Two-step Method Research Articles

Biological sex affects functional variation across the human genome.

Humans display sexual dimorphism across many traits, but little is known about underlying genetic mechanisms and impacts on disease. We utilized single-cell RNA-seq of 480 lymphoblastoid cell lines to reveal that the vast majority (79%) of sex-biased genes are targets of transcription factors that display sex-biased expression. Further, we developed a two-step regression method that identified sex-biased expression quantitative trait loci (sb-eQTL) across the genome. In contrast to previous work, these sb-eQTL are abundant (n=10,754; FDR 5%) and reproducible (replication up to π1=0.56). These sb-eQTL are enriched in over 600 GWAS phenotypes, including 120 sb-eQTL associated with the female-biased autoimmune disease multiple sclerosis. Our results demonstrate widespread genetic impacts on sexual dimorphism and identify possible mechanisms and clinical targets for sex differences in diverse diseases.

Superhydrophilic and Underwater Superaerophobic Dual-Function Peony-Shaped Selenide Micro-nano Array Self-Supported Electrodes for High-Efficiency Overall Water Splitting Driven by Renewable Energy.

With the intensification of global environmental pollution and resource scarcity, hydrogen has garnered significant attention as an ideal alternative to fossil fuels due to its high energy density and nonpolluting nature. Consequently, the urgent development of electrocatalytic water-splitting electrodes for hydrogen production is imperative. In this study, a superwetting selenide catalytic electrode with a peony-flower-shaped micronano array (MoS2/Co0.8Fe0.2Se2/NixSey/nickel foam (NF)) was synthesized on NF via a two-step hydrothermal method. The optimal catalytic activity of cobalt-iron selenide was achieved by adjusting the Co/Fe ratio. The intrinsic catalytic activity of the electrodes was enhanced by incorporating transition metal selenides, which then served as a precursor for the subsequent loading of MoS2 nanoflowers on the surface to fully expose the active sites. Furthermore, the superwetting properties of the electrode accelerated electrolyte penetration and electron/mass transfer, while also facilitating bubble detachment from the electrode surface, thereby preventing "bubble shielding effect". This resulted in superior oxygen evolution reaction (OER) and hydrogen evolution reaction (HER) performance, as well as overall water splitting capabilities. In a 1.0 M KOH solution, the electrode required only 166 and 195 mV overpotential to achieve a current density of 10 mA cm-2 for OER and HER, respectively. When functioning as a bifunctional catalytic electrode, only 1.60 V of voltage was necessary to drive the electrolyzer to reach a current density of 10 mA cm-2. Moreover, laboratory simulations of wind and solar energy-driven water splitting validated the feasibility of establishing a sustainable energy-to-hydrogen production chain. This work provides new insights into the preparation of low-overpotential, high-catalytic-activity superhydrophilic and underwater superaerophobic catalytic electrodes by rationally adjusting elemental ratios and exploring changes in electrode surface wettability.

Entrepreneurs’ Spirit and Corporate Green Development: The Mediating Role of New-Quality Productivity

Abstract: As a fundamental unit of sustainable economic development, corporate green development is significantly influenced by entrepreneurs’ spirit and new-quality productivity. Therefore, it is crucial to explore the intrinsic connections among entrepreneurs’ spirit, new-quality productivity, and corporate green development. This study leverages data from 17,079 A-share manufacturing companies from 2012 to 2022. It employs a dual-dimensional fixed-effects model to investigate the mechanisms, pathways, and effects of entrepreneurs’ spirit on corporate green development, with new-quality productivity serving as a mediating variable. The findings reveal that (1) stability tests using the IV method and Heckman’s two-step method indicate that entrepreneurs’ spirit significantly promotes corporate green development; (2) mediation-effect tests show that new-quality productivity partially mediates the relationship between entrepreneurs’ spirit and corporate green development; and (3) heterogeneity-effect tests demonstrate that the promoting effect of entrepreneurs’ spirit on corporate green development is more pronounced in large enterprises compared to small- and medium-sized enterprises, in eastern enterprises compared to those in central and western regions, and in less competitive enterprises compared to more competitive ones. These conclusions not only enrich the research on corporate green development but also aid in the formulation of corporate-green-development strategies, thereby contributing to sustainable economic development.

