Pole Expansion Research Articles

Electronic structure and aromaticity of large-scale hexagonal graphene nanoflakes.

With the help of the recently developed SIESTA-pole (Spanish Initiative for Electronic Simulations with Thousands of Atoms) - PEXSI (pole expansion and selected inversion) method [L. Lin, A. García, G. Huhs, and C. Yang, J. Phys.: Condens. Matter 26, 305503 (2014)], we perform Kohn-Sham density functional theory calculations to study the stability and electronic structure of hydrogen passivated hexagonal graphene nanoflakes (GNFs) with up to 11,700 atoms. We find the electronic properties of GNFs, including their cohesive energy, edge formation energy, highest occupied molecular orbital-lowest unoccupied molecular orbital energy gap, edge states, and aromaticity, depend sensitively on the type of edges (armchair graphene nanoflakes (ACGNFs) and zigzag graphene nanoflakes (ZZGNFs)), size and the number of electrons. We observe that, due to the edge-induced strain effect in ACGNFs, large-scale ACGNFs' edge formation energy decreases as their size increases. This trend does not hold for ZZGNFs due to the presence of many edge states in ZZGNFs. We find that the energy gaps E(g) of GNFs all decay with respect to 1/L, where L is the size of the GNF, in a linear fashion. But as their size increases, ZZGNFs exhibit more localized edge states. We believe the presence of these states makes their gap decrease more rapidly. In particular, when L is larger than 6.40 nm, we find that ZZGNFs exhibit metallic characteristics. Furthermore, we find that the aromatic structures of GNFs appear to depend only on whether the system has 4N or 4N + 2 electrons, where N is an integer.

Metallic nanoparticles on waveguide structures: effects on waveguide mode properties and the promise of sensing applications: erratum

We present a treatment of metallic nanoparticles on waveguide (WG) structures, treating the scenario where the spacing between the metallic nanoparticles is much less than the wavelength of light. We derive an effective medium treatment of the layer containing the nanoparticles, introducing transfer matrices for the layer. The coefficients of the transfer matrices take into account the interaction of the nanoparticles with each other, as well as local field corrections to the interaction of the nanoparticles with the material beneath them. Used with the WG mode pole expansions for the Fresnel coefficients of the WG structure, this allows for simple expressions for the shift and width of the WG mode resonance wave vector induced by the nanoparticles. As an example, we work out the simple case where the nanoparticles are treated as point dipoles, and use it to investigate the potential of this kind of structure for sensing applications.

Analytic representations of bath correlation functions for ohmic and superohmic spectral densities using simple poles.

We present a scheme to express a bath correlation function (BCF) corresponding to a given spectral density (SD) as a sum of damped harmonic oscillations. Such a representation is needed, for example, in many open quantum system approaches. To this end we introduce a class of fit functions that enables us to model ohmic as well as superohmic behavior. We show that these functions allow for an analytic calculation of the BCF using pole expansions of the temperature dependent hyperbolic cotangent. We demonstrate how to use these functions to fit spectral densities exemplarily for cases encountered in the description of photosynthetic light harvesting complexes. Finally, we compare absorption spectra obtained for different fits with exact spectra and show that it is crucial to take properly into account the behavior at small frequencies when fitting a given SD.

SIESTA-PEXSI: massively parallel method for efficient and accurate ab initio materials simulation without matrix diagonalization

We describe a scheme for efficient large-scale electronic-structure calculations based on the combination of the pole expansion and selected inversion (PEXSI) technique with the SIESTA method, which uses numerical atomic orbitals within the Kohn–Sham density functional theory (KSDFT) framework. The PEXSI technique can efficiently utilize the sparsity pattern of the Hamiltonian and overlap matrices generated in SIESTA, and for large systems it has a much lower computational complexity than that associated with the matrix diagonalization procedure. The PEXSI technique can be used to evaluate the electron density, free energy, atomic forces, density of states and local density of states without computing any eigenvalue or eigenvector of the Kohn–Sham Hamiltonian. It can achieve accuracy fully comparable to that obtained from a matrix diagonalization procedure for general systems, including metallic systems at low temperature. The PEXSI method is also highly scalable. With the recently developed massively parallel PEXSI technique, we can make efficient use of more than 10 000 processors on high performance machines. We demonstrate the performance and accuracy of the SIESTA-PEXSI method using several examples of large scale electronic structure calculations, including 1D, 2D and bulk problems with insulating, semi-metallic, and metallic character.

