Validation of a partial coherence interferometry method for estimating retinal shape

To validate a simple partial coherence interferometry (PCI) based retinal shape method, estimates of retinal shape were determined in 60 young adults using off-axis PCI, with three stages of modeling using variants of the Le Grand model eye, and magnetic resonance imaging (MRI). Stage 1 and 2 involved a basic model eye without and with surface ray deviation, respectively and Stage 3 used model with individual ocular biometry and ray deviation at surfaces. Considering the theoretical uncertainty of MRI (12-14%), the results of the study indicate good agreement between MRI and all three stages of PCI modeling with <4% and <7% differences in retinal shapes along horizontal and vertical meridians, respectively. Stage 2 and Stage 3 gave slightly different retinal co-ordinates than Stage 1 and we recommend the intermediate Stage 2 as providing a simple and valid method of determining retinal shape from PCI data.

Self-assembly of hydrophobin proteins from the fungus Trichoderma reesei

Hydrophobins are small surface active proteins that are produced by filamentous fungi. The surface activity of hydrophobin proteins leads to the formation of a film at the air-water interface and adsorption to surfaces. The formation of these hydrophobin films and coatings is important in many stages of fungal development. Furthermore, these properties make hydrophobins interesting for potential use in technical applications. The surfactant-like properties of hydrophobins from Trichoderma reesei were studied at the air-water interface, at solid surfaces, and in solution. The hydrophobin HFBI was observed to spontaneously form a cohesive film on a water drop. The film was imaged using atomic force microscopy from both sides, revealing a monomolecular film with a defined molecular structure. The use of hydrophobins as surface immobilization carriers for enzymes was studied using fusion proteins of HFBI or HFBII and an enzyme. Furthermore, sitespecifically modified variants of HFBI were shown to retain their ability to selfassemble at interfaces and to be able to bind a second layer of proteins by biomolecular recognition. In order to understand the function of hydrophobins at interfaces, an understanding of their overall behavior and self-assembly is needed. HFBI and HFBII were shown to associate in solution into dimers and tetramers in a concentration-dependent manner. The association dynamics and protein-protein interactions of HFBI and HFBII were studied using Förster resonance energy transfer and size exclusion chromatography. It was shown that the surface activity of HFBI is not directly dependent on the formation of multimers in solution.

Association of FOXE1 Polyalanine Repeat Region with Papillary Thyroid Cancer

CONTEXT: Polyalanine tract variations in transcription factors have been identified for a wide spectrum of developmental disorders. The thyroid transcription factor forkhead factor E1 (FOXE1) contains a polymorphic polyalanine tract with 12-22 alanines. Single-nucleotide polymorphisms (SNP) close to this locus are associated with papillary thyroid cancer (PTC), and a strong linkage disequilibrium block extends across this region. OBJECTIVE: The objective of the study was to assess whether the FOXE1 polyalanine repeat region was associated with PTC and to assess the effect of polyalanine repeat region variants on protein expression, DNA binding, and transcriptional function on FOXE1-responsive promoters. DESIGN: This was a case-control study. SETTING: The study was conducted at a tertiary referral hospital. PATIENTS AND METHODS: The FOXE1 polyalanine repeat region and tag SNP were genotyped in 70 PTC, with a replication in a further 92 PTC, and compared with genotypes in 5767 healthy controls (including 5667 samples from the Wellcome Trust Case Control Consortium). In vitro studies were performed to examine the protein expression, DNA binding, and transcriptional function for FOXE1 variants of different polyalanine tract lengths. RESULTS: All the genotyped SNP were in tight linkage disequilibrium, including the FOXE1 polyalanine repeat region. We confirmed the strong association of rs1867277 with PTC (overall P = 1 × 10(-7), odds ratio 1.84, confidence interval 1.31-2.57). rs1867277 was in tight linkage disequilibrium with the FOXE1 polyalanine repeat region (r(2) = 0.95). FOXE1(16Ala) was associated with PTC with an odds ratio of 2.23 (confidence interval 1.42-3.50; P = 0.0005). Functional studies in vitro showed that FOXE1(16Ala) was transcriptionally impaired compared with FOXE1(14Ala), which was not due to differences in protein expression or DNA binding. CONCLUSIONS: We have confirmed the previous association of FOXE1 with PTC. Our data suggest that the coding polyalanine expansion in FOXE1 may be responsible for the observed association between FOXE1 and PTC.

