GPU Acceleration of Partial Differential Equation Solvers

Differential equations are often directly solvable by analytical means only in their one dimensional version. Partial differential equations are generally not solvable by analytical means in two and three dimensions, with the exception of few special cases. In all other cases, numerical approximation methods need to be utilized. One of the most popular methods is the finite element method. The main areas of focus, here, are the Poisson heat equation and the plate bending equation. The purpose of this paper is to provide a quick walkthrough of the various approaches that the authors followed in pursuit of creating optimal solvers, accelerated with the use of graphical processing units, and comparing them in terms of accuracy and time efficiency with existing or self-made non-accelerated solvers.

A Van der Pol-Mathieu equation for the dynamics of dust grain charge in dusty plasmas

The chaotic profile of dust grain dynamics associated with dust-acoustic oscillations in a dusty plasma is considered. The collective behaviour of the dust plasma component is described via a multi-fluid model, comprising Boltzmann distributed electrons and ions, as well as an equation of continuity possessing a source term for the dust grains, the dust momentum and Poisson's equations. A Van der Pol–Mathieu-type nonlinear ordinary differential equation for the dust grain density dynamics is derived. The dynamical system is cast into an autonomous form by employing an averaging method. Critical stability boundaries for a particular trivial solution of the governing equation with varying parameters are specified. The equation is analysed to determine the resonance region, and finally numerically solved by using a fourth-order Runge–Kutta method. The presence of chaotic limit cycles is pointed out.

Coupled consolidation of a solid, infinite cylinder using a Terzaghi formulation

Axisymmetric consolidation is a classical boundary value problem for geotechnical engineers. Under some circumstances an analysis in which the changes in pore pressure, effective stress and displacement can be uncoupled from each other is sufficient, leading to a Terzaghi formulation of the axisymmetric consolidation equation in terms of the pore pressure. However, representation of the Mandel-Cryer effect usually requires more complex, coupled, Biot formulations. A new coupled formulation for the plane strain, axisymmetric consolidation problem is presented for small, linear elastic deformations. A single, easily evaluated parameter couples changes in pore pressure to changes in effective stress, and the resulting differential equation for pore pressure dissipation is very similar to Terzaghi’s classic formulation. The governing equations are then solved using finite differences and the consolidation of a solid infinite cylinder analysed, calculating the variation with time and with radius of the excess pore pressure and the radial displacement. Comparison with a previously published semi-analytical solution indicates that the formulation successfully embodies the Mandel-Cryer effect.

Analytical description of stochastic field-Line wandering in magnetic turbulence

A nonperturbative nonlinear statistical approach is presented to describe turbulent magnetic systems embedded in a uniform mean magnetic field. A general formula in the form of an ordinary differential equation for magnetic field-line wandering (random walk) is derived. By considering the solution of this equation for different limits several new results are obtained. As an example, it is demonstrated that the stochastic wandering of magnetic field-lines in a two-component turbulence model leads to superdiffusive transport, contrary to an existing diffusive picture. The validity of quasilinear theory for field-line wandering is discussed, with respect to different turbulence geometry models, and previous diffusive results are shown to be deduced in appropriate limits.

Modelling the mechanical response of the Reed-mouthpiece-lip system of a clarinet. Part I. A one-dimensional distributed model

The motion of a clarinet reed that is clamped to a mouthpiece and supported by a lip is simulated in the time-domain using finite difference methods. The reed is modelled as a bar with non-uniform cross section, and is described using a one-dimensional, fourth-order partial differential equation. The interactions with the mouthpiece Jay and the player's lip are taken into account by incorporating conditional contact forces in the bar equation. The model is completed by clamped-free boundary conditions for the reed. An implicit finite difference method is used for discretising the system, and values for the physical parameters are chosen both from laboratory measurements and by accurate tuning of the numerical simulations. The accuracy of the numerical system is assessed through analysis of frequency warping effects and of resonance estimation. Finally, the mechanical properties of the system are studied by analysing its response to external driving forces. In particular, the effects of reed curling are investigated.