Axial active magnetic bearing design

The purpose of this paper is to propose a useful method to implement active magnetic bearings (AMBs) on an existing rotating shaft which rotates on conventional bearings. This is feasible if AMBs can produce the same reaction loads of conventional ones and if the size of the vane is large enough to host an AMB. As this substitution could give some difficulties due to the different size between magnetic bearings and conventional ones, a set of equations are performed to show that a variation of some parameters can solve this problem. The coil ratio is the geometrical parameter introduced to develop the present analysis. The variation of coil ratio does not produce a variation of the pole’s surface so that the reaction load does not change. The results are analyzed by numerical analysis by mathematical relationships involving the design parameters, magneto-static simulations and dynamic simulation on the shaft when it is tested by a step response and performing frequency response parameterized with coil ratio. Results show that the displacement carried out by the step response is always the same, when the journal ratio and frequency response are varied, confirming that the reaction load, produced by pole expansion, remains the same when the coil ratio varies. The simulations and results are performed by finite element method magnetic and MATLab software.

Pole Expansion for Solving a Type of Parametrized Linear Systems in Electronic Structure Calculations

We present a new method for solving parametrized linear systems. Under certain assumptions on the parametrization, solutions to the linear systems for all parameters can be accurately approximated by linear combinations of solutions to linear systems for a small set of fixed parameters. Combined with either direct solvers or preconditioned iterative solvers for each linear system with a fixed parameter, the method is particularly suitable for situations when solutions to a large number of distinct parameters or a large number of right-hand sides are required. The method is also simple to parallelize. We demonstrate the applicability of the method to the calculation of the response functions in electronic structure theory. We demonstrate the numerical performance of the method using a benzene molecule and a DNA molecule.

Accelerating atomic orbital-based electronic structure calculation via pole expansion and selected inversion

We describe how to apply the recently developed pole expansion and selected inversion (PEXSI) technique to Kohn–Sham density function theory (DFT) electronic structure calculations that are based on atomic orbital discretization. We give analytic expressions for evaluating the charge density, the total energy, the Helmholtz free energy and the atomic forces (including both the Hellmann–Feynman force and the Pulay force) without using the eigenvalues and eigenvectors of the Kohn–Sham Hamiltonian. We also show how to update the chemical potential without using Kohn–Sham eigenvalues. The advantage of using PEXSI is that it has a computational complexity much lower than that associated with the matrix diagonalization procedure. We demonstrate the performance gain by comparing the timing of PEXSI with that of diagonalization on insulating and metallic nanotubes. For these quasi-1D systems, the complexity of PEXSI is linear with respect to the number of atoms. This linear scaling can be observed in our computational experiments when the number of atoms in a nanotube is larger than a few hundreds. Both the wall clock time and the memory requirement of PEXSI are modest. This even makes it possible to perform Kohn–Sham DFT calculations for 10 000-atom nanotubes with a sequential implementation of the selected inversion algorithm. We also perform an accurate geometry optimization calculation on a truncated (8, 0) boron nitride nanotube system containing 1024 atoms. Numerical results indicate that the use of PEXSI does not lead to loss of the accuracy required in a practical DFT calculation.

Random noise and pole-dynamics in unstable front propagation

The current paper is a corrected version of our previous paper arXiv:adap-org/9608001. Similarly to previous version we investigate the problem of flame propagation. This problem is studied as an example of unstable fronts that wrinkle on many scales. The analytic tool of pole expansion in the complex plane is employed to address the interaction of the unstable growth process with random initial conditions and perturbations. We argue that the effect of random noise is immense and that it can never be neglected in sufficiently large systems. We present simulations that lead to scaling laws for the velocity and acceleration of the front as a function of the system size and the level of noise, and analytic arguments that explain these results in terms of the noisy pole dynamics.This version corrects some very critical errors made in arXiv:adap-org/9608001 and makes more detailed description of excess number of poles in system, number of poles that appear in the system in unit of time, life time of pole. It allows us to understand more correctly dependence of the system parameters on noise than in arXiv:adap-org/9608001

Metallic nanoparticles on waveguide structures: effects on waveguide mode properties and the promise of sensing applications

We present a treatment of metallic nanoparticles on waveguide (WG) structures, treating the scenario where the spacing between the metallic nanoparticles is much less than the wavelength of light. We derive an effective medium treatment of the layer containing the nanoparticles, introducing transfer matrices for the layer. The coefficients of the transfer matrices take into account the interaction of the nanoparticles with each other, as well as local field corrections to the interaction of the nanoparticles with the material beneath them. Used with the WG mode pole expansions for the Fresnel coefficients of the WG structure, this allows for simple expressions for the shift and width of the WG mode resonance wave vector induced by the nanoparticles. As an example, we work out the simple case where the nanoparticles are treated as point dipoles, and use it to investigate the potential of this kind of structure for sensing applications.

