Rules and mechanics

So far in this book, we have seen a large number of methods for generating content for existing games. So, if you have a game already, you could now generate many things for it: maps, levels, terrain, vegetation, weapons, dungeons, racing tracks. But what if you don’t already have a game, and want to generate the game itself? What would you generate, and how? At the heart of any game are its rules. This chapter will discuss representations for game rules of different kinds, along with methods to generate them, and evaluation functions and constraints that help us judge complete games rather than just isolated content artefacts. Our main focus here will be on methods for generating interesting, fun, and/or balanced game rules. However, an important perspective that will permeate the chapter is that game rule encodings and evaluation functions can encode game design expertise and style, and thus help us understand game design. By formalising aspects of the game rules, we define a space of possible rules more precisely than could be done through writing about rules in qualitative terms; and by choosing which aspects of the rules to formalise, we define what aspects of the game are interesting to explore and introduce variation in. In this way, each game generator can be thought of an executable micro-theory of game design, though often a simplified, and sometimes even a caricatured one

Microscale consolidation analysis of relaxation behavior of single living chondrocytes subjected to varying strain-rates

Besides the elastic stiffness, the relaxation behavior of single living cells is also of interest of various researchers when studying cell mechanics. It is hypothesized that the relaxation response of the cells is governed by both intrinsic viscoelasticity of the solid phase and fluid-solid interactions mechanisms. There are a number of mechanical models have been developed to investigate the relaxation behavior of single cells. However, there is lack of model enable to accurately capture both of the mechanisms. Therefore, in this study, the porohyperelastic (PHE) model, which is an extension of the consolidation theory, combined with inverse Finite Element Analysis (FEA) technique was used at the first time to investigate the relaxation response of living chondrocytes. This model was also utilized to study the dependence of relaxation behavior of the cells on strain-rates. The stress-relaxation experiments under the various strain-rates were conducted with the Atomic Force Microscopy (AFM). The results have demonstrated that the PHE model could effectively capture the stress-relaxation behavior of the living chondrocytes, especially at intermediate to high strain-rates. Although this model gave some errors at lower strain-rates, its performance was acceptable. Therefore, the PHE model is properly a promising model for single cell mechanics studies. Moreover, it has been found that the hydraulic permeability of living chondrocytes reduced with decreasing of strain-rates. It might be due to the intracellular fluid volume fraction and the fluid pore pressure gradients of chondrocytes were higher when higher strain-rates applied.

The fluid nature of action research

Action research is a fluid, unfolding process of research. It involves cycles of questioning, gathering data, critical reflection and deciding on a course of action (Stringer, 2008). Through action research, educators research their own practice in their own setting. They learn from their experiences as the action research cycles progress, and apply new learning to practice.

Simulating droplet motion on virtual leaf surfaces

A curvilinear thin film model is used to simulate the motion of droplets on a virtual leaf surface, with a view to better understand the retention of agricultural sprays on plants. The governing model, adapted from Roy et al. (2002 J. Fluid Mech. 454, 235–261) with the addition of a disjoining pressure term, describes the gravity- and curvature driven flow of a small droplet on a complex substrate: a cotton leaf reconstructed from digitized scan data. Coalescence is the key mechanism behind spray coating of foliage, and our simulations demonstrate that various experimentally observed coalescence behaviours can be reproduced qualitatively. By varying the contact angle over the domain, we also demonstrate that the presence of a chemical defect can act as an obstacle to the droplet’s path, causing break-up. In simulations on the virtual leaf, it is found that the movement of a typical spray size droplet is driven almost exclusively by substrate curvature gradients. It is not until droplet mass is sufficiently increased via coalescence that gravity becomes the dominating force.

A tensor-based morphometry study of genetic influences on brain structure using a new fluid registration method

We incorporated a new Riemannian fluid registration algorithm into a general MRI analysis method called tensor-based morphometry to map the heritability of brain morphology in MR images from 23 monozygotic and 23 dizygotic twin pairs. All 92 3D scans were fluidly registered to a common template. Voxelwise Jacobian determinants were computed from the deformation fields to assess local volumetric differences across subjects. Heritability maps were computed from the intraclass correlations and their significance was assessed using voxelwise permutation tests. Lobar volume heritability was also studied using the ACE genetic model. The performance of this Riemannian algorithm was compared to a more standard fluid registration algorithm: 3D maps from both registration techniques displayed similar heritability patterns throughout the brain. Power improvements were quantified by comparing the cumulative distribution functions of the p-values generated from both competing methods. The Riemannian algorithm outperformed the standard fluid registration.