Three dimensional Sklyanin algebras and Gröbner bases

We consider Sklyanin algebras $S$ with 3 generators, which are quadratic algebras over a field $\K$ with $3$ generators $x,y,z$ given by $3$ relations $pxy+qyx+rzz=0$, $pyz+qzy+rxx=0$ and $pzx+qxz+ryy=0$, where $p,q,r\in\K$. this class of algebras has enjoyed much attention. In particular, using tools from algebraic geometry, Feigin, Odesskii \cite{odf}, and Artin, Tate and Van Den Bergh, showed that if at least two of the parameters $p$, $q$ and $r$ are non-zero and at least two of three numbers $p^3$, $q^3$ and $r^3$ are distinct, then $S$ is Artin--Schelter regular. More specifically, $S$ is Koszul and has the same Hilbert series as the algebra of commutative polynomials in 3 indeterminates (PHS). It has became commonly accepted that it is impossible to achieve the same objective by purely algebraic and combinatorial means like the Groebner basis technique. The main purpose of this paper is to trace the combinatorial meaning of the properties of Sklyanin algebras, such as Koszulity, PBW, PHS, Calabi-Yau, and to give a new constructive proof of the above facts due to Artin, Tate and Van Den Bergh. Further, we study a wider class of Sklyanin algebras, namely
the situation when all parameters of relations could be different. We call them generalized Sklyanin algebras. We classify up to isomorphism all generalized Sklyanin algebras with the same Hilbert series as commutative polynomials on
3 variables. We show that generalized Sklyanin algebras in general position have a Golod–Shafarevich Hilbert series (with exception of the case of field with two elements).

Boundary conditions in the simplest model of linear and second harmonic magneto-optical effects

This paper is concerned with linear and nonlinear magneto- optical effects in multilayered magnetic systems when treated by the simplest phenomenological model that allows their response to be represented in terms of electric polarization, The problem is addressed by formulating a set of boundary conditions at infinitely thin interfaces, taking into account the existence of surface polarizations. Essential details are given that describe how the formalism of distributions (generalized functions) allows these conditions to be derived directly from the differential form of Maxwell's equations. Using the same formalism we show the origin of alternative boundary conditions that exist in the literature. The boundary value problem for the wave equation is formulated, with an emphasis on the analysis of second harmonic magneto-optical effects in ferromagnetically ordered multilayers. An associated problem of conventions in setting up relationships between the nonlinear surface polarization and the fundamental electric field at the interfaces separating anisotropic layers through surface susceptibility tensors is discussed. A problem of self- consistency of the model is highlighted, relating to the existence of resealing procedures connecting the different conventions. The linear approximation with respect to magnetization is pursued, allowing rotational anisotropy of magneto-optical effects to be easily analyzed owing to the invariance of the corresponding polar and axial tensors under ordinary point groups. Required representations of the tensors are given for the groups infinitym, 4mm, mm2, and 3m, With regard to centrosymmetric multilayers, nonlinear volume polarization is also considered. A concise expression is given for its magnetic part, governed by an axial fifth-rank susceptibility tensor being invariant under the Curie group infinityinfinitym.

Pyrrolidinium Ionic Liquid Crystals with Pendant Mesogenic Groups

New ionic liquid crystals (including ionic metallomesogens) based oil the pyrrolidinium core are presented. N-Methylpyrrolidine was quaternized with different mesogenic groups connected to a flexible, omega-bromosubstituted alkyl spacer. The length of the flexible alkyl spacer between the cationic head group and the rigid mesogenic group was varied. The substituted pyrrolidinium cations were combined with bromide, bis(trifluoromethylsulfonyl)imide, tetrakis (2-thenoyltrifluoroacetonato)europate(III), and tetrabromouranyl anions. The influence of the type of mesogenic unit, the lengths of the flexible spacer and terminal alkyl chain, the size of the mesogenic group, and the type of anion oil the thermotropic mesomorphic behavior was investigated. Furthermore, the phase behavior was thoroughly compared with the previously reported mesomorphism of N-alkyl-N-methylpyrrolidinium salts. Low-ordered smectic A phases of the de Vries type, smectic C phases, higher-ordered smectic F/I phases, as well its crystal smectic phases (E and G, J, H, or K) were observed and investigated by polarizing optical microscopy, differential scanning calorimetry, and powder X-ray diffraction.