A novel technique including two steps for modulus prediction in polymer halloysite nanotube composites

A two-step methodology has been developed utilizing the models of Paul and Takayanagi to determine the modulus of polymer halloysite nanotube (HNT) products. Initially, HNTs and the adjacent interphase are considered as pseudoparticles, and their modulus is evaluated using the Paul model. Subsequently, the modulus of a nanocomposite, consisting of a polymer medium and pseudoparticles, is predicted by Takayanagi equation. The impacts of various factors on the modulus of the products are analyzed, and the results from the two-step method are compared with experimental data from different samples. It has been observed that the modulus of samples progressively increases with an increase in interphase depth. Also, a higher interphase modulus contributes to an enhanced modulus of samples. Nevertheless, excessively high interphase moduli (Ei > 60 GPa) result in only a marginal improvement in the modulus of nanocomposites. Additionally, narrower HNTs are advantageous for producing stronger samples, though the modulus of the nanocomposites slightly diminishes at very high HNT radii (R > 55 nm). The outputs of two-step method agree with the experimental moduli of various HNT-filled systems.

Effect of particle size on SiO2 nanofluid viscosity determined by a two-step method

AbstractAccording to review of the literature, the influence of nanoparticle diameter with irregular shapes on viscosity requires further research since there is no relation between particle size and nanofluid stability. In this study, SiO2/EG–water-based nanofluid samples were prepared, and their viscosities were experimentally determined. SiO2 nanoparticles had sizes of 7, 15, and 40 nm, and the base fluid was a 50% ethylene glycol and 50% water mixture. Nanofluid samples were prepared using a two-step technique. Viscosity change was measured every 10 °C from 20 to 60 °C. The maximum viscosity values were observed for 7, 15, and 40 nm particles over an entire concentration range. Considering all measurements, the highest viscosity increase was 60.51% for 3% SiO2 (7 nm) at 60 °C, and the lowest viscosity change was 7.72% for 1% SiO2 (40 nm) at 40 °C. The most stable sample of the current study was 1% SiO2 (15 nm), and its Zeta potential was − 35.6 mV. Finally, a new empirical equation that included temperature, particle diameter, and concentration terms is suggested to predict dynamic viscosity, with R adj 2 = 0.98. It was also compared with previous correlations.

Phase reconstruction by phase shift estimation with reliable parameter minimization

Abstract Achieving a balance between accuracy and speed in phase reconstruction is a challenging problem. In phase-shifting interferometry, increasing the speed by reducing the number of phase shifts while maintaining high accuracy is highly desirable. We propose an accurate and efficient two-step phase reconstruction method utilizing random phase shift. This method directly estimates the phase shift through reliable parameter minimization, allowing for easy and precise phase reconstruction. Simulations and experiments demonstrate the superior performance of our method across various scenarios, outperforming well-known two-step phase-shifting algorithms. We expect this paper to provide a general and powerful tool for phase reconstruction.

Automated segmentation and classification of supraspinatus fatty infiltration in shoulder magnetic resonance image using a convolutional neural network.

Goutallier's fatty infiltration of the supraspinatus muscle is a critical condition in degenerative shoulder disorders. Deep learning research primarily uses manual segmentation and labeling to detect this condition. Employing unsupervised training with a hybrid framework of segmentation and classification could offer an efficient solution. To develop and assess a two-step deep learning model for detecting the region of interest and categorizing the magnetic resonance image (MRI) supraspinatus muscle fatty infiltration according to Goutallier's scale. A retrospective study was performed from January 1, 2019 to September 20, 2020, using 900 MRI T2-weighted images with supraspinatus muscle fatty infiltration diagnoses. A model with two sequential neural networks was implemented and trained. The first sub-model automatically detects the region of interest using a U-Net model. The second sub-model performs a binary classification using the VGG-19 architecture. The model's performance was computed as the average of five-fold cross-validation processes. Loss, accuracy, Dice coefficient (CI. 95%), AU-ROC, sensitivity, and specificity (CI. 95%) were reported. Six hundred and six shoulders MRIs were analyzed. The Goutallier distribution was presented as follows: 0 (66.50%); 1 (18.81%); 2 (8.42%); 3 (3.96%); 4 (2.31%). Segmentation results demonstrate high levels of accuracy (0.9977 ± 0.0002) and Dice score (0.9441 ± 0.0031), while the classification model also results in high levels of accuracy (0.9731 ± 0.0230); sensitivity (0.9000 ± 0.0980); specificity (0.9788 ± 0.0257); and AUROC (0.9903 ± 0.0092). The two-step training method proposed using a deep learning model demonstrated strong performance in segmentation and classification tasks.

