Nonequilibrium arrhythmic states and transitions in a mathematical model for diffuse fibrosis in human cardiac tissue

We present a comprehensive numerical study of spiral-and scroll-wave dynamics in a state-of-the-art mathematical model for human ventricular tissue with fiber rotation, transmural heterogeneity, myocytes, and fibroblasts. Our mathematical model introduces fibroblasts randomly, to mimic diffuse fibrosis, in the ten Tusscher-Noble-Noble-Panfilov (TNNP) model for human ventricular tissue; the passive fibroblasts in our model do not exhibit an action potential in the absence of coupling with myocytes; and we allow for a coupling between nearby myocytes and fibroblasts. Our study of a single myocyte-fibroblast (MF) composite, with a single myocyte coupled to N-f fibroblasts via a gap-junctional conductance G(gap), reveals five qualitatively different responses for this composite. Our investigations of two-dimensional domains with a random distribution of fibroblasts in a myocyte background reveal that, as the percentage P-f of fibroblasts increases, the conduction velocity of a plane wave decreases until there is conduction failure. If we consider spiral-wave dynamics in such a medium we find, in two dimensions, a variety of nonequilibrium states, temporally periodic, quasiperiodic, chaotic, and quiescent, and an intricate sequence of transitions between them; we also study the analogous sequence of transitions for three-dimensional scroll waves in a three-dimensional version of our mathematical model that includes both fiber rotation and transmural heterogeneity. We thus elucidate random-fibrosis-induced nonequilibrium transitions, which lead to conduction block for spiral waves in two dimensions and scroll waves in three dimensions. We explore possible experimental implications of our mathematical and numerical studies for plane-, spiral-, and scroll-wave dynamics in cardiac tissue with fibrosis.

Minimum power consumption for drag reduction on a circular cylinder by tangential surface motion

We investigate the effect of a prescribed tangential velocity on the drag force on a circular cylinder in a spanwise uniform cross flow. Using a combination of theoretical and numerical techniques we make an attempt at determining the optimal tangential velocity profiles which will reduce the drag force acting on the cylindrical body while minimizing the net power consumption characterized through a non-dimensional power loss coefficient (C-PL). A striking conclusion of our analysis is that the tangential velocity associated with the potential flow, which completely suppresses the drag force, is not optimal for both small and large, but finite Reynolds number. When inertial effects are negligible (R e << 1), theoretical analysis based on two-dimensional Oseen equations gives us the optimal tangential velocity profile which leads to energetically efficient drag reduction. Furthermore, in the limit of zero Reynolds number (Re -> 0), minimum power loss is achieved for a tangential velocity profile corresponding to a shear-free perfect slip boundary. At finite Re, results from numerical simulations indicate that perfect slip is not optimum and a further reduction in drag can be achieved for reduced power consumption. A gradual increase in the strength of a tangential velocity which involves only the first reflectionally symmetric mode leads to a monotonic reduction in drag and eventual thrust production. Simulations reveal the existence of an optimal strength for which the power consumption attains a minima. At a Reynolds number of 100, minimum value of the power loss coefficient (C-PL = 0.37) is obtained when the maximum in tangential surface velocity is about one and a half times the free stream uniform velocity corresponding to a percentage drag reduction of approximately 77 %; C-PL = 0.42 and 0.50 for perfect slip and potential flow cases, respectively. Our results suggest that potential flow tangential velocity enables energetically efficient propulsion at all Reynolds numbers but optimal drag reduction only for Re -> infinity. The two-dimensional strategy of reducing drag while minimizing net power consumption is shown to be effective in three dimensions via numerical simulation of flow past an infinite circular cylinder at a Reynolds number of 300. Finally a strategy of reducing drag, suitable for practical implementation and amenable to experimental testing, through piecewise constant tangential velocities distributed along the cylinder periphery is proposed and analysed.

