Single layer lead iodide: Computational exploration of structural, electronic and optical properties, strain induced band modulation and the role of spin-orbital-coupling

Graphitic like layered materials exhibit intriguing electronic structures and thus the search for new types of two-dimensional (2D) monolayer materials is of great interest for developing novel nano-devices. By using density functional theory (DFT) method, here we for the first time investigate the structure, stability, electronic and optical properties of monolayer lead iodide (PbI2). The stability of PbI2 monolayer is first confirmed by phonon dispersion calculation. Compared to the calculation using generalized gradient approximation, screened hybrid functional and spin–orbit coupling effects can not only predicts an accurate bandgap (2.63 eV), but also the correct position of valence and conduction band edges. The biaxial strain can tune its bandgap size in a wide range from 1 eV to 3 eV, which can be understood by the strain induced uniformly change of electric field between Pb and I atomic layer. The calculated imaginary part of the dielectric function of 2D graphene/PbI2 van der Waals type hetero-structure shows significant red shift of absorption edge compared to that of a pure monolayer PbI2. Our findings highlight a new interesting 2D material with potential applications in nanoelectronics and optoelectronics.

Two-scale computational modelling of water flow in unsaturated soils containing irregular-shaped inclusions

The focus of this paper is two-dimensional computational modelling of water flow in unsaturated soils consisting of weakly conductive disconnected inclusions embedded in a highly conductive connected matrix. When the inclusions are small, a two-scale Richards’ equation-based model has been proposed in the literature taking the form of an equation with effective parameters governing the macroscopic flow coupled with a microscopic equation, defined at each point in the macroscopic domain, governing the flow in the inclusions. This paper is devoted to a number of advances in the numerical implementation of this model. Namely, by treating the micro-scale as a two-dimensional problem, our solution approach based on a control volume finite element method can be applied to irregular inclusion geometries, and, if necessary, modified to account for additional phenomena (e.g. imposing the macroscopic gradient on the micro-scale via a linear approximation of the macroscopic variable along the microscopic boundary). This is achieved with the help of an exponential integrator for advancing the solution in time. This time integration method completely avoids generation of the Jacobian matrix of the system and hence eases the computation when solving the two-scale model in a completely coupled manner. Numerical simulations are presented for a two-dimensional infiltration problem.

Finite volume evolution Galerkin method for hyperbolic conservation laws with spatially varying flux functions

We present a generalization of the finite volume evolution Galerkin scheme [M. Lukacova-Medvid'ova,J. Saibertov'a, G. Warnecke, Finite volume evolution Galerkin methods for nonlinear hyperbolic systems, J. Comp. Phys. (2002) 183 533-562; M. Luacova-Medvid'ova, K.W. Morton, G. Warnecke, Finite volume evolution Galerkin (FVEG) methods for hyperbolic problems, SIAM J. Sci. Comput. (2004) 26 1-30] for hyperbolic systems with spatially varying flux functions. Our goal is to develop a genuinely multi-dimensional numerical scheme for wave propagation problems in a heterogeneous media. We illustrate our methodology for acoustic waves in a heterogeneous medium but the results can be generalized to more complex systems. The finite volume evolution Galerkin (FVEG) method is a predictor-corrector method combining the finite volume corrector step with the evolutionary predictor step. In order to evolve fluxes along the cell interfaces we use multi-dimensional approximate evolution operator. The latter is constructed using the theory of bicharacteristics under the assumption of spatially dependent wave speeds. To approximate heterogeneous medium a staggered grid approach is used. Several numerical experiments for wave propagation with continuous as well as discontinuous wave speeds confirm the robustness and reliability of the new FVEG scheme.

