Microtubule self-organization is gravity-dependent

Although weightlessness is known to affect living cells, the manner by which this occurs is unknown. Some reaction-diffusion processes have been theoretically predicted as being gravity-dependent. Microtubules, a major constituent of the cellular cytoskeleton, self-organize in vitro by way of reaction-diffusion processes. To investigate how self-organization depends on gravity, microtubules were assembled under low gravity conditions produced during space flight. Contrary to the samples formed on an in-flight 1 × g centrifuge, the samples prepared in microgravity showed almost no self-organization and were locally disordered.

Theoretical prediction of a crystal structure.

The diffusion equation method of global minimization is applied to compute the crystal structure of S6, with no a priori knowledge about the system. The experimental lattice parameters and positions and orientations of the molecules in the unit cell are predicted correctly.

Ecological chaos in the wake of invasion.

Irregularities in observed population densities have traditionally been attributed to discretization of the underlying dynamics. We propose an alternative explanation by demonstrating the evolution of spatiotemporal chaos in reaction-diffusion models for predator-prey interactions. The chaos is generated naturally in the wake of invasive waves of predators. We discuss in detail the mechanism by which the chaos is generated. By considering a mathematical caricature of the predator-prey models, we go on to explain the dynamical origin of the irregular behavior and to justify our assertion that the behavior we present is a genuine example of spatiotemporal chaos.

Modulation of Sarco/Endoplasmic Reticulum Ca2+-ATPase 2 (SERCA2) function by acetylation following the treatment with histone deacetylase inhibitor suberoylanilide hydroxamic acid (SAHA)

Background: Acetylation and deacetylation at specific lysine (K) residues is mediated by histone acetylases (HATs) and deacetylases (HDACs), respectively. HATs and HDACs act on both histone and non-histone proteins, regulating various processes, including cardiac impulse propagation. Aim of the present work was to establish whether the function of the Ca2+ ATPase SERCA2, one of the major players in Ca2+ reuptake during excitation-contraction coupling in cardiac myocytes (CMs), could be modulated by direct K acetylation. Materials and methods: HL-1 atrial mouse cells (donated by Prof. Claycomb), zebrafish and Streptozotocin-induced diabetic rat CMs were treated with the pan-inhibitor of class I and II HDACs suberanilohydroxamic acid (SAHA) for 1.5 hour. Evaluation of SERCA2 acetylation was analyzed by co-immunoprecipitation. SERCA2 activity was measured on microsomes by pyruvate/NADH coupled reaction assay. SERCA2 mutants were obtained after cloning wild-type and mutated sequences into the pCDNA3 vector and transfected into HEK cells. Ca2+ transients in CMs (loading with Fluo3-AM, field stimulation, 0.5 Hz) and in transfected HEK cells (loading with FLUO-4, caffeine pulse) were recorded. Results: Co-Immunoprecipitation experiments performed on HL-1 cells demonstrated a significant increase in the acetylation of SERCA2 after SAHA-treatment (2.5 µM, n=3). This was associated with an increase in SERCA2 activity in microsomes obtained from HL-1 cells, after SAHA exposure (n=5). Accordingly, SAHA-treatment significantly shortened the Ca2+ reuptake time of adult zebrafish CMs. Further, SAHA 2.5 nM restored to control values the recovery time of Ca2+ transients decay in diabetic rat CMs. HDAC inhibition also improved contraction parameters, such as fraction of shortening, and increased pump activity in microsomes isolated from diabetic CMs (n=4). Notably, the K464, identified by bioinformatic tools as the most probable acetylation site on human SERCA2a, was mutated into Glutamine (Q) or Arginine (R) mimicking acetylation and deacetylation respectively. Measurements of Ca2+ transients in HEK cells revealed that the substitution of K464 with R significantly delayed the transient recovery time, thus indicating that deacetylation has a negative impact on SERCA2 function. Conclusions: Our results indicate that SERCA2 function can be improved by pro-acetylation interventions and that this mechanism of regulation is conserved among species. Therefore, the present work provides the basis to open the search for novel pharmacological tools able to specifically improve SERCA2 activity in diseases where its expression and/or function is impaired, such as diabetic cardiomyopathy.

Well posedness of an integrodifferential kinetic model of Fokker-Planck type for angiogenesis.

