Continuum Sensitivity Research Articles

Continuum and Discrete Analytical Methods for Vibration and Buckling Eigenvalues Shape Sensitivities

AbstractGradient-based optimization techniques need precise and efficient sensitivities. Numerical sensitivity methods such as finite differences are easy to implement but imprecise and computationally inefficient. In contrast, analytical sensitivity methods, such as the discrete and continuum ones are highly accurate and efficient. Continuum Sensitivity Analysis (CSA) is an analytical method used to calculate derivatives of shape or value parameters. While CSA has been successfully applied in static analysis and dynamic problems in the time domain, this work presents an extension of the approach to eigenvalue sensitivities for the first time. However, CSA revealed limitations, prompting the exploration of an alternative approach based on discrete analytical differentiation. This method is employed for the first time in shape sensitivities. The derivatives of the stiffness and mass matrices required by the method are calculated analytically, resulting in high accuracy and computational efficiency. In addition, an element agnostic approach has been developed leveraging primary analysis matrices to calculate their derivative. This characteristic, along with the nonintrusivity, makes the method employable with standard commercial software. Both approaches have been applied and validated in a wide range of scenarios, involving vibration and buckling problems.

Design Optimization of HTS Field Coils for High Power Density Motors Based on Continuum Sensitivity Analysis

This study proposes an optimization method for designing HTS field coils for high power density motors based on continuum sensitivity analysis. The continuum sensitivity of a superconducting system represents the gradient of the objective function with respect to the superconducting material shape, taking the critical current characteristics into account. The continuum sensitivity was coupled with the level set method through the design velocity field, and the design of the HTS field coil was performed by solving the level set equation. The applicability of the proposed method was verified by designing a 200 kW HTS motor to maximize the torque density. The design optimization provided an optimal solution through the evolution of the topology and shape of the HTS field coil. The optimized geometry was employed to design field coils consisting of racetrack coils wound with HTS tape. Finally, further designs with different cross-sectional areas of the field coils demonstrated that the proposed method can design HTS motors with minimal HTS tape for a given rated power and motor size.

Continuum Sensitivity Analysis for Shape Optimization of Transient Eddy Current Systems

This study proposes a shape sensitivity analysis for transient eddy current systems. The continuum sensitivity analysis is a deterministic optimization technique for designing the shape and topology of electromagnetic systems. Despite substantial research on the sensitivity analysis, most of the work has focused on static and steady-state issues. However, some problems require transient analysis. In this paper, the shape sensitivity formula for a transient eddy current system was derived by the continuum approach using the adjoint variable technique and material derivative concept. In the sensitivity analysis using the derived sensitivity formula, the state variable equation is an initial-value problem to be solved forward in time. Conversely, the adjoint variable equation is a terminal-value problem to be solved backward in time. Three numerical examples were tested to demonstrate the feasibility and usability of the derived sensitivity formula.

Continuum sensitivity and design optimization of superconducting systems under critical current densities with magnetic field dependence

This paper presents an approach for deriving the continuum sensitivity of superconducting systems operating at critical current densities and an optimization method based on the continuum sensitivity. In the sensitivity problem, the superconducting systems is represented by a variational state equation, wherein the magnetic permeability depends on the magnetic field, which is transformed from a state equation with a field-dependent source. The design sensitivity is derived using the material derivative concept of continuum mechanics and the adjoint variable method. The adjoint system has a material property represented as a symmetric tensor that contains the sensitivity of the current density with respect to the magnetic field. The design sensitivity is represented in the analytical form of a surface integral on the interface between the superconducting material and its surroundings, which depends on the sensitivity of the current density. The optimization scheme is constructed based on the continuum design sensitivity. In the design optimization, the level set method is used to express the shape variation of the superconducting materials. The numerical example of infinite solenoids demonstrates that the design sensitivity provides an accurate design solution considering the critical current condition. In addition, the design example of a magnetic resonance imaging solenoid shows that the derived design sensitivity has the inherent ability for attaining the compact design by treating the input current of a superconducting system as a critical condition.

