Shape Sensitivity Research Articles

Uncertainty quantification of 3D acoustic shape sensitivities with generalized [formula omitted]-order perturbation boundary element methods

This paper presents a novel perburbation-based method for uncertainty quantification of acoustic fields and their shape sensitivities. In this work, the frequencies of impinging acoustic waves are regarded as random variables. Taylor’s series expansions of acoustic boundary integral equations are derived to obtain nth-order derivatives of acoustic state functions with respect to frequencies. Acoustic shape sensitivity is obtained by directly differentiating acoustic boundary integral equation with respect to shape design variables, and then the nth-order derivatives of shape sensitivity with respect to random frequencies are formulated with Taylor’s series expansions. Based on the nth-order perturbation theory, the statistical characteristics of acoustic state functions and their shape sensitivities can be evaluated. Numerical examples are presented to demonstrate the validity and effectiveness of the proposed algorithm.

Framework of acoustic analysis and shape optimization for three-dimensional doubly periodic multilayered structures

In this research, a framework of acoustic analysis and shape optimization, based on isogeometric boundary element method (IGA-BEM), is proposed for three-dimensional doubly periodic multilayered structures. The study addresses a gap in the literature by focusing on the shape optimization of such structures, which has not been extensively explored previously. The interface between different acoustic media is an infinite doubly periodic surface, which can be constructed by an open non-uniform rational B-splines. A periodic IGA-BEM is developed for the sound field analysis of the doubly periodic multilayered structure, in which the Ewald method is used to accelerate the calculation of periodic Green function. Furthermore, the shape derivative of the doubly periodic multiple boundaries is derived by imposing boundary perturbation and using the adjoint variable method. The control points of the NURBS surfaces are defined as the shape design variables, and all shape sensitivities can be quickly calculated by discretizing the shape derivative formula. Finally, in according with shape sensitivities, the corresponding shape optimization problem is solved by the method of moving asymptotes, so that the optimized shape design can be obtained. A series of numerical examples validates the accuracy and applicability of the proposed approaches.

Cortical development in the structural model and free energy minimization.

A model of neocortical development invoking Friston's Free Energy Principle is applied within the Structural Model of Barbas etal. and the associated functional interpretation advanced by Tucker and Luu. Evolution of a neural field with Hebbian and anti-Hebbian plasticity, maximizing synchrony and minimizing axonal length by apoptotic selection, leads to paired connection systems with mirror symmetry, interacting via Markov blankets along their line of reflection. Applied to development along the radial lines of development in the Structural Model, a primary Markov blanket emerges between the centrifugal synaptic flux in layers 2,3 and 5,6, versus the centripetal flow in layer 4, and axonal orientations in layer 4 give rise to the differing shape and movement sensitivities characteristic of neurons of dorsal and ventral neocortex. Prediction error minimization along the primary blanket integrates limbic and subcortical networks with the neocortex. Synaptic flux bypassing the blanket triggers the arousal response to surprising stimuli, enabling subsequent adaptation. As development progresses ubiquitous mirror systems separated by Markov blankets and enclosed blankets-within-blankets arise throughout neocortex, creating the typical order and response characteristics of columnar and noncolumnar cortex.

Reconstruction of Voronoi diagrams in inverse potential problems

In this paper we propose and analyze a numerical method for the recovery of a piecewise constant parameter with multiple phases in the inverse potential problem. The potential is assumed to be constant in each phase, and the phases are modeled by a Voronoi diagram generated by a set of sites, which are used as control parameters. We first reformulate the inverse problem as an optimization problem with respect to the position of the sites. Combining techniques of non-smooth shape calculus and sensitivity of Voronoi diagrams, we are able to compute the gradient of the cost function, under standard non-degeneracy conditions of the diagram. We provide two different formulas for the gradient, a volumetric and an interface one, which are compared in numerical experiments. We provide several numerical experiments to investigate the dependence of the reconstruction on the problem parameters, such as noise, number of sites and initialization.

