Computational modes and grid imprinting on five quasi-uniform spherical C-grids

Currently, most operational forecasting models use latitude-longitude grids, whose convergence of meridians towards the poles limits parallel scaling. Quasi-uniform grids might avoid this limitation. Thuburn et al, JCP, 2009 and Ringler et al, JCP, 2010 have developed a method for arbitrarily-structured, orthogonal C-grids (TRiSK), which has many of the desirable properties of the C-grid on latitude-longitude grids but which works on a variety of quasi-uniform grids. Here, five quasi-uniform, orthogonal grids of the sphere are investigated using TRiSK to solve the shallow-water equations. We demonstrate some of the advantages and disadvantages of the hexagonal and triangular icosahedra, a Voronoi-ised cubed sphere, a Voronoi-ised skipped latitude-longitude grid and a grid of kites in comparison to a full latitude-longitude grid. We will show that the hexagonal-icosahedron gives the most accurate results (for least computational cost). All of the grids suffer from spurious computational modes; this is especially true of the kite grid, despite it having exactly twice as many velocity degrees of freedom as height degrees of freedom. However, the computational modes are easiest to control on the hexagonal icosahedron since they consist of vorticity oscillations on the dual grid which can be controlled using a diffusive advection scheme for potential vorticity.

Molecular modelling studies of binding of DACD derivatives into G-Quadruplex DNA: comparison of force field and quantum polarized ligand docking methods

The DNA G-qadruplexes are one of the targets being actively explored for anti-cancer therapy by inhibiting them through small molecules. This computational study was conducted to predict the binding strengths and orientations of a set of novel dimethyl-amino-ethyl-acridine (DACA) analogues that are designed and synthesized in our laboratory, but did not diffract in Synchrotron light.Thecrystal structure of DNA G-Quadruplex(TGGGGT)4(PDB: 1O0K) was used as target for their binding properties in our studies.We used both the force field (FF) and QM/MM derived atomic charge schemes simultaneously for comparing the predictions of drug binding modes and their energetics. This study evaluates the comparative performance of fixed point charge based Glide XP docking and the quantum polarized ligand docking schemes. These results will provide insights on the effects of including or ignoring the drug-receptor interfacial polarization events in molecular docking simulations, which in turn, will aid the rational selection of computational methods at different levels of theory in future drug design programs. Plenty of molecular modelling tools and methods currently exist for modelling drug-receptor or protein-protein, or DNA-protein interactionssat different levels of complexities.Yet, the capasity of such tools to describevarious physico-chemical propertiesmore accuratelyis the next step ahead in currentresearch.Especially, the usage of most accurate methods in quantum mechanics(QM) is severely restricted by theirtedious nature. Though the usage of massively parallel super computing environments resulted in a tremendous improvement in molecular mechanics (MM) calculations like molecular dynamics,they are still capable of dealing with only a couple of tens to hundreds of atoms for QM methods. One such efficient strategy that utilizes thepowers of both MM and QM are the QM/MM hybrid methods. Lately, attempts have been directed towards the goal of deploying several different QM methods for betterment of force field based simulations, but with practical restrictions in place. One of such methods utilizes the inclusion of charge polarization events at the drug-receptor interface, that is not explicitly present in the MM FF.

Response theory for equilibrium and non-equilibrium statistical mechanics: causality and generalized Kramers-Kronig relations

We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific results are provided for the case of arbitrary order harmonic response, which allows for a very comprehensive K-K analysis and the establishment of sum rules connecting the asymptotic behavior of the harmonic generation susceptibility to the short-time response of the perturbed system. These results set in a more general theoretical framework previous findings obtained for optical systems and simple mechanical models, and shed light on the very general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks that any experimental and model generated dataset must obey. The theory exposed in the present paper is dual to the time-dependent theory of perturbations to equilibrium states and to non-equilibrium steady states, and has in principle similar range of applicability and limitations. In order to connect the equilibrium and the non equilibrium steady state case, we show how to rewrite the classical response theory by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. These results, taking into account the chaotic hypothesis by Gallavotti and Cohen, might be relevant in several fields, including climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, K-K relations might be robust tools for the definition of a self-consistent theory of climate change.

