Verification of high-order mixed FEM solution of transient Magnetic diffusion problems

We develop and present high order mixed finite element discretizations of the time dependent electromagnetic diffusion equations for solving eddy current problems on 3D unstructured grids. The discretizations are based on high order H(grad), H(curl) and H(div) conforming finite element spaces combined with an implicit and unconditionally stable generalized Crank-Nicholson time differencing method. We develop three separate electromagnetic diffusion formulations, namely the E (electric field), H (magnetic field) and the A-{phi} (potential) formulations. For each formulation, we also provide a consistent procedure for computing the secondary variables F (current flux density) and B (magnetic flux density), as these fields are required for the computation of electromagnetic force and heating terms. We verify the error convergence properties of each formulation via a series of numerical experiments on canonical problems with known analytic solutions. The key result is that the different formulations are equally accurate, even for the secondary variables J and B, and hence the choice of which formulation to use depends mostly upon relevance of the Natural and Essential boundary conditions to the problem of interest. In addition, we highlight issues with numerical verification of finite element methods which can lead to false conclusions on the accuracy of the methods

Vector Finite Element Modeling of the Full-Wave Maxwell Equations to Evaluate Power Loss in Bent Optical Fibers

We measure the loss of power incurred by the bending of a single mode step-indexed optical fiber using vector finite element modeling of the full-wave Maxwell equations in the optical regime. We demonstrate fewer grid elements can be used to model light transmission in longer fiber lengths by using high-order basis functions in conjunction with a high order energy conserving time integration method. The power in the core is measured at several points to determine the percentage loss. We also demonstrate the effect of bending on the light polarization

Development and Application of Compatible Discretizations of Maxwell's Equations

We present the development and application of compatible finite element discretizations of electromagnetics problems derived from the time dependent, full wave Maxwell equations. We review the H(curl)-conforming finite element method, using the concepts and notations of differential forms as a theoretical framework. We chose this approach because it can handle complex geometries, it is free of spurious modes, it is numerically stable without the need for filtering or artificial diffusion, it correctly models the discontinuity of fields across material boundaries, and it can be very high order. Higher-order H(curl) and H(div) conforming basis functions are not unique and we have designed an extensible C++ framework that supports a variety of specific instantiations of these such as standard interpolatory bases, spectral bases, hierarchical bases, and semi-orthogonal bases. Virtually any electromagnetics problem that can be cast in the language of differential forms can be solved using our framework. For time dependent problems a method-of-lines scheme is used where the Galerkin method reduces the PDE to a semi-discrete system of ODE's, which are then integrated in time using finite difference methods. For time integration of wave equations we employ the unconditionally stable implicit Newmark-Beta method, as well as the high order energy conserving explicit Maxwell Symplectic method; for diffusion equations, we employ a generalized Crank-Nicholson method. We conclude with computational examples from resonant cavity problems, time-dependent wave propagation problems, and transient eddy current problems, all obtained using the authors massively parallel computational electromagnetics code EMSolve

Coupling Magnetic Fields and ALE Hydrodynamics for 3D Simulations of MFCG's

We review the development of a full 3D multiphysics code for the simulation of explosively driven Magnetic Flux Compression Generators (MFCG) and related pulse power devices. In a typical MFCG the device is seeded with an initial electric current and the device is then detonated. The detonation compresses the magnetic field and amplifies the current. This is a multiphysics problem in that detonation kinetics, electromagnetic diffusion and induction, material deformation, and thermal effects are all important. This is a tightly coupled problem in that the different physical quantities have comparable spatial and temporal variation, and hence should be solved simultaneously on the same computational mesh

Full Wave Analysis of RF Signal Attenuation in a Lossy Rough Surface Cave using a High Order Time Domain Vector Finite Element Method

We present a computational study of signal propagation and attenuation of a 200 MHz planar loop antenna in a cave environment. The cave is modeled as a straight and lossy random rough wall. To simulate a broad frequency band, the full wave Maxwell equations are solved directly in the time domain via a high order vector finite element discretization using the massively parallel CEM code EMSolve. The numerical technique is first verified against theoretical results for a planar loop antenna in a smooth lossy cave. The simulation is then performed for a series of random rough surface meshes in order to generate statistical data for the propagation and attenuation properties of the antenna in a cave environment. Results for the mean and variance of the power spectral density of the electric field are presented and discussed

A QR accelerated volume-to-surface boundary condition for finite element solution of eddy current problems

