Magnetohydrodynamic turbulence

We simulate incompressible, MHD turbulence using a pseudo-spectral code. Our major conclusions are as follows.

1) MHD turbulence is most conveniently described in terms of counter propagating shear Alfvén and slow waves. Shear Alfvén waves control the cascade dynamics. Slow waves play a passive role and adopt the spectrum set by the shear Alfvén waves. Cascades composed entirely of shear Alfvén waves do not generate a significant measure of slow waves.

2) MHD turbulence is anisotropic with energy cascading more rapidly along k_⊥ than along k_∥, where k_⊥ and k_∥ refer to wavevector components perpendicular and parallel to the local magnetic field. Anisotropy increases with increasing k_⊥ such that excited modes are confined inside a cone bounded by k_∥ ∝ k^γ_⊥ where γ less than 1. The opening angle of the cone, θ(k_⊥) ∝ k^-(1-γ)_⊥, defines the scale dependent anisotropy.

3) MHD turbulence is generically strong in the sense that the waves which comprise it suffer order unity distortions on timescales comparable to their periods. Nevertheless, turbulent fluctuations are small deep inside the inertial range. Their energy density is less than that of the background field by a factor θ² (k_⊥)≪1.

4) MHD cascades are best understood geometrically. Wave packets suffer distortions as they move along magnetic field lines perturbed by counter propagating waves. Field lines perturbed by unidirectional waves map planes perpendicular to the local field into each other. Shear Alfvén waves are responsible for the mapping's shear and slow waves for its dilatation. The amplitude of the former exceeds that of the latter by 1/θ(k_⊥) which accounts for dominance of the shear Alfvén waves in controlling the cascade dynamics.

5) Passive scalars mixed by MHD turbulence adopt the same power spectrum as the velocity and magnetic field perturbations.

6) Decaying MHD turbulence is unstable to an increase of the imbalance between the flux of waves propagating in opposite directions along the magnetic field. Forced MHD turbulence displays order unity fluctuations with respect to the balanced state if excited at low k by δ(t) correlated forcing. It appears to be statistically stable to the unlimited growth of imbalance.

7) Gradients of the dynamic variables are focused into sheets aligned with the magnetic field whose thickness is comparable to the dissipation scale. Sheets formed by oppositely directed waves are uncorrelated. We suspect that these are vortex sheets which the mean magnetic field prevents from rolling up.

8) Items (1)-(5) lend support to the model of strong MHD turbulence put forth by Goldreich and Sridhar (1995, 1997). Results from our simulations are also consistent with the GS prediction γ = 2/3. The sole not able discrepancy is that the 1D power law spectra, E(k_⊥) ∝ k^-∝_⊥, determined from our simulations exhibit ∝ ≈ 3/2, whereas the GS model predicts ∝ = 5/3.

Velocity resolved - scalar modeled simulations of high Schmidt number turbulent transport

