A fractal-based 2D expansion method for multi-scale volume data visualization

Abstract  

Visualization of volume data is difficult to realize and control because the most common output device is a two-dimensional (2D) display and the most common input device is a mouse, which only allows 2D operation. For example, volume rendering projects the data structure onto a 2D image plane, but this type of view-dependent method gives rise to occlusion. In addition, 2D mouse operation does not allow direct selection of three-dimensional (3D) regions or coordinates. In this article, we propose a method that expands the octree structure of volume data onto a 2D plane. The proposed method uses the self-similarity of the fractal diagram and achieves multi-scale visualization of volume data in two dimensions. With this method, we can browse the entire domain of volume data without occlusion. For greater effectiveness, we combined the proposed method and existing 3D-based methods. Since each cell has a one-to-one correspondence with squares in the Sierpinski carpet, we can assign arbitrary 3D regions or positions by selecting the corresponding squares. This provides direct access to 3D regions and coordinates by 2D mouse operation. We propose some functions for interactive visualization and discuss how to exploit the advantages and lessen the disadvantages of the proposed method.     

Conservative space-time mesh refinement methods for the FDTD solution of Maxwell’s equations

A new variational space-time mesh refinement method is proposed for the FDTD solution of Maxwell’s equations. The main advantage of this method is to guarantee the conservation of a discrete energy that implies that the scheme remains L² stable under the usual CFL condition. The only additional cost induced by the mesh refinement is the inversion, at each time step, of a sparse symmetric positive definite linear system restricted to the unknowns located on the interface between coarse and fine grid. The method is presented in a rather general way and its stability is analyzed. An implementation is proposed for the Yee scheme. In this case, various numerical results in 3-D are presented in order to validate the approach and illustrate the practical interest of space-time mesh refinement methods.     

A robust security framework for 3D images

Abstract  

Three-dimensional (3D) visualization of spatial and non-spatial data is a well-established practice having numerous applications. The cheapest and the most efficient way to 3D visualization is 3D images/Anaglyphs. 3D images contain 3D information of the objects present in the image. These images are easily obtained by superimposing left and right eye images in different color in a single image. In this paper, a novel security framework, viz., watermarking scheme, is presented to ensure their security. The proposed security framework is employed in fractional Fourier transform domain of secret color channel followed by the embedding using singular value decomposition. The secret channels (SEC) are obtained by applying reversible integer transform on the RGB channels. The experimental results prove the robustness and imperceptibility of the proposed watermarking scheme.     

Improved generation of anti-tumor immunity by antigen dose limitation

Background  

The malignant cells of cutaneous T cell lymphoma (CTCL) display immunogenic peptides derived from the clonal T cell receptor (TCR) providing an attractive model for refinement of anti-tumor immunization methodology. To produce a clinically meaningful anti-tumor response, induction of cytotoxic anti-CTCL cells must be maximized while suppressive T regulatory cells (Treg) should be minimized. We have demonstrated that engulfment of apoptotic CTCL cells by dendritic cells (DC) can lead to either CD8 anti-CTCL responses or immunosuppressive Treg induction. Treg generation is favored when the number of apoptotic cells available for ingestion is high.     

Four-dimensional geometric element definitions and interferences via five-dimensional homogeneous processing

Abstract  

We have systematized various studies on 4-D visualization and interaction thus far, and we proposed 4-D geometric algorithms via 5-D homogeneous processing. Our framework uses 5 × 5 matrices and 5 × 5 determinants to express various types of transformations, and it simplifies geometric operations without the use of division operations. Using the proposed scheme, we developed an interactive 4-D space display system. The simplicity, generality, and duality of 5-D homogeneous processing are effective not only for 4-D geometric operations but also for interference problems among various 4-D objects. However, the processing regarding geometric characteristics of 4-D objects was not considered in our previous works. In this paper, we describe 4-D geometric elements, in general, and we discuss 4-D computational geometry via 5-D homogeneous processing. Unified geometric operations without the use of division operations constitute the most important part of 5-D homogeneous processing. We systematize the methods for 4-D geometric element definitions and interferences via 5-D homogeneous processing. In the field of 4-D visualization, the proposed algorithms can be potentially used in a user interface for feature detection of a 4-D object and collision detection of several 4-D objects. We comprehensively develop and advance the theoretical framework in the field of 4-D graphics. It is expected that this method of processing will be useful for the performance improvement of 4-D graphics systems.     