A three-dimensional hybrid smoothed finite element method (H-SFEM) for nonlinear solid mechanics problems

This paper presents a novel three-dimensional hybrid smoothed finite element method (H-SFEM) for solid mechanics problems. In 3D H-SFEM, the strain field is assumed to be the weighted average between compatible strains from the finite element method (FEM) and smoothed strains from the node-based smoothed FEM with a parameter α equipped into H-SFEM. By adjusting α, the upper and lower bound solutions in the strain energy norm and eigenfrequencies can always be obtained. The optimized α value in 3D H-SFEM using a tetrahedron mesh possesses a close-to-exact stiffness of the continuous system, and produces ultra-accurate solutions in terms of displacement, strain energy and eigenfrequencies in the linear and nonlinear problems. The novel domain-based selective scheme is proposed leading to a combined selective H-SFEM model that is immune from volumetric locking and hence works well for nearly incompressible materials. The proposed 3D H-SFEM is an innovative and unique numerical method with its distinct features, which has great potential in the successful application for solid mechanics problems.

Effect of inflow and outflow angles on the computational hemodynamics in abdominal aortic aneurysm

To help with the clinical screening and diagnosis of abdominal aortic aneurysm (AAA), we evaluated the effect of inflow angle (IA) and outflow bifurcation angle (BA) on the distribution of blood flow and wall shear stress (WSS) in an idealized AAA model. A 2D incompressible Newtonian flow is assumed and the computational simulation is performed using finite volume method. The results showed that the largest WSS often located at the proximal and the distal end of the AAA. An increase in IA resulted in an increase in maximum WSS. We also found that WSS was maximal when BA was 90°. IA and BA are two important geometrical factors, they may help with AAA risk assessment along with the commonly used AAA diameter.

Comparison between computational models of abdominal aortic aneurysm

Objective: To compare the differences in the hemodynamic parameters of abdominal aortic aneurysm (AAA) between fluid-structure interaction model (FSIM) and fluid-only model (FM), so as to discuss their application in the research of AAA. Methods: An idealized AAA model was created based on patient-specific AAA data. In FM, the flow, pressure and wall shear stress (WSS) were computed using finite volume method. In FSIM, an Arbitrary Lagrangian-Eulerian algorithm was used to solve the flow in a continuously deforming geometry. The hemodynamic parameters of both models were obtained for discussion. Results: Under the same inlet velocity, there were only two symmetrical vortexes in the AAA dilation area for FSIM. In contrast, four recirculation areas existed in FM; two were main vortexes and the other two were secondary flow, which were located between the main recirculation area and the arterial wall. Six local pressure concentrations occurred in the distal end of AAA and the recirculation area for FM. However, there were only two local pressure concentrations in FSIM. The vortex center of the recirculation area in FSIM was much more close to the distal end of AAA and the area was much larger because of AAA expansion. Four extreme values of WSS existed at the proximal of AAA, the point of boundary layer separation, the point of flow reattachment and the distal end of AAA, respectively, in both FM and FSIM. The maximum wall stress and the largest wall deformation were both located at the proximal and distal end of AAA. Conclusions: The number and center of the recirculation area for both models are different, while the change of vortex is closely associated with the AAA growth. The largest WSS of FSIM is 36% smaller than that of FM. Both the maximum wall stress and largest wall displacement shall increase with the outlet pressure increasing. FSIM needs to be considered for studying the relationship between AAA growth and shear stress.

Mesh-free approximations via the error reproducing kernel method and applications to nonlinear systems developing shocks

Error estimates for the error reproducing kernel method (ERKM) are provided. The ERKM is a mesh-free functional approximation scheme [A. Shaw, D. Roy, A NURBS-based error reproducing kernel method with applications in solid mechanics, Computational Mechanics (2006), to appear (available online)], wherein a targeted function and its derivatives are first approximated via non-uniform rational B-splines (NURBS) basis function. Errors in the NURBS approximation are then reproduced via a family of non-NURBS basis functions, constructed using a polynomial reproduction condition, and added to the NURBS approximation of the function obtained in the first step. In addition to the derivation of error estimates, convergence studies are undertaken for a couple of test boundary value problems with known exact solutions. The ERKM is next applied to a one-dimensional Burgers equation where, time evolution leads to a breakdown of the continuous solution and the appearance of a shock. Many available mesh-free schemes appear to be unable to capture this shock without numerical instability. However, given that any desired order of continuity is achievable through NURBS approximations, the ERKM can even accurately approximate functions with discontinuous derivatives. Moreover, due to the variation diminishing property of NURBS, it has advantages in representing sharp changes in gradients. This paper is focused on demonstrating this ability of ERKM via some numerical examples. Comparisons of some of the results with those via the standard form of the reproducing kernel particle method (RKPM) demonstrate the relative numerical advantages and accuracy of the ERKM.

