Swarm pattern transformation methodologies

The work reported in this paper is motivated by the need for developing swarm pattern transformation methodologies. Two methods, namely a macroscopic method and a mathematical method are investigated for pattern transformation. The first method is based on macroscopic parameters while the second method is based on both microscopic and macroscopic parameters. A formal definition to pattern transformation considering four special cases of transformation is presented. Simulations on a physics simulation engine are used to confirm the feasibility of the proposed transformation methods. A brief comparison between the two methods is also presented.

Investigating feasible tools for swarm pattern transformation

Abstract-The work reported in this paper is motivated by the need for developing swarm pattern transformation methodologies. Two methods, namely a macroscopic method and a mathematical method are investigated for pattern transformation. The first method is based on macroscopic parameters while the second method is based on both microscopic and macroscopic parameters. A formal definition to pattern transformation considering four special cases of transformation is presented. Simulations on a physics simulation engine are used to confirm the feasibility of the proposed transformation methods. A brief comparison between the two methods is also presented.

Introduction. Stochastic physics and climate modelling

Finite computing resources limit the spatial resolution of state-of-the-art global climate simulations to hundreds of kilometres. In neither the atmosphere nor the ocean are small-scale processes such as convection, clouds and ocean eddies properly represented. Climate simulations are known to depend, sometimes quite strongly, on the resulting bulk-formula representation of unresolved processes. Stochastic physics schemes within weather and climate models have the potential to represent the dynamical effects of unresolved scales in ways which conventional bulk-formula representations are incapable of so doing. The application of stochastic physics to climate modelling is a rapidly advancing, important and innovative topic. The latest research findings are gathered together in the Theme Issue for which this paper serves as the introduction.

Effects of Thomson-scattering geometry on white-light imaging of an interplanetary shock: synthetic observations from forward magnetohydrodynamic modelling

Stereoscopic white-light imaging of a large portion of the inner heliosphere has been used to track interplanetary coronal mass ejections. At large elongations from the Sun, the white-light brightness depends on both the local electron density and the efficiency of the Thomson-scattering process. To quantify the effects of the Thomson-scattering geometry, we study an interplanetary shock using forward magnetohydrodynamic simulation and synthetic white-light imaging. Identifiable as an inclined streak of enhanced brightness in a time–elongation map, the travelling shock can be readily imaged by an observer located within a wide range of longitudes in the ecliptic. Different parts of the shock front contribute to the imaged brightness pattern viewed by observers at different longitudes. Moreover, even for an observer located at a fixed longitude, a different part of the shock front will contribute to the imaged brightness at any given time. The observed brightness within each imaging pixel results from a weighted integral along its corresponding ray-path. It is possible to infer the longitudinal location of the shock from the brightness pattern in an optical sky map, based on the east–west asymmetry in its brightness and degree of polarisation. Therefore, measurement of the interplanetary polarised brightness could significantly reduce the ambiguity in performing three-dimensional reconstruction of local electron density from white-light imaging.

GSHMC: an efficient method for molecular simulation

The hybrid Monte Carlo (HMC) method is a popular and rigorous method for sampling from a canonical ensemble. The HMC method is based on classical molecular dynamics simulations combined with a Metropolis acceptance criterion and a momentum resampling step. While the HMC method completely resamples the momentum after each Monte Carlo step, the generalized hybrid Monte Carlo (GHMC) method can be implemented with a partial momentum refreshment step. This property seems desirable for keeping some of the dynamic information throughout the sampling process similar to stochastic Langevin and Brownian dynamics simulations. It is, however, ultimate to the success of the GHMC method that the rejection rate in the molecular dynamics part is kept at a minimum. Otherwise an undesirable Zitterbewegung in the Monte Carlo samples is observed. In this paper, we describe a method to achieve very low rejection rates by using a modified energy, which is preserved to high-order along molecular dynamics trajectories. The modified energy is based on backward error results for symplectic time-stepping methods. The proposed generalized shadow hybrid Monte Carlo (GSHMC) method is applicable to NVT as well as NPT ensemble simulations.

Boundary condition effects in the simulation study of equilibrium properties of magnetic dipolar fluids

In this paper we investigate the equilibrium properties of magnetic dipolar (ferro-) fluids and discuss finite-size effects originating from the use of different boundary conditions in computer simulations. Both periodic boundary conditions and a finite spherical box are studied. We demonstrate that periodic boundary conditions and subsequent use of Ewald sum to account for the long-range dipolar interactions lead to a much faster convergence (in terms of the number of investigated dipolar particles) of the magnetization curve and the initial susceptibility to their thermodynamic limits. Another unwanted effect of the simulations in a finite spherical box geometry is a considerable sensitivity to the container size. We further investigate the influence of the surface term in the Ewald sum-that is, due to the surrounding continuum with magnetic permeability mu(BC)-on the convergence properties of our observables and on the final results. The two different ways of evaluating the initial susceptibility, i.e., (1) by the magnetization response of the system to an applied field and (2) by the zero-field fluctuation of the mean-square dipole moment of the system, are compared in terms of speed and accuracy.