ALMA–IRDC: dense gas mass distribution from cloud to core scales

ABSTRACT Infrared dark clouds (IRDCs) are potential hosts of the elusive early phases of high mass star formation (HMSF). Here, we conduct an in-depth analysis of the fragmentation properties of a sample of 10 IRDCs, which have been highlighted as some of the best candidates to study HMSF within the Milky Way. To do so, we have obtained a set of large mosaics covering these IRDCs with Atacama Large Millimeter/submillimeter Array (ALMA) at Band 3 (or 3 mm). These observations have a high angular resolution (∼3 arcsec; ∼0.05 pc), and high continuum and spectral line sensitivity (∼0.15 mJy beam−1 and ∼0.2 K per 0.1 km s−1 channel at the N2H+ (1 − 0) transition). From the dust continuum emission, we identify 96 cores ranging from low to high mass (M = 3.4−50.9 M⊙) that are gravitationally bound (αvir = 0.3−1.3) and which would require magnetic field strengths of B = 0.3−1.0 mG to be in virial equilibrium. We combine these results with a homogenized catalogue of literature cores to recover the hierarchical structure within these clouds over four orders of magnitude in spatial scale (0.01–10 pc). Using supplementary observations at an even higher angular resolution, we find that the smallest fragments (<0.02 pc) within this hierarchy do not currently have the mass and/or the density required to form high-mass stars. None the less, the new ALMA observations presented in this paper have facilitated the identification of 19 (6 quiescent and 13 star-forming) cores that retain >16 M⊙ without further fragmentation. These high-mass cores contain trans-sonic non-thermal motions, are kinematically sub-virial, and require moderate magnetic field strengths for support against collapse. The identification of these potential sites of HMSF represents a key step in allowing us to test the predictions from high-mass star and cluster formation theories.

The ram pressure stripped radio tails of galaxies in the Coma cluster

ABSTRACT Previous studies have revealed a population of galaxies in galaxy clusters with ram pressure stripped (RPS) tails of gas and embedded young stars. We observed 1.4 GHz continuum and H i emission with the Very Large Array in its B-configuration in two fields of the Coma cluster to study the radio properties of RPS galaxies. The best continuum sensitivities in the two fields are 6 and 8 µJy per 4 arcsec beam, respectively, which are 4 and 3 times deeper than those previously published. Radio continuum tails are found in 10 (8 are new) out of 20 RPS galaxies, unambiguously revealing the presence of relativistic electrons and magnetic fields in the stripped tails. Our results also hint that the tail has a steeper spectrum than the galaxy. The 1.4 GHz continuum in the tails is enhanced relative to their H α emission by a factor of ∼7 compared to the main bodies of the RPS galaxies. The 1.4 GHz continuum of the RPS galaxies is also enhanced relative to their infrared emission by a factor of ∼2 compared to star-forming galaxies. The enhancement is likely related to ram pressure and turbulence in the tail. We furthermore present H i detections in three RPS galaxies and upper limits for the other RPS galaxies. The cold gas in D100’s stripped tail is dominated by molecular gas, which is likely a consequence of the high ambient pressure. No evidence of radio emission associated with ultra-diffuse galaxies is found in our data.

Continuum-Sensitivity-Based Optimization of Interior Permanent Magnet Synchronous Motor With Shape Constraint for Permanent Magnet

This article proposes a continuum-sensitivity-based method to obtain the optimal design for an interior permanent magnet synchronous motor (IPMSM). Compared with the finite difference method, the continuum sensitivity analysis shortens the computation time significantly when there are numerous design variables. We combine the continuum sensitivity with the shape constraint so that both the shape and the size can be optimized simultaneously and within a short time. This proposed design optimization method is applied to IPMSM rotor design, and its feasibility is verified. The proposed method is expected to be effective for various design problems that require the shape and the size to be optimized simultaneously.

Continuum Sensitivity Analysis for Electrode Shape Optimization in Electrostatic System with State Variable Constraint

This article proposes an electrode shape optimization strategy with state variable constraints. The continuum sensitivity formula is used for the electrostatic system to determine the extremum of objective functions with state variable constraints. We use the gradient projection method and a restoration process to treat geometric and state variable constraints. The geometric changes of the design parameter are determined by the velocity field calculated from the constrained sensitivity analysis and are expressed by the level set method. The application models are tested to demonstrate the feasibility and utility of the proposed method.