Validation and application of the square wave voltammetry method for the electrochemical determination of eszopiclone in pharmaceutical formulations and human biological fluids using glassy carbon electrode

A buffer solution of Britton-Robinson (B-R) pH 6.5 was utilized to validate and apply a square wave voltammetry (SWV) method for the electrochemical determination of Eszopiclone (ESP) in pharmaceuticals and biological samples. The cyclic voltammetry (CV) and differential pulse voltammetry (DPV) methods were employed in the initial study of the voltammetric behavior of the ESP compound. The rotating glassy carbon (GC) indicator electrode (2.0 mm2), Pt auxiliary electrode, and Ag/AgCl reference electrode were used for ESP determination. ESP was analyzed to produce a sharp reduction peak at a potential of −750 mV. The best shape and high sensitivity of SWV cathodic current for ESP, were observed using GC electrode, B-R, pH 6.5, accumulation time (tacc) of 60-second, accumulation potential (Eacc) of - 0.1 V, amplitude voltage of 150 mV, frequency of 15 Hz, scan rate of 150 mV s−1, and stirrer rate of 1000 round per minute (rpm). The electroanalytical performance of the SWV method was evaluated through study of repeatability, stability, calibration curve, recovery, and limits of detection and quantification (LOD,LOQ). Under the optimal conditions, the SWV response was linear in the range from 3 × 10−6 to 5 × 10−5 mol/L (n = 10). The SWV method achieved a LOD of 1.9 × 10-8 mol/L (7.5 ppb), and a LOQ of 6.41 × 10−8 mol L−1 (24.93 ppb). The validated SWV method was appeared the good repeatability, sensitivity and stability for the determination of ESP. It was given a very stable SWV current for 90 min, with a 0.141 % relative standard deviation (RSD%). The SWV method was applied to the determination of ESP in pharmaceutical tablets and biological samples.

Shape Factor and Sensitivity Analysis on Stagnation Point of Bioconvective Tetra-hybrid Nanofluid over Porous Stretched Vertical Cylinder

Shape Factor and Sensitivity Analysis on Stagnation Point of Bioconvective Tetra-hybrid Nanofluid over Porous Stretched Vertical Cylinder

Shape Optimization for Lithium-Ion Battery with Porous Electrodes

In this presentation, we introduce a gradient-based shape optimization framework to design porous electrodes for maximum energy storage. Lithium-ion batteries are becoming an increasingly important energy source and storage device. Large surface area that advocates high reaction rates often leads to small porosities that deteriorate electrochemical transport, which significantly restricts ion penetration depth, limiting the material utilization in planar electrodes. Consequently, architected electrodes are required to optimize performance.We consider a model with two materials, namely porous electrode and pure electrolyte. Density-based topology optimization with continuous material volume fraction has previously been implemented on lithium-ion battery system for both half-cell and full-cell model to maximizes its energy storage. Despite the capability of producing complex interdigitated structures, an appropriate penalization scheme for intermediate materials is required for the optimizer to provide near binary designs. Setting up such a penalization is often time-consuming due to the large number of design-dependent variables that affect the forward model differently. Alternatively, the shape optimization approach used in this work produces binary designs naturally by morphing conformal meshes, circumventing inaccuracies associated with fuzzy interfaces. Shape sensitivities are computed via the adjoint method and leveraging automatic differentiation. The optimization problem is solved using a nonlinear programming technique.In this presentation, we perform shape optimization on a half-cell model to maximize its energy storage when a fixed charging current is applied. We study multiple arrangements of physical parameters and compare their performance against a monolithic electrode. Both 2D and 3D results are presented.