A computational algorithm for the verification of tautologies in propositional calculus

A computational algorithm (based on Smullyan's analytic tableau method) that varifies whether a given well-formed formula in propositional calculus is a tautology or not has been implemented on a DEC system 10. The stepwise refinement approch of program development used for this implementation forms the subject matter of this paper. The top-down design has resulted in a modular and reliable program package. This computational algoritlhm compares favourably with the algorithm based on the well-known resolution principle used in theorem provers.

Numerical modelling of deformation behaviour of red blood cells in microvessels using the coupled SPH-DEM method

This thesis developed an advanced computational model to investigate the motion and deformation properties of red blood cells in capillaries. The novel model is based on the meshfree particle methods and is capable of modelling the large deformation of red blood cells moving through blood vessels. The developed model was employed to simulate the deformation behaviour of healthy and malaria infected red blood cells as well as the motion of red blood cells in stenosed capillaries.

A computational study of Compton profiles of water - methanol solutions

The molecular level structure of mixtures of water and alcohols is very complicated and has been under intense research in the recent past. Both experimental and computational methods have been used in the studies. One method for studying the intra- and intermolecular bindings in the mixtures is the use of the so called difference Compton profiles, which are a way to obtain information about changes in the electron wave functions. In the process of Compton scattering a photon scatters inelastically from an electron. The Compton profile that is obtained from the electron wave functions is directly proportional to the probability of photon scattering at a given energy to a given solid angle. In this work we develop a method to compute Compton profiles numerically for mixtures of liquids. In order to obtain the electronic wave functions necessary to calculate the Compton profiles we need some statistical information about atomic coordinates. Acquiring this using ab-initio molecular dynamics is beyond our computational capabilities and therefore we use classical molecular dynamics to model the movement of atoms in the mixture. We discuss the validity of the chosen method in view of the results obtained from the simulations. There are some difficulties in using classical molecular dynamics for the quantum mechanical calculations, but these can possibly be overcome by parameter tuning. According to the calculations clear differences can be seen in the Compton profiles of different mixtures. This prediction needs to be tested in experiments in order to find out whether the approximations made are valid.

Computational studies on new chemical species in the gas-phase and the solid-state.

There is intense activity in the area of theoretical chemistry of gold. It is now possible to predict new molecular species, and more recently, solids by combining relativistic methodology with isoelectronic thinking. In this thesis we predict a series of solid sheet-type crystals for Group-11 cyanides, MCN (M=Cu, Ag, Au), and Group-2 and 12 carbides MC2 (M=Be-Ba, Zn-Hg). The idea of sheets is then extended to nanostrips which can be bent to nanorings. The bending energies and deformation frequencies can be systematized by treating these molecules as an elastic bodies. In these species Au atoms act as an 'intermolecular glue'. Further suggested molecular species are the new uncongested aurocarbons, and the neutral Au_nHg_m clusters. Many of the suggested species are expected to be stabilized by aurophilic interactions. We also estimate the MP2 basis-set limit of the aurophilicity for the model compounds [ClAuPH_3]_2 and [P(AuPH_3)_4]^+. Beside investigating the size of the basis-set applied, our research confirms that the 19-VE TZVP+2f level, used a decade ago, already produced 74 % of the present aurophilic attraction energy for the [ClAuPH_3]_2 dimer. Likewise we verify the preferred C4v structure for the [P(AuPH_3)_4]^+ cation at the MP2 level. We also perform the first calculation on model aurophilic systems using the SCS-MP2 method and compare the results to high-accuracy CCSD(T) ones. The recently obtained high-resolution microwave spectra on MCN molecules (M=Cu, Ag, Au) provide an excellent testing ground for quantum chemistry. MP2 or CCSD(T) calculations, correlating all 19 valence electrons of Au and including BSSE and SO corrections, are able to give bond lengths to 0.6 pm, or better. Our calculated vibrational frequencies are expected to be better than the currently available experimental estimates. Qualitative evidence for multiple Au-C bonding in triatomic AuCN is also found.

