Multilayer Structure Research Articles

Influence of the laser power and powder feed rate on the porosity, dilution, and building efficiency of pure copper parts fabricated via directed energy deposition with a blue laser

AbstractWe examined single- and multilayer formations in the directed energy deposition for manufacturing pure copper parts using a blue laser with a wavelength of 445 nm. We investigated the influence of laser power and hatching pitch on the surface quality of single-layer structures as well as evaluated the porosity and dilution of multilayer structures fabricated at various laser powers and powder feed rates using energy-dispersive X-ray spectrometry. In addition, the applicability of the simplified method based on the ratio of the built height and penetration depth to the AM process has been examined, and the predicted elemental content was compared with the results obtained from the SEM–EDS analysis. Based on these findings, a range of building conditions that reduce the dilution, suppress the porosity, and improve the building efficiency of the built parts was established. We found that a good surface quality of the single-layer structure was obtained at laser powers and hatching pitches ranging between 150 and 180 W and 0.4 and 0.5 mm, respectively. A higher laser power and a lower powder feed rate decreased the porosity and increased the building efficiency while promoting dilution with the substrate. At a laser power of 180 W and a powder feed rate of 10 mg/s, the built structure exhibited a minimum porosity of 0.1% and a maximum building efficiency of 36%. Dilution with the substrate was the lowest at a laser power of 180 W and a powder feed rate of 20 mg/s, and the proportion of Cu reached 99.0 wt% at a distance of 200 µm from the built structure–substrate interface. The predict method of the dilution based on the ratio between the built height and penetration depth can be integrated in the AM process despite a low prediction accuracy near the substrate due to the complex mixture in the Fe–Cu system.

Efficient and Stable Quantum‐Dot Light‐Emitting Diodes with Trilayer PIN Architecture

AbstractAlthough the performance of quantum dot light‐emitting diodes (QLEDs) has been greatly improved in recent years, the multilayer device structure has become increasingly complex, limiting the practical application of QLEDs. Here, a novel trilayer PIN QLED with only three functional layers, which are Spiro‐OMeTAD:TFB bulk‐heterojunction (BHJ) hole transport layer (HTL), quantum‐dot emitting layer and ZnMgO electron transport layer is demonstrated. Due to the enhanced hole injection capability and suppressed electron leakage of Spiro‐OMeTAD:TFB BHJ HTL, the trilayer PIN QLED can show an excellent external quantum efficiency (EQE) of 25.1% and an impressive brightness of 299300 cd m−2 at only 8 V, which are significantly higher than those of conventional QLED. Moreover, the device stability is also remarkably improved due to the mitigation of hole accumulation and removal of unstable PEDOT:PSS. By using liquid alloy EGaIn as cathode, a fully solution‐processed vacuum‐free trilayer PIN QLED with a higher EQE of 27.3% can be further realized. The developed trilayer PIN QLEDs, with better performance and fewer functional layers, can promote the commercialization of QLED technology.

Electromagnetic Absorption Mechanism of TPMS‐Based Metastructures: Synergy Between Materials and Structures

Abstract3D metastructure absorbers have gained attention for their lightweight, load‐bearing capabilities, and superior electromagnetic wave absorption. However, the complex interplay between unit cell geometry, material properties, and electromagnetic response is not well understood, hindering the design of high‐performance devices. A multi‐scale model, validated is presented by simulations and experiments, that clarify the relationship between materials, structures, and electromagnetic behavior in 3D metastructures. By systematically investigating strut‐based and sheet‐based structures, volume fraction, unit size, crystal lattice orientation, and density gradient within TPMS‐based unit cells, it is revealed that unit geometry significantly influences electromagnetic field propagation and reflection loss. Specifically, under the same unit size, sheet‐based TPMS metastructures exhibit stronger reflectivity than strut‐based ones, while multilayer structures show the opposite trend. The direct correlation is also further confirmed between geometric symmetry and polarization insensitivity, with orthogonal isotropic superstructures displaying excellent polarization‐insensitive properties. This finding provides a new design principle for achieving robust, angle‐independent absorption in these materials. This work enhances understanding of the structure‐electromagnetic behavior interplay, guiding the design of next‐generation broadband, wide‐angle, and polarization‐insensitive devices.

