Continuum Sensitivity Research Articles

THE EXPANDED VERY LARGE ARRAY: A NEW TELESCOPE FOR NEW SCIENCE

Since its commissioning in 1980, the Very Large Array (VLA) has consistently demonstrated its scientific productivity. However, its fundamental capabilities have changed little since 1980, particularly in the key areas of sensitivity, frequency coverage, and velocity resolution. These limitations have been addressed by a major upgrade of the array, which began in 2001 and will be completed at the end of 2012. When completed, the Expanded VLA -- the EVLA -- will provide complete frequency coverage from 1 to 50 GHz, a continuum sensitivity of typically 1 microJy/beam (in 9 hours with full bandwidth), and a modern correlator with vastly greater capabilities and flexibility than the VLA's. In this paper we describe the goals of the EVLA project, its current status, and the anticipated expansion of capabilities over the next few years. User access to the array through the OSRO and RSRO programs is described. The following papers in this special issue, derived from observations in its early science period, demonstrate the astonishing breadth of this most flexible and powerful general-purpose telescope.

THE TWO-COMPONENT RADIO LUMINOSITY FUNCTION OF QUASI-STELLAR OBJECTS: STAR FORMATION AND ACTIVE GALACTIC NUCLEUS

Despite decades of study, it remains unclear whether there are distinct radio-loud and radio-quiet populations of quasi-stellar objects (QSOs). Early studies were limited by inhomogeneous QSO samples, inadequate sensitivity to probe the radio-quiet population, and degeneracy between redshift and luminosity for flux-density-limited samples. Our new 6 GHz EVLA observations allow us for the first time to obtain nearly complete (97%) radio detections in a volume-limited color-selected sample of 179 QSOs more luminous than M_i = -23 from the Sloan Digital Sky Survey (SDSS) Data Release Seven in the narrow redshift range 0.2 < z < 0.3. The dramatic improvement in radio continuum sensitivity made possible with the new EVLA allows us, in 35 minutes of integration, to detect sources as faint as 20 microJy, or log[L_6 (W/Hz)] ~ 21.5 at z = 0.25, well below the radio luminosity, log[L_6 (W/Hz)] ~ 22.5, that separates star-forming galaxies from radio-loud active galactic nuclei (AGNs) driven by accretion onto a super-massive black hole. We calculate the radio luminosity function (RLF) for these QSOs using three constraints: (a) EVLA 6 GHz observations for log[L_6 (W/Hz)] < 23.5, (b) NRAO-VLA Sky Survey (NVSS) observations for log[L_6 (W/Hz)] > 23.5, and (c) the total number of SDSS QSOs in our volume-limited sample. We show that the RLF can be explained as a superposition of two populations, dominated by AGNs at the bright end and star formation in the QSO host galaxies at the faint end.

EXPANDED VERY LARGE ARRAY OBSERVATIONS OF GALACTIC SUPERNOVA REMNANTS: WIDE-FIELD CONTINUUM AND SPECTRAL-INDEX IMAGING

The radio continuum emission from the Galaxy has a rich mix of thermal and non-thermal emission. This very richness makes its interpretation challenging since the low radio opacity means that a radio image represents the sum of all emission regions along the line of sight. These challenges make the existing narrowband radio surveys of the Galactic plane difficult to interpret: e.g., a small region of emission might be a supernova remnant (SNR) or an H II region, or a complex combination of both. Instantaneous wide bandwidth radio observations in combination with the capability for high-resolution spectral-index mapping can be directly used to disentangle these effects. Here we demonstrate simultaneous continuum and spectral-index imaging capability at the full continuum sensitivity and resolution using newly developed wide-band wide-field imaging algorithms. Observations were conducted in the L and C bands with a total bandwidth of 1 and 2 GHz, respectively. We present preliminary results in the form of a full-field continuum image covering the wide-band sensitivity pattern of the EVLA centered on a large but poorly studied SNR (G55.7 + 3.4) and relatively narrower field continuum and spectral-index maps of three fields containing SNR and diffused thermal emission. We demonstrate that spatially resolved spectral-index maps differentiate regions with emission of different physical origins (spectral-index variation across composite SNRs and separation of thermal and non-thermal emission), superimposed along the line of sight. The wide-field image centered on the SNR G55.7+3.4 also demonstrates the excellent wide-field wide-band imaging capability of the EVLA.

