In three-dimensional (3D)-printed tissue models, sensitive, noninvasive techniques are required to detect in situ changes in hydrogel structure caused by cellular remodeling. We demonstrate herein that circular dichroism (CD) spectroscopy provides a reliable method for detecting hydrogel structural variations. We probe directly the plasmonic optical activity of chiral gold nanorods (c-AuNRs) embedded within the hydrogel matrix, in response to variations in the local environment. Unlike extinction spectroscopy, we found that CD features such as zero-point crossings do not get masked by the strong scattering due to the porous hydrogel structure and are therefore sensitive to changes in the refractive index of the medium, reversible swelling and deswelling of the hydrogel, and other interactions between the hydrogel and the c-AuNR surface. By culturing metastatic breast cancer cells within the 3D hydrogel nanocomposite, we demonstrate that CD can noninvasively probe the restructuring of the hydrogel. This study highlights the potential of CD spectroscopy in combination with c-AuNRs to investigate complex changes in biological or polymeric systems.

A novel integration scheme is proposed for the accurate numerical evaluation of test (reaction) integrals needed for solving complex direct or inverse electromagnetic problems using surface integral equation (SIE) formulations and the method of moments. Significant effort has already been devoted to improving the numerical evaluation of source integrals yielding potentials (or their derivatives), especially for triangular elements. However, numerical techniques for accurately evaluating the subsequent test integrals have been largely neglected, with simple numerical integration schemes being used that either ignore or are developed with incomplete knowledge of the detailed behavior of potentials (or their derivatives) near edges and vertices. Consequently, simple numerical quadrature schemes are found to be either of limited accuracy or slowly convergent with respect to increasing the sampling for self, edge- or vertex-adjacent source, and test triangle pairs. Here, we describe a simple model derived from static potential integrals that properly describes and bounds the potentials and their derivatives near vertices. From it, we are able to construct appropriate, separable radial-angular quadrature schemes that are both exponentially convergent and applicable to all potential forms of interest arising from both EFIE and MFIE operators. Numerical results are presented that demonstrate the wide-ranging applicability and improved convergence rates of the proposed scheme, and these are compared to some previously reported testing schemes. The method's sensitivity to test triangle shape and the ratio choice of angular-to-radial sampling rates is also briefly explored.

AbstractIsomer discrimination is of paramount importance across various sectors, including pharmaceuticals, agriculture, and the food industry, owing to their unique physicochemical characteristics. Because of their extremely similar characteristics, traditional analytical methods fail or encounter severe limitations in isomer discrimination. To overcome this grand challenge, a novel sensing strategy is proposed based on surface‐enhanced Raman scattering (SERS) substrates (i.e., plasmonic platforms) combined with machine learning algorithms. These plasmonic platforms exhibit exceptional signal uniformity across wide regions and sensitivity, enabling the discrimination of structural isomers (hydroquinone, resorcinol, pyrocatechol), geometric isomers ((Z/E)‐stilbene, (Z/E)‐resveratrol), and optical isomers (R/S‐ibuprofen). Notably, for the analysis of optical isomers, 1‐naphthalenethiol is employed as a probe to facilitate specific isomer orientation on the surface of the plasmonic platform through, for the first time, π–π interactions. The integration of machine learning methodologies, such as Partial Least Squares Regression and Artificial Neural Networks, significantly enhances both quantitative analysis and classification accuracy, achieving detection limits as low as 2 × 10⁻⁸ m. Validation with commercially available ibuprofen samples shows excellent agreement with traditional circular dichroism results, highlighting the method's robustness and precision. The strategy provides a versatile, ultrasensitive, and reliable solution for isomer discrimination, with broad applications in pharmaceuticals, environmental monitoring, and clinical diagnostics.

In this communication, we present the combination of a high scalability implementation of the multibranch-multiresolution preconditioner with the domain decomposition method for the electromagnetic analysis of geometrically complex strutures with different levels of multi-scale features and discretized with a possible non-conformal mesh. Finally, a numerical experiment is shown to illustrate the great efficiency of the proposed approach for the solution of large multi-scale objects.

