Cosmological Bounces Induced by a Fermion Condensate.

We show that it is possible for fermion condensation of the Nambu-Jona-Lasinio type to induce a nonsingular bounce that smoothly connects a phase of slow contraction to a phase of expansion. A chiral condensate-a nonzero vacuum expectation value of the spinor bilinear ⟨Ψ[over ¯]Ψ⟩-can form spontaneously after a slow contraction phase smooths and flattens the universe and the Ricci curvature exceeds a critical value. In this approach, a high density of spin-aligned free fermions is not required, which avoids the problem of generating a large anisotropy and initiating chaotic mixmaster behavior during the bounce phase.

Electrical discharge triggers quasicrystal formation in an eolian dune.

We report the discovery of a dodecagonal quasicrystal Mn72.3Si15.6Cr9.7Al1.8Ni0.6-composed of a periodic stacking of atomic planes with quasiperiodic translational order and 12-fold symmetry along the two directions perpendicular to the planes-accidentally formed by an electrical discharge event in an eolian dune in the Sand Hills near Hyannis, Nebraska, United States. The quasicrystal, coexisting with a cubic crystalline phase with composition Mn68.9Si19.9Ni7.6Cr2.2Al1.4, was found in a fulgurite consisting predominantly of fused and melted sand along with traces of melted conductor metal from a nearby downed power line. The fulgurite may have been created by a lightning strike that combined sand with material from downed power line or from electrical discharges from the downed power line alone. Extreme temperatures of at least 1,710 °C were reached, as indicated by the presence of SiO2 glass in the sample. The dodecagonal quasicrystal is an example of a quasicrystal of any kind formed by electrical discharge, suggesting other places to search for quasicrystals on Earth or in space and for synthesizing them in the laboratory.

Wave propagation and band tails of two-dimensional disordered systems in the thermodynamic limit.

Understanding the nature and formation of band gaps associated with the propagation of electromagnetic, electronic, or elastic waves in disordered materials as a function of system size presents fundamental and technological challenges. In particular, a basic question is whether band gaps in disordered systems exist in the thermodynamic limit. To explore this issue, we use a two-stage ensemble approach to study the formation of complete photonic band gaps (PBGs) for a sequence of increasingly large systems spanning a broad range of two-dimensional photonic network solids with varying degrees of local and global order, including hyperuniform and nonhyperuniform types. We discover that the gap in the density of states exhibits exponential tails and the apparent PBGs rapidly close as the system size increases for nearly all disordered networks considered. The only exceptions are sufficiently stealthy hyperuniform cases for which the band gaps remain open and the band tails exhibit a desirable power-law scaling reminiscent of the PBG behavior of photonic crystals in the thermodynamic limit.

Rapidly descending dark energy and the end of cosmic expansion.

If dark energy is a form of quintessence driven by a scalar field ϕ evolving down a monotonically decreasing potential V(ϕ) that passes sufficiently below zero, the universe is destined to undergo a series of smooth transitions. The currently observed accelerated expansion will cease; soon thereafter, expansion will come to end altogether; and the universe will pass into a phase of slow contraction. In this paper, we consider how short the remaining period of expansion can be given current observational constraints on dark energy. We also discuss how this scenario fits naturally with cyclic cosmologies and recent conjectures about quantum gravity.

Gap Sensitivity Reveals Universal Behaviors in Optimized Photonic Crystal and Disordered Networks.

Through an extensive series of high-precision numerical computations of the optimal complete photonic band gap (PBG) as a function of dielectric contrast α for a variety of crystal and disordered heterostructures, we reveal striking universal behaviors of the gap sensitivity S(α)≡dΔ(α)/dα, the first derivative of the optimal gap-to-midgap ratio Δ(α). In particular, for all our crystal networks, S(α) takes a universal form that is well approximated by the analytic formula for a 1D quarter-wave stack, S_{QWS}(α). Even more surprisingly, the values of S(α) for our disordered networks converge to S_{QWS}(α) for sufficiently large α. A deeper understanding of the simplicity of this universal behavior may provide fundamental insights about PBG formation and guidance in the design of novel photonic heterostructures.

Accidental synthesis of a previously unknown quasicrystal in the first atomic bomb test.

