Combinatorics of Past-similarity in Higher Dimensional Transition Systems
نویسنده
چکیده
The key notion to understand the left determined Olschok model category of star-shaped Cattani-Sassone transition systems is past-similarity. Two states are past-similar if they have homotopic pasts. An object is fibrant if and only if the set of transitions is closed under past-similarity. A map is a weak equivalence if and only if it induces an isomorphism after the identification of all past-similar states. The last part of this paper is a discussion about the link between causality and homotopy.
منابع مشابه
شبیه سازی ذوب سیستمهای دو بعدی
The study of a two-dimensional (2-D) system started nearly half a century ago when Peierls and Landau showed the lack of long range translational order in a two-dimensional solid. In 1968, Mermin proved that despite the absence of long range translational order. Two-dimensional solids can still exhibit a different kind of long range bond orientation. During the last decade, fascinating theori...
متن کاملNumerical Analysis of the Effect of External Circumferential Elliptical Cracks in Transition Thickness Zone of Pressurized Pipes Using XFEM
The present work investigates the effect of the elliptical three-dimensional (3D) cracks on a pipe with thickness transition, considering internal pressure. Level sets were defined using the extended finite element method (XFEM), the stress intensity factors (SIFs) of 3D cracks were investigated and compared between straight pipes and pipes with thickness transition. The results show that the X...
متن کامل(1+1)-dimensional turbulence systems reduced from (2+1)-dimensional Lax integrable dispersive long wave equation
After extending the Clarkson-Kruskal’s direct similarity reduction ansatz to a more general form, one may obtain various new types of reduction equations. Especially, some lower dimensional turbulence systems or chaotic systems may be obtained from the general type of similarity reductions of a higher dimensional Lax integrable model with nonintegrable boundary and/or the initial conditions. In...
متن کاملOn Numerical Investigation of Non-dimensional Constant Representing the Occurrence of Secondary Peaks in the Nusselt Distribution Curves
The Study of heat transfer augmentation in micro scale and electronic packaging systems are some of the paramount areas of the impending universe. In such systems the cooling of the heat sinks are generally achieved through the impingement of air jet. Assuming the air jet to be continues & incompressible fluid, the heat dissipation rate over the target surface seems to either uniform or well ch...
متن کاملFractal Replication in Time-manipulated One-dimensional Cellular Automata
Properties of elementary one-dimensional cellular automata (CAs) have been studied extensively in the past by varying the number of states each cell can take, the neighborhood of the cell, or the transition rules by which each cell is updated. This paper describes a previously untried variation on a CA system, where each cell is able to anticipate its state one step in the future, and the entir...
متن کامل