Right-wing authoritarianism, social dominance orientation and prejudice against threatening and competitive ethnic groups

This research rests on the assumption that individual differences approaches to prejudice benefit from all integration of intergroup factors. Following Duckitt (2001), we assumed that two prominent individual differences variables, right-wing authoritarianism (RWA) and social dominance orientation (SDO), would differentially predict majority members' levels of ethnic prejudice depending on specific factors of the intergroup context: RWA as all index of motivational concerns about social cohesion, stability and security should drive prejudice against outgroups perceived as socially threatening, and SDO as an index of concerns about ingroup superiority and dominance should predict prejudice against outgroups perceived as potential competitors for power-status. Across two studies (Ns = 82, 176), using between-participants and within-participants experimental designs, the effects of RWA on prejudice were particularly powerful when the outgroup was manipulated to be socially threatening, but the effects of SDO on prejudice appeared not to increase when the outgroup was manipulated to be competitive. In Study 2, presenting the outgroup as having low status also increased the effect of RWA, but not the effect of SDO. These results support the differential prediction assumption for RWA, but not for SDO. Implications for the conceptualisation of RWA and SDO are discussed. Copyright (C) 2008 John Wiley & Sons, Ltd.

Differential expression of steroid 5 alpha-reductase isozymes and association with disease severity and angiogenic genes predict their biological role in prostate cancer

The biological role of steroid 5 alpha-reductase isozymes (encoded by the SRD5A1 and SRD5A2 genes) and angiogenic factors that play important roles in the pathogenesis and vascularization of prostate cancer (PC) is poorly understood. The sub-cellular expression of these isozymes and vascular endothelial growth factor (VEGF) in PC tissue microarrays (n=62) was examined using immunohistochemistry. The effect of SRD5A inhibition on the angiogenesis pathway genes in PC was also examined in prostate cell lines, LNCaP, PC3, and RWPE-1, by treating them with the SRD5A inhibitors finasteride and dutasteride, followed by western blot, quantitative PCR, and ELISA chip array techniques. In PC tissues, nuclear SRD5A1 expression was strongly associated with higher cancer Gleason scores (P=0.02), higher cancer stage (P=0.01), and higher serum prostate specific antigen (PSA) levels (P=0.01), whereas nuclear SRD5A2 expression was correlated with VEGF expression (P=0.01). Prostate tumor cell viability was significantly reduced in dutasteride-treated PC3 and RWPE-1 cells compared with finasteride-treated groups. Expression of the angiogenesis pathway genes transforming growth factor beta 1 (TGFB1), endothelin (EDN1), TGF alpha (TGFA), and VEGFR1 was upregulated in LNCaP cells, and at least 7 out of 21 genes were upregulated in PC3 cells treated with finasteride (25 mu M). Our findings suggest that SRD5A1 expression predominates in advanced PC, and that inhibition of SRD5A1 and SRD5A2 together was more effective in reducing cell numbers than inhibition of SRD5A2 alone. However, these inhibitors did not show any significant difference in prostate cell angiogenic response. Interestingly, some angiogenic genes remained activated after treatment, possibly due to the duration of treatment and tumor resistance to inhibitors. Endocrine-Related Cancer (2010) 17 757-770

Contextualism as an important facet of individualism-collectivism: personhood beliefs across 37 national groups

Beliefs about personhood are understood to be a defining feature of individualism-collectivism (I-C), but they have been insufficiently explored, given the emphasis of research on values and self-construals. We propose the construct of contextualism, referring to beliefs about the importance of context in understanding people, as a facet of cultural collectivism. A brief measure was developed and refined across 19 nations (Study 1: N = 5,241), showing good psychometric properties for cross-cultural use and correlating well at the nation level with other supposed facets and indicators of I-C. In Study 2 (N = 7,623), nation-level contextualism predicted ingroup favoritism, corruption and differential trust of ingroup and outgroup members, while controlling for other facets of I-C, across 34 nations. We conclude that contextualism is an important part of cultural collectivism. This highlights the importance of beliefs alongside values and self-representations, and contributes to a wider understanding of cultural processes.

