Shape Perturbations Research Articles

An asymmetric fitting function for condensed-phase Raman spectroscopy.

Asymmetric lineshapes are experimentally observed in the Raman spectra of different classes of condensed matter. Determination of the peak parameters, typically done with symmetric pseudo-Voigt functions, in such situations yields unreliable results. While a wide choice of asymmetric fitting functions is possible, for the function to be practically useful, it should satisfy several criteria: simple analytic form, minimum parameters, description of the symmetric shape as "zero case", estimation of the desired peak parameters in a straightforward way and, above all, adequate description of the experimental data. In this work we formulate the asymmetric pseudo-Voigt function by damped perturbation of the original symmetric shapes with one asymmetry-related parameter. The damped character of the perturbation ensures by construction consistent behavior of the line tails. We test the asymmetric function by fitting the experimental Raman spectra. The results show that the function is able to describe a wide range of experimentally observed asymmetries for different natures of asymmetric broadening, including 3D and 2D crystals, nanoparticles, polymers, and molecular solids and liquids.

On optimality of column geometry

Critical loads of columns under compressive follower forces have been widely discussed in the literature. By means of shape optimization, improvements by factors of more than eight could be achieved. However, the obtained solutions turn out to be not robust against perturbations of shape or material parameters. The aim of this paper is to explain this sensitivity effect, basing on a study of eigenforms. Further, a robust alternative to the classical optimization approach is proposed.

Inclusion boundary reconstruction and sensitivity analysis in electrical impedance tomography

Reconstruction of conductive inclusions in a homogeneous background medium is commonly seen in electrical impedance tomography (EIT). One of the methods to deal with the inclusion reconstruction problems is the shape-based method. With prior knowledge of conductivity of target inclusions, the boundary of inclusions is parameterized by several shape coefficients and recovered from EIT measurements. This paper presents a shape-based inclusion reconstruction method and its numerical implementation with boundary element method (BEM). A shape perturbation method (SPM) is proposed to calculate the shape sensitivity in EIT. To evaluate the accuracy of the presented method, a series of numerical tests are conducted. The characteristics of EIT shape sensitivity are analysed. Some factors influencing the reconstruction performance are discussed.

Bingham fluids: deformation and energy dissipation in triangular cross section tube flow

Flow of Bingham plastics through straight, long tubes with non-circular cross-sections is studied by means of an analytical method that allows to model a wide spectrum of tube geometries. Shear stress normal to equal velocity lines, velocity field and plug zones are explored, in particular in a tube with equilateral triangular cross-section for small values of the Bingham number Bi, and they are compared with corresponding numerical solutions. We show that a circular plug is present at the center of the triangular tube cross-section, consistent with numerical simulations as well as with previous results in the literature, if calculations up to and including first order in the shape perturbation parameter $$\epsilon$$ are taken into account. However with the inclusion of the second order terms in the algorithm this structure is no longer present and no plug zone is predicted for the same pressure drop. We find that in that case normal shear stresses are always greater than the yield stress of the fluid. As a result, the central region becomes a pseudo-plug since it presents small but non-vanishing relative deformations and does not move as a rigid core. The energy dissipation function for the Bingham fluid flow is written in terms of natural coordinates. Its distribution depends only on the normal shear stress at any point with Bingham number as a parameter.

Deformation Based Curved Shape Representation.

In this paper, we introduce a deformation based representation space for curved shapes in . Given an ordered set of points sampled from a curved shape, the proposed method represents the set as an element of a finite dimensional matrix Lie group. Variation due to scale and location are filtered in a preprocessing stage, while shapes that vary only in rotation are identified by an equivalence relationship. The use of a finite dimensional matrix Lie group leads to a similarity metric with an explicit geodesic solution. Subsequently, we discuss some of the properties of the metric and its relationship with a deformation by least action. Furthermore, invariance to reparametrization or estimation of point correspondence between shapes is formulated as an estimation of sampling function. Thereafter, two possible approaches are presented to solve the point correspondence estimation problem. Finally, we propose an adaptation of k-means clustering for shape analysis in the proposed representation space. Experimental results show that the proposed representation is robust to uninformative cues, e.g., local shape perturbation and displacement. In comparison to state of the art methods, it achieves a high precision on the Swedish and the Flavia leaf datasets and a comparable result on MPEG-7, Kimia99 and Kimia216 datasets.

