Open Cone Research Articles

Role of the crown in tree resistance against high winds.

Rather than using wooden sticks to simulate the breakage of trees in high winds as in most research, we employ fresh samples from camphor and Formosa gum with branches and leaves to certify the crucial role of the tree crown. By using a blowdown wind tunnel with a maximum wind speed of 50 m/s, we purposely reduce the number of leaves and show that the drag force will drop by as much as two thirds when half pruned. Based on real observations, we model the leaf by an open and full cone in the presence of light and strong winds, and calculate how their corresponding cross-sectional area A and drag force F vary with wind speed v. Different slopes before and after the formation of a full cone are predicted and confirmed when these two quantities are plotted in full-log scale. Compared to the empirical value, our simple model gave α=2/5 and 2/3 for A∝v^{-α} and β=4/5 and 2/3 for F∝v^{β} at low and high winds. Discrepancies can be accounted for by including further details, such as the reorientation of open cones and the movement of branches.

Ground states of elliptic problems over cones

Given a reflexive Banach space X, we consider a class of functionals \(\Phi \in C^1(X,{\mathbb {R}})\) that do not behave in a uniform way, in the sense that the map \(t \mapsto \Phi (tu)\), \(t>0\), does not have a uniform geometry with respect to \(u\in X\). Assuming instead such a uniform behavior within an open cone \(Y \subset X \setminus \{0\}\), we show that \(\Phi \) has a ground state relative to Y. Some further conditions ensure that this relative ground state is the (absolute) ground state of \(\Phi \). Several applications to elliptic equations and systems are given.

Integral transforms and the regularisation method in the time‐domain excitation of open PEC slotted cone scatterers

An initial-boundary value problem for the transient electromagnetic field in the presence of a complicated-shape scatterer is studied. The considered biconical zero-thickness and perfectly conducting surface with periodic longitudinal slots has many special cases, each of which is of separate practical interest. A new analytical-numerical technique is presented that is based on the Mehler–Fock integral transform and the method of analytical regularisation. The source of excitation of the slotted bicone is a radial electric dipole with an arbitrary time dependence on the field. The proposed method makes it possible to obtain an analytical and numerical solution of the problem to carry out a qualitative and numerical analysis, and to study the characteristic features of the main scattering. Due to the use of the method, the initial-boundary value problem is reduced to a Fredholm type of the second kind system of linear algebraic equations (SLAE-2). The dependences of the condition number on the problem parameters and the estimation of the SLAE-2 convergence with larger truncation orders are given. The far-field radiation patterns are plotted for various values of the problem parameters, the behaviour of the near field at the apex of the slotted cone is studied, and the regime of the slot wave propagation is analysed.

Siegel domains over Finsler symmetric cones

Abstract Let Ω be a proper open cone in a real Banach space V. We show that the tube domain V ⊕ i ⁢ Ω {V\oplus i\Omega} over Ω is biholomorphic to a bounded symmetric domain if and only if Ω is a normal linearly homogeneous Finsler symmetric cone, which is equivalent to the condition that V is a unital JB-algebra in an equivalent norm and Ω is the interior of { v 2 : v ∈ V } {\{v^{2}:v\in V\}} .

Evaluating topographic variation as a guide to Cassia crossbill refugia

The Cassia crossbill (Loxia sinesciuris) feeds exclusively on seeds held in serotinous cones of lodgepole pine (Pinus contorta latifolia). Its population, confined to 67 km2 of pine in southern Idaho, declined by ~ 80% between 2003 and 2011 apparently because an increase in the occurrence of hot summer days (≥32 °C) caused the serotinous cones to open and shed their seeds. We hypothesized that the propensity for serotinous cones to open varies across the landscape depending on the maximum temperatures cones experienced. We tested a suite of abiotic variables for predicting the occurrence of open serotinous cones among 1547 trees at 170 sites. The best-supported model indicated that trees with open cones were less frequent on northeastern aspects and as slope increased. Fewer open cones were expected on northeast aspects because they receive less direct solar radiation. However, the decrease in trees with open cones as slope increased on southwest aspects was unexpected. Increased convection on slopes could reduce maximum cone temperatures and account for the decrease of open cones on steeper slopes, regardless of aspects. Although cones are less likely to open on steeper slopes, slopes with southerly aspects are likely the least favorable for pine recruitment and survival. The most favorable sites for both lodgepole pine and the persistence of closed cones are slopes on northeast aspects. Such locations are often dominated by subalpine fir (Abies bifolia). Reforestation of fir-dominated areas with lodgepole pine, therefore, provides a means to expand microclimatic refugia for Cassia crossbills.