Tumor induced angiogenesis processes including the effect of stochastic motion and branching of blood vessels can be described coupling a (nonlocal in time) integrodifferential kinetic equation of Fokker–Planck type with a diffusion equation for the tumor induced ingiogenic factor. The chemotactic force field depends on the flux of blood vessels through the angiogenic factor. We develop an existence and uniqueness theory for this system under natural assumptions on the initial data. The proof combines the construction of fundamental solutions for associated linearized problems with comparison principles, sharp estimates of the velocity integrals and compactness results for this type of kinetic and parabolic operators

Numerically optimized implementations, mitigation and simulations of polarisation mode dispersion in real-time transmission systems

The aim of this thesis is to present numerical investigations of the polarisation mode dispersion (PMD) effect. Outstanding issues on the side of the numerical implementations of PMD are resolved and the proposed methods are further optimized for computational efficiency and physical accuracy. Methods for the mitigation of the PMD effect are taken into account and simulations of transmission system with added PMD are presented. The basic outline of the work focusing on PMD can be divided as follows. At first the widely-used coarse-step method for simulating the PMD phenomenon as well as a method derived from the Manakov-PMD equation are implemented and investigated separately through the distribution of a state of polarisation on the Poincaré sphere, and the evolution of the dispersion of a signal. Next these two methods are statistically examined and compared to well-known analytical models of the probability distribution function (PDF) and the autocorrelation function (ACF) of the PMD phenomenon. Important optimisations are achieved, for each of the aforementioned implementations in the computational level. In addition the ACF of the coarse-step method is considered separately, based on the result which indicates that the numerically produced ACF, exaggerates the value of the correlation between different frequencies. Moreover the mitigation of the PMD phenomenon is considered, in the form of numerically implementing Low-PMD spun fibres. Finally, all the above are combined in simulations that demonstrate the impact of the PMD on the quality factor (Q=factor) of different transmission systems. For this a numerical solver based on the coupled nonlinear Schrödinger equation is created which is otherwise tested against the most important transmission impairments in the early chapters of this thesis.

Some Properties of Mittag-Leffler Functions and Matrix-Variate Analogues: A Statistical Perspective

Mathematical Subject Classification 2010:26A33, 33E99, 15A52, 62E15.

Special Functions and Pathways for Problems in Astrophysics: An Essay in Honor of A.M. Mathai

The paper provides a review of A.M. Mathai's applications of the theory of special functions, particularly generalized hypergeometric functions, to problems in stellar physics and formation of structure in the Universe and to questions related to reaction, diffusion, and reaction-diffusion models. The essay also highlights Mathai's recent work on entropic, distributional, and differential pathways to basic concepts in statistical mechanics, making use of his earlier research results in information and statistical distribution theory. The results presented in the essay cover a period of time in Mathai's research from 1982 to 2008 and are all related to the thematic area of the gravitationally stabilized solar fusion reactor and fractional reaction-diffusion, taking into account concepts of non-extensive statistical mechanics. The time period referred to above coincides also with Mathai's exceptional contributions to the establishment and operation of the Centre for Mathematical Sciences, India, as well as the holding of the United Nations (UN)/European Space Agency (ESA)/National Aeronautics and Space Administration (NASA) of the United States/ Japanese Aerospace Exploration Agency (JAXA) Workshops on basic space science and the International Heliophysical Year 2007, around the world. Professor Mathai's contributions to the latter, since 1991, are a testimony for his social con-science applied to international scientific activity.

Noise-induced standing waves in oscillatory systems with time-delayed feedback

In oscillatory reaction-diffusion systems, time-delay feedback can lead to the instability of uniform oscillations with respect to formation of standing waves. Here, we investigate how the presence of additive, Gaussian white noise can induce the appearance of standing waves. Combining analytical solutions of the model with spatio-temporal simulations, we find that noise can promote standing waves in regimes where the deterministic uniform oscillatory modes are stabilized. As the deterministic phase boundary is approached, the spatio-temporal correlations become stronger, such that even small noise can induce standing waves in this parameter regime. With larger noise strengths, standing waves could be induced at finite distances from the (deterministic) phase boundary. The overall dynamics is defined through the interplay of noisy forcing with the inherent reaction-diffusion dynamics.

Lattice Boltzmann modeling of fluid flow and solute transport in karst aquifers

A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.

Lattice Boltzmann Modeling of Fluid Flow and Solute Transport in Karst Aquifers

A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.

Core Reactor Calculation Using the Adaptive Remeshing with a Current Error Estimator

With the objective to improve the reactor physics calculation on a 2D and 3D nuclear reactor via the Diffusion Equation, an adaptive automatic finite element remeshing method, based on the elementary area (2D) or volume (3D) constraints, has been developed. The adaptive remeshing technique, guided by a posteriori error estimator, makes use of two external mesh generator programs: Triangle and TetGen. The use of these free external finite element mesh generators and an adaptive remeshing technique based on the current field continuity show that they are powerful tools to improve the neutron flux distribution calculation and by consequence the power solution of the reactor core even though they have a minor influence on the critical coefficient of the calculated reactor core examples. Two numerical examples are presented: the 2D IAEA reactor core numerical benchmark and the 3D model of the Argonauta research reactor, built in Brasil.

