Discontinuous Fields Research Articles

Structural discontinuity induced surface second harmonic generation in single, thin zinc-blende GaAs nanowires.

We investigate optical second harmonic generation (SHG) from individual self-catalyzed zinc-blende (ZB) GaAs nanowires (NWs), where the polarimetry strongly depends on the NW diameter. We report a direct observation on the SHG induced by surface nonlinear susceptibilities in a single, ultra-thin GaAs NW. By considering the contributions from both optical field and structural discontinuities in our theoretical model, we can well explain the optical SHG polarimetry from NWs with different diameters. We also show that the optical in-coupling coefficient arising from the depolarization electromagnetic field can determine the polarization of the SHG. The results open perspectives for further geometry-based studies on the origin and control of SHG in small nanostructures.

Flow Simulation in Heterogeneous Porous Media With the Moving Least-Squares Method

The two-point-flux finite-volume method is the most widely used technique for discretizing Darcy's law in commercial reservoir simulators. The prevalence of that method within the oil-and-gas industry mostly stems from its simple implementation, intuitive understanding, and high execution speed. However, the method is known to suffer from severe inaccuracies when using non-$K$-orthogonal meshes, which reservoir engineers may need to discretize complex heterogeneous reservoirs. In these cases, the simulation inaccuracies may trigger costly business decisions about facilities and well management based on the erroneous prediction of flow streams. The moving least-squares method, with some novel enhancements presented in this paper to specifically handle discontinuous and anisotropic permeability fields, offers an attractive alternative for two main reasons. First, the reconstruction scheme relies on neighborhoods of points located at cell centers and, therefore, does not directly rely on the mesh topology or whether the mesh is $K$-orthogonal. Second, higher-order approximations can be obtained by increasing the size of neighborhoods. In particular, transported fields can be approximated using a second-order basis, which together with the use of limiters enables a much more accurate resolution of sharp fronts than the resolution obtained with a first-order scheme, as typically encountered in commercial simulators. Numerical experiments are shown that support these claims. Solving Poisson's equation highlights the ability of the new method to use non-$K$-orthogonal meshes and discontinuous tensors. Next, two oil-water problems underline the importance of obtaining an accurate pressure-gradient approximation to drive the flow. Finally, simulations in a complex, anisotropic reservoir focus on the robustness of the new method to several meshes.

Plankton patchiness in the Polar Front region of the West Spitsbergen Shelf

MEPS Marine Ecology Progress Series Contact the journal Facebook Twitter RSS Mailing List Subscribe to our mailing list via Mailchimp HomeLatest VolumeAbout the JournalEditorsTheme Sections MEPS 560:1-18 (2016) - DOI: https://doi.org/10.3354/meps11925 FEATURE ARTICLEPlankton patchiness in the Polar Front region of the West Spitsbergen Shelf Emilia Trudnowska*, Marta Gluchowska, Agnieszka Beszczynska-Möller, Katarzyna Blachowiak-Samolyk, Slawomir Kwasniewski Institute of Oceanology Polish Academy of Sciences, 81-712 Sopot, Poland *Corresponding author: emilia@iopan.gda.pl ABSTRACT: Plankton patchiness, a widely known but poorly studied phenomenon, was investigated concurrently with measurements of environmental conditions in the Polar Front region west of Spitsbergen in summer (June-July) 2012. Continuous high-resolution observations were made using a laser optical plankton counter, a fluorometer and CTD along several sections in the surface 50 m of the sea with additional data from zooplankton net sampling and full-depth range hydrographical measurements at stations. The observed patches differed in terms of size, number and distribution patterns. They occupied only a minor portion of the studied ocean area (2-17%), but contained plankton concentrations that were 3-17 times higher than the concentrations in the background waters. The generation and existence of patches was associated with particular conditions created by increased primary production, optimal hydrography, discontinuities in the density field and/or the presence of meanders or eddies. The distribution of small size fraction patches, consisting of the phytoplankton, inorganic particles and detritus, was closely related to specific patterns in hydrography. The medium-size zooplankton and marine snow were concentrated mainly in conjunction with discontinuities in density field. The distribution of the large copepods was independent of any oceanographic feature detected in this study, which points towards biological cues as factors regulating zooplankton aggregation processes. Diverse mechanisms of patch formation as well as their ecological significance are discussed in the context of planktonic responses to the structured environment in the region of the Polar Front. KEY WORDS: Zooplankton · Patchiness · Zooplankton distribution · Laser optical plankton counter · Eddy · Polar Front · West Spitsbergen Current Full text in pdf format Information about this Feature Article NextCite this article as: Trudnowska E, Gluchowska M, Beszczynska-Möller A, Blachowiak-Samolyk K, Kwasniewski S (2016) Plankton patchiness in the Polar Front region of the West Spitsbergen Shelf. Mar Ecol Prog Ser 560:1-18. https://doi.org/10.3354/meps11925 Export citation RSS - Facebook - Tweet - linkedIn Cited by Published in MEPS Vol. 560. Online publication date: November 24, 2016 Print ISSN: 0171-8630; Online ISSN: 1616-1599 Copyright © 2016 Inter-Research.