Design and demonstration of a simple, low-cost transparent solar absorber for glass window applications

Windows are a major source of heat loss from buildings in cold climates. Developing coatings for windows that retain high visible transparency and strongly absorbs solar energy in the near infrared region can help reduce energy consumption and cost for indoor heating. Nanophotonic structures based on metasurface and metamaterials have shown great potential for such applications. Unfortunately, most of the designs proposed so far are difficult to fabricate or expensive. In this work, we report the experimental demonstration of a low-cost alternative based on Ni/SiO2/Ni multilayer structure. The device provides a large increase in temperature under solar illumination while retaining high visible transmission. Our optical and thermal measurements reveal that the performance of the device remains stable over a long period. The combination of low cost, ease of fabrication, good optical and thermal performance, and long-term stability makes it a promising design for passive heating of windows in cold climates.

Quantum-inspired genetic algorithm for designing planar multilayer photonic structure

Quantum-inspired genetic algorithm for designing planar multilayer photonic structure

AI Predictive Analytics for Verifying Pharmaceutical Authenticity and Combating Drug Counterfeiting

A significant worry in recent years has been the counterfeiting of medicines. The distribution and manufacture of fake or falsified drugs are both criminal and harmful to the public's health. The severity of this issue differs significantly from one country to another, primarily due to variations in the adherence to national regulations and processes. Thus, preventing the sale of fake drugs has become an urgent matter, particularly in poor and developing nations. The study presents a new multi-layered validation structure for pharmaceutical authenticity verification that uses Generative Adversarial Networks (GANs), Convolutional Neural Networks (CNNs) and blockchain technology for artificial intelligence predictive analytics. The goal is to tackle the widespread problem of counterfeit drugs. Using GANs to sift through past data, the suggested strategy improves the detection of minor package variations by identifying trends and traits linked to counterfeit drugs. Using the GAN-generated enhanced dataset, a CNN is trained to accurately and specifically categorize drug packaging.Further, the framework uses blockchain technology to provide trustworthy and transparent recordkeeping of drugs in realtime as they move through the supply chain. Increased patient safety directly results from our system's thorough audit trail, which solves the problems of fake medications and regulatory compliance. The suggested approach reduces counterfeit dangers and provides a scalable paradigm for other industries to use when dealing with similar authenticity verification issues, which means it can find more uses in safety-critical fields. The success of the multi-layered validation structure model is evaluated using performance metrics such as accuracy, recall, and F1-score. It achieves a fantastic accuracy rate of over 95%.

THIN FILM METHANE SENSOR BASED ON CARBON COMPOSITE

Today, with the oil and gas industry playing a key role in the global energy sector, issues related to the effective control and detection of methane leaks are becoming an integral part of the strategic tasks of the industry. The article is devoted to the research and development of a thin-film sensor for detecting methane in the air using a carbon composite. The technical result of this study is the creation of a highly sensitive and energy efficient sensor for measuring methane concentration. The basis for the sensitive element is a thin film of a carbon composite, consisting of a polymer, single-wall carbon nanotubes and graphene oxide, with aluminum electrodes. The sensor has a number of advantages, including responding to the presence of methane without the need for heating, the simplicity of the sensitive material preparation process, and low cost. The ability to quickly start small-scale production, simplified manufacturing due to the use of only one pair of electrodes, as well as increased energy efficiency due to the absence of the need for heating are also positive characteristics of this device. The study presents the results of manufacturing the sensor, including the steps of cleaning the surface of the substrate, creating a shadow mask, spraying electrodes, forming a thin film of the composite by centrifugation, as well as analyzing the microstructure of the sensor using an atomic force microscope. Also presented are data on obtaining multilayer structures of thin-film resistive sensors based on a polymer matrix nanocomposite, single-wall carbon nanotubes and graphene oxide, including the process of creating electrodes. This study is important for the development of methane monitoring methods in the oil and gas industry and other industrial areas, offering promising technical solutions to ensure environmental and economic sustainability of production.