Liver vessel MRI image segmentation based on dual-path diffusion model

Accurate segmentation of liver blood vessels in magnetic resonance imaging (MRI) images is a challenging task due to the complex tree-like structure and anisotropic diffusion properties of blood vessels. To solve this problem, we propose a new Dual-Path Diffusion Model (DPDM) framework. The framework consists of two collaborative diffusion paths: a local feature learning path based on convolution operations and a global context modeling path based on transform blocks. Local path encodes rich shape priors and preserve spatial details, while global path captures long-distance dependencies and enhance representation. In the decoding phase, the boundary features from the boundary path are fused with the features of the ordinary path decoding, which further enhances the shape sensitivity. In addition, we leverage a multi-task learning scheme to jointly optimize vascular segmentation and boundary prediction tasks in an end-to-end manner. Experiments on retrospective clinical dataset demonstrate that the proposed DPDM framework achieves excellent performance on the liver vessel segmentation task. Compared with state-of-the-art methods, our approach achieved a 6.0% and 7.3% performance improvement in Dice coefficient and IoU index, respectively. Our approach offers a promising solution for automated blood vessel segmentation in precision medicine.

Second-order Arnoldi accelerated boundary element method for two-dimensional broadband acoustic shape sensitivity analysis

This paper proposes a novel approach for broadband acoustic shape sensitivity analysis based on the direct differentiation approach. Since the system matrices of the boundary element method (BEM) for the analysis of acoustic state and acoustic sensitivity have frequency dependence, repeated calculations are needed at different frequencies. This is very time-consuming, especially for sensitivity calculations used in shape optimization design. The Taylor series expansion of the Hankel function is carried out to separate the frequency-dependent and frequency-independent terms in the acoustic shape sensitivity boundary integral equation to construct a frequency-independent system matrix. In addition, due to the formation of asymmetric full-coefficient matrices in acoustic shape sensitivity equations based on the BEM, repeatedly solving system equations is also extremely time-consuming at broadband frequencies for large scale issues. The second-order Arnoldi approach was employed to create a reduced-order model that maintains the key features of the initial full-order model. The strong singular and supersingular integrals within the sensitivity equations can be calculated directly utilizing the singularity elimination technique. Finally, several numerical examples confirm the accuracy and efficiency of the proposed algorithm.

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.

The role of environmental sensitivity in the experience and processing of emotions: implications for well-being.

Several theories suggest that people differ significantly in their environmental sensitivity, defined as the capacity to perceive and process information about the environment. More sensitive people, who make up between 25% and 30% of the population, are not only more negatively affected by adverse experiences but also benefit disproportionately from positive ones, in line with differential susceptibility theory. Heightened emotional reactivity has been identified as one of the key markers of sensitivity. However, the current understanding of the relationship between sensitivity and the experience and processing of emotions remains limited. In the current paper we propose a new conceptual framework for the multiple ways in which environmental sensitivity may impact on different aspects of the experience and processing of emotions. This includes heightened perception of emotions, increased emotional reactivity, as well as the important role of emotion regulation for the well-being of highly sensitive people. In addition, we also consider rearing experiences in shaping sensitivity and emotion regulation. The reviewed empirical studies largely support the conceptual model but more research is needed to explore the dynamics between sensitivity and emotions further. Finally, we discuss several implications for well-being before making a case for the inclusion of individual differences in environmental sensitivity in affective science. This article is part of the theme issue 'Sensing and feeling: an integrative approach to sensory processing and emotional experience'.

Sensitive quantification of mevalonate pathway intermediates and prediction of relative novel analogs by chemical derivatization-based LC-MS/MS

The mevalonate (MVA) pathway plays a crucial role in the occurrence and progression of various diseases, such as osteoporosis, breast cancer, and lung cancer, etc. However, determining all the MVA pathway intermediates is still challenging due to their high polarity, low concentration, chelation effect with metal compartments, and poor mass spectrometric response. In this study, we established a liquid chromatography-tandem mass spectrometry (LC-MS/MS) method coupled with N2, N2, N4, N4-tetramethyl-6-(4-(piperazin-1-ylsulfonyl) phenyl)-1,3,5-triazine-2,4-diamine (Tmt-PP) labeling for the simultaneous analysis of all MVA intermediates in biospecimens. Chemical derivatization significantly improved the chromatographic retention, peak shape, and detection sensitivity of the analytes. Moreover, we employed a method named mass spectrum calculation to achieve the absolute quantification of the isomers, i.e., isopentenyl pyrophosphate (IPP) and dimethylallyl pyrophosphate (DMAPP). The established method was fully qualified and applied to explore the difference of these metabolites in cisplatin-resistant non-small cell lung cancer (NSCLC) cells. Additionally, several MVA intermediate analogs, including isopentenyl monophosphate or dimethylallyl monophosphate (IMP/DMAMP), geranyl monophosphate (GMP), 5-triphosphomevalonate (MTP), and isopentenyl triphosphate or dimethylallyl triphosphate (ITP/DMATP), were identified for the first time using a knowledge-driven prediction strategy. We further explored the tissue distribution of these novel metabolites. Overall, this work developed a sensitive quantification method for all MVA intermediates, which will enhance our understanding of the role of this pathway in various health and disease conditions. The novel metabolites we discovered warrant further investigations into their biosynthesis and biological functions.