A tutorial on pseudospectral methods for computational optimal control

[English] This paper is a tutorial introduction to pseudospectral optimal control. With pseudospectral methods, a function is approximated as a linear combination of smooth basis functions, which are often chosen to be Legendre or Chebyshev polynomials. Collocation of the differential-algebraic equations is performed at orthogonal collocation points, which are selected to yield interpolation of high accuracy. Pseudospectral methods directly discretize the original optimal control problem to recast it into a nonlinear programming format. A numerical optimizer is then employed to find approximate local optimal solutions. The paper also briefly describes the functionality and implementation of PSOPT, an open source software package written in C++ that employs pseudospectral discretization methods to solve multi-phase optimal control problems. The software implements the Legendre and Chebyshev pseudospectral methods, and it has useful features such as automatic differentiation, sparsity detection, and automatic scaling. The use of pseudospectral methods is illustrated in two problems taken from the literature on computational optimal control. [Portuguese] Este artigo e um tutorial introdutorio sobre controle otimo pseudo-espectral. Em metodos pseudo-espectrais, uma funcao e aproximada como uma combinacao linear de funcoes de base suaves, tipicamente escolhidas como polinomios de Legendre ou Chebyshev. A colocacao de equacoes algebrico-diferenciais e realizada em pontos de colocacao ortogonal, que sao selecionados de modo a minimizar o erro de interpolacao. Metodos pseudoespectrais discretizam o problema de controle otimo original de modo a converte-lo em um problema de programa cao nao-linear. Um otimizador numerico e entao empregado para obter solucoes localmente otimas. Este artigo tambem descreve sucintamente a funcionalidade e a implementacao de um pacote computacional de codigo aberto escrito em C++ chamado PSOPT. Tal pacote emprega metodos de discretizacao pseudo-spectrais para resolver problemas de controle otimo com multiplas fase. O PSOPT permite a utilizacao de metodos de Legendre ou Chebyshev, e possui caractersticas uteis tais como diferenciacao automatica, deteccao de esparsidade e escalonamento automatico. O uso de metodos pseudo-espectrais e ilustrado em dois problemas retirados da literatura de controle otimo computacional.

Comments, with reply, on "Computational algorithms for pole assignment" by N.K. Nichols

Some points of the paper by N.K. Nichols (see ibid., vol.AC-31, p.643-5, 1986), concerning the robust pole assignment of linear multiinput systems, are clarified. It is stressed that the minimization of the condition number of the closed-loop eigenvector matrix does not necessarily lead to robustness of the pole assignment. It is shown why the computational method, which Nichols claims is robust, is in fact numerically unstable with respect to the determination of the gain matrix. In replying, Nichols presents arguments to support the choice of the conditioning of the closed-loop poles as a measure of robustness and to show that the methods of J Kautsky, N. K. Nichols and P. VanDooren (1985) are stable in the sense that they produce accurate solutions to well-conditioned problems.

A simple analysis of thermodynamic properties for classical plasmas: I. theory

By eliminating the short range negative divergence of the Debye–Hückel pair distribution function, but retaining the exponential charge screening known to operate at large interparticle separation, the thermodynamic properties of one-component plasmas of point ions or charged hard spheres can be well represented even in the strong coupling regime. Predicted electrostatic free energies agree within 5% of simulation data for typical Coulomb interactions up to a factor of 10 times the average kinetic energy. Here, this idea is extended to the general case of a uniform ionic mixture, comprising an arbitrary number of components, embedded in a rigid neutralizing background. The new theory is implemented in two ways: (i) by an unambiguous iterative algorithm that requires numerical methods and breaks the symmetry of cross correlation functions; and (ii) by invoking generalized matrix inverses that maintain symmetry and yield completely analytic solutions, but which are not uniquely determined. The extreme computational simplicity of the theory is attractive when considering applications to complex inhomogeneous fluids of charged particles.

On computational algorithms for pole assignment

A number of computationally reliable direct methods for pole assignment by feedback have recently been developed. These direct procedures do not necessarily produce robust solutions to the problem, however, in the sense that the assigned poles are insensitive to perturbalions in the closed-loop system. This difficulty is illustrated here with results from a recent algorithm presented in this TRANSACTIONS and its causes are examined. A measure of robustness is described, and techniques for testing and improving robustness are indicated.

Modular non-computational-connectionist-hybrid neural network approach to robotic systems

Spiking neural networks are usually limited in their applications due to their complex mathematical models and the lack of intuitive learning algorithms. In this paper, a simpler, novel neural network derived from a leaky integrate and fire neuron model, the ‘cavalcade’ neuron, is presented. A simulation for the neural network has been developed and two basic learning algorithms implemented within the environment. These algorithms successfully learn some basic temporal and instantaneous problems. Inspiration for neural network structures from these experiments are then taken and applied to process sensor information so as to successfully control a mobile robot.

Controlling the computational modes of the arbitrarily structured C-grid

The arbitrarily structured C-grid, TRiSK (Thuburn, Ringler, Skamarock and Klemp, 2009, 2010) is being used in the ``Model for Prediction Across Scales'' (MPAS) and is being considered by the UK Met Office for their next dynamical core. However the hexagonal C-grid supports a branch of spurious Rossby modes which lead to erroneous grid-scale oscillations of potential vorticity (PV). It is shown how these modes can be harmlessly controlled by using upwind-biased interpolation schemes for PV. A number of existing advection schemes for PV are tested, including that used in MPAS, and none are found to give adequate results for all grids and all cases. Therefore a new scheme is proposed; continuous, linear-upwind stabilised transport (CLUST), a blend between centred and linear-upwind with the blend dependent on the flow direction with respect to the cell edge. A diagnostic of grid-scale oscillations is proposed which gives further discrimination between schemes than using potential enstrophy alone and indeed some schemes are found to destroy potential enstrophy while grid-scale oscillations grow. CLUST performs well on hexagonal-icosahedral grids and unrotated skipped latitude-longitude grids of the sphere for various shallow water test cases. Despite the computational modes, the hexagonal icosahedral grid performs well since these modes are easy and harmless to filter. As a result TRiSK appears to perform better than a spectral shallow water model.