Analytical Approach of three-dimensional Flawed Multilayered Structure for EC Inspection

This article is devoted to the development of two current source models for the analysis of 3D electromagnetic phenomena in a conductive part of spherical geometry based on the second-order magnetic vector potential method for eddy current nondestructive testing (ECNDT). The first model, for a homogeneous single-layer sphere, allows the analytical calculation of all electromagnetic quantities in the charge. The second allows to treat in addition to the three-dimensional aspect of the problem, the heterogeneity of the charge (with several layers of different conductivities). An investigations using a multifrequency system have shown better results in detection of small cracks. The observations take about the calculation of normalized impedance based on dissipate energy and Joule losses in conductive material.

Developing computational and experimental models of heat transfer through multi-layered textile structures

Object signature management is a critical and urgent task that helps conceal and restrict the detection of contemporary optoelectronic systems. The design of thermal camouflage textiles and material solutions constitute a significant scientific area, however publications in this area are restricted because of military competitiveness and technological secrecy. Research on thermal camouflage materials has drawn interest both domestically and internationally for a variety of purposes, especially in military applications. Multi-layered Textile Structures (MTS) is a material with several advantages, such as its simple structure, capacity to combine many different materials with many different qualities, and great applicability. The article includes a model of computation and simulation of heat transfer through multi-layer textiles, as well as tests to assess the heat shielding effect and heat radiation energy of some samples of multi-layer textiles made of domestic materials. The initial computational and experimental results constitute an important foundation for further research and application of multi-layered textile structures.

Multi-scale finite element analysis of laser-assisted forming of CF/PEEK composite corner structures

Laser-assisted forming can significantly increase the forming efficiency of thermoplastic composites. However, when forming CF/PEEK curved corner structures using laser-assisted forming, bending spring-back generated by the prepreg tape constrains the shape accuracy of the component. The bending deformation of unidirectional resin matrix composite materials is highly nonlinear. In this study, a multi-scale finite element method is used to obtain the bending properties of CF/PEEK composites for bending spring-back phenomenon of thermoplastic composite samples and predict the spring-back angle of CF/PEEK corner structures fabricated via laser-assisted forming. The average material properties were first calculated using RVE. Following this, a mesoscale model was developed to analyze kink deformation of the composite. Finally, the macroscopic prepreg bending spring-back was calculated. It was determined that the main mechanism of corner forming corresponds to the occurrence of a fiber kinking phenomenon on the interior of the corner. Furthermore, spring-back deformation is caused by residual stresses resulting from insufficient fiber kinking. The accuracy of the simulation results is verified via corner forming experiments. This study contributes to a deeper understanding of the spring-back mechanisms of laser-assisted forming of corner structures and provides a theoretical guidance for precision forming of multilayer thermoplastic composite bent structures.

A Bottom-Up Approach to Assemble Cell-Laden Biomineralized Nanofiber Mats into 3D Multilayer Periosteum Mimics for Bone Regeneration.

The creation of complex multilayer periosteal graft structures is challenging. This study introduced a novel bottom-up approach to assemble cell-laden nanofiber mats into a three-dimensional (3D) multilayer periosteum mimic, successfully replicating the hierarchical complexity of the natural periosteum. These nanofiber mats, which were fabricated by electrospinning, surface modification, and stimulated body fluid (SBF) immersion, are composed of nanoscale polycaprolactone (PCL) fibers coated with a mineralized collagen layer along the fiber orientation. They closely resembled the natural periosteal matrix, thereby promoting osteogenic differentiation of rat bone marrow mesenchymal stem cells (rBMSCs) in vitro. The biomimetic periosteum, constructed via layer-by-layer assembly, offered advantages such as a multilayer nanofibrous structure, controlled cell distribution, a reservoir for osteoprogenitors, and enhanced pro-osteogenic potential. The rat calvarial bone defect model confirmed its potent bone repair capacity. This study presents an efficient approach to construct tissue-engineered periosteum mimics, holding promise for serving as periosteal grafts in orthopedic applications.