Surrogate-based shape optimization and sensitivity analysis on the aerodynamic performance of HCW configuration

With an additional wing upon the fuselage, the novel high-pressure capturing wing (HCW) configuration exhibits remarkable aerodynamic characteristics at hypersonic speeds under beneficial aerodynamic interference. This bi-wing structure can also enhance the lift at subsonic speeds, positioning HCW configuration as an excellent aerodynamic layout under wide-speed range conditions. In this paper, a single-wing principle HCW configuration is carried out to analyze the influence of the variations in the geometric parameters of the HCW on the aerodynamic performance. Drawing on extant research, four key geometric parameters of the HCW are chosen as design variables, and the hypersonic as well as supersonic conditions are selected for surrogate-based shape optimization. Utilizing polynomial response surface method and method of moving asymptotes, the single-objective optimization studies are carried out with the objectives of maximum lift-to-drag ratio at Ma = 6 and minimum drag coefficient at Ma = 3. Subsequently, the sensitivity analysis is performed for each design parameter. The above methods exhibit notable precision and favorable results. The results show that except for the leading-edge sweep angle, the other three optimization results exhibit divergent trends in their variations. The setting angle has the most significant influence on the aerodynamic forces, owing to the influences of its variation on the shock wave intensity and reflection angle. Based on the stronger intensity of shock wave, this sensitivity indices are higher at Ma = 6. The other three parameters (half-span, leading-edge sweep angle, and trailing-edge sweep angle) modify the aerodynamic forces by adjusting the area of high-pressure region on HCW. Due to the different flow field structures, optimum parameters exhibit diverse effects on lift coefficient and lift-to-drag ratio.

Explicit design optimization of air rudders for maximizing stiffness and fundamental frequency

In aerospace engineering, there is a growing demand for lightweight design through topology optimization. This paper presents a novel design optimization method for stiffened air rudders, commonly used for aircraft attitude control, based on the Moving Morphable Component (MMC) method. The stiffeners within the irregular enclosed design domain are modeled as MMCs and discretized by shell elements, accurately capturing their geometry and evolution during optimization process using explicit parameters. In order to maximize the stiffness and fundamental frequency of the rudder structures, numerical analysis algorithms were developed with shape sensitivity analysis conducted. To comply with the manufacturing requirement, a minimum thickness is prescribed for the stiffeners, and the thickness and density penalty schemes are proposed to meet the minimum thickness constraint and prevent the occurrence of spurious modes respectively. The method’s effectiveness was demonstrated through optimization examples of a typical trapezoidal air rudder, illustrating the significance of stiffener’s distribution on design objectives. The explicit modeling characteristics allow for directly importing the optimization results into CAD systems, significantly enhancing the engineering applicability.

The large-scale organization of shape processing in the ventral and dorsal pathways is dissociable from attention.

