Impuls-based dynamic simulation of higher order and numerical results

First, we will provide a short introduction to the impulse-based method for dynamic simulation. Till now, impulses were frequently used to resolve collisions between rigid bodies. In the last years, we have extended these techniques to simulate constraint forces. Important properties of the new impulse method are: (1) Simulation in Cartesian coordinates, (2) complete elimination of the constraint drift known from Lagrange multiplier methods, (3) simple integration of collision and friction and (4) real-time performance even for complex multibody systems like six-legged walking machines. In order to demonstrate the potential of the impulse-based method, we report on numerical experiments. We compare the following dynamic simulation methods: (1) Generalized (or reduced) coordinates, (2) the Lagrange multiplier method with and without several stabilization methods like Baumgarte, the velocity correction and a projection method, (3) impulse-based methods of integration order 2, 4, 6, 8, and 10. We have simulated the mathematical pendulum, the double and the triple pendulum with all of these dynamic simulation methods and report on the attainable accuracy. It turned out that the impulse methods of higher integration order are all of O(h3) but have very small factors and are therefore relatively accurate. A Lagrange multiplier method fully stabilized by impulse-based techniques turned out to be the best of the Lagrange multiplier methods tested

Direct Measurements of Magnetic Twist in the Solar Corona

In the present work we study evolution of magnetic helicity in the solar corona. We compare the rate of change of a quantity related to the magnetic helicity in the corona to the flux of magnetic helicity through the photosphere and find that the two rates are similar. This gives observational evidence that helicity flux across the photosphere is indeed what drives helicity changes in solar corona during emergence. For the purposes of estimating coronal helicity we neither assume a strictly linear force-free field, nor attempt to construct a non-linear force-free field. For each coronal loop evident in Extreme Ultraviolet (EUV) we find a best-matching line of a linear force-free field and allow the twist parameter alpha to be different for each line. This method was introduced and its applicability was discussed in Malanushenko et. al. (2009). The object of the study is emerging and rapidly rotating AR 9004 over about 80 hours. As a proxy for coronal helicity we use the quantity averaged over many reconstructed lines of magnetic field. We argue that it is approximately proportional to "flux-normalized" helicity H/Phi^2, where H is helicity and Phi is total enclosed magnetic flux of the active region. The time rate of change of such quantity in the corona is found to be about 0.021 rad/hr, which is compatible with the estimates for the same region obtained using other methods Longcope et. al. (2007), who estimated the flux of normalized helicity of about 0.016 rad/hr

Accurate and Computational: A review of color reproduction in Full-color 3D printing

As functional 3D printing becomes more popular with industrial manufacturing applications, it is time to start discussing high-fidelity appearance reproduction of 3D objects, particularly in faithful colors. To date, there is only limited research on accurate color reproduction and on universal color reproduction method for different color 3D printing materials. To systematically understand colorization principles and color transmission in color 3D printing, an exhaustive literature review is stated to show the state of the art of color reproduction methods for full-color 3D printing, such as optical parameter modeling, colorimetric difference evaluation, computer aided colorization and voxel droplet jetting. Meanwhile, the challenges in developing an accurate color reproduction framework suitable for different printing materials are fully analyzed in this literature review. In full-color 3D printing, coloring, rendering and acquisition constitute the core issues for accurate color reproduction, and their specific concepts are explained in concrete examples. Finally, the future perspectives of a universal color reproduction framework for accurate full-color 3D printing are discussed, which can overcome the limitations of printing materials, combined with computational boundary contoning

Analysis of parametric biological models with non-linear dynamics

In this paper we present recent results on parametric analysis of biological models. The underlying method is based on the algorithms for computing trajectory sets of hybrid systems with polynomial dynamics. The method is then applied to two case studies of biological systems: one is a cardiac cell model for studying the conditions for cardiac abnormalities, and the second is a model of insect nest-site choice.Comment: In Proceedings HSB 2012, arXiv:1208.315

Infinite Exchangeability for Sets of Desirable Gambles

Sets of desirable gambles constitute a quite general type of uncertainty model with an interesting geometrical interpretation. We study infinite exchangeability assessments for them, and give a counterpart of de Finetti's infinite representation theorem. We show how the infinite representation in terms of frequency vectors is tied up with multivariate Bernstein (basis) polynomials. We also lay bare the relationships between the representations of updated exchangeable models, and discuss conservative inference (natural extension) under exchangeability

Piecewise Rational Manifold Surfaces with Sharp Features

We present a construction of a piecewise rational free-form surface of arbitrary topological genus which may contain sharp features: creases, corners or cusps. The surface is automatically generated from a given closed triangular mesh. Some of the edges are tagged as sharp ones, defining the features on the surface. The surface is C s smooth, for an arbitrary value of s, except for the sharp features defined by the user. Our method is based on the manifold construction and follows the blending approach