AVG delamination: a cause of early cannulation arteriovenous graft dysfunction in hemodialysis patients

Background A series of cases have reported graft delamination as a rare complication of early-cannulation arteriovenous graft (ecAVG). The unique multilayer structure of ecAVGs contributes to the property of cannulation as early as hours after implantation, but on other hand it takes the risk of graft delamination. However, the underlying mechanism and management of graft delamination as well as its effects on the long-term patency of ecAVGs have not been systemically analyzed. Methodsz A retrospective study was conducted in a cohort of patients who required an ecAVG for hemodialysis (HD) access in our center between April 2017 and December 2021. The characteristics of graft delamination and the outcomes of its different treatments were analyzed. Results A total of 144 ecAVGs were established in 141 end-stage renal disease (ESRD) patients, including 124 (86.1%) Acuseal grafts and 20 (13.9%) Flixene grafts. During follow-up 24.5(11.5, 45.8) months, 11 (7.6%) subjects had graft infection with an incidence of 0.03 patient-year. Thirteen (9.0%) subjects had graft delamination at 9.3(5.0,12.4) months after ecAVG implantation, with an incidence of 0.04 per patient-year. ecAVG delamination was observed in both Acuseal grafts (0.037 per patient-year) and Flixene grafts (0.055 per patient-year). Thrombosis or venous hypertension was the most common complaints. Seven delamination was observed at 1.3 (0.1, 4.2) months after an endovascular procedure. The primary patency, primary assistant patency and secondary patency in delamination group were significantly lower than that in non-delamination group (p < 0.05). Post-procedure primary patency of group A (percutaneous transluminal angioplasty, PTA), group B (stenting) and group C (partial graft replacement, PGR) were 1.3 (0.45,4.22) months, 5.3 (3.05,6.85) months and 8.45 (4.78,14.53) months respectively (p = 0.029). Conclusions Graft delamination was not a rare complication of ecAVGs in this cohort. It significantly reduced the long-term patency of AVGs. PGR might be a more effective therapeutic way than endovascular treatments.

Architecture of the Toxoplasma gondii apical polar ring and its role in gliding motility and invasion

In Toxoplasma gondii, the conoid comprises a cone with spiraling tubulin fibers, preconoidal rings, and intraconoidal microtubules. This dynamic organelle undergoes extension and retraction through the apical polar ring (APR) during egress, gliding, and invasion. The forces involved in conoid extrusion are beginning to be understood, and its role in directing F-actin flux to the pellicular space, thereby controlling parasite motility, has been proposed. However, the contribution of the APR and its interactions with the conoid remain unclear. To gain insight into the APR architecture, ultrastructure expansion microscopy was applied to pinpoint known and newly identified APR proteins (APR2 to APR7). Our results revealed that the APR is constructed as a fixed multilayered structure. Notably, conditional depletion of APR2 resulted in significant impairments in motility and invasion. Electron microscopy and cryoelectron tomography revealed that depletion of APR2 alters APR integrity, affecting conoid extrusion and causing cytosolic leakage of F-actin. These findings implicate the APR structure in directing the apico-basal flux of F-actin to regulate parasite motility and invasion.

Thermal stress concentration points and stress mutations in nano-multilayer film structures

In the multilayer film-substrate system, thermal stress concentration and stress mutations cause film buckling, delamination and cracking, leading to device failure. In this paper, we investigated a multilayer film system composed of a substrate and three film layers. The thermal stress distribution inside the structure was calculated by the finite element method, revealing significant thermal stress differences between the layers. This is mainly due to the mismatch of the coefficient of thermal expansion between materials. Different materials respond differently to changes in external temperature, leading to compression between layers. There are obvious thermal stress concentration points at the corners of the base layer and the transition layer, which is due to the sudden change of the shape at the geometric section of the structure, resulting in a sudden increase in local stress. To address this issue, we chamfered the substrate and added an intermediate layer between the substrate and the transition layer to assess whether these modifications could reduce or eliminate the thermal stress concentration points and extend the service life of the multilayer structure. The results indicate that chamfering and adding the intermediate layer effectively reduce stress discontinuities and mitigate thermal stress concentration points, thereby improving interlayer bonding strength.

