Ultra-sensitive pressure dependence of bandgap of rutile-GeO2 revealed by many body perturbation theory

The reported values of bandgap of rutile GeO2 calculated by the standard density functional theory within local-density approximation (LDA)/generalized gradient approximation (GGA) show a wide variation (similar to 2 eV), whose origin remains unresolved. Here, we investigate the reasons for this variation by studying the electronic structure of rutile-GeO2 using many-body perturbation theory within the GW framework. The bandgap as well as valence bandwidth at Gamma-point of rutile phase shows a strong dependence on volume change, which is independent of bandgap underestimation problem of LDA/GGA. This strong dependence originates from a change in hybridization among O-p and Ge-(s and p) orbitals. Furthermore, the parabolic nature of first conduction band along X-Gamma-M direction changes towards a linear dispersion with volume expansion. (C) 2015 AIP Publishing LLC.

Numerical study of bluff body flow structures

Our recent progress in numerical studies of bluff body flow structures and a new method for the numerical analysis of near wake flow field for high Reynolds number flow are introduced. The paper consists of three parts. In part one, the evolution of wake vortex structure and variation of forces on a flat plate in harmonic oscillatory flows and in in-line steady-harmonic combined flows are presented by an improved discrete vortex method, as the Keulegan-Carpenter number (KC) varies from 2 to 40 and ratios of U-m to U-0 are of O(10(-1)), O(10) and O(10), respectively. In part 2, a domain decomposition hybrid method, combining the finite-difference and vortex methods for numerical simulation of unsteady viscous separated flow around a bluff body, is introduced. By the new method, some high resolution numerical visualization on near wake evolution behind a circular cylinder at Re = 10(2), 10(3) and 3 x 10(3) are shown. In part 3, the mechanism and the dynamic process for the three-dimensional evolution of the Karman vortex and vortex filaments in braid regions as well as the early features of turbulent structure in the wake behind a circular cylinder are presented numerically by the vortex dynamics method.

On the non-linear stability theory of spinning solid bodies with liquid-filled cavities and its application to the columbus problem

In this paper, we first present a system of differential-integral equations for the largedisturbance to the general case that any arbitrarily shaped solid body with a cavity contain-ing viscous liquid rotates uniformly around the principal axis of inertia, and then develop aweakly non-linear stability theory by the Lyapunov direct approach. Applying this theoryto the Columbus problem, we have proved the consistency between the theory and Kelvin'sexperiments.

Computation of flow over a rotating body on unstructured Chimera mesh

Flow around moving boundary is ubiquitous in engineering applications. To increse the efficienly of the algorithm to handle moving boundaries is still a major challenge in Computational Fluid Dynamics (CFD). The Chimera grid method is one type of method to handle moving boundaries. A concept of domain de-composition has been proposed in this paper. In this method, sub-domains are meshed independently and governing equations are also solved separately on them. The Chimera grid method was originally used only on structured (curvilinear) meshes. However, in a problem which involves both moving boundary and complex geometry, the number of sub-domains required in a traditional (structured) Chimera method becomes fairly large. Thus the time required in the interior boundary locating, link-building and data exchanging also increases. The use of unstructured Chimera grid can reduce the time consumption significantly by the reduction of domain(block) number. Generally speaking, unstructured Chimera grid method has not been developed. In this paper, a well-known pressure correction scheme - SIMPLEC is modified and implemented on unstructured Chimera mesh. A new interpolation scheme regarding the pressure correction is proposed to prevent the possible decoupling of pressure. A moving-mesh finite volume approach is implemented in an inertial reference frame. This approach is then used to compute incompressible flow around a rotating circular and elliptic cylinder. These numerical examples demonstrate the capability of the proposed scheme in handling moving boundaries. The numerical results are in good agreement with other experimental and computational data in literature. The method proposed in this paper can be efficiently applied to more challenge cases such as free-falling objects or heavy particles in fluid.

