114 resultados para mathematical understanding


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The idea of a structural landscape is based on the fact that a large number of crystal structures can be associated with a particular organic molecule. Taken together, all these structures constitute the landscape. The landscape includes polymorphs, pseudopolymorphs and solvates. Under certain circumstances, it may also include multicomponent crystals (or co-crystals) that contain the reference molecule as one of the components. Under still other circumstances, the landscape may include the crystal structures of molecules that are closely related to the reference molecule. The idea of a landscape is to facilitate the understanding of the process of crystallization. It includes all minima that can, in principle, be accessed by the molecule in question as it traverses the path from solution to the crystal. Isonicotinamide is a molecule that is known to form many co-crystals. We report here a 2 : 1 co-crystal of this amide with 3,5-dinitrobenzoic acid, wherein an unusual N-H center dot center dot center dot N hydrogen-bonded pattern is observed. This crystal structure offers some hints about the recognition processes between molecules that might be implicated during crystallization. Also included is a review of other recent results that illustrate the concept of the structural landscape.

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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.

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Isolated magnetic nanowires have been studied extensively and the magnetization reversal mechanism is well understood in these systems. But when these nanowires are joined together in different architectures, they behave differently and can give novel properties. Using this approach, one can engineer the network architectures to get artificial anisotropy. Here, we report six-fold anisotropy by joining the magnetic nanowires into hexagonal network. For this study, we also benchmark the widely used micromagnetic packages: OOMMF, Nmag, and LLG-simulator. Further, we propose a local hysteresis method by post processing the spatial magnetization information. With this approach we obtained the hysteresis of nanowires to understand the six-fold anisotropy and the reversal mechanism within the hexagonal networks.

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The rapid emergence of infectious diseases calls for immediate attention to determine practical solutions for intervention strategies. To this end, it becomes necessary to obtain a holistic view of the complex hostpathogen interactome. Advances in omics and related technology have resulted in massive generation of data for the interacting systems at unprecedented levels of detail. Systems-level studies with the aid of mathematical tools contribute to a deeper understanding of biological systems, where intuitive reasoning alone does not suffice. In this review, we discuss different aspects of hostpathogen interactions (HPIs) and the available data resources and tools used to study them. We discuss in detail models of HPIs at various levels of abstraction, along with their applications and limitations. We also enlist a few case studies, which incorporate different modeling approaches, providing significant insights into disease. (c) 2013 Wiley Periodicals, Inc.

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Catch the twist: The cis Piv-Pro conformer (Piv=pivaloyl) of peptides is no longer inaccessible. Any cis X-Pro tertiary-amide-bond conformer can be stabilized in crystals of peptides by accommodating the unavoidable distortion of the dihedral angle of the peptide bond to the carbonyl group of the Pro residue (see picture), in this case through ni−1→πi* interactions. Steric clashes were not observed in the cis Piv-Pro rotamers studied.

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Mechanism of ion transport in glasses continues to be incompletely understood. Several of the theoretical models in vogue fail to rationalize conductivity behaviour when d.c. and a.c. measurements are considered together. While they seem to involve the presence of at least two components in d.c. activation energy, experiments fail to reveal that feature. Further, only minor importance is given to the influence of structure of the glass on the ionic conductivity behaviour. In this paper, we have examined several general aspects of ion transport taking the example of ionically conducting glasses in pseudo binary, yNa(2)B(4)O(7)center dot(1-y) M (a) O (b) (with y = 0 center dot 25-0 center dot 79 and M (a) O (b) = PbO, TeO2 and Bi2O3) system of glasses which have also been recently characterized. Ion transport in them has been studied in detail. We have proposed that non-bridging oxygen (NBO) participation is crucial to the understanding of the observed conductivity behaviour. NBO-BO switching is projected as the first important step in ion transport and alkali ion jump is a subsequent event with a characteristically lower barrier which is, therefore, not observed in any study. All important observations in d.c. and a.c. transport in glasses are found consistent with this model.

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Here, we report for the first time a simple thermal oxidation strategy for the large area synthesis of Ge/GeO2 nanoholes from Ge and studied the luminescence of Ge/GeO2 and hole formation mechanism through phase and luminescence mapping. Photoluminescence mapping reveals that the emission in the visible range is only from the hole region, which provokes the necessity of the nanoholes. Such materials can also be used to convert ultraviolet to visible radiation for detection by conventional phototubes and to coat blue or ultraviolet diodes to obtain white light.

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In a networked society, governing advocacy groups and networks through decentralized systems of policy implementation has been the interest of governance network literature. This paper addresses the topic of governing networks in the context of Indian agrarian societies by taking the case example of a welfare scheme for the Indian rural poor. We explore context-specific regulatory dynamics through the situated agent based architectural framework. The effects of various regulatory strategies that can be adopted by governing node are tested under various action arenas through experimental design. Results show the impact of regulatory strategies on the resource dependencies and asymmetries in the network relationships. This indicates that the optimal feasible regulatory strategy in networked society is institutionally rational and is context dependent. Further, we show that situated MAS architecture is a natural fit for institutional understanding of the dynamics (Ostrom et al. in Rules, games, and common-pool resources, 1994).