Mutations of mitochondrial DNA polymerase gamma: an important cause of neurological disorders

Thesis focuses on mutations of POLG1 gene encoding catalytic subunit polγ-α of mitochondrial DNA polymerase gamma holoenzyme (polG) and the association of mutations with different clinical phenotypes. In addition, particular defective mutant variants of the protein were characterized biochemically in vitro. PolG-holoenzyme is the sole DNA polymerase found in mitochondria. It is involved in replication and repair of the mitochondrial genome, mtDNA. Holoenzyme also includes the accessory subunit polγ-β, which is required for the enhanced processivity of polγ-α. Defective polγ-α causes accumulation of secondary mutations on mtDNA, which leads to a defective oxidative phosphorylation system. The clinical consequences of such mutations are variable, affecting nervous system, skeletal muscles, liver and other post-mitotic tissues. The aims of the studies included: 1) Determination of the role of POLG1 mutations in neurological syndromes with features of mitochondrial dysfunction and an unknown molecular cause. 2) Development and set up of diagnostic tests for routine clinical purposes. 3) Biochemical characterization of the functional consequences of the identified polγ-α variants. Studies describe new neurological phenotypes in addition to PEO caused by POLG1 mutations, including parkinsonism, premature amenorrhea, ataxia and Parkinson s disease (PD). POLG1 mutations and polymorphisms are both common and/or potential genetic risk factors at least among the Finnish population. The major findings and applications reported here are: 1) POLG1 mutations cause parkinsonism and premature menopause in PEO families in either a recessive or a dominant manner. 2) A common recessive POLG1 mutations (A467T and W748S) in the homozygous state causes severe adult or juvenile-onset ataxia without muscular symptoms or histological or mtDNA abnormalities in muscles. 3) A common recessive pathogenic change A467T can also cause a mild dominant disease in heterozygote carriers. 4) The A467T variant shows reduced polymerase activity due to defective template binding. 5) Rare polyglutamine tract length variants of POLG1 are significantly enriched in Finnish idiopathic Parkinson s disease patients. 6) Dominant mutations are clearly restricted to the highly conserved polymerase domain motifs, whereas recessive ones are more evenly distributed along the protein. The present results highlight and confirm the new role of mitochondria in parkinsonism/Parkinson s disease and describe a new mitochondrial ataxia. Based on these results, a POLG1 diagnostic routine has been set up in Helsinki University Central Hospital (HUSLAB).

Genotype-Phenotype Relationships in Long QT Syndrome: Role of Mental Stress, Adrenergic Activity and a Common KCNH2 Polymorphism