Role of FGF21 in mediating the effect of phosphatidylcholine on GBM.

The causal relationship and mechanisms between lipids and glioblastoma (GBM) remain unclear. This study aims to investigate the independent causal relationship between liposomal phosphatidylcholine 16:0_22:6 (PC16) and GBM, and to identify the potential mediating role of the inflammatory factor-fibroblast growth factor 21(FGF21). Utilizing summary statistics from genome-wide association studies (GWAS) of lipids (179 types in 7174 Finnish individuals), GBM (243 cases and 287137 controls), and inflammatory factors (91 types in 14824 European individuals), a two-sample Mendelian Randomization (MR) approach was employed to establish the causal link between liposomal PC16 and GBM. Additionally, a two-step MR method was used to quantify the proportion of the causal effect of PC16 on GBM that is mediated by the inflammatory factor FGF21. MR analyses revealed a strong causal relationship between PC16 and GBM (OR=1.72, 95% CI: 1.11-2.68, P=0.016), but no reverse causality was observed from GBM to PC16 (OR=1.01, 95% CI: 0.99-1.02, P=0.38). Mediation analysis showed a strong causal relationship between PC16 and the FGF21 (OR = 0.94, 95% CI: 0.89-0.99, P=0.018) as well as between FGF21 and GBM (OR = 0.42, 95% CI: 0.25-0.71, P=0.001), with the mediation effect accounting for 9.78% of the total effect. This suggests that the causal relationship between PC16 and GBM is likely mediated by the intermediary factor FGF21. No evidence of pleiotropy was found in the sensitivity analysis of these positive results. In summary, the findings of this study suggest that liposomal PC16 may increase the risk of GBM occurrence, and FGF21 may play a significant mediating role in this causal relationship.

Increasing softening point of isotropic spinnable asphalt by two-step preparation from ethylene tar residue modified with bio tar residue

Carbon fiber prepared from asphalt may be a critical type of low-weight chemical material of excellent mechanical performances. Here, an isotropic spinnable asphalt (EBA) was prepared from ethylene tar residue (ETR) by a two-step method of bio tar residue (BTR) through co-polymerization-air blowing, and isotropic asphalt carbon fibers were prepared from the product asphalt. The main types of molecules contained in the two feedstocks were determined by 1H NMR and LDI-TOF MS analyses. The co-polymerization behavior and thermal stability of the asphalt blends were analyzed using polarized light microscopy and thermogravimetric analyzer, respectively. Finally, the morphology and mechanical properties of carbon fibers made from EBA were evaluated by scanning electron microscope and universal testing machine. The results show that BTR contains much more oxygen-containing functional groups and unique long-chain sawtooth molecular structure; the former can promote the reactivity of the co-polymerization reaction, and the latter can limit the formation of large-plane cyclic aromatic hydrocarbon polymers due to the spatial resistance effect to greatly reduce the content of the mesophase. The softening point of the product asphalt shows a tendency of increasing and then decreasing with the increase of the proportion of BTR in the raw material mixture, and a reaction mechanism based on linear and bulky molecules is proposed to explain it by analogy with the structure of macromolecules. Consequently, the EBA made from a mixture of ETR and BTR at ideal moderate proportions has excellent performance in terms of softening point and mesophase content than ETRO made from ETR alone, and the carbon fiber made has a high tensile strength of 1.82 GPa with an elastic modulus of 38.9 GPa, which has reached the level of high tensile strength carbon fiber. Therefore, the use of inexpensive renewable energy bio-asphalt in the modification of heavy oil to obtain high softening point isotropic asphalt for preparing isotropic carbon fiber with excellent properties is achievable.