A3COSMOS: the dust attenuation of star-forming galaxies at z = 2.5–4.0 from the COSMOS-ALMA archive

ABSTRACT We present an analysis of the dust attenuation of star-forming galaxies at z = 2.5–4.0 through the relationship between the UV spectral slope (β), stellar mass (M*), and the infrared excess (IRX = LIR/LUV) based on far-infrared continuum observations from the Atacama Large Millimeter/sub-millimeter Array (ALMA). Our study exploits the full ALMA archive over the COSMOS field processed by the A3COSMOS team, which includes an unprecedented sample of ∼1500 galaxies at z ∼ 3 as primary or secondary targets in ALMA band 6 or 7 observations with a median continuum sensitivity of 126 $\rm {\mu Jy\, beam}^{-1}$ (1σ). The detection rate is highly mass dependent, decreasing drastically below log (M*/M⊙) = 10.5. The detected galaxies show that the IRX–β relationship of massive (log M*/M⊙ > 10) main-sequence galaxies at z = 2.5–4.0 is consistent with that of local galaxies, while starbursts are generally offset by $\sim 0.5\, {\rm dex}$ to larger IRX values. At the low-mass end, we derive upper limits on the infrared luminosities through stacking of the ALMA data. The combined IRX–M* relation at $\rm {log\, ({\it M}_{\ast }/\mathrm{M}_{\odot })\gt 9}$ exhibits a significantly steeper slope than reported in previous studies at similar redshifts, implying little dust obscuration at log M*/M⊙ < 10. However, our results are consistent with earlier measurements at z ∼ 5.5, indicating a potential redshift evolution between z ∼ 2 and z ∼ 6. Deeper observations targeting low-mass galaxies will be required to confirm this finding.

Nonintrusive continuum sensitivity analysis for fluid applications

Continuum Sensitivity Analysis (CSA) provides an analytic method of computing derivatives for structures, fluids and fluid-structure-interaction problems with respect to shape or value parameters. CSA does not require mesh sensitivity to calculate local shape sensitivity, thereby contributing to its computational efficiency. CSA involves solving linear sensitivity equations with the corresponding sensitivity boundary conditions. Spatial gradients of flow variables are required to construct the sensitivity boundary conditions, the accuracy of which significantly affects the flow shape derivatives. A method called Spatial Gradient Reconstruction (SGR) is used to accurately compute the flow spatial gradients that are further used to set the sensitivity boundary conditions. Here we present a nonintrusive CSA formulation for calculating the material derivatives of flow variables with respect to shape design parameters. Nonintrusive CSA means CSA without any modification to the black-box program used for the CFD flow analysis. Moreover, nonintrusive CSA is flow solver agnostic, in that, knowledge of the solver's discretization is not needed. An example of two-dimensional flow over a NACA0012 airfoil demonstrates the application of nonintrusive CSA to steady flow problems involving Euler (compressible inviscid) equations over unstructured grids with finite volume spatial discretization. Accuracy was studied by investigating convergence for a family of six high-quality grids, ranging from four thousand to four million cells. Factors such as the accuracy of the flow spatial gradients, flow sensitivity boundary conditions, weak implementation of the boundary conditions in the finite volume framework, and the use of an approximate flux Jacobian matrix, all of which affect the accuracy of the material derivatives, are discussed. A novelty of this work is that the sensitivity analysis is done nonintrusively using FLUENT and SU2 software to establish the use of black-box codes for obtaining flow derivatives using the CSA approach.

A piecewise constant level set method for damage identification of continuum structures based on natural frequencies

The damage identification of continuum structures from the observation of its natural frequencies is investigated. The piecewise constant level set (PCLS) method is applied to represent the shape and topology of the damaged region. The functional derivative of the objective function with respect to PCLS function is derived with the application of the continuum sensitivity analysis. A regularized restarted conjugate gradient algorithm is proposed. Identifications of single and multiple damaged regions in 2D cantilever structures are discussed, illustrating the validity of the proposed algorithm.

Shape optimization of interface between ferromagnetic material and air in eddy current system using continuum sensitivity analysis and level-set method

Shape optimization of interface between ferromagnetic material and air in eddy current system using continuum sensitivity analysis and level-set method

Multi-scale computational modeling of lightweight aluminum-lithium alloys

The present study addresses the multi-scale computational modeling of a lightweight Aluminum-Lithium (Al-Li) 2070 alloy. The Al-Li alloys display significant anisotropy in material properties because of their strong crystallographic texture. To understand the relationships between processing, microstructural textures at different material points and tailored material properties, a multi-scale simulation is performed by controlling the texture evolution during deformation. To achieve the multi-scale framework, a crystal plasticity model based on a one-point probability descriptor, Orientation Distribution Function (ODF), is implemented to study the texture evolution. Next, a two-way coupled multi-scale model is developed, where the deformation gradient at the macro-scale integration points is passed to the micro-scale ODF model and the homogenized stress tensor at the micro-scale is passed back to the macro-scale model. A gradient-based optimization scheme which incorporates the multi-scale continuum sensitivity method is utilized to calibrate the slip system parameters of the alloy using the available experimental data. Next, the multi-scale simulations are performed for compression and tension using the calibrated crystal plasticity model, and the texture data is compared to the experiments. With the presented multi-scale modeling scheme, we achieve the location-specific texture predictions for a new generation Al-Li alloy for different deformation processes.