Wideband generalized admittance matrix representation for the analysis and design of waveguide filters with coaxial excitation

A very efficient technique for the full‐wave analysis and design of complex passive waveguide filters, including rectangular cavities with metallic cylindrical posts and coaxial excitation, is presented. This novel technique provides the wideband generalized admittance matrix representation of the whole structure in the form of pole expansions, thus extracting the most expensive computations from the frequency loop. For this purpose, the structure is properly segmented into its key building blocks, all of them characterized in terms of wideband admittance matrices. Then, an efficient iterative algorithm for combining these matrices, and finally providing the wideband generalized admittance matrix of the complete structure, is followed. In order to validate the accuracy and efficiency of this full‐wave modal technique, four different waveguide filters have been considered. In particular, the design of a compact four‐pole in‐line filter with tuning screws and of an evanescent‐mode filter, both operating in the X‐band and including a standard (vertical) coaxial excitation, are first presented. Finally, two C‐band six‐resonator comb‐line filters, one of them with a cross‐coupling configuration, and both excited with a collinear end‐launcher transition based on a disc‐ended coaxial, are also designed. Numerical data from a commercial software, as well as measurements of a manufactured prototype, are included for verification purposes.

Breast Envelope Expansion in Augmentation Mammoplasty: Comparative Data Analysis in Submuscular and Subglandular Planes.

Aim: Longevity and aesthetic outcome of augmentation mammoplasty partly depends on breast envelopestability. Changes in breast envelope, on the other hand, are dynamic and depends on the pocket selection. Aretrospective data analysis was done to establish the effects of interaction between implant and its pocket onbreast envelope.Methods: Augmentation mammoplasty using an inframammary crease incision was selected and retrospectivedata of augmentation mammoplasty was retrieved. Each breast was treated as a single unit and data of 2,000augmented breasts was analysed. Data of preoperative nipple to the marked incision on stretched skin and sixmonths postoperative nipple to neo IMC measurements changes were analysed when implants were placed inpartial submuscular and subglandular plane.Results: With a similar mean preoperative marked incision in a stretched skin, postoperative results in partialsubmuscular pocket showed less lower pole expansion as compared to subglandular plane.Conclusion: Skin envelope in a submuscular plane, is supported better when pectoralis enforces posterior wall ofthe breast envelope.is a need of mass awareness and social support of T.B sufferers; and sympathetic attitude of Health CareProviders.Key Words: Breast morphometry, Submuscular Biplane Augmentation, Breast Envelope Dynamics.

Complications of Acellular Dermal Matrices in Breast Surgery

Acellular dermal matrices have been used in breast surgery for a decade. They are widely used in implant-based breast reconstruction to provide coverage of the inferolateral aspects of the prosthesis. Numerous benefits have been reported with this approach including improved fold control, better support and control of the implant pocket with concomitant reduced risk of malposition, and improved lower pole expansion. Seroma, infection, mastectomy skin necrosis, and expander/implant loss are the most commonly reported complications with this approach, and the incidences vary widely among studies. Patient selection and adherence to established intraoperative technique principles related to acellular dermal matrix use are both critical to minimizing the risk of complications. Acellular dermal matrices are also being used in aesthetic breast surgery, revision breast surgery, and nipple reconstruction, but clinical experience is limited. This article reviews the complications associated with the use of matrices in breast surgery from the published literature.