Invariant weakly convex cocompact subspaces for surface groups in $A_2$-buildings

This paper deals with non-Archimedean representations of punctured surface groups in $\operatorname {PGL}_3$, associated actions on (not necessarily discrete) Euclidean buildings of type $A_2$, and degenerations of convex real projective structures on surfaces. The main result is that, under good conditions on Fock-Goncharov generalized shear parameters, non-Archimedean representations acting on the Euclidean building preserve a cocompact weakly convex subspace, which is part flat surface and part tree. In particular the eigenvalue and length(s) spectra are given by an explicit finite $A_2$-complex. We use this result to describe degenerations of convex real projective structures on surfaces for an open cone of parameters. The main tool is a geometric interpretation of Fock-Goncharov parameters in $A_2$-buildings.

The Quantitative Influence of Coordinated Halogen Atoms on the Catalytic Performance of Bisiminoacenaphthylnickel Complexes in Ethylene Polymerization.

In experiments, nickel bromine complexes usually show a better catalytic performance in ethylene polymerization compared to their nickel chlorine analogues. Therefore, the present modeling study has been performed to investigate the effect of coordinated halogen atoms on the catalytic performances of two bisiminoacenaphthyl nickel systems, namely, Ni-Br and Ni-Cl. By using the multiple linear regression analysis (MLRA), the catalytic activity can be well predicted by the descriptors of effective net charge (Qeff ) and bite angle (β), with correlation coefficient R2 values over 0.91. Meanwhile, the molecular weights of polyethylene are predicted by the descriptors of Qeff and open cone angle (θ). The calculated contributions of each descriptor show that the electronic effect is the predominant factor in Ni-Br system, while the steric effect becomes the dominant factor in Ni-Cl system. The different determined effect is expected to the main reason for the different catalytic performance between two Ni systems.

Non-forking and preservation of NIP and dp-rank

We investigate the question of whether the restriction of an NIP type p∈S(B) which does not fork over A⊆B to A is also NIP, and the analogous question for dp-rank. We show that if B contains a Morley sequence I generated by p over A, then p↾AI is NIP and similarly preserves the dp-rank. This yields positive answers for generically stable NIP types and the analogous case of stable types. With similar techniques we also provide a new more direct proof for the latter. Moreover, we introduce a general construction of “trees whose open cones are models of some theory” and in particular an inp-minimal theory DTR of dense trees with random graphs on open cones, which exemplifies a negative answer to the question.

Imploded cross-sections

In this survey article, we describe imploded cross-sections, which were developed in order to solve the problem that the cross-section of a Hamiltonian K-space is usually not symplectic. In some specific examples we contrast the intersection homology of some imploded cross-sections with their homology intersection spaces. Moreover, we compute the homology of intersection spaces associated to the open cone of a simply connected, smooth, oriented manifold and the suspension of such a manifold.

The wall-chamber structures of the real Grothendieck groups

For a finite-dimensional algebra A over a field K with n simple modules, the real Grothendieck group K0(projA)R:=K0(projA)⊗ZR≅Rn gives stability conditions of King. We study the associated wall-chamber structure of K0(projA)R by using the Koenig–Yang correspondences in silting theory. First, we introduce an equivalence relation on K0(projA)R called TF equivalence by using numerical torsion pairs of Baumann–Kamnitzer–Tingley. Second, we show that the open cone in K0(projA)R spanned by the g-vectors of each 2-term silting object gives a TF equivalence class, and this gives a one-to-one correspondence between the basic 2-term silting objects and the TF equivalence classes of full dimension. Finally, we determine the wall-chamber structure of K0(projA)R in the case that A is a path algebra of an acyclic quiver.