The potential of imposed magnetic fields for enhancing ignition probability and fusion energy yield in indirect-drive inertial confinement fusion

We examine the potential that imposed magnetic fields of tens of Tesla that increase to greater than 10 kT (100 MGauss) under implosion compression may relax the conditions required for ignition and propagating burn in indirect-drive inertial confinement fusion (ICF) targets. This may allow the attainment of ignition, or at least significant fusion energy yields, in presently performing ICF targets on the National Ignition Facility (NIF) that today are sub-marginal for thermonuclear burn through adverse hydrodynamic conditions at stagnation [Doeppner et al., Phys. Rev. Lett. 115, 055001 (2015)]. Results of detailed two-dimensional radiation-hydrodynamic-burn simulations applied to NIF capsule implosions with low-mode shape perturbations and residual kinetic energy loss indicate that such compressed fields may increase the probability for ignition through range reduction of fusion alpha particles, suppression of electron heat conduction, and potential stabilization of higher-mode Rayleigh-Taylor instabilities. Optimum initial applied fields are found to be around 50 T. Given that the full plasma structure at capsule stagnation may be governed by three-dimensional resistive magneto-hydrodynamics, the formation of closed magnetic field lines might further augment ignition prospects. Experiments are now required to further assess the potential of applied magnetic fields to ICF ignition and burn on NIF.

Homogeneity test for functional data

ABSTRACTIn the context of functional data analysis, we propose new sample tests for homogeneity. Based on some well-known depth measures, we construct four different statistics in order to measure distance between the two samples. A simulation study is performed to check the efficiency of the tests when confronted with shape and magnitude perturbation. Finally, we apply these tools to measure the homogeneity in some samples of real data, and we obtain good results using this new method.

Perturbation theory-based field analysis of arbitrary-shaped microstrip patch antenna

In this paper, the concept of perturbation theory is applied to derive a general electric field (E-field) expression for any arbitrary-shaped microstrip patch antenna. The arbitrary shape is created by adding small perturbation in a regular patch shape, which is used to find perturbed and unperturbed electromagnetic wave solutions for resultant E-field of patch antenna. Ansoft HFSS simulator is used to validate the derived field expression in curvilinear coordinates for a regular circular-shaped patch. Then the proposed field analysis is applied to develop two new arbitrary-shaped patches in C-band for desired E-field patterns.

Impact of aerosol microphysical properties on mass scattering cross sections

We assessed the sensitivity of simulated mass scattering cross sections (αλsca) of three aerosol species to perturbed particle microphysical properties and derived constraints on these microphysical properties, suitable for the north-western Mediterranean basin, from a comparison between code calculations and observations. In detail, we calculated αλsca of mineral dust, organic carbon and sulfate at three wavelengths in the visible range (λ1=0,450μm; λ2=0,525μm; λ3=0,635μm) with a T-matrix optical code, considering ±20% perturbations on size distribution, refractive index and mass density (respect to reference values mainly taken from the OPAC database), and spheroids with two different axial ratios as shape perturbations (reference shape: sphere). Then, we compared the simulation results with a set of observed αλsca of mineral dust, aged organics and ammonium sulfate sources, available at the same three wavelengths of the code calculations. These observations, provided by the Institute of Environmental Assessment and Water Research (IDAEA-CSIC), have been derived through Multilinear Regression (MLR) analysis from measurements of aerosol mass concentrations and optical properties, collected during a 4-year campaign at the Montseny regional background station (Spain) and representative of the north-western Mediterranean basin. We observed quite different impacts of the microphysical perturbations on αλsca values and spectral dependence for different aerosol species, due mainly to the different size of the particles respect to the visible wavelengths. Moreover, by means of a compatibility test on best fit parameters, we constrained the mineral dust log-normal size distribution to a geometric radius and a standard deviation of rg=3,583·10−1μm and σg=1,600, respectively (effective radius: reff=6,221·10−1μm), the organic carbon log-normal size distribution parameters to rg=2,544·10−2μm and σg=1,760 (reff=5,656·10−2μm), the organic carbon real refractive index to nR=(1,576;1,576;1,576) at (λ1;λ2;λ3), the sulfate log-normal size distribution parameters to rg=8,340·10−2μm and σg=1,624 (reff=1,501·10−1μm) and the sulfate real refractive index to nR=(1,547;1,545;1,543) at (λ1;λ2;λ3), in the north-western Mediterranean basin. Regarding the other perturbed microphysical properties, we found the reference prescriptions to be suitable for this geographical region, according to the same analysis procedure.

Numerical Solution of Diffraction Problems: A High-Order Perturbation of Surfaces and Asymptotic Waveform Evaluation Method

The rapid and robust simulation of linear waves interacting with layered periodic media is a crucial capability in many areas of scientific and engineering interest. High-order perturbation of surfaces (HOPS) algorithms are interfacial methods which recursively estimate scattering quantities via perturbation in the interface shape heights/slopes. For a single incidence wavelength such methods are the most efficient available in the parameterized setting we consider here. In the current contribution we generalize one of these HOPS schemes by incorporating a further expansion in the wavelength about a base configuration which constitutes an “asymptotic waveform evaluation” (AWE). We not only provide a detailed specification of the algorithm, but also verify the scheme and point out its benefits and shortcomings. With numerical experiments we show the remarkable efficiency, fidelity, and high-order accuracy one can achieve with an implementation of this algorithm.

