Magnetic structure of our Galaxy: A review of observations

The magnetic structure in the Galactic disk, the Galactic center and the Galactic halo can be delineated more clearly than ever before. In the Galactic disk, the magnetic structure has been revealed by starlight polarization within 2 or 3 kpc of the Solar vicinity, by the distribution of the Zeeman splitting of OH masers in two or three nearby spiral arms, and by pulsar dispersion measures and rotation measures in nearly half of the disk. The polarized thermal dust emission of clouds at infrared, mm and submm wavelengths and the diffuse synchrotron emission are also related to the large-scale magnetic field in the disk. The rotation measures of extragalactic radio sources at low Galactic latitudes can be modeled by electron distributions and large-scale magnetic fields. The statistical properties of the magnetized interstellar medium at various scales have been studied using rotation measure data and polarization data. In the Galactic center, the non-thermal filaments indicate poloidal fields. There is no consensus on the field strength, maybe mG, maybe tens of uG. The polarized dust emission and much enhanced rotation measures of background radio sources are probably related to toroidal fields. In the Galactic halo, the antisymmetric RM sky reveals large-scale toroidal fields with reversed directions above and below the Galactic plane. Magnetic fields from all parts of our Galaxy are connected to form a global field structure. More observations are needed to explore the untouched regions and delineate how fields in different parts are connected.Comment: 10+1 pages. Invited Review for IAU Symp.259: Cosmic Magnetic Fields: From Planets, to Stars and Galaxies (Tenerife, Spain. Nov.3-7, 2009). K.G. Strassmeier, A.G. Kosovichev & J.E. Beckman (eds.

Robust topology optimization of three-dimensional photonic-crystal band-gap structures

We perform full 3D topology optimization (in which "every voxel" of the unit cell is a degree of freedom) of photonic-crystal structures in order to find optimal omnidirectional band gaps for various symmetry groups, including fcc (including diamond), bcc, and simple-cubic lattices. Even without imposing the constraints of any fabrication process, the resulting optimal gaps are only slightly larger than previous hand designs, suggesting that current photonic crystals are nearly optimal in this respect. However, optimization can discover new structures, e.g. a new fcc structure with the same symmetry but slightly larger gap than the well known inverse opal, which may offer new degrees of freedom to future fabrication technologies. Furthermore, our band-gap optimization is an illustration of a computational approach to 3D dispersion engineering which is applicable to many other problems in optics, based on a novel semidefinite-program formulation for nonconvex eigenvalue optimization combined with other techniques such as a simple approach to impose symmetry constraints. We also demonstrate a technique for \emph{robust} topology optimization, in which some uncertainty is included in each voxel and we optimize the worst-case gap, and we show that the resulting band gaps have increased robustness to systematic fabrication errors.Comment: 17 pages, 9 figures, submitted to Optics Expres

Optimal Design of Photonic Crystals

Ph.DDOCTOR OF PHILOSOPH

Efficient reduced-basis approximation of scalar nonlinear time-dependent convection-diffusion problems, and extension to compressible flow problems

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2006.Includes bibliographical references (p. 61-65).In this thesis, the reduced-basis method is applied to nonlinear time-dependent convection-diffusion parameterized partial differential equations (PDEs). A proper orthogonal decomposition (POD) procedure is used for the construction of reduced-basis approximation for the field variables. In the presence of highly nonlinear terms, conventional reduced-basis would be inefficient and no longer superior to classical numerical approaches using advanced iterative techniques. To recover the computational advantage of the reduced-basis approach, an empirical interpolation approximation method is employed to define the coefficient-function approximation of the nonlinear terms. Next, the coefficient-function approximation is incorporated into the reduced-basis method to obtain a reduced-order model of nonlinear time-dependent parameterized convection-diffusion PDEs. Two formulations for the reduced-order models are proposed, which construct the reduced-basis space for the nonlinear functions and residual vector respectively. Finally, an offline-online procedure for rapid and inexpensive evaluation of the reduced-order model solutions and outputs, as well as associated asymptotic a posterior error estimators are developed.(cont.) The operation count for the online stage depends only on the dimension of our reduced-basis approximation space and the dimension of our coefficient-function approximation space. The extension of the reduced-order model to a system of equations is also explored.by Han Men.S.M

Constraining the regular Galactic Magnetic Field with the 5-year WMAP polarization measurements at 22 GHz

[ABRIDGED] The knowledge of the regular component of the Galactic magnetic field gives important information about the structure and dynamics of the Milky Way, as well as constitutes a basic tool to determine cosmic rays trajectories. It can also provide clear windows where primordial magnetic fields could be detected. We want to obtain the regular (large scale) pattern of the magnetic field distribution of the Milky Way that better fits the polarized synchrotron emission as seen by the 5-year WMAP data at 22 GHz. We have done a systematic study of a number of Galactic magnetic field models: axisymmetric, bisymmetric, logarithmic spiral arms, concentric circular rings with reversals and bi-toroidal. We have explored the parameter space defining each of these models using a grid-based approach. In total, more than one million models are computed. The model selection is done using a Bayesian approach. For each model, the posterior distributions are obtained and marginalised over the unwanted parameters to obtain the marginal 1-D probability distribution functions. In general, axisymmetric models provide a better description of the halo component, although attending to their goodness-of-fit, the rest of the models cannot be rejected. In the case of disk component, the analysis is not very sensitive for obtaining the disk large scale structure, because of the effective available area (less than 8% of the whole map and less than 40% of the disk). Nevertheless, within a given family of models, the best-fit parameters are compatible with those found in the literature. The family of models that better describes the polarized synchrotron halo emission is the axisymmetric one, with magnetic spiral arms with a pitch angle of ~24 degrees, and a strong vertical field of 1 microG at z ~ 1 kpc. When a radial variation is fitted, models require fast variations.Comment: 14 pages, 9 figures. Accepted for publication in A&

