Ken Hawick - Academia.edu (original) (raw)
Papers by Ken Hawick
We have investigated the anomalous scaling behaviour of the Ising model on small-world networks b... more We have investigated the anomalous scaling behaviour of the Ising model on small-world networks based on 2- and 3-dimensional lattices using Monte Carlo simulations. Our main result is that even at low p, the shift in the critical temperature Δ T_c scales as p^s, with s ≈ 0.50 for 2-D systems, s ≈ 0.698 for 3-D and s ≈ 0.75 for 4-D. We have also verified that a z-preserving rewiring algorithm still exhibits small-world effects and yet is more directly comparable with the conventional Ising model; the small-world effect is due to enhanced long-range correlations and not the change in effective dimension. We find the critical exponents β and ν exhibit a monotonic change between an Ising-like transition and mean-field behaviour in 2- and 3-dimensional systems.
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Concurrency and Computation: Practice and Experience, 2012
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The Cahn-Hilliard-Cook equation continues to be a useful model describing binary phase separation... more The Cahn-Hilliard-Cook equation continues to be a useful model describing binary phase separation in systems such as alloys and other physical and chemical applications. We describe our investigation of this field equation and report on the various discretisation schemes we used to integrate the system in one-, twoand three-dimensions. We also discuss how the equation can be visualised effectively in these different dimensions and consider how these techniques can usefully be applied to other partial differential equations.
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We show how compiler technology can generate fast and efficient yet human-readable data-parallel ... more We show how compiler technology can generate fast and efficient yet human-readable data-parallel simulation code for solving certain partial differential equation (PDE) based problems. We present a code parser and generator based on an ANTLR grammar and tree walking approach that transforms a mathematical formulation of an equation such as the Cahn-Hilliard family into simulation software in C++ or in NVIDIA’s Compute Unified Device Architecture (CUDA) language for programming Graphical Processing Units (GPUS). We present software architectural ideas, generated specimen code and detailed performance data on modern GPUs. We discuss how code generation techniques can be used to speed up code development and computational run time for related complex system simulation problems.
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Computational scientific simulations have long used parallel computers to increase their performa... more Computational scientific simulations have long used parallel computers to increase their performance. Recently graphics cards have been utilised to provide this functionality. GPGPU APIs such as NVidia’s CUDA can be used to harness the power of GPUs for purposes other than computer graphics. GPUs are designed for processing twodimensional data. In previous work we have presented several two-dimensional Cahn-Hilliard simulations that each utilise different CUDA memory types and compared their results. In this paper we extend these ideas to three dimensions. As GPUs are not intended for processing threedimensional data arrays, the performance of the memory optimisations is expected to change. Here we present several three-dimensional Cahn-Hilliard simulations to explore the challenges and the performance of the different memory types in three-dimensions. The results show that the simulation design with the best performance in threedimensions uses a different memory type to the optimal...
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to apply quickly for many applications domains. Recent developments in computer libraries such as... more to apply quickly for many applications domains. Recent developments in computer libraries such as the Standard Template Library of the C++ language and the Message Passing Package associated with the Python Language provide a way to implement very high level parallel containers in support of application programming. A parallel container is an implementation of a data structure such as a list, or vector, or set, that has associated with it the necessary methods and state knowledge to distribute the contents of the structure across the memory of a parallel computer or a computer cluster. A key idea is that of the parallel iterator which allows a single high level statement written by the applications programmer to invoke a parallel operation across the entire data structure’s contents while avoiding the need for knowledge of how the distribution is actually carried out. This transparency approach means that optimised parallel algorithms can be separated from the applications domain co...
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The emergence of complex spatial patterns in agent-based models is closely connected with the sym... more The emergence of complex spatial patterns in agent-based models is closely connected with the symmetries and relationships present between individual microscopic constituents. Games such as Rock-Paper-Scissors (RPS) have a closed cycle relationship amongst players which extends the symmetry. RPS and related games can be played by agents arranged on a spatial grid and have been shown to generate many complex spatial patterns. We consider the implications of extending the individual RPS game complexity to five-cycle games such as “Rock-Paper-ScissorsLizard-Spock” that have competing cyclic reactions. We simulate large spatial systems using a reaction-rate formulation which are simulated for long run times to capture the dynamic equilibrium regime. We report on the stable and unstable phase mixtures that arise in these agent models and comment on the effects that drive them.
