Presence Of Inhomogeneous Media Research Articles

A variety of nonautonomous complex wave solutions for the (2+1)-dimensional nonlinear Schrödinger equation with variable coefficients in nonlinear optical fibers

This paper presents a physical model described by the (2+1)-dimensional nonlinear Schrödinger equation with variable coefficients (2D-VcNLSE). The 2D-VcNLSE is related to many physical phenomena in nonlinear optical fibers, Bose-Einstein condensates, and water waves. We study new types of nonautonomous complex wave solutions in the presence of inhomogeneous media. Various structures of these solutions such as bright and dark soliton and similarity solutions are investigated. Furthermore, different exact solutions for the 2D-VcNLSE are obtained via the G′/G-expansion method. Through 3D- and contour plots, we show that the dynamical behaviors of the obtained solutions can be effectively controlled by modulating the values of the arbitrary functions in these solutions.

TU-B-T-6B-01: Transition to Heterogeneity Corrections

With the publication of the AAPM's TG-65 report on inhomogeneity corrections for photon beams, physicians and physicists must clearly understand how implementation of such corrections impact dose prescriptions. The TG report details the physics of the heterogeneity algorithms, methods to evaluate these prescriptions, limitations, and most importantly, how to implement. The report gives clear recommendations as to the dialogue needed before implementation takes place. A clinic should perform simultaneous plans by planning and treating the patient with no corrections applied. A simultaneous plan is generated that applies the correction ‘after the fact’, thereby leaving the homogeneous (and therefore given doses) intact. This will educate the staff as how prescriptions may (or may not) be altered according to the differences observed. In addition, planning volume margins may be affected according the algorithms' ability to calculate penumbra in the presence of inhomogeneous media, particularly lung. In addition, classic beam arrangements may need to be scrutinized due to the impact of increased exit dosing observed with corrections applied. MDAH found that implementation of inhomogeneity corrections was fairly easy to accomplish, even in a busy clinic. Accounting for heterogeneity resulted in better PTV coverage by changing beam weighting, without significantly changing isocenter dose. The distance from PTV to block edge also increased in some situations. Failure to account for tissue heterogeneity could lead to dose calculation errors, particularly to the PTV, which often results in significant underdosing. Accounting for tissue heterogeneity using many commercially available algorithms changes the dose to the PTV much more than will the future use of Monte-Carlo-based dose calculation algorithms. Heterogeneity corrections are particularly important when using IMRT, particularly in lung cancer treatment. They concluded that the benefits of accounting for tissue inhomogeneity vastly outweigh the minor difficulties with its implementation, will result in more accurate calculation of dose distributions, and hopefully in better outcomes for patients. The use of heterogeneity corrections also allowed the use of higher energy photon beams in 3D planning, because of greater confidence in dose calculation accuracy. This course will give direction along with caveats in applying inhomogeneity corrections from the perspective of physics and physicians. In addition, there will be a review of current algorithms commercially available, along with a historical perspective on how various stages of algorithms impacted the radiotherapy community on evaluating and using inhomogeneity corrections. Educational Objectives: The physicist will learn - 1. the details of TG-65 2. details on commercially available algorithms including limitations 3. the MDAH approach to implementing corrections 4. a historical perspective of studies on evaluating corrections 5. TG-65's recommendation plan for a clinic's implementation.

A Staggered Upwind Embedded Boundary (SUEB) Method to Eliminate the FDTD Staircasing Error

In spite of its flexibility and second-order accuracy in a homogeneous medium, Yee's finite-difference time-domain (FDTD) method suffers from serious degradation when treating material interfaces, greatly reducing its accuracy in the presence of inhomogeneous media and perfect conductors. Indeed, such so-called staircasing approximation may lead to local zeroth-order and global first-order errors. In this work, an embedded FDTD scheme, the staggered upwind embedded boundary (SUEB) method, is developed for the solution of oneand two-dimensional Maxwell's equations. This simple embedded technique uses upwind conditions in the FDTD method to correctly represent the location and physical conditions of material and metallic boundaries, hence eliminating problems caused by the staircasing approximation. Accuracy analysis has been made to show that the SUEB method maintains a second-order accuracy globally. Since the entire problem has been embedded into the simple staggered grid similar to that employed by the Yee's scheme, extra effort is only needed when treating the grid points close to the interfaces. Therefore, little additional computational cost is needed over Yee's scheme. The SUEB method has been validated by analytical solutions for plane wave normally incident to a planar boundary and for the TM wave propagation in the presence of a dielectric cylinder and a perfectly electrically conducting cylinder.

Forward model theoretical basis for a superconducting imaging surface magnetoencephalography system

A novel magnetoencephalography (MEG) system was designed at Los Alamos National Laboratory (LANL) that incorporates a helmet-shaped superconductor in order to increase the signal to noise ratio. The magnetic field perturbations caused by the superconducting surface must be included in the forward physics for accurate source localization. In this paper, the theoretical basis for the forward model that calculates the field of any magnetic source in the presence of an arbitrarily shaped superconducting surface is presented. Appropriate magnetic field integral equations are derived that provide a description of the physics of the forward model. These equations are derived starting from Maxwell's equations in the presence of inhomogeneous media, with the appropriate boundary conditions for a superconductor. A discretized version of this equation is then compared with known analytic solutions for simple superconducting surface geometries.

Convergence of the finite element method as applied to electromagnetic scattering problems in the presence of inhomogeneous media

Approximate radiation boundary conditions (BCs) make partial-differential-equation-based methods attractive for the solution of electromagnetic scattering problems, especially for geometrically complex inhomogenous targets. These BCs allow for an exterior boundary value problem (BVP) to be approximated by an interior BVP. The use of the second-order Bayliss-Turkel BC for two-dimensional inhomogeneous targets is considered. In numerical experiments the rate of convergence with respect to mesh size previously predicted continues to hold.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>