Most general isotropic charged fluid solution for Buchdahl model in ℱ(𝒬) gravity

In this work, we investigated a most general isotropic charged fluid solution for the Buchdahl model via a two-step method in ℱ(𝒬)-gravity framework for the first time. In this context, a linear function of the form ℱ(𝒬) = ζ 1 𝒬 + ζ 2 and a particular transformation is used to solve the Einstein-Maxwell Equations (EMEs) employing the Buchdahl ansatz: e Υ(r) = μ(1+λ r 2)/μ+λ r 2, where ζ 1, ζ 2, λ and μ are constant parameters. The Schwarzschild de Sitter (AdS) exterior solution is joined to the interior solution at the boundary to determine the constant parameters. It should be emphasized that, for a given transformation, the Buchdahl ansatz only offers a mathematically feasible solution in the context of electric charge, where pressure and density are maximum at the center and decrease monotonically towards the boundary when 0 < μ < 1. We taken into account the compact star EX01785-248 with M = (1.3±0.2)M ⊙; Radius = 12.02+0.55 -0.55 km for graphical analysis.The physical acceptability of the model in the context of ℱ(𝒬) gravity has been evaluated by looking at the necessary physical properties, including energy conditions, causality condition, hydrostatic equilibrium, pressure-density ratio, etc. Additionally, we predicted the maximum mass limit of different compact objects for various parameter values along with the mass-radius relation. The maximum masses range (1.927 - 2.321) M ⊙ are obtained for our solution. It can be observed that when the coupling parameter ζ 1 for ℱ(𝒬 gravity is smaller, then our solution yields massive stars. The present investigation provides novel insights and realistic implications regarding the formation of compact astrophysical objects.

Two-step optimization for accelerating deep image prior-based PET image reconstruction.

Deep learning, particularly convolutional neural networks (CNNs), has advanced positron emission tomography (PET) image reconstruction. However, it requires extensive, high-quality training datasets. Unsupervised learning methods, such as deep image prior (DIP), have shown promise for PET image reconstruction. Although DIP-based PET image reconstruction methods demonstrate superior performance, they involve highly time-consuming calculations. This study proposed a two-step optimization method to accelerate end-to-end DIP-based PET image reconstruction and improve PET image quality. The proposed two-step method comprised a pre-training step using conditional DIP denoising, followed by an end-to-end reconstruction step with fine-tuning. Evaluations using Monte Carlo simulation data demonstrated that the proposed two-step method significantly reduced the computation time and improved the image quality, thereby rendering it a practical and efficient approach for end-to-end DIP-based PET image reconstruction.

Dual-doped medium-entropy phosphides for complete urea electrolysis

Developing dual-functional electrocatalysts for urea-water decomposition still faces significant challenges. In this study, the vanadium (V) and cerium (Ce) co-doped FeCoNi medium-entropy phosphide (VCe-FeCoNiP/NF) were effectively fabricated on nickel foam (NF) via “two-step method,” which involved hydrothermal treatment followed by phosphorization. Experimental results indicate that, benefiting from dual-ion doping and medium-entropy configuration, VCe-FeCoNiP/NF demonstrates unique electronic effects among the multimetallic elements, thereby exhibited remarkable catalytic activity for both urea oxidation reaction (UOR) and hydrogen evolution reaction (HER). Under urea-water conditions (1 M KOH with 0.33 M urea), the VCe-FeCoNi/NF catalyst merely required 1.338 V (vs RHE) and an overpotential of 173 mV to attain a current density of 100 mA·cm−2 for UOR and HER, respectively. Moreover, it could stably operate at a current density of 20 mA·cm−2 for 225 h in overall urea-water decomposition. This work provides new insights for designing high-performance urea-water electrolysis catalysts.

Synergistic heterostructural interface of CoP and WC for high-performance wide pH-universal hydrogen evolution electrocatalysis

The development of cost-effective catalysts with high activity and stability over a wide pH range is urgent, but there are great challenges in the selection and design of catalyst materials. In this work, cobalt phosphide nanoparticles were modified onto tungsten carbide nanowire arrays (CoP@WC/CC) on carbon cloth substrate by a two-step method. The construction of CoP@WC heterostructure results in the downward shift of the d-band center, which optimizes the adsorption energy of catalyst and reaction intermediates. Meanwhile, the synergistic effect of CoP and WC contributes to the alkaline HER kinetic process. In addition, binder-free self-supporting nanoarray have excellent electrical conductivity, large specific surface area and strong structure, which is conducive to charge/matter exchange and catalyst stability. The results show that CoP@WC/CC can effectively drive HER over a wide pH range and exhibit better catalytic performance than the single component control sample. In 0.5 M H2SO4 and 1 M KOH, CoP@WC/CC can drive the current density of 10 mA cm−2 with only 52 and 70 mV, while showing excellent stability without obvious performance degradation during 100 h of constant current test. A proton exchange membrane water electrolysis (PEMWE) using CoP@WC/CC catalyst operates stably for 200,000 s at 30 mA cm−2. This study provides a new reference for the design and development of high efficiency, low cost and wide pH-universal hydrogen evolution electrocatalysts.