Effects of geometric shape on the hydrodynamics of a self-propelled flapping foil

The hydrodynamics of a free flapping foil is studied numerically. The foil undergoes a forced vertical oscillation and is free to move horizontally. The effect of chord-thickness ratio is investigated by varying this parameter while fixing other ones such as the Reynolds number, the density ratio, and the flapping amplitude. Three different flow regimes have been identified when we increase the chord-thickness ratio, i.e., left-right symmetry, back-and-forth chaotic motion, and unidirectional motion with staggered vortex street. It is observed that the chord-thickness ratio can affect the symmetry-breaking bifurcation, the arrangement of vortices in the wake, and the terminal velocity of the foil. The similarity in the symmetry-breaking bifurcation of the present problem to that of a flapping body under constraint is discussed. A comparison between the dynamic behaviors of an elliptic foil and a rectangular foil at various chord-thickness ratios is also presented.

Exact solutions and transformation properties of nonlinear partial differential equations from general relativity

Various families of exact solutions to the Einstein and Einstein-Maxwell field equations of General Relativity are treated for situations of sufficient symmetry that only two independent variables arise. The mathematical problem then reduces to consideration of sets of two coupled nonlinear differential equations.

The physical situations in which such equations arise include: a) the external gravitational field of an axisymmetric, uncharged steadily rotating body, b) cylindrical gravitational waves with two degrees of freedom, c) colliding plane gravitational waves, d) the external gravitational and electromagnetic fields of a static, charged axisymmetric body, and e) colliding plane electromagnetic and gravitational waves. Through the introduction of suitable potentials and coordinate transformations, a formalism is presented which treats all these problems simultaneously. These transformations and potentials may be used to generate new solutions to the Einstein-Maxwell equations from solutions to the vacuum Einstein equations, and vice-versa.

The calculus of differential forms is used as a tool for generation of similarity solutions and generalized similarity solutions. It is further used to find the invariance group of the equations; this in turn leads to various finite transformations that give new, physically distinct solutions from old. Some of the above results are then generalized to the case of three independent variables.

I. Rigid body penetration into brittle materials. II. Phase change effect on shock wave propagation

Part I.

We have developed a technique for measuring the depth time history of rigid body penetration into brittle materials (hard rocks and concretes) under a deceleration of ~ 10⁵ g. The technique includes bar-coded projectile, sabot-projectile separation, detection and recording systems. Because the technique can give very dense data on penetration depth time history, penetration velocity can be deduced. Error analysis shows that the technique has a small intrinsic error of ~ 3-4 % in time during penetration, and 0.3 to 0.7 mm in penetration depth. A series of 4140 steel projectile penetration into G-mixture mortar targets have been conducted using the Caltech 40 mm gas/ powder gun in the velocity range of 100 to 500 m/s.

We report, for the first time, the whole depth-time history of rigid body penetration into brittle materials (the G-mixture mortar) under 10⁵ g deceleration. Based on the experimental results, including penetration depth time history, damage of recovered target and projectile materials and theoretical analysis, we find:

1. Target materials are damaged via compacting in the region in front of a projectile and via brittle radial and lateral crack propagation in the region surrounding the penetration path. The results suggest that expected cracks in front of penetrators may be stopped by a comminuted region that is induced by wave propagation. Aggregate erosion on the projectile lateral surface is < 20% of the final penetration depth. This result suggests that the effect of lateral friction on the penetration process can be ignored.

2. Final penetration depth, P_max, is linearly scaled with initial projectile energy per unit cross-section area, e_s , when targets are intact after impact. Based on the experimental data on the mortar targets, the relation is P_max(mm) 1.15e_s (J/mm² ) + 16.39.

3. Estimation of the energy needed to create an unit penetration volume suggests that the average pressure acting on the target material during penetration is ~ 10 to 20 times higher than the unconfined strength of target materials under quasi-static loading, and 3 to 4 times higher than the possible highest pressure due to friction and material strength and its rate dependence. In addition, the experimental data show that the interaction between cracks and the target free surface significantly affects the penetration process.

4. Based on the fact that the penetration duration, t_max, increases slowly with e_s and does not depend on projectile radius approximately, the dependence of t_max on projectile length is suggested to be described by t_max(μs) = 2.08e_s (J/mm² + 349.0 x m/(πR²), in which m is the projectile mass in grams and R is the projectile radius in mm. The prediction from this relation is in reasonable agreement with the experimental data for different projectile lengths.