Genetic pleiotropy between multiple sclerosis and schizophrenia but not bipolar disorder: differential involvement of immune-related gene loci

Converging evidence implicates immune abnormalities in schizophrenia (SCZ), and recent genome-wide association studies (GWAS) have identified immune-related single-nucleotide polymorphisms (SNPs) associated with SCZ. Using the conditional false discovery rate (FDR) approach, we evaluated pleiotropy in SNPs associated with SCZ (n=21 856) and multiple sclerosis (MS) (n=43 879), an inflammatory, demyelinating disease of the central nervous system. Because SCZ and bipolar disorder (BD) show substantial clinical and genetic overlap, we also investigated pleiotropy between BD (n=16 731) and MS. We found significant genetic overlap between SCZ and MS and identified 21 independent loci associated with SCZ, conditioned on association with MS. This enrichment was driven by the major histocompatibility complex (MHC). Importantly, we detected the involvement of the same human leukocyte antigen (HLA) alleles in both SCZ and MS, but with an opposite directionality of effect of associated HLA alleles (that is, MS risk alleles were associated with decreased SCZ risk). In contrast, we found no genetic overlap between BD and MS. Considered together, our findings demonstrate genetic pleiotropy between SCZ and MS and suggest that the MHC signals may differentiate SCZ from BD susceptibility.Molecular Psychiatry advance online publication, 28 January 2014; doi:10.1038/mp.2013.195.

Solutions of fourth-order parabolic equation modeling thin film growth

In this paper we study the well-posedness for a fourth-order parabolic equation modeling epitaxial thin film growth. Using Kato's Method [1], [2] and [3] we establish existence, uniqueness and regularity of the solution to the model, in suitable spaces, namelyC⁰([0,T];L^p(Ω)) where  with 1<α<2, n∈N and n≥2. We also show the global existence solution to the nonlinear parabolic equations for small initial data. Our main tools are L_p–L_q-estimates, regularization property of the linear part of e^−tΔ2 and successive approximations. Furthermore, we illustrate the qualitative behavior of the approximate solution through some numerical simulations. The approximate solutions exhibit some favorable absorption properties of the model, which highlight the stabilizing effect of our specific formulation of the source term associated with the upward hopping of atoms. Consequently, the solutions describe well some experimentally observed phenomena, which characterize the growth of thin film such as grain coarsening, island formation and thickness growth.

Beyond managerial talent: ‘key group’ identification and differential compensation practices in multinational companies

With the maturation of strategic human resource management scholarship, there appears to be a greater call to move from monolithic workforce management to a more strategic and differentiated emphasis on employees with the greatest capacity to enhance competitive advantage. There has been little consideration in the literature as to whether organizations formally identify key groups of employees based on their impact on organizational learning and core competences. Using survey evidence from 260 multinational companies (MNCs), this paper explores the extent to which key groups of employees are formally recognized and whether they are subject to differential compensation practices. The results demonstrate that just in excess of half of these MNCs identify a key group. There was considerable differentiation in the compensation practices between these key groups, managers and the largest occupational group in the workforce. The results give rise to questions worthy of future investigation, namely whether the differentiated approaches used lead to improved performance outcomes.

Informal caregiving and mental ill health – differential relationships by workload, gender, age and area-remoteness in a UK region

Informal caregiving can be a demanding role which has been shown to impact on physical, psychological and social wellbeing. Methodological weaknesses including small sample sizes and subjective measures of mental health have led to inconclusive evidence about the relationship between informal caregiving and mental health. This paper reports on a study carried out in a UK region which investigated the relationship between informal caregiving and mental ill health. The analysis was conducted by linking three datasets, the Northern Ireland Longitudinal Study, the Northern Ireland Enhanced Prescribing Database and the Proximity to Service Index from the Northern Ireland Statistics and Research Agency. Our analysis used both a subjective measure of mental ill health, i.e. a question asked in the 2011 Census, and an objective measure, whether the respondents had been prescribed antidepressants by a General Practitioner between 2010 and 2012. We applied binary logistic multilevel modelling to these two responses to test whether, and for what sub-groups of the population, informal caregiving was related to mental ill health. The results showed that informal caregiving per se was not related to mental ill health although there was a strong relationship between the intensity of the caregiving role and mental ill health. Females under 50, who provided over 19 hours of care, were not employed or worked part-time and who provided care in both 2001 and 2011 were at a statistically significantly elevated risk of mental ill health. Caregivers in remote areas with limited access to shops and services were also at a significantly increased risk as evidenced by prescription rates for antidepressants. With community care policies aimed at supporting people to remain at home, the paper highlights the need for further research in order to target resources appropriately.