Neuroreceptor availability and cerebral morphology in human obesity

Obesity is a major challenge to human health worldwide. Little is known about the brain mechanisms that are associated with overeating and obesity in humans. In this project, multimodal neuroimaging techniques were utilized to study brain neurotransmission and anatomy in obesity. Bariatric surgery was used as an experimental method for assessing whether the possible differences between obese and non-obese individuals change following the weight loss. This could indicate whether obesity-related altered neurotransmission and cerebral atrophy are recoverable or whether they represent stable individual characteristics. Morbidly obese subjects (BMI ≥ 35 kg/m2) and non-obese control subjects (mean BMI 23 kg/m2) were studied with positron emission tomography (PET) and magnetic resonance imaging (MRI). In the PET studies, focus was put on dopaminergic and opioidergic systems, both of which are crucial in the reward processing. Brain dopamine D2 receptor (D2R) availability was measured using [11C]raclopride and µ-opioid receptor (MOR) availability using [11C]carfentanil. In the MRI studies, voxel-based morphometry (VBM) of T1-weighted MRI images was used, coupled with diffusion tensor imaging (DTI). Obese subjects underwent bariatric surgery as their standard clinical treatment during the study. Preoperatively, morbidly obese subjects had significantly lower MOR availability but unaltered D2R availability in several brain regions involved in reward processing, including striatum, insula, and thalamus. Moreover, obesity disrupted the interaction between the MOR and D2R systems in ventral striatum. Bariatric surgery and concomitant weight loss normalized MOR availability in the obese, but did not influence D2R availability in any brain region. Morbidly obese subjects had also significantly lower grey and white matter densities globally in the brain, but more focal changes were located in the areas associated with inhibitory control, reward processing, and appetite. DTI revealed also signs of axonal damage in the obese in corticospinal tracts and occipito-frontal fascicles. Surgery-induced weight loss resulted in global recovery of white matter density as well as more focal recovery of grey matter density among obese subjects. Altogether these results show that the endogenous opioid system is fundamentally linked to obesity. Lowered MOR availability is likely a consequence of obesity and may mediate maintenance of excessive energy uptake. In addition, obesity has adverse effects on brain structure. Bariatric surgery however reverses MOR dysfunction and recovers cerebral atrophy. Understanding the opioidergic contribution to overeating and obesity is critical for developing new psychological or pharmacological treatments for obesity. The actual molecular mechanisms behind the positive change in structure and neurotransmitter function still remain unclear and should be addressed in the future research.

Pattern formation with a conservation law

Pattern formation in systems with a conserved quantity is considered by studying the appropriate amplitude equations. The conservation law leads to a large-scale neutral mode that must be included in the asymptotic analysis for pattern formation near onset. Near a stationary bifurcation, the usual Ginzburg--Landau equation for the amplitude of the pattern is then coupled to an equation for the large-scale mode. These amplitude equations show that for certain parameters all roll-type solutions are unstable. This new instability differs from the Eckhaus instability in that it is amplitude-driven and is supercritical. Beyond the stability boundary, there exist stable stationary solutions in the form of strongly modulated patterns. The envelope of these modulations is calculated in terms of Jacobi elliptic functions and, away from the onset of modulation, is closely approximated by a sech profile. Numerical simulations indicate that as the modulation becomes more pronounced, the envelope broadens. A number of applications are considered, including convection with fixed-flux boundaries and convection in a magnetic field, resulting in new instabilities for these systems.

Um problema de dispersão de poluentes em rios e canais por meio do método de separação de variáveis

Neste trabalho obtém-se uma solução analítica para a equação de advecção-difusão aplicada a problemas de dispersão de poluentes em rios e canais. Para tanto, consideram-se os casos unidimensionais e bidimensionais em regime transiente com coeficientes de difusividade e velocidades constantes. A abordagem utilizada para a resolução deste problema é o método de Separação de Variáveis. Os modelos resolvidos foram simulados utilizando o MatLab. Apresentam-se os resultados das simulações numéricas em formato gráfico. Os resultados de algumas simulações numéricas existem na literatura e puderam ser comparados. O modelo proposto mostrou-se coerente em relação aos dados considerados. Para outras simulações não foram encontrados comparativos na literatura, todavia esses problemas governados por equações diferenciais parciais, mesmo lineares, não são de fácil solução analítica. Sendo que, muitas delas representam importantes problemas de matemática e física, com diversas aplicações na engenharia. Dessa forma, é de grande importância a disponibilidade de um maior número de problemas-teste para avaliação de desempenho de formulações numéricas, cada vez mais eficazes, já que soluções analíticas oferecem uma base mais segura para comparação de resultados.