5. Deduced penetration velocity time histories suggest that whole penetration history is divided into three stages: (1) An initial stage in which the projectile velocity change is small due to very small contact area between the projectile and target materials; (2) A steady penetration stage in which projectile velocity continues to decrease smoothly; (3) A penetration stop stage in which projectile deceleration jumps up when velocities are close to a critical value of ~ 35 m/s.

6. Deduced averaged deceleration, a, in the steady penetration stage for projectiles with same dimensions is found to be a(g) = 192.4v + 1.89 x 10⁴, where v is initial projectile velocity in m/s. The average pressure acting on target materials during penetration is estimated to be very comparable to shock wave pressure.

7. A similarity of penetration process is found to be described by a relation between normalized penetration depth, P/P_max, and normalized penetration time, t/t_max, as P/P_max = f(t/t_max, where f is a function of t/t_max. After f(t/t_max is determined using experimental data for projectiles with 150 mm length, the penetration depth time history for projectiles with 100 mm length predicted by this relation is in good agreement with experimental data. This similarity also predicts that average deceleration increases with decreasing projectile length, that is verified by the experimental data.

8. Based on the penetration process analysis and the present data, a first principle model for rigid body penetration is suggested. The model incorporates the models for contact area between projectile and target materials, friction coefficient, penetration stop criterion, and normal stress on the projectile surface. The most important assumptions used in the model are: (1) The penetration process can be treated as a series of impact events, therefore, pressure normal to projectile surface is estimated using the Hugoniot relation of target material; (2) The necessary condition for penetration is that the pressure acting on target materials is not lower than the Hugoniot elastic limit; (3) The friction force on projectile lateral surface can be ignored due to cavitation during penetration. All the parameters involved in the model are determined based on independent experimental data. The penetration depth time histories predicted from the model are in good agreement with the experimental data.

9. Based on planar impact and previous quasi-static experimental data, the strain rate dependence of the mortar compressive strength is described by σ_f/σ⁰_f = exp(0.0905(log(έ/έ_0) ^1.14, in the strain rate range of 10^-7/s to 10³/s (σ⁰_f and έ are reference compressive strength and strain rate, respectively). The non-dispersive Hugoniot elastic wave in the G-mixture has an amplitude of ~ 0.14 GPa and a velocity of ~ 4.3 km/s.

Part II.

Stress wave profiles in vitreous GeO₂ were measured using piezoresistance gauges in the pressure range of 5 to 18 GPa under planar plate and spherical projectile impact. Experimental data show that the response of vitreous GeO₂ to planar shock loading can be divided into three stages: (1) A ramp elastic precursor has peak amplitude of 4 GPa and peak particle velocity of 333 m/s. Wave velocity decreases from initial longitudinal elastic wave velocity of 3.5 km/s to 2.9 km/s at 4 GPa; (2) A ramp wave with amplitude of 2.11 GPa follows the precursor when peak loading pressure is 8.4 GPa. Wave velocity drops to the value below bulk wave velocity in this stage; (3) A shock wave achieving final shock state forms when peak pressure is > 6 GPa. The Hugoniot relation is D = 0.917 + 1.711u (km/s) using present data and the data of Jackson and Ahrens [1979] when shock wave pressure is between 6 and 40 GPa for ρ₀ = 3.655 gj cm³ . Based on the present data, the phase change from 4-fold to 6-fold coordination of Ge⁺⁴ with O^-2 in vitreous GeO₂ occurs in the pressure range of 4 to 15 ± 1 GPa under planar shock loading. Comparison of the shock loading data for fused SiO₂ to that on vitreous GeO₂ demonstrates that transformation to the rutile structure in both media are similar. The Hugoniots of vitreous GeO₂ and fused SiO₂ are found to coincide approximately if pressure in fused SiO₂ is scaled by the ratio of fused SiO₂to vitreous GeO₂ density. This result, as well as the same structure, provides the basis for considering vitreous Ge0₂ as an analogous material to fused SiO₂ under shock loading. Experimental results from the spherical projectile impact demonstrate: (1) The supported elastic shock in fused SiO₂ decays less rapidly than a linear elastic wave when elastic wave stress amplitude is higher than 4 GPa. The supported elastic shock in vitreous GeO₂ decays faster than a linear elastic wave; (2) In vitreous GeO₂ , unsupported shock waves decays with peak pressure in the phase transition range (4-15 GPa) with propagation distance, x, as α 1/x^-3.35 , close to the prediction of Chen et al. [1998]. Based on a simple analysis on spherical wave propagation, we find that the different decay rates of a spherical elastic wave in fused SiO₂ and vitreous GeO₂ is predictable on the base of the compressibility variation with stress under one-dimensional strain condition in the two materials.