The objective of this thesis is to develop a framework to conduct velocity resolved - scalar modeled (VR-SM) simulations, which will enable accurate simulations at higher Reynolds and Schmidt (Sc) numbers than are currently feasible. The framework established will serve as a first step to enable future simulation studies for practical applications. To achieve this goal, in-depth analyses of the physical, numerical, and modeling aspects related to Sc>>1 are presented, specifically when modeling in the viscous-convective subrange. Transport characteristics are scrutinized by examining scalar-velocity Fourier mode interactions in Direct Numerical Simulation (DNS) datasets and suggest that scalar modes in the viscous-convective subrange do not directly affect large-scale transport for high Sc. Further observations confirm that discretization errors inherent in numerical schemes can be sufficiently large to wipe out any meaningful contribution from subfilter models. This provides strong incentive to develop more effective numerical schemes to support high Sc simulations. To lower numerical dissipation while maintaining physically and mathematically appropriate scalar bounds during the convection step, a novel method of enforcing bounds is formulated, specifically for use with cubic Hermite polynomials. Boundedness of the scalar being transported is effected by applying derivative limiting techniques, and physically plausible single sub-cell extrema are allowed to exist to help minimize numerical dissipation. The proposed bounding algorithm results in significant performance gain in DNS of turbulent mixing layers and of homogeneous isotropic turbulence. Next, the combined physical/mathematical behavior of the subfilter scalar-flux vector is analyzed in homogeneous isotropic turbulence, by examining vector orientation in the strain-rate eigenframe. The results indicate no discernible dependence on the modeled scalar field, and lead to the identification of the tensor-diffusivity model as a good representation of the subfilter flux. Velocity resolved - scalar modeled simulations of homogeneous isotropic turbulence are conducted to confirm the behavior theorized in these a priori analyses, and suggest that the tensor-diffusivity model is ideal for use in the viscous-convective subrange. Simulations of a turbulent mixing layer are also discussed, with the partial objective of analyzing Schmidt number dependence of a variety of scalar statistics. Large-scale statistics are confirmed to be relatively independent of the Schmidt number for Sc>>1, which is explained by the dominance of subfilter dissipation over resolved molecular dissipation in the simulations. Overall, the VR-SM framework presented is quite effective in predicting large-scale transport characteristics of high Schmidt number scalars, however, it is determined that prediction of subfilter quantities would entail additional modeling intended specifically for this purpose. The VR-SM simulations presented in this thesis provide us with the opportunity to overlap with experimental studies, while at the same time creating an assortment of baseline datasets for future validation of LES models, thereby satisfying the objectives outlined for this work.

The impact of year-to-year changes in the weather on the seasonal dynamics of lakes

The methods currently used to monitor and model lakes were developed when weather conditions were very different to what they are today. Most are based on samples collected at weekly or fortnightly intervals and cannot quantify the effects of short-term, more extreme, variations in the weather. In this article, the author presents some examples to show the importance of developing new monitoring methods using case studies from a number of lakes in the English Lake District. The impact of year-to-year changes and short-term changes on the dynamics of of lakes are highlighted.

The impact of year-to-year changes in the weather on the seasonal dynamics of lakes

Year-to-year changes in the weather have a pronounced effect on the quality of the water abstracted from many reservoirs in the UK. In upland reservoirs, the most common weather-related problem is the appearance of coloured water following dry summers and the re-wetting of peat during the winter (Naden & McDonald 1989; George 2000). In lowland reservoirs, the most serious weather-related issue is the growth of bloom- forming species of algae during warm, calm summers (National Rivers Authority 1989). Both of these problems are likely to get worse as the climate becomes warmer and extreme variations in the weather become more common. In this article, the authors describe some of the ways in which recent changes in the weather have influenced the quality of the water stored in a large reservoir in the south-east of England. The reservoir selected for study is the Queen Elizabeth II (QEII), a bankside reservoir situated in the Thames valley. The quality of water stored in this reservoir is generally very good but summer blooms of algae have become increasingly common in recent years.

Structure Prediction of G-Protein Coupled Receptors

G-protein coupled receptors (GPCRs) form a large family of proteins and are very important drug targets. They are membrane proteins, which makes computational prediction of their structure challenging. Homology modeling is further complicated by low sequence similarly of the GPCR superfamily.

In this dissertation, we analyze the conserved inter-helical contacts of recently solved crystal structures, and we develop a unified sequence-structural alignment of the GPCR superfamily. We use this method to align 817 human GPCRs, 399 of which are nonolfactory. This alignment can be used to generate high quality homology models for the 817 GPCRs.

To refine the provided GPCR homology models we developed the Trihelix sampling method. We use a multi-scale approach to simplify the problem by treating the transmembrane helices as rigid bodies. In contrast to Monte Carlo structure prediction methods, the Trihelix method does a complete local sampling using discretized coordinates for the transmembrane helices. We validate the method on existing structures and apply it to predict the structure of the lactate receptor, HCAR1. For this receptor, we also build extracellular loops by taking into account constraints from three disulfide bonds. Docking of lactate and 3,5-dihydroxybenzoic acid shows likely involvement of three Arg residues on different transmembrane helices in binding a single ligand molecule.