A multigroup diffusion solver using pseudo transient continuation for a radiation-hydrodynamic code with patch-based AMR

We present a scheme to solve the nonlinear multigroup radiation diffusion (MGD) equations. The method is incorporated into a massively parallel, multidimensional, Eulerian radiation-hydrodynamic code with Adaptive Mesh Refinement (AMR). The patch-based AMR algorithm refines in both space and time creating a hierarchy of levels, coarsest to finest. The physics modules are time-advanced using operator splitting. On each level, separate “level-solve” packages advance the modules. Our multigroup level-solve adapts an implicit procedure which leads to a two-step iterative scheme that alternates between elliptic solves for each group with intra-cell group coupling. For robustness, we introduce pseudo transient continuation (Ψtc). We analyze the magnitude of the Ψtc parameter to ensure positivity of the resulting linear system, diagonal dominance and convergence of the two-step scheme. For AMR, a level defines a subdomain for refinement. For diffusive processes such as MGD, the refined level uses Dirichlet boundary data at the coarse–fine interface and the data is derived from the coarse level solution. After advancing on the fine level, an additional procedure, the sync-solve (SS), is required in order to enforce conservation. The MGD SS reduces to an elliptic solve on a combined grid for a system of G equations, where G is the number of groups. We adapt the “partial temperature” scheme for the SS; hence, we reuse the infrastructure developed for scalar equations. Results are presented. We consider a multigroup test problem with a known analytic solution. We demonstrate utility of Ψtc by running with increasingly larger timesteps. Lastly, we simulate the sudden release of energy Y inside an Al sphere (r = 15 cm) suspended in air at STP. For Y = 11 kT, we find that gray radiation diffusion and MGD produce similar results. However, if Y = 1 MT, the two packages yield different results. Our large Y simulation contradicts a long-standing theory and demonstrates the inadequacy of gray diffusion.     

Neuron participation in a synchrony-encoding assembly

Background  

Synchronization of action potentials between neurons is considered to be an encoding process that allows the grouping of various and multiple features of an image leading to a coherent perception. How this coding neuronal assembly is configured is debated. We have previously shown that the magnitude of synchronization between excited neurons is stimulus-dependent. In the present investigation we compare the levels of synchronization between synchronizing individual neurons and the synchronizing pool of cells to which they belong.     

Aligning 3D time-of-flight MRA datasets for quantitative longitudinal studies: evaluation of rigid registration techniques

Objective

3D Time-of-flight (TOF) magnetic resonance angiography is commonly used for vascular analyses. A quantification of longitudinal morphological changes usually requires the registration of TOF image sequences acquired at different time points. The aim of this study was to evaluate the precision of different 3D rigid registration setups such that an optimal quantification of morphological changes can be achieved.

Methods

Eight different rigid registration techniques were implemented and evaluated in this study using the target registration error (TRE) calculated based on 554 landmarks defined in twenty TOF datasets. The registration techniques differed in integration of brain and vessel segmentation masks and usage of a multi-resolution framework. Furthermore, the benefit of a prior volume-of-interest definition for registration accuracy was evaluated.

Results

The results revealed that the highest registration accuracies can be achieved using a multi-resolution framework and a cerebrovascular segmentation as mask. Numerically, a mean TRE of 1.1 mm was calculated. If applicable, a prior definition of a volume-of-interest allows a reduction of the TRE to only 0.6 mm.

Conclusion

TOF datasets should be registered using vessel segmentations as mask, multi-resolution framework and previous volume-of-interest definition if possible to obtain the highest registration precision. This is especially the case for longitudinal datasets that are separated by several months while the registration technique seems less important for datasets that are only separated by a few days.     

A robust numerical scheme for highly compressible magnetohydrodynamics: Nonlinear stability,implementation and tests

The ideal MHD equations are a central model in astrophysics, and their solution relies upon stable numerical schemes. We present an implementation of a new method, which possesses excellent stability properties. Numerical tests demonstrate that the theoretical stability properties are valid in practice with negligible compromises to accuracy. The result is a highly robust scheme with state-of-the-art efficiency. The scheme’s robustness is due to entropy stability, positivity and properly discretised Powell terms. The implementation takes the form of a modification of the MHD module in the FLASH code, an adaptive mesh refinement code. We compare the new scheme with the standard FLASH implementation for MHD. Results show comparable accuracy to standard FLASH with the Roe solver, but highly improved efficiency and stability, particularly for high Mach number flows and low plasma β. The tests include 1D shock tubes, 2D instabilities and highly supersonic, 3D turbulence. We consider turbulent flows with RMS sonic Mach numbers up to 10, typical of gas flows in the interstellar medium. We investigate both strong initial magnetic fields and magnetic field amplification by the turbulent dynamo from extremely high plasma β. The energy spectra show a reasonable decrease in dissipation with grid refinement, and at a resolution of 512³ grid cells we identify a narrow inertial range with the expected power law scaling. The turbulent dynamo exhibits exponential growth of magnetic pressure, with the growth rate higher from solenoidal forcing than from compressive forcing. Two versions of the new scheme are presented, using relaxation-based 3-wave and 5-wave approximate Riemann solvers, respectively. The 5-wave solver is more accurate in some cases, and its computational cost is close to the 3-wave solver.     