The first test explosion of a nuclear bomb, the Trinity test of 16 July 1945, resulted in the fusion of surrounding sand, the test tower, and copper transmission lines into a glassy material known as "trinitite." Here, we report the discovery, in a sample of red trinitite, of a hitherto unknown composition of icosahedral quasicrystal, Si61Cu30Ca7Fe2 It represents the oldest extant anthropogenic quasicrystal currently known, with the distinctive property that its precise time of creation is indelibly etched in history. Like the naturally formed quasicrystals found in the Khatyrka meteorite and experimental shock syntheses of quasicrystals, the anthropogenic quasicrystals in red trinitite demonstrate that transient extreme pressure-temperature conditions are suitable for the synthesis of quasicrystals and for the discovery of new quasicrystal-forming systems.

Phoamtonic designs yield sizeable 3D photonic band gaps.

We show that it is possible to construct foam-based heterostructures with complete photonic band gaps. Three-dimensional foams are promising candidates for the self-organization of large photonic networks with combinations of physical characteristics that may be useful for applications. The largest band gap found is based on 3D Weaire-Phelan foam, a structure that was originally introduced as a solution to the Kelvin problem of finding the 3D tessellation composed of equal-volume cells that has the least surface area. The photonic band gap has a maximal size of 16.9% (at a volume fraction of 21.6% for a dielectric contrast [Formula: see text]) and a high degree of isotropy, properties that are advantageous in designing photonic waveguides and circuits. We also present results for 2 other foam-based heterostructures based on Kelvin and C15 foams that have somewhat smaller but still significant band gaps.

Hyperuniform disordered waveguides and devices for near infrared silicon photonics.

We introduce a hyperuniform-disordered platform for the realization of near-infrared photonic devices on a silicon-on-insulator platform, demonstrating the functionality of these structures in a flexible silicon photonics integrated circuit platform unconstrained by crystalline symmetries. The designs proposed advantageously leverage the large, complete, and isotropic photonic band gaps provided by hyperuniform disordered structures. An integrated design for a compact, sub-volt, sub-fJ/bit, hyperuniform-clad, electrically controlled resonant optical modulator suitable for fabrication in the silicon photonics ecosystem is presented along with simulation results. We also report results for passive device elements, including waveguides and resonators, which are seamlessly integrated with conventional silicon-on-insulator strip waveguides and vertical couplers. We show that the hyperuniform-disordered platform enables improved compactness, enhanced energy efficiency, and better temperature stability compared to the silicon photonics devices based on rib and strip waveguides.

Hyperuniformity and anti-hyperuniformity in one-dimensional substitution tilings.

This work considers the scaling properties characterizing the hyperuniformity (or anti-hyperuniformity) of long-wavelength fluctuations in a broad class of one-dimensional substitution tilings. A simple argument is presented which predicts the exponent α governing the scaling of Fourier intensities at small wavenumbers, tilings with α > 0 being hyperuniform, and numerical computations confirm that the predictions are accurate for quasiperiodic tilings, tilings with singular continuous spectra and limit-periodic tilings. Quasiperiodic or singular continuous cases can be constructed with α arbitrarily close to any given value between -1 and 3. Limit-periodic tilings can be constructed with α between -1 and 1 or with Fourier intensities that approach zero faster than any power law.

Previously unknown quasicrystal periodic approximant found in space.

We report the discovery of Al34Ni9Fe2, the first natural known periodic crystalline approximant to decagonite (Al71Ni24Fe5), a natural quasicrystal composed of a periodic stack of planes with quasiperiodic atomic order and ten-fold symmetry. The new mineral has been approved by the International Mineralogical Association (IMA 2018-038) and officially named proxidecagonite, which derives from its identity to periodic approximant of decagonite. Both decagonite and proxidecagonite were found in fragments from the Khatyrka meteorite. Proxidecagonite is the first natural quasicrystal approximant to be found in the Al-Ni-Fe system. Within this system, the decagonal quasicrystal phase has been reported to transform at ~940 °C to Al13(Fe,Ni)4, Al3(Fe,Ni)2 and the liquid phase, and between 800 and 850 °C to Al13(Fe,Ni)4, Al3(Fe,Ni) and Al3(Fe,Ni)2. The fact that proxidecagonite has not been observed in the laboratory before and formed in a meteorite exposed to high pressures and temperatures during impact-induced shocks suggests that it might be a thermodynamically stable compound at high pressure. The most prominent structural motifs are pseudo-pentagonal symmetry subunits, such as pentagonal bipyramids, that share edges and corners with trigonal bipyramids and which maximize shortest Ni-Al over Ni-Ni contacts.

Light Localization in Local Isomorphism Classes of Quasicrystals.

