Dispersion and energy relations in periodic chains and grids

In this study wave propagation, dispersion relations, and energy relations for linear elastic periodic systems are analyzed. In particular, the dispersion relations for monoatomic chain of infinite dimension are obtained analytically by writing the Block-type wave equation for a unit cell in order to capture the dynamic behavior for chains under prescribed vibration. By comparing the discretized model (mass-spring chain) with the solid bar system, the nonlinearity of the dispersion relation for chain indicates that the periodic lattice is dispersive in contrast to the continuous rod, which is non dispersive. Further investigations have been performed considering one-dimensional diatomic linear elastic mass-spring chain. The dispersion relations, energy velocity, and group velocity have been derived. At certain range of frequencies harmonic plane waves do not propagate in contrast with monoatomic chain. Also, since the diatomic chain considered is a linear elastic chain, both of the energy velocity and the group velocity are identical. As long as the linear elastic condition is considered the results show zero flux condition without residual energy. In addition, this paper shows that the diatomic chain dispersion relations are independent on the unit cell scheme. Finally, an extension for the study covers the dispersion and energy relations for 2D- grid system. The 2x2 grid system show a periodicity of the dispersion surface in the wavenumber domain. In addition, the symmetry of the surface can be exploited to identify an Irreducible Brillouin Zone (IBZ). Compact representations of the dispersion properties of multidimensional periodic systems are obtained by plotting frequency as the wave vector’s components vary along the boundary of the IBZ, which leads to a widely accepted and effective visualization of bandgaps and overall dispersion properties.

Further development of discrete computational techniques for calculation of restricted diffusion propagators in porous media

Magnetic resonance is a well-established tool for structural characterisation of porous media. Features of pore-space morphology can be inferred from NMR diffusion-diffraction plots or the time-dependence of the apparent diffusion coefficient. Diffusion NMR signal attenuation can be computed from the restricted diffusion propagator, which describes the distribution of diffusing particles for a given starting position and diffusion time. We present two techniques for efficient evaluation of restricted diffusion propagators for use in NMR porous-media characterisation. The first is the Lattice Path Count (LPC). Its physical essence is that the restricted diffusion propagator connecting points A and B in time t is proportional to the number of distinct length-t paths from A to B. By using a discrete lattice, the number of such paths can be counted exactly. The second technique is the Markov transition matrix (MTM). The matrix represents the probabilities of jumps between every pair of lattice nodes within a single timestep. The propagator for an arbitrary diffusion time can be calculated as the appropriate matrix power. For periodic geometries, the transition matrix needs to be defined only for a single unit cell. This makes MTM ideally suited for periodic systems. Both LPC and MTM are closely related to existing computational techniques: LPC, to combinatorial techniques; and MTM, to the Fokker-Planck master equation. The relationship between LPC, MTM and other computational techniques is briefly discussed in the paper. Both LPC and MTM perform favourably compared to Monte Carlo sampling, yielding highly accurate and almost noiseless restricted diffusion propagators. Initial tests indicate that their computational performance is comparable to that of finite element methods. Both LPC and MTM can be applied to complicated pore-space geometries with no analytic solution. We discuss the new methods in the context of diffusion propagator calculation in porous materials and model biological tissues.

New computational approaches for inelastic x-ray scattering

Inelastic x-ray scattering spectroscopy is a versatile experimental technique for probing the electronic structure of materials. It provides a wealth of information on the sample's atomic-scale structure, but extracting this information from the experimental data can be challenging because there is no direct relation between the structure and the measured spectrum. Theoretical calculations can bridge this gap by explaining the structural origins of the spectral features. Reliable methods for modeling inelastic x-ray scattering require accurate electronic structure calculations. This work presents the development and implementation of new schemes for modeling the inelastic scattering of x-rays from non-periodic systems. The methods are based on density functional theory and are applicable for a wide variety of molecular materials. Applications are presented in this work for amorphous silicon monoxide and several gas phase systems. Valuable new information on their structure and properties could be extracted with the combination of experimental and computational methods.