Induction of Supramolecular Chirality in the Self-Assemblies of Lipophilic Pyrimidine Derivatives by Choice of the Amino Acid-Based Chiral Spacer

A new family of supramolecular organogelators, based on chiral amino acid derivatives of 2,4,6-trichloro-pyrimidine-5-carbaldehyde, has been synthesized. L-alanine was incorporated as a spacer between the pyrimidine core and long hydrocarbon tails to compare the effect of chirality and hydrogen bonding to that of the achiral analogue. The role of aromatic moiety on the chiral spacer was also investigated by introducing L-phenyl alanine moieties. The presence of intermolecular hydrogen-bonding leading to the chiral self-assembly was probed by concentration-dependent FTIR and UV/Vis spectroscopies, in addition to circular dichroism (CD) studies. Temperature and concentration-dependent CD spectroscopy ascribed to the formation of -sheet-type H-bonded networks. The morphology and the arrangements of the molecules in the freeze-dried gels were examined by scanning electron microscopy (SEM), transmission electron microscopy (TEM), atomic force microscopy (AFM), and X-ray diffraction (XRD) techniques. Calculation of the length of each molecular system by energy minimization in its extended conformation and comparison with the small-angle XRD pattern reveals that this class of gelator molecules adopts a lamellar organization. Polarized optical microscopy (POM) and differential scanning calorimetry (DSC) indicate that the solid state phase behavior of these molecules is totally dependent on the choice of their amino acid spacers. Structure-induced aggregation properties based on the H-bonding motifs and the packing of the molecule in three dimensions leading to gelation was elucidated by rheological studies. However, viscoelasticity was shown to depend only marginally on the H-bonding interactions; rather it depends on the packing of the gelators to a greater extent.

Sr2+ and Cd2+ coordination polymers: the effect of the different coordinating behaviour of a newly designed tricarboxylic acid

This article presents the investigation of the coordination behavior of a newly synthesized tricarboxylate ligand, obtained by joining imidazole dicarboxylic acid and 4-carboxybenzyl moieties cbimdaH(3), 1-(4-carboxybenzyl)-1H-imidazole-4,5-dicarboxylic acid]. Two novel coordination polymers were obtained through solvothermal reactions under similar conditions namely Sr(cbimdaH)(H2O)](n) (1) and Cd-2(cbimdaH)(2)(H2O)(6)](n)center dot(DMF)(3n)(H2O)(3n) (2), with the ligand behaving as a dianionic tricarboxylate linker. The single crystal X-ray structures show that while 1 forms a 3D coordination polymer, 2 forms a 1D polymer which is further assembled in three dimensions through supramolecular interactions (H-bonding). Complex 1 consists of Sr2+ ions in a distorted dodecahedral coordination geometry, while 2 consists of Cd2+ ions in distorted pentagonal bipyramidal geometries. A topology study reveals that 1 has a new topology based on the 5,6-coordinated 3D net architecture. The luminescence properties of the complexes in the solid state and their thermal stabilities were studied.

Versatility of azide in serendipitous assembly of Copper(II) Magnetic Polyclusters

Engineering at the molecular level is one of the most exciting new developments for the generation of functional materials. However, the concept of designing polynuclear extended structures from bottom up is still not mature. Although progress has been made with secondary building units (SBUs) in metal organic frameworks (MOFs), the control seems to be just an illusion when it comes to bridging ligands such as the azide ion. When we say that the azido ligand is versatile in its bridging capabilities, what we mean is that it would be difficult to predict or control its bridging properties. However, this kind of serendipity is not always bad news. For example, scientists have shown that the azido ligand can mediate magnetic exchanges between paramagnetic metals in a predictable fashion (usually depending upon the bonding geometries). Therefore, it is a well-respected ligand in polynuclear assemblies. Serendipitous assemblies offer new magnetic structures that we may not otherwise even think about synthesizing. The azido ligand forms a variety of complexes with copper(II) using different blocking amines or pyridine based ligands. Its structural nature changes upon changing the substitution on amine, as well as the amount of blocking ligand. In principle, if we take any of these complexes and provide more coordination sites to the bridging azido ligands by removing a fraction of the blocking ligands, we can get new complexes with intricate structural networks and therefore different magnetic properties with the same components as used for the parent complex. In this Account, we mainly discuss the development of a number of new topological and magnetic exchange systems synthesized using this concept. Not all of these new complexes can be grouped according to their basic building structures or even by the ratio of the metal to blocking ligand. Therefore, we divided the discussion by the nuclearity of the basic building structures. Some of the complexes with the same nuclearities have very similar or even almost identical basic structures. However, the way these building units are joined together (by the azido bridges) to form the overall extended structures differ almost in every case. The complexes having the Cu-6 core are particularly interesting from a structural point of view. Although they have almost identical basic structures, some of them are extended in three dimensions, but two of them are extended in two dimensions by two different bridging networks. In the complexes having linear Cu-4 basic units, we find that using similar ligands does not always give the same bridging networks even within the basic building structures. These complexes have also enriched the field of molecular magnetism. One of the complexes with a Cu-3 building unit has provided us with the opportunity to study the competing behavior of two different kinds of magnetic exchange mechanism (ferromagnetic and antiferromagnetic) acting simultaneously between two metal ions. Through density functional theory calculations, we showed how they work independently and their additive nature to produce the overall effect. The exciting methodology for the generation of copper(II) polyclusters presented in this Account will provide the opportunity to explore analogous serendipitous assembly of diverse structures with interesting magnetic behavior using other transition metal ions having more than one unpaired electrons.