We study a continuum of photonic quasicrystal heterostructures derived from local isomorphism (LI) classes of pentagonal quasicrystal tilings. These tilings are obtained by direct projection from a five-dimensional hypercubic lattice. We demonstrate that, with the sole exception of the Penrose LI class, all other LI classes result in degenerate, effectively localized states, with precisely predictable and tunable properties (frequencies, frequency splittings, and densities). We show that localization and tunability are related to a mathematical property of the pattern known as "restorability," i.e., whether the tiling can be uniquely specified given only a set of rules that fix all allowed clusters smaller than some bound.

Shock Synthesis of Five-component Icosahedral Quasicrystals.

Five-component icosahedral quasicrystals with compositions in the range Al68-73Fe11-16Cu10-12Cr1-4Ni1-2 were recently recovered after shocking metallic CuAl5 and (Mg0.75Fe0.25)2SiO4 olivine in a stainless steel 304 chamber, intended to replicate a natural shock that affected the Khatyrka meteorite. The iron in those quasicrystals might have originated either from reduction of Fe2+ in olivine or from the stainless steel chamber. In this study, we clarify the shock synthesis mechanism of icosahedral quasicrystals through two new shock recovery experiments. When CuAl5 and Fe2+-bearing olivine were isolated in a Ta capsule, no quasicrystals were found. However, with only metallic starting materials, numerous micron-sized five-component icosahedral quasicrystals, average composition Al72Cu12Fe12Cr3Ni1, were found at the interface between CuAl5 and stainless steel, demonstrating nucleation of quasicrystals under shock without any redox reaction. We present detailed characterization of recovered quasicrystals and discuss possible mechanisms for generating sufficiently high temperatures to reach melting with relatively weak shocks. We discuss the implications of our five-component quasicrystal for the stability of quasicrystals, which have previously only been considered in alloy systems with four or fewer components. Even small amounts of additional metals expand the stability range of the icosahedral phase and facilitate routine syntheses without extraordinary precision in preparation of starting mixtures.

Corrigendum: Hyperuniformity variation with quasicrystal local isomorphism class.

A prefactor was omitted in Equation (7) of the initial manuscript. The correct form of the equation is provided in this Corrigendum.

Evidence of cross-cutting and redox reaction in Khatyrka meteorite reveals metallic-Al minerals formed in outer space.

We report on a fragment of the quasicrystal-bearing CV3 carbonaceous chondrite Khatyrka recovered from fine-grained, clay-rich sediments in the Koryak Mountains, Chukotka (Russia). We show higher melting-point silicate glass cross-cutting lower melting-point Al-Cu-Fe alloys, as well as unambiguous evidence of a reduction-oxidation reaction history between Al-Cu-Fe alloys and silicate melt. The redox reactions involve reduction of FeO and SiO2 to Fe and Fe-Si metal, and oxidation of metallic Al to Al2O3, occurring where silicate melt was in contact with Al-Cu-Fe alloys. In the reaction zone, there are metallic Fe and Fe-Si beads, aluminous spinel rinds on the Al-Cu-Fe alloys, and Al2O3 enrichment in the silicate melt surrounding the alloys. From this and other evidence, we demonstrate that Khatyrka must have experienced at least two distinct events: first, an event as early as 4.564 Ga in which the first Al-Cu-Fe alloys formed; and, second, a more recent impact-induced shock in space that led to transformations of and reactions between the alloys and the meteorite matrix. The new evidence firmly establishes that the Al-Cu-Fe alloys (including quasicrystals) formed in outer space in a complex, multi-stage process.

Collisions in outer space produced an icosahedral phase in the Khatyrka meteorite never observed previously in the laboratory.

We report the first occurrence of an icosahedral quasicrystal with composition Al62.0(8)Cu31.2(8)Fe6.8(4), outside the measured equilibrium stability field at standard pressure of the previously reported Al-Cu-Fe quasicrystal (AlxCuyFez, with x between 61 and 64, y between 24 and 26, z between 12 and 13%). The new icosahedral mineral formed naturally and was discovered in the Khatyrka meteorite, a recently described CV3 carbonaceous chondrite that experienced shock metamorphism, local melting (with conditions exceeding 5 GPa and 1,200 °C in some locations), and rapid cooling, all of which likely resulted from impact-induced shock in space. This is the first example of a quasicrystal composition discovered in nature prior to being synthesized in the laboratory. The new composition was found in a grain that has a separate metal assemblage containing icosahedrite (Al63Cu24Fe13), currently the only other known naturally occurring mineral with icosahedral symmetry (though the latter composition had already been observed in the laboratory prior to its discovery in nature). The chemistry of both the icosahedral phases was characterized by electron microprobe, and the rotational symmetry was confirmed by means of electron backscatter diffraction.

