace transform methodology and the kernels are presented in terms of the three-parameter Mittag-Leffler functions. Recent results associated with a generalized Langevin equation are recovered.

Fortran programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

C programs for solving the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Numerical study of the coupled time-dependent Gross-Pitaevskii equation: Application to Bose-Einstein condensation

The Bose-Einstein condensate of several types of trapped bosons at ultralow temperature was described using the coupled time dependent Gross-Pitaevskii equation. Both the stationary and time evolution problems were analyzed using this approach. The ground state stationary wave functions were found to be sharply peaked near the origin for attractive interatomic interaction for larger nonlinearity while for a repulsive interatomic interaction the wave function extends over a larger region of space.

Numerical study of the Ginzburg-Landau-Langevin equation: coherent structures and noise perturbation theory

Pós-graduação em Física - IFT

Conditions for the validity of the quantum Langevin equation

From microscopic models, a Langevin equation can, in general, be derived only as an approximation. Two possible conditions to validate this approximation are studied. One is, for a linear Langevin equation, that the frequency of the Fourier transform should be close to the natural frequency of the system. The other is by the assumption of "slow" variables. We test this method by comparison with an exactly soluble model and point out its limitations. We base our discussion on two approaches. The first is a direct, elementary treatment of Senitzky. The second is via a generalized Langevin equation as an intermediate step.

Spectrum reconstruction from a scattering measurement using the adjoint Boltzmann transport equation for photons

Quality control of medical radiological systems is of fundamental importance, and requires efficient methods for accurately determine the X-ray source spectrum. Straightforward measurements of X-ray spectra in standard operating require the limitation of the high photon flux, and therefore the measure has to be performed in a laboratory. However, the optimal quality control requires frequent in situ measurements which can be only performed using a portable system. To reduce the photon flux by 3 magnitude orders an indirect technique based on the scattering of the X-ray source beam by a solid target is used. The measured spectrum presents a lack of information because of transport and detection effects. The solution is then unfolded by solving the matrix equation that represents formally the scattering problem. However, the algebraic system is ill-conditioned and, therefore, it is not possible to obtain a satisfactory solution. Special strategies are necessary to circumvent the ill-conditioning. Numerous attempts have been done to solve this problem by using purely mathematical methods. In this thesis, a more physical point of view is adopted. The proposed method uses both the forward and the adjoint solutions of the Boltzmann transport equation to generate a better conditioned linear algebraic system. The procedure has been tested first on numerical experiments, giving excellent results. Then, the method has been verified with experimental measurements performed at the Operational Unit of Health Physics of the University of Bologna. The reconstructed spectra have been compared with the ones obtained with straightforward measurements, showing very good agreement.

A study of electrochemical transport and diffuse charge dynamics using a Langevin equation

This thesis aims to develop new numerical and computational tools to study electrochemical transport and diffuse charge dynamics at small scales. Previous efforts at modeling electrokinetic phenomena at scales where the noncontinuum effects become significant have included continuum models based on the Poisson-Nernst-Planck equations and atomic simulations using molecular dynamics algorithms. Neither of them is easy to use or conducive to electrokinetic transport modeling in strong confinement or over long time scales. This work introduces a new approach based on a Langevin equation for diffuse charge dynamics in nanofluidic devices, which incorporates features from both continuum and atomistic methods. The model is then extended to include steric effects resulting from finite ion size, and applied to the phenomenon of double layer charging in a symmetric binary electrolyte between parallel-plate blocking electrodes, between which a voltage is applied. Finally, the results of this approach are compared to those of the continuum model based on the Poisson-Nernst-Planck equations.

Fully Anisotropic Solution of the Three Dimensional Boltzmann Transport Equation

The development of accurate modeling techniques for nanoscale thermal transport is an active area of research. Modern day nanoscale devices have length scales of tens of nanometers and are prone to overheating, which reduces device performance and lifetime. Therefore, accurate temperature profiles are needed to predict the reliability of nanoscale devices. The majority of models that appear in the literature obtain temperature profiles through the solution of the Boltzmann transport equation (BTE). These models often make simplifying assumptions about the nature of the quantized energy carriers (phonons). Additionally, most previous work has focused on simulation of planar two dimensional structures. This thesis presents a method which captures the full anisotropy of the Brillouin zone within a three dimensional solution to the BTE. The anisotropy of the Brillouin zone is captured by solving the BTE for all vibrational modes allowed by the Born Von-Karman boundary conditions.

Production cross section of neutron cluster from the reaction of light neutron rich nuclei

Within the Boltzmann-Langevin equation, the neutron cluster production cross sections in the reactions induced by Be-14, He-8, He-6, Li-11, B-17, Be-11, C-19 on C-12 at 35MeV/u were studied. The experimental data for (4)n production cross section from Be-14+C-12 at 35MeV/u can be reproduced. It is found that the production cross section of neutron cluster is large in the reaction that the projectile has more halo nucleons. And the projectiles with big mass number are easy to produce the neutron cluster, when they have the same number of halo nucleons. The neutron cluster is probably mainly from the halo nucleons of projectile.