The Australia Telescope Compact Array Broad-band Backend: description and first results★

Here we describe the Compact Array Broadband Backend (CABB) and present first results obtained with the upgraded Australia Telescope Compact Array (ATCA). The 16-fold increase in observing bandwidth, from 2 x 128 MHz to 2 x 2048 MHz, high bit sampling, and addition of 16 zoom windows (each divided into a further 2048 channels) provide major improvements for all ATCA observations. The benefits of the new system are: (1) hugely increased radio continuum and polarization sensitivity as well as image fidelity, (2) substantially improved capability to search for and map emission and absorption lines over large velocity ranges, (3) simultaneous multi-line and continuum observations, (4) increased sensitivity, survey speed and dynamic range due to high-bit sampling, and (5) high velocity resolution, while maintaining full polarization output. The new CABB system encourages all observers to make use of both spectral line and continuum data to achieve their full potential. Given the dramatic increase of the ATCA capabilities in all bands (ranging from 1.1 to 105 GHz) CABB enables scientific projects that were not feasible before the upgrade, such as simultaneous observations of multiple spectral lines, on-the-fly mapping, fast follow-up of radio transients (e.g., the radio afterglow of new supernovae) and maser observations at high velocity resolution and full polarization. The first science results presented here include wide-band spectra, high dynamic-range images, and polarization measurements, highlighting the increased capability and discovery potential of the ATCA.

A multi-scale multi-frequency deconvolution algorithm for synthesis imaging in radio interferometry

Aims : We describe MS-MFS, a multi-scale multi-frequency deconvolution algorithm for wide-band synthesis-imaging, and present imaging results that illustrate the capabilities of the algorithm and the conditions under which it is feasible and gives accurate results. Methods : The MS-MFS algorithm models the wide-band sky-brightness distribution as a linear combination of spatial and spectral basis functions, and performs image-reconstruction by combining a linear-least-squares approach with iterative $\chi^2$ minimization. This method extends and combines the ideas used in the MS-CLEAN and MF-CLEAN algorithms for multi-scale and multi-frequency deconvolution respectively, and can be used in conjunction with existing wide-field imaging algorithms. We also discuss a simpler hybrid of spectral-line and continuum imaging methods and point out situations where it may suffice. Results : We show via simulations and application to multi-frequency VLA data and wideband EVLA data, that it is possible to reconstruct both spatial and spectral structure of compact and extended emission at the continuum sensitivity level and at the angular resolution allowed by the highest sampled frequency.

A New Unified Design Environment for Optimization of Electric Machines Based on Continuum Sensitivity and B-Spline Parametrization

In this paper, a unified design environment is developed for the optimization of electric machines based on continuum sensitivity. For electromagnetic (EM) system analysis, COMSOL scripting environment is used. Optimization module is developed by MATLAB programming, which can be combined with COMSOL script commands. The modules are combined into one MATLAB project, and iteration process necessary for the optimization of EM system can be performed efficiently. During the design process, visual feedback of the current design status is given to the designer. In addition, the B-Spline parametrization of the nodal points is implemented to obtain smooth boundary of the device. The developed software is applied to the problem of finding uniform flux density distribution at the air gap of an electromagnet to verify its feasibility and effectiveness.

Generalized Continuum Sensitivity Formula for Shape Optimization of High-Frequency Devices in Frequency Domain

This paper presents a generalized continuum design sensitivity formula that is applicable to any shape design problems of high-frequency devices in frequency domain. The derived sensitivity formula is expressed in terms of surface integrals over a part of the interface between different materials and of the conducting boundary undergoing shape modification during iterative design process. Using the proposed approach, it is easy to deal with the shape optimization concerning conducting surfaces as well as dielectric contours. The method has been successfully applied to the optimization of high-frequency waveguides where the numerical implementation is thoroughly investigated from the viewpoint of constructing adjoint systems and calculating sensitivity values.