Development of Air–Ti Gas-Surface Reaction Mechanisms and Rate Calculations

Gas-surface reaction mechanisms and rates were developed for an air–titanium surface to support finite-rate catalytic surface reaction models used in computational fluid dynamics. For the surface dissociation/recombination reactions, a two-step reaction method was applied based on the assumption that two atoms must be positioned in adjacent cells to recombine. Transition state theory was used to calculate the surface reactions for adsorbed diatomic molecules to dissociate to the adjacent unit cell or atoms located in the adjacent cells to recombine into diatomic molecules. For the second step, atoms located in the adjacent cells are allowed to further dissociate to another cell (total separation), or totally separated atoms recombine into the adjacent cells. A stochastic gas-surface kinetics simulation code, STOKIN, was developed to simulate gas-surface reactions and to calculate the equilibrium constants of second molecular dissociation ⇌ recombination processes. Thermodynamic properties of the adsorbates (enthalpies, entropies, and heat capacities) were calculated using density functional theory along with statistical mechanics assuming no rotational and translational contributions to the entropies and heat capacities due to the adsorbates’ inability to freely move or rotate on the surface.

Bioinspired transparent ultratough birefringent photonic films with engineerable interference colors derived from in-situ synthesis of CaCO3

Chameleons can rapidly modify their coloration by manipulating the arrangement of iridophores encompassing guanine crystals in their dermis, which enables incident light to undergo birefringence. Various biomaterials have been designed to mimic the arrangement of guanine crystals, yet instances of synthesizing bottom-up structures with anisotropy for optical functionality remain rare. In this study, we report a novel two-step gas diffusion method for in-situ synthesis of CaCO3 (Vaterite) within a hydrogel to fabricate a bio-photonic film displaying birefringence interference colors. This strategy enables the successful fabrication of an inorganic–organic photonic film with superior mechanical properties and flexibility, resulting in high transparency, superior toughness, and adjustable optical anisotropy. Through a combination of experiment and simulation results, we elucidated the critical role played by shape factor (distribution) and structural factor (particle size) in producing transmitted interference colors. Finally, the birefringent photonic films prepared using the dot-plate method can function as optical patterns accurately representing the “on”/“off” state within a binary system. This system offers high spatial resolution, excellent repeatability, and precise controllability of optical properties, making it applicable in fields such as information encryption and decrytion. Our study has successfully synthesized photonic material with anisotropic structure though in-situ method while elucidating the underlying mechanism governing their ability to generate transmission interference colors, thus opening up new avenues for transparent flexible polarized optics, imperceptible wearable devices, and advanced information encryption.

A robust photoelectrothermal evaporator with hierarchical NiCo2S4 nanowires grown on nickel foam for a high rate of clean water production

Interfacial solar steam generation (ISSG) stands as a promising technology in addressing global water scarcity, stemming from reasons like global warming and population growth. Despite its potential, ISSG faces challenges due to varying weather conditions and solar intensity fluctuations. To overcome these limitations, a novel approach by integrating photothermal and electrothermal Joule-heating effects is introduced in this study for a high-efficiency and salt-resistant all-weather, all-day seawater desalination. Hierarchical NiCo2S4 nanowires are fabricated on a Ni-foam (NCNNF) using a facile two-step hydrothermal method. Under photothermal evaporation, the NCNNF evaporator produces an evaporation rate of 1.57 ± 0.08 kg m−2 h−1 with an evaporation efficiency of 77 % under 1sun illumination with good anti-fouling ability. In a simple water desalination setup, the surface temperature of the evaporator in a wet state reaches ∼63.5 ± 0.25 °C within 10 min by applying an input voltage of 1 V and 1sun irradiation condition, yielding an outstanding evaporation rate of 21.3 ± 3.6 kg m−2 h−1 and evaporation efficiency of 80 %. The proposed evaporation device can resist salt accumulation on the evaporator surface in long-term operations. The present results would be utilized in developing high-performance Joule-heating assisted solar water evaporation devices, especially for all-day, all-weather desalination to produce clean potable water.