Stochastic modelling of rainfall from satellite data

Satellite-based rainfall monitoring is widely used for climatological studies because of its full global coverage but it is also of great importance for operational purposes especially in areas such as Africa where there is a lack of ground-based rainfall data. Satellite rainfall estimates have enormous potential benefits as input to hydrological and agricultural models because of their real time availability, low cost and full spatial coverage. One issue that needs to be addressed is the uncertainty on these estimates. This is particularly important in assessing the likely errors on the output from non-linear models (rainfall-runoff or crop yield) which make use of the rainfall estimates, aggregated over an area, as input. Correct assessment of the uncertainty on the rainfall is non-trivial as it must take account of • the difference in spatial support of the satellite information and independent data used for calibration • uncertainties on the independent calibration data • the non-Gaussian distribution of rainfall amount • the spatial intermittency of rainfall • the spatial correlation of the rainfall field This paper describes a method for estimating the uncertainty on satellite-based rainfall values taking account of these factors. The method involves firstly a stochastic calibration which completely describes the probability of rainfall occurrence and the pdf of rainfall amount for a given satellite value, and secondly the generation of ensemble of rainfall fields based on the stochastic calibration but with the correct spatial correlation structure within each ensemble member. This is achieved by the use of geostatistical sequential simulation. The ensemble generated in this way may be used to estimate uncertainty at larger spatial scales. A case study of daily rainfall monitoring in the Gambia, west Africa for the purpose of crop yield forecasting is presented to illustrate the method.

Linear viscoelasticity from molecular dynamics simulation of entangled polymers

The linear viscoelastic (LVE) spectrum is one of the primary fingerprints of polymer solutions and melts, carrying information about most relaxation processes in the system. Many single chain theories and models start with predicting the LVE spectrum to validate their assumptions. However, until now, no reliable linear stress relaxation data were available from simulations of multichain systems. In this work, we propose a new efficient way to calculate a wide variety of correlation functions and mean-square displacements during simulations without significant additional CPU cost. Using this method, we calculate stress−stress autocorrelation functions for a simple bead−spring model of polymer melt for a wide range of chain lengths, densities, temperatures, and chain stiffnesses. The obtained stress−stress autocorrelation functions were compared with the single chain slip−spring model in order to obtain entanglement related parameters, such as the plateau modulus or the molecular weight between entanglements. Then, the dependence of the plateau modulus on the packing length is discussed. We have also identified three different contributions to the stress relaxation:  bond length relaxation, colloidal and polymeric. Their dependence on the density and the temperature is demonstrated for short unentangled systems without inertia.

Comparison of stochastic parametrization approaches in a single-column model

We discuss and test the potential usefulness of single-column models (SCMs) for the testing of stchastic physics schemes that have been proposed for use in general circulation models (GCMs). We argue that although single column tests cannot be definitive in exposing the full behaviour of a stochastic method in the full GCM, and although there are differences between SCM testing of deterministic and stochastic methods, nonetheless SCM testing remains a useful tool. It is necessary to consider an ensemble of SCM runs produced by the stochastic method. These can be usefully compared to deterministic ensembles describing initial condition uncertainty and also to combinations of these (with structural model changes) into poor man's ensembles. The proposed methodology is demonstrated using an SCM experiment recently developed by the GCSS community, simulating the transitions between active and suppressed periods of tropical convection.

New insights on growth mechanisms of protein clusters at surfaces: an AFM and simulation study

Despite its relevance to a wide range of technological and fundamental areas, a quantitative understanding of protein surface clustering dynamics is often lacking. In inorganic crystal growth, surface clustering of adatoms is well described by diffusion-aggregation models. In such models, the statistical properties of the aggregate arrays often reveal the molecular scale aggregation processes. We investigate the potential of these theories to reveal hitherto hidden facets of protein clustering by carrying out concomitant observations of lysozyme adsorption onto mica surfaces, using atomic force microscopy. and Monte Carlo simulations of cluster nucleation and growth. We find that lysozyme clusters diffuse across the substrate at a rate that varies inversely with size. This result suggests which molecular scale mechanisms are responsible for the mobility of the proteins on the substrate. In addition the surface diffusion coefficient of the monomer can also be extracted from the comparison between experiments and simulations. While concentrating on a model system of lysozyme-on-mica, this 'proof of concept' study successfully demonstrates the potential of our approach to understand and influence more biomedically applicable protein-substrate couples.

Comparison of stochastic parameterisation approaches in a single-column model

We discuss and test the potential usefulness of single-column models (SCMs) for the testing of stochastic physics schemes that have been proposed for use in general circulation models (GCMs). We argue that although single column tests cannot be definitive in exposing the full behaviour of a stochastic method in the full GCM, and although there are differences between SCM testing of deterministic and stochastic methods, SCM testing remains a useful tool. It is necessary to consider an ensemble of SCM runs produced by the stochastic method. These can be usefully compared to deterministic ensembles describing initial condition uncertainty and also to combinations of these (with structural model changes) into poor man's ensembles. The proposed methodology is demonstrated using an SCM experiment recently developed by the GCSS (GEWEX Cloud System Study) community, simulating transitions between active and suppressed periods of tropical convection.