Magnetorotational instability driven dynamos at low magnetic Prandtl numbers

Numerical simulations of the magnetorotational instability (MRI) with zero initial net flux in a non-stratified isothermal cubic domain are used to demonstrate the importance of magnetic boundary conditions. In fully periodic systems the level of turbulence generated by the MRI strongly decreases as the magnetic Prandtl number (Pm), which is the ratio of kinematic viscosity and magnetic diffusion, is decreased. No MRI or dynamo action below Pm=1 is found, agreeing with earlier investigations. Using vertical field conditions, which allow magnetic helicity fluxes out of the system, the MRI is found to be excited in the range 0.1

Nanophotonic Light Trapping In Thin Solar Cells

Over the last several decades there have been significant advances in the study and understanding of light behavior in nanoscale geometries. Entire fields such as those based on photonic crystals, plasmonics and metamaterials have been developed, accelerating the growth of knowledge related to nanoscale light manipulation. Coupled with recent interest in cheap, reliable renewable energy, a new field has blossomed, that of nanophotonic solar cells.

In this thesis, we examine important properties of thin-film solar cells from a nanophotonics perspective. We identify key differences between nanophotonic devices and traditional, thick solar cells. We propose a new way of understanding and describing limits to light trapping and show that certain nanophotonic solar cell designs can have light trapping limits above the so called ray-optic or ergodic limit. We propose that a necessary requisite to exceed the traditional light trapping limit is that the active region of the solar cell must possess a local density of optical states (LDOS) higher than that of the corresponding, bulk material. Additionally, we show that in addition to having an increased density of states, the absorber must have an appropriate incoupling mechanism to transfer light from free space into the optical modes of the device. We outline a portfolio of new solar cell designs that have potential to exceed the traditional light trapping limit and numerically validate our predictions for select cases.

We emphasize the importance of thinking about light trapping in terms of maximizing the optical modes of the device and efficiently coupling light into them from free space. To further explore these two concepts, we optimize patterns of superlattices of air holes in thin slabs of Si and show that by adding a roughened incoupling layer the total absorbed current can be increased synergistically. We suggest that the addition of a random scattering surface to a periodic patterning can increase incoupling by lifting the constraint of selective mode occupation associated with periodic systems.

Lastly, through experiment and simulation, we investigate a potential high efficiency solar cell architecture that can be improved with the nanophotonic light trapping concepts described in this thesis. Optically thin GaAs solar cells are prepared by the epitaxial liftoff process by removal from their growth substrate and addition of a metallic back reflector. A process of depositing large area nano patterns on the surface of the cells is developed using nano imprint lithography and implemented on the thin GaAs cells.

Nonlinear Effects in Granular Crystals with Broken Periodicity

When studying physical systems, it is common to make approximations: the contact interaction is linear, the crystal is periodic, the variations occurs slowly, the mass of a particle is constant with velocity, or the position of a particle is exactly known are just a few examples. These approximations help us simplify complex systems to make them more comprehensible while still demonstrating interesting physics. But what happens when these assumptions break down? This question becomes particularly interesting in the materials science community in designing new materials structures with exotic properties In this thesis, we study the mechanical response and dynamics in granular crystals, in which the approximation of linearity and infinite size break down. The system is inherently finite, and contact interaction can be tuned to access different nonlinear regimes. When the assumptions of linearity and perfect periodicity are no longer valid, a host of interesting physical phenomena presents itself. The advantage of using a granular crystal is in its experimental feasibility and its similarity to many other materials systems. This allows us to both leverage past experience in the condensed matter physics and materials science communities while also presenting results with implications beyond the narrower granular physics community. In addition, we bring tools from the nonlinear systems community to study the dynamics in finite lattices, where there are inherently more degrees of freedom. This approach leads to the major contributions of this thesis in broken periodic systems. We demonstrate the first defect mode whose spatial profile can be tuned from highly localized to completely delocalized by simply tuning an external parameter. Using the sensitive dynamics near bifurcation points, we present a completely new approach to modifying the incremental stiffness of a lattice to arbitrary values. We show how using nonlinear defect modes, the incremental stiffness can be tuned to anywhere in the force-displacement relation. Other contributions include demonstrating nonlinear breakdown of mechanical filters as a result of finite size, and the presents of frequency attenuation bands in essentially nonlinear materials. We finish by presenting two new energy harvesting systems based on our experience with instabilities in weakly nonlinear systems.