Shape formation of ferrofluid under external magnetic fields using level set method

The shape formation of ferrofluid under magnetic field has been considered to be one of most difficult problems to analyze. In this paper we present a numerical implementation of the level set method for the equilibrium shape calculation of ferrofluid under magnetic field. The magnetic-fluid coupled system has an extremum value of electromagnetic system energy. When the system is composed of magnetic permeable material and current sources, the system energy is a maximum at the equilibrium state. The level set method is adopted for shape capturing since it can easily handle shape variations of fluid including topological changes such as merging, splitting, and even disappearing of connected material regions. The velocity field for the level set method is calculated using a shape derivative of continuum sensitivity analysis that is derived by employing the material derivative concept. The numerical results for a model problem of some ferrofluid on a glass plate show that the level set method works well for the ferrofluid shape formation.

A Level Set Method for Shape Optimization of Electromagnetic Systems

We present a level set method for numerical shape optimization of electromagnetic systems. The level set method does not only lead to efficient computational schemes, but also is able to handle topological changes such as merging, splitting and even disappearing of connected components. The velocity field on boundaries is obtained by a shape derivative of continuum sensitivity analysis using the material derivative concept and an adjoint variable technique. Two numerical results of dielectric optimization between electrodes showed that the level set method is feasible and effective in solving shape optimization problems of electromagnetic systems.

Inverse determination of boundary heat fluxes in a porous enclosure dynamically coupled with thermal transport

The inverse natural convection problem of estimating the heat source profiles in a porous enclosure is proposed in the present work. The physical model for the momentum conservation equation makes use of the Darcy–Brinkman equation, which allows the no-slip boundary condition on a solid wall to be satisfied. An iterative Fletcher–Reeves conjugate gradient method is applied such that the gradient of the cost function is introduced when the appropriate sensitivity and adjoint problems are defined. Particularly, the pressure-based SIMPLE algorithm is adopted to solve the continuum direct, sensitivity and adjoint problems in unification. Effects of thermal Rayleigh number, Darcy number, heat flux profiles, sensor locations and quantity on the accuracy of inverse solutions are investigated with or without the measurement errors. Additionally, the fluid and heat transport structures in the uniform porous layer are analyzed using the streamlines and heatlines, and the heat transfer potential is also explained by the variation of overall Nusselt number. Noise data solutions are regularized by stopping the iterations with the discrepancy principle of Alifanov, before the high frequency components of the random noises are reproduced. The present method solves inverse strong convection problem satisfactorily without any a priori information about the unknown heat flux to be estimated.

GRI: focusing on the evolving violent universe

The gamma-ray imager (GRI) is a novel mission concept that will provide an unprecedented sensitivity leap in the soft gamma-ray domain by using for the first time a focusing lens built of Laue diffracting crystals. The lens will cover an energy band from 200–1,300 keV with an effective area reaching 600 cm2. It will be complemented by a single reflection multilayer coated mirror, extending the GRI energy band into the hard X-ray regime, down to ∼10 keV. The concentrated photons will be collected by a position sensitive pixelised CZT stack detector. We estimate continuum sensitivities of better than 10 − 7 ph cm − 2s − 1keV − 1 for a 100 ks exposure; the narrow line sensitivity will be better than 3 × 10 − 6 ph cm − 2s − 1 for the same integration time. As focusing instrument, GRI will have an angular resolution of better than 30 arcsec within a field of view of roughly 5 arcmin—an unprecedented achievement in the gamma-ray domain. Owing to the large focal length of 100 m of the lens and the mirror, the optics and detector will be placed on two separate spacecrafts flying in formation in a high elliptical orbit. R&D work to enable the lens focusing technology and to develop the required focal plane detector is currently underway, financed by ASI, CNES, ESA, and the Spanish Ministery of Education and Science. The GRI mission has been proposed as class M mission for ESAs Cosmic Vision 2015–2025 program. GRI will allow studies of particle acceleration processes and explosion physics in unprecedented detail, providing essential clues on the innermost nature of the most violent and most energetic processes in the universe.