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Simulations users at all levels make heavy use of compute resources to drive computational simula... more Simulations users at all levels make heavy use of compute resources to drive computational simulations for greatly varying applications areas of research using different simulation paradigms. Simulations are implemented in many software forms, ranging from highly standardised and general models that run in proprietary software packages to ad hoc hand-crafted simulations codes for very specific applications. Visualisation of the workings or results of a simulation is another highly valuable capability for simulation developers and practitioners. There are many different software libraries and methods available for creating a visualisation layer for simulations, and it is often a difficult and time-consuming process to assemble a toolkit of these libraries and other resources that best suits a particular simulation model. We present here a break-down of the main simulation paradigms, and discuss differing toolkits and approaches that different researchers have taken to tackle coupled ...
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Population-based evolutionary algorithms continue to play an important role in artifically intell... more Population-based evolutionary algorithms continue to play an important role in artifically intelligent systems, but can not always easily use parallel computation. We have com- bined a geometric (any-space) particle swarm optimisation algorithm with use of Ferreira's Karva language of gene expression programming to produce a hybrid that can ac- celerate the genetic operators and which can rapidly attain a good solution. We show how Graphical Processing Units (GPUs) can be exploited for this. While the geometric par- ticle swarm optimiser is not markedly faster that genetic programming, we show it does attain good solutions faster, which is important for the problems discussed when the fit- ness function is inordinately expensive to compute.
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Modern interface devices such as depth field cameras and touch sensitive screen offer new scope f... more Modern interface devices such as depth field cameras and touch sensitive screen offer new scope for navigation large and complex image data sets. Image sequences from movies or simulations can be treated as hyper-bricks of navigable data. We have implemented an image navigation interface framework that supports a compatible set of both depth-field hand gestures and touch-screen finger movements. We report on how these two apparently disparate interfaces can be combined in a unifying software architecture and explore the human computer interaction space of suitable gestural and touch idioms and metaphors suitable for rapid interactive navigation and rendering of a sequence of images from a simulation, from photographic stills, or frames of a movie. We compare the two sorts of interaction and discuss a descriptive vocabulary for these and suggest some directions for development and use in other bulk data navigation interfaces.
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Droplet nucleation occurs when a small fluctuation in a system forms and subsequently grows in ma... more Droplet nucleation occurs when a small fluctuation in a system forms and subsequently grows in magnitude. Raindrop formation is a familiar everyday example. Droplets can be modelled using a field equation such as the Cahn-Hilliard system [1, 2, 3]. Attempts to understand and describe growth processes in material physico-chemical systems are often made using nucleation theory, which works well in the dilute limit. The range of validity of nucleation theoretical models can be explored using microscopic simulation models in which nucleating clusters can be counted and measured exactly. The Becker-Doring nucleation theory is described and its range of validity is discussed for binary alloy simulations using the Kawasaki exchange model in various concentration regimes. Graph labeling and enumeration techniques are employed to study the range of sizes of clusters present in nucleating systems.
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Recent developments in processing devices such as graphical processing units and multi-core syste... more Recent developments in processing devices such as graphical processing units and multi-core systems offer opportunities to make use of parallel techniques at the chip level to obtain high performance. We discuss the difficulties in establishing suitable benchmark codes for making comparisons across these device architectures and in a way that is representative of key applications. We report on our use of classical dynamical particle collision simulation codes as benchmarks for comparing modern GPUs. We discuss our findings in terms of architectural features for parallelism as well as clock speed issues.
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Computer games on mobile platforms are increasingly popular and modern devices offer games develo... more Computer games on mobile platforms are increasingly popular and modern devices offer games developers unconventional user interface technologies based on device orientation. We describe a maze game implemented both for Android mobile phone and tablet devices that supports navigation though a generated landscape using tilt motions accessed via the devices accelerometer sensors. We report on implementation issues including device sensitivity, resolution and appropriate ways to utilise tilt motion in a practical game or simulation. We discuss future directions for this technology and possible uses in simulations as well as games.