We are concerned with the solution of time-dependent electromagnetic eddy current problems using a finite element formulation on three-dimensional unstructured meshes. We allow for multiple conducting regions, and our goal is to develop an efficient computational method that does not require a computational mesh of the air/vacuum regions. This requires a sophisticated global boundary condition specifying the total fields on the conductor boundaries. We propose a Biot-Savart law based volume-to-surface boundary condition to meet this requirement. This Biot-Savart approach is demonstrated to be very accurate. In addition, this approach can be accelerated via a low-rank QR approximation of the discretized Biot-Savart law

Suppression of Richtmyer-Meshkov instability via special pairs of shocks and phase transitions

The classical Richtmyer-Meshkov instability is a hydrodynamic instability characterizing the evolution of an interface following shock loading. In contrast to other hydrodynamic instabilities such as Rayleigh-Taylor, it is known for being unconditionally unstable: regardless of the direction of shock passage, any deviations from a flat interface will be amplified. In this article, we show that for negative Atwood numbers, there exist special sequences of shocks which result in a nearly perfectly suppressed instability growth. We demonstrate this principle computationally and experimentally with stepped fliers and phase transition materials. A fascinating immediate corollary is that in specific instances a phase transitioning material may self-suppress RMI

Cold non-ischemic heart preservation with continuous perfusion prevents early graft failure in orthotopic pig-to-baboon xenotransplantation

Background Successful preclinical transplantations of porcine hearts into baboon recipients are required before commencing clinical trials. Despite years of research, over half of the orthotopic cardiac xenografts were lost during the first 48 hours after transplantation, primarily caused by perioperative cardiac xenograft dysfunction (PCXD). To decrease the rate of PCXD, we adopted a preservation technique of cold non-ischemic perfusion for our ongoing pig-to-baboon cardiac xenotransplantation project. Methods Fourteen orthotopic cardiac xenotransplantation experiments were carried out with genetically modified juvenile pigs (GGTA1- KO/hCD46/hTBM) as donors and captive-bred baboons as recipients. Organ preservation was compared according to the two techniques applied: cold static ischemic cardioplegia (IC; n = 5) and cold non-ischemic continuous perfusion (CP; n = 9) with an oxygenated albumin-containing hyperoncotic cardioplegic solution containing nutrients, erythrocytes and hormones. Prior to surgery, we measured serum levels of preformed anti-non-Gal-antibodies. During surgery, hemodynamic parameters were monitored with transpulmonary thermodilution. Central venous blood gas analyses were taken at regular intervals to estimate oxygen extraction, as well as lactate production. After surgery, we measured troponine T and serum parameters of the recipient's kidney, liver and coagulation functions. Results In porcine grafts preserved with IC, we found significantly depressed systolic cardiac function after transplantation which did not recover despite increasing inotropic support. Postoperative oxygen extraction and lactate production were significantly increased. Troponin T, creatinine, aspartate aminotransferase levels were pathologically high, whereas prothrombin ratios were abnormally low. In three of five IC experiments, PCXD developed within 24 hours. By contrast, all nine hearts preserved with CP retained fully preserved systolic function, none showed any signs of PCXD. Oxygen extraction was within normal ranges; serum lactate as well as parameters of organ functions were only mildly elevated. Preformed anti-non-Gal-antibodies were similar in recipients receiving grafts from either IC or CP preservation. Conclusions While standard ischemic cardioplegia solutions have been used with great success in human allotransplantation over many years, our data indicate that they are insufficient for preservation of porcine hearts transplanted into baboons: Ischemic storage caused severe impairment of cardiac function and decreased tissue oxygen supply, leading to multi-organ failure in more than half of the xenotransplantation experiments. In contrast, cold non-ischemic heart preservation with continuous perfusion reliably prevented early graft failure. Consistent survival in the perioperative phase is a prerequisite for preclinical long-term results after cardiac xenotransplantation

GMOs: Non-Health Issues

The controversy over genetically modified [GM] organisms is often framed in terms of possible hazards for human health. Articles in a previous volume of this *Encyclopedia* give a general overview of GM crops [@Mulvaney2014] and specifically examine human health [@Nordgard2014] and labeling [@Bruton2014] issues surrounding GM organisms. This article explores several other aspects of the controversy: environmental concerns, political and legal disputes, and the aim of "feeding the world" and promoting food security. Rather than discussing abstract, hypothetical GM organisms, this article explores the consequences of the GM organisms that have actually been deployed in the particular contexts that they have been deployed, on the belief that there is little point in discussing GM organisms in an idealized or context-independent way