Locked and Unlocked Chains of Planar Shapes

We extend linkage unfolding results from the well-studied case of polygonal linkages to the more general case of linkages of polygons. More precisely, we consider chains of nonoverlapping rigid planar shapes (Jordan regions) that are hinged together sequentially at rotatable joints. Our goal is to characterize the families of planar shapes that admit locked chains, where some configurations cannot be reached by continuous reconfiguration without self-intersection, and which families of planar shapes guarantee universal foldability, where every chain is guaranteed to have a connected configuration space. Previously, only obtuse triangles were known to admit locked shapes, and only line segments were known to guarantee universal foldability. We show that a surprisingly general family of planar shapes, called slender adornments, guarantees universal foldability: roughly, the distance from each edge along the path along the boundary of the slender adornment to each hinge should be monotone. In contrast, we show that isosceles triangles with any desired apex angle less than 90 degrees admit locked chains, which is precisely the threshold beyond which the inward-normal property no longer holds.Comment: 23 pages, 25 figures, Latex; full journal version with all proof details. (Fixed crash-induced bugs in the abstract.

Dissipative surface solitons in periodic structures

We report dissipative surface solitons forming at the interface between a semi-infinite lattice and a homogeneous Kerr medium. The solitons exist due to balance between amplification in the near-surface lattice channel and two-photon absorption. The stable dissipative surface solitons exist in both focusing and defocusing media, when propagation constants of corresponding states fall into a total semi-infinite and or into one of total finite gaps of the spectrum (i.e. in a domain where propagation of linear waves is inhibited for the both media). In a general situation, the surface solitons form when amplification coefficient exceeds threshold value. When a soliton is formed in a total finite gap there exists also the upper limit for the linear gain.Comment: 5 pages, 3 figures, to appear in Europhysics Letter

3',4'-Dihydroxyflavonol antioxidant attenuates aiastolic dysfunction and cardiac remodeling in streptozotocin-induced diabetic m(Ren2)27 rats

Background Diabetic cardiomyopathy (DCM) is an increasingly recognized cause of chronic heart failure amongst diabetic patients. Both increased reactive oxygen species (ROS) generation and impaired ROS scavenging have been implicated in the pathogenesis of hyperglycemia-induced left ventricular dysfunction, cardiac fibrosis, apoptosis and hypertrophy. We hypothesized that 3',4'-dihydroxyflavonol (DiOHF), a small highly lipid soluble synthetic flavonol, may prevent DCM by scavenging ROS, thus preventing ROS-induced cardiac damage. Methodology/Principal Findings Six week old homozygous Ren-2 rats were randomized to receive either streptozotocin or citrate buffer, then further randomized to receive either DiOHF (1 mg/kg/day) by oral gavage or vehicle for six weeks. Cardiac function was assessed via echocardiography and left ventricular cardiac catheterization before the animals were sacrificed and hearts removed for histological and molecular analyses. Diabetic Ren-2 rats showed evidence of diastolic dysfunction with prolonged deceleration time, reduced E/A ratio, and increased slope of end-diastolic pressure volume relationship (EDPVR) in association with marked interstitial fibrosis and oxidative stress (all P<0.05 vs control Ren-2). Treatment with DiOHF prevented the development of diastolic dysfunction and was associated with reduced oxidative stress and interstitial fibrosis (all P<0.05 vs untreated diabetic Ren-2 rats). In contrast, few changes were seen in non-diabetic treated animals compared to untreated counterparts. Conclusions Inhibition of ROS production and action by DiOHF improved diastolic function and reduced myocyte hypertrophy as well as collagen deposition. These findings suggest the potential clinical utility of antioxidative compounds such as flavonols in the prevention of diabetes-associated cardiac dysfunction

Investigating the Fibrillar Ultrastructure and Mechanics in Keloid Scars Using In Situ Synchrotron X-ray Nanomechanical Imaging

Fibrotic scarring is prevalent in a range of collagenous tissue disorders. Understanding the role of matrix biophysics in contributing to fibrotic progression is important to develop therapies, as well as to elucidate biological mechanisms. Here, we demonstrate how microfocus small-angle X-ray scattering (SAXS), with in situ mechanics and correlative imaging, can provide quantitative and position-resolved information on the fibrotic matrix nanostructure and its mechanical properties. We use as an example the case of keloid scarring in skin. SAXS mapping reveals heterogeneous gradients in collagen fibrillar concentration, fibril pre-strain (variations in D-period) and a new interfibrillar component likely linked to proteoglycans, indicating evidence of a complex 3D structure at the nanoscale. Furthermore, we demonstrate a proof-of-principle for a diffraction-contrast correlative imaging technique, incorporating, for the first time, DIC and SAXS, and providing an initial estimate for measuring spatially resolved fibrillar-level strain and reorientation in such heterogeneous tissues. By application of the method, we quantify (at the microscale) fibrillar reorientations, increases in fibrillar D-period variance, and increases in mean D-period under macroscopic tissue strains of ~20%. Our results open the opportunity of using synchrotron X-ray nanomechanical imaging as a quantitative tool to probe structure–function relations in keloid and other fibrotic disorders in situ

