Coincidence Problem in Cyclic Phantom Models of the Universe

We examine cyclic phantom models for the universe, in which the universe is dominated sequentially by radiation, matter, and a phantom dark energy field, followed by a standard inflationary phase. Since this cycle repeats endlessly, the Universe spends a substantial portion of its lifetime in a state for which the matter and dark energy densities have comparable magnitudes, thus ameliorating the coincidence problem. We calculate the fraction of time that the universe spends in such a coincidental state and find that it is nearly the same as in the case of a phantom model with a future big rip. In the limit where the dark energy equation of state parameter, w, is close to -1, we show that the fraction of time, f, for which the ratio of the dark energy density to the matter density lies between r_1 and r_2, is f = -(1+w) ln [(\sqrt{r_2} + \sqrt{1+r_2})/(\sqrt{r_1} + \sqrt{1+r_1})].Comment: 4 pages, no figures, discussion and references adde

Contractual Versus Non-Contractual Trade: The Role of Institutions in China

Recent research has demonstrated the importance of institutional quality at the country level for both the volume of trade and the ability to trade in differentiated goods that rely on contract enforcement. This paper takes advantage of cross-provincial variation in institutional quality in China, and export data that distinguishes between foreign and domestic exporters and processing versus ordinary trade, to show that institutional quality is a significant factor in determining Chinese provincial export patterns. Institutions matter more for processing trade, and more for foreign firms, just as we would expect from a greater reliance on contracts in these cases.

Exact Potts Model Partition Functions for Strips of the Honeycomb Lattice

We present exact calculations of the Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature-like variable $v$ on $n$-vertex strip graphs $G$ of the honeycomb lattice for a variety of transverse widths equal to $L_y$ vertices and for arbitrarily great length, with free longitudinal boundary conditions and free and periodic transverse boundary conditions. These partition functions have the form $Z(G,q,v)=\sum_{j=1}^{N_{Z,G,\lambda}} c_{Z,G,j}(\lambda_{Z,G,j})^m$, where $m$ denotes the number of repeated subgraphs in the longitudinal direction. We give general formulas for $N_{Z,G,j}$ for arbitrary $L_y$. We also present plots of zeros of the partition function in the $q$ plane for various values of $v$ and in the $v$ plane for various values of $q$. Explicit results for partition functions are given in the text for $L_y=2,3$ (free) and $L_y=4$ (cylindrical), and plots of partition function zeros are given for $L_y$ up to 5 (free) and $L_y=6$ (cylindrical). Plots of the internal energy and specific heat per site for infinite-length strips are also presented.Comment: 39 pages, 34 eps figures, 3 sty file

2,2-Bis[(2-halo-4-aminophenoxy)phenyl]-hexafluoropropane

There are provided the aromatic diamines 2,2-bis-[(2-halo-4-aminophenoxy)-phenyl]hexafluoropropane, where the attached ortho halogen is preferably chlorine, and 4,4'-bis(4-aminophenoxy)biphenyl, as novel monomers for polyimide polymerizations. The former, when reacted with 2,2-bis(3,4-dicarboxyphenyl)hexafluoropropane dianhydride, provides a polyimide having exceptional high-temperature performance. The latter diamine is a low-cost monomer for polyimide production

High-temperature polyimides prepared from 2,2-bis-[(2-halo-4-aminophenoxy)-phenyl]hexafluoropropane

There are provided the aromatic diamines 2,2-bis-[(2-halo-4-aminophenoxy)-phenyl]hexafluoropropane, where the attached ortho halogen is preferably chlorine, and 4,4'-bis(4-aminophenoxy)biphenyl, as novel monomers for polyimide polymerizations. The former, when reacted with 2,2-bis(3,4-dicarboxyphenyl)hexafluoropropane dianhydride, provides a polyimide having exceptional high-temperature performance. The latter diamine is a low-cost monomer for polyimide production

Fiber reinforced thermoplastic resin matrix composites

Polyimide polymer composites having a combination of enhanced thermal and mechanical properties even when subjected to service temperatures as high as 700.degree. F. are described. They comprise (a) from 10 to 50 parts by weight of a thermoplastic polyimide resin prepared from 2,2-bis[4-(4-aminophenoxy)phenyl]hexafluoropropane and (b) from 90 to 50 parts by weight of continuous reinforcing fibers, the total of (a) and (b) being 100 parts by weight. Composites based on polyimide resin formed from 2,2-bis[4-(4-aminophenoxy)phenyl]hexafluoropropane and pyromellitic dianhydride and continuous carbon fibers retained at least about 50% of their room temperature shear strength after exposure to 700.degree. F. for a period of 16 hours in flowing air. Preferably, the thermoplastic polyimide resin is formed in situ in the composite material by thermal imidization of a corresponding amide-acid polymer prepared from 2,2-bis[4-(4-aminophenoxy)phenyl]hexafluoropropane. It is also preferred to initially size the continuous reinforcing fibers with up to about one percent by weight of an amide-acid polymer prepared from 2,2-bis[4-(4-aminophenoxy)phenyl]hexafluoropropane. In this way imidization at a suitable elevated temperature results in the in-situ formation of a substantially homogeneous thermoplastic matrix of the polyimide resin tightly and intimately bonded to the continuous fibers. The resultant composites tend to have optimum thermo-mechanical properties

Prediction of Nontrivial Band Topology and Superconductivity in Mg2_2Pb

The interplay of BCS superconductivity and nontrivial band topology is expected to give rise to opportunities for creating topological superconductors, achieved through pairing spin-filtered boundary modes via superconducting proximity effects. The thus-engineered topological superconductivity can, for example, facilitate the search for Majorana fermion quasiparticles in condensed matter systems. Here we report a first-principles study of Mg$_2$Pb and predict that it should be a superconducting topological material. The band topology of Mg$_2$Pb is identical to that of the archetypal quantum spin Hall insulator HgTe, while isostructural and isoelectronic Mg$_2$Sn is topologically trivial; a trivial to topological transition is predicted for Mg$_2$Sn$_{1-x}$Pb$_x$ for x~0.77. We propose that Mg$_2$Pb-Mg$_2$Sn quantum wells should generate robust spin-filtered edge currents in analogy to HgTe/CdTe quantum wells. In addition, our calculations predict that Mg$_2$Pb should become superconducting upon electron doping. Therefore, Mg$_2$Pb is expected to provide a practical material platform for studying emergent phenomena arising from the interplay of superconductivity and band topology.Comment: 5 figure

Photoluminescence modification by high-order photonic band with abnormal dispersion in ZnO inverse opal

We measured the angle- and polarization-resolved reflection and photoluminescence spectra of ZnO inverse opals. Significant enhancement of spontaneous emission is observed. The enhanced emission not only has good directionality but also can be linearly polarized. A detailed theoretical analysis and numerical simulation reveal that such enhancement is caused by the abnormal dispersion of a high-order photonic band. The frozen mode at a stationary inflection point of a dispersion curve can strongly modify the intensity, directionality and polarization of spontaneous emission.Comment: 22 pages, 11 figures, figures modified, references added, more explanation adde