Related papers: Particulate exotica
It is shown that mathematical physics differential equations have properties that allow describing processes such as the structures emergence, discrete transitions, quantum jumps. The peculiarity is that such properties are hidden. They do…
We study smooth, proper embeddings of noncompact surfaces in 4-manifolds, focusing on exotic planes and annuli, i.e., embeddings pairwise homeomorphic to the standard embeddings of R^2 and R^2-int D^2 in R^4. We encounter two uncountable…
It is known that the long line supports $2^{\aleph_1}$ many non-diffeomorphic differential structures. We show that the long plane supports a similar number of exotic differential structures, ie structures which are not merely diffeomorphic…
Why are materials with specific characteristics more abundant than others? This is a fundamental question in materials science and one that is traditionally difficult to tackle, given the vastness of compositional and configurational space.…
Scores of exotic hadrons, particularly tetraquarks and pentaquarks in the heavy-quark sector, have been observed in the past 20 years, and more continue to be discovered to this day. Unlike mesons and baryons, such exotics are not mandated…
We study the dynamics of a particle in a space that is non-differentiable. Non-smooth geometrical objects have an inherently probabilistic nature and, consequently, introduce stochasticity in the motion of a body that lives in their realm.…
Diffeology extends differential geometry to spaces beyond smooth manifolds. This paper explores diffeology's key features and illustrates its utility with examples including singular and quotient spaces, and applications in symplectic…
The coupled interior-atmosphere system of terrestrial exoplanets remains poorly understood. Exoplanets show a wide variety of sizes, densities, surface temperatures, and interior structures, with important knock-on effects for this coupled…
The late-time cosmological dynamics of disformal gravity are investigated using dynamical systems methods. It is shown that in the general case there are no stable attractors that screen fifth-forces locally and simultaneously describe a…
Classical mechanics can be formulated using a symplectic structure on classical phase space, while quantum mechanics requires a complex-differentiable structure on that same space. Complex-differentiable structures on a given real manifold…
We show that any finitely presented group with an index two subgroup is realized as the fundamental group of a closed smooth non-orientable four-manifold that admits an exotic smooth structure, which is obtained by performing a Gluck twist.…
This article examines how the physical presence of field energy and particulate matter can be interpreted in terms of the topological properties of space-time. The theory is developed in terms of vector and matrix equations of exterior…
The interplay between order and geometry in soft condensed matter systems is an active field with many striking results and even more open problems. Ordered structures on curved surfaces appear in multi-electron helium bubbles, viral and…
The role of global topology in the dynamics of the Universe is poorly understood. Along with observational programmes for determining the topology of the Universe, some small theoretical steps have recently been made. Heuristic…
Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…
We study the relationship between exotic R^4's and Stein surfaces as it applies to smoothing theory on more general open 4-manifolds. In particular, we construct the first known examples of large exotic R^4's that embed in Stein surfaces.…
Differentials on Riemann surfaces correspond to translation surfaces with conical singularities, and affine transformations acting on them preserve the orders of these singularities. This viewpoint allows the moduli spaces of differentials…
Studies have shown that quantum states reside in a Hilbert space bundle. When a quantum system depends on continuous external parameters, these parameters define additional dimensions in the base space of the bundle. While much of the…
This paper proposes a new notion of smoothness of algebras, termed differential smoothness, that combines the existence of a top form in a differential calculus over an algebra together with a strong version of the Poincar\'e duality…
Time is, figuratively and literally, becoming the new dimension for crystalline matter. As such, rapid recent progress on time-varying media gave rise to the notion of temporal and spatiotemporal crystals. Fundamentally rethinking the role…