In this paper, a new technique, based on machine learning (ML) and dimensionality reduction, is proposed for drastically improving the performance in the evaluation of the singular and near singular potential integrals in the method of moments (MoM). The MoM source surface integral is first reduced to a line integral via a dimensionality reduction method, and, then, an ML algorithm is trained on a set of line integrals evaluated with Gauss-Legendre (GL) quadrature schemes of different orders. Finally, the trained ML algorithm is used to determine the minimum number of GL sample points and weights required for each potential line integral to get the requested accuracy.

In computational electromagnetics, the accuracy of simulations is significantly influenced by the meshing quality of the structures under analysis. Higher mesh density generally translates into higher accuracy as it provides a more detailed representation of the structure, although at the expense of greater demands on computational resources. This is particularly true in multiscale problems, where the different levels of detail make the impact of mesh density and quality even more critical. In this context, adaptive meshing techniques, especially through h-refinement, arise as a powerful tool for addressing these problems [1, 2]. H-refinement involves locally refining the mesh in areas lacking accuracy depending on an error estimation process. This method allows for targeted subdivisions in regions with higher errors, thereby systematically reducing the overall error and achieving the desired level of accuracy.

The interest in the electromagnetic behavior of periodic structures has significantly increased due to their crucial role in advancing cutting-edge applications in nanoscale and metasurface devices in scattering networks, plasmonic crystals, and nanophotonics. The rise of these technologies makes the improvement of the state-of-the-art methods in computational electromagnetics for the efficient solution of these kind of periodic structures even more crucial than ever. Traditional approaches predominantly centered on methods tailored for infinite periodic structures based on Floquet’s theorem and the Ewald transformation. However, although these methods have been demonstrated as powerful tools in the design process, they are not suitable for integration with other systems and sensors due to the limitation of infinite periodic structures or the accurate modeling of complex physical phenomena like edge effects and standing waves, vital phenomena for certain applications.

In this communication, we present the combination of a high scalability implementation of the multibranch-multiresolution preconditioner with the domain decomposition method for the electromagnetic analysis of geometrically complex structures with different levels of multiscale features and discretized with a possible nonconformal mesh. Finally, a numerical experiment is shown to illustrate the great efficiency of the proposed approach for the solution of large multiscale objects.

For effective solution of direct or inverse electromagnetic problems in complex structures using Surface Integral Equation (SIE) methodologies via the Method of Moments (MoM), it is crucial to perform a cost-efficient numerical evaluation of double surface reaction integrals. The success and accuracy of SIE methods are significantly dependent on the proficient and exact computation of these double surface (reaction) integrals.

In this communication, the performance of the generalized minimum residual method (GMRES) preconditioned by a domain decomposition method (DDM) scheme embedded in a surface integral equation (SIE) formulation is studied. In realistic large multiscale problems the individual subdomain solutions, which in a DDM scheme acts as the preconditioners, have to be obtained by Krylov subspace iterative processes with a decisive influence on the outcome of the overall iterative process that deals with subdomains mutual couplings. The convergence and accuracy of the global solution, as well as the degree of correlation between them, are studied for left, right and flexible-right preconditioned GMRES to draw conclusions which maximize the efficiency in the application of the SIE-DDM implementation to challenging problems.

Discontinuous Galerkin (DG) approaches [1] used to connect two non-conformal surfaces in the Method of Moments typical employ Interior Penalty (IP) methods to mitigate charge accumulation along the half RWG basis functions connection boundary. These IP approaches are introduced via a combined impedance matrix $(Z-\beta$. $I P$). Alternatively in soft non-conforming problems, Multi-branch (MB-RWG) basis functions can be utilized [2]. Generalizations of multibranch basis functions can lead to higher degress of nonconformality as the use of $N^{+}-N^{-}$ branches MB_RWG [3] when $N^{+}$ and $N^{-}$ triangles have common vertices at the endpoints of the shared countour, but not along the contour.

The production of colloidal metal nanostructures with complex geometries usually involves shape-directing additives, such as metal ions or thiols, which stabilize high-index facets. These additives may however affect the nanoparticles' surface chemistry, hindering applications, e.g., in biology or catalysis. We report herein the preparation of gold bipyramids with no need for additives and shape yields up to 99%, using pentatwinned Au nanorods as seeds and cetyltrimethylammonium chloride as surfactant. For high-growth solution:seed ratios, the bipyramids exhibit an unusual "belted" structure. Three-dimensional electron microscopy revealed the presence of high-index {117}, {115}, and {113} side facets, with {113} and {112} facets at the belt. Belted bipyramids exhibit strong near-field enhancement and high extinction in the near-infrared, in agreement with electromagnetic simulations. These Ag-free bipyramids were used to seed chiral overgrowth using 1,1 '-binaphthyl-2,2 '-diamine as a chiral inducer, with g-factor up to 0.02, likely the highest reported for bipyramid seeds so far.