利用碎裂反应研究6He和6Li的团簇结构

本文在碎裂反应实验的基础上研究了原子核的团簇结构以及晕核的特性。由兰州放射性束流线(RIBLL)提供的6He和6Li次级束与Be靶的反应，用24单元的CsI（Tl）阵列探测器测量了6He和6Li的碎裂产物的能量以及小范围内的角分布。用脉冲形状的方法鉴别出了6He与6Li的轻带电粒子碎片。通过重构不变质量谱的方法得到了RGM预言的6He和6Li的3核子共振态。拟合实验数据发现6Li在Ex=22.9MeV和Ex=30.3MeV出现t+3He团簇共振态，6He在Ex=19.2MeV和Ex=29.8MeV出现t+t团簇共振态。并且与理论以及其它的实验的结果进行了比较。这是在实验上首次通过重构不变质量谱的方法直接观测到6He和6Li的三核子共振态。比较了6He和6Li的碎片产生几率，结果表明丰中子的6He产生丰中子碎片的几率要比6Li大，而产生缺中子碎片的几率要比6Li低，结论与BLE的计算是一致的。通过比较6He和6Li反应产生3He和3H的截面角分布，发现丰中子核反应容易产生丰中子的碎片这种现象在前角区更为敏感，随着角度的增大差别逐渐变小。因此前角区的3H与3He的发射产额比是一个鉴别晕核的灵敏探针。用双碎片关联和电粒子产额估算了6He碎裂各出射道的分支比，还估算了6Li碎裂成双带电粒子出射道的相对比例。由出射道的分支比估算了自由发射的中子质子比，并且与QMD的结果进行了比较，发现晕核的自由发射中子质子比要比稳定核大，这也可作为鉴别晕核的一种探针。另外用同位旋相关的BLE(Boltzmann-Langevin Equation)模型计算了轻丰中子核反应中子团簇集团产生的截面，发现3，4n团簇的截面最大，其中4n的产生截面与实验值相近。还计算了丰质子核反应的轻带电粒子发射的同位旋效应，发现质子晕核反应中轻带电粒子的产额相对于稳定核会突然的增大。这也为寻找和判断晕核结构提供了新的手段

Stochastic models and simulation of ion channel dynamics

The behaviour of ion channels within cardiac and neuronal cells is intrinsically stochastic in nature. When the number of channels is small this stochastic noise is large and can have an impact on the dynamics of the system which is potentially an issue when modelling small neurons and drug block in cardiac cells. While exact methods correctly capture the stochastic dynamics of a system they are computationally expensive, restricting their inclusion into tissue level models and so approximations to exact methods are often used instead. The other issue in modelling ion channel dynamics is that the transition rates are voltage dependent, adding a level of complexity as the channel dynamics are coupled to the membrane potential. By assuming that such transition rates are constant over each time step, it is possible to derive a stochastic differential equation (SDE), in the same manner as for biochemical reaction networks, that describes the stochastic dynamics of ion channels. While such a model is more computationally efficient than exact methods we show that there are analytical problems with the resulting SDE as well as issues in using current numerical schemes to solve such an equation. We therefore make two contributions: develop a different model to describe the stochastic ion channel dynamics that analytically behaves in the correct manner and also discuss numerical methods that preserve the analytical properties of the model.

Classical Langevin dynamics of a charged particle moving on a sphere and diamagnetism: A surprise

It is generally known that the orbital diamagnetism of a classical system of charged particles in thermal equilibrium is identically zero —the Bohr-van Leeuwen theorem. Physically, this null result derives from the exact cancellation of the orbital diamagnetic moment associated with the complete cyclotron orbits of the charged particles by the paramagnetic moment subtended by the incomplete orbits skipping the boundary in the opposite sense. Motivated by this crucial but subtle role of the boundary, we have simulated here the case of a finite but unbounded system, namely that of a charged particle moving on the surface of a sphere in the presence of an externally applied uniform magnetic field. Following a real space-time approach based on the classical Langevin equation, we have computed the orbital magnetic moment that now indeed turns out to be non-zero and has the diamagnetic sign. To the best of our knowledge, this is the first report of the possibility of finite classical diamagnetism in principle, and it is due to the avoided cancellation.

Electron energy distributions and transport coefficients in N2 in E times B fields

Using the concept of energy-dependent effective field intensity, electron transport coefficients in nitrogen have been determined in E times B fields (E = electric field intensity, B = magnetic flux density) by the numerical solution of the Boltzmann transport equation for the energy distribution of electrons. It has been observed that as the value of B/p (p = gas pressure) is increased from zero, the perpendicular drift velocity increased linearly at first, reaches a maximum value, and then decreases with increasing B/p. In general, the electron mean energy is found to be a function of Eavet/p( Eavet = averaged effective electric field intensity) only, but the other transport coefficients, such as transverse drift velocity, perpendicular drift velocity, and the Townsend ionization coefficient, are functions of both E/p and B/p.

Multicarrier conduction and Boltzmann transport analysis of heavy hole mobility in HgCdTe near room temperature

Magnetotransport measurements in pulsed fields up to 15 T have been performed on mercury cadmium telluride (Hg1-xCdxTe, x similar to 0.2) bulk as well as liquid phase epitaxially grown samples to obtain the resistivity and conductivity tensors in the temperature range 220-300 K. Mobilities and densities of various carriers participating in conduction have been extracted using both conventional multicarrier fitting (MCF) and mobility spectrum analysis. The fits to experimental data, particularly at the highest magnetic fields, were substantially improved when MCF is applied to minimize errors simultaneously on both resistivity and conductivity tensors. The semiclassical Boltzmann transport equation has been solved without using adjustable parameters by incorporating the following scattering mechanisms to fit the mobility: ionized impurity, polar and nonpolar optical phonons, acoustic deformation potential, and alloy disorder. Compared to previous estimates based on the relaxation time approximation with outscattering only, polar optical scattering and ionized impurity scattering limited mobilities are shown to be larger due to the correct incorporation of the inscattering term taking into account the overlap integrals in the valence band.