Numerical determination of boundary heat fluxes in an enclosure dynamically with natural convection through Fletcher–Reeves gradient method

An iterative Fletcher–Reeves conjugate gradient method (CGM) is adopted to estimate the boundary heat fluxes in a fluid-saturated enclosure, where the fluid flow is dynamically coupled with the heat convection. The sets of direct, sensitivity and adjoint equations required for the solution of the inverse problem are formulated in terms of an arbitrary domain in two dimensions. The methodology of conjugate gradient method solves the inverse natural convection problem satisfactorily without any a priori information about the unknown heat fluxes. The pressure-correction method is utilized to solve the continuum direct, sensitivity and adjoint problems by enforcing global mass and energy conservations. Effects of boundary heat flux profile and thermal Rayleigh number on the convective heat transport are investigated. The effects of position and number of temperature sensors on the inverse problem solution are also addressed in this paper. Inverse solutions of noise data are regularized with the Discrepancy Principle of Alifanov; otherwise, the high frequency components of the random noise were reproduced.

Multiobjective optimization for crash safety design of vehicles using stepwise regression model

In automotive industry, structural optimization for crashworthiness criteria is of special importance. Due to the high nonlinearities, however, there exists substantial difficulty to obtain accurate continuum or discrete sensitivities. For this reason, metamodel or surrogate model methods have been extensively employed in vehicle design with industry interest. This paper presents a multiobjective optimization procedure for the vehicle design, where the weight, acceleration characteristics and toe-board intrusion are considered as the design objectives. The response surface method with linear and quadratic basis functions is employed to formulate these objectives, in which optimal Latin hypercube sampling and stepwise regression techniques are implemented. In this study, a nondominated sorting genetic algorithm is employed to search for Pareto solution to a full-scale vehicle design problem that undergoes both the full frontal and 40% offset-frontal crashes. The results demonstrate the capability and potential of this procedure in solving the crashworthiness design of vehicles.

Design and Optimization of Coreless Components Using Admittance Matrix and Efficiently Calculated Sensitivities

This paper presents a novel technique for designing coreless components (inductors and transformers) based on the admittance matrix at quasi-static approximation. In addition, an optimization method based on continuum sensitivity is applied. Efficiency of the design method is shown for inductors that have axisymmetry and carry azimuthal currents. In order to avoid coupling between closely located inductors, a shielding structure is proposed and shape-optimized to confine the magnetic energy

Efficient Global and Local Force Calculations Based on Continuum Sensitivity Analysis

Equations derived from the continuum design sensitivity analysis (CDSA), in conjunction with the material derivatives for a continuous medium and using the energy-based approach, have been successfully applied to the calculation of both total force and force distributions. The resultant expressions are similar to the Maxwell Stress Tensor, Magnetic Charge Method, and Virtual Work Method but have several advantages over the traditional approaches. Numerical implementation of the scheme leads to efficient calculations and improved accuracy

Control of macrosegregation during the solidification of alloys using magnetic fields

Numerical modeling of convection damping and macrosegregation suppression during solidification of alloys with prominent mushy zones through the use of tailored magnetic fields is demonstrated here. Macrosegregation leads to commonly observed defects such as freckles, channels and segregates in cast alloys that severely affect the performance and suitability of the alloy for further applications. The current work demonstrates the successful use of magnetic fields in suppressing thermosolutal convection and eliminating some of these defects in solidifying metallic alloys. The computational model presented utilizes volume-averaged governing transport equations and stabilized finite element techniques to discretize these equations. A finite-dimensional optimization problem, based on the continuum sensitivity method is considered to design the time history of the imposed magnetic field required to effectively damp convection. The coefficients that determine this time variation are the main design parameters of this optimization problem. Continuum sensitivity equations are derived by design-differentiating the governing equations of the direct problem. The cost functional here is given by the square of the L 2 norm of an expression representing the deviation of the volume-averaged velocity corresponding to conditions of convection less growth. The cost functional minimization process is realized through a non-linear conjugate gradient algorithm that utilizes finite element solutions of the continuum direct and sensitivity problems. Design of the time history of the imposed magnetic field is highlighted through different examples with the main objective being the suppression of convection and macrosegregation during alloy solidification.

