Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Self assembly”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8

Self assembly properties of primitive organic compounds

A central event in the origin of life was the self-assembly of amphiphilic, lipid-like compounds into closed microenvironments. If a primitive macromolecular replicating system could be encapsulated within a vesicular membrane, the components of the system would share the same microenvironment, and the result would be a step toward true cellular function. The goal of our research has been to determine what amphiphilic molecules might plausibly have been available on the early Earth to participate in the formation of such boundary structures. To this end, we have investigated primitive organic mixtures present in carbonaceous meteorites such as the Murchison meteorite, which contains 1-2 percent of its mass in the form of organic carbon compounds. It is likely that such compounds contributed to the inventory of organic carbon on the prebiotic earth, and were available to participate in chemical evolution leading to the emergence of the first cellular life forms. We found that Murchison components extracted into non-polar solvent systems are surface active, a clear indication of amphiphilic character. One acidic fraction self-assembles into vesicular membranes that provide permeability barriers to polar solutes. Other evidence indicates that the membranes are bimolecular layers similar to those formed by contemporary membrane lipids. We conclude that bilayer membrane formation by primitive amphiphiles on the early Earth is feasible. However, only a minor fraction of acidic amphiphiles assembles into bilayers, and the resulting membranes require narrowly defined conditions of pH and ionic composition to be stable. It seems unlikely, therefore, that meteoritic infall was a direct source of membrane amphiphiles. Instead, the hydrocarbon components and their derivatives more probably would provide an organic stock available for chemical evolution. Our current research is directed at possible reactions which would generate substantial quantities of membranogenic amphiphiles. One possibility is photochemical oxidation of hydrocarbons.

Deamer, D. W.↗

Characterizing the Self-Assembly Properties of Monoolein Lipid Isosteres

Living cells feature lipid compartments which exhibit a variety of shapes and structures that assist essential cellular processes. Many natural cell compartments frequently adopt convoluted nonlamellar lipid architectures that facilitate specific biological reactions. Improved methods for controlling the structural organization of artificial model membranes would facilitate investigations into how membrane morphology affects biological functions. Monoolein (MO) is a single-chain amphiphile which forms nonlamellar lipid phases in aqueous solution and has wide applications in nanomaterial development, the food industry, drug delivery, and protein crystallization. However, even if MO has been extensively studied, simple isosteres of MO, while readily accessible, have seen limited characterization. An improved understanding of how relatively minor changes in lipid chemical structure affect self assembly and membrane topology could instruct the construction of artificial cells and organelles for modeling biological structures and facilitate nanomaterial-based applications. Here, we investigate the differences in self-assembly and large-scale organization between MO and two MO lipid isosteres. We show that replacing the ester linkage between the hydrophilic headgroup and hydrophobic hydrocarbon chain with a thioesther or amide functional group results in the assembly of lipid structures with different phases not resembling those formed by MO. Using light and cryo-electron microscopy, small-angle X-ray scattering, and infrared spectroscopy, we demonstrate differences in the molecular ordering and large-scale architectures of the self-assembled structures made from MO and its isosteric analogues. These results improve our understanding of the molecular underpinnings of lipid mesophase assembly and may facilitate the development of MO-based materials for biomedicine and as model lipid compartments.

60 APPLIED LIFE SCIENCES↗

Self-Assembled Thermoresponsive Molecular Brushes as Nanoreactors for Asymmetric Aldol Addition in Water

The manipulation and tunability of self-assembled block copolymers through external stimuli presents an attractive strategy to develop smart polymer-based nanoreactors as supports for non-orthogonal tandem catalysis. We report on thermoresponsive core-shell micelles based on poly[norbornene-poly(2-methyl-2-oxazoline-block-2-propyl-2-oxazoline)]-graft-poly[norbornene L-proline] (P[NB-P(MeOx-b-PropOx)]-graft-P[NB-L-proline]) as catalyst supports for L-proline. These molecular brushes exhibit large differences in lower critical solution temperature behavior and nanostructure size in water depending on the chain-lengths and proline connectivity. L-Proline-mediated aldol reactions expose the efficiency by which the molecular brushes self-assemble into micelles. Molecular brushes with an extended backbone show higher activity and selectivity, suggesting better core-shell segregation of the micelles and exclusion of water from the catalytic site. Catalytic efficiencies are not improved above the cloud point temperature, the catalytic be-havior is rather sensitive to conformational changes of the polymer chains.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Study of self-assembly behavior and ionic conductivity of conjugated liquid crystals with T-shaped facial-polyphilic structure

