Homotopy Theory of Strong and Weak Topological Insulators

We use homotopy theory to extend the notion of strong and weak topological insulators to the non-stable regime (low numbers of occupied/empty energy bands). We show that for strong topological insulators in d spatial dimensions to be "truly d-dimensional", i.e. not realizable by stacking lower-dimensional insulators, a more restrictive definition of "strong" is required. However, this does not exclude weak topological insulators from being "truly d-dimensional", which we demonstrate by an example. Additionally, we prove some useful technical results, including the homotopy theoretic derivation of the factorization of invariants over the torus into invariants over spheres in the stable regime, as well as the rigorous justification of replacing $T^d$ by $S^d$ and $T^{d_k}\times S^{d_x}$ by $S^{d_k+d_x}$ as is common in the current literature.Comment: 11 pages, 3 figure

Shear-induced reaction-limited aggregation kinetics of Brownian particles at arbitrary concentrations

The aggregation of interacting Brownian particles in sheared concentrated suspensions is an important issue in colloid and soft matter science per se. Also, it serves as a model to understand biochemical reactions occurring in vivo where both crowding and shear play an important role. We present an effective medium approach within the Smoluchowski equation with shear which allows one to calculate the encounter kinetics through a potential barrier under shear at arbitrary colloid concentrations. Experiments on a model colloidal system in simple shear flow support the validity of the model in the range considered. By generalizing Kramers' rate theory to the presence of collective hydrodynamics, our model explains the significant increase in the shear-induced reaction-limited aggregation kinetics upon increasing the colloid concentration

Approximating the monomer-dimer constants through matrix permanent

The monomer-dimer model is fundamental in statistical mechanics. However, it is #P-complete in computation, even for two dimensional problems. A formulation in matrix permanent for the partition function of the monomer-dimer model is proposed in this paper, by transforming the number of all matchings of a bipartite graph into the number of perfect matchings of an extended bipartite graph, which can be given by a matrix permanent. Sequential importance sampling algorithm is applied to compute the permanents. For two-dimensional lattice with periodic condition, we obtain $0.6627\pm0.0002$, where the exact value is $h_2=0.662798972834$. For three-dimensional lattice with periodic condition, our numerical result is $0.7847\pm0.0014$, {which agrees with the best known bound $0.7653 \leq h_3 \leq 0.7862$.}Comment: 6 pages, 2 figure

An investigation of standard thermodynamic quantities as determined via models of nuclear multifragmentation

Both simple and sophisticated models are frequently used in an attempt to understand how real nuclei breakup when subjected to large excitation energies, a process known as nuclear multifragmentation. Many of these models assume equilibriumthermodynamics and produce results often interpreted as evidence of a phase transition. This work examines one class of models and employs standard thermodynamical procedure to explore the possible existence and nature of a phase transition. The role of various terms, e.g. Coulomb and surface energy, is discussed.Comment: 19 two-column format pages with 24 figure

The liquid to vapor phase transition in excited nuclei

For many years it has been speculated that excited nuclei would undergo a liquid to vapor phase transition. For even longer, it has been known that clusterization in a vapor carries direct information on the liquid- vapor equilibrium according to Fisher's droplet model. Now the thermal component of the 8 GeV/c pion + 197Au multifragmentation data of the ISiS Collaboration is shown to follow the scaling predicted by Fisher's model, thus providing the strongest evidence yet of the liquid to vapor phase transition.Comment: four pages, four figures, first two in color (corrected typo in Ref. [26], corrected error in Fig. 4

Assumption-free estimation of the genetic contribution to refractive error across childhood

Purpose: Studies in relatives have generally yielded high heritability estimates for refractive error: twins 75–90%, families 15–70%. However, because related individuals often share a common environment, these estimates are inflated (via misallocation of unique/common environment variance). We calculated a lower-bound heritability estimate for refractive error free from such bias. Methods: Between the ages 7 and 15 years, participants in the Avon Longitudinal Study of Parents and Children (ALSPAC) underwent non-cycloplegic autorefraction at regular research clinics. At each age, an estimate of the variance in refractive error explained by single nucleotide polymorphism (SNP) genetic variants was calculated using genome-wide complex trait analysis (GCTA) using high-density genome-wide SNP genotype information (minimum N at each age=3,404). Results: The variance in refractive error explained by the SNPs (“SNP heritability”) was stable over childhood: Across age 7–15 years, SNP heritability averaged 0.28 (SE=0.08,

