Second-Order Two-Scale Analysis Method for the Heat Conductive Problem with Radiation Boundary Condition in Periodical Porous Domain

In this paper a second-order two-scale (SOTS) analysis method is developed for a static heat conductive problem in a periodical porous domain with radiation boundary condition on the surfaces of cavities. By using asymptotic expansion for the temperature field and a proper regularity assumption on the macroscopic scale, the cell problem, effective material coefficients, homogenization problem, first-order correctors and second-order correctors are obtained successively. The characteristics of the asymptotic model is the coupling of the cell problems with the homogenization temperature field due to the nonlinearity and nonlocality of the radiation boundary condition. The error estimation is also obtained for the original solution and the SOTS's approximation solution. Finally the corresponding finite element algorithms are developed and a simple numerical example is presented.     

Time-Harmonic Acoustic Scattering in a Complex Flow: A Full Coupling Between Acoustics and Hydrodynamics

For the numerical simulation of time harmonic acoustic scattering in a complex geometry, in presence of an arbitrary mean flow, the main difficulty is the coexistence and the coupling of two very different phenomena: acoustic propagation and convection of vortices. We consider a linearized formulation coupling an augmented Galbrun equation (for the perturbation of displacement) with a time harmonic convection equation (for the vortices). We first establish the well-posedness of this time harmonic convection equation in the appropriate mathematical framework. Then the complete problem, with Perfectly Matched Layers at the artificial boundaries, is proved to be coercive + compact, and a hybrid numerical method for the solution is proposed, coupling finite elements for the Galbrun equation and a Discontinuous Galerkin scheme for the convection equation. Finally a 2D numerical result shows the efficiency of the method.     

A Finite Volume Method for the Multi Subband Boltzmann Equation with Realistic 2D Scattering in Double Gate MOSFETs

We propose a deterministic solver for the time-dependent multi-subband Boltzmann transport equation (MSBTE) for the two dimensional (2D) electron gas in double gate metal oxide semiconductor field effect transistors (MOSFETs) with flared out source/drain contacts. A realistic model with six-valleys of the conduction band of silicon and both intra-valley and inter-valley phonon-electron scattering is solved. We propose a second order finite volume method based on the positive and flux conservative (PFC) method to discretize the Boltzmann transport equations (BTEs). The transport part of the BTEs is split into two problems. One is a 1D transport problem in the position space, and the other is a 2D transport problem in the wavevector space. In order to reduce the splitting error, the 2D transport problem in the wavevector space is solved directly by using the PFC method instead of splitting into two 1D problems. The solver is applied to a nanoscale double gate MOSFET and the current-voltage characteristic is investigated. Comparison of the numerical results with ballistic solutions show that the scattering influence is not ignorable even when the size of a nanoscale semiconductor device goes to the scale of the electron mean free path.     

Matched Asymptotic Expansions of the Eigenvalues of a 3-D Boundary-Value Problem Relative to Two Cavities Linked by a Hole of Small Size

In this article, we consider a domain consisting of two cavities linked by a hole of small size. We derive a numerical method to compute an approximation of the eigenvalues of an elliptic operator without refining in the neighborhood of the hole. Several convergence rates are obtained and illustrated by numerical simulations.     

Numerical Analysis of Inverse Elasticity Problem with Signorini's Condition

An optimal control problem is considered to find a stable surface traction, which minimizes the discrepancy between a given displacement field and its estimation. Firstly, the inverse elastic problem is constructed by variational inequalities, and a stable approximation of surface traction is obtained with Tikhonov regularization. Then a finite element discretization of the inverse elastic problem is analyzed. Moreover, the error estimation of the numerical solutions is deduced. Finally, a numerical algorithm is detailed and three examples in two-dimensional case illustrate the efficiency of the algorithm.     

A Second-Order Scheme with Nonuniform Time Steps for a Linear Reaction-Subdiffusion Problem

It is reasonable to assume that a discrete convolution structure dominatesthe local truncation error of any numerical Caputo formula because the fractional timederivative and its discrete approximation have the same convolutional form. We suggest an error convolution structure (ECS) analysis for a class of interpolation-type approximations to the Caputo fractional derivative. Our assumptions permit the use ofadaptive time steps, such as is appropriate for accurately resolving the initial singularity of the solution and also certain complex behavior away from the initial time.The ECS analysis of numerical approximations has two advantages: (i) to localize (andsimplify) the analysis of the approximation error of a discrete convolution formula ongeneral nonuniform time grids; and (ii) to reveal the error distribution information inthe long-time integration via the global consistency error. The core result in this paper is an ECS bound and a global consistency analysis of the nonuniform Alikhanovapproximation, which is constructed at an offset point by using linear and quadraticpolynomial interpolation. Using this result, we derive a sharp $L^2$-norm error estimateof a second-order Crank-Nicolson-like scheme for linear reaction-subdiffusion problems. An example is presented to show the sharpness of our analysis.     