Microwave-assisted hydrothermal synthesis of Ag/Bi2MoO6/ZnO heterojunction with nano Ag as electronic accelerator pump for high-efficienty photocatalytic degradation of levofloxacin

The fluoroquinolone antibiotics, as a category of emerging refractory organic pollutants, have triggered intensive attention due to their persistent ecotoxicology for aquatic environments. Herein, a novel Ag/Bi2MoO6/ZnO (Ag/BMO/ZnO) heterojunction was prepared using a two-step microwave-assisted hydrothermal method for photocatalytic degradation of levofloxacin (LFX). The optimal Ag/BMO/ZnO delivers higher photocatalytic degradation efficiency toward LFX reaching 86.4 %, which is 3 times and 7 times higher than those of neat Bi2MoO6 and ZnO, respectively. This can mainly be attributed that the existence of heterojunction between Bi2MoO6 and ZnO promotes the transmission of photogenerated charges (e−/h+). Furthermore, the introduction of Ag nanoparticles serves as an electron accelerator pump, which can also effectively accelerate the transport and separation of the photogenerated e−/h+. Both of these indirectly retard the recombination of e−/h+. The radical capture assays demonstrate that 1O2, OH, h+ and O2– are responsible for the the degradation of LFX and the 1O2 is the primary reactive oxygen species (ROS). Moreover, based on the identification of degradation intermediates via the liquid-chromatography-mass spectrometry (LC-MS) technique, the possible degradation routes of LFX were plausibly inferred. In conclusion, this work provides a new perspective toward antibiotics removal by developing novel heterojunction photocatalysts anchored with precious nanoparticles.

A "signal-off" anodic photoelectrochemical sensor based on ZnIn2S4/TiO2 heterojunction for dopamine detection

Dopamine (DA) is an important neurotransmitter. Abnormal levels of it in human body can increase the risk of many neurological diseases. Thus, developing a simple, sensitive detection method of DA is crucial. In this paper, we reported a "signal-off" anodic PEC sensor based on fluorine-doped tin oxide (FTO) glass modified ZnIn2S4/TiO2 heterojunction (ZnIn2S4/TiO2/FTO) for DA detection. The experimental results show that the ZnIn2S4/TiO2/FTO electrode prepared by two-step hydrothermal method has a good photocurrent response performance under visible light. After incubation with DA, the photocurrent response decreases significantly because DA can rapidly oxidizes to polydopamine (PDA) through the action of superoxide radical (·O2−) and hydroxyl radical (·OH) intermediate species, which are intermediates produced by the ZnIn2S4/TiO2/FTO electrode under visible light irradiation. The constructed PEC sensor has a good linear relationship in the concentration range from 0.5 to 1000.0 μM, and its detection limit is 0.253 μM. In addition, the results of the proposed PEC sensor in real serum samples are satisfactory. The PEC sensor provides a promising platform for DA detection, laying the foundation for future advances in disease diagnosis and prevention.

Dynamic deformation measurement with 2-frame phase-shifting speckle interferometry based on speckle statistics and wavefront multiplexing.

Phase-shifting speckle interferometry could achieve full-field deformation measurement of rough surfaces. To meet the dynamic requirement and further improve the accuracy, a two-step synchronous phase-shifting measurement system is established based on the polarization-sensitive phase modulation ability of a liquid crystal spatial light modulator; by multiplexing the reference wavefront, an accurate phase shift is generated between two independent recording channels, and a common-path self-reference vortex interference structure is built for precise spatial registration. Meanwhile, according to the speckle statistical principle, a novel two-frame phase-shifting algorithm as well as a two-step spatial registration strategy is presented to strengthen the robustness of intensity and position differences caused by spatial-multiplexing; thereby, accurate transient deformation can be directly obtained from phase-shifting speckle interferograms recorded before and after deformation. The effectiveness and accuracy of the proposal are validated from the out-of-plane deformation measurement experiment by comparing with the traditional two-step and four-step phase-shifting methods. The dynamic ability is exhibited through reconstructing mechanical and thermal deformations across various application scenarios.

Two-step scattering theory method for designing metamaterials

Abstract A two-step method for designing an acoustic metamaterial with desired properties is proposed. At the first step, the scattering matrices of its elements are calculated using the Lippmann-Schwinger type equation. For scatterers of small wave size, the problem is reduced to determining the phases of several scattering coefficients. At the second step, the particular design of metamaterial elements is determined. This problem can be considered an inverse scattering problem or a problem of optimizing the geometric parameters of a metamaterial element. The second approach turns out to be more practically applicable. As an example, a metamaterial in the form of a reflective layer with a narrow waveguide channel is considered, and the design of its elements is determined with the proposed method.