Consumo de combustível na operação de subsolagem realizada antes e depois de diferentes sistemas de preparo periódico do solo

A subsolagem tem aumentado nos últimos anos de forma indiscriminada, faltando estudos que norteiem os melhores procedimentos para que novos problemas não sejam acrescentados devido a subsolagens inadequadas ou mesmo em solos onde a operação é desnecessária, e principalmente buscar redução no consumo de combustível. Dessa forma, este trabalho teve o objetivo de avaliar o consumo de combustível na operação de subsolagem efetuada antes e depois de diferentes sistemas de preparo periódico do solo, classificado como Nitossolo Vermelho distroférrico. Os preparos foram realizados com arado de discos, arado de discos mais uma gradagem de nivelamento, grade pesada, grade pesada mais gradagem de nivelamento e escarificador. A realização da subsolagem depois dos sistemas de preparo periódico requereu 15% menos de potência na barra de tração. A subsolagem depois dos diferentes sistemas de preparo economizou 16,5% de combustível por área. O deslizamento das rodas motrizes e a velocidade média operacional obtiveram melhor desempenho quando se realizou a subsolagem depois do preparo do solo.

On a control of a non-ideal mono-rail system with periodics coefficients

In this work, the problem in the loads transport (in platforms or suspended by cables) it is considered. The system in subject is composed for mono-rail system and was modeled through the system: inverted pendulum, car and motor and the movement equations were obtained through the Lagrange equations. In the model, was considered the interaction among of the motor and system dynamics for several potencies motor, that is, the case studied is denominated a non-ideal periodic problem. The non-ideal periodic problem dynamics was analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, one was made it analyzes quantitative of the problem through the analysis of the Floquet multipliers. Finally, the non-ideal problem was controlled. The method that was used for analysis and control of non-ideal periodic systems is based on the Chebyshev polynomial expansion, in the Picard iterative method and in the Lyapunov-Floquet transformation (L-F trans formation). This method was presented recently in [3-9].

Análise da estabilidade de sistemas dinâmicos periódicos usando Teoria de Sinha

Pós-graduação em Matemática - IBILCE

Aplicação de métodos computacionais no estudo das fases intermetálicas ordenadas pt-sn

Fuel cells are a very promising solution to the problems of power generation and emission of pollutant to the environment, excellent to be used in stationary application and mobile application too. The high cost of production of these devices, mainly due to the use of noble metals as anode, is a major obstacle to massive production and deployment of this technology, however the use of intermetallic phases of platinum combined with other metals less noble has been evaluated as electrodes in order to minimize production costs and still being able to significantly improve the catalytic performance of the anode. The study of intermetallic phases, exclusively done by experimental techniques is not complete and demand that other methods need to be applied to a deeper understanding of the behavior geometric properties and the electronic structure of the material, to this end the use of computer simulation methods, which have proved appropriate for a broader understanding of the geometric and electronic properties of the materials involved, so far not so well understood.. The use of computational methods provides answers to explain the behavior of the materials and allows assessing whether the intermetallic may be a good electrode. In this research project was used the Quantum-ESPRESSO package, based on the DFT theory, which provides the self-consistent field calculations with great precision, calculations of the periodic systems interatomic force, and other post-processing calculations that points to a knowledge of the geometric and electronic properties of materials, which may be related to other properties of them, even the electrocatalytic. The electronic structure is determined from the optimized geometric structure of materials by analyzing the density of states (DOS) projected onto atomic orbital, which determines the influence of the electrocatalytic properties of the material... (Complete abstract click electronic access below)