Long QT syndrome is a congenital or acquired arrhythmic disorder which manifests as a prolonged QT-interval on the electrocardiogram and as a tendency to develop ventricular arrhythmias which can lead to sudden death. Arrhythmias often occur during intense exercise and/or emotional stress. The two most common subtypes of LQTS are LQT1, caused by mutations in the KCNQ1 gene and LQT2, caused by mutations in the KCNH2 gene. LQT1 and LQT2 patients exhibit arrhythmias in different types of situations: in LQT1 the trigger is usually vigorous exercise whereas in LQT2 arrhythmia results from the patient being startled from rest. It is not clear why trigger factors and clinical outcome differ from each other in the different LQTS subtypes. It is possible that stress hormones such as catecholamines may show different effects depending on the exact nature of the genetic defect, or sensitivity to catecholamines varies from subject to subject. Furthermore, it is possible that subtle genetic variants of putative modifier genes, including those coding for ion channels and hormone receptors, play a role as determinants of individual sensitivity to life-threatening arrhythmias. The present study was designed to identify some of these risk modifiers. It was found that LQT1 and LQT2 patients show an abnormal QT-adaptation to both mental and physical stress. Furthermore, as studied with epinephrine infusion experiments while the heart was paced and action potentials were measured from the right ventricular septum, LQT1 patients showed repolarization abnormalities which were related to their propensity to develop arrhythmia during intense, prolonged sympathetic tone, such as exercise. In LQT2 patients, this repolarization abnormality was noted already at rest corresponding to their arrhythmic episodes as a result of intense, sudden surges in adrenergic tone, such as fright or rage. A common KCNH2 polymorphism was found to affect KCNH2 channel function as demonstrated by in vitro experiments utilizing mammalian cells transfected with the KCNH2 potassium channel as well as QT-dynamics in vivo. Finally, the present study identified a common β-1-adrenergic receptor genotype that is related a shorter QT-interval in LQT1 patients. Also, it was discovered that compound homozygosity for two common β-adrenergic polymorphisms was related to the occurrence of symptoms in the LQT1 type of long QT syndrome. The studies demonstrate important genotype-phenotype differences between different LQTS subtypes and suggest that common modifier gene polymorphisms may affect cardiac repolarization in LQTS. It will be important in the future to prospectively study whether variant gene polymorphisms will assist in clinical risk profiling of LQTS patients.

Genetic background of bipolar disorder and related cognitive impairments

Bipolar disorder (BP) is a complex psychiatric disorder characterized by episodes of mania and depression. BP affects approximately 1% of the world’s population and shows no difference in lifetime prevalence between males and females. BP arises from complex interactions among genetic, developmental and environmental factors, and it is likely that several predisposing genes are involved in BP. The genetic background of BP is still poorly understood, although intensive and long-lasting research has identified several chromosomal regions and genes involved in susceptibility to BP. This thesis work aims to identify the genetic variants that influence bipolar disorder in the Finnish population by candidate gene and genome-wide linkage analyses in families with many BP cases. In addition to diagnosis-based phenotypes, neuropsychological traits that can be seen as potential endophenotypes or intermediate traits for BP were analyzed. In the first part of the thesis, we examined the role of the allelic variants of the TSNAX/DISC1 gene cluster to psychotic and bipolar spectrum disorders and found association of distinct allelic haplotypes with these two groups of disorders. The haplotype at the 5’ end of the Disrupted-in-Schizophrenia-1 gene (DISC1) was over-transmitted to males with psychotic disorder (p = 0.008; for an extended haplotype p = 0.0007 with both genders), whereas haplotypes at the 3’ end of DISC1 associated with bipolar spectrum disorder (p = 0.0002; for an extended haplotype p = 0.0001). The variants of these haplotypes also showed association with different cognitive traits. The haplotypes at the 5’ end associated with perseverations and auditory attention, while the variants at the 3’ end associated with several cognitive traits including verbal fluency and psychomotor processing speed. Second, in our complete set of BP families with 723 individuals we studied six functional candidate genes from three distinct signalling systems: serotonin-related genes (SLC6A4 and TPH2), BDNF -related genes (BDNF, CREB1 and NTRK2) and one gene related to the inflammation and cytokine system (P2RX7). We replicated association of the functional variant Val66Met of BDNF with BP and better performance in retention. The variants at the 5’ end of SLC6A4 also showed some evidence of association among males (p = 0.004), but the widely studied functional variants did not yield any significant results. A protective four-variant haplotype on P2RX7 showed evidence of association with BP and executive functions: semantic and phonemic fluency (p = 0.006 and p = 0.0003, respectively). Third, we analyzed 23 bipolar families originating from the North-Eastern region of Finland. A genome-wide scan was performed using the 6K single nucleotide polymorphism (SNP) array. We identified susceptibility loci at chromosomes 7q31 with a LOD score of 3.20 and at 9p13.1 with a LOD score of 4.02. We followed up both linkage findings in the complete set of 179 Finnish bipolar families. The finding on chromosome 9p13 was supported (maximum LOD score of 3.02), but the susceptibility gene itself remains unclarified. In the fourth part of the thesis, we wanted to test the role of the allelic variants that have associated with bipolar disorder in recent genome-wide association studies (GWAS). We could confirm findings for the DFNB31, SORCS2, SCL39A3, and DGKH genes. The best signal in this study comes from DFNB31, which remained significant after multiple testing corrections. Two variants of SORCS2 were allelic replications and presented the same signal as the haplotype analysis. However, no association was detected with the PALB2 gene, which was the most significantly associated region in the previous GWAS. Our results indicate that BP is heterogeneous and its genetic background may accordingly vary in different populations. In order to fully understand the allelic heterogeneity that underlies common diseases such as BP, complete genome sequencing for many individuals with and without the disease is required. Identification of the specific risk variants will help us better understand the pathophysiology underlying BP and will lead to the development of treatments with specific biochemical targets. In addition, it will further facilitate the identification of environmental factors that alter risk, which will potentially provide improved occupational, social and psychological advice for individuals with high risk of BP.