Computational Studies on Bimetallic Clusters

The chemical and physical properties of bimetallic clusters have attracted considerable attention due to the potential technological applications of mixed-metal systems. It is of fundamental interests to study clusters because they are the link between atomic surface and bulk properties. More information of metal-metal bond in small clusters can be hence released. The studies in my thesis mainly focus on the two different kinds of bimetallic clusters: the clusters consisting of extraordinary shaped all metal four-membered rings and a series of sodium auride clusters. As described in most general organic chemistry books nowadays, a group of compounds are classified as aromatic compounds because of their remarkable stabilities, particular geometrical and energetic properties and so on. The notation of aromaticity is essentially qualitative. More recently, the connection has been made between aromaticity and energetic and magnetic properties. Also, the discussions of the aromatic nature of molecular rings are no longer limited to organic compounds obeying the Hückel’s rule. In our research, we mainly applied the GIMIC method to several bimetallic clusters at the CCSD level, and compared the results with those obtained by using chemical shift based methods. The magnetically induced ring currents can be generated easily by employing GIMIC method, and the nature of aromaticity for each system can be therefore clarified. We performed intensive quantum chemical calculations to explore the characters of the anionic sodium auride clusters and the corresponding neutral clusters since it has been fascinating in investigating molecules with gold atom involved due to its distinctive physical and chemical properties. As small gold clusters, the sodium auride clusters seem to form planar structures. With the addition of a negative charge, the gold atom in anionic clusters prefers to carry the charge and orients itself away from other gold atoms. As a result, the energetically lowest isomer for an anionic cluster is distinguished from the one for the corresponding neutral cluster. Mostly importantly, we presented a comprehensive strategy of ab initio applications to computationally implement the experimental photoelectron spectra.

Computational Methods for Reconstruction and Analysis of Genome-Scale Metabolic Networks

Metabolism is the cellular subsystem responsible for generation of energy from nutrients and production of building blocks for larger macromolecules. Computational and statistical modeling of metabolism is vital to many disciplines including bioengineering, the study of diseases, drug target identification, and understanding the evolution of metabolism. In this thesis, we propose efficient computational methods for metabolic modeling. The techniques presented are targeted particularly at the analysis of large metabolic models encompassing the whole metabolism of one or several organisms. We concentrate on three major themes of metabolic modeling: metabolic pathway analysis, metabolic reconstruction and the study of evolution of metabolism. In the first part of this thesis, we study metabolic pathway analysis. We propose a novel modeling framework called gapless modeling to study biochemically viable metabolic networks and pathways. In addition, we investigate the utilization of atom-level information on metabolism to improve the quality of pathway analyses. We describe efficient algorithms for discovering both gapless and atom-level metabolic pathways, and conduct experiments with large-scale metabolic networks. The presented gapless approach offers a compromise in terms of complexity and feasibility between the previous graph-theoretic and stoichiometric approaches to metabolic modeling. Gapless pathway analysis shows that microbial metabolic networks are not as robust to random damage as suggested by previous studies. Furthermore the amino acid biosynthesis pathways of the fungal species Trichoderma reesei discovered from atom-level data are shown to closely correspond to those of Saccharomyces cerevisiae. In the second part, we propose computational methods for metabolic reconstruction in the gapless modeling framework. We study the task of reconstructing a metabolic network that does not suffer from connectivity problems. Such problems often limit the usability of reconstructed models, and typically require a significant amount of manual postprocessing. We formulate gapless metabolic reconstruction as an optimization problem and propose an efficient divide-and-conquer strategy to solve it with real-world instances. We also describe computational techniques for solving problems stemming from ambiguities in metabolite naming. These techniques have been implemented in a web-based sofware ReMatch intended for reconstruction of models for 13C metabolic flux analysis. In the third part, we extend our scope from single to multiple metabolic networks and propose an algorithm for inferring gapless metabolic networks of ancestral species from phylogenetic data. Experimenting with 16 fungal species, we show that the method is able to generate results that are easily interpretable and that provide hypotheses about the evolution of metabolism.