The unique self-assembly of liquid crystals (LCs), combined with their potential application as organic semiconductors, has become a focus of recent research. Here, a joint experimental and computational study of the self-assembly and ionic conduction was carried out on a series of T-shaped conjugated LCs consisting of three incompatible components. By extending the EOn side-chain length, several experimental evaluations confirmed a decrease of the order-disorder transition temperature, while coarse-grained simulations revealed a structural evolution from a smectic phase to a columnar phase. Ionic conductivity of these molecules was achieved by adding Li salt, leading to a maximum conductivity of 1.1 × 10 −3 siemens per centimeter observed at 120°C. All-atom simulations were performed to examine the Li-ion solvation environment and to evaluate the intrachain and interchain Li-ion hopping mechanisms. The molecule with a long EOn side chain was found to generate a densely distributed network of Li-ion solvation sites, which can facilitate effective interchain hopping to promote ion transport.

Liu, Ziwei [Cornell Univ., Ithaca, NY (United Stat↗

DNA-caged nanoparticles via electrostatic self-assembly

DNA-modified nanoparticles enable DNA sensing and therapeutics in nanomedicine and are also crucial for nanoparticle self-assembly with DNA-based materials. However, methods to conjugate DNA to nanoparticle surfaces are limited, inefficient, and lack control. Inspired by DNA tile nanotechnology, we demonstrate a new approach to nanoparticle modification based on electrostatic attraction between negatively charged DNA tiles and positively charged nanoparticles. This approach does not disrupt nanoparticle surfaces and leverages the programmability of DNA nanotechnology to control DNA presentation. We demonstrated this approach using a variety of nanoparticles, including polymeric micelles, polystyrene beads, gold nanoparticles, and superparamagnetic iron oxide nanoparticles with sizes ranging from 5–20 nm in diameter. DNA cage formation was confirmed through transmission electron microscopy (TEM), neutralization of zeta potential, and a series of fluorescence experiments. DNA cages present “handle” sequences that can be used for reversible target attachment or self-assembly. Handle functionality was verified in solution, at the solid–liquid interface, and inside fixed cells, corresponding to applications in biosensing, DNA microarrays, and erasable immunocytochemistry. Finally, these experiments demonstrate the versatility of the electrostatic DNA caging approach and provide a new pathway to nanoparticle modification with DNA that will empower further applications of these materials in medicine and materials science.

60 APPLIED LIFE SCIENCES↗

Deciphering supramolecular and polymer-like behavior in metallogels: real-time insights into temperature-modulated gelation and rapid self-assembly dynamics

Bis(pyridyl) urea-based gelators, namely L2 and its isomeric mixture ( L1 + L2 ), are known to self-assemble into 1D architectures capable of inducing supramolecular gelation. Coordination with metal ions such as Ag( I ), Cu( II ), and Fe( III ) introduces structural reinforcement, enabling the formation of distinct 3D networks governed by metal-specific coordination geometries. Here, we present a comprehensive investigation into the temperature-responsive behavior (20–60 °C) of L2 and L1 + L2 , both in the absence and presence of Ag( I ), Dy( III ), Fe( III ), Cu( II ), and Ho( III ), using real-time small-angle neutron scattering (SANS). To probe long-term structural evolution/kinetics of self-assembly, real-time small-angle X-ray scattering (SAXS) was employed on L2 + Ag gels, complemented by differential scanning calorimetry (DSC) to evaluate thermal transitions. Our results reveal strikingly divergent gelation behaviors: L2 forms a highly rigid, covalent polymer-like network, while L1 + L2 exhibits remarkable thermal adaptability. Upon metal coordination, the assemblies exhibit pronounced crystallinity and exceptional thermal stability, as evidenced by persistent Bragg reflections and invariant d-spacings. Intriguingly, L2 : Fe (2 : 1) and L1 : L2 : Fe (0.5 : 0.5 : 1) in acetonitrile-d 3 (ACN-d 3 ) deviate from this trend, forming thermally labile amorphous gels. These systems show a complete loss of crystalline order, reduced Porod exponents—indicative of collapsed or branched fiber morphologies—and prominent melting and glass transition events in DSC. Fitting SANS and SAXS data to the correlation length model unveiled insightful nanostructural features. While most systems displayed minimal temperature-induced variation in mesh size or surface morphology, L2 : Ag in dimethyl sulfoxide-d 6 (DMSO-d 6 )/D 2 O and L2 : Fe (1 : 1) in ACN-d 3 exhibited a rare combination of thermally stable correlation lengths and increasing high- q exponents—strongly suggesting progressive fiber densification or surface smoothing within a robust gel framework. These findings highlight the tunability and structural resilience of supramolecular gels through precise control of ligand architecture, metal coordination, and temperature, offering valuable design principles for functional soft materials.