Associations of interleukin-1 (IL-1) gene variation and IL-1 receptor antagonist phenotypes with immunological responses, metabolic dysregulation and type 2 diabetes

The upstream proinflammatory interleukin-1 (IL-1) cytokines, together with a naturally occurring IL-1 receptor antagonist (IL-1Ra), play a significant role in several diseases and physiologic conditions. The IL-1 proteins affect glucose homeostasis at multiple levels contributing to vascular injuries and metabolic dysregulations that precede diabetes. An association between IL-1 gene variations and IL-1Ra levels has been suggested, and genetic studies have reported associations with metabolic dysregulation and altered inflammatory responses. The principal aims of this study were to: 1) examine the associations of IL-1 gene variation and IL-1Ra expression in the development and persistence of thyroid antibodies in subacute thyroiditis; 2) investigate the associations of common variants in the IL-1 gene family with plasma glucose and insulin concentrations, glucose homeostasis measures and prevalent diabetes in a representative population sample; 3) investigate genetic and non-genetic determinants of IL-1Ra phenotypes in a cross-sectional setting in three independent study populations; 4) investigate in a prospective setting (a) whether variants of the IL-1 gene family are predictors for clinically incident diabetes in two population-based observational cohort studies; and (b) whether the IL-1Ra levels predict the progression of metabolic syndrome to overt diabetes during the median follow-up of 10.8 and 7.1 years. Results from on patients with subacte thyroiditis showed that the systemic IL-1Ra levels are elevated during a specific proinflammatory response and they correlated with C-reactive protein (CRP) levels. Genetic variation in the IL-1 family seemed to have an association with the appearance of thyroid peroxidase antibodies and persisting local autoimmune responses during the follow-up. Analysis of patients suffering from diabetes and metabolic traits suggested that genetic IL-1 variation and IL-1Ra play a role in glucose homeostasis and in the development of type 2 diabetes. The coding IL-1 beta SNP rs1143634 was associated with traits related to insulin resistance in cross-sectional analyses. Two haplotype variants of the IL-1 beta gene were associated with prevalent diabetes or incident diabetes in a prospective setting and both of these haplotypes were tagged by rs1143634. Three variants of the IL-1Ra gene and one of the IL-1 beta gene were consistently identified as significant, independent determinants of the IL-1Ra phenotype in two or three populations. The proportion of the phenotypic variation explained by the genetic factors was modest however, while obesity and other metabolic traits explained a larger part. Body mass index was the strongest predictor of systemic IL-1Ra concentration overall. Furthermore, the age-adjusted IL-1Ra concentrations were elevated in individuals with metabolic syndrome or diabetes when compared to those free of metabolic dysregulation. In prospective analyses the systemic IL-1Ra levels were found as independent predictors for the development of diabetes in people with metabolic syndrome even after adjustment for multiple other factors, including plasma glucose and CRP levels. The predictive power of IL-1Ra was better than that of CRP. The prospective results also provided some evidence for a role of common IL-1 alpha promoter SNP rs1800587 in the development of type 2 diabetes among men and suggested that the role may be gender specific. Likewise, common variations in the IL-1 beta coding region may have a gender specific association with diabetes development. Further research on the potential benefits of IL-1Ra measurements in identifying individuals at high risk for diabetes, who then could be targeted for specific treatment interventions, is warranted. It has been reported in the recent literature that IL-1Ra secreted from adipose tissue has beneficial effects on glucose homeostasis. Furthermore, treatment with recombinant human IL-1Ra has been shown to have a substantial therapeutic potential. The genetic results from the prospective analyses performed in this study remain inconclusive, but together with the cross-sectional analyses they suggest gender-specific effects of the IL-1 variants on the risk of diabetes. Larger studies with more extensive genotyping and resequencing may help to pinpoint the exact variants responsible and to further elucidate the biological mechanisms for the observed associations. This would improve our understanding of the pathways linking inflammation and obesity with glucose and insulin metabolism.

