Hard sphere packings within cylinders

The packing of hard spheres (HS) of diameter $\sigma$ in a cylinder has been used to model experimental systems, such as fullerenes in nanotubes and colloidal wire assembly. Finding the densest packings of HS under this type of confinement, however, grows increasingly complex with the cylinder diameter, $D$. Little is thus known about the densest achievable packings for $D>2.873\sigma$. In this work, we extend the identification of the packings up to $D=4.00\sigma$ by adapting Torquato-Jiao's adaptive-shrinking-cell formulation and sequential-linear-programming (SLP) technique. We identify 17 new structures, almost all of them chiral. Beyond $D\approx2.85\sigma$, most of the structures consist of an outer shell and an inner core that compete for being close packed. In some cases, the shell adopts its own maximum density configuration, and the stacking of core spheres within it is quasiperiodic. In other cases, an interplay between the two components is observed, which may result in simple periodic structures. In yet other cases, the very distinction between core and shell vanishes, resulting in more exotic packing geometries, including some that are three-dimensional extensions of structures obtained from packing hard disks in a circle.Comment: 11 pages, 11 figure

Smoothing and flattening the universe through slow contraction versus inflation

In a systematic study, we use an equivalent pair of improved numerical relativity codes based on a tetrad-formulation of the classical Einstein-scalar field equations to examine whether slow contraction or inflation (or both) can resolve the homogeneity, isotropy and flatness problems. Our finding, based on a set of gauge/frame invariant diagnostics, is that slow contraction robustly and rapidly smooths and flattens spacetime beginning from initial conditions that are outside the perturbative regime of the flat Friedmann-Robertson-Walker metric, whereas inflation fails these tests. We present new numerical evidence supporting the conjecture that the combination of ultralocal evolution and an effective equation-of-state with pressure much greater than energy density is the key to having robust and rapid smoothing. The opposite of ultralocality occurs in expanding spacetimes, which is the leading obstruction to smoothing following a big bang.Comment: 18 pages, 6 figures, 1 tabl

Classification of BATSE, Swift, and Fermi Gamma-Ray Bursts from Prompt Emission Alone

Although it is generally assumed that there are two dominant classes of gamma-ray bursts (GRB) with different typical durations, it has been difficult to unambiguously classify GRBs as short or long from summary properties such as duration, spectral hardness, and spectral lag. Recent work used t-distributed stochastic neighborhood embedding (t-SNE), a machine learning algorithm for dimensionality reduction, to classify all Swift gamma-ray bursts as short or long. Here, the method is expanded, using two algorithms, t-SNE and UMAP, to produce embeddings that are used to provide a classification for the 1911 BATSE bursts, 1321 Swift bursts, and 2294 Fermi bursts for which both spectra and metadata are available. Although the embeddings appear to produce a clear separation of each catalog into short and long bursts, a resampling-based approach is used to show that a small fraction of bursts cannot be robustly classified. Further, 3 of the 304 bursts observed by both Swift and Fermi have robust but conflicting classifications. A likely interpretation is that in addition to the two predominant classes of GRBs, there are additional, uncommon types of bursts which may require multi-wavelength observations in order to separate from more typical short and long GRBs.Comment: ApJ, in pres

Robustness of slow contraction to cosmic initial conditions

We present numerical relativity simulations of cosmological scenarios in which the universe is smoothed and flattened by undergoing a phase of slow contraction and test their sensitivity to a wide range of initial conditions. Our numerical scheme enables the variation of all freely specifiable physical quantities that characterize the initial spatial hypersurface, such as the initial shear and spatial curvature contributions as well as the initial field and velocity distributions of the scalar that drives the cosmological evolution. In particular, we include initial conditions that are far outside the perturbative regime of the well-known attractor scaling solution. We complement our numerical results by analytically performing a complete dynamical systems analysis and show that the two approaches yield consistent results.Comment: 41 pages, 18 figures; accepted for publication in JCA

Ultralocality and Slow Contraction

We study the detailed process by which slow contraction smooths and flattens the universe using an improved numerical relativity code that accepts initial conditions with non-perturbative deviations from homogeneity and isotropy along two independent spatial directions. Contrary to common descriptions of the early universe, we find that the geometry first rapidly converges to an inhomogeneous, spatially-curved and anisotropic ultralocal state in which all spatial gradient contributions to the equations of motion decrease as an exponential in time to negligible values. This is followed by a second stage in which the geometry converges to a homogeneous, spatially flat and isotropic spacetime. In particular, the decay appears to follow the same history whether the entire spacetime or only parts of it are smoothed by the end of slow contraction.Comment: 27 pages, 10 figure

The Ultimate Fate of Life in an Accelerating Universe

The ultimate fate of life in a universe with accelerated expansion is considered. Previous work showed that life cannot go on indefinitely in a universe dominated by a cosmological constant. In this paper we consider instead other models of acceleration (including quintessence and Cardassian expansion). We find that it is possible in these cosmologies for life to persist indefinitely. As an example we study potentials of the form $V \propto \phi^n$ and find the requirement $n < -2$.Comment: 8 pages, RevTex. (V2 has a reference added, additional minor changes.

Controlling Chaos through Compactification in Cosmological Models with a Collapsing Phase

We consider the effect of compactification of extra dimensions on the onset of classical chaotic "Mixmaster" behavior during cosmic contraction. Assuming a universe that is well-approximated as a four-dimensional Friedmann-Robertson--Walker model (with negligible Kaluza-Klein excitations) when the contraction phase begins, we identify compactifications that allow a smooth contraction and delay the onset of chaos until arbitrarily close the big crunch. These compactifications are defined by the de Rham cohomology (Betti numbers) and Killing vectors of the compactification manifold. We find compactifications that control chaos in vacuum Einstein gravity, as well as in string theories with N = 1 supersymmetry and M-theory. In models where chaos is controlled in this way, the universe can remain homogeneous and flat until it enters the quantum gravity regime. At this point, the classical equations leading to chaotic behavior can no longer be trusted, and quantum effects may allow a smooth approach to the big crunch and transition into a subsequent expanding phase. Our results may be useful for constructing cosmological models with contracting phases, such as the ekpyrotic/cyclic and pre-big bang models.Comment: 1 figure. v2/v3: minor typos correcte

Phase diagram of the Shastry-Sutherland Compound SrCu2(BO3)2 under extreme combined conditions of field and pressure

Motivated by the intriguing properties of the Shastry-Sutherland compound SrCu2(BO3)2 under pressure, with a still debated intermediate plaquette phase appearing at around 20 kbar and a possible deconfined critical point at higher pressure upon entering the antiferromagnetic phase, we have investigated its high-field properties in this pressure range using tunnel diode oscillator (TDO) measurements. The two main new phases revealed by these measurements are fully consistent with those identified by infinite Projected Entangled Pair states (iPEPS) calculations of the Shastry-Sutherland model, a 1/5 plateau and a 10 x 2 supersolid. Remarkably, these phases are descendants of the full-plaquette phase, the prominent candidate for the intermediate phase of SrCu2(BO3)2. The emerging picture for SrCu2(BO3)2 is shown to be that of a system dominated by a tendency to an orthorhombic distortion at intermediate pressure, an important constraint on any realistic description of the transition into the antiferromagnetic phase