Pajoubpong, Jinnipha [Univ. of Cincinnati, OH (Uni↗

Directed Synthesis of Gold Nanoparticle Superstructures Using Self-Assembling Peptoids Containing Metal-Bonding N-Heterocyclic Carbenes

N-Heterocyclic carbene (NHC) ligands, with strong metal-binding affinity, offer a robust platform for constructing organic–inorganic nanohybrids with high stability and tunable properties. However, achieving precise structural control in a simple manner remains challenging. Here, we report a one-pot synthesis of nanohybrids using self-assembling peptoids functionalized with histidine-2-ylidene, which simultaneously enable peptoid assembly and NHC–metal binding. Histidine-2-ylidene-functionalized peptoids were designed to self-assemble and provide NHC binding sites, while AuNPs served as the inorganic component due to NHCs’ strong affinity for gold surfaces. The resulting peptoid-NHC@AuNPs form well-defined vesicles that are characterized by UV–vis spectroscopy, X-ray photoelectron spectroscopy, and electron microscopy. Importantly, the vesicle size and morphology can be tuned via the peptoid sequence or environmental conditions. Further experiments highlight the crucial role of the NHC sites in the formation and stabilization of these nanohybrids. This modular strategy offers a versatile route to fabricating functional NHC-based nanohybrids for potential applications in sensing.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Ordered organic thin films self-assembled from the vapor phase

Organic films self-assembled from a liquid phase, as in Langmuir-Blodgett or adsorption from solution, have received much attention in the past decade as techniques to achieve highly oriented-ordered polymeric thin films. Many organic compounds including some of the same fatty acids have been vapor deposited as well. However, organic pigments and dyes comprise a major class of important materials which have very low solubilities yet excellent thermal stabilities, making them ideally suited for film deposition from the vapor phase. Surprisingly, such molecular systems exhibit a significant propensity to self order, a high sensitivity to deposition parameters, and a range of microstructural forms that cannot be duplicated by the less energetic mechanisms associated with solution adsorption processes. Molecular solids such as heterocyclic polynuclear aromatics are excellent candidates for film formation by vacuum deposition means. Over the past decade, our work and that of others investigating a wide variety of perylene and phthalocyanine derivatives identified five deposition parameters that can significantly affect film morphology, physical microstructure, and type and extent of ordering developed in vacuum and vapor transport grown films. These parameters are substrate temperature, deposition rate, substrate chemistry and epitaxy, ambient gas convective flows, and post deposition annealing. Examples of how each of these conditions manifest themselves in the film structure and ordering, most frequently revealed by scanning electron microscopy, reflection absorption infrared spectroscopy (RAIR), and grazing incidence x-ray diffraction (GIX), are presented.

