2: Tessellar phase diagram for p>, ď : q for the example in Figure 9.1. The elements in pSC, ďq are labeled with the natural numbers. Elements S P SC with trivial tessellar homology are indicated only by label.

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Fig. 1.1: A discretization of pX, T q with the associated face partial...

Fig. 1.3: An associated discrete resolution ď J on the top-cells X J of...

Fig. 1.4: The SC-graded chain complex pC tile pXq, ∆ tile q [left] of...

Fig. 1.6: Associated complex A pβq, computed over K " Z 2 coefficients,...

Fig. 5.1: The topological space pX, T q and semi-flow φ [left 1]. A...

The algebra of semi-flows: a tale of two topologies

Preprint

Full-text available

Jul 2022

To capture the global structure of a dynamical system we reformulate dynamics in terms of appropriately constructed topologies, which we call flow topologies; we call this process topologization. This yields a description of a semi-flow in terms of a bi-topological space, with the first topology corresponding to the (phase) space and the second to...

Figure 1. The subset Ω (36) in (b,d,f) for several choices ((a), (c),...

Figure 2. The flow of the vector field (40) in Example 1 for two values...

Figure 4. V(ϕ) for several choices of γ, see Example 5. The constant c...

Global Models of Collapsing Scalar Field: Endstate

Article

Full-text available

May 2024

The study of dynamic singularity formation in spacetime, focusing on scalar field collapse models, is analyzed. We revisit key findings regarding open spatial topologies, concentrating on minimal conditions necessary for singularity and apparent horizon formation. Moreover, we examine the stability of initial data in the dynamical system governed b...

2: Tessellar phase diagram for p>, ď : q for the example in Figure 9.1. The elements in pSC, ďq are labeled with the natural numbers. Elements S P SC with trivial tessellar homology are indicated only by label.

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