Inhomogeneous Domain Research Articles

An extended Krylov subspace model-order reduction technique to simulate wave propagation in unbounded domains

In this paper we present a novel extended Krylov subspace reduced-order modeling technique to efficiently simulate time- and frequency-domain wavefields in open complex structures. To simulate the extension to infinity, we use an optimal complex-scaling method which is equivalent to an optimized perfectly matched layer in which the frequency is fixed. Wavefields propagating in strongly inhomogeneous open domains can now be modeled as a non-entire function of the complex-scaled wave operator. Since this function contains a square root singularity, we apply an extended Krylov subspace technique to construct fast converging reduced-order models. Specifically, we use a modified version of the extended Krylov subspace algorithm as proposed by Jagels and Reichel [14], since this algorithm allows us to balance the computational costs associated with computing powers of the wave operator and its inverse. Numerical experiments from electromagnetics and acoustics illustrate the performance of the method.

Discontinuous Galerkin Inspired Framework for Vector Generalized Finite-Element Methods

Discontinuous Galerkin methods have been extensively used in simulations of various electromagnetic problems, in both time and frequency domains. In this paper, we exploit features of these methods to provide a framework that can be used to overcome a fundamental bottleneck in using as well as augmenting the capabilities of vector generalized finite element methods (VGFEM). This approach permits the use of VGFEM for analysis of piecewise inhomogeneous domains without defining additional constraints on basis functions and allows hybridization with other finite element formulations. Interior penalty discontinuous Galerkin method (IP-DGM) is used to enable communication among partitioned domains. We will present several results that demonstrate applications of these hybrid methods as well as their convergence characteristics.

Phosphatidylinositol Patches in a Reconstituted Lipid Membrane and its Dynamics

Amoeboid locomotion is one of the fundamental modes of cell motion that accompanies dynamic deformation of plasma membrane. From yeast to human cell, localized activation of small GTPase and phosphatidylinositol signaling initiates breaking of intracellular symmetry and are thought to play critical roles in generating polarized membrane extension and retraction. Although it is generally believed that some forms of reaction-diffusion driven mechanisms underlie these “symmetry breaking” events, the physicochemical basis of its onset, i.e. autonomous nucleation events of the localized signaling patches and actin polymerization remains unclear. Here, we report on the behavior observed in our “two-dimensional reconstituted-system” consisting of a cytosolic extract and a solid-supported lipid membrane. We tested whether the solid-supported lipid membrane in a microchamber containing cytosol extracted by Dictyostelium discoideum provides an appropriate microenvironment for localized signaling by observing translocation of PH-domain protein and PTEN which were tagged with RFP and GFP respectively. Signal intensities were analyzed by a confocal laser scanning fluorescence and bright field microscopy. We found that both the PH-domain protein and PTEN attached to the membrane composed of both lipid extract and 2- or 3- component lipid mixture. In the case of lipid extract membrane, inhomogeneous domain formation of micrometer scale was observed. We examined the effect of several inhibitors related phosphatidylinositol signaling and found different patterning of the lipid membranes. We will discuss how the current system may be employed to address the origin of self-organized PIP2/PIP3 patches during amoeboid deformation.

Inelastic X-ray scattering in YBa2Cu3O6.6 reveals giant phonon anomalies and elastic central peak due to charge-density-wave formation

The electron-phonon interaction is a major factor influencing the competition between collective instabilities in correlated-electron materials, but its role in driving high-temperature superconductivity in the cuprates remains poorly understood. We have used high-resolution inelastic x-ray scattering to monitor low-energy phonons in YBa$_2$Cu$_3$O$_{6.6}$ (superconducting $\bf T_c = 61$ K), which is close to a charge density wave (CDW) instability. Phonons in a narrow range of momentum space around the CDW ordering vector exhibit extremely large superconductivity-induced lineshape renormalizations. These results imply that the electron-phonon interaction has sufficient strength to generate various anomalies in electronic spectra, but does not contribute significantly to Cooper pairing. In addition, a quasi-elastic "central peak" due to CDW nanodomains is observed in a wide temperature range above and below $\bf T_c$, suggesting that the gradual onset of a spatially inhomogeneous CDW domain state with decreasing temperature is a generic feature of the underdoped cuprates.