Limit cycles of discontinuous piecewise polynomial vector fields

When the first average function is non-zero we provide an upper bound for the maximum number of limit cycles bifurcating from the periodic solutions of the center x˙=−y((x2+y2)/2)m and y˙=x((x2+y2)/2)m with m≥1, when we perturb it inside a class of discontinuous piecewise polynomial vector fields of degree n with k pieces. The positive integers m, n and k are arbitrary. The main tool used for proving our results is the averaging theory for discontinuous piecewise vector fields.

Multi-Hole Core Photonic Crystal Fiber Guiding Light in Subwavelength Air Holes

We present a novel multi-hole core photonic crystal fiber for guiding and confining light in subwavelength-diameter low-refractive-index air holes of core, even when light is guided based on total internal reflection. The low-loss, broadband and single-mode guiding properties of the fiber are studied. The propagation mechanism in subwavelength and low-refractive-index holes is analyzed by evanescent wave coupling. Light confinement and enhancement are caused by large discontinuity of the electric field at dielectric interfaces. Multiple subwavelength air holes in the core can guide light together, coupling and coherent with each other. Arrays of air holes in the core can be used as a means of patterning light on a submicrometer regime. The high light intensity in multiple long holes enables a variety of applications in nonlinear light management, optical modulation, and gas sensing.

Application of the Continuous and Discontinuous Fields of Plastic Deformations to the Evaluation of the Initial Thickness of Bent Tubes

The paper presents the derived equations for calculations of the initial wall thickness g0 of a tube bent to elbow. The expressions for calculating g0 are presented in a suitable measure of the “great active actual radius Rj” in the bending zone for an exact-generalized solution (continuous fields) and for three formal simplifications (discontinuous fields) of the first-, second-, and third-orders. The expressions to calculate the components of deformation for a generalized solution (continuous fields) are obtained on the basis of kinematically admissible fields of plastic deformations. In any case, a value of initial tube thickness depends on the radius and on the angle of bending αb on the external diameter of the tube, on the displacement of the neutral axis, and on the allowable (required) elbow thickness according to European, American, or other national technical standard or regulations. The initial thickness also depends on the coordinates of the point where the allowable thickness was determined and on the technological–material coefficient of the bending zone range k (defined during the tests). The obtained calculation results are presented in the form of graphs and in table.

Enhancement of acousto-optical coupling in two-dimensional air-slot phoxonic crystal cavities by utilizing surface acoustic waves

A phoxonic crystal is a periodically patterned material that can simultaneously localize optical and acoustic modes. The acousto-optical coupling in two-dimensional air-slot phoxonic crystal cavities is investigated numerically. The photons can be well confined in the slot owing to the large electric field discontinuity at the air/dielectric interfaces. Besides, the surface acoustic modes lead to the localization of the phonons near the air-slot. The high overlap of the photonic and phononic cavity modes near the slot results in a significant enhancement of the moving interface effect, and thus strengthens the total acousto-optical interaction. The results of two cavities with different slot widths show that the coupling strength is dependent on the slot width. It is expected to achieve a strong acousto-optical/optomechanical coupling in air-slot phoxonic crystal structures by utilizing surface acoustic modes.