Solvent-dependent modulation of metal–metal electronic interactions in a dinuclear cyanoruthenate complex: a detailed electrochemical, spectroscopic and computational study

The dinuclear complex [{Ru(CN)4}2(μ-bppz)]4− shows a strongly solvent-dependent metal–metal electronic interaction which allows the mixed-valence state to be switched from class 2 to class 3 by changing solvent from water to CH2Cl2. In CH2Cl2 the separation between the successive Ru(II)/Ru(III) redox couples is 350 mVand the IVCT band (from the UV/Vis/NIR spectroelectrochemistry) is characteristic of a borderline class II/III or class III mixed valence state. In water, the redox separation is only 110 mVand the much broader IVCT transition is characteristic of a class II mixed-valence state. This is consistent with the observation that raising and lowering the energy of the d(π) orbitals in CH2Cl2 or water, respectively, will decrease or increase the energy gap to the LUMO of the bppz bridging ligand, which provides the delocalisation pathway via electron-transfer. IR spectroelectrochemistry could only be carried out successfully in CH2Cl2 and revealed class III mixed-valence behaviour on the fast IR timescale. In contrast to this, time-resolved IR spectroscopy showed that the MLCTexcited state, which is formulated as RuIII(bppz˙−)RuII and can therefore be considered as a mixed-valence Ru(II)/Ru(III) complex with an intermediate bridging radical anion ligand, is localised on the IR timescale with spectroscopically distinct Ru(II) and Ru(III) termini. This is because the necessary electron-transfer via the bppz ligand is more difficult because of the additional electron on bppz˙− which raises the orbital through which electron exchange occurs in energy. DFT calculations reproduce the electronic spectra of the complex in all three Ru(II)/Ru(II), Ru(II)/Ru(III) and Ru(III)/Ru(III) calculations in both water and CH2Cl2 well as long as an explicit allowance is made for the presence of water molecules hydrogen-bonded to the cyanides in the model used. They also reproduce the excited-state IR spectra of both [Ru(CN)4(μ-bppz)]2– and [{Ru(CN)4}2(μ-bppz)]4− very well in both solvents. The reorganization of the water solvent shell indicates a possible dynamical reason for the longer life time of the triplet state in water compared to CH2Cl2.

Models, moulds and mass production: the mechanics of stylistic influence form the Mediterranean to Bactria

Classical Greek and Roman influence on the material culture of Central Asia and northwestern India is often considered in the abstract. This article attempts to examine the mechanisms of craft production and movement of artisans and objects which made such influence possible, through four case studies: (1) Mould-made ceramics in Hellenistic eastern Bactria; (2) Plaster casts used in the production of metalware from Begram; (3) Terracotta figurines and the moulds used to produce them, from various archaeological sites; and (4) Mass production of identical gold adornments in the nomadic tombs from Tillya Tepe. The implications of such techniques for our understanding of the development of Gandhāran art are also discussed.

Continuum sea ice rheology determined from subcontinuum mechanics

[1] A method is presented to calculate the continuum-scale sea ice stress as an imposed, continuum-scale strain-rate is varied. The continuum-scale stress is calculated as the area-average of the stresses within the floes and leads in a region (the continuum element). The continuum-scale stress depends upon: the imposed strain rate; the subcontinuum scale, material rheology of sea ice; the chosen configuration of sea ice floes and leads; and a prescribed rule for determining the motion of the floes in response to the continuum-scale strain-rate. We calculated plastic yield curves and flow rules associated with subcontinuum scale, material sea ice rheologies with elliptic, linear and modified Coulombic elliptic plastic yield curves, and with square, diamond and irregular, convex polygon-shaped floes. For the case of a tiling of square floes, only for particular orientations of the leads have the principal axes of strain rate and calculated continuum-scale sea ice stress aligned, and these have been investigated analytically. The ensemble average of calculated sea ice stress for square floes with uniform orientation with respect to the principal axes of strain rate yielded alignment of average stress and strain-rate principal axes and an isotropic, continuum-scale sea ice rheology. We present a lemon-shaped yield curve with normal flow rule, derived from ensemble averages of sea ice stress, suitable for direct inclusion into the current generation of sea ice models. This continuum-scale sea ice rheology directly relates the size (strength) of the continuum-scale yield curve to the material compressive strength.