Bulk crystal SiC blue LED with p–n homojunction structure fabricated by dressed-photon-phonon–assisted annealing

To fabricate a high-efficiency light emitting diode using indirect-transition-type bulk crystal SiC having a p–n homojunction structure, annealing was performed using stimulated emission via dressed photons generated at the inhomogeneous domain boundaries of Al dopant sites. This device emitted electroluminescence (EL) due to a two-step transition process via dressed-photon–phonons generated at the inhomogeneous domain boundaries of the Al dopant sites. The EL emission peak wavelength was 480–515 nm when the device was driven by a direct current and 390 nm when driven by a pulsed current. The external quantum efficiency of the EL emission was 1 %, and the internal quantum efficiency was as high as 10 %.

Measurement of multimode coherent phonons in nanometric spaces in a homojunction-structured silicon light emitting diode

This paper reports the results of measuring the sidebands in the emitted visible spectrum of a novel homo- junction-structured silicon (Si) light emitting diode (LED), which was fabricated by Joule annealing assisted by dressed- photon-phonons. Using pump-probe spectroscopy, both the fundamentals and higher-order harmonics of the longitudi- nal optical (LO) phonon were observed for the first time. These fundamentals and harmonics are the constituent com- ponents of the multimode coherent phonons generated in the nanometric spaces around the inhomogeneous domain boundaries of boron doped in the Si LED. Furthermore, it was confirmed that the fourth-order harmonics of the LO phonon are the origin of the sidebands in the emission spec- trum of the Si LED.

Thermal Analysis of High-Power Integrated Circuits and Packages Using Nonconformal Domain Decomposition Method

A nonconformal domain decomposition method (DDM) is proposed to solve moderately stiff parabolic partial differential equations in inhomogeneous domains. The proposed nonconformal DDM decomposes the entire problem domain into many nonoverlapping subdomains. Consequently, it is effective in addressing complex thermal problems of electronic systems with multiscaled features. Moreover, the time discretization employed is based on an unconditionally stable and implicit Euler scheme. The unconditionally stable time-marching algorithm is beneficial since the time-step size is no longer governed by the spatial discretization of the mesh, but rather by the desired accuracy. Additionally, this paper includes numerical investigations of the convergence properties of the proposed nonconformal DDM. Finally, numerical results are shown for a chip-package-printed circuit board example with thermal cooling by both natural convection and forced convection of heat sinks.

Properties of Individually Addressable Ferroelectric Nanocapacitor Arrays Fabricated by Focused Ion Beam Milling

Well-ordered large-areas individual addressable ferroelectric nanocapacitor arrays with Pt top electrode and various lateral sizes down to below 100 nm have been fabricated by focused ion beam (FIB) milling on Nb-doped single-crystal SrTiO3(001) substrate. The well-shaped "butterfly" displacement-voltage loop is indicative of strong ferroelectricity of the nanocapacitor arrays. All cells in the arrays with a top to bottom polarization in the initial milled state. The as-grown state domain images with various contrasts illustrate that the cells have different domain structure. The dispersion of properties and size effects exist jointly in the arrays. The piezoresponse of same cell size are different, and the difference increases with increasing cell size. The piezoresponse properties of some individual cell don't exhibit size dependence, but the properties of all cells have an obvious size depended tendency that the piezoresponse values decreases statistically with decreasing cell size. The size effects were dominated by the ion damage owing to high damaged-layer-to-volume ratio in the smaller cells, while the dispersion of properties was dominated by the inhomogeneous texture and various domain structures of the cells.