Towards a simple and reliable method for calculating uplift capacity of plate anchors in sand

This paper investigates the uplift capacity of horizontal plate anchors in sand through finite element analyses and centrifuge experiments. The finite element simulations adopt a sophisticated bounding surface plasticity model that accounts for stress- and density-dependent behaviour, as well as loading- and fabric-related anisotropic effects in sands. Failure mechanisms at peak anchor capacity show that failure occurs progressively, with a marked decrease in mobilised friction angle within the shear bands close to the anchor edge. Numerical simulations of a large set of centrifuge experiments on rectangular, strip, and circular plates at different relative densities and stress levels are in good agreement for dense conditions, but perform more poorly for loose conditions due mainly to the open cone yield surface in the bounding surface model. Equivalent comparisons with current limit equilibrium methods highlight the challenges in direct application of element-level strength equations. Finally, the paper proposes a modified limit equilibrium solution based on a “rigid-block” failure mechanism extending to the soil surface, but with anchor factors that encompass the results from the finite element simulations. The modified solution provides a higher level of agreement with results from a large database of plate and pipeline test data than existing limit equilibrium methods.

Sobolev inequalities with jointly concave weights on convex cones

Using optimal mass transport arguments, we prove weighted Sobolev inequalities of the form ∫ E | u ( x ) | q ω ( x ) d x 1 / q ⩽ K 0 ∫ E | ∇ u ( x ) | p σ ( x ) d x 1 / p , u ∈ C 0 ∞ ( R n ) , (WSI)where p ⩾ 1 and q > 0 is the corresponding Sobolev critical exponent. Here E ⊆ R n is an open convex cone, and ω , σ : E → ( 0 , ∞ ) are two homogeneous weights verifying a general concavity-type structural condition. The constant K 0 = K 0 ( n , p , q , ω , σ ) > 0 is given by an explicit formula. Under mild regularity assumptions on the weights, we also prove that K 0 is optimal in (WSI) if and only if ω and σ are equal up to a multiplicative factor. Several previously known results, including the cases for monomials and radial weights, are covered by our statement. Further examples and applications to partial differential equations are also provided.

A comparison of the influence of synthesis methods on the photocatalytic activity of nitrogen doped titania-carbon nanotube nanohybrids

The effect of the solgel and hydrothermal synthesis methods on the physicochemical properties and photocatalytic activity of nanohybrids consisting of nitrogen-doped TiO2 supported on varying ammounts (0 – 5 wt.%) of oxidized carbon nanotubes (NTiO2–oxCNT) are compared. Hydrothermal synthesis promotes the formation of cylindrical pores independent of oxCNT content while solgel synthesis results in closed pores which transition to an open cone shape upon incorporation of oxCNTs. The point of zero charge for the nanohybrids is in the acidic range. Hydrothermally synthesized nanohybrids demonstrated high photocatalytic decolorization (up to 99.8 %) of Reactive red 120 (RR 120) than their solgel-synthesized counterparts (up to 93.1 %). A 97.4 % decolorization and 84 % TOC removal was achieved by the nanohybrid NTiO2–oxCNT 5 wt.% oxCNT (5H) at 30 ppm RR 120. The LC−OCD-OND technique demonstrates that the nanohybrid (5H) is selective for the degradation of the biopolymers and low molecular weight neutrals in real industrial textile wastewater under 150 min under visible light.

PiC-code KARAT simulation of coherent Cherenkov radiation from a bunch passing through a hollow conical target

In the report we present simulation results for angular distributions of the radiation as well as spectral distributions obtained by the PiC code KARAT for the conditions of the experiment [1]. We show that for strict satisfaction of the condition θcone=θCR/2 (θcone is an opening cone angle, θCR=arcos 1/βn) is the Cherenkov angle, β =v/c, n is a refractive index) a propagating radiation beam is retained a hollow structure for distances much larger than a radiator length. We simulated “radii” of such a structure at different distances from an exit radiator surface and estimated a divergence of the Cherenkov radiation (CR) beam.