Direct error in constitutive equation formulation for plane stress inverse elasticity problem

We present a new computational formulation for inverse problems in elasticity with full field data. The formulation is a variant of an error in the constitutive equation formulation, but allows direct solution for the modulus field and accommodates discontinuous strain fields. The development of the formulation is motivated by the relatively poor performance of current direct formulations, reported so far in literature, in dealing with discontinuities in the strain and material property distribution. The formulation relies on minimizing the error in the constitutive equation with a momentum equation constraint. Numerical results on model problems show that the formulation is capable of handling discontinuous and noisy strain fields, and also converging with mesh refinement for continuous and discontinuous material property distributions. The application to reconstruct the elastic modulus distribution in solid breast tumors is shown.

Design optimization of a high-breakdown-voltage GaN-based vertical HFET with composite current-blocking layer

This work proposes a GaN-based vertical heterostructure field-effect transistor with composite insulated current-blocking layer (GaN CCBL-VHFET) to improve the breakdown voltage (BV) of the current aperture vertical electron transistor (CAVET) and obtain high CBL performance. When utilizing a composite current-blocking layer, the electric field (E-field) discontinuity at the CBL/low-k dielectric interface results in a more uniform E-field distribution along the GaN buffer layer, significantly improving the BV. Simulation results show that the BV and ON-resistance ($$R_{\mathrm{ON}}$$RON) of the device with two low-k dielectric layers are 1744 V and 0.91 m$$\Omega \,\mathrm{cm}^{2}$$Ωcm2, respectively. Furthermore, the average breakdown E-field is extremely high, reaching 291 V/$${\upmu }$$μm. Compared with the conventional GaN CAVET, the BV of the GaN CCBL-VHFET increases by about 94 % while retaining low $$R_{\mathrm{ON}}$$RON. Furthermore, the challenge of activating Mg in the CBL is avoided for this device structure.

Elemental enriched spaces for the treatment of weak and strong discontinuous fields

This paper presents a finite element that incorporates weak, strong and both weak plus strong discontinuities with linear interpolations of the unknown jumps for the modeling of internal interfaces. The new enriched space is built by subdividing each triangular or tetrahedral element in several standard linear sub-elements. The new degrees of freedom coming from the assembly of the sub-elements can be eliminated by static condensation at the element level, resulting in two main advantages: first, an elemental enrichment instead of a nodal one, which presents an important reduction of the computing time when the internal interface is moving all around the domain and second, an efficient implementation involving minor modifications allowing to reuse existing finite element codes. The equations for the internal interface are constructed by imposing the local equilibrium between the stresses in the bulk of the element and the tractions driving the cohesive law, with the proper equilibrium operators to account for the linear kinematics of the discontinuity. To improve the continuity of the unknowns on both sides of the elements on which a static condensation is done, a contour integral has been added. These contour integrals named inter-elemental forces can be interpreted as a “do nothing” boundary condition (Coppola-Owen and Codina, 2011) published in another context, or as the usage of weighting functions that ensure convergence of the approach as proposed by J.C. Simo (Simo and Rifai, 1990). A series of numerical tests for scalar unknowns as a simple representation of more general numerical simulations are presented to illustrate the performance of the enriched elemental space.

Extended Finite-Element Method for Weak Discontinuities in Electric Fields

In this paper, the extended finite-element method (XFEM) is used for modeling weak discontinuities in electric fields. For a weak discontinuous domain, the first-order derivative of the electric potential is discontinuous although the electric potential, degree of freedom, is continuous. In order to improve the approximation space of the conventional finite element method (CFEM), the enrichment function of the key of XFEM is used to model weak discontinuous solutions independent of the mesh. Interfaces among different materials can be described well by using the level set method. Numerical examples applied to the parallel plate electrodes in 1-D and the insulating oil with a bubble in 2-D static electric field involving error analysis, computational time, and electric field computations are provided to demonstrate the utility of XFEM in electric fields.