Optical microscopy methods for understanding learning and memory

Structural dynamics of dendritic spines is one of the key correlative measures of synaptic plasticity for encoding short-term and long-term memory. Optical studies of structural changes in brain tissue using confocal microscopy face difficulties of scattering. This results in low signal-to-noise ratio and thus limiting the imaging depth to few tens of microns. Multiphoton microscopy (MpM) overcomes this limitation by using low-energy photons to cause localized excitation and achieve high resolution in all three dimensions. Multiple low-energy photons with longer wavelengths minimize scattering and allow access to deeper brain regions at several hundred microns. In this article, we provide a basic understanding of the physical phenomena that give MpM an edge over conventional microscopy. Further, we highlight a few of the key studies in the field of learning and memory which would not have been possible without the advent of MpM.

Structure-function hierarchies and von Karman-Howarth relations for turbulence in magnetohydrodynamical equations

We generalize the method of A. M. Polyakov, Phys. Rev. E 52, 6183 (1995)] for obtaining structure-function relations in turbulence in the stochastically forced Burgers equation, to develop structure-function hierarchies for turbulence in three models for magnetohydrodynamics (MHD). These are the Burgers analogs of MHD in one dimension Eur. Phys. J.B 9, 725 (1999)], and in three dimensions (3DMHD and 3D Hall MHD). Our study provides a convenient and unified scheme for the development of structure-function hierarchies for turbulence in a variety of coupled hydrodynamical equations. For turbulence in the three sets of MHD equations mentioned above, we obtain exact relations for third-order structure functions and their derivatives; these expressions are the analogs of the von Karman-Howarth relations for fluid turbulence. We compare our work with earlier studies of such relations in 3DMHD and 3D Hall MHD.

Formation and Thermal Stability of Gold-Silica Nanohybrids: Insight into the Mechanism and Morphology by Electron Tomography

Gold-silica hybrids are appealing in different fields of applications like catalysis, sensorics, drug delivery, and biotechnology. In most cases, the morphology and distribution of the heterounits play significant roles in their functional behavior. Methods of synthesizing these hybrids, with variable ordering of the heterounits, are replete; however, a complete characterization in three dimensions could not be achieved yet. A simple route to the synthesis of Au-decorated SiO2 spheres is demonstrated and a study on the 3D ordering of the heterounits by scanning transmission electron microscopy (STEM) tomography is presentedat the final stage, intermediate stages of formation, and after heating the hybrid. The final hybrid evolves from a soft self-assembled structure of Au nanoparticles. The hybrid shows good thermal stability up to 400 degrees C, beyond which the Au particles start migrating inside the SiO2 matrix. This study provides an insight in the formation mechanism and thermal stability of the structures which are crucial factors for designing and applying such hybrids in fields of catalysis and biotechnology. As the method is general, it can be applied to make similar hybrids based on SiO2 by tuning the reaction chemistry as needed.

Fermions in Synthetic Non-Abelian Gauge Fields

Quantum emulation property of the cold atoms has generated a lot of interest in studying systems with synthetic gauge fields. In this article, we describe the physics of two component Fermi gas in the presence of synthetic non-Abelian SU(2) gauge fields. Even for the non-interacting system with the gauge fields, there is an interesting change in the topology of the Fermi surface by tuning only the gauge field strength. When a trapping potential is used in conjunction with the gauge fields, the non-interacting system has the ability to produce novel Hamiltonians and show characteristic change in the density profile of the cloud. Without trap, the gauge fields act as an attractive interaction amplifier and for special kinds of gauge field configurations, there are two-body bound states for any attraction even in three dimensions. For a many body system, the gauge fields can induce a crossover from a weak superfluid to a strong superfluid with transition temperature as high as the Fermi temperature. The superfluid state obtained for a very large gauge field strength is a superfluid of new kind of bosons, called ``rashbons'', the properties of which are independent of its constituent two component fermions and are solely determined by the gauge field strength. We also discuss the collective excitations over the superfluid ground states and the experimental relevance of the physics.