Dynamic analysis of bubble-driven liquid flows using time-resolved particle image velocimetry and proper orthogonal decomposition techniques

Abstract  

An experimental study to evaluate dynamic structures of flow motion and turbulence characteristics in bubble-driven water flow in a rectangular tank with a varying flow rate of compressed air is conducted. Liquid flow fields are measured by time-resolved particle image velocimetry (PIV) with fluorescent tracer particles to eliminate diffused reflections, and by an image intensifier to acquire enhanced clean particle images. By proper orthogonal decomposition (POD) analysis, the energy distributions of spatial and temporal modes are acquired. Time-averaged velocity and turbulent kinetic energy distributions are varied with the air flow rates. With increasing Reynolds number, bubble-induced turbulent motion becomes dominant rather than the recirculating flow near the side wall. Detailed spatial structures and the unsteady behavior of dominant dynamic modes associated with turbulent kinetic energy distributions are addressed.     

An efficient local time-stepping scheme for solution of nonlinear conservation laws

We develop an efficient local time-stepping algorithm for the method of lines approach to numerical solution of transient partial differential equations. The need for local time-stepping arises when adaptive mesh refinement results in a mesh containing cells of greatly different sizes. The global CFL number and, hence, the global time step, are defined by the smallest cell size. This can be inefficient as a few small cells may impose a restrictive time step on the whole mesh. A local time-stepping scheme allows us to use the local CFL number which reduces the total number of function evaluations. The algorithm is based on a second order Runge–Kutta time integration. Its important features are a small stencil and the second order accuracy in the L² and L^∞ norms.     

Study on flow distribution for room air conditioner using visualization technique

Abstract  

Flow distributions of a room air conditioner (RAC) have been analyzed by a visualization technique such as a particle image velocimetry (PIV) in this study. Flow structures have been investigated inside and outside the RAC to improve efficiencies. Accuracies of the measured velocities by the PIV have been confirmed by a Pitot tube at important locations around the RAC. Then, a numerical analysis has been performed by developed computer programs to design parts for the RAC with improved efficiencies. The design guideline has been proposed based on the analyzed results to reduce the condensation problem and increase the flow rate. Finally, shapes of a fan with high flow rates and an outlet with reduced condensation problems have been obtained based on the developed experimental and numerical methods in this study.     

Early visual evoked potentials are modulated by eye position in humans induced by whole body rotations

Background  

To reach and grasp an object in space on the basis of its image cast on the retina requires different coordinate transformations that take into account gaze and limb positioning. Eye position in the orbit influences the image's conversion from retinotopic (eye-centered) coordinates to an egocentric frame necessary for guiding action. Neuroimaging studies have revealed eye position-dependent activity in extrastriate visual, parietal and frontal areas that is along the visuo-motor pathway. At the earliest vision stage, the role of the primary visual area (V1) in this process remains unclear. We used an experimental design based on pattern-onset visual evoked potentials (VEP) recordings to study the effect of eye position on V1 activity in humans.     

A fourth-order adaptive mesh refinement algorithm for the multicomponent,reacting compressible Navier–Stokes equations

In this paper, we present a fourth-order in space and time block-structured adaptive mesh refinement algorithm for the compressible multicomponent reacting Navier–Stokes equations. The algorithm uses a finite-volume approach that incorporates a fourth-order discretisation of the convective terms. The time-stepping algorithm is based on a multi-level spectral deferred corrections method that enables explicit treatment of advection and diffusion coupled with an implicit treatment of reactions. The temporal scheme is embedded in a block-structured adaptive mesh refinement algorithm that includes subcycling in time with spectral deferred correction sweeps applied on levels. Here we present the details of the multi-level scheme paying particular attention to the treatment of coarse–fine boundaries required to maintain fourth-order accuracy in time. We then demonstrate the convergence properties of the algorithm on several test cases including both non-reacting and reacting flows. Finally we present simulations of a vitiated dimethyl ether jet in 2D and a turbulent hydrogen jet in 3D, both with detailed kinetics and transport.     