A Nodal Finite Element Method for a Thermally Coupled Eddy-Current Problem with Moving Conductors

This paper aims to design and analyze a solution method for a time-dependent, nonlinear and thermally coupled eddy-current problem with a movingconductor on hyper-velocity. We transform the problem into an equivalent coupledsystem and use the nodal finite element discretization (in space) and the implicit Euler method (in time) for the coupled system. The resulting discrete coupled system isdecoupled and implicitly solved by a time step-length iteration method and the Picarditeration. We numerically and theoretically prove that the finite element approximations have the optimal error estimates and both the two iteration methods possess thelinear convergence. For the proposed method, numerical stability and accuracy of theapproximations can be held even for coarser mesh partitions and larger time steps.We also construct a preconditioner for the discrete operator defined by the linearizedbilinear form and show that this preconditioner is uniformly effective. Numerical experiments are done to confirm the theoretical results and illustrate that the proposedmethod is well behaved in large-scale numerical simulations.     

Modified Lateral Thoracodorsal Flap: A Way Out of a Difficult Problem

Background

Breast deformities, often attributable to surgical mutilations as a result of mammary carcinoma treatment, still are a challenge to plastic surgeons. Interesting alternatives for the frequently used musculocutaneous flaps are local flaps such as the lateral thoracodorsal flap developed by Holmström in 1986. This flap is simple to raise and involves no sacrifice of important muscular structures. This report aims to demonstrate the use of the modified lateral thoracodorsal flap in an immediate mammary reconstruction for a patient who refused any other scar.

Methods

A case report describes a patient presenting with breast cancer after reduction mammaplasty who was treated with a skin-sparing mastectomy and immediate reconstruction.

Results

Satisfactory defect correction was accomplished with adequate silicone implant covering and a natural ptotic breast shape.

Conclusions

The versatility of this flap and its simple execution make it an important option for diverse breast reconstruction situations. The lateral thoracodorsal flap provides aesthetic results similar to those with other reconstruction methods, but without major complexity. The authors believe that it could be an interesting tool for the treatment of a breast anomaly.     

A Priori and a Posteriori Error Estimates for H(div)-Elliptic Problem with Interior Penalty Method

In this paper, we propose and analyze the interior penalty discontinuous Galerkin method for H(div)-elliptic problem. An optimal a priori error estimate in the energy norm is proved. In addition, a residual-based a posteriori error estimator is obtained. The estimator is proved to be both reliable and efficient in the energy norm. Some numerical testes are presented to demonstrate the effectiveness of our method.     

Underutilization of Lymphadenectomy for Gallbladder Cancer: A Persistent Problem with Dire Consequences

Annals of Surgical Oncology -     

A Hybrid Finite Element-Laplace Transform Method for the Analysis of Transient Electromagnetic Scattering by an Over-Filled Cavity in the Ground Plane

A hybrid finite element-Laplace transform method is implemented to analyze the time domain electromagnetic scattering induced by a 2-D overfilled cavity embedded in the infinite ground plane. The algorithm divides the whole scattering domain into two, interior and exterior, sub-domains. In the interior sub-domain which covers the cavity, the problem is solved via the finite element method. The problem is solved analytically in the exterior sub-domain which slightly overlaps the interior subdomain and extends to the rest of the upper half plane. The use of the Laplace transform leads to an analytical link condition between the overlapping sub-domains. The analytical link guides the selection of the overlapping zone and eliminates the need to use the conventional Schwartz iteration. This dramatically improves the efficiency for solving transient scattering problems. Numerical solutions are tested favorably against analytical ones for a canonical geometry. The perfect link over the artificial boundary between the finite element approximation in the interior and analytical solution in the exterior further indicates the reliability of the method. An error analysis is also performed.     