Isotropic finite volume discretization

Finite volume methods traditionally employ dimension by dimension extension of the one-dimensional reconstruction and averaging procedures to achieve spatial discretization of the governing partial differential equations on a structured Cartesian mesh in multiple dimensions. This simple approach based on tensor product stencils introduces an undesirable grid orientation dependence in the computed solution. The resulting anisotropic errors lead to a disparity in the calculations that is most prominent between directions parallel and diagonal to the grid lines. In this work we develop isotropic finite volume discretization schemes which minimize such grid orientation effects in multidimensional calculations by eliminating the directional bias in the lowest order term in the truncation error. Explicit isotropic expressions that relate the cell face averaged line and surface integrals of a function and its derivatives to the given cell area and volume averages are derived in two and three dimensions, respectively. It is found that a family of isotropic approximations with a free parameter can be derived by combining isotropic schemes based on next-nearest and next-next-nearest neighbors in three dimensions. Use of these isotropic expressions alone in a standard finite volume framework, however, is found to be insufficient in enforcing rotational invariance when the flux vector is nonlinear and/or spatially non-uniform. The rotationally invariant terms which lead to a loss of isotropy in such cases are explicitly identified and recast in a differential form. Various forms of flux correction terms which allow for a full recovery of rotational invariance in the lowest order truncation error terms, while preserving the formal order of accuracy and discrete conservation of the original finite volume method, are developed. Numerical tests in two and three dimensions attest the superior directional attributes of the proposed isotropic finite volume method. Prominent anisotropic errors, such as spurious asymmetric distortions on a circular reaction-diffusion wave that feature in the conventional finite volume implementation are effectively suppressed through isotropic finite volume discretization. Furthermore, for a given spatial resolution, a striking improvement in the prediction of kinetic energy decay rate corresponding to a general two-dimensional incompressible flow field is observed with the use of an isotropic finite volume method instead of the conventional discretization. (C) 2014 Elsevier Inc. All rights reserved.

Design and Modeling of an Active Five-Axis Compliant Micromanipulator

This paper presents the design and modeling of an active five-axis compliant micromanipulator whose tip orientation can be independently controlled by large angles about two axes and the tip-position can be controlled in three dimensions. These features enable precise control of the contact point of the tip and the tip-sample interaction forces with three-dimensional nanoscale objects, including those features that are conventionally inaccessible. Control of the tip-motion is realized by means of electromagnetic actuation combined with a novel kinematic and structural design of the micromanipulator, which, in addition, also ensures compatibility with existing high-resolution motion-measurement systems. The design and analysis of the manipulator structure and those of the actuation system are first presented. Quasi-static and dynamic lumped-parameter (LP) models are then derived for the five-axis compliant micromanipulator. Finite element (FE) analysis is employed to validate these models, which are subsequently used to study the effects of tip orientation on the mechanical characteristics of the five-axis micromanipulator. Finally, a prototype of the designed five-axis manipulator is fabricated by means of focused ion-beam milling (FIB).

Discrete Vortex Method-Based Model for Ground-Effect Studies

A discrete vortex method-based model has been proposed for two-dimensional/three-dimensional ground-effect prediction. The model merely requires two-dimensional sectional aerodynamics in free flight. This free-flight data can be obtained either from experiments or a high-fidelity computational fluid dynamics solver. The first step of this two-step model involves a constrained optimization procedure that modifies the vortex distribution on the camber line as obtained from a discrete vortex method to match the free-flight data from experiments/computational fluid dynamics. In the second step, the vortex distribution thus obtained is further modified to account for the presence of the ground plane within a discrete vortex method-based framework. Whereas the predictability of the lift appears as a natural extension, the drag predictability within a potential flow framework is achieved through the introduction of what are referred to as drag panels. The need for the use of the generalized Kutta-Joukowski theorem is emphasized. The extension of the model to three dimensions is by the way of using the numerical lifting-line theory that allows for wing sweep. The model is extensively validated for both two-dimensional and three-dimensional ground-effect studies. The work also demonstrates the ability of the model to predict lift and drag coefficients of a high-lift wing in ground effect to about 2 and 8% accuracy, respectively, as compared to the results obtained using a Reynolds-averaged Navier-Stokes solver involving grids with several million volumes. The model shows a lot of promise in design, particularly during the early phase.