A thermo‐mechanical energetic cohesive zone model accounting for Kapitza interfaces

AbstractThe objective of this contribution is to study computational aspects of modeling thermo‐mechanical solids containing mechanically energetic, geometrically non‐coherent Kapitza interfaces under cyclic loading. The interface is termed energetic in the sense that it possesses its own energy, entropy, constitutive relations and dissipation. To date, classical thermo‐mechanical cohesive zone models do not account for elastic interfaces. Therefore we propose a novel interface model that couples the classical cohesive zone formulation to the interface elasticity theory under the Kapitza assumption within a thermo‐mechanical framework. In other words, such an interface model allows for discontinuities in geometry, temperature and normal stress fields, while not permitting a jump in the normal heat flux across the interface. The equations governing a fully non‐linear transient problem are given. In particular, a comparison is made between the results of the classical thermo‐mechanical cohesive zone model and our novel (cohesive + energetic Kapitza) interface formulation. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Evaluation of two momentum control variable schemes and their impact on the variational assimilation of radarwind data: Case study of a squall line

Different choices of control variables in variational assimilation can bring about different influences on the analyzed atmospheric state. Based on the WRF model’s three-dimensional variational assimilation system, this study compares the behavior of two momentum control variable options—streamfunction velocity potential (ψ–χ) and horizontal wind components (U–V)—in radar wind data assimilation for a squall line case that occurred in Jiangsu Province on 24 August 2014. The wind increment from the single observation test shows that the ψ–χ control variable scheme produces negative increments in the neighborhood around the observation point because streamfunction and velocity potential preserve integrals of velocity. On the contrary, the U–V control variable scheme objectively reflects the information of the observation itself. Furthermore, radial velocity data from 17 Doppler radars in eastern China are assimilated. As compared to the impact of conventional observation, the assimilation of radar radial velocity based on the U–V control variable scheme significantly improves the mesoscale dynamic field in the initial condition. The enhanced low-level jet stream, water vapor convergence and low-level wind shear result in better squall line forecasting. However, the ψ–χ control variable scheme generates a discontinuous wind field and unrealistic convergence/divergence in the analyzed field, which lead to a degraded precipitation forecast.

Transient modelling of flexible belt drive dynamics using the equations of a deformable string with discontinuities

ABSTRACTDynamics of a belt drive is analysed using a non-linear model of an extensible string at contour motion, in which the trajectories of particles of the belt are predetermined. The equations of string dynamics at the tight and slack spans are considered in a fixed domain by transforming into a spatial frame. Assuming the absence of slip of the belt on the surface of the pulleys, we arrive at a new model with a discontinuous velocity field and concentrated contact forces. Finite difference discretization allows numerical analysis of the resulting system of partial differential equations with delays. Example solution for the acceleration of a belt drive and an investigation of its frequency response depending on the velocity are presented and discussed.

Accurate Feeding of Nanoantenna by Singular Optics for Nanoscale Translational and Rotational Displacement Sensing.

Identifying subwavelength objects and displacements is of crucial importance in optical nanometrology. We show in this Letter that nanoantennas with subwavelength structures can be excited precisely by incident beams with singularity. This accurate feeding beyond the diffraction limit can lead to dynamic control of the unidirectional scattering in the far field. The combination of the field discontinuity of the incoming singular beam with the rapid phase variation near the antenna leads to remarkable sensitivity of the far-field scattering to the displacement at a scale much smaller than the wavelength. This Letter introduces a far-field deep subwavelength position detection method based on the interaction of singular optics with nanoantennas.

Design optimisation of AlGaN/GaN metal insulator semiconductor high electron mobility transistor with high‐K/low‐K compound gate dielectric layer for millimeter‐wave application

A novel high DC and radio-frequency (RF) characteristics AlGaN/GaN metal insulator semiconductor high electron mobility transistor (MIS-HEMT) with a high-K/low-K compound gate dielectric layer (CGD) is proposed. Owing to the different dielectric constants, the discontinuity of the electric field at the high-K/low-K interface can modulate the distribution of the electric field along the channel under gate. Hence, enhancement of DC and RF characteristics can be achieved. The optimised results of the AlGaN/GaN MIS-HEMT with CGD structure revealed that the DC transconductance gm and the maximum saturation current Ids increased about 10.5 and 6.9% compared with the traditional AlGaN/GaN MIS-HEMT with single high-K gate dielectric layer (SGD), respectively. Also, the cutoff frequency ft and the maximum oscillation frequency f max of 74.2 GHz and 129.2 GHz are obtained and improved about 18.5 and 14.7% compared with the device with SGD structure.