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Visualisation of the interior of a threedimensional(3D) solid model is not a trivial operation an... more Visualisation of the interior of a threedimensional(3D) solid model is not a trivial operation and di↵erent possible approaches work best for di↵erent sorts of model data. It is useful when developing a 3D simulation model or when analysing 3D data to have a software tool that allows cut-aways, and fly-throughs and other interactive means of solid model visualisation. This article describes a highly interactive program built using portable C++ and OpenGL to load in a sequence of hyperbrick 3D data set files and to support data shifts, rotations, cut-aways and many other rendering options. A hyperbrick data format was designed especially to allow inter-operation with simulation programs that can easy generate output in this simple “.hrbk” format. A description of the main ideas is given alongwith a design and code outline and several rendering examples. Some areas for further tool development are given.
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Cellular automaton models such as Conway’s Game of Life have long been shown to exhibit a high de... more Cellular automaton models such as Conway’s Game of Life have long been shown to exhibit a high degree of spatial complexity. Spatial patterns can be analysed and categorised in this and other models and used as a basis for cataloging other related models and their behaviour classes. An interesting variation arises when a third state is introduced and we explore the consequences of this in models like Silverman’s “Brian’s Brain” – sometimes known as the “Game of Death” where “zombies” are introduced into the spatial model. The third state and the microscopic rules associated with the three constituent species gives rise to a rich new set of phases and behaviours with can be simulated and catalogued statistically. We focus on the early transient behaviour following a random system initialisation and the initial thinning out following by a subsequent explosion in species diversity.
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Graphical Processing Units(GPUs) are usually programmed to provide data-parallel acceleration to ... more Graphical Processing Units(GPUs) are usually programmed to provide data-parallel acceleration to a host processor. Modern GPUs typically have an internal multi-processor (MP) structure that can be exploited in an unusual way to offer semiindependent task parallelism providing the MPs can operate within their own localised memory and apply data-parallelism to their own problem subset. We describe a combined simulation and statistical analysis application using component labelling and benchmark it on a range of modern GPU and CPU devices with various numbers of cores. As well as demonstrating a high degree of job parallelism and throughput we find a typical GPU MP outperforms a conventional CPU core.
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Lattice gas cellular automata (LGCA) models provide a relatively fast means of simulating fluid f... more Lattice gas cellular automata (LGCA) models provide a relatively fast means of simulating fluid flow and can give both quantitative and qualitative insights into flow patterns around complex obstacles. Symmetry requirements inherent in the Navier-Stokes equation mandate that lattice-gas approximations to the full field equations be run on triangular lattices in two dimensions and on a 3-D projection of a four dimensional face centred hyper-cubic for three dimensions. Graphics Processing Units (GPUs) offer powerful data-parallel processing capabilities for many simulations as well as the graphics calculations required to simulate them. We describe how GPUs can be used to implement mesh structures for simulating lattice gases. We present performance data on how to optimise data layout in the various levels of localised memory available in modern GPUs and discuss data transfer issues between CPU and GPU and between processing GPU and graphics GPU in a unified simulation platform. We il...
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Conways’s Game-of-Life (GoL) is one of a family of spatial cellular automata rule sets that emplo... more Conways’s Game-of-Life (GoL) is one of a family of spatial cellular automata rule sets that employ the Moore neighbourhood on a rectilinear lattice of cells. GoL generalises to set of other automata using different neighbournumbers that lead to birth and survival. These models exhibit different static properties and also different long term dynamical equilibrium points. We define some quantifiable metrics and explore how some well known GoL variants can be categorised into groupings, categorised by their static properties and dynamical equilibria. We also explore effects due to differing initial crowding levels of the live seed cell population, and how this affects the categories.
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Pair-annihilation process models capture the behaviour of important reactions amongst fundamental... more Pair-annihilation process models capture the behaviour of important reactions amongst fundamental physical but also chemical systems. We develop a lattice-based pairannihilation model based on Kawasaki exchange dynamics and with diffusion properties controlled by a latticegas temperature. We investigate the effect of multi-species screening in the model when anti-ferromagnetic repulsive coupling forces are used. We find a phase transition manifested by an annihilation induced population collapse around T=0.22 and an additional phase transition in the number of species present around Q=5. We describe a number of quantitative metrics based on graph component labeling and contrast the behaviours of the ferromagnetic and anti-ferromagnetic variants of the model.