Debe, M. K.↗

Synthesis and Self-Assembly of Monodisperse Graphene Nanoribbons: Access to Submicron Architectures with Long-Range Order and Uniform Orientation

Fabricating organic semiconducting materials into large-scale well-organized architectures is critical for building high performance molecular electronics. While graphene nanoribbons (GNRs) hold enormous promise for various device applications, their assembly into a well-structured monolayer or multilayer architecture poses a substantial challenge. Here we report the preparation of length-defined monodisperse GNRs via the integrated iterative binomial synthesis (IIBS) strategy and their self-assembly into submicron-architectures with long-range order, uniform orientation as well as regular layers. Further, the use of short alkyl side chains benefits forming stable multi-layers through interlocking structures. By changing the length and backbone shapes of these monodisperse GNRs, various three-dimensional assemblies including multilayer stripes, monolayer stripes, and nanowires, can be achieved, leading to different photophysical properties and band gaps. The discovery of these intriguing self-assembly behaviors of length-defined GNRs is expected to open the door for various future applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Influence of Terminal Carboxyl Groups on the Structure and Reactivity of Functionalized m-Carboranethiolate Self-Assembled Monolayers

The structure and function of self-assembled monolayers (SAMs) at the nanoscale are determined by the steric and electronic effects of their building blocks. Carboranethiol molecules form pristine monolayers that provide tunable two-dimensional systems to probe lateral and interfacial interactions. Additional ω-functionality, such as carboxyl groups, can be introduced to change the properties of the exposed surfaces. Here, two geometrically similar isomeric m-carborane analogues of m-mercaptobenzoic acid, 1-COOH-7-SH-1,7-C 2 B 10 H 10 and racem-1-COOH-9-SH-1,7-C 2 B 10 H 10 , are characterized and their SAMs on Au{111} are examined. The latter isomer belongs to the rare group of chiral cage molecules and becomes, to our knowledge, the first example assembled on Au{111}. Although different in symmetry, molecules of both isomers assemble into similar hexagonal surface patterns. The nearest-neighbor spacing of 8.4 ± 0.4 Å is larger than that of non-carboxylated isomers, consistent with the increased steric demands of the carboxyl groups. Computational modeling reproduced this spacing and suggests a tilt relative to the surface normal. However, tilt domains are not observed experimentally, suggesting the presence of strong lateral interactions. Analyses of the influence of the functional groups through the pseudo-aromatic m-carborane skeleton showed that the thiol group attached to either carbon or boron atoms increases the carboxyl group acidity in solution. In contrast, the acidity of the exposed carboxyl group in the SAMs decreases upon surface attachment; computational analyses suggest that the driving force of this shift is the dielectric of the environment in the monolayer as a result of confined intermolecular interactions, proximity to the Au surface, and partial desolvation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

On-Surface Reactions of Electronically Active Self-Assembled Monolayers for Electrode Work Function Tuning

Self-assembled monolayers (SAMs) help improve the performance of organic electronic devices through interface passivation and enhanced carrier transport. Yet, there is limited information regarding the chemical structure of the SAMs upon functionalization and subsequent thermal treatment. Here, we studied the on-surface reaction of carbazole-derived SAMs on model gold electrodes, focusing on the chemical structure changes induced by thermal treatments. Furthermore, we correlate the microscopic changes with their impact on the electrode’s work function. The carbazole-based SAMs first transform into organometallic complexes. At higher annealing temperatures, SAMs convert to oligomeric complexes. The observed chemical reactions significantly reduce the electrode work function and facilitate electron injection in n-type organic thin-film transistors. Our results highlight the on-surface synthesis of electronically active SAMs as an alternative approach for modifying the work function of electrodes for organic electronics.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Autonomous discovery of emergent morphologies in directed self-assembly of block copolymer blends

The directed self-assembly (DSA) of block copolymers (BCPs) is a powerful approach to fabricate complex nanostructure arrays, but finding morphologies that emerge with changes in polymer architecture, composition, or assembly constraints remains daunting because of the increased dimensionality of the DSA design space. Here, we demonstrate machine-guided discovery of emergent morphologies from a cylinder/lamellae BCP blend directed by a chemical grating template, conducted without direct human intervention on a synchrotron x-ray scattering beamline. This approach maps the morphology-template phase space in a fraction of the time required by manual characterization and highlights regions deserving more detailed investigation. These studies reveal localized, template-directed partitioning of coexisting lamella- and cylinder-like subdomains at the template period length scale, manifesting as previously unknown morphologies such as aligned alternating subdomains, bilayers, or a “ladder” morphology. This work underscores the pivotal role that autonomous characterization can play in advancing the paradigm of DSA.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Investigations into Spin- and Unpolarized Secondary Electron-Induced Reactions in Self-Assembled Monolayers of Cysteine