Quantifying the periodicty of Inter Movement Intervals of Leg Movements

ims: Periodic leg movements in sleep (PLMS) are a frequent finding in polysomnography. Most patients with restless legs syndrome (RLS) display PLMS. However, since PLMS are also often recorded in healthy elderly subjects, the clinical significance of PLMS is still discussed controversially. Leg movements are seen concurrently with arousals in obstructive sleep apnoea (OSA) may also appear periodically. Quantitative assessment of the periodicity of LM/PLM as measured by inter movement intervals (IMI) is difficult. This is mainly due to influencing factors like sleep architecture and sleep stage, medication, inter and intra patient variability, the arbitrary amplitude and sequence criteria which tend to broaden the IMI distributions or make them even multi-modal. Methods: Here a statistical method is presented that enables eliminating such effects from the raw data before analysing the statistics of IMI. Rather than studying the absolute size of IMI (measured in seconds) we focus on the shape of their distribution (suitably normalized IMI). To this end we employ methods developed in Random Matrix Theory (RMT). Patients: The periodicity of leg movements (LM) of four patient groups (10 to 15 each) showing LM without PLMS (group 1), OSA without PLMS (group 2), PLMS and OSA (group 3) as well as PLMS without OSA (group 4) are compared. Results: The IMI of patients without PLMS (groups 1 and 2) and with PLMS (groups 3 and 4) are statistically different. In patients without PLMS the distribution of normalized IMI resembles closely the one of random events. In contrary IMI of PLMS patients show features of periodic systems (e.g. a pendulum) when studied in normalized manner. Conclusions: For quantifying PLMS periodicity proper normalization of the IMI is crucial. Without this procedure important features are hidden when grouping LM/PLM over whole nights or across patients. The clinical significance of PLMS might be eluded when properly separating random LM from LM that show features of periodic systems.

Experimental and Theoretical Electron Density Analysis of Copper Pyrazine Nitrate Quasi-Low-Dimensional Quantum Magnets

The accurate electron density distribution and magnetic properties of two metal-organic polymeric magnets, the quasi-one-dimensional (1D) Cu(pyz)(NO3)2 and the quasi-two-dimensional (2D) [Cu(pyz)2(NO3)]NO3·H2O, have been investigated by high-resolution single-crystal X-ray diffraction and density functional theory calculations on the whole periodic systems and on selected fragments. Topological analyses, based on quantum theory of atoms in molecules, enabled the characterization of possible magnetic exchange pathways and the establishment of relationships between the electron (charge and spin) densities and the exchange-coupling constants. In both compounds, the experimentally observed antiferromagnetic coupling can be quantitatively explained by the Cu-Cu superexchange pathway mediated by the pyrazine bridging ligands, via a σ-type interaction. From topological analyses of experimental charge-density data, we show for the first time that the pyrazine tilt angle does not play a role in determining the strength of the magnetic interaction. Taken in combination with molecular orbital analysis and spin density calculations, we find a synergistic relationship between spin delocalization and spin polarization mechanisms and that both determine the bulk magnetic behavior of these Cu(II)-pyz coordination polymers.

Periodic oscillations in feedback systems with combined pulse modulation

This paper presents a systematic method of investigating the existence of limit cycle oscillations in feedback systems with combined integral pulse frequency-pulse width (IPF-P/V) modulation. The method is based on the non-linear discrete equivalence of the continuous feedback system containing the IPF-PW modulator.

Homonuclear NOE in spatially periodic spin systems

The nuclear Overhauser effect equations are solved analytically for a homonuclear group of spins whose sites are periodically arranged, including the special cases where the spins lie at the vertices of a regular polygon and on a one-dimensional lattice. t is shown that, for long correlation times, the equations governing magnetization transfer resemble a diffusion equation. Furthermore the deviation from exact diffusion is quantitatively related to the molecular tumbling correlation time. Equations are derived for the range of magnetization travel subsequent to the perturbation of a single spin in a lattice for both the case of strictly dipolar relaxation and the more general situation where additional T1 mechanisms may be active. The theory given places no restrictions on the delay (or mixing) times, and it includes all the spins in the system. Simulations are presented to confirm the theory.

Majorana fermions in superconducting 1D systems having periodic, quasiperiodic, and disordered potentials

We present a unified study of the effect of periodic, quasiperiodic, and disordered potentials on topological phases that are characterized by Majorana end modes in one-dimensional p-wave superconducting systems. We define a topological invariant derived from the equations of motion for Majorana modes and, as our first application, employ it to characterize the phase diagram for simple periodic structures. Our general result is a relation between the topological invariant and the normal state localization length. This link allows us to leverage the considerable literature on localization physics and obtain the topological phase diagrams and their salient features for quasiperiodic and disordered systems for the entire region of parameter space. DOI: 10.1103/PhysRevLett.110.146404