Fluid registration of diffusion tensor images using information theory

We apply an information-theoretic cost metric, the symmetrized Kullback-Leibler (sKL) divergence, or $J$-divergence, to fluid registration of diffusion tensor images. The difference between diffusion tensors is quantified based on the sKL-divergence of their associated probability density functions (PDFs). Three-dimensional DTI data from 34 subjects were fluidly registered to an optimized target image. To allow large image deformations but preserve image topology, we regularized the flow with a large-deformation diffeomorphic mapping based on the kinematics of a Navier-Stokes fluid. A driving force was developed to minimize the $J$-divergence between the deforming source and target diffusion functions, while reorienting the flowing tensors to preserve fiber topography. In initial experiments, we showed that the sKL-divergence based on full diffusion PDFs is adaptable to higher-order diffusion models, such as high angular resolution diffusion imaging (HARDI). The sKL-divergence was sensitive to subtle differences between two diffusivity profiles, showing promise for nonlinear registration applications and multisubject statistical analysis of HARDI data.

Quantitative genetic modeling of lateral ventricular shape and volume using multi-atlas fluid image alignment in twins

Despite substantial progress in measuring the 3D profile of anatomical variations in the human brain, their genetic and environmental causes remain enigmatic. We developed an automated system to identify and map genetic and environmental effects on brain structure in large brain MRI databases . We applied our multi-template segmentation approach ("Multi-Atlas Fluid Image Alignment") to fluidly propagate hand-labeled parameterized surface meshes into 116 scans of twins (60 identical, 56 fraternal), labeling the lateral ventricles. Mesh surfaces were averaged within subjects to minimize segmentation error. We fitted quantitative genetic models at each of 30,000 surface points to measure the proportion of shape variance attributable to (1) genetic differences among subjects, (2) environmental influences unique to each individual, and (3) shared environmental effects. Surface-based statistical maps revealed 3D heritability patterns, and their significance, with and without adjustments for global brain scale. These maps visualized detailed profiles of environmental versus genetic influences on the brain, extending genetic models to spatially detailed, automatically computed, 3D maps.

Improving fluid registration through white matter segmentation in a twin study design

Robust and automatic non-rigid registration depends on many parameters that have not yet been systematically explored. Here we determined how tissue classification influences non-linear fluid registration of brain MRI. Twin data is ideal for studying this question, as volumetric correlations between corresponding brain regions that are under genetic control should be higher in monozygotic twins (MZ) who share 100% of their genes when compared to dizygotic twins (DZ) who share half their genes on average. When these substructure volumes are quantified using tensor-based morphometry, improved registration can be defined based on which method gives higher MZ twin correlations when compared to DZs, as registration errors tend to deplete these correlations. In a study of 92 subjects, higher effect sizes were found in cumulative distribution functions derived from statistical maps when performing tissue classification before fluid registration, versus fluidly registering the raw images. This gives empirical evidence in favor of pre-segmenting images for tensor-based morphometry.

Automated ventricular mapping with multi-atlas fluid image alignment reveals genetic effects in Alzheimer's disease

We developed and validated a new method to create automated 3D parametric surface models of the lateral ventricles in brain MRI scans, providing an efficient approach to monitor degenerative disease in clinical studies and drug trials. First, we used a set of parameterized surfaces to represent the ventricles in four subjects' manually labeled brain MRI scans (atlases). We fluidly registered each atlas and mesh model to MRIs from 17 Alzheimer's disease (AD) patients and 13 age- and gender-matched healthy elderly control subjects, and 18 asymptomatic ApoE4-carriers and 18 age- and gender-matched non-carriers. We examined genotyped healthy subjects with the goal of detecting subtle effects of a gene that confers heightened risk for Alzheimer's disease. We averaged the meshes extracted for each 3D MR data set, and combined the automated segmentations with a radial mapping approach to localize ventricular shape differences in patients. Validation experiments comparing automated and expert manual segmentations showed that (1) the Hausdorff labeling error rapidly decreased, and (2) the power to detect disease- and gene-related alterations improved, as the number of atlases, N, was increased from 1 to 9. In surface-based statistical maps, we detected more widespread and intense anatomical deficits as we increased the number of atlases. We formulated a statistical stopping criterion to determine the optimal number of atlases to use. Healthy ApoE4-carriers and those with AD showed local ventricular abnormalities. This high-throughput method for morphometric studies further motivates the combination of genetic and neuroimaging strategies in predicting AD progression and treatment response. © 2007 Elsevier Inc. All rights reserved.

Automated 3D mapping & shape analysis of the lateral ventricles via fluid registration of multiple surface-based atlases

We developed and validated a new method to create automated 3D parametric surface models of the lateral ventricles, designed for monitoring degenerative disease effects in clinical neuroscience studies and drug trials. First we used a set of parameterized surfaces to represent the ventricles in a manually labeled set of 9 subjects' MRIs (atlases). We fluidly registered each of these atlases and mesh models to a set of MRIs from 12 Alzheimer's disease (AD) patients and 14 matched healthy elderly subjects, and we averaged the resulting meshes for each of these images. Validation experiments on expert segmentations showed that (1) the Hausdorff labeling error rapidly decreased, and (2) the power to detect disease-related alterations monotonically improved as the number of atlases, N, was increased from 1 to 9. We then combined the segmentations with a radial mapping approach to localize ventricular shape differences in patients. In surface-based statistical maps, we detected more widespread and intense anatomical deficits as we increased the number of atlases, and we formulated a statistical stopping criterion to determine the optimal value of N. Anterior horn anomalies in Alzheimer's patients were only detected with the multi-atlas segmentation, which clearly outperformed the standard single-atlas approach.