Optimal allocation of carbon credits to emitting agents in a carbon economy

Reduction of carbon emissions is of paramount importance in the context of global warming. Countries and global companies are now engaged in understanding systematic ways of achieving well defined emission targets. In fact, carbon credits have become significant and strategic instruments of finance for countries and global companies. In this paper, we formulate and suggest a solution to the carbon allocation problem, which involves determining a cost minimizing allocation of carbon credits among different emitting agents. We address this challenge in the context of a global company which is faced with the challenge of determining an allocation of carbon credit caps among its divisions in a cost effective way. The problem is formulated as a reverse auction problem where the company plays the role of a buyer or carbon planning authority and the different divisions within the company are the emitting agents that specify cost curves for carbon credit reductions. Two natural variants of the problem: (a) with unlimited budget and (b) with limited budget are considered. Suitable assumptions are made on the cost curves and in each of the two cases we show that the resulting problem formulation is a knapsack problem that can be solved optimally using a greedy heuristic. The solution of the allocation problem provides critical decision support to global companies engaged seriously in green programs.

Manipulation of the Hydration Levels in Minerals of Sodium Cadmium Bisulfate toward the Design of Functional Materials

Several variants of hydrated sodium cadmium bisulfate, Na(2)Cd(2)(SO(4))(3) center dot 3H(2)O, Na(2)Cd(SO(4))(2) center dot 2H(2)O, and Na(2)Cd(SO(4))(2) center dot 4H(2)O have been synthesized, and their thermal properties followed by phase transitions have been invesigated. The formation of these phases depends on the stochiometry and the time taken for crystallization from water. Na(2)Cd(2)(SO(4))(3)center dot 3H(2)O, which crystallizes in the trigonal system, space group P3c, is grown from the aqueous solution in about four weeks. The krohnkite type mineral Na(2)Cd(SO(4))(2) center dot 2H(2)O and the mineral astrakhanite, also known as blodite, Na(2)Cd (SO(4))(2)center dot 4H(2)O, crystallize concomittantly in about 24 weeks. Both these minerals belong to the monoclinic system(space group P2(1)/c). Na(2)Cd(2)(SO(4))(3)center dot 3H(2)O loses water completely when heated to 250 degrees C and transforms to a dehydrated phase (cubic system, space group I (4) over bar 3d) whose structure has been established using ab initio powder diffration techniques. Na(2)Cd(SO(4))(2)center dot 2H(2)O transforms to alpha-Na(2)Cd(SO(4))(2) (space group C2/c) on heating to 150 degrees C which is a known high ionic conductor and remains intact over prolonged periods of exposure to moisture (over six months). However, when alpha-Na(2)Cd(SO(4))(2) is heated to 570 degrees C followed by sudden quenching in liquid nitrogen beta-Na(2)Cd(SO(4))(2) (P2(1)/c) is formed. beta-Na(2)Cd(SO(4))(2) takes up water from the atmosphere and gets converted completely to the krohnkite type mineral in about four weeks. Further, beta-Na(2)Cd(SO(4))(2) has a conductivity behavior comparable to the a-form up to 280 degrees C, the temperature required for the transformation of the beta- to alpha-form. These experiments demonstrate the possibility of utilizing the abundantly available mineral sources as precursors to design materials with special properties.