Constraining the Volume Density of Dusty Star-forming Galaxies through the First 3 mm Number Counts from ALMA

Abstract We carry out a blind search of 3 mm continuum sources using the ALMA Science Archive to derive the first galaxy number counts at this wavelength. The analyzed data are drawn from observations toward three extragalactic legacy fields: COSMOS, CDF-S, and the UDS comprising more than 130 individual ALMA Band 3 pointings and an effective survey area of ≈200 arcmin2 with a continuum sensitivity that allows for the direct detection of unlensed Dusty Star-forming Galaxies (DSFGs) dust emission beyond the epoch of reionization. We present a catalog of 16 sources detected at >5σ with flux densities from which number counts are derived. These number counts are then used to place constraints on the volume density of DSFGs with an empirical backward evolution model. Our measured 3 mm number counts indicate that the contribution of DSFGs to the cosmic star formation rate density at z ≳ 4 is non-negligible. This is contrary to the generally adopted assumption of a sharply decreasing contribution of obscured galaxies at z > 4 as inferred by optical and near-infrared surveys. This work demonstrates the power of ALMA-3 mm observations, which can reach outstanding continuum sensitivities during typical spectral line science programs. Further constraints on 3 mm selected galaxies will be essential to refine models of galaxy formation and evolution as well as models of early universe dust production mechanisms.

The expanded Giant Metrewave Radio Telescope

With 30 antennas and a maximum baseline length of 25 km, the Giant Metrewave Radio Telescope (GMRT) is the premier low-frequency radio interferometer today. We have carried out a study of possible expansions of the GMRT, via adding new antennas and installing focal plane arrays (FPAs), to improve its point-source sensitivity, surface brightness sensitivity, angular resolution, field of view, and U-V coverage. We have carried out array configuration studies, aimed at minimizing the number of new GMRT antennas required to obtain a well-behaved synthesized beam over a wide range of angular resolutions for full-synthesis observations. This was done via two approaches, tomographic projection and random sampling, to identify the optimal locations for the new antennas. We report results for the optimal locations of the antennas of an expanded array (the "EGMRT"), consisting of the existing 30 GMRT antennas, 30 new antennas at short distances, $\leq 2.5$ km from the array centre, and 26 new antennas at long distances, $\approx 5-25$ km from the array centre. The collecting area and the field of view of the proposed EGMRT array would be larger by factors of, respectively, $\approx 3$ and $\approx 30$, than those of the GMRT. Indeed, the EGMRT continuum sensitivity and survey speed with 550-850 MHz FPAs installed on the 45 antennas within a distance of $\approx 2.5$ km of the array centre would be far better than those of any existing interferometer, and comparable to the sensitivity and survey speed of Phase-1 of the Square Kilometre Array.

The XXL Survey

We present the 25 square-degree GMRT-XXL-N 610 MHz radio continuum survey, conducted at 50 cm wavelength with the Giant Metrewave Radio Telescope (GMRT) towards the XXL Northern field (XXL-N). We combined previously published observations of the XMM-Large Scale Structure (XMM-LSS) field, located in the central part of XXL-N, with newly conducted observations towards the remaining XXL-N area, and imaged the combined data-set using the Source Peeling and Atmospheric Modeling (SPAM) pipeline. The final mosaic encompasses a total area of 30.4 square degrees, with rms <150 μJy beam−1 over 60% of the area. The rms achieved in the inner 9.6 square degree area, enclosing the XMM-LSS field, is about 200 μJy beam−1, while that over the outer 12.66 square degree area (which excludes the noisy edges) is about 45 μJy beam−1. The resolution of the final mosaic is 6.5 arcsec. We present a catalogue of 5434 sources detected at ≥7 ×rms. We verify, and correct the reliability of, the catalog in terms of astrometry, flux, and false detection rate. Making use of the (to date) deepest radio continuum survey over a relatively large (2 square degree) field, complete at the flux levels probed by the GMRT-XXL-N survey, we also assess the survey’s incompleteness as a function of flux density. The radio continuum sensitivity reached over a large field with a wealth of multi-wavelength data available makes the GMRT-XXL-N 610 MHz survey an important asset for studying the physical properties, environments and cosmic evolution of radio sources, in particular radio-selected active galactic nuclei (AGN).