Proliferation of Listeria monocytogenes L-form cells by formation of internal and external vesicles.

L-forms are cell wall-deficient bacteria that divide through unusual mechanisms, involving dynamic perturbations of the cellular shape and generation of vesicles, independently of the cell-division protein FtsZ. Here we describe FtsZ-independent mechanisms, involving internal and external vesicles, by which Listeria monocytogenes L-forms proliferate. Using micromanipulation of single cells and vesicles, we show that small vesicles are formed by invagination within larger intracellular vesicles, receive cytoplasmic content, and represent viable progeny. In addition, the L-forms can reproduce by pearling, that is, generation of extracellular vesicles that remain transiently linked to their mother cell via elastic membranous tubes. Using photobleaching and fluorescence recovery, we demonstrate cytoplasmic continuity and transfer through these membranous tubes. Our findings indicate that L-forms' polyploidy and extended interconnectivity through membranous tubes contribute to the generation of viable progeny independently of dedicated division machinery, and further support L-forms as models for studies of potential multiplication mechanisms of hypothetical primitive cells.

A stable high-order perturbation of surfaces method for numerical simulation of diffraction problems in triply layered media

The accurate numerical simulation of linear waves interacting with periodic layered media is a crucial capability in engineering applications. In this contribution we study the stable and high-order accurate numerical simulation of the interaction of linear, time-harmonic waves with a periodic, triply layered medium with irregular interfaces. In contrast with volumetric approaches, High-Order Perturbation of Surfaces (HOPS) algorithms are inexpensive interfacial methods which rapidly and recursively estimate scattering returns by perturbation of the interface shape. In comparison with Boundary Integral/Element Methods, the stable HOPS algorithm we describe here does not require specialized quadrature rules, periodization strategies, or the solution of dense non-symmetric positive definite linear systems. In addition, the algorithm is provably stable as opposed to other classical HOPS approaches. With numerical experiments we show the remarkable efficiency, fidelity, and accuracy one can achieve with an implementation of this algorithm.

Crack growth propagation using standard FEM

This paper is part of research lines providing numerical methods for structural capability related to an evolving crack length in two-dimensional linear-elastic fracture mechanics of isotropic materials. We propose a numerical approach which efficiently simplifies more sophisticated approaches and yet, yield accurate results. Widely employed in academia, they are hardly used commercially unless ad hoc libraries are implemented. The proposed strategy improves early works where crack growth can be treated as a shape perturbation of the domain with existing cracks. The numerical results prove the accuracy of our strategy in comparison with both numerical and experimental outcomes present in literature.

13.4km OAM state propagation by recirculating fiber loop.

Enabled by an enhanced effective index separation (Δneff = 1.7 × 10-4) and low transmission loss (0.8dB/km), OAM states are propagated over 13.4km in an air core fiber using a recirculating fiber loop. We observe that intermodal crosstalk decreases rapidly with increasing effective index separation, Δneff, and an order of magnitude lower crosstalk may be achieved just by doubling Δneff. We find that, in agreement with coupled power theory, our fiber has mode coupling properties analogous to elliptical core PM fibers, which yield ~10 × or more lower crosstalk than for conventional LP fiber mode orders with the same Δneff. This confirms that, for OAM modes, birefringent perturbations rather than shape perturbations matter most. In the process of performing the loop experiment, we demonstrate that OAM states in these fibers can be preserved with low loss (≤ 0.2dB) and low crosstalk (-15dB) while splicing distinct segments of the air-core fiber. For well-designed fibers, we demonstrate that OAM modes can travel distances relevant for large-scale data centers.

Shape optimization of rigid inclusions for elastic plates with cracks

In the paper, we consider an optimal control problem of finding the most safe rigid inclusion shapes in elastic plates with cracks from the viewpoint of the Griffith rupture criterion. We make use of a general Kirchhoff–Love plate model with both vertical and horizontal displacements, and nonpenetration conditions are fulfilled on the crack faces. The dependence of the first derivative of the energy functional with respect to the crack length on regular shape perturbations of the rigid inclusion is analyzed. It is shown that there exists a solution of the optimal control problem.