Optimizing Agility in the Pharmaceutical Supply Chain Using Digital Twins to Cope with the Ripple Effect

The pharmaceutical supply chain is a multilayered and complex structure designed to deliver medicines to customers in a timely manner while ensuring optimal quality and quantity of medicines. The COVID-19 outbreak exposed the vulnerability and uncertainty of the pharmaceutical supply chain, so managing the risks in the pharmaceutical supply chain has become particularly important. This study demonstrates that digital twin (DT) technology can improve pharmaceutical supply chain agility and reduce the ripple effect caused by disruptions. The ripple effect refers to the effect that a sudden disruption at one node in the supply chain has on causing a chain reaction in the rest of the supply chain. The most used risk management method today is the Enterprise Resource Planning (ERP) system, which allows for real-time data sharing but has limitations in predicting and modeling the entire supply chain and lacks the ability to make quick decisions and simulate the entire supply chain. DT technology creates a virtual model of the supply chain, which enables continuous communication and information exchange between real assets and the virtual model, offering a promising alternative to risk management for pharmaceutical supply chains. risk management by providing a promising alternative. This study utilizes the AnyLogistix platform to construct a DT model and demonstrates the effectiveness of DT technology in reducing ripple effects and improving supply chain agility using quantitative analysis. This paper focuses on analyzing the pharmaceutical supply chain for 75mg aspirin tablets in London. A supply chain that operates normally, a supply chain that introduces a disruptive event (closure of the logistics center due to an earthquake), and a supply chain that applies a proactive strategy (activation of an alternate logistics center) to mitigate risk are simulated separately. The positive impact of DT technology on the supply chain is evaluated by analyzing the methods of key performance indicators (KPIs) such as inventory level, order fulfillment rate, and delivery time. The experimental results show that DT technology enhances the responsiveness, flexibility, speed, and proactivity of the supply chain, which significantly improves the agility of the supply chain. Proactive and effective strategies also reduce the financial impact of disruptions and service levels are quickly recovered. In addition, the proactive strategy stabilized inventory levels and reduced delayed orders. The above key metrics confirm the hypothesis that DT technology can improve supply chain agility and effectively reduce the ripple effect. Despite the significant conclusions drawn in this paper, there are some limitations. Firstly, sensitivity analysis and t-test were not used in the study for secondary testing, which resulted in the lack of reliability of the validation results. In addition, the possible interaction between the ripple effect and the bullwhip effect was not discussed, leading to a confounding factor in the experimental results. The above issues can be considered in further research in the future. Finally, this paper explores the possibilities and uses of introducing machine learning techniques and considers the supply chain risk factors of globalization. In summary, this study validates the potential of digital twin technology in improving agility and coping with ripple effects in pharmaceutical supply chains. As research continues, DT technology is expected to improve supply chain efficiency and reduce supply chain risk while ensuring patient safety.

Controllable Multilayer of High‐performance Si/C Anode Materials Synthesized at Low Temperature from Industrial Ca‐Si Alloy and CCl4 for Lithium‐ion Batteries

AbstractA simple and energy‐saving synthesis process for the high‐performance Si/C anode material of lithium‐ion batteries is advantageous for application. In this paper, the layered Si/C composite was synthesized by a low temperature one‐pot synthesis from industrial Ca−Si alloy and CCl4. The effect of synthesis temperature on the structure and performance of the products was investigated. We found that low temperature favors to the multilayer structure of Si/C. Taking the advantage of the layered structure, the Si/C‐300 anode material prepared at the temperature of 300 °C has good electrochemical performance of a reversible capacity of more than 1000 mAh g−1 at a current density of 2 A g−1 for 300 cycles, with a capacity retention ratio of 82.8 %, and an ICE of 77.0 %. At a high current density of 6 A g−1, the specific discharge capacity of 721.6 mAh g−1 can be achieved. The synthesis method provides a promising route to high performance silicon‐carbon anode materials.

2D heterostructures of graphene oxide and MoS2 to improve sensitivity performance of flexible pressure sensor with shell biological structure

Inspired by the multilayer structure of the shellfish, a novel two-dimensional (2D) composite structure consisting of graphene oxide, MoS2 and graphene oxide (G/M/G) was integrated to the flexible pressure sensing. The composite structure was prepared by the vacuum suction filtration in order to imitate the high toughness of shellfish. Based on the strategy of strain engineering, a comprehensive experimental bench capable of meeting different strain conditions was connected to a push–pull meter and an LCR digital bridge, and then a computer was used to record the changes in transducer capacitance when an external load was applied to the meter. Graphene oxide (GO) and G/M/G supercells were constructed, and density functional theory (DFT) simulations of the initial energy band structure under strain-free conditions were carried out to determine the relationship between the band gap, conductivity, capacitance, and sensitivity of the G/M/G structure based on band gap theory, and to easily understand the mechanism of the shellfish heterostructure leading to enhanced sensitivity of the sensors. Using two-point bending and axial tensile tests, a flexible pressure sensing device was designed to realize positive strains in the ranges of 0%–5 % and 5%–50 %. The results show that the sensitivity of both GO and G/M/G capacitive pressure sensors decreased with increased strain, and the sensitivity of the G/M/G sensors was significantly improved by 75%–102 % compared to the GO sensors at the same strain. The parallel-plate capacitor model and crack growth theory well explain the experimental results at small and large strains. Our results provide new concepts for the design of novel flexible sonar with high sensitivity and large strain operating range by a simple vacuum filtration method, which can be extended to the design of other high-performance 2D flexible electronic devices.