Conditional independence in quantum many-body systems

In this thesis, I will discuss how information-theoretic arguments can be used to produce sharp bounds in the studies of quantum many-body systems. The main advantage of this approach, as opposed to the conventional field-theoretic argument, is that it depends very little on the precise form of the Hamiltonian. The main idea behind this thesis lies on a number of results concerning the structure of quantum states that are conditionally independent. Depending on the application, some of these statements are generalized to quantum states that are approximately conditionally independent. These structures can be readily used in the studies of gapped quantum many-body systems, especially for the ones in two spatial dimensions. A number of rigorous results are derived, including (i) a universal upper bound for a maximal number of topologically protected states that is expressed in terms of the topological entanglement entropy, (ii) a first-order perturbation bound for the topological entanglement entropy that decays superpolynomially with the size of the subsystem, and (iii) a correlation bound between an arbitrary local operator and a topological operator constructed from a set of local reduced density matrices. I also introduce exactly solvable models supported on a three-dimensional lattice that can be used as a reliable quantum memory.

The interplay of localization and interactions in quantum many-body systems

Disorder and interactions both play crucial roles in quantum transport. Decades ago, Mott showed that electron-electron interactions can lead to insulating behavior in materials that conventional band theory predicts to be conducting. Soon thereafter, Anderson demonstrated that disorder can localize a quantum particle through the wave interference phenomenon of Anderson localization. Although interactions and disorder both separately induce insulating behavior, the interplay of these two ingredients is subtle and often leads to surprising behavior at the periphery of our current understanding. Modern experiments probe these phenomena in a variety of contexts (e.g. disordered superconductors, cold atoms, photonic waveguides, etc.); thus, theoretical and numerical advancements are urgently needed. In this thesis, we report progress on understanding two contexts in which the interplay of disorder and interactions is especially important.

The first is the so-called “dirty” or random boson problem. In the past decade, a strong-disorder renormalization group (SDRG) treatment by Altman, Kafri, Polkovnikov, and Refael has raised the possibility of a new unstable fixed point governing the superfluid-insulator transition in the one-dimensional dirty boson problem. This new critical behavior may take over from the weak-disorder criticality of Giamarchi and Schulz when disorder is sufficiently strong. We analytically determine the scaling of the superfluid susceptibility at the strong-disorder fixed point and connect our analysis to recent Monte Carlo simulations by Hrahsheh and Vojta. We then shift our attention to two dimensions and use a numerical implementation of the SDRG to locate the fixed point governing the superfluid-insulator transition there. We identify several universal properties of this transition, which are fully independent of the microscopic features of the disorder.

The second focus of this thesis is the interplay of localization and interactions in systems with high energy density (i.e., far from the usual low energy limit of condensed matter physics). Recent theoretical and numerical work indicates that localization can survive in this regime, provided that interactions are sufficiently weak. Stronger interactions can destroy localization, leading to a so-called many-body localization transition. This dynamical phase transition is relevant to questions of thermalization in isolated quantum systems: it separates a many-body localized phase, in which localization prevents transport and thermalization, from a conducting (“ergodic”) phase in which the usual assumptions of quantum statistical mechanics hold. Here, we present evidence that many-body localization also occurs in quasiperiodic systems that lack true disorder.