Solving the radiation diffusion and energy balance equations using pseudo-transient continuation

We develop a scheme for the system coupling the radiation diffusion and matter energy balance equations. The method is based on fully implicit, first-order, backward Euler differencing; Picard-Newton iterations solve the nonlinear system. We show that iterating on the radiation energy density and the emission source is more robust. Since the Picard-Newton scheme may not converge for all initial conditions and time steps, pseudo-transient continuation (Ψtc) is introduced. The combined Ψtc-Picard-Newton scheme is analyzed. We derive conditions on the Ψtc parameter that guarantee physically meaningful iterates, e.g., positive energies. Successive Ψtc iterates are bounded and the radiation energy density and emission source tend to equilibrate. The scheme is incorporated into a multiply dimensioned, massively parallel, Eulerian, radiation-hydrodynamic computer program with automatic mesh refinement (AMR). Three examples are presented that exemplify the scheme's performance. (1) The Pomraning test problem that models radiation flow into cold matter. (2) A similar, but more realistic problem simulating the propagation of an ionization front into tenuous hydrogen gas with a Saha model for the equation-of-state. (3) A 2D axisymmetric (R,Z) simulation with real materials featuring jetting, radiatively driven, interacting shocks.     

Adaptive mesh refinement for stochastic reaction–diffusion processes

We present an algorithm for adaptive mesh refinement applied to mesoscopic stochastic simulations of spatially evolving reaction–diffusion processes. The transition rates for the diffusion process are derived on adaptive, locally refined structured meshes. Convergence of the diffusion process is presented and the fluctuations of the stochastic process are verified. Furthermore, a refinement criterion is proposed for the evolution of the adaptive mesh. The method is validated in simulations of reaction–diffusion processes as described by the Fisher–Kolmogorov and Gray–Scott equations.     

Top-down and bottom-up modulation of language related areas – An fMRI Study

Background  

One major problem for cognitive neuroscience is to describe the interaction between stimulus and task driven neural modulation. We used fMRI to investigate this interaction in the human brain. Ten male subjects performed a passive listening and a semantic categorization task in a factorial design. In both tasks, words were presented auditorily at three different rates.     

Mesh refinement algorithms in an unstructured solver for multiphase flow simulation using discrete particles

This study developed spray-adaptive mesh refinement algorithms with directional sensitivity in an unstructured solver to improve spray simulation for internal combustion engine application. Inadequate spatial resolution is often found to cause inaccuracies in spray simulation using the Lagrangian–Eulerian approach due to the over-estimated diffusion and inappropriate liquid–gas phase coupling. Dynamic mesh refinement algorithms adaptive to fuel sprays and vapor gradients were developed in order to increase the grid resolution in the spray region to improve simulation accuracy. The local refinement introduced the coarse-fine face interface that requires advanced numerical schemes for flux calculation and grid rezoning with moving boundaries. To resolve the issue in flux calculation, this work implemented the refinement/coarsening algorithms into a collocated solver to avoid tedious interpolations in solving the momentum equations. A pressure correction method was applied to address unphysical pressure oscillations due to the collocation of pressure and velocity. An edge-based algorithm was used to evaluate the edge-centered quantities in order to account for the contributions from all the cells around an edge at the coarse-fine interface. A quasi-second-order upwind scheme with strong monotonicity was also modified to accommodate the coarse-fine interface for convective fluxes. To resolve the issue related to grid rezoning, rezoning was applied to the initial baseline mesh only and the new locations of the refined grids were obtained by interpolating the updated baseline mesh. The time step constraints were also re-evaluated to account for the change resulting from mesh refinement. The present refinement algorithm was used in simulating fuel sprays in an engine combustion chamber. It was found that the present approach could produce the same level of results as those using the uniformly fine mesh with substantially reduced computer time. Results also showed that this approach could alleviate the artifacts related to the Lagrangian discrete modeling of spray drops due to insufficient spatial resolution.     

A finite element method with mesh adaptivity for computing vortex states in fast-rotating Bose–Einstein condensates

Numerical computations of stationary states of fast-rotating Bose–Einstein condensates require high spatial resolution due to the presence of a large number of quantized vortices. In this paper we propose a low-order finite element method with mesh adaptivity by metric control, as an alternative approach to the commonly used high-order (finite difference or spectral) approximation methods. The mesh adaptivity is used with two different numerical algorithms to compute stationary vortex states: an imaginary time propagation method and a Sobolev gradient descent method. We first address the basic issue of the choice of the variable used to compute new metrics for the mesh adaptivity and show that refinement using simultaneously the real and imaginary part of the solution is successful. Mesh refinement using only the modulus of the solution as adaptivity variable fails for complicated test cases. Then we suggest an optimized algorithm for adapting the mesh during the evolution of the solution towards the equilibrium state. Considerable computational time saving is obtained compared to uniform mesh computations. The new method is applied to compute difficult cases relevant for physical experiments (large nonlinear interaction constant and high rotation rates).