D-MG Tradeoff and Optimal Codes for a Class of AF and DF Cooperative Communication Protocols

Cooperative relay communication in a fading channel environment under the orthogonal amplify-and-forward (OAF), non-orthogonal and orthogonal selection decode-and-forward (NSDF and OSDF) protocols is considered here. The diversity-multiplexing gain tradeoff (DMT) of the three protocols is determined and DMT-optimal distributed space-time code constructions are provided. The codes constructed are sphere decodable and in some instances incur minimum possible delay. Included in our results is the perhaps surprising finding that the OAF and NAF protocols have identical DMT when the time durations of the broadcast and cooperative phases are optimally chosen to suit the respective protocol. Two variants of the NSDF protocol are considered: fixed-NSDF and variable-NSDF protocol. In the variable-NSDF protocol, the fraction of time occupied by the broadcast phase is allowed to vary with multiplexing gain. In the two-relay case, the variable-NSDF protocol is shown to improve on the DMT of the best previously-known static protocol for higher values of multiplexing gain. Our results also establish that the fixed-NSDF protocol has a better DMT than the NAF protocol for any number of relays.

Passive vibration isolation of reaction wheel disturbances using a low frequency flexible space platform

Reaction wheel assemblies (RWAs) are momentum exchange devices used in fine pointing control of spacecrafts. Even though the spinning rotor of the reaction wheel is precisely balanced to minimize emitted vibration due to static and dynamic imbalances, precision instrument payloads placed in the neighborhood can always be severely impacted by residual vibration forces emitted by reaction wheel assemblies. The reduction of the vibration level at sensitive payloads can be achieved by placing the RWA on appropriate mountings. A low frequency flexible space platform consisting of folded continuous beams has been designed to serve as a mount for isolating a disturbance source in precision payloads equipped spacecrafts. Analytical and experimental investigations have been carried out to test the usefulness of the low frequency flexible platform as a vibration isolator for RWAs. Measurements and tests have been conducted at varying wheel speeds, to quantify and characterize the amount of isolation obtained from the reaction wheel generated vibration. These tests are further extended to other variants of similar design in order to bring out the best isolation for given disturbance loads. Both time and frequency domain analysis of test data show that the flexible beam platform as a mount for reaction wheels is quite effective and can be used in spacecrafts for passive vibration control. (C) 2011 Elsevier Ltd. All rights reserved.

Designed Cyclic Permutants of HIV-1 gp120: Implications for Envelope Trimer Structure and Immunogen Design

Most HIV-1 broadly neutralizing antibodies are directed against the gp120 subunit of the env surface protein. Native env consists of a trimer of gp120-gp41 heterodimers, and in contrast to monomeric gp120, preferentially binds CD4 binding site (CD4bs)-directed neutralizing antibodies over non-neutralizing ones. Some cryo-electron tomography studies have suggested that the V1V2 loop regions of gp120 are located close to the trimer interface. We have therefore designed cyclically permuted variants of gp120 with and without the h-CMP and SUMO2a trimerization domains inserted into the V1V2 loop. h-CMP-V1cyc is one such variant in which residues 153 and 142 are the N- and C-terminal residues, respectively, of cyclically permuted gp120 and h-CMP is fused to the N-terminus. This molecule forms a trimer under native conditions and binds CD4 and the neutralizing CD4bs antibodies b12 with significantly higher affinity than wild-type gp120. It binds non-neutralizing CD4bs antibody F105 with lower affinity than gp120. A similar derivative, h-CMP-V1cycl, bound the V1V2 loop-directed broadly neutralizing antibodies PG9 and PG16 with similar to 20-fold higher affinity than wild-type JRCSF gp120. These cyclic permutants of gp120 are properly folded and are potential immunogens. The data also support env models in which the V1V2 loops are proximal to the trimer interface.