ALMA Survey of Lupus Protoplanetary Disks. II. Gas Disk Radii

Abstract We present Atacama Large Millimeter/Sub-Millimeter Array (ALMA) Band 6 observations of a complete sample of protoplanetary disks in the young (∼1–3 Myr) Lupus star-forming region, covering the 1.33 mm continuum and the 12CO, 13CO, and C18O J = 2–1 lines. The spatial resolution is ∼0.″25 with a medium 3σ continuum sensitivity of 0.30 mJy, corresponding to M dust ∼ 0.2 M ⊕. We apply Keplerian masking to enhance the signal-to-noise ratios of our 12CO zero-moment maps, enabling measurements of gas disk radii for 22 Lupus disks; we find that gas disks are universally larger than millimeter dust disks by a factor of two on average, likely due to a combination of the optically thick gas emission and the growth and inward drift of the dust. Using the gas disk radii, we calculate the dimensionless viscosity parameter, α visc, finding a broad distribution and no correlations with other disk or stellar parameters, suggesting that viscous processes have not yet established quasi-steady states in Lupus disks. By combining our 1.33 mm continuum fluxes with our previous 890 μm continuum observations, we also calculate the millimeter spectral index, α mm, for 70 Lupus disks; we find an anticorrelation between α mm and millimeter flux for low-mass disks (M dust ≲ 5), followed by a flattening as disks approach α mm ≈ 2, which could indicate faster grain growth in higher-mass disks, but may also reflect their larger optically thick components. In sum, this work demonstrates the continuous stream of new insights into disk evolution and planet formation that can be gleaned from unbiased ALMA disk surveys.

Continuum shape sensitivity analysis for aeroelastic gust using an arbitrary lagrangian-eulerian reference frame

Continuum Sensitivity Analysis (CSA), a method to determine response derivatives with respect to design variables, is derived here for the first time in an arbitrary Lagrangian-Eulerian (ALE) reference frame. CSA differentiates nonlinear governing system of equations to arrive at a linear system of partial differential continuum sensitivity equations (CSEs), here, for fluid-structure interaction (FSI). The CSEs and associated sensitivity boundary conditions are derived here for the first time for FSI, using the boundary velocity formulation, carefully distinguishing design velocity from flow velocity and ALE mesh velocity. Whereas boundary conditions must be differentiated using the material (total) derivative, it is sometimes advantageous to derive the CSEs using local (partial) derivatives. The benefit is that geometric sensitivity, known as design velocity, may not be required in the domain. It is shown here that this advantage is realized when the ALE frame undergoes only the rigid body motion associated with the structure to which it is attached. It is further shown that the advantage is not realized when the ALE mesh deforms due to the flexible motion of the fluid-structure interface. The equations for the transient gust response of a two-dimensional airfoil in compressible flow, flexibly attached to a rigid body mass, are presented as a model problem to illustrate a detailed derivation.

Continuum Sensitivity Analysis and Shape Optimization of Dirichlet Conductor Boundary in Electrostatic System

This paper proposes an optimization method using the continuum sensitivity analysis for conductor shape design in the electrostatic system. The continuum sensitivity formula for a conductor shape is analytically derived by employing the material derivative concept from continuum mechanics and the adjoint variable technique. The geometry change of the conductor surface is determined by the velocity field from the derived sensitivity formula, and it is expressed by the level set method. Two numerical examples are tested to show the feasibility and usefulness of the proposed method.

Multiple Level-Set Methods for Optimal Design of Nonlinear Magnetostatic System

This paper proposes an optimal design method using continuum sensitivity analysis and the multiple level-set methods for multi-material shape optimization in nonlinear magnetostatic systems. The general shape sensitivity formula for the nonlinear magnetostatic system is derived based on the material derivative concept of continuum mechanics and the adjoint variable method. In the multiple level-set methods, the sign combination of level-set functions is used to identify the different material regions and their interfaces. The multi-material shapes are simultaneously deformed by solving the multiple level-set equations coupled with the velocity fields in the sensitivity formula. Two numerical examples are employed to show the usefulness of the proposed design method.