The two visual pathways model posits that visual information is processed through two distinct cortical systems: The ventral pathway promotes visual recognition, while the dorsal pathway supports visuomotor control. Recent evidence suggests the dorsal pathway is also involved in shape processing and may contribute to object perception, but it remains unclear whether this sensitivity is independent of attentional mechanisms that were localized to overlapping cortical regions. To address this question, we conducted two fMRI experiments that utilized different parametric scrambling manipulations in which human participants viewed novel objects in different levels of scrambling and were instructed to attend to either the object or to another aspect of the image (e.g. color of the background). Univariate and multivariate analyses revealed that the large-scale organization of shape selectivity along the dorsal and ventral pathways was preserved regardless of the focus of attention. Attention did modulate shape sensitivity, but these effects were similar across the two pathways. These findings support the idea that shape processing is at least partially dissociable from attentional processes and relies on a distributed set of cortical regions across the visual pathways.

Shape optimization of embedded solids using implicit Vertex-Morphing

One of the biggest challenges in optimizing the shape of complex solids is the requirement to maintain a reasonable mesh quality not only at the boundary but also for the bulk discretization of the interior. Thus, additional regularization and, in many cases, re-meshing of the structure during the iterative process is unavoidable with a Lagrangian description. By tracking the shape update using an Eulerian representation, embedded boundary methods are a promising technique for eliminating mesh distortion problems.This work consistently combines the unique features of implicit Vertex-Morphing and embedded boundary methods, facilitating the node-based shape optimization of solids with industrial complexity. One of the crucial elements for solving the primal problem on a fixed background grid is an efficient and robust quadrature scheme. To this end, we incorporate the open-source C++ framework QuESo (https://github.com/manuelmessmer/QuESo) developed for the numerical integration of arbitrarily complex embedded solids defined by oriented boundary meshes, e.g., in STereoLithography (STL) format. Meanwhile, applying the Helmholtz/Sobolev-based (implicit) filter to the vertices of the embedded boundary mesh not only exploits the extensive design space of node-based optimization but also ensures robust control over the feature size. To realize the above methodology, this work introduces a novel sensitivity analysis that yields mesh-independent shape gradients with respect to the immersed boundary. Through a specific sensitivity weighting, we recover a continuous gradient field from discrete values calculated at the nodes of the background grid. In addition, the presented workflow ensures robust enforcement of challenging geometrical constraints, including minimum wall thicknesses and design space limitations.We critically assess our approach with benchmarks and structures of industrial relevance. In all examples, trivariate B-Spline bases span the background grid, providing highly accurate finite element solutions and shape sensitivities at every iteration. Moreover, the elimination of mesh distortion problems enables a successful termination at the local optimum, even for large shape modifications.

Toward Improved Simulations of Disruptive Reservoirs in Global Hydrological Modeling

AbstractAccurate simulation of reservoirs has been a challenge for global hydrological models due to highly discontinuous water management and uncertainties in reservoir shape representation. In addition, at a global scale, it is crucial to consider those reservoirs that disrupt the downstream flow regime. We augment the mesoscale Hydrological Model with a newly developed lake module (LM) that incorporates an existing reservoir regulation scheme with non‐consumptive demand predictions from random forest. We also evaluate the sensitivity of reservoir shape on streamflow and evaporation for three shape approximations of varying complexities. We tested the LM across 31 non‐consumptive reservoirs covering an extensive range of hydroclimatic characteristics and demonstrate the applicability by using freely available global reservoir information. Streamflow simulations with reservoirs and model calibration show a median Kling‐Gupta Efficiency improvement of +0.94 (calibration) and +0.77 (validation) when compared against model simulations without reservoirs and default parameter set. We find reservoir evaporation highly sensitive to reservoir shape with half‐pyramid approximation consistently resulting in best fit at reservoirs with surveyed bathymetry. In contrast, the linear approximation (rectangular prism) produced a median bias of +114% relative to half‐pyramid, for estimating evaporation, across all the reservoirs. Streamflow simulations were insensitive to the reservoir shape. Our analysis shows that 30% of the non‐consumptive hydropower reservoirs of the GRanD data set are non‐disruptive and can be excluded without loss to model realism. Further work is necessary for testing the regulation approach in reservoirs with consumptive water usage.