Migration of Implants: A Problem with Injectable Polyacrylamide Gel in Aesthetic Plastic Surgery

Polyacrylamide gel (PAAG) has been used as a soft tissue filler material for cosmetic purposes in Europe and China since 1997. The various complications of PAAG have been reported. A total of 15 patients who received PAAG injections at other institutions were treated for gel migration in the authors’ hospitals. During treatment, the authors found that the injected PAAG had not formed capsules within the muscle and was encapsulated only by thin fibrous tissue in skin and mammary glands. Consequently, the filler material migrated easily because of muscular activity or the influence of gravity, especially when the capsule was broken by incorrect massage or incidental force. It is suggested that PAAG should not be injected into muscular tissue or subcutaneous areas with active movement, such as joints and muscles involved in facial expression with thin skin. After years of gel implantation, the thinned capsule may result in an increasing incidence of this complication. Management and some clinical findings in relation to the complication also are discussed.     

Pseudostress-Based Mixed Finite Element Methods for the Stokes Problem in Rn with Dirichlet Boundary Conditions I: A Priori Error Analysis

We consider a non-standard mixed method for the Stokes problem in Rⁿ, n∈{2,3}, with Dirichlet boundary conditions, in which, after using the incompressibility condition to eliminate the pressure, the pseudostress tensor σ and the velocity vectorubecome the only unknowns. Then, we apply the Babuška-Brezzi theory to prove the well-posedness of the corresponding continuous and discrete formulations. In particular, we show that Raviart-Thomas elements of order k≥0 for σ and piecewise polynomials of degree k foruensure unique solvability and stability of the associated Galerkin scheme. In addition, we introduce and analyze an augmented approach for our pseudostress-velocity formulation. The methodology employed is based on the introduction of the Galerkin least-squares type terms arising from the constitutive and equilibrium equations, and the Dirichlet boundary condition for the velocity, all of them multiplied by suitable stabilization parameters. We show that these parameters can be chosen so that the resulting augmented variational formulation is defined by a strongly coercive bilinear form, whence the associated Galerkin scheme becomes well posed for any choice of finite element subspaces. For instance, Raviart-Thomas elements of order k≥0 for σ and continuous piecewise polynomials of degree k+1 forubecome a feasible choice in this case. Finally, become a feasible choice in this case. Finally, extensive numerical experiments illustrating the good performance of the methods and comparing them with other procedures available in the literature, are provided.     

Preoperative Ultrasonic Assessment of Thin Melanocytic Skin Lesions Using a 100-MHz Ultrasound Transducer: A Comparative Study

BACKGROUND It has been shown that tumor thickness (TT) of melanocytic skin lesions (MSL) of less than 1 mm vertical thickness assessed by 20 MHz are often incorrectly evaluated.
OBJECTIVE We aimed to evaluate the accuracy of 100-MHz ultrasound for the determination of TT of thin MSL, compared with conventional 20-MHz ultrasound and histologic findings.
METHODS Thirty-seven patients with 50 suspicious MSL, including tumor diameter up to 1 cm and maximum vertical TT of less than 1 mm, were recruited. The agreement between the histologically and ultrasographically measured TT was analyzed using Bland and Altman plots.
RESULTS Compared to histology, 20-MHz ultrasound (33.9 μm) as well as 100-MHz (16 μm) resulted in overestimation of TT that was twofold higher for 20-MHz ultrasound. The latter also revealed wider 95% limits of agreement (4.9 to 63 μm) than 100-MHz ultrasound (3.5 to 28.7 μm).
CONCLUSION Analysis of agreement clearly demonstrated that the performance of 100-MHz ultrasound is superior to conventional 20-MHz ultrasound, even though a relatively small positive bias was observed in 100-MHz ultrasound, indicating a systematic error. We consider 100-MHz ultrasound a useful tool for the noninvasive determination of TT of thin MSL in vivo.     

Annual Periodic Increases in Serum Carcinoembryonic Antigen Concurrent with Ground-Glass Opacity in the Lung: Report of a Case

A 63-year-old woman underwent a video-assisted thoracoscopic lobectomy for cancer of the right lung in 1999. The following year, a lesion with ground-glass opacity was found in the left lung, and pathological examination after a partial lung resection revealed atypical adenomatous hyperplasia with expression of carcinoembryonic antigen (CEA). During postoperative screening tests for tumor recurrence, there were periodic increases in the serum CEA level by twofold above the normal levels in 2002 and 2003. Clinical evaluations, including laboratory tests, radiographic imaging, and endoscopy examinations, showed no evidence of a CEA-producing tumor, except for a new ground-glass opacity in the left lung. To our knowledge, this is the first report of periodic increases in serum CEA levels in a patient with ground-glass opacity in the lung, not reflecting recurrence of the lung tumor.