Classically Stable Nonsingular Cosmological Bounces.

One of the fundamental questions of theoretical cosmology is whether the Universe can undergo a nonsingular bounce, i.e., smoothly transit from a period of contraction to a period of expansion through violation of the null energy condition (NEC) at energies well below the Planck scale and at finite values of the scale factor such that the entire evolution remains classical. A common claim has been that a nonsingular bounce either leads to ghost or gradient instabilities or a cosmological singularity. In this Letter, we consider a well-motivated class of theories based on the cubic Galileon action and present a procedure for explicitly constructing examples of a nonsingular cosmological bounce without encountering any pathologies and maintaining a subluminal sound speed for comoving curvature modes throughout the NEC violating phase. We also discuss the relation between our procedure and earlier work.

Shock synthesis of quasicrystals with implications for their origin in asteroid collisions.

We designed a plate impact shock recovery experiment to simulate the starting materials and shock conditions associated with the only known natural quasicrystals, in the Khatyrka meteorite. At the boundaries among CuAl5, (Mg0.75Fe(2+) 0.25)2SiO4 olivine, and the stainless steel chamber walls, the recovered specimen contains numerous micron-scale grains of a quasicrystalline phase displaying face-centered icosahedral symmetry and low phason strain. The compositional range of the icosahedral phase is Al68-73Fe11-16Cu10-12Cr1-4Ni1-2 and extends toward higher Al/(Cu+Fe) and Fe/Cu ratios than those reported for natural icosahedrite or for any previously known synthetic quasicrystal in the Al-Cu-Fe system. The shock-induced synthesis demonstrated in this experiment reinforces the evidence that natural quasicrystals formed during a shock event but leaves open the question of whether this synthesis pathway is attributable to the expanded thermodynamic stability range of the quasicrystalline phase at high pressure, to a favorable kinetic pathway that exists under shock conditions, or to both thermodynamic and kinetic factors.

Natural quasicrystal with decagonal symmetry.

We report the first occurrence of a natural quasicrystal with decagonal symmetry. The quasicrystal, with composition Al71Ni24Fe5, was discovered in the Khatyrka meteorite, a recently described CV3 carbonaceous chondrite. Icosahedrite, Al63Cu24Fe13, the first natural quasicrystal to be identified, was found in the same meteorite. The new quasicrystal was found associated with steinhardtite (Al38Ni32Fe30), Fe-poor steinhardtite (Al50Ni40Fe10), Al-bearing trevorite (NiFe2O4) and Al-bearing taenite (FeNi). Laboratory studies of decagonal Al71Ni24Fe5 have shown that it is stable over a narrow range of temperatures, 1120 K to 1200 K at standard pressure, providing support for our earlier conclusion that the Khatyrka meteorite reached heterogeneous high temperatures [1100 < T(K) ≤ 1500] and then rapidly cooled after being heated during an impact-induced shock that occurred in outer space 4.5 Gya. The occurrences of metallic Al alloyed with Cu, Ni, and Fe raises new questions regarding conditions that can be achieved in the early solar nebula.

Icosahedral AlCuFe quasicrystal at high pressure and temperature and its implications for the stability of icosahedrite.

The first natural-occurring quasicrystal, icosahedrite, was recently discovered in the Khatyrka meteorite, a new CV3 carbonaceous chondrite. Its finding raised fundamental questions regarding the effects of pressure and temperature on the kinetic and thermodynamic stability of the quasicrystal structure relative to possible isochemical crystalline or amorphous phases. Although several studies showed the stability at ambient temperature of synthetic icosahedral AlCuFe up to ~35 GPa, the simultaneous effect of temperature and pressure relevant for the formation of icosahedrite has been never investigated so far. Here we present in situ synchrotron X-ray diffraction experiments on synthetic icosahedral AlCuFe using multianvil device to explore possible temperature-induced phase transformations at pressures of 5 GPa and temperature up to 1773 K. Results show the structural stability of i-AlCuFe phase with a negligible effect of pressure on the volumetric thermal expansion properties. In addition, the structural analysis of the recovered sample excludes the transformation of AlCuFe quasicrystalline phase to possible approximant phases, which is in contrast with previous predictions at ambient pressure. Results from this study extend our knowledge on the stability of icosahedral AlCuFe at higher temperature and pressure than previously examined, and provide a new constraint on the stability of icosahedrite.