In vitro comparison of subharmonic-aided pressure estimation sensitivity among microfluidic monodisperse microbubbles, sonazoid, and definity

The subharmonic response of microbubble-based ultrasound contrast agents (UCAs) typically exhibits an inverse linear relationship with the surrounding ambient pressure. Although SHAPE has been clinically successful, the sensitivity of SHAPE at lower pressures is suboptimal. While previous studies optimized SHAPE using commercially available UCAs without considering their size distribution, in this study, two SHAPE-specific monodisperse microbubble (MMB) UCAs with different bubble diameters were compared with commercial polydisperse UCAs as well as their buoyancy-separated subpopulations. UCAs were imaged in a hydrostatic tank containing 350 ml of deionized water. The pressure within the tank was increased from 0–100 mmHg. Using a modified Logiq E10 scanner (GE HealthCare) with acoustic power optimization, SHAPE data was acquired using subharmonic imaging mode with a C1-6 curvilinear probe at 2.5 MHz (receiving at 1.25 MHz). After identification of the optimal acoustic output power, MMB with a mean diameter 1.66 mm demonstrated a mean SHAPE sensitivity of −0.207 dB/mmHg (r2 = 0.94). The second MMB with a mean diameter 3.45 mm demonstrated a mean SHAPE sensitivity of −0.300 dB/mmHg (r2 = 0.92). In contrast, this was 2.5–4 times more sensitive than the two polydisperse UCAs (slope range of −0.081 to −0.074 dB/mmHg) and 1.45–5 times more sensitive than the buoyancy-separated UCAs (ranging −0.061 to −0.142 dB/mmHg). These results suggest that SHAPE-optimized MMB are more sensitive to measuring changes in pressure.

Determination of the vertical distribution of in-cloud particle shape using SLDR-mode 35 GHz scanning cloud radar

Abstract. In this study we present an approach that uses the polarimetric variable SLDR (slanted linear depolarization ratio) from a scanning polarimetric cloud radar MIRA-35 in the SLDR configuration, to derive the vertical distribution of particle shape (VDPS) between the top and base of mixed-phase cloud systems. The polarimetric parameter SLDR was selected for this study due to its strong sensitivity to shape and low sensitivity to the wobbling effect of particles at different antenna elevation angles. For the VDPS method, elevation scans from 90 to 30∘ elevation angle were deployed to estimate the vertical profile of the particle shape by means of the polarizability ratio, which is a measure of the density-weighted axis ratio. Results were obtained by retrieving the best fit between observed SLDR from 90 to 30∘ elevation angle and respective values simulated with a spheroidal scattering model. The applicability of the new method is demonstrated by means of three case studies of isometric, columnar, and plate-like hydrometeor shapes, respectively, which were obtained from measurements at the Mediterranean site of Limassol, Cyprus. The identified hydrometeor shapes are demonstrated to fit well to the cloud and thermodynamic conditions which prevailed at the time of observation. A fourth case study demonstrates a scenario where ice particle shapes tend to evolve from a pristine state at the cloud top toward a more isometric shape or less dense particles at the cloud base. Either aggregation or riming processes contribute to this vertical change of microphysical properties. The new height-resolved identification of hydrometeor shape and the potential of the VDPS method to derive its vertical distribution are helpful tools to understand complex processes such as riming or aggregation, which occur particularly in mixed-phase clouds.

Design and discussion of off-axis reflective double-pass optical systems.

In most off-axis reflective optical systems, light beams only pass each optical element once. A double-pass structure can increase the number of beam reflections while using the same number of elements as conventional systems, which can be advantageous for some optical systems, with benefits that include high system compactness and cost-friendliness. In this paper, a design method for off-axis reflective double-pass optical systems is proposed that enables effective control of the overlap of a beam that passes through the double-pass surface twice. Furthermore, we designed and analyzed various geometric folding structure double-pass optical systems that include three-mirror reflections to explore their optimization potential and volume control capabilities. Subsequently, the effect of the double-pass structure on the optical system's performance is investigated using the system volume as an indicator. The results obtained show that when a system inherently requires a longer total optical length to enable better aberration correction, a double-pass structure may reduce the system volume. Finally, we discuss the impact of the double-pass configuration on the optical system's position sensitivity and surface shape sensitivity.