Protein structure prediction relies on accurate force fields. We next present an effort to improve the quality of charge assignment for large atomic models. In particular, we introduce the formalism of the polarizable charge equilibration scheme (PQEQ) and we describe its implementation in the molecular simulation package Lammps. PQEQ allows fast on the fly charge assignment even for reactive force fields.

Key to the larvae of the genera of the sub-family Orthocladiinae from Larvae and Pupae of midges of the sub-family Orthocladiinae of the fauna of the USSR. [Translation from: Larvae and pupae of midges of the subfamily Orthocladiinae of the fauna of the USSR (Diptera, Chironomidae = Tendipedidae) (ed. Pankratova V.Ya.), 51-55. Leningrad, Nauka, 1970. ]

A key to the larvae of the genera of the sub-family Orthocladiinae from Larvae and Pupae of midges of the sub-family Orthocladiinae. Parts of the key refer to the rest of the publication which is not included in this partial translation.

Seasonal variation in the diurnal periodicity of activity of the perch, Perca fluviatilis L. [Translation from: Kalamies 1973(3) 3.]

The most common catch of the amateur angler is the perch and it is the diurnal periodicity of activity (& catchability) which is examined in this study based on earlier articles and manuscripts by the authors. Of all environmental factors, variation in light and temperature are the chief reasons in establishing the times of activity periods. Winter, summer and autumn activity was studied. The spawning perch was found to be more active than the non-spawning perch. The time of day in which the fish may be active is dependant on its ability to sense changes in the external environment. Its adaptation to light is the reason for day-activity in the winter, and also accounts for the fact that hardly any activity occurs between sunset and sunrise when this period exceeds 6 hours.

(Ce,Cu)∶LiNbO3晶体非挥发全息记录理论研究与优化

根据双中心带输运模型,对(Ce,Cu)∶LiNbO3晶体双中心非挥发全息记录进行了理论研究与优化。推导了(Ce,Cu)∶LiNbO3晶体的微观参量,采用数值方法通过严格求解模拟双中心带输运方程来模拟全息记录过程。分析了记录过程中,记录与敏化光强、Ce和Cu掺杂浓度以及晶体微观参量对(Ce,Cu)∶LiNbO3晶体双中心全息记录的影响。发现(Ce,Cu)∶LiNbO3晶体非挥发全息记录中实现高衍射效率与固定效率的主导因素是深中心Cu,在记录过程中,深中心Cu建立起了很强的空间电荷场。数值模拟的结果经过实验验

LiNbO3∶Fe∶Rh晶体近红外非挥发全息记录

采用双中心记录方案在双掺杂LiNbO3∶Fe∶Rh晶体中实现了近红外非挥发全息记录,研究了LiNbO3∶Fe∶Rh晶体在633 nm,752 nm,799 nm波长下的全息记录性能。结果表明,在使用近红外记录光时,其记录灵敏度随敏化光强的变化趋势与双中心短波长记录时的不同。通过和LiNbO3∶Fe∶Mn等传统双掺杂铌酸锂晶体的近红外波段记录效果对比,发现同时掺杂Fe和Rh可增强晶体对近红外光的吸收,获得更高的浅中心Fe光生伏特系数,从而能够在LiNbO3∶Fe∶Rh晶体中实现近红外波段的光折变全息记录。

Ecological significance of seasonal variation in clutch-size of Arctodiaptomus bacillifer in alpine lakes of high altitudes (Val Bognanco) [Translation from: Bollettino di Zoologia 37 491-492, 1970]

This brief paper describes the significance of seasonal variation in clutch-size of the copepod Arctodiaptomus bacillifer in alpine lakes of high altitudes (Val Bognanco). Seasonal dynamics of the zooplankton of these lakes was studied during summer and autumn of 1968 and 1969and results are summarised.