Human Acellular Dermis versus No Acellular Dermis in Tissue Expansion Breast Reconstruction

Human acellular dermis has been adopted for routine use in tissue expander reconstruction. The purported benefits include higher intraoperative fill volume, facilitation of lower pole expansion, and enhanced definition of the lower pole of the breast. Recently, concerns have arisen about an increase in postoperative complications with its use. A retrospective review was conducted of patients who had immediate postmastectomy breast reconstruction with a tissue expander from July of 2001 to July of 2011. All tissue expander reconstructions before 2005 were performed submuscularly only and all subsequent to 2005 with the use of AlloDerm (LifeCell, Branchburg, N.J.) acellular dermis. Patient demographics were collected, and complications were recorded. The study cohort included 346 patients and 511 immediate breast reconstructions; 232 patients and 346 breasts were reconstructed with and 114 patients and 165 breasts without acellular dermis. Age, body mass index, diabetes, and tobacco use were equivalent in the two groups. Seroma occurrence in the acellular dermis group was nearly twice (30.0 versus 15.1 percent) that of the no acellular dermis breasts, but the tissue expander loss was only slightly higher (11.6 versus 8.5 percent) and not statistically significant. Body mass index in patients who lost their tissue expander was 31 kg/m, statistically significantly higher than in those who did not. The presence of acellular dermis did not increase the incidence of tissue expander loss, despite a doubling of frequency of seroma. Prior radiation and use of acellular dermis did culminate in a prohibitively high loss rate of the tissue expander.

Active magnetic bearing design study

The purpose of this paper is to propose a useful method to implement active magnetic bearings (AMBs) on an existing rotating shaft which rotates on conventional bearings. This is feasible if AMBs can produce the same reaction loads of conventional ones and if the size of vane is large enough to host an AMB. As this substitution could offer some difficulties due to the different size between magnetic bearings and conventional ones, a set of equations are performed to show that a variation of some parameters can solve this problem. The journal ratio is the geometrical parameter introduced to develop the present analysis. The variation of journal ratio does not produce a variation of the pole’s surface so that the reaction load does not change. The results are analyzed by numerical analysis by mathematical relationships involving the design parameters, magneto-static simulations and dynamic simulation on shaft when it is tested by disturbance rejection and reference tracking input in order to analyze the differences on dynamic behavior of the shaft on its suspended sections. Results show that the displacement pattern of the suspended sections remains unchanged, confirming that the reaction load, produced by pole expansion, remains the same varying the journal ratio.

Pole expansion of self-energy and interaction effect for topological insulators

We study effect of interactions on time-reversal-invariant topological insulators. Their topological indices are expressed by interacting Green's functions. Under the local self-energy approximation, we connect topological index and surface states of an interacting system to an auxiliary noninteracting system, whose Hamiltonian is related to the pole-expansions of the local self-energy. This finding greatly simplifies the calculation of interacting topological indices and gives an noninteracting pictorial description of interaction driven topological phase transitions. Our results also bridge studies of the correlated topological insulating materials with the practical dynamical-mean-field-theory calculations.

High order quadratures for the evaluation of interfacial velocities in axi-symmetric Stokes flows

We propose new high order accurate methods to compute the evolution of axi-symmetric interfacial Stokes flow. The velocity at a point on the interface is given by an integral over the surface. Quadrature rules to evaluate these integrals are developed using asymptotic expansions of the integrands, both locally about the point of evaluation, and about the poles, where the interface crosses the axis of symmetry. The local expansions yield methods that converge to the chosen order pointwise, for fixed evaluation point. The pole expansions yield corrections that remove maximal errors of low order, introduced by singular behaviour of the integrands as the evaluation point approaches the poles. An interesting example of roundoff error amplification due to cancellation is also addressed. The result is a uniformly accurate fifth order method. Second order, pointwise fifth order, and uniform fifth order methods are applied to compute three sample flows, each of which presents a different computational difficulty: an initially bar-belled drop that pinches in finite time, a drop in a strain flow that approaches a steady state, and a continuously extending drop. In each case, the fifth order methods significantly improve the ability to resolve the flow. The examples furthermore give insight into the effect of the corrections needed for uniformity. We determine conditions under which the pointwise method is sufficient to obtain resolved results, and others under which the corrections significantly improve the results.