Evaluation of the body burdens of heavy metals in five commercially important fishes from different locations in Kainji Lake

The level and distribution of some heavy metals viz Cadmium, Lead, Copper Zinc, and Cobalt in five commercially important fishes, water and sediments at three different locations in Kainj Lake were determined using standard methods. The results show that the ranges of heavy metals mu g/g in fishes in Dam site Laotian are: Cd (0.05~c0.01-20~c01), (Pb(ND-1.12 plus or minus )1), Cu (0.81~c25-2.93~c06), Zn (20.89 arrow right .15-36.78~c2.97), Co(0.08~c01-0.27~c02); in cover Dam, the ranges are Cd (0.04~c02-0.16~c0.2), Pb (nd-02~c01), Cu(0.75~c05-2.61~c13), Zn(15.70~c1.55-32.23~c2.70), Co(0.04~c02-0.25~c0.01) and in Yuna they are Cd (0.05~c01-0.14~c02), Pb (nd-0.32~c01), Cu (0.23~c07-2.70~c05), Zn(15.50 plus or minus `.35-25.62~c2.47), Co(0.07~c02-23~c0.01). The metals concentration (mg/l) in the water sample from Dam site, cover dam and Yuna respectively are Cd(0.007~c001,. 004~c001 and 0.005~001), Pb(013~c001, ND and ND), Cu(.055~c008.030~c007, 05 plus or minus .010), Zn(0.13~c01, 0.060 plus or minus .0055) and Co (.026 plus or minus .022 plus or minus .004, .024 plus or minus .004), while the metals concentration ( mu g/g) in sediments sample from Dam site, cover dam and Yuna are respectively Cd(.05 plus or minus .01, .02 plus or minus .01), Pb(16.00~c1.00, ND and 9.33~c1.01), Cu(24.00~c1.34, 4.26 plus or minus .91 and 11.08~c1.32), Zn(42.00~c1.00, 35~c10 and 38.00 plus or minus .45), Co(15.00~c1.17, 8.69~c1.21 and 10.91~c44). The concentrations of the tested heavy metals are within the acceptable standards of WHO (1987a)

Toxic blue-green algae: The "problem" in perspective

The incidence of blue-green algal blooms and surface scum-formation are certainly not new phenomena. Many British and European authors have been faithfully describing the unmistakable symptoms of blue-green algal scums for over 800 years. There is no disputing that blue-green algal toxins are extremely harmful. Three quite separate categories of compound have been separated: neurotoxins; hepatotoxins and lipopolysaccharides. There is a popular association between blue-green algae and eutrophication. Certainly the main nuisance species - of Microcystis, Anabaena and Aphanizomenon are rare in oligotrophic lakes and reservoirs. Several approaches have been proposed for the control of blue-green algae. Distinction is made between methods for discharging algae already present (eg algicides; straw bales; viruses; parasitic fungi and herbivorous ciliates), and methods for averting an anticipated abundance in the future (phosphorous control, artificial circulation etc).

The problem of the co-existence of Arctodiaptomus bacillifer (Koelb.), Acanthodiaptomus denticornis (Wierz.) and Heterocope saliens Lill [Translation from: Memorie dell'Istituto Italiano di Idrobiologia Dott.Marco de Marchi 8 81-94, 1954]

In freshwater environments of modest size and without notable ecological structure, there is usually present only one diaptomid species. When two or more diaptomid species are present in the same habitat, generally their body dimensions are distinctly different. There are only four examples of co-existence of Arctodiaptomus bacillifer (Koelb.) and Acanthodiaptomus denticornis (Wierz.) situated at higher altitudes alpine lakes. The article discusses the results of sampling in the summer of 1953 and the problem of the co-existence of Arctodiaptomus bacillifer, Acanthodiaptomus denticornis and Heterocope saliens.

Influence of local geology on earthquake ground motion

As a simplified approach for estimating theoretically the influence of local subsoils upon the ground motion during an earthquake, the problem of an idealized layered system subjected to vertically incident plane body waves was studied. Both the technique of steady-state analysis and the technique of transient analysis have been used to analyze the problem.

In the steady-state analysis, a recursion formula has been derived for obtaining the response of a layered system to sinusoidally steady-state input. Several conclusions are drawn concerning the nature of the amplification spectrum of a nonviscous layered system having its layer stiffnesses increasing with depth. Numerical examples are given to demonstrate the effect of layer parameters on the amplification spectrum of a layered system.

In the transient analysis, two modified shear beam models have been established for obtaining approximately the response of a layered system to earthquake-like excitation. The method of continuous modal analysis was adopted for approximate analysis of the models, with energy dissipation in the layers, if any, taken into account. Numerical examples are given to demonstrate the accuracy of the models and the effect of a layered system in modifying the input motion.