Effect of chromophore-chromophore electrostatic interactions in the NLO response of functionalized organic-inorganic sol-gel materials

In the last years, important non-linear optical results on sol-gel and polymeric materials have been reported, with values comparable to those found in crystals. These new materials contain push-pull chromophores either incorporated as guest in a high Tg polymeric matrix (doped polymers) or grafted onto the polymeric matrix. These systems present several advantages; however they require significant improvement at the molecular level - by designing optimized chromophores with very large molecular figure of merit, specific to each application targeted. Besides, it was recently stated in polymers that the chromophore-chromophore electrostatic interactions, which are dependent of chromophore concentration, have a strong effect into their non-linear optical properties. This has not been explored at all in sol-gel systems. In this work, the sol-gel route was used to prepare hybrid organic-inorganic thin films with different NLO chromophores grafted into the skeleton matrix. Combining a molecular engineering strategy for getting a larger molecular figure of merit and by controlling the intermolecular dipole-dipole interactions through both: the tuning of the push-pull chromophore concentration and the control of TEOS (Tetraethoxysilane) concentration, we have obtained a r33 coefficient around 15 pm/V at 633 nm for the classical DR1 azo-chromophore and a r33 around 50 pm/V at 831 nm for a new optimized chromophore structure.Comment: 10 pages, 11 figures, 1 tabl

Sensitization and desensitization of burn patients as potential candidates for vascularized composite allotransplantation

Sensitization describes the acquired ability of the immune system to react to foreign human leukocyte antigens (HLA) by producing antibodies and developing memory cells. In the field of transplantation, recipient preformed HLA antibodies due to previous sensitization have been identified - beneath ABO incompatibility - as a major factor for acute graft rejection. Several reasons for sensitization have largely been studied, such as previous blood transfusions, pregnancies or former transplants. Recent studies indicate that the use of assist devices (e.g. ECMO) or cadaveric skin allotransplantation providing temporary coverage in burn patients may lead to additional sensitization. As vascularized composite allotransplantation (VCA) has become a rapidly advancing therapeutic option for reconstruction of complex tissue defects in burns, it seems even more important to become familiar with immunological principles and to be cautiously aware of both sources of sensitization and therapeutic concepts in burns avoiding sensitization. This may also include emergency VCAs in burn patients as potential strategy for early definitive reconstruction avoiding procedures triggering HLA antibody formation. We hereby provide an overview on current evidence in the field of pre- and peritrans-plant sensitization, followed by posttransplant strategies of desensitization and their potential impact on future treatments of burn patients. (C) 2015 Elsevier Ltd and ISBI. All rights reserved.Peer reviewe

The postulates of gravitational thermodynamics

The general principles and logical structure of a thermodynamic formalism that incorporates strongly self-gravitating systems are presented. This framework generalizes and simplifies the formulation of thermodynamics developed by Callen. The definition of extensive variables, the homogeneity properties of intensive parameters, and the fundamental problem of gravitational thermodynamics are discussed in detail. In particular, extensive parameters include quasilocal quantities and are naturally incorporated into a set of basic general postulates for thermodynamics. These include additivity of entropies (Massieu functions) and the generalized second law. Fundamental equations are no longer homogeneous first-order functions of their extensive variables. It is shown that the postulates lead to a formal resolution of the fundamental problem despite non-additivity of extensive parameters and thermodynamic potentials. Therefore, all the results of (gravitational) thermodynamics are an outgrowth of these postulates. The origin and nature of the differences with ordinary thermodynamics are analyzed. Consequences of the formalism include the (spatially) inhomogeneous character of thermodynamic equilibrium states, a reformulation of the Euler equation, and the absence of a Gibbs-Duhem relation.Comment: 28 pages, Revtex, no figures. An important sentence and several minor corrections included. To appear in Physical Review