Acellular Dermis-Assisted Breast Reconstruction With the Use of Crescentric Tissue Expansion: A Functional Cosmetic Analysis of 40 Consecutive Patients

Crescentric tissue expanders have the potential to improve postoperative aesthetic results via selective lower pole expansion; however, limited data are available on their efficacy. The authors assess postoperative functional and cosmetic outcomes of acellular dermis-assisted breast reconstruction with crescentric tissue expansion. This study is a single-institution, retrospective review of 40 consecutive patients who underwent acellular dermis-assisted breast reconstruction with crescentric tissue expansion. Demographic data, operative details, and procedural outcomes were recorded and assessed. Cosmetic outcomes were assessed using the Breast Evaluation Questionnaire. Fifty-eight breasts representing 36 bilateral and 22 unilateral reconstructions were analyzed. Of these, 45 (78%) underwent tissue expander (TE) to implant exchange. The mean interval between stage 1 and stage 2 was 92 +/- 20 days, with a total follow-up time of 141 +/- 16 days. The average intraoperative expander fill volume was 213.5 mL, with an average final fill of 285 mL (range, 180-740 mL). The average number of expansions was 1.6. Overall, there were five complications (8.6%). Eighty-three percent of patients participated in the breast evaluation questionnaire. Answers to each question were reported using a qualitative five-point scale that ranged from 1 (very dissatisfied) to 5 (very satisfied). For the bilateral reconstructions, the average score in all contexts was 4.5 +/- 0.3, 4.33 +/- 0.5, and 4.36 +/- 0.33 for size, shape, and firmness, respectively. For unilateral reconstructions, the average scores were 4.0 +/- 0.58, 3.93 +/- 0.38, and 4.13 +/- 0.21, respectively. Crescentric expander-based reconstruction with acellular dermis assistance is well tolerated, especially in smaller breasted women. Functional and cosmetic outcomes were acceptable and comparable to previous reports of traditional expander-based reconstructions.

Pole expansion of the Lorenz-Mie coefficients

A spectral approach to the Lorenz-Mie problem was adopted to obtain a pole expansion of the Lorenz-Mie coefficients in the complex variable z = 4=(n2 - 1), where n2 is the dielectric permittivity of the scatterer. In the absence of magnetic properties (which is assumed), n is the refractive index of the scatterer. It is shown that the Lorenz-Mie coefficients are meromorphic functions of z with simple poles. The poles and the residues are functions of the size parameter x = ka = 2a/ and of the order of the Lorenz-Mie coefficient, l, but are independent of the material properties. This leads to a numerically efficient representation of the Lorenz-Mie coefficients.

Acellular Dermis–Assisted Prosthetic Breast Reconstruction versus Complete Submuscular Coverage: A Head-to-Head Comparison of Outcomes

Complete submuscular tissue expander coverage affords the best protection against implant exposure but restricts lower pole expansion. Techniques using acellular dermis as a pectoralis muscle extension can allow for more rapid fill of the expander and better control of the inframammary fold. This study compares both techniques with regard to relevant outcomes. Results of 100 consecutive breast expander reconstructions performed by two surgeons between 2004 and 2007 were retrospectively reviewed. Patient demographics, expander coverage type, adjuvant treatment, length and characteristics of the expansion, and incidence and types of complications were analyzed. One hundred women underwent breast reconstruction with 172 expanders, in 50 using complete submuscular placement and in 50 using partial subpectoral placement with acellular dermis. The patient groups were similar in terms of demographic data. Mean number of fills to complete reconstruction was 4.31 in the submuscular group and 1.72 in the acellular dermis group (p = 0.0001). Mean intraoperative fill volume was 130 cc in the submuscular group, compared with 412 cc per expander in the acellular dermis group (p = 0.0001). Fisher's exact test demonstrated no significant difference in total complication rate between the two groups (14 percent versus 18 percent; p = 0.79). Acellular dermis allowed for a greater initial fill of saline. This potentially improves cosmetic outcome, as it better capitalizes on preserved mastectomy skin for reconstruction. The authors conclude that acellular dermis-assisted implant breast reconstruction has a safety profile no worse than that of complete submuscular coverage but offers the benefit of fewer expansions and the potential for more predictable secondary revisions.

Partial-wave Scattering and Statistical Mechanics via the l-wave Non-local Separable Potential of Rank-two

The equilibrium statistical mechanics relations are shown to be related to T-matrix, which describes the scattering processes taking place in the thermodynamic system consisting of free particles and independent correlated pairs, interacting via the separable non-local potential of rank two in the lth partial wave. Thermodynamic properties are related to the correlated states, when making a pole expansion of the analytically continued momentum matrix element of R l (z), the difference between the resolvents of the interacting and free Hamiltonians. It is shown that local potentials equivalent to the nonlocal ones have an attractive part which is responsible for a bound state and negative values of some thermodynamic properties.