Computational Methods for Detecting Large-Scale Chromosome Rearrangements in SNP Data

Large-scale chromosome rearrangements such as copy number variants (CNVs) and inversions encompass a considerable proportion of the genetic variation between human individuals. In a number of cases, they have been closely linked with various inheritable diseases. Single-nucleotide polymorphisms (SNPs) are another large part of the genetic variance between individuals. They are also typically abundant and their measuring is straightforward and cheap. This thesis presents computational means of using SNPs to detect the presence of inversions and deletions, a particular variety of CNVs. Technically, the inversion-detection algorithm detects the suppressed recombination rate between inverted and non-inverted haplotype populations whereas the deletion-detection algorithm uses the EM-algorithm to estimate the haplotype frequencies of a window with and without a deletion haplotype. As a contribution to population biology, a coalescent simulator for simulating inversion polymorphisms has been developed. Coalescent simulation is a backward-in-time method of modelling population ancestry. Technically, the simulator also models multiple crossovers by using the Counting model as the chiasma interference model. Finally, this thesis includes an experimental section. The aforementioned methods were tested on synthetic data to evaluate their power and specificity. They were also applied to the HapMap Phase II and Phase III data sets, yielding a number of candidates for previously unknown inversions, deletions and also correctly detecting known such rearrangements.

Computational Techniques for Haplotype Inference and for Local Alignment Significance

This thesis which consists of an introduction and four peer-reviewed original publications studies the problems of haplotype inference (haplotyping) and local alignment significance. The problems studied here belong to the broad area of bioinformatics and computational biology. The presented solutions are computationally fast and accurate, which makes them practical in high-throughput sequence data analysis. Haplotype inference is a computational problem where the goal is to estimate haplotypes from a sample of genotypes as accurately as possible. This problem is important as the direct measurement of haplotypes is difficult, whereas the genotypes are easier to quantify. Haplotypes are the key-players when studying for example the genetic causes of diseases. In this thesis, three methods are presented for the haplotype inference problem referred to as HaploParser, HIT, and BACH. HaploParser is based on a combinatorial mosaic model and hierarchical parsing that together mimic recombinations and point-mutations in a biologically plausible way. In this mosaic model, the current population is assumed to be evolved from a small founder population. Thus, the haplotypes of the current population are recombinations of the (implicit) founder haplotypes with some point--mutations. HIT (Haplotype Inference Technique) uses a hidden Markov model for haplotypes and efficient algorithms are presented to learn this model from genotype data. The model structure of HIT is analogous to the mosaic model of HaploParser with founder haplotypes. Therefore, it can be seen as a probabilistic model of recombinations and point-mutations. BACH (Bayesian Context-based Haplotyping) utilizes a context tree weighting algorithm to efficiently sum over all variable-length Markov chains to evaluate the posterior probability of a haplotype configuration. Algorithms are presented that find haplotype configurations with high posterior probability. BACH is the most accurate method presented in this thesis and has comparable performance to the best available software for haplotype inference. Local alignment significance is a computational problem where one is interested in whether the local similarities in two sequences are due to the fact that the sequences are related or just by chance. Similarity of sequences is measured by their best local alignment score and from that, a p-value is computed. This p-value is the probability of picking two sequences from the null model that have as good or better best local alignment score. Local alignment significance is used routinely for example in homology searches. In this thesis, a general framework is sketched that allows one to compute a tight upper bound for the p-value of a local pairwise alignment score. Unlike the previous methods, the presented framework is not affeced by so-called edge-effects and can handle gaps (deletions and insertions) without troublesome sampling and curve fitting.