Von Neumann Entropy in QFT

In the framework of Quantum Field Theory, we provide a rigorous, operator algebraic notion of entanglement entropy associated with a pair of open double cones $O \subset \tilde O$ of the spacetime, where the closure of $O$ is contained in $\tilde O$. Given a QFT net $A$ of local von Neumann algebras $A(O)$, we consider the von Neumann entropy $S_A(O, \tilde O)$ of the restriction of the vacuum state to the canonical intermediate type $I$ factor for the inclusion of von Neumann algebras $A(O)\subset A(\tilde O)$ (split property). We show that this canonical entanglement entropy $S_A(O, \tilde O)$ is finite for the chiral conformal net on the circle generated by finitely many free Fermions (here double cones are intervals). To this end, we first study the notion of von Neumann entropy of a closed real linear subspace of a complex Hilbert space, that we then estimate for the local free fermion subspaces. We further consider the lower entanglement entropy $\underline S_A(O, \tilde O)$, the infimum of the vacuum von Neumann entropy of $F$, where $F$ here runs over all the intermediate, discrete type $I$ von Neumann algebras. We prove that $\underline S_A(O, \tilde O)$ is finite for the local chiral conformal net generated by finitely many commuting $U(1)$-currents.

Synthesis, Crystal Structure, and Biological Activity of a Multidentate Calix[4]arene Ligand Doubly Functionalized by 2-Hydroxybenzeledene-Thiosemicarbazone.

The design and synthesis of a novel tert-butyl-calix[4]arene functionalized at 1, 3 positions of the lower rim with two terminal 2-hydroxybenzeledene-thiosemicarbazone moieties is reported. The new ligand with multi-dentate chelating properties was fully characterized by several techniques: ESI-Mass spectroscopy, FT-IR, 1H-NMR, and single crystal X-ray diffraction. The solid state structure confirms that the calix[4]arene macrocycle has the expected open cone conformation, with two opposite phenyl rings inclined outwards with large angles. The conformation of the two alkoxythiosemicarbazone arms produces a molecule with a C2 point group symmetry. An interesting chiral helicity is observed, with the two thiosemicarbazone groups oriented in opposite directions like a two-blade propeller. A water molecule is encapsulated in the center of the two-blade propeller through multiple H-bond coordinations. The antibacterial, antifungal, anticancer, and cytotoxic activities of the calix[4]arene-thiosemicarbazone ligand and its metal derivatives (Co2+, Ni2+, Cu2+, and Zn2+) were investigated. A considerable antibacterial activity (in particular against E. coli, MIC, and MBC = 31.25 μg/mL) was observed for the ligand and its metal derivatives. Significant antifungal activities against yeast (C. albicans) were also observed for the ligand (MIC = 31.25 μg/mL and MBC = 125 μg/mL) and for its Co2+ derivative (MIC = 62.5 μg/mL). All compounds show cytotoxicity against the tested cancerous cells. For the Saos-2 cell line, the promising anticancer activity of ligand L (IC50 < 25 μg/mL) is higher than its metal derivatives. The microscopic analysis of DAPI-stained cells shows that the treated cells change in morphology, with deformation and fragmentation of the nuclei. The hemo-compatibility study demonstrated that this class of compounds are suitable candidates for further in vivo investigations.

The Gromov-Hausdorff hyperspace of a Euclidean space

We investigate the hyperspace GH(Rn) of the isometry classes of all non-empty compact subsets of a Euclidean space in the Gromov-Hausdorff metric. It is proved that for any n≥1, GH(Rn) is homeomorphic to the orbit space 2Rn/E(n) of the hyperspace 2Rn of all non-empty compact subsets of a Euclidean space Rn equipped with the Hausdorff metric and the natural action of the Euclidean group E(n). This is further applied to prove that 2Rn/E(n) is homeomorphic to the open cone OCone(Ch(Bn)/O(n)), where Ch(Bn) stands for the set of all A∈2Rn for which the closed Euclidean unit ball Bn is the least circumscribed ball (the Chebyshev ball). These results lead to determine the complete topological structure of GH(Rn) for n≤2, namely, we prove that GH(Rn) is homeomorphic to the Hilbert cube with a removed point. We also prove that for n≤2, GH(Bn) is homeomorphic to the Hilbert cube.