Gelation and cross-link inhomogeneity of phenolic resins studied by 13C-NMR spectroscopy and small-angle X-ray scattering

The gelation mechanism and cross-link inhomogeneity of phenolic resins prepared via polycondensation of phenol and formaldehyde under acidic conditions were studied by using 13C-NMR spectroscopy and small-angle X-ray scattering. The structural analysis of the gelation process indicated the presence of two different mechanisms of the formation and growth of the inhomogeneity that depend on the initial formaldehyde-to-phenol molar ratio: (i) when there is an insufficient amount of a cross-linker at the initial stage of gelation, inhomogeneous domains with a loosely cross-linked network appear and the degree of cross-linking in the domain increases with the reaction time. (ii) When there is a sufficient amount of a cross-linker at the initial stage of gelation, inhomogeneous domains with a tightly cross-linked network appear, followed by an increase in the size of the domains.

Relationship between grain size and the degrees of orientation in a twinned ErBa2Cu3Oy superconductor oriented in modulated rotating magnetic fields

ABSTRACTWe report the dependences of the degrees of tri- or bi-axial orientation on strength of applied magnetic fields of modulated rotating field (MRF) for twinned ErBa2Cu3Oy (Er123) powder samples oriented in epoxy resin under various MRF conditions. Introduction of a pulverization process in the Er123 powders improved the degrees of inplane orientations, and is effective for enhancing the inplane magnetic anisotropy of Er123 grains with twin microstructure. Formation of inhomogeneous domain structure is a dominant factor of the enhancement, and the present study indicates possibility of tri- or bi-axial orientation of the twinned Er123 grains even under relatively low MRF conditions around 1 T.

High temperature Aurivillius piezoelectrics: the effect of (Li, Ln) modification on the structure and properties of (Li, Ln)0.06(Na, Bi)0.44Bi2Nb2O9 (Ln = Ce, Nd, La and Y)

High temperature Aurivillius piezoelectrics, (Li, Ln)(0.06)(Na, Bi)(0.44)Bi(2)Nb(2)O(9) (NBN-LiLn), with Li and Ln (Ce, Nd, La and Y) co-substitution at the A site, were prepared using a solid-state reaction process. Taking cation disordering between A site and the (Bi(2)O(2))(2+) layers into consideration, the crystal structure of (Li, Nd)(0.06)(Na, Bi)(0.44)Bi(2)Nb(2)O(9) (NBN-LiNd) was refined by using the Rietveld method with powder X-ray diffraction, which was confirmed to be a two-layer Aurivillius oxide with an orthorhombic space group, A2(1)am [a = 5.48666(9) Å, b = 5.46046(8) Å, c = 24.9122(4) Å and Z = 4], at room temperature. LiNd substitution induced a decrease in cation disorder and an increase in orthorhombic distortion. The ferroelectric to paraelectric phase transition temperature (T(c)) of the NBN-LiLn (Ln = Ce, Nd, La and Y) ceramics ranged from 751 to 842 °C and the T(c) increased as the radii of the Ln(3+) (Ce(3+), Nd(3+), La(3+) and Y(3+)) was decreased. The NBN-LiCe and NBN-LiNd had a d(33) of 31 and 29 pC N(-1), respectively, which is much higher than the reported d(33) values of other Aurivillius ceramics with a high T(c) (T(c) > 650 °C, d(33) < 20 pC N(-1)). With increasing annealing temperature, a significant degradation in d(33) was observed for NBN-LiCe, while no drop in d(33) was observed up to 650 °C for NBN-LiNd. The inhomogeneous domain structures determined the dissimilar piezoelectric behaviors of NBN-LiCe and NBN-LiNd.

Three dimensional smoothed fixed grid finite element method for the solution of unconfined seepage problems

A three dimensional numerical analysis for unconfined seepage problems in inhomogeneous and anisotropic domains with arbitrary geometry is presented in this paper. The unconfined seepage problems are nonlinear in its nature due to unknown location of the phreatic surface and nonlinear boundary conditions which complicates its solution. The presented method is based on the application of non-boundary-fitted meshes and is an extension of the recently proposed two dimensional smoothed fixed grid finite element method. The main objective of using this method is to facilitate solution of variable domain problems and improve the accuracy of the formulation of the boundary intersecting elements. In this method, the gradient smoothing technique is used to obtain the element matrices. This technique simplifies the solution significantly by reducing the volume integrals over the elements into area integrals on the faces of smoothing cells. To locate the free surface, an initial guess for the unknown geometry is selected and modified in each iteration to eventually satisfy nonlinear boundary condition. The application of the proposed technique for three dimensional seepage problems is carried out for different examples including rectangular, trapezoidal and semi-cylindrical dams and the results are compared with those available in the literature.