Using formal reasoning on a model of tasks for FreeRTOS

FreeRTOS is an open-source real-time microkernel that has a wide community of users. We present the formal specification of the behaviour of the task part of FreeRTOS that deals with the creation, management, and scheduling of tasks using priority-based preemption. Our model is written in the Z notation, and we verify its consistency using the Z/Eves theorem prover. This includes a precise statement of the preconditions for all API commands. This task model forms the basis for three dimensions of further work: (a) the modelling of the rest of the behaviour of queues, time, mutex, and interrupts in FreeRTOS; (b) refinement of the models to code to produce a verified implementation; and (c) extension of the behaviour of FreeRTOS to multi-core architectures. We propose all three dimensions as benchmark challenge problems for Hoare's Verified Software Initiative.

NMR relaxation studies in doped poly-3-methylthiophene

NMR relaxation rates (1/T-1), magnetic susceptibility, and electrical conductivity studies in doped poly-3-methylthiophene are reported in this paper. The magnetic susceptibility data show the contributions from both Pauli and Curie spins, with the size of the Pauli term depending strongly on the doping level. Proton and fluorine NMR relaxation rates have been studied as a function of temperature (3-300 K) and field (for protons at 0.9, 9.0, 16.4, and 23.4 T, and for fluorine at 9.0 T). The temperature dependence of T-1 is classified into three regimes: (a) For T < (g mu(B) B/2k(B)), the relaxation mechanism follows a modified Korringa relation due to electron-electron interactions and disorder. H-1-T-1 is due to the electron-nuclear dipolar interaction in addition to the contact term. (b) For the intermediate temperature range (g mu(B) B/2k(B)) < T < T-BPP (the temperature where the contribution from the reorientation motion to the T-1 is insignificant) the relaxation mechanism is via spin diffusion to the paramagnetic centers. (c) In the high-temperature regime and at low Larmor frequency the relaxation follows the modified Bloembergen, Purcell, and Pound model. T-1 data analysis has been carried out in light of these models depending upon the temperature and frequency range of study. Fluorine relaxation data have been analyzed and attributed to the PF6 reorientation. The cross relaxation among the H-1 and F-19 nuclei has been observed in the entire temperature range suggesting the role of magnetic dipolar interaction modulated by the reorientation of the symmetric molecular subgroups. The data analysis shows that the enhancement in the Korringa ratio is greater in a less conducting sample. Intra-and interchain hopping of charge carriers is found to be a dominant relaxation mechanism at low temperature. Frequency dependence of T-1(-1) on temperature shows that at low temperature T < (g mu(B) B/2k(B))] the system shows three dimensions and changes to quasi one dimension at high temperature. Moreover, a good correlation between electrical conductivity, magnetic susceptibility, and NMR T-1 data has been observed.

“Evangelización con espíritu” (EG 261) : la unidad de la teología, la espiritualidad y la pastoral al servicio del anuncio del evangelio: una lectura de la exhortación pastoral Evangelii Gaudium desde la Teología Espiritual

Resumen: Uno de los grandes “maestros en teología” en la Argentina de los últimos tiempos, Lucio Gera (+07.08.2012), cuyo segundo aniversario de fallecido honramos en este número de la revista Teología, hablaba de la ineludible exigencia posconciliar de integrar teología, espiritualidad y pastoral. El capítulo V de Evangelii gaudium, “Evangelizadores con Espíritu” (cf. EG 259ss), se ubica especialmente en este horizonte de convicciones porque tiene un inconfundible contenido teológico, un marcado acento espiritual y una clara orientación y lenguaje pastoral, pero sobre todo en razón de expresar una íntima compenetración entre estas tres dimensiones. En este artículo, que reelabora y amplía una presentación oral en la Jornada Evangelii gaudium, organizada por la Facultad de Teología de la UCA el pasado 5 de junio, se asume el vigor de la propuesta de una “evangelización con espíritu” (EG 261) y se reflexiona, en diálogo con nuestra iglesia local, sobre cuatro aspectos relacionados con ella: 1. una teología de la “evangelización con espíritu”, es decir, “con Espíritu Santo”; 2. una espiritualidad contemplativa: amar la Palabra y gustar ser pueblo; 3. el estilo pastoral mariano de la evangelización; y 4. la danza de la teología, la espiritualidad y la pastoral al servicio de la alegría de evangelizar.