Computational electromagnetics (CEM) has become an indispensable tool for engineers in a wide range of applications in the aerospace and naval industries. The complexity of these industries, with challenges such as advanced antenna design, Electromagnetic Environmental Effects (E3), and radar cross section (RCS) control, demands the use of powerful simulation tools. However, new times bring new advances to the industry and, with them, new challenges to the computational electromagnetic field. Seeking cutting-edge advances in very low observability (VLO) techniques and E3 in modern platforms further underscores the need for these tools, capable of dealing with multiple scales and all kinds of novel modern materials (metamaterials).

One of the elements that affects the overall accuracy of the solution of Surface Integral Equations (SIEs) via the Method of Moments (MoM) is the accuracy in the numerical evaluation of the double surface reaction integrals that constitute the system matrix, especially for its near-field part (present in any applied fast solution method). Each reaction integral is formed by a source (inner) integral, that can be singular, and a test (outer) integral. The source integral singularity is due to its kernel that is the background Green’s function for the Electric Field Integral Equation (EFIE) or the gradient of the background Green’s function for the Magnetic Field Integral Equation (MFIE).

The development of new surface integral equations (SIEs) methods able to efficiently solve non-conformal discretization has become a source of extensive studies in recent years in search for an accurate method able to simplify the CAD generation processes, especially when dealing with realistic projects involving piecewise objects.

The development of a multitrace method including an automatic and multilevel quasi-Helmholtz decomposition, until now only applied to perfect electrical conductors, is here presented for the simulation, via the method of moments, of arbitrary complex geometries composed of piecewise homogeneous composite objects in order to improve the conditioning. A numerical experiment demonstrates the flexibility of the proposed approach for the solution of objects composed of multiple materials.

Non-conformal surface integral equation (SIE) methods have received considerable attention from the research community in recent years, in search of procedures to simplify the generation of computer-aided-design (CAD) and mesh models for electromagnetic solution of complex problems or in the context of collaborative projects.

The electromagnetic behavior of periodic structures has gained great interest in recent years due to their fundamental role in the development of scattering networks, plasmonic crystals and many other fields related to nanophotonics, including nanoscale and metasurface devices. Linked to this interest is an increasing demand for the development of tools capable of modelling the electromagnetic behaviour of periodic structures as efficiently as possible. In the context of surface integral equation (SIE) methods based on the method of moments (MoM), most of the existing literature has focused on the development of techniques based on the Ewald method, which requires modelling the system with an infinite periodic structure or dealing with complex physical issues to correctly model the edge effects or the standing waves, whose accurate prediction can be critical in some applications.

This paper presents a discontinuous Galerkin (DG) integral equation (IE) method for the electromagnetic analysis of arbitrarily-shaped plasmonic assemblies. The use of nonconformal meshes provides improved flexibility for CAD prototyping and tessellation of the input geometry. The formulation can readily address nonconformal multi-material junctions (where three or more material regions meet), allowing to set very different mesh sizes depending on the material properties of the different subsystems. It also enables the use of h-refinement techniques to improve accuracy without burdening the computational cost. The continuity of the equivalent electric and magnetic surface currents across the junction contours is enforced by a combination of boundary conditions and local, weakly imposed, interior penalties within the junction regions. A comprehensive study is made to compare the performance of different IE-DG alternatives applied to plasmonics. The numerical experiments conducted validate the accuracy and versatility of this formulation for the resolution of complex nanoparticle assemblies.

The numerical evaluation of the double surface integrals that arise in the method of moments has captured considerable attention in recent years. Although most of the literature has focused on the evaluation of the source integral, the development of efficient and accurate procedures for the evaluation of the test integral is also needed. In this work, an integration scheme using a hybrid source singularity subtraction-cancellation scheme is proposed to improve the accuracy and efficiency of test integral evaluation arising in the magnetic field integral equation.