Finding sands in the eyes: vulnerabilities discovery in IoT with EUFuzzer on human machine interface

In supervisory control and data acquisition (SCADA) systems or the Internet of Things (IoT), human machine interface (HMI) performs the function of data acquisition and control, providing the operators with a view of the whole plant and access to monitoring and interacting with the system. The compromise of HMI will result in lost of view (LoV), which means the state of the whole system is invisible to operators. The worst case is that adversaries can manipulate control commands through HMI to damage the physical plant. HMI often relies on poorly understood proprietary protocols, which are time-sensitive, and usually keeps a persistent connection for hours even days. All these factors together make the vulnerability mining of HMI a tough job. In this paper, we present EUFuzzer, a novel fuzzing tool to assist testers in HMI vulnerability discovery. EUFuzzer first identifies packet fields of the specific protocol and classifies all fields into four types, then using a relatively high efficiency fuzzing method to test HMI. The experimental results show that EUFuzzer is capable of identifying packet fields and revealing bugs. EUFuzzer also successfully triggers flaws of actual proprietary SCADA protocol implementation on HMI, which the SCADA software vendor has confirmed that four were zero-day vulnerabilities and has taken measures to patch up

Designing Phononic Crystals With Convex Optimization

Designing phononic crystals by creating frequency bandgaps is of particular interest in the engineering of elastic and acoustic microstructured materials. Mathematically, the problem of optimizing the frequency bandgaps is often nonconvex, as it requires the maximization of the higher indexed eigenfrequency and the minimization of the lower indexed eigenfrequency. A novel algorithm [1] has been previously developed to reformulate the original nonlinear, nonconvex optimization problem to an iteration-specific semidefinite program (SDP). This algorithm separates two consecutive eigenvalues — effectively maximizing bandgap (or bandwidth) — by separating the gap between two orthogonal subspaces, which are comprised columnwise of “important” eigenvectors associated with the eigenvalues being bounded. By doing so, we avoid the need of computation of eigenvalue gradient by computing the gradient of affine matrices with respect to the decision variables. In this work, we propose an even more efficient algorithm based on linear programming (LP). The new formulation is obtained via approximation of the semidefinite cones by judiciously chosen linear bases, coupled with “delayed constraint generation”. We apply the two convex conic formulations, namely, the semidefinite program and the linear program, to solve the bandgap optimization problems. By comparing the two methods, we demonstrate the efficacy and efficiency of the LP-based algorithm in solving the category of eigenvalue bandgap optimization problems.United States. Air Force Office of Scientific Research (FA9550-11- 1-0141

Fabrication-Adaptive Optimization, with an Application to Photonic Crystal Design

It is often the case that the computed optimal solution of an optimization problem cannot be implemented directly, irrespective of data accuracy, due to either (i) technological limitations (such as physical tolerances of machines or processes), (ii) the deliberate simplification of a model to keep it tractable (by ignoring certain types of constraints that pose computational difficulties), and/or (iii) human factors (getting people to "do" the optimal solution). Motivated by this observation, we present a modeling paradigm called "fabrication-adaptive optimization" for treating issues of implementation/fabrication. We develop computationally-focused theory and algorithms, and we present computational results for incorporating considerations of implementation/fabrication into constrained optimization problems that arise in photonic crystal design. The fabrication-adaptive optimization framework stems from the robust regularization of a function. When the feasible region is not a normed space (as typically encountered in application settings), the fabrication-adaptive optimization framework typically yields a non-convex optimization problem. (In the special case where the feasible region is a finite-dimensional normed space, we show that fabrication-adaptive optimization can be re-cast as an instance of modern robust optimization.) We study a variety of problems with special structures on functions, feasible regions, and norms, for which computation is tractable, and develop an algorithmic scheme for solving these problems in spite of the challenges of non-convexity. We apply our methodology to compute fabrication-adaptive designs of two-dimensional photonic crystals with a variety of prescribed features

Bandgap Optimization of Two-Dimensional Photonic Crystals Using Semidefinite Programming and Subspace Methods

In this paper, we consider the optimal design of photonic crystal structures for two-dimensional square lattices. The mathematical formulation of the bandgap optimization problem leads to an infinite-dimensional Hermitian eigenvalue optimization problem parametrized by the dielectric material and the wave vector. To make the problem tractable, the original eigenvalue problem is discretized using the finite element method into a series of finite-dimensional eigenvalue problems for multiple values of the wave vector parameter. The resulting optimization problem is large-scale and non-convex, with low regularity and non-differentiable objective. By restricting to appropriate eigenspaces, we reduce the large-scale non-convex optimization problem via reparametrization to a sequence of small-scale convex semidefinite programs (SDPs) for which modern SDP solvers can be efficiently applied. Numerical results are presented for both transverse magnetic (TM) and transverse electric (TE) polarizations at several frequency bands. The optimized structures exhibit patterns which go far beyond typical physical intuition on periodic media design