On the Letac-Massam conjecture and existence of high dimensional Bayes estimators for graphical models

The Wishart distribution defined on the open cone of positive-definite matrices plays a central role in multivariate analysis and multivariate distribution theory. Its domain of parameters is often referred to as the Gindikin set. In recent years, varieties of useful extensions of the Wishart distribution have been proposed in the literature for the purposes of studying Markov random fields and graphical models. In particular, generalizations of the Wishart distribution, referred to as Type I and Type II (graphical) Wishart distributions introduced by Letac and Massam in Annals of Statistics (2007) play important roles in both frequentist and Bayesian inference for Gaussian graphical models. These distributions have been especially useful in high-dimensional settings due to the flexibility offered by their multiple-shape parameters. Concerning Type I and Type II Wishart distributions, a conjecture of Letac and Massam concerns the domain of multiple-shape parameters of these distributions. The conjecture also has implications for the existence of Bayes estimators corresponding to these high dimensional priors. The conjecture, which was first posed in the Annals of Statistics, has now been an open problem for about 10 years. In this paper, we give a necessary condition for the Letac and Massam conjecture to hold. More precisely, we prove that if the Letac and Massam conjecture holds on a decomposable graph, then no two separators of the graph can be nested within each other. For this, we analyze Type I and Type II Wishart distributions on appropriate Markov equivalent perfect DAG models and succeed in deriving the aforementioned necessary condition. This condition in particular identifies a class of counterexamples to the conjecture.

Morphological study of damage evolution in woven-laminates subjected to high-velocity impact

The aim of this experimental work was to study the evolution of damage in woven E-glass fiber/polyester laminates of four different thicknesses. After being impacted, these plates were inspected by nondestructive inspection techniques: ultrasound by C-Scan and B-Scan and visual inspection in order to confirm the qualitative and quantitative results. The damage presented an opening cone shape towards the rear face of thin laminates. On the other hand, two different opening cones of delamination grew towards the front and rear faces after a certain thickness in thick laminates.

X-ray crystallography and molecular dynamics studies of the inclusion complexes of geraniol in β-cyclodextrin, heptakis (2,6-di-O-methyl)-β-cyclodextrin and heptakis (2,3,6-tri-O-methyl)-β-cyclodextrin

Abstract The inclusion of the linear monoterpene, geraniol (gr) in β-cyclodextrin (β-CD), heptakis(2,6-di-O-methyl)-β-cyclodextrin (DM-β-CD) and heptakis(2,3,6-tri-O-methyl)-β-cyclodextrin (TM-β-CD) has been studied by X-ray crystallography and Molecular Dynamics simulations. The gr/β-CD complex crystallizes as a head-to-head dimer in the P21 space group stacking along the crystallographic a-axis in a channel packing mode. Two guest molecules are accommodated almost axially inside the dimeric cavity with their aliphatic ends laying in the interface region of the dimer facing each other and their hydroxylic ends protruding from the narrow β-CD rims. The guest molecules of the adjacent dimers in a channel are interconnected via CH ⋯O and hydrogen bonds forming an internal wire. Both the gr/DM-β-CD and gr/TM-β-CD complexes crystallize in the P212121 space group and stack along the crystallographic b-axis in a head-to-tail manner. DM-β-CD host adopts the conformation of a rigid and well-shaped open cone upon complexation, in which the guest molecule is found highly disordered over 5 sites with varying depths of immersion. The gr/DM-β-CD complex units are arranged in channels and the gr molecules within these channels are also interconnected via CH ⋯O bonds. On the other hand, TM-β-CD host is found severely distorted adopting a ‘closed’ cup-shaped conformation. The guest is partially encapsulated in the wide rim of TM-β-CD and it is found disordered over 3 sites with quite different orientations. The complex units are arranged forming screw channels, with the main part of the guest laying outside the host cavity and filling the intermediate space between the succeeding hosts. The MD analysis based on the crystallographically determined structures sheds light on the dynamic behavior of the geraniol upon complexation with these hosts, its conformation variations and the interconversion of the inclusion modes in solution. Finally, MM/GBSA-calculations revealed that the ascending order in binding affinity ΔG values is: gr/TM-β-CD