Cysteine is the simplest thiolated, chiral amino acid and is often used as the anchor for studies of self-assembled monolayers (SAMs) of complex biomolecules such as peptides. Understanding the interaction of SAMs of cysteine with low-energy secondary electrons (SEs) produced by X-rays can further our understanding of radiation damage in biomolecules. In particular, if the electrons are polarized, chiral-selective chemistry could have bearing on the origin of homochirality in nature. In the present paper, we use synchrotron radiation-based X-ray photoelectron spectroscopy to determine the changes that occur in the bonding of self-assembled layers of cysteine on gold as a result of soft X-ray irradiation. To investigate the possibility of chiral selectivity resulting from the interaction of low-energy, spin-polarized SEs (SPSEs), measurements were conducted on cysteine adsorbed on a 3 nm-thick gold layer deposited on a CoPt thin-film multilayer with perpendicular magnetic anisotropy. Time-dependent measurements of the C 1s, N 1s, O 1s, S 2p, and Au 4f core levels are used to follow the changes in surface chemistry and determine reaction cross-sections as a function of SE exposure. Analysis of the data results in cross-sections in the range of 5-7 Mb and suggests possible reaction pathways. Changing the magnetization direction of the CoPt multilayer produces SPSEs with opposite polarity. Some evidence of spin-dependent reactions is indicated but is inconclusive. Possible reasons for the discrepancy are posited.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Patternable Mesoporous Thin Film Quantum Materials via Block Copolymer Self-Assembly: An Emergent Technology?

Recent developments in quantum materials hold promise for revolutionizing energy and information technologies. The use of soft matter self-assembly, for example, by employing block copolymers (BCPs) as structure directing or templating agents, offers facile pathways toward quantum metamaterials with highly tunable mesostructures via scalable solution processing. Here, we report the preparation of patternable mesoporous niobium carbonitride-type thin film superconductors through spin-coating of a hybrid solution containing an amphiphilic BCP swollen by niobia sol precursors and subsequent thermal processing in combination with photolithography. Spin-coated as-made BCP-niobia hybrid thin films on silicon substrates after optional photolithographic definition are heated in air to produce a porous oxide, and subsequently converted in a multistep process to carbonitrides via treatment with high temperatures in reactive gases including ammonia. Grazing incidence small-angle X-ray scattering suggests the presence of ordered mesostructures in as-made BCP-niobia films without further annealing, consistent with a distorted alternating gyroid morphology that is retained upon thermal treatments. Wide-angle X-ray scattering confirms the synthesis of phase-pure niobium carbonitride nanocrystals with rock-salt lattices within the mesoscale networks. Electrical transport measurements of unpatterned thin films show initial exponential rise in resistivity characteristic of thermal activation in granular systems down to 12.8 K, at which point resistivity drops to zero into a superconducting state. Magnetoresistance measurements determine the superconducting upper critical field to be over 16 T, demonstrating material quality on par with niobium carbonitrides obtained from traditional solid-state synthesis methods. Here. we discuss how such cost-effective and scalable solution-based quantum materials fabrication approaches may be integrated into existing microelectronics processing, promising the emergence of a technology with tremendous academic and industrial potential by combining the capabilities of soft matter self-assembly with quantum materials.

36 MATERIALS SCIENCE↗

Effects of tacticity and chiral center-to-dipole distance on mesogen-free liquid crystalline self-assembly of sulfonyl-containing comb-like polymers