Robust solver based on modified particle swarm optimization for improved solution of diffusion transport through containment facilities

Accurate estimation of mass transport parameters is necessary for overall design and evaluation processes of the waste disposal facilities. The mass transport parameters, such as effective diffusion coefficient, retardation factor and diffusion accessible porosity, are estimated from observed diffusion data by inverse analysis. Recently, particle swarm optimization (PSO) algorithm has been used to develop inverse model for estimating these parameters that alleviated existing limitations in the inverse analysis. However, PSO solver yields different solutions in successive runs because of the stochastic nature of the algorithm and also because of the presence of multiple optimum solutions. Thus the estimated mean solution from independent runs is significantly different from the best solution. In this paper, two variants of the PSO algorithms are proposed to improve the performance of the inverse analysis. The proposed algorithms use perturbation equation for the gbest particle to gain information around gbest region on the search space and catfish particles in alternative iterations to improve exploration capabilities. Performance comparison of developed solvers on synthetic test data for two different diffusion problems reveals that one of the proposed solvers, CPPSO, significantly improves overall performance with improved best, worst and mean fitness values. The developed solver is further used to estimate transport parameters from 12 sets of experimentally observed diffusion data obtained from three diffusion problems and compared with published values from the literature. The proposed solver is quick, simple and robust on different diffusion problems. (C) 2012 Elsevier Ltd. All rights reserved.

Operator-splitting finite element algorithms for computations of high-dimensional parabolic problems

An operator-splitting finite element method for solving high-dimensional parabolic equations is presented. The stability and the error estimates are derived for the proposed numerical scheme. Furthermore, two variants of fully-practical operator-splitting finite element algorithms based on the quadrature points and the nodal points, respectively, are presented. Both the quadrature and the nodal point based operator-splitting algorithms are validated using a three-dimensional (3D) test problem. The numerical results obtained with the full 3D computations and the operator-split 2D + 1D computations are found to be in a good agreement with the analytical solution. Further, the optimal order of convergence is obtained in both variants of the operator-splitting algorithms. (C) 2012 Elsevier Inc. All rights reserved.

A Nearly Exact Reformulation of the Girsanov Linearization for Stochastically Driven Nonlinear Oscillators

The Girsanov linearization method (GLM), proposed earlier in Saha, N., and Roy, D., 2007, ``The Girsanov Linearisation Method for Stochastically Driven Nonlinear Oscillators,'' J. Appl. Mech., 74, pp. 885-897, is reformulated to arrive at a nearly exact, semianalytical, weak and explicit scheme for nonlinear mechanical oscillators under additive stochastic excitations. At the heart of the reformulated linearization is a temporally localized rejection sampling strategy that, combined with a resampling scheme, enables selecting from and appropriately modifying an ensemble of locally linearized trajectories while weakly applying the Girsanov correction (the Radon-Nikodym derivative) for the linearization errors. The semianalyticity is due to an explicit linearization of the nonlinear drift terms and it plays a crucial role in keeping the Radon-Nikodym derivative ``nearly bounded'' above by the inverse of the linearization time step (which means that only a subset of linearized trajectories with low, yet finite, probability exceeds this bound). Drift linearization is conveniently accomplished via the first few (lower order) terms in the associated stochastic (Ito) Taylor expansion to exclude (multiple) stochastic integrals from the numerical treatment. Similarly, the Radon-Nikodym derivative, which is a strictly positive, exponential (super-) martingale, is converted to a canonical form and evaluated over each time step without directly computing the stochastic integrals appearing in its argument. Through their numeric implementations for a few low-dimensional nonlinear oscillators, the proposed variants of the scheme, presently referred to as the Girsanov corrected linearization method (GCLM), are shown to exhibit remarkably higher numerical accuracy over a much larger range of the time step size than is possible with the local drift-linearization schemes on their own.