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We have investigated the anomalous scaling behaviour of the Ising model on small-world networks b... more We have investigated the anomalous scaling behaviour of the Ising model on small-world networks based on 2- and 3-dimensional lattices using Monte Carlo simulations. Our main result is that even at low p, the shift in the critical temperature Δ T_c scales as p^s, with s ≈ 0.50 for 2-D systems, s ≈ 0.698 for 3-D and s ≈ 0.75 for 4-D. We have also verified that a z-preserving rewiring algorithm still exhibits small-world effects and yet is more directly comparable with the conventional Ising model; the small-world effect is due to enhanced long-range correlations and not the change in effective dimension. We find the critical exponents β and ν exhibit a monotonic change between an Ising-like transition and mean-field behaviour in 2- and 3-dimensional systems.
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Concurrency and Computation: Practice and Experience, 2012
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The Cahn-Hilliard-Cook equation continues to be a useful model describing binary phase separation... more The Cahn-Hilliard-Cook equation continues to be a useful model describing binary phase separation in systems such as alloys and other physical and chemical applications. We describe our investigation of this field equation and report on the various discretisation schemes we used to integrate the system in one-, twoand three-dimensions. We also discuss how the equation can be visualised effectively in these different dimensions and consider how these techniques can usefully be applied to other partial differential equations.
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We show how compiler technology can generate fast and efficient yet human-readable data-parallel ... more We show how compiler technology can generate fast and efficient yet human-readable data-parallel simulation code for solving certain partial differential equation (PDE) based problems. We present a code parser and generator based on an ANTLR grammar and tree walking approach that transforms a mathematical formulation of an equation such as the Cahn-Hilliard family into simulation software in C++ or in NVIDIA’s Compute Unified Device Architecture (CUDA) language for programming Graphical Processing Units (GPUS). We present software architectural ideas, generated specimen code and detailed performance data on modern GPUs. We discuss how code generation techniques can be used to speed up code development and computational run time for related complex system simulation problems.
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Computational scientific simulations have long used parallel computers to increase their performa... more Computational scientific simulations have long used parallel computers to increase their performance. Recently graphics cards have been utilised to provide this functionality. GPGPU APIs such as NVidia’s CUDA can be used to harness the power of GPUs for purposes other than computer graphics. GPUs are designed for processing twodimensional data. In previous work we have presented several two-dimensional Cahn-Hilliard simulations that each utilise different CUDA memory types and compared their results. In this paper we extend these ideas to three dimensions. As GPUs are not intended for processing threedimensional data arrays, the performance of the memory optimisations is expected to change. Here we present several three-dimensional Cahn-Hilliard simulations to explore the challenges and the performance of the different memory types in three-dimensions. The results show that the simulation design with the best performance in threedimensions uses a different memory type to the optimal...
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to apply quickly for many applications domains. Recent developments in computer libraries such as... more to apply quickly for many applications domains. Recent developments in computer libraries such as the Standard Template Library of the C++ language and the Message Passing Package associated with the Python Language provide a way to implement very high level parallel containers in support of application programming. A parallel container is an implementation of a data structure such as a list, or vector, or set, that has associated with it the necessary methods and state knowledge to distribute the contents of the structure across the memory of a parallel computer or a computer cluster. A key idea is that of the parallel iterator which allows a single high level statement written by the applications programmer to invoke a parallel operation across the entire data structure’s contents while avoiding the need for knowledge of how the distribution is actually carried out. This transparency approach means that optimised parallel algorithms can be separated from the applications domain co...
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The emergence of complex spatial patterns in agent-based models is closely connected with the sym... more The emergence of complex spatial patterns in agent-based models is closely connected with the symmetries and relationships present between individual microscopic constituents. Games such as Rock-Paper-Scissors (RPS) have a closed cycle relationship amongst players which extends the symmetry. RPS and related games can be played by agents arranged on a spatial grid and have been shown to generate many complex spatial patterns. We consider the implications of extending the individual RPS game complexity to five-cycle games such as “Rock-Paper-ScissorsLizard-Spock” that have competing cyclic reactions. We simulate large spatial systems using a reaction-rate formulation which are simulated for long run times to capture the dynamic equilibrium regime. We report on the stable and unstable phase mixtures that arise in these agent models and comment on the effects that drive them.