In this report, new approaches were implemented to achieve novel ferroelectric liquid crystalline self-assembly in mesogen-free comb-like isotactic polyoxypropylenes (iPOPs) bearing mono- or di-sulfonyl groups, which have potential to exhibit high spontaneous polarization for applications in advanced electronic devices. iPOPs with n-alkylsulfonylpentylthioether side chains (iPOP-SC 5 SO 2 C n , where C n is the alkyl tail with n being either 12 or 8) were prepared via a post-polymerization substitution reaction from isotactic poly[(R)-(–)-epichlorohydrin]. Here, the effects of main-chain tacticity, chiral center-to-dipole distance, number of sulfonyl dipoles per side chain, and n-alkyl tail length on the liquid crystalline self-assembly behavior were investigated by comparing iPOPs with their atactic counterparts. First, when the sulfonyl dipole was placed far away from the chiral center in iPOP-SC 5 SO 2 C n compared with our previously reported isotactic polyethers with n-alkylsulfonyl side chains (iPOP-SO 2 C n ), the dipole–dipole interactions among the side chains decreased, which led to more liquid crystalline phases. Smectic E (SmE) and A (SmA) phases were observed after crystal melting; however, the main-chain chiral center was found to have an insignificant effect on the liquid crystalline assembly when compared to the atactic samples. Second, the longer C n tails increased the transition temperatures as a result of stronger van der Waals interactions. Third, after the thioether linkage in the side chain was oxidized into the sulfonyl group, the chiral center–dipole and dipole–dipole interactions in the resultant polymers (i.e., iPOP-SO 2 C 5 SO 2 C n ) enhanced. As a result, the liquid crystalline phase transitions (i.e., crystal → SmE → SmA → I) were pushed to higher temperatures. The knowledge gained in this study will help us further design and achieve the ferroelectric smectic C* phase in mesogen-free comb-like sulfonylated liquid crystalline polymers.

36 MATERIALS SCIENCE↗

Spectroelectrochemical determination of thiolate self-assembled monolayer adsorptive stability in aqueous and non-aqueous electrolytes

Self-assembled monolayers (SAM) are ubiquitous in studies of modified electrodes for sensing, electrocatalysis, and environmental and energy applications. However, determining their adsorptive stability is crucial to ensure robust experiments. Here, in this work, the stable potential window (SPW) in which a SAM-covered electrode can function without inducing SAM desorption was determined for aromatic SAMs on gold electrodes in aqueous and non-aqueous solvents. The SPWs were determined by employing cyclic voltammetry, attenuated total reflectance surface-enhanced infrared absorption spectroscopy (ATR-SEIRAS), and surface plasmon resonance (SPR). The electrochemical and spectroscopic findings concluded that all the aromatic SAMs used displayed similar trends and SPWs. In aqueous systems, the SPW lies between the reductive desorption and oxidative desorption, with pH being the decisive factor affecting the range of the SPW, with the widest SPW observed at pH 1. In the non-aqueous electrolytes, the desorption of SAMs was observed to be slow and progressive. The polarity of the solvent was the main factor in determining the SPW. The lower the polarity of the solvent, the larger the SPW, with 1-butanol displaying the widest SPW. This work showcases the power of spectroelectrochemical analysis and provides ample future directions for the use of non-polar solvents to increase SAM stability in electrochemical applications.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Optimal design of chemoepitaxial guideposts for the directed self-assembly of block copolymer systems using an inexact Newton algorithm

Directed self-assembly (DSA) of block copolymers (BCPs) is one of the most promising developments in the cost-effective production of nanoscale devices. The process makes use of the natural tendency for BCP melts to form nanoscale structures upon phase separation. The phase separation can be directed through the use of chemically patterned substrates to promote the formation of morphologies that are essential to the production of semiconductor devices. Moreover, the design of substrate pattern can be formulated as an optimization problem for which we seek optimal substrate designs that effectively produce given target morphologies. In this paper, we adopt a phase field model given by a nonlocal Cahn–Hilliard partial differential equation (PDE) based on the minimization of the Ohta–Kawasaki free energy, and present an efficient PDE-constrained optimization framework for the optimal design problem. The design variables are the locations of circular- or strip-shaped guiding posts that are used to model the substrate chemical pattern. To solve the ensuing optimization problem, we propose a variant of an inexact Newton conjugate gradient algorithm tailored to this problem. Additionally, we demonstrate the effectiveness of our computational strategy on numerical examples that span a range of target morphologies. Owing to our second-order optimizer and fast state solver, the numerical results demonstrate five orders of magnitude reduction in computational cost over previous work. The efficiency of our framework and the fast convergence of our optimization algorithm enable us to rapidly solve the optimal design problem in not only two, but also three spatial dimensions.

97 MATHEMATICS AND COMPUTING↗