We are presenting techniques for simulating the motion and the deformation of cloth, fabrics or, more generally, deformable surfaces. Our main goal is to be able to simulate any kind of surface without imposing restrictions on shape or geometrical environment. In particular, we are considering difficult situations with respect to deformations and collisions, like wrinkled fabric falling on the ground. Thus, we have enhanced existing algorithms in order to cope with any possible situation. A mechanical model has been implemented to deal with any irregular triangular meshes, handle high deformations despite rough discretisation, and cope with complex interacting collisions. Thus, it should deal efficiently with situations where nonlinearities and discontinuities are really non marginal. Collision detection has also been improved to efficiently detect self-collisions, and also to correctly consider collision orientations despite the lack of surface orientation information from preset geometrical contexts, using consistency checking and correction. We illustrate these features through simulation examples.

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Versatile and efficient techniques for simulating cloth and other deformable objects

We present a new approach to clustering, based on the physical properties of an inhomogeneous ferromagnet. No assumption is made regarding the underlying distribution of the data. We assign a Potts spin to each data point and introduce an interaction between neighboring points, whose strength is a decreasing function of the distance between the neighbors. This magnetic system exhibits three phases. At very low temperatures, it is completely ordered; all spins are aligned. At very high temperatures, the system does not exhibit any ordering, and in an intermediate regime, clusters of relatively strongly coupled spins become ordered, whereas different clusters remain uncorrelated. This intermediate phase is identified by a jump in the order parameters. The spin-spin correlation function is used to partition the spins and the corresponding data points into clusters. We demonstrate on three synthetic and three real data sets how the method works. Detailed comparison to the performance of other techniques clearly indicates the relative success of our method.

Data clustering using a model granular magnet

To address the misconceptions that students typically hold concerning quantum mechanics, instructors should couple computer-based visualizations with research-based pedagogical strategies.

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Improving students’ understanding of quantum mechanics

Despite their importance in activated processes, transition-event durations--which are much shorter than first passage times--have not received a complete theoretical treatment. The authors therefore study the distribution rhob(t) of durations of transition events over a barrier in a one-dimensional system undergoing overdamped Langevin dynamics. The authors show that rhob(t) is determined by a Fokker-Planck equation with absorbing boundary conditions and obtain a number of results, including (i) the analytic form of the asymptotic short-time transient behavior, which is universal and independent of the potential function; (ii) the first nonuniversal correction to the short-time behavior leading to an estimate of a key physical time scale; (iii) following previous work, a recursive formulation for calculating, exactly, all moments of rhob based solely on the potential function-along with approximations for the distribution based on a small number of moments; and (iv) a high-barrier approximation to the long-time (t-->infinity) behavior of rhob(t). The authors also find that the mean event duration does not depend simply on the barrier-top frequency (curvature) but is sensitive to details of the potential. All of the analytic results are confirmed by transition-path-sampling simulations implemented in a novel way. Finally, the authors discuss which aspects of the duration distribution are expected to be general for more complex systems.

Transition-event durations in one-dimensional activated processes

We extend the Hoshen–Kopelman (HK) algorithm for cluster labeling to non-lattice environments, where sites are placed at random at non-lattice points. This extension is useful for continuum systems and disordered networks. Our extension of the HK algorithm relies on several data structures that describe network connectivity regardless of its dimensionality. Just as for the classic HK algorithm on lattices, our extension is completed in a single pass through the sites of the network and cluster relabeling operates on a vector whose size is much smaller than the size of the network. Our extension of the HK algorithm works for any environment (lattice or non-lattice) of any dimensionality, type (sites, bonds or both), and with arbitrary connectivity between the sites. The proposed extension is illustrated through a simple network consisting of 16 sites and 24 bonds, and applied to a complex network extracted from a 3D micro-focused X-ray CT image of Bentheimer sandstone consisting of 3677 sites and 8952 bonds.

Extension of Hoshen–Kopelman algorithm to non-lattice environments

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Christian Wolfgang

Papers

An Introduction to Computer Simulation Methods: Applications to Physical Systems (3rd Edition)