Bookmarks Related papers MentionsView impact
Simulations users at all levels make heavy use of compute resources to drive computational simula... more Simulations users at all levels make heavy use of compute resources to drive computational simulations for greatly varying applications areas of research using different simulation paradigms. Simulations are implemented in many software forms, ranging from highly standardised and general models that run in proprietary software packages to ad hoc hand-crafted simulations codes for very specific applications. Visualisation of the workings or results of a simulation is another highly valuable capability for simulation developers and practitioners. There are many different software libraries and methods available for creating a visualisation layer for simulations, and it is often a difficult and time-consuming process to assemble a toolkit of these libraries and other resources that best suits a particular simulation model. We present here a break-down of the main simulation paradigms, and discuss differing toolkits and approaches that different researchers have taken to tackle coupled ...
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Population-based evolutionary algorithms continue to play an important role in artifically intell... more Population-based evolutionary algorithms continue to play an important role in artifically intelligent systems, but can not always easily use parallel computation. We have com- bined a geometric (any-space) particle swarm optimisation algorithm with use of Ferreira's Karva language of gene expression programming to produce a hybrid that can ac- celerate the genetic operators and which can rapidly attain a good solution. We show how Graphical Processing Units (GPUs) can be exploited for this. While the geometric par- ticle swarm optimiser is not markedly faster that genetic programming, we show it does attain good solutions faster, which is important for the problems discussed when the fit- ness function is inordinately expensive to compute.
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Modern interface devices such as depth field cameras and touch sensitive screen offer new scope f... more Modern interface devices such as depth field cameras and touch sensitive screen offer new scope for navigation large and complex image data sets. Image sequences from movies or simulations can be treated as hyper-bricks of navigable data. We have implemented an image navigation interface framework that supports a compatible set of both depth-field hand gestures and touch-screen finger movements. We report on how these two apparently disparate interfaces can be combined in a unifying software architecture and explore the human computer interaction space of suitable gestural and touch idioms and metaphors suitable for rapid interactive navigation and rendering of a sequence of images from a simulation, from photographic stills, or frames of a movie. We compare the two sorts of interaction and discuss a descriptive vocabulary for these and suggest some directions for development and use in other bulk data navigation interfaces.
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Droplet nucleation occurs when a small fluctuation in a system forms and subsequently grows in ma... more Droplet nucleation occurs when a small fluctuation in a system forms and subsequently grows in magnitude. Raindrop formation is a familiar everyday example. Droplets can be modelled using a field equation such as the Cahn-Hilliard system [1, 2, 3]. Attempts to understand and describe growth processes in material physico-chemical systems are often made using nucleation theory, which works well in the dilute limit. The range of validity of nucleation theoretical models can be explored using microscopic simulation models in which nucleating clusters can be counted and measured exactly. The Becker-Doring nucleation theory is described and its range of validity is discussed for binary alloy simulations using the Kawasaki exchange model in various concentration regimes. Graph labeling and enumeration techniques are employed to study the range of sizes of clusters present in nucleating systems.
Bookmarks Related papers MentionsView impact
Recent developments in processing devices such as graphical processing units and multi-core syste... more Recent developments in processing devices such as graphical processing units and multi-core systems offer opportunities to make use of parallel techniques at the chip level to obtain high performance. We discuss the difficulties in establishing suitable benchmark codes for making comparisons across these device architectures and in a way that is representative of key applications. We report on our use of classical dynamical particle collision simulation codes as benchmarks for comparing modern GPUs. We discuss our findings in terms of architectural features for parallelism as well as clock speed issues.
Bookmarks Related papers MentionsView impact
Computer games on mobile platforms are increasingly popular and modern devices offer games develo... more Computer games on mobile platforms are increasingly popular and modern devices offer games developers unconventional user interface technologies based on device orientation. We describe a maze game implemented both for Android mobile phone and tablet devices that supports navigation though a generated landscape using tilt motions accessed via the devices accelerometer sensors. We report on implementation issues including device sensitivity, resolution and appropriate ways to utilise tilt motion in a practical game or simulation. We discuss future directions for this technology and possible uses in simulations as well as games.