A Quasi-Conforming Point Interpolation Method (QC-PIM) for Elasticity Problems

It is well known that a high-order point interpolation method (PIM) based on the standard Galerkin formations is not conforming, and thus the solution may not always be convergent. This paper proposes a new interesting technique called quasi-conforming point interpolation method (QC-PIM) for solving elasticity problems, by devising a novel scheme that smears the discontinuity. In the QC-PIM, the problem domain is first discretized by a set of background cells (typically triangles that can be automatically generated), and the average displacements on the interfaces of the two neighboring cells are assumed to be equal. We prove that when the size of background cells approaches to zero, all the additional potential energy coming from the discontinuous displacement field becomes zero, which ensures the pass of the standard patch test and hence the convergence. Numerical experiments verify that QC-PIM can produce the convergent solutions with higher accuracy and convergent rate that is in between fully conforming linear and quadratic models.

Isogeometric Analysis of Deformation, Inelasticity and Fracture In Thin-Walled Structures

The basic idea of isogeometric analysis (IGA) is to use splines, which are the functions commonly used in computer-aided design (CAD) to describe the geometry, as the basis function for the analysis as well. A main advantage is that a sometimes elaborate meshing process is by-passed. Another benefit is that spline basis-functions possess a higher-order degree of continuity, which enables a more accurate representation of the stress. Further, the order of continuity of the basis-functions can be reduced locally by knot insertion. This feature can be used to model interfaces and cracks as discontinuities in the displacement field.In order to study failure-mechanisms in thin-walled composite materials, an accurate representation of the full three-dimensional stress field is mandatory. A continuum shell formulation is an obvious choice. Continuum shell elements can be developed based on the isogeometric concept. They exploit NURBS basis functions to construct the mid-surface of the shell. In combination with a higher-order B-spline basis function in the thickness direction a complete three-dimensional representation of the shell is obtained. This isogeometric shell formulation can be implemented in a standard finite element code using Bézier extraction.Weak and strong discontinuities can be introduced in the B-spline function using knot-insertion to model material interfaces and delaminations rigorously as discontinuities in the displacement field. The exact representation of material interfaces vastly improves the accuracy of the through-the- thickness stress field. The ability to provide a double knot insertion enables a straightforward analysis of delamination growth in layered composite shells. Illustrative examples will be given.

Contact Modelling in Isogeometric Analysis: Application to Sheet Metal Forming Processes

Isogeometric Analysis (IGA) has been growing in popularity in the past few years essentially due to the extra flexibility it introduces with the use of higher degrees in the basis functions leading to higher convergence rates. IGA also offers the capability of easily reproducing discontinuous displacement and/or strain fields by just manipulating the multiplicity of the knot parametric coordinates. Another advantage of IGA is that it uses the Non-Uniform Rational B-Splines (NURBS) basis functions, that are very common in CAD solid modelling, and consequently it makes easier the transition from CAD models to numerical analysis. In this work it is explored the contact analysis in IGA for both implicit and explicit time integration schemes. Special focus will be given on contact search and contact detection techniques under NURBS patches for both the rigid tools and the deformed sheet blank.

An investigation on coupled thermoelastic interactions in a thick plate due to axi-symmetric temperature distribution under an exact heat conduction with a delay

Present work is concerned with a recently proposed heat conduction model: an exact heat conduction model with a single delay term. The main purpose of this paper is to examine the effects of the single phase-lag parameter/delay term on wave propagation in an infinitely extended thick plate due to axisymmetric temperature distribution applied in the lower and upper surfaces of the plate. The problem is formulated by using the new heat conduction model in such a way that other existing models can be extracted as special cases. Potential function concept including the Laplace and Hankel Transform method is used to find the solution in the transformed domain. Inversion of Hankel Transform is done analytically to obtain the solution in Laplace transform domain. By using a suitable analytical approach, the complete analysis on the wave propagation and discontinuities of different wave fields are found out. Furthermore, a numerical method for the Laplace inversion is applied to obtain the distributions of different physical fields like, temperature, displacement and stresses in the middle plane of the plate. Analysis of the results obtained under new model along with a comparison of the respective results obtained in other models is presented in detailed way. The findings in the present work are believed to bring out some lights concerning the new heat conduction model that involves a single delay parameter.