Focal aberrations of large-aperture HOPG von-Hàmos x-ray spectrometers

Focal aberrations of large-aperture highly oriented pyrolytic graphite (HOPG) crystals in von-Hàmos geometry are investigated by experimental and computational methods. A mosaic HOPG crystal film of 100 μm thickness diffracts 8 keV x-rays. This thickness is smaller than the absorption depth of the symmetric 004-reflection, which amounts to 257 μm. Cylindrically bent crystals with 110mm radius of curvature and up to 100 mm collection width produce a X-shaped halo around the focus. This feature vanishes when the collection aperture is reduced, but axial spectral profiles show that the resolution is not affected. X-ray topography reveals significant inhomogeneous crystallite domains of 2±1mm diameter along the entire crystal. Rocking curves shift by about ±20arcmin between domains, while their full width at half-maximum varies between 30 and 50 arcmin. These inhomogeneities are not imprinted at the focal spot, since the monochromatically reflecting area of the crystal is large compared to inhomogeneities. Ray-tracing calculations using a Monte-Carlo-based algorithm developed for mosaic crystals reproduce the X-shaped halo in the focal plane, stemming from the mosaic defocussing in the non-dispersive direction in combination with large apertures. The best achievable resolution is found by analyzing a diversity of rocking curve widths, source sizes and crystal thicknesses for 8 keV x-rays to be ΔE/E ∼ 10−4. Finally a general analytic expression for the shape of the aberration is derived.

Disordered-based theory of pseudogap, superconducting gap, and Fermi arc of cuprates

A model for cuprate superconductors based on weakly coupled inhomogeneous electronic domains forming an array of Josephson junctions is studied. This approach provides physical insights to the most important properties of these materials like the pseudogap phase as forming by the onset of intradomains superconducting amplitudes and the zero resistivity critical temperature Tc due to phase coherence activated by Josephson coupling. The formation of the Fermi arcs and the dichotomy in k-space follow from the direction dependence of the junctions tunneling supercurrent and the quantum fluctuations of the d-wave order parameter symmetry on the CuO2 planes. This procedure reproduces the details of the cuprate Bi2212 phase diagram.

Interconnect Joule Heating under Transient Currents using the Transmission Line Matrix Method

The quality and reliability of interconnects in microelectronics is a major challenge considering the increasing level of integration and high current densities. This work studied the problem of transient Joule heating in interconnects in a two-dimensional (2D) inhomogeneous domain using the transmission line matrix (TLM) method. Computational efficiency of the TLM method and its ability to accept non-uniform 2D and 3D mesh and variable time step makes it a good candidate for multi-scale analysis of Joule heating in on-chip interconnects. The TLM method was implemented with link-resistor (LR) and link-line (LL) formulations, and the results were compared with a finite element (FE) model. The overall behavior of the TLM models were in good agreement with the FE model while, near the heat source, the transient TLM solutions developed slower than the FE solution. The steady-state results of the TLM and FE models were identical. The two TLM formulations yielded slightly different transient results, with the LL result growing slower, particularly at the source boundary and becoming unstable at short time-steps. It was concluded that the LR formulation is more accurate for transient thermal analysis.

Subpicosecond Domain Switching in Discrete Regions of Pb(Zr0.35Ti0.65)O3 Thick Films

