scholarly journals A Generalized Cubic Exponential B-Spline Scheme with Shape Control

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Baoxing Zhang ◽  
Hongchan Zheng ◽  
Lulu Pan

In this paper, a generalized cubic exponential B-spline scheme is presented, which can generate different kinds of curves, including the conics. Such a scheme is obtained by generalizing the cubic exponential B-spline scheme based on an iteration from the generation of exponential polynomials and a suitable function with two parameters μ and ν. By changing the values of μ and ν, the sensitivity of the shape of the subdivision curve to the initial control value v0 can be changed and different kinds of curves can then be obtained by adjusting the value of v0. For this new scheme, we show that, with any admissible choice of μ and ν, it owns the same smoothness order and support as the cubic exponential B-spline scheme. Besides, based on a different iteration and another suitable function, we construct a similar nonstationary scheme to generate more curves with different shapes and show the role of iterations and suitably chosen functions in the construction and analysis of such schemes. Several examples are given to illustrate the performance of our new schemes.

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3116
Author(s):  
Baoxing Zhang ◽  
Hongchan Zheng

This paper presents a variant scheme of the cubic exponential B-spline scheme, which, with two parameters, can generate curves with different shapes. This variant scheme is obtained based on the iteration from the generation of exponentials and a suitably chosen function. For such a scheme, we show its C2-convergence and analyze the effect of the parameters on the shape of the generated curves and also discuss its convexity preservation. In addition, a non-uniform version of this variant scheme is derived in order to locally control the shape of the generated curves. Numerical examples are given to illustrate the performance of the new schemes in this paper.


2020 ◽  
Vol 10 (1) ◽  
pp. 110-123
Author(s):  
Gaël Kermarrec ◽  
Hamza Alkhatib

Abstract B-spline curves are a linear combination of control points (CP) and B-spline basis functions. They satisfy the strong convex hull property and have a fine and local shape control as changing one CP affects the curve locally, whereas the total number of CP has a more general effect on the control polygon of the spline. Information criteria (IC), such as Akaike IC (AIC) and Bayesian IC (BIC), provide a way to determine an optimal number of CP so that the B-spline approximation fits optimally in a least-squares (LS) sense with scattered and noisy observations. These criteria are based on the log-likelihood of the models and assume often that the error term is independent and identically distributed. This assumption is strong and accounts neither for heteroscedasticity nor for correlations. Thus, such effects have to be considered to avoid under-or overfitting of the observations in the LS adjustment, i.e. bad approximation or noise approximation, respectively. In this contribution, we introduce generalized versions of the BIC derived using the concept of quasi- likelihood estimator (QLE). Our own extensions of the generalized BIC criteria account (i) explicitly for model misspecifications and complexity (ii) and additionally for the correlations of the residuals. To that aim, the correlation model of the residuals is assumed to correspond to a first order autoregressive process AR(1). We apply our general derivations to the specific case of B-spline approximations of curves and surfaces, and couple the information given by the different IC together. Consecutively, a didactical yet simple procedure to interpret the results given by the IC is provided in order to identify an optimal number of parameters to estimate in case of correlated observations. A concrete case study using observations from a bridge scanned with a Terrestrial Laser Scanner (TLS) highlights the proposed procedure.


Author(s):  
Emanuele Roccia ◽  
Marco G. Genoni ◽  
Luca Mancino ◽  
Ilaria Gianani ◽  
Marco Barbieri ◽  
...  

AbstractThe physics that governs quantum monitoring may involve other degrees of freedom than the ones initialised and controlled for probing. In this context we address the simultaneous estimation of phase and dephasing characterizing a dispersive medium, and we explore the role of frequency correlations within a photon pair generated via parametric down-conversion, when used as a probe for the medium. We derive the ultimate quantum limits on the estimation of the two parameters, by calculating the corresponding quantum Cramér-Rao bound; we then consider a feasible estimation scheme, based on the measurement of Stokes operators, and address its absolute performances in terms of the correlation parameters, and, more fundamentally, of the role played by correlations in the simultaneous achievability of the quantum Cramér- Rao bounds for each of the two parameters.


