32790564
Efficient and Accurate Collision Detection for Granular Flow Simulation
Abstract In this paper, we present efficient algorithms for contact detection and accurate contact mechanics in granular flow simulations. The contact detection algorithms that we present are applicable to arbitrarily shaped rigid particles in a variety of environments including interactive as well as non-interactive. We present a very accurate force displacement model for characterizing the behavior of particles in contact. These algorithms are applied to granular flow simulations, in particular, soybean flow through an inclined chute. There are two phases of this research, namely, the development of contact detection algorithms and the development of accurate contact mechanics based force-displacement models. In the first phase, the algorithms consist of two stages. The first stage involves finding candidate particles for possible contacts. The second stage involves detecting precise contact between these candidates. In our application, the soybeans, which are approximately ellipsoidal in shape, are well approximated by a cluster of overlapping spheres. Detecting precise contact between spherical shapes is quite simple and hence, in this paper, we will focus only on the first stage of the first phase. The primary data structure used in the first stage is an octree. We build an octree for the enclosure/chute (containing the n particles) and use it in the algorithm for detecting possible contacts. The average time complexity of this stage of the first phase is O(n) and the worst case is O ( n log n ). In phase two, we develop a very accurate force-displacement model for dealing with the contact mechanics of soybean flow through an inclined chute. This model is a reasonably close approximation to the widely accepted Mindlin force-displacement model for elastic frictional contacts. Our force-displacement model accounts for normal and tangential direction contact forces acting between particles and/or particles and the chute walls. We also present examples of soybean flow simulations with fast contact detection and accurate contact mechanics.
122655121
An accurate tangential force-displacement model for granular-flow simulations: contacting spheres with plastic deformation, force-driven formulation
An elasto-plastic frictional tangential force-displacement (TFD) model for spheres in contact for accurate and efficient granular-flow simulations is presented in this paper: the present TFD is consistent with the elasto-plastic normal force displacement (NFD) model presented in [ASME Journal of Applied Mechanics 67 (2) (2000) 363: Proceedings of the Royal Society of London, Series A 455 (1991) (1999) 4013]. The proposed elasto-plastic frictional TFD model is accurate, and is validated against non-linear finite-element analyses involving plastic flows under both loading and unloading conditions. The novelty of the present TFD model lies in (i) the additive decomposition of the elasto-plastic contact area radius into an elastic part and a plastic part, (ii) the correction of the particles' radii at the contact point, and (iii) the correction of the particles' elastic moduli. The correction of the contact-area radius represents an effect of plastic deformation in colliding particles; the correction of the radius of curvature represents a permanent indentation after impact; the correction of the elastic moduli represents a softening of the material due to plastic flow. The construction of both the present elasto-plastic frictional TFD model and its consistent companion, the elasto-plastic NFD model, parallels the formalism of the continuum theory of elasto-plasticity. Both NFD and TFD models form a coherent set of force-displacement (FD) models not available hitherto for granular-flow simulations, and are consistent with the Hertz, Cattaneo, Mindlin, Deresiewicz contact mechanics theory. Together. these FD models will allow for efficient simulations of granular flows (or granular gases) involving a large number of particles.
34379910
Global asymptotic stabilization of feedforward nonlinear systems with a delay in the input
In this paper, by constructing appropriate Lyapunov–Krasovskii functionals (LKF) and applying the model transformation of time-delay systems, a design scheme of state feedback controller for a class of feedforward nonlinear systems with a delay in the input is proposed. The designed controllers have a very simple structure and do not involve any saturation or recursive computation, which is widely applied in designing a controller of feedforward nonlinear systems. Using the transformation of coordinates and the property of Hurwitz polynomial, the problem of designing controller can be converted into the problem of finding a parameter, which can be solved by solving the optimization problem with linear matrix inequalities (LMIs) constraints. A simulation example is given to show the effectiveness of the proposed design procedure.
16742949
Evaluation of the matrix exponential function using finite elements in time
The evaluation of a matrix exponential function is a classic problem of computational linear algebra. Many different methods have been employed for its numerical evaluation (Moler C and van Loan C 1978 SIAM Review 20 4), none of which produce a definitive algorithm which is broadly applicable and sufficiently accurate, as well as being reasonably fast. Herein, we employ a method which evaulates a matrix exponential as the solution to a first-order initial value problem in a fictitious time variable. The new aspect of the present implementation of this method is to use finite elements in the fictitious time variable. (Weatherford C A, Red E, and Wynn A 2002 Journal of Molecular Structure 592 47) Then using an expansion in a properly chosen time basis, we are able to make accurate calculations of the exponential of any given matrix as the solution to a set of simultaneous equations.
32875582
Invariant object recognition by shape space analysis
This paper describes a new approach to invariant object recognition. In this approach, an object is represented by a set of key points called landmarks. All possible translation, scaling, and rotation of the object are placed into an equivalent class and associated to a single point in a complex projective space called the shape space. Object recognition is then achieved by distance calculations in this shape space. This approach is invariant to object translation, scaling, and rotation, and is computationally simple. Our experimental results also indicate that it is insensitive to noise and moderate occlusions.
20657103
Linear MMSE space-time equalizer for MIMO multicode CDMA systems
We propose an enhanced chip-level linear space-time (ST) equalizer for multiple-input multiple-output (MIMO) multicode code-division multiple-access (CDMA) systems. In the MIMO multicode CDMA systems, the reuse of the same spreading codes in different transmit antennas significantly degrades the equalization performance if the ST equalizer uses a minimum mean-squared error (MMSE) weighting vector that minimizes the mean-squared error of the equalizer output chip sequence. As the CDMA despreader concatenated to an ST equalizer distorts interstream interference components differently from multipath interference and background noise components, the chip-level MMSE weighting vector usually steers in suboptimal directions in the signal space. Therefore, we propose a new MMSE weighting vector that takes the despreading effect into account in this paper. Simulation results show a substantial performance improvement through the new weighting vector
117014333
Exact Controllability of Semilinear Evolution Systems and Its Application
In this paper, we obtain several abstract results concerning the exact controllability of semilinear evolution systems. First, we prove the null local exact controllability of semilinear first-order systems by means of the contraction mapping principle; in this case, we do not assume any compactness. Next, we derive the global and/or local exact controllability of semilinear second-order systems by means of the Schauder fixed-point theorem; in this case, we assume only the embedding of the related spaces having some compactness, which is reasonable for many concrete problems. Our main result shows that the observability of the dual of the linearized system implies the exact controllability of the original semilinear system. Finally, we apply our abstract results to the exact controllability of the semilinear wave equation.