Bookmarks Related papers MentionsView impact
Visualisation of the interior of a threedimensional(3D) solid model is not a trivial operation an... more Visualisation of the interior of a threedimensional(3D) solid model is not a trivial operation and di↵erent possible approaches work best for di↵erent sorts of model data. It is useful when developing a 3D simulation model or when analysing 3D data to have a software tool that allows cut-aways, and fly-throughs and other interactive means of solid model visualisation. This article describes a highly interactive program built using portable C++ and OpenGL to load in a sequence of hyperbrick 3D data set files and to support data shifts, rotations, cut-aways and many other rendering options. A hyperbrick data format was designed especially to allow inter-operation with simulation programs that can easy generate output in this simple “.hrbk” format. A description of the main ideas is given alongwith a design and code outline and several rendering examples. Some areas for further tool development are given.
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Cellular automaton models such as Conway’s Game of Life have long been shown to exhibit a high de... more Cellular automaton models such as Conway’s Game of Life have long been shown to exhibit a high degree of spatial complexity. Spatial patterns can be analysed and categorised in this and other models and used as a basis for cataloging other related models and their behaviour classes. An interesting variation arises when a third state is introduced and we explore the consequences of this in models like Silverman’s “Brian’s Brain” – sometimes known as the “Game of Death” where “zombies” are introduced into the spatial model. The third state and the microscopic rules associated with the three constituent species gives rise to a rich new set of phases and behaviours with can be simulated and catalogued statistically. We focus on the early transient behaviour following a random system initialisation and the initial thinning out following by a subsequent explosion in species diversity.
Bookmarks Related papers MentionsView impact
Graphical Processing Units(GPUs) are usually programmed to provide data-parallel acceleration to ... more Graphical Processing Units(GPUs) are usually programmed to provide data-parallel acceleration to a host processor. Modern GPUs typically have an internal multi-processor (MP) structure that can be exploited in an unusual way to offer semiindependent task parallelism providing the MPs can operate within their own localised memory and apply data-parallelism to their own problem subset. We describe a combined simulation and statistical analysis application using component labelling and benchmark it on a range of modern GPU and CPU devices with various numbers of cores. As well as demonstrating a high degree of job parallelism and throughput we find a typical GPU MP outperforms a conventional CPU core.
Bookmarks Related papers MentionsView impact
Lattice gas cellular automata (LGCA) models provide a relatively fast means of simulating fluid f... more Lattice gas cellular automata (LGCA) models provide a relatively fast means of simulating fluid flow and can give both quantitative and qualitative insights into flow patterns around complex obstacles. Symmetry requirements inherent in the Navier-Stokes equation mandate that lattice-gas approximations to the full field equations be run on triangular lattices in two dimensions and on a 3-D projection of a four dimensional face centred hyper-cubic for three dimensions. Graphics Processing Units (GPUs) offer powerful data-parallel processing capabilities for many simulations as well as the graphics calculations required to simulate them. We describe how GPUs can be used to implement mesh structures for simulating lattice gases. We present performance data on how to optimise data layout in the various levels of localised memory available in modern GPUs and discuss data transfer issues between CPU and GPU and between processing GPU and graphics GPU in a unified simulation platform. We il...
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Conways’s Game-of-Life (GoL) is one of a family of spatial cellular automata rule sets that emplo... more Conways’s Game-of-Life (GoL) is one of a family of spatial cellular automata rule sets that employ the Moore neighbourhood on a rectilinear lattice of cells. GoL generalises to set of other automata using different neighbournumbers that lead to birth and survival. These models exhibit different static properties and also different long term dynamical equilibrium points. We define some quantifiable metrics and explore how some well known GoL variants can be categorised into groupings, categorised by their static properties and dynamical equilibria. We also explore effects due to differing initial crowding levels of the live seed cell population, and how this affects the categories.
Bookmarks Related papers MentionsView impact
Pair-annihilation process models capture the behaviour of important reactions amongst fundamental... more Pair-annihilation process models capture the behaviour of important reactions amongst fundamental physical but also chemical systems. We develop a lattice-based pairannihilation model based on Kawasaki exchange dynamics and with diffusion properties controlled by a latticegas temperature. We investigate the effect of multi-species screening in the model when anti-ferromagnetic repulsive coupling forces are used. We find a phase transition manifested by an annihilation induced population collapse around T=0.22 and an additional phase transition in the number of species present around Q=5. We describe a number of quantitative metrics based on graph component labeling and contrast the behaviours of the ferromagnetic and anti-ferromagnetic variants of the model.
Bookmarks Related papers MentionsView impact