2021 ◽  
pp. 096739112110324
Author(s):  
Mihir N Velani ◽  
Ritesh R Patel

The role of nanodielectrics in the electrical power system is becoming crucial owing to its superior properties and potential applications in the field. Yet, the materials face limited breakdown strength and thermal properties. Further, the nanodielectrics have not found a comprehensive commercial platform because of the costly manufacturing process, and characterization and testing facilities. Therefore, to reduce the involved cost, in this work, an FE (finite element) based computational technique has been implemented to visualize the effect of shape, size, and filler concentration under the application of high voltage (HV). The epoxy-based nanodielectrics have been modeled incorporating a range of different shapes and size nanofillers—Al2O3, BN, BeO, SiO2, and TiO2. The paper discusses the 2D-analysis of the modeled nanodielectric in the steady-state electrostatic fields and thermal domains. It shows the insights of the nanofillers’ choice to ensure a perfect blend of electrical and thermal properties. The epoxy with square-shaped BeO fillers showed a rise in the electric field of nearly 1.5 times than unfilled neat epoxy, which indicates a significant surge in thermal conductivity at specific filler loading.


2021 ◽  
Author(s):  
Olivier Bernard ◽  
Weiran Li ◽  
Fidel Costa ◽  
Caroline Bouvet de Maisonneuve

<p>One of the major challenges faced by volcanologists to investigate controls on eruption dynamics is to quantify both pre-eruptive volatile budgets and timescales of magma ascent. Indeed, petrological investigations of the two parameters usually rely on different methods/analytical techniques that are not always applicable/accessible. Recent studies have shown that the abundance and zoning pattern of F, Cl, and OH in apatite can be used to determine both pre-eruptive volatile budget and magma degassing rates that can, under some conditions, be related to magma ascent rates ([1],[2]).</p><p>Here we apply the two methods to apatite in the Rabaul 2006 eruption deposits (Papua-New-Guinea). This was a VEI-4 eruption and occurred in three main phases: (1) a sub-plinian onset followed 12h after its start by (2) a mixed strombolian-effusive phase, which subsequently evolved into (3) discrete vulcanian explosions. We sampled deposits of the three phases: (1) pumices, (2) fragments of lava flow, and (3) fragments of cow-pad bombs.</p><p>We calculated pre-eruptive water contents using apatite included in clinopyroxene as they keep a better record of reservoir conditions from the time of entrapment. We found that the magma that fed the sub-plinian phase contained the highest water content of about 2 wt.%, while magmas that fed the lava flow and the vulcanian phase were drier, with 0.2 to 0.5 wt.% less H<sub>2</sub>O. X-ray maps acquired with an EPMA show that only apatite crystals in the groundmass of the vulcanian and effusive deposits are zoned in F and Cl at the crystal rims, whereas those from the sub-plinian deposits and included in clinopyroxenes are not zoned. This indicates that the zoning is related to syn- or immediately pre-eruptive changes of Cl-F-H<sub>2</sub>O during magma ascent towards the surface and can thus be modelled as diffusive reequilibration of the crystal and the melt. We obtained maximum diffusion timescales of <8 hours for the unzoned apatite in sub-plinian deposits, timescales of 20–22 hours for apatite in vulcanian deposits, and 600–1500 hours for those in the lava flow. Thus, the time scales increase with decreasing explosivity of the eruptions, as it could be expected if magma ascent rate played the key role of eruption dynamics. However, the degassing timescales of the effusive phase are significantly longer than the eruption duration itself, which can be explained if the magma started rising in the system 1–3 months prior to the onset of the eruption. The volatile-rich, fast-rising magma that fed the initial sub-plinian phase propagated through, disturbed and remobilized the shallower, more degassed batch of magma, which was erupted during the following effusive phase. Deeper, volatile-poor magma that kept moving up the open conduit, was responsible for the late vulcanian explosions.</p><p>Our results show that apatite is a powerful tool for probing slight changes in magma volatile chemistry and ascent rates that can vary between different phases of the same eruption and produce different eruption styles.</p><p> </p><p>[1] Li and Costa, 2020, GCA [2] Li et al. 2020, EPSL</p>


2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Jiamao Li ◽  
Jingwei Hou ◽  
Yu Gong ◽  
Chengjian Xiao ◽  
Lei Yue ◽  
...  

