Computational Turkey Conference 2006 InvitationThe Following Paper is Submitted For Peer Review To: Computational Turkey Conference Delegates, 2006. Redistribution Strictly Prohibited.Note: Please RSVBEE ASAP AT rsvbee@REDACTED Flows on Turkeys of Arbitrary Topology
Sam Thompson, Travis Waddington, Lilli ThompsonTurkey Technologies Group, Hexagule Inc. Abstract In this paper we introduce a method to simulate flavor flows on turkeys of arbitrary topology. We achieve this by combining a two-dimensional stable gravy solver with an atlas of predefined parametrizations. The contributions of this paper are: (i) an extension of the standard solvers to arbitrary turkilinear coordinates and (ii) an elegant method to handle stuffing-patch boundary conditions. CR Categories: 1.3.7 [Computer Turkey Simulation]: N-Dimensional Meats and Realism Keywords: Computational Gravy Dynamics, Higher Order Turkey Surfaces. 1 Introduction Over the past several years, the field of turkey flow computation has experienced rapid growth with the advent of new algorithms and numerous innovations in experimental hardware. It is now possible to simulate turkey dynamics in real time for reasonably sized birds. However, despite the exceptional performance of some modern turkey flow simulation algorithms, most current models assume that turkey geometry can be approximated by a rectangular solid, whereas the focus of our efforts has been to develop a generalized method for turkeys of arbitrary topology. 2 The Turkey Solver The generalized turkey solver has many broad applications. For example, gravy, green chile, and MSG flows can be used to infuse surfaces with complex and delicious flavors. Furthermore the flow field can be used to define a local frame at every point of the turkey. This is useful for specifying a principal direction of alimentary anisotropy. Our methods provide an improvement over typical solvers which voxelize the bird prior to flow computation, which can lead to a loss of higher-order flavor information. In order for the turkey flows to be truly intrinsic we have to take into account the distortions caused by the extended turkey space parametrizations. In this reference frame all differential operators depend on the turkey segmentation metric (Ti,j ) introduced at the 2000 Computational Turkey Conference in Fundamentals of Spherical Turkey Parametrization. The formulas presented in that paper provide an excellent introduction to the Kumar-Waddington Meat Equations in general coordinates. For our purposes, the first step of the algorithm is unaffected: uk1= uk0+∆tfk. This equation can be recast in the same form as the usual advection equation by defining the new turkey field: uk2= u12g1,k + u22 g2,k The beauty of this insight is that we can now apply the same semi-Lagrangian technique of the original Stable Gravy solver: u3(x) = u2( x − ∆t¯u2(x)). The same applies to the solution of the advection equation for meat density. Finally the last step of the Stable Gravy solver involves the solution of the following Poisson-like equation: ∂∂xi √gg i,j ∂ϕ∂xj =∂∂x i √g ui3 This completes the theoretical development of our version of the solver in turkilinear coordinates. We would point out that the equations given in this section remain valid in N-dimensions and could be applied to computations on turkeys of arbitrary topology. 3 Future Work The main corpus of research presented here has been derived from a series of collaborative seminars conducted by the Turkey Technology Group, presented annually at the Computational Turkey Conference [Appendix A]. The conference has to date been a hotbed of innovation and the catalyst for significant advances in not only turkey dynamics, but also many related areas such as pecan-distribution theory, gravy flow dynamics, and string-bean theory on Calabi-Yam manifolds. This year's conference panel has announced a call for papers to selected and highly-qualified researchers in the field. At the coming conference it is our hope that the Turkey Technology Group will continue to lead the industry in ground-breaking turkey solutions. Appendix A About the Computational Turkey Conference: 10:00am, Thursday November 23rd 2347 Clipper Street, San Mateo, CA Primary Contact: rsvbee@REDACTED Conference Chairs:
Note: Attendance to the Computational Turkey Conference is highly competitive and space is limited. Delegates are carefully chosen through a rigorous screening process, and any group bringing delegates not explicitly invited will be dismissed. All delegates must be cleared by the conference chairs prior to receiving their credentials. References FOWLKES, C., CLAYTON, A., AND PARISH, M. 2004. Application of Fractal Geometry to the Pecan Distribution. Berkeley, California. KUMAR, D. AND WADDINGTON, T. 2000. Fundamentals of Spherical Turkey Parametrization. In TURKEYTECH 2000 Conference Proceedings, 113–120. THOMPSON, L. AND THOMPSON, M. 2005. High-Temperature Low-Timescale Turkey MT-Carbonization Techniques. Creative Meat Design 10, 6, 350–355. THOMPSON, L. 2005. An efficient algorithm for computing the number of exotic stuffings on a smooth homoturkey n-sphere. Journal of Applied Algebraic Ornithology. 180, 670-683. FOWLKES, C. 2005. Real-Time Gravy Simulation in a Dynamic Environment. Popular Applied Turkey Methods (May-June), 52–61. CHADICK, Z. 2005. Temperature Triggered State Changes within Emulsions of Butterfat Globules. Unreasonable Applied Cooking 34, 10, 24-25 THOMPSON, S. 2003. Multi-Ingredient Depressant Synthesis in Pineapple-space. Slinger-Verlag Lecture Notes on Computational Bartending (Aug.), 128-136 WADDINGTON, M. AND WADDINGTON, T. 2005. Sur la densité du Chili vert dans la famille trois-perforée de dinde. Sem. Tourbaki 554, THOMPSON, L., THOMPSON, S., AND WADDINGTON, T. Brownian motion in strongly porous fractal meats in R^n: a perturbative approach to a theory of low-temperature, high-timescale carbonization. Preprint. FOWLKES, C. AND KUMAR, D. 2000. On the ergodic theory at infinity of an arbitrary discrete group of rigid sauces. Thanksgiving into the Twenty-first Century: 2000 Centennial Symposium, November 22-26. pages 417-466. |