Volumes of polytopes in spaces of constant curvature

We overview the volume calculations for polyhedra in Euclidean, spherical and hyperbolic spaces. We prove the Sforza formula for the volume of an arbitrary tetrahedron in $H^3$ and $S^3$. We also present some results, which provide a solution for Seidel problem on the volume of non-Euclidean tetrahedron. Finally, we consider a convex hyperbolic quadrilateral inscribed in a circle, horocycle or one branch of equidistant curve. This is a natural hyperbolic analog of the cyclic quadrilateral in the Euclidean plane. We find a few versions of the Brahmagupta formula for the area of such quadrilateral. We also present a formula for the area of a hyperbolic trapezoid.Comment: 22 pages, 9 figures, 58 reference

A review of thermal absorbers and their integration methods for the combined solar photovoltaic/thermal (PV/T) modules

Thermal absorbers and their integration methods are critical to solar photovoltaic/thermal (PV/T) modules. These two elements directly influence the cooling effort of PV layers and as a result, the related electrical/thermal/overall efficiency. This paper conducts a critical review on the essential thermal absorbers and their integration methods for the currently-available PV modules for the purpose of producing the combined PV/T modules. A brief overview of different PV/T technologies is initially summarized, including aspects of their structure, efficiencies, thermal governing expressions and their applications. Seven different types of thermal absorbers and four corresponding integration methods are subsequently discussed and summarized in terms of their advantages/disadvantages and the associated application for various PV/T modules. Compared to traditional thermal absorbers, such as sheet-and-tube structure, rectangular tunnel with or without fins/grooves and flat-plate tube, these four types, i.e. micro-channel heat pipe array/heat mat, extruded heat exchanger, roll-bond heat exchanger and cotton wick structure, are promising due to the significant enhancement in terms of efficiency, structure, weight, and cost etc. The appropriate or suitable integration method varies in different cases, i.e. the ethylene-vinyl acetate (EVA) based lamination method seems the best option for integration of PV layer with thermal absorber when compared with other conventional methods, such as direct contact, thermal adhesive and mechanical fixing. Finally, suggestions for further research topics are proposed from five aspects. The overall research results would provide useful information for the assistance of further development of solar PV/T modules with high feasibility for widespread application in energy supply even at district or city-level in the near future

Excitation cross section of erbium-doped GaN waveguides under 980 nm optical pumping

This is the published version. Copyright 2015 American Institute of PhysicsExcitation cross section of erbium-doped GaN waveguides is measured to be approximately 2.2×10−21cm2 at 980 nm pumping wavelength. This cross section value is found relatively insensitive to the crystalline quality of epilayers. However, spontaneous emission carrier lifetimes in these waveguides are directly related to both the crystalline quality and the optical loss, and thus can be used as a material quality indicator

Carrier lifetime in erbium-doped GaN waveguide emitting in 1540 nm wavelength

This is the published version. Copyright 2010 American Institute of PhysicsWe report the characteristics of an erbium-doped GaNsemiconductorwaveguideamplifier grown by metal-organic chemical vapor deposition. We demonstrated that both 980 and 1480 nm optical pumping were efficient to create population inversion between the I413/2 and I415/2 energy levels. The carrier lifetime in the I413/2 energy band was measured to be approximately 1.5 ms in room temperature, which is slightly shorter than that in erbium-doped silica due to the interaction between the erbium ions and the semiconductor lattice structure. But it is significantly longer than the carrier lifetime in a typical semiconductor optical amplifier which is in the nanosecond regime

First-Principles Dynamical Coherent-Potential Approximation Approach to the Ferromagnetism of Fe, Co, and Ni

Magnetic properties of Fe, Co, and Ni at finite temperatures have been investigated on the basis of the first-principles dynamical CPA (Coherent Potential Approximation) combined with the LDA (Local Density Approximation) + $U$ Hamiltonian in the Tight-Binding Linear Muffintin Orbital (TB-LMTO) representation. The Hamiltonian includes the transverse spin fluctuation terms. Numerical calculations have been performed within the harmonic approximation with 4th-order dynamical corrections. Calculated single-particle densities of states in the ferromagnetic state indicate that the dynamical effects reduce the exchange splitting, suppress the band width of the quasi-particle state, and causes incoherent excitations corresponding the 6 eV satellites. Results of the magnetization vs temperature curves, paramagnetic spin susceptibilities, and the amplitudes of local moments are presented. Calculated Curie temperatures ($T_{\rm C}$) are reported to be 1930K for Fe, 2550K for Co, and 620K for Ni; $T_{\rm C}$ for Fe and Co are overestimated by a factor of 1.8, while $T_{\rm C}$ in Ni agrees with the experimental result. Effective Bohr magneton numbers calculated from the inverse susceptibilities are 3.0 $\mu_{\rm B}$ (Fe), 3.0 $\mu_{\rm B}$ (Co), and 1.6 $\mu_{\rm B}$ (Ni), being in agreement with the experimental ones. Overestimate of $T_{\rm C}$ in Fe and Co is attributed to the neglects of the higher-order dynamical effects as well as the magnetic short range order.Comment: 10 pages, 13 figure