Double diffusive Marangoni convection flow of electrically conducting fluid in a square cavity with chemical reaction

Double diffusive Marangoni convection flow of viscous incompressible electrically conducting fluid in a square cavity is studied in this paper by taking into consideration of the effect of applied magnetic field in arbitrary direction and the chemical reaction. The governing equations are solved numerically by using alternate direct implicit (ADI) method together with the successive over relaxation (SOR) technique. The flow pattern with the effect of governing parameters, namely the buoyancy ratio W, diffusocapillary ratio w, and the Hartmann number Ha, is investigated. It is revealed from the numerical simulations that the average Nusselt number decreases; whereas the average Sherwood number increases as the orientation of magnetic field is shifted from horizontal to vertical. Moreover, the effect of buoyancy due to species concentration on the flow is stronger than the one due to thermal buoyancy. The increase in diffusocapillary parameter, w caus

Geochronological (U–Pb, U–Th–total Pb, Sm–Nd) and geochemical (REE, 87Sr/86Sr, δ18O, δ13C) tracing of intraplate tectonism and associated fluid flow in the Warburton Basin, Australia

The Warburton Basin of central Australia has experienced a complex tectonic and fluid-flow history, resulting in the formation of various authigenic minerals. Geochemical and geochronological analyses were undertaken on vein carbonates from core samples of clastic sediments. Results were then integrated with zircon U–Pb dating and uraninite U–Th–total Pb dating from the underlying granite. Stable and radiogenic isotopes (δ18O, Sr and εNd), as well as trace element data of carbonate veins indicate that >200 °C basinal fluids of evolved meteoric origin circulated through the Warburton Basin. Almost coincidental ages of these carbonates (Sm–Nd; 432 ± 12 Ma) with primary zircon (421 ± 3.8 Ma) and uraninite (407 ± 16 Ma) ages from the granitic intrusion point towards a substantial period of active tectonism and an elevated thermal regime during the mid Silurian. We hypothesise that such a thermal regime may have resulted from extensional tectonism and concomitant magmatic activity following regional orogenesis. This study shows that the combined application of geochemical and geochronological analyses of both primary and secondary species may constrain the timing of tectonomagmatic events and associated fluid flow in intraplate sedimentary basins. Furthermore, this work suggests that the Sm–Nd-isotopic system is surprisingly robust and can record geologically meaningful age data from hydrothermal mineral species.

Unsteady-Flow Of A Viscous-Fluid Between 2 Parallel Disks With A Time-Varying Gap Width And A Magnetic-Field

The unsteady incompressible viscous fluid flow between two parallel infinite disks which are located at a distance h(t*) at time t* has been studied. The upper disk moves towards the lower disk with velocity h'(t*). The lower disk is porous and rotates with angular velocity Omega(t*). A magnetic field B(t*) is applied perpendicular to the two disks. It has been found that the governing Navier-Stokes equations reduce to a set of ordinary differential equations if h(t*), a(t*) and B(t*) vary with time t* in a particular manner, i.e. h(t*) = H(1 - alpha t*)(1/2), Omega(t*) = Omega(0)(1 - alpha t*)(-1), B(t*) = B-0(1 - alpha t*)(-1/2). These ordinary differential equations have been solved numerically using a shooting method. For small Reynolds numbers, analytical solutions have been obtained using a regular perturbation technique. The effects of squeeze Reynolds numbers, Hartmann number and rotation of the disk on the flow pattern, normal force or load and torque have been studied in detail

Experiments on a plume with off-source heating: Implications for cloud fluid dynamics

We report here on a series of laboratory experiments on plumes, undertaken with the object of simulating the effect of the heat release that occurs in clouds on condensation of water vapor. The experimental technique used for this purpose relies on ohmic heating generated in an electrically conducting plume fluid subjected to a suitable alternating voltage across specified axial stations in the plume flow [Bhat et al., 1989]. The present series of experiments achieves a value of the Richardson number that is toward the lower end of the range that characteristics cumulus clouds. It is found that the buoyancy enhancement due to heating disrupts the eddy structures in the flow and reduces the dilution owing to entrainment of ambient fluid that would otherwise have occurred in the central region of the plume. Heating also reduces the spread rate of the plume, but as it accelerates the flow as well, the overall specific mass flux in the plume does not show a very significant change at the heat input employed in the experiment. However, there is some indication that the entrainment rate (proportional to the streamwise derivative of the mass flux) is slightly higher immediately after heat injection and slightly lower farther downstream. The measurements support a previous proposal for a cloud scenario [Bhat and Narasimha, 1996] and demonstrate how fresh insights into certain aspects of the fluid dynamics of clouds may be derived from the experimental techniques employed here.