Optimal fitting of strain-controlled flattenable mesh surfaces

A flattenable mesh surface is a polygonal mesh surface that can be unfolded into a planar patch without stretching any polygon. This paper presents a new method for computing a slightly stretched flattenable mesh surface M from a piecewise-linear surface patch P∈R3, where the shape approximation error between M and P is minimized and the strain of stretching on M is controlled. Prior approaches result in either a flattenable surface that could be quite different from the input shape or a (discrete) developable surface has relative simple shape. The techniques investigated in this paper overcome these difficulties. First, we introduce a new surface modeling method to conduct a sequence of nearly isometric deformations to morph a flattenable mesh surface to a new shape which has a better approximation of the input surface. Second, in order to get better initial surfaces for fitting and overcome topological obstacles, a shape perturbation scheme is investigated to obtain the optimal surface fitting result. Last, to improve the scalability of our optimal surface fitting algorithm, a coarse-to-fine fitting framework is exploited so that very dense flattenable mesh surfaces can be modeled and boundaries of the input surfaces can be interpolated.

Morphological instability of a solid sphere of dilute ternary alloy growing by diffusion from its melt

The diffusion-limited growth of an initially spherical particle of dilute ternary alloy in contact with its melt has been studied from a theoretical point of view and the effects of interface kinetics and multicomponent diffusion have been characterized on the development of a shape perturbation of the sphere. When both concentrations of the diffusing species are imposed in the far-field, the different radii related to the absolute and relative stability of the particle with respect to the development of spherical harmonics have been determined when a linear kinetics law is considered for the solid/liquid interface. The development of the shape fluctuations of the sphere has been also characterized when the flux of both species are set in the far-field.

Shape-Related Toxicity of Titanium Dioxide Nanofibres.

Titanium dioxide (TiO2) nanofibres are a novel fibrous nanomaterial with increasing applications in a variety of fields. While the biological effects of TiO2 nanoparticles have been extensively studied, the toxicological characterization of TiO2 nanofibres is far from being complete. In this study, we evaluated the toxicity of commercially available anatase TiO2 nanofibres using TiO2 nanoparticles (NP) and crocidolite asbestos as non-fibrous or fibrous benchmark materials. The evaluated endpoints were cell viability, haemolysis, macrophage activation, trans-epithelial electrical resistance (an indicator of the epithelial barrier competence), ROS production and oxidative stress as well as the morphology of exposed cells. The results showed that TiO2 nanofibres caused a cell-specific, dose-dependent decrease of cell viability, with larger effects on alveolar epithelial cells than on macrophages. The observed effects were comparable to those of crocidolite, while TiO2 NP did not decrease cell viability. TiO2 nanofibres were also found endowed with a marked haemolytic activity, at levels significantly higher than those observed with TiO2 nanoparticles or crocidolite. Moreover, TiO2 nanofibres and crocidolite, but not TiO2 nanoparticles, caused a significant decrease of the trans-epithelial electrical resistance of airway cell monolayers. SEM images demonstrated that the interaction with nanofibres and crocidolite caused cell shape perturbation with the longest fibres incompletely or not phagocytosed. The expression of several pro-inflammatory markers, such as NO production and the induction of Nos2 and Ptgs2, was significantly increased by TiO2 nanofibres, as well as by TiO2 nanoparticles and crocidolite. This study indicates that TiO2 nanofibres had significant toxic effects and, for most endpoints with the exception of pro-inflammatory changes, are more bio-active than TiO2 nanoparticles, showing the relevance of shape in determining the toxicity of nanomaterials. Given that several toxic effects of TiO2 nanofibres appear comparable to those observed with crocidolite, the possibility that they exert length dependent toxicity in vivo seems worthy of further investigation.

Error Field Impact on Plasma Boundary in ITER Scenarios

Discrepancies in magnetic field maps produced by confinement coils in thermonuclear fusion reactors may drive plasma to lose stability and must be carefully controlled during the whole time evolution of each shot using suitable correction coils. Even when kept below safety thresholds, these error fields (EFs) may alter the geometry of magnetic flux lines, defining the plasma geometry. This paper, using high accuracy 3-D magnetic field computations for confinement coils, addresses the issue of evaluating the effect of EFs on the plasma boundary shape during the shot, modeled as a sequence of equilibrium configurations. In particular, a procedure that can compute the shape perturbations due to given deformations of the coils has been set up and used to carry out an analysis of relationship between the EF and shape perturbations during the time evolution of International Tokamak Experimental Reactor programmed scenario.

The Delta Medial Axis: A fast and robust algorithm for filtered skeleton extraction

In this paper, we present the Delta Medial Axis (DMA), a quasi-linear algorithmic solution addressing several of the main concerns of discrete medial axes (MA) computation. First, its sensitivity to small shape perturbations is counterbalanced by a single parameter (delta), used in a pruning strategy that implicitly takes into account the local topology of the boundary. Second, the discrete nature of images is addressed by approximating the original MA definition in continuous space. Third, to allow real-time performances, a set of algorithmic optimizations is proposed. We compare our approach both qualitatively and quantitatively to recent state of the art solutions, and show that the DMA presents an excellent choice for a wide range of applications. Finally, to allow fast and efficient use of our algorithm, we propose the complete pseudo-code.