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Cardiac fibroblasts, when coupled functionally with myocytes, can modulate the electrophysiological properties of cardiac tissue. We present systematic numerical studies of such modulation of electrophysiological properties in mathematical models for (a) single myocyte-fibroblast (MF) units and (b) two-dimensional (2D) arrays of such units; our models build on earlier ones and allow for zero-, one-, and two-sided MF couplings. Our studies of MF units elucidate the dependence of the action-potential (AP) morphology on parameters such as E-f, the fibroblast resting-membrane potential, the fibroblast conductance G(f), and the MF gap-junctional coupling G(gap). Furthermore, we find that our MF composite can show autorhythmic and oscillatory behaviors in addition to an excitable response. Our 2D studies use (a) both homogeneous and inhomogeneous distributions of fibroblasts, (b) various ranges for parameters such as G(gap), G(f), and E-f, and (c) intercellular couplings that can be zero-sided, one-sided, and two-sided connections of fibroblasts with myocytes. We show, in particular, that the plane-wave conduction velocity CV decreases as a function of G(gap), for zero-sided and one-sided couplings; however, for two-sided coupling, CV decreases initially and then increases as a function of G(gap), and, eventually, we observe that conduction failure occurs for low values of G(gap). In our homogeneous studies, we find that the rotation speed and stability of a spiral wave can be controlled either by controlling G(gap) or E-f. Our studies with fibroblast inhomogeneities show that a spiral wave can get anchored to a local fibroblast inhomogeneity. We also study the efficacy of a low-amplitude control scheme, which has been suggested for the control of spiral-wave turbulence in mathematical models for cardiac tissue, in our MF model both with and without heterogeneities.

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Due to rapid improvements in on-board instrumentation and atmospheric observation systems, in most cases, aircraft are able to steer clear of regions of adverse weather. However, they still encounter unexpected bumpy flight conditions in regions away from storms and clouds. This is the phenomenon of clear air turbulence (CAT), which has been a challenge to our understanding as well as efforts at prediction. While most of such cases result in mild discomfort, a few cases can be violent leading to serious injuries to passengers and damage to the aircraft. The underlying physical mechanisms have been sought to be explained in terms of fluid dynamic instabilities and waves in the atmosphere. The main mechanisms which have been proposed are: (i) Kelvin-Helmholtz instability of shear layers, (ii) waves generated from flow over mountains, (iii) inertia-gravity waves from clouds and other sources, (iv) spontaneous imbalance theory and (v) horizontal vortex tubes. This has also undergone a change over the years. We present an overview of the mechanisms proposed and their implications for prediction.

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Inter-domain linkers (IDLs)' bridge flanking domains and support inter-domain communication in multi-domain proteins. Their sequence and conformational preferences enable them to carry out varied functions. They also provide sufficient flexibility to facilitate domain motions and, in conjunction with the interacting interfaces, they also regulate the inter-domain geometry (IDG). In spite of the basic intuitive understanding of the inter-domain orientations with respect to linker conformations and interfaces, we still do not entirely understand the precise relationship among the three. We show that IDG is evolutionarily well conserved and is constrained by the domain-domain interface interactions. The IDLs modulate the interactions by varying their lengths, conformations and local structure, thereby affecting the overall IDG. Results of our analysis provide guidelines in modelling of multi-domain proteins from the tertiary structures of constituent domain components.

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A systematic study was done to understand the influence of volume fractions and bilayer spacings for metal/nitride multilayer coating using finite element method (FEM). An axisymmetric model was chosen to model the real situation by incorporating metal and substrate plasticity. Combinations of volume fractions and bilayer spacings were chosen for FEM analysis consistent with experimental results. The model was able to predict trends in cracking with respect to layer spacing and volume fraction. Metal layer plasticity is seen to greatly influence the stress field inside nitride. It is seen that the thicker metal induces higher tensile stresses inside nitride and hence leads to lower cracking loads. Thin metal layers < 10 nm were seen to have curved interfaces, and hence, the deformation mode was interfacial delamination in combination with edge cracking. There is an optimum seen with respect to volume fraction similar to 13% and metal layer thickness similar to 30 nm, which give maximum crack resistance.

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Estimation of design quantiles of hydrometeorological variables at critical locations in river basins is necessary for hydrological applications. To arrive at reliable estimates for locations (sites) where no or limited records are available, various regional frequency analysis (RFA) procedures have been developed over the past five decades. The most widely used procedure is based on index-flood approach and L-moments. It assumes that values of scale and shape parameters of frequency distribution are identical across all the sites in a homogeneous region. In real-world scenario, this assumption may not be valid even if a region is statistically homogeneous. To address this issue, a novel mathematical approach is proposed. It involves (i) identification of an appropriate frequency distribution to fit the random variable being analyzed for homogeneous region, (ii) use of a proposed transformation mechanism to map observations of the variable from original space to a dimensionless space where the form of distribution does not change, and variation in values of its parameters is minimal across sites, (iii) construction of a growth curve in the dimensionless space, and (iv) mapping the curve to the original space for the target site by applying inverse transformation to arrive at required quantile(s) for the site. Effectiveness of the proposed approach (PA) in predicting quantiles for ungauged sites is demonstrated through Monte Carlo simulation experiments considering five frequency distributions that are widely used in RFA, and by case study on watersheds in conterminous United States. Results indicate that the PA outperforms methods based on index-flood approach.