A liquid-phase reducing method of synthesizing Pt nanocrystals was demonstrated, and dendrite-, cube-, and cuboctahedron-shaped Pt nanocrystals (NCs) with well-defined monomorphic were successfully synthesized through iodine ions mediated with the CTAB agent. When the KI concentration was increased to thirty times of K2PtCl4 at the nucleation stage, the high-quality Pt nanodendrites could be obtained. However, no matter how many KI were added at the growth age, only cube- and cuboctahedron-shaped Pt nanocrystals formed. The results of high-resolution TEM, EDX, and XRD indicated that the size and shape of Pt NCs could be turned by changing the concentration and time of KI. In the nucleation stage, it might be due to that some iodine ions adsorb on the surfaces of Pt NCs, which probably cause the rapid growth process resulting in the formation of Pt nanodendrites. In the growth stage, although high concentrations of I− ions could contribute to the shape control and generate bigger particles of Pt NCs, small Pt particles do not grow into dendrites. The insight into the role of I− ions in synthesis of Pt NCs reported here provided a viewpoint for clearly understanding the formation mechanism of anisotropic platinum nanostructures.


1997 ◽  
Vol 272 (3) ◽  
pp. H1333-H1341 ◽  
Author(s):  
M. X. He ◽  
S. Wang ◽  
H. F. Downey

To test the role of inorganic phosphate (Pi) in downregulation of myocardial contractile force at the onset of ischemia, Pi of rat hearts was determined with 31P nuclear magnetic resonance spectroscopy. Forty cycles of brief hypoperfusion (30% of baseline flow for 33 s) were used to achieve a time resolution of 0.512 s for comparing dynamic changes in Pi and contractile force. Initial control values of left ventricular developed pressure (LVP), heart rate, and oxygen consumption were 136 +/- 11 mmHg, 236 +/- 4 beats/min, and 95 +/- 3 microl O2 x min(-1) x g(-1); these values were unchanged at the end of the experiment. During the first 10 s of hypoperfusion, Pi increased at a rate (percentage of the total observed change) faster than the decrease in LVP; Pi and LVP then changed at the same rate during the remainder of the hypoperfusion. ADP did not change in advance of LVP. Intracellular pH did not change. The results indicate that Pi plays an important role in initiating the downregulation of myocardial contractile force at the onset of ischemia. Perfusion pressure also declined faster than LVP at the onset of ischemia, indicating potential importance of vascular collapse in contractile downregulation during early ischemia.


1992 ◽  
Vol 103 (4) ◽  
pp. 1215-1222 ◽  
Author(s):  
J.R. Sims ◽  
S. Karp ◽  
D.E. Ingber

Studies were carried out with capillary endothelial cells cultured on fibronectin (FN)-coated dishes in order to analyze the mechanism of cell and nuclear shape control by extracellular matrix (ECM). To examine the role of the cytoskeleton in shape determination independent of changes in transmembrane osmotic pressure, membranes of adherent cells were permeabilized with saponin (25 micrograms/ml) using a buffer that maintains the functional integrity of contractile microfilaments. Real-time videomicroscopic studies revealed that addition of 250 microM ATP resulted in time-dependent retraction and rounding of permeabilized cells and nuclei in a manner similar to that observed in intact living cells following detachment using trypsin-EDTA. Computerized image analysis confirmed that permeabilized cells remained essentially rigid in the absence of ATP and that retraction was stimulated in a dose-dependent manner as the concentration of ATP was raised from 10 to 250 microM. Maximal rounding occurred by 30 min with projected cell and nuclear areas being reduced by 69 and 41%, respectively. ATP-induced rounding was also accompanied by a redistribution of microfilaments resulting in formation of a dense net of F-actin surrounding retracted nuclei. Importantly, ATP-stimulated changes in cell, cytoskeletal, and nuclear form were prevented in permeabilized cells using a synthetic myosin peptide (IRICRKG) that has been previously shown to inhibit actomyosin filament sliding in muscle. In contrast, both the rate and extent of cell and nuclear rounding were increased in permeabilized cells exposed to ATP when the soluble FN peptide, GRGDSP, was used to dislodge immobilized FN from cell surface integrin receptors.(ABSTRACT TRUNCATED AT 250 WORDS)


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