AbstractThe time dependence of the domain switching current density, Jsw(t), under pulsed voltages on a ferroelectric parallel‐plate capacitor is the consequence of region‐by‐region polarization reversals across the film. As the distributive coercive voltage of domain nucleation increases from zero to the maximum applied voltage during the capacitor charging time, Jsw(t) is proportional to the domain switching speed at each time. By transforming the spatially inhomogeneous domain nucleation distribution into a temporal distribution of coercive fields (Ec), a local lnJsw versus Ec−1 plot is derived for each domain, following the Merz equation. This provides insight into the independent domain switching dynamics at different nucleation sites in Pb(Zr0.35Ti0.65)O3 thick films over a large current range. Although the activation field of the slope of the lnJsw(t) versus Ec−1 plot varies with film area and temperature, all the plots extrapolate to a single point (J0, E0) from which the ultimate domain switching current density of J0 =1.4 × 108 A cm−2 at the highest field of E0 = 0.20‐0.25 MV cm−1 is derived. Unexpectedly, J0 and E0 are independent of the film thickness and area, after correction for a small interfacial‐layer effect. This analysis provides rigorous evidence for nucleation rate‐limited domain switching with a subpicosecond nucleation time and the relative unimportance of domain forward‐growth time across film thicknesses between 0.14 and 2 μm. This work paves the way to improve the efficiency of ferroelectric thick‐film functionality in electronic and optoelectronic devices with ultrafast clock rates.

&amp;lt;i&amp;gt;L&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt;-Estimations of Vector Fields in Unbounded Domains

Some new estimations of scalar products of vector fields in unbounded domains are investigated. Lp-estimations for the vector fields were proved in special weighted functional spaces. The paper generalizes our earlier results for bounded domains. Estimations for scalar products make it possible to investigate wide classes of mathematical physics problems in physically inhomogeneous domains. Such estimations allow studying issues of correctness for problems with non-smooth coefficients. The paper analyses solvability of stationary set of Maxwell equations in inhomogeneous unbounded domains based on the proved Lp-estimations.

Inhomogeneous nucleation and domain wall motion with Barkhausen avalanches in epitaxial PbZr0.4Ti0.6O3 thin films

We investigated the ferroelectric (FE) domain nucleation and domain wall motion in epitaxial PbZr0.4Ti0.6O3 capacitors by using modified piezoresponse force microscopy with the domaintracing method. From time-dependent FE domain evolution images, we observed that defectmediated inhomogeneous nucleation occurred with a stochastic nature. In addition, we found that the number of nuclei N(t) was linearly proportional to log t, where t is the accumulated time of the applied pulse fields. The time-dependence of N(t) suggests a distribution of energy barriers for nucleation, which may determine the stochastic nature of domain nucleation. We also observed that the domain grew with consecutive Barkhausen avalanches and that the growth direction became anisotropic when the domain radius was larger than a critical radius of about 100 nm.

Spatially resolved twin domain distribution and lattice parameter variations in the near-surface region of SrTiO3 single crystals

We investigated the twin domain distribution and lattice parameter variations associated with the displacive phase transition in SrTiO3 by means of X-ray diffraction with high spatial resolution. By using 4.5-keV photons, the probed region is the first micrometer near the surface. We find a very inhomogeneous domain distribution, showing both regions with large monodomains and highly twinned regions, as well as large needle domains. Also, the lattice parameters in these different regions vary substantially.

A Perfectly Matched Layer Absorbing Boundary Condition and Wave-Maker Modeling for Wave Propagation Problems in Inhomogeneous Infinite-Domains

For wave propagation problems in infinite-domains, truncation of the far-field by an artificial boundary is essential to define a bounded domain of interest; resultant difficulties are the radiation condition and generation of incident waves. Instead of the radiation condition, an absorbing boundary condition (ABC) is implemented in an inhomogeneous exterior domain, based on the perfectly matched layer (PML) technique. Complex coordinate stretching, a key PML concept, analytically continues a governing equation in the domain of interest into a PML equation as an anisotropic absorbing boundary in the exterior domain; a system of equivalent equations governs waves in the whole computational domain, and thus the PML is reflectionless at the artificial boundary, an interface between the PML and the domain of interest. For generation of incident waves, wave-maker modeling is proposed based on an idea of plain topography and wave-ray tracing. A source function along the interface is a curvilinear integral in a weak form for the governing equation. Finite element examples for wave propagation in one-dimension verify ability and efficiency of techniques with PML ABCs; besides, those for wave scattering by a circular cylinder on a slope show effectiveness of the wave-maker modeling.