Continuum gradient-based shape optimization of conducting shields for power frequency magnetic field mitigation

A shape optimization technique for quasistatic field problems has been developed. The optimization is based on computing the continuum sensitivity function by solving an adjoint problem. We show how this technique can be used to compute, in a very efficient way, the optimal shape of a conducting (or ferromagnetic) shielding structure, in order to minimize the magnetic field in the region of interest. A two-dimensional example of shielding three-phase underground cables is considered

Design of microstructure-sensitive properties in elasto-viscoplastic polycrystals using multi-scale homogenization

Evolution of properties during processing of materials depends on the underlying material microstructure. A finite element homogenization approach is presented for calculating the evolution of macro-scale properties during processing of microstructures. A mathematically rigorous sensitivity analysis of homogenization is presented that is used to identify optimal forging rates in processes that would lead to a desired microstructure response. Macro-scale parameters such as forging rates are linked with microstructure deformation using boundary conditions drawn from the theory of multi-scale homogenization. Homogenized stresses at the macro-scale are obtained through volume-averaging laws. A constitutive framework for thermo-elastic–viscoplastic response of single crystals is utilized along with a fully-implicit Lagrangian finite element algorithm for modelling microstructure evolution. The continuum sensitivity method (CSM) used for designing processes involves differentiation of the governing field equations of homogenization with respect to the processing parameters and development of the weak forms for the corresponding sensitivity equations that are solved using finite element analysis. The sensitivity of the deformation field within the microstructure is exactly defined and an averaging principle is developed to compute the sensitivity of homogenized stresses at the macro-scale due to perturbations in the process parameters. Computed sensitivities are used within a gradient-based optimization framework for controlling the response of the microstructure. Development of texture and stress–strain response in 2D and 3D FCC aluminum polycrystalline aggregates using the homogenization algorithm is compared with both Taylor-based simulations and published experimental results. Processing parameters that would lead to a desired equivalent stress–strain curve in a sample poly-crystalline microstructure are identified for single and two-stage loading using the design algorithm.

The continuum sensitivity method for the computational design of three-dimensional deformation processes

Although simulation of metal forming processes using modern computational tools has reached an advanced stage, there is still a great need to develop computational techniques for process design. In this work, the continuum sensitivity method (CSM) is extended to three-dimensions (3D) to accurately compute sensitivity fields and in particular changes in the design objectives as a result of infinitesimal perturbations to the design parameters. CSM involves differentiation of the governing field equations of the direct problem (constitutive, contact and kinematic problems) with respect to the design variables and development of the weak forms for the corresponding sensitivity equations. The present 3D developments include a novel regularized approach to the contact sensitivity problem that addresses the non-differentiability of the contact constraints. The computed sensitivity fields are used in a gradient-based optimization framework for process design (optimization) in 3D metal forming applications. A typical design problem at each optimization iteration involves simultaneous solution of a direct problem and a number of sensitivity problems corresponding to each of the design variables. Relevant 3D design problems related to preform and die design for desired properties in the final product are considered highlighting the features and potential of the metal forming design simulator developed.

Efficient force calculations based on continuum sensitivity analysis

Using continuum design sensitivity analysis (CDSA), in conjunction with the virtual work principle, equations have been derived for calculating forces without the need to solve the adjoint system. The resultant expressions are similar to the Maxwell stress tensor, but have the important advantage of the integration taking place on the surface of material rather than in the air outside. Implementation of the scheme leads to efficient calculations and improved accuracy.