Conditions are established, under which the theory is applicable to predict the influence of local subsoils on the ground motion during an earthquake. To demonstrate the applicability of the models to actual cases, three examples of actually recorded earthquake events are examined. It is concluded that significant modification of the incoming seismic waves, as predicted by the theory, is likely to occur in well defined soft subsoils during an earthquake, provided that certain conditions concerning the nature of the incoming seismic waves are satisfied.

The body social: an enactive approach to the self

This paper takes a new look at an old question: what is the human self? It offers a proposal for theorizing the self from an enactive perspective as an autonomous system that is constituted through interpersonal relations. It addresses a prevalent issue in the philosophy of cognitive science: the body-social problem. Embodied and social approaches to cognitive identity are in mutual tension. On the one hand, embodied cognitive science risks a new form of methodological individualism, implying a dichotomy not between the outside world of objects and the brain-bound individual but rather between body-bound individuals and the outside social world. On the other hand, approaches that emphasize the constitutive relevance of social interaction processes for cognitive identity run the risk of losing the individual in the interaction dynamics and of downplaying the role of embodiment. This paper adopts a middle way and outlines an enactive approach to individuation that is neither individualistic nor disembodied but integrates both approaches. Elaborating on Jonas' notion of needful freedom it outlines an enactive proposal to understanding the self as co-generated in interactions and relations with others. I argue that the human self is a social existence that is organized in terms of a back and forth between social distinction and participation processes. On this view, the body, rather than being identical with the social self, becomes its mediator

Ensaismo, ação coletiva e Estado nacional : uma metainterpretação de obras selecionadas da literatura Brasiliana

O objetivo da tese é expor o movimento de coordenação coletiva que subjaz a um conjunto selecionado de obras de autores brasileiros da primeira metade do século XX reunidas sob o título Coleção Brasiliana. Sustenta-se a hipótese de que esse grupo de intelectuais interveio regularmente no debate público durante três ou quatro décadas do século passado de forma racional e concertada com vistas a construir no futuro próximo um Estado nacional no Brasil. Se o diagnóstico procede, esteve-se às voltas com um problema de ação coletiva, posto que um Estado de tipo nacional é um bem público. A estratégia de solução intraelite consistiu na criação de uma cultura política de massas baseada na idéia de ?imperativo nacional? que, mobilizando ideologicamente a opinião pública e os governantes, logrou êxito quanto aos objetivos inscritos de antemão em sua retórica: por fim à desordem, restituir a organização da nação e criar instituições políticas congruentes com a realidade do país. Para efeito do trabalho ora apresentado, os processos de state building envolvem, entre os itens de maior importância, a territorialização eficaz, a legitimação da autoridade pública e a organização da solidariedade social. No caso do Brasil, uma vez resolvido o dilema de ação coletiva relativamente aos intelectuais, emergiria mais tarde, em 1937, a estrutura institucional destinada a fixar regras, reduzir incertezas e/ou custos de informação, dotar os atores de expectativas recíprocas, enfim, trazer regularidade e curso estável às trocas entre os indivíduos: o Estado Novo. O trabalho se divide em quatro capítulos, seguidos de considerações finais ligeiras. No Capítulo I, realizo um balanço pessoal sobre a recepção da rationalchoice no meio acadêmico brasileiro, além de chamar a atenção para certas estigmatizações comuns. No Capítulo II, o conceito de racionalidade individual é submetido a exame epistêmico e ontológico não exaustivo. Busco ainda aproximá-lo de aspectos externos que tendem a alterar sua substância na origem. No Capítulo III, ofereço o referencial geral sobre a formação dos estados nacionais, afora indicações rápidas quanto aos desafios que os esperam no século XXI. No Capítulo IV, última parte do texto, observo de maneira panorâmica as etapas de formação do Estado nacional no Brasil para depois discutir o modelo de país que os intelectuais brasilianos tinham em mente para o século XX. Também procuro especificar o método de trabalho (escolha dos autores, organização por tópicos e aplicação da perspectiva neo-institucionalista). As páginas restantes se destinam à exposição das idéias brasilianas. Fecho a tese com uma síntese geral acrescida de análise sobre a coordenação dos intelectuais em torno do projeto de Estado-nação no Brasil