The evolution of cosmic string loops in Kerr-de Sitter spacetimes

The equation of cosmic string loops in Kerr-de Sitter spacetimes is derived. Having solved the equation numerically, we find that the loops can expand and exist except for too small ones.Comment: 8 page

High resolution micro arthrography of hard and soft tissues in a murine model

SummaryObjectiveRecent developments on high resolution micro computed tomography (μCT) allow imaging of soft tissues in small animal joints. Nevertheless, μCT images cannot distinguish soft tissues from synovial fluid due to their similar mass density, limiting the 3D assessment of soft tissues volume and thickness. This study aimed to evaluate a lead chromate contrast agent for μCΤ arthrography of rat knee joints ex vivo.DesignIntact tibiofemoral rat joints were injected with the contrast agent at different concentrations and imaged using a μCT at 2.7 μm isotropic voxel size. Cartilage thickness was measured using an automated procedure, validated against histological measurements, and analyzed as a function of μCT image resolution. Changes in hard and soft tissues were also analyzed in tibiofemoral joints 4 weeks after surgical destabilization of the medial meniscus (DMM).ResultsThe contrast agent diffused well throughout the whole knee cavity without penetrating the tissues, therefore providing high contrast at the boundaries between soft tissues and synovial fluid space. Thickness analysis of cartilage demonstrated a high similarity between histology and μ-arthrography approaches (R2 = 0.90). Four weeks after surgical DMM, the development of osteophytes (Oph) and cartilage ulcerations was recognizable with μCT, as well as a slight increase in trabecular bone porosity, and decrease in trabecular thickness.ConclusionsA lead chromate-based contrast agent allowed discriminating the synovial fluid from soft tissues of intact knee joints, and thus made possible both qualitative and quantitative assessment of hard and soft tissues in both intact and DMM tibiofemoral joints using high resolution μCT

Tensor network states and geometry

Tensor network states are used to approximate ground states of local Hamiltonians on a lattice in D spatial dimensions. Different types of tensor network states can be seen to generate different geometries. Matrix product states (MPS) in D=1 dimensions, as well as projected entangled pair states (PEPS) in D>1 dimensions, reproduce the D-dimensional physical geometry of the lattice model; in contrast, the multi-scale entanglement renormalization ansatz (MERA) generates a (D+1)-dimensional holographic geometry. Here we focus on homogeneous tensor networks, where all the tensors in the network are copies of the same tensor, and argue that certain structural properties of the resulting many-body states are preconditioned by the geometry of the tensor network and are therefore largely independent of the choice of variational parameters. Indeed, the asymptotic decay of correlations in homogeneous MPS and MERA for D=1 systems is seen to be determined by the structure of geodesics in the physical and holographic geometries, respectively; whereas the asymptotic scaling of entanglement entropy is seen to always obey a simple boundary law -- that is, again in the relevant geometry. This geometrical interpretation offers a simple and unifying framework to understand the structural properties of, and helps clarify the relation between, different tensor network states. In addition, it has recently motivated the branching MERA, a generalization of the MERA capable of reproducing violations of the entropic boundary law in D>1 dimensions.Comment: 18 pages, 18 figure

Block Spin Density Matrix of the Inhomogeneous AKLT Model

We study the inhomogeneous generalization of a 1-dimensional AKLT spin chain model. Spins at each lattice site could be different. Under certain conditions, the ground state of this AKLT model is unique and is described by the Valence-Bond-Solid (VBS) state. We calculate the density matrix of a contiguous block of bulk spins in this ground state. The density matrix is independent of spins outside the block. It is diagonalized and shown to be a projector onto a subspace. We prove that for large block the density matrix behaves as the identity in the subspace. The von Neumann entropy coincides with Renyi entropy and is equal to the saturated value.Comment: 20 page

Effect of large strain on dielectric and ferroelectric properties of Ba0.5Sr0.5TiO3 thin films

BaxSr1−xTiO3 is ideally suited as a tunable medium for radio frequency passive component. In this context we have studied the effect of biaxial strain on the dielectric and ferroelectricproperties of Ba0.5Sr0.5TiO3thin filmsgrown epitaxially on SrTiO3 (001) substrates. The lattice parameters of the films determined by high-resolution x-ray diffraction with the thickness varying from 160 to 1000 nm indicated large biaxial compressive strain which decreased from 2.54% to 1.14% with increasing film thickness. Temperature-dependent measurements of the dielectric constant in our strained Ba0.5Sr0.5TiO3thin films revealed a significant increase in the Curie temperature as the film thickness is below 500 nm. Enhanced ferroelectric behavior was observed for highly strained films with a remanent polarization of 15 μC/cm2 in the 160-nm-thick layer. However, the thick films(≥500 nm) exhibited weak temperature dependence of the dielectric constant without any pronounced peak corresponding to the Curie temperature, which may suggest inhomogeneous strain distribution in the thick films

Entanglement and Density Matrix of a Block of Spins in AKLT Model

We study a 1-dimensional AKLT spin chain, consisting of spins $S$ in the bulk and $S/2$ at both ends. The unique ground state of this AKLT model is described by the Valence-Bond-Solid (VBS) state. We investigate the density matrix of a contiguous block of bulk spins in this ground state. It is shown that the density matrix is a projector onto a subspace of dimension $(S+1)^{2}$. This subspace is described by non-zero eigenvalues and corresponding eigenvectors of the density matrix. We prove that for large block the von Neumann entropy coincides with Renyi entropy and is equal to $\ln(S+1)^{2}$.Comment: Revised version, typos corrected, references added, 31 page

Effective local connectivity properties

We investigate, and prove equivalent, effective versions of local connectivity and uniformly local arcwise connectivity for connected and computably compact subspaces of Euclidean space. We also prove that Euclidean continua that are computably compact and effectively locally connected are computably arcwise connected.Comment: Final versio

Nutrient cycling in bedform induced hyporheic zones

The hyporheic zone is an ecotone connecting the stream and groundwater ecosystem that plays a significant role for stream biogeochemistry. Water exchange across the stream-sediment interface and biogeochemical reactions in the streambed concur to affect subsurface solute concentrations and eventually nutrient cycling in the fluvial corridor. In this paper we investigate the interplay of hydrological and biogeochemical processes in a duned streambed and their effect on spatial distribution of solutes. We employ a numerical model to simulate the turbulent water flow and the pressure distribution over the dunes, and then to evaluate the flow field and the biogeochemical reactions in the hyporheic sediments. Sensitivity analyses are performed to analyze the influence of hydrological and chemical properties of the system on solute reaction rates. The results demonstrate the effect of stream velocity and sediment permeability on the chemical zonation. Changing sediment permeability as well as stream velocity directly affects the nutrient supply and the residence times in the streambed, thus controlling the reaction rates under the dune. Stream-water quality is also shown to influence the reactive behavior of the sediments. In particular, the availability of dissolved organic carbon determines whether the streambed acts as a net sink or source of nitrate. This study represents a step towards a better understanding of the complex interactions between hydrodynamical and biogeochemical processes in the hyporheic zon

The circular loop equation of a cosmic string with time-varying tension in de Sitter spacetimes

In this work the equation of circular loops of cosmic string possessing time-dependent tension is studied in the de Sitter spacetime. We find that the cosmic string loops with initial radius $r(t_{0})>0.707L$, L de Sitter radius, should not collapse to form a black holes. It is also found that in the case of $r(t_{0})<0.707L$ a loop of cosmic string whose tension depends on some power of cosmic time can not become a black hole if the power is lower than a critical value which is associated with the initial size of the loop.Comment: 6 page