Soft sensor model for endpoint carbon content and temperature in BOF steelmaking based on just-in-time learning with multilayer structure preservation and sparse information enhancement

Ensuring precise prediction of the endpoint carbon content and temperature is paramount in controlling the endpoint of the basic oxygen furnace (BOF) steelmaking process. However, due to the frequent fluctuations in real-time blowing conditions, the conventional just-in-time learning soft sensor approach encounters challenges in effectively anticipating the blowing endpoint. To address these aforementioned issues, this research introduces a novel approach known as the pattern-oriented multilayer structure preservation and sparse information enhancement model (POMLSP-SIE). This approach involves dynamically generating a dataset with the same distribution based on the characteristics of the query sample pattern. It is combined with a multi-pathway dimension reduction model to preserve multi-view spatial geometry information while reducing data dimension. The low-dimensional embedding serves as dictionaries containing various hierarchical structural characteristics. Significant information within these dictionaries is sparsely represented to amplify its influence during the regression prediction process while diminishing the impact of less relevant information. This refinement aims to rectify the problem of static regression models being weak to adapt to changing working conditions, ultimately enhancing prediction performance. The effectiveness of the proposed method is substantiated through an experimental study utilising real converter steelmaking process data, thereby confirming its practical applicability.

Effect of defects on the thermomagnetic instabilities of superconducting radio-frequency cavities with a multilayer structure

Abstract Vortex motion can lead to significant energy dissipation, resulting in hot spots and thermomagnetic instabilities that are detrimental to the application of superconductors. This paper presents a theoretical examination of thermomagnetic instabilities triggered by vortex motion within a Nb$_{3}$Sn-I-Nb cavity featuring a multilayer structure. The investigation is conducted using Ginzburg-Landau theory in conjunction with the heat diffusion equation. The numerical simulations align well with experimental data from Nb$_{3}$Sn superconducting cavities. Given that the performance of SRF cavities is highly sensitive to various defects, this study also considers the interaction between vortices and these defects. It reveals the impact of edge cracks and impurities on temperature rise and the quality factor. The findings indicate that edge cracks significantly reduce the threshold field for thermomagnetic instability in superconducting radio-frequency (SRF) cavities. The performance of SRF cavities is influenced not only by the RF field amplitude and frequency but also by the length and number of edge cracks. These results offer valuable insights for evaluating the performance of SRF cavities subjected to RF fields.

Multilayer-coating process for the synthesis of nickel-silicate composite with high Ni loading as high-rate performance lithium-ion anode material

BackgroundMetal silicates possess several important advantages as electrode materials for lithium-ion batteries (LIBs), including straightforward synthesis, low cost, and high thermal stability. A green synthesis routes that are capable of increasing metal loading and reducing the impact on the environment are required. MethodsA Ni-silicate with a multilayer structure and a Ni/Si molar ratio of 0.25 is first prepared using the co-precipitation method. The as-synthesized product is then repeatedly immersed in a Ni2+ solution to obtain Ni-silicate with the desired Ni contents (Ni/Si molar ratio: 0.50–2.00). Finally, the resulting Ni-silicate is reconstructed by hydrothermal treatment under various temperatures (70 °C, 100 °C, 150 °C) and durations (3 h and 24 h) to obtain Ni-phyllosilicate. The effects of the hydrothermal treatment temperature, hydrothermal time, and Ni/Si ratio on the structure, morphology, and surface area of the Ni-silicate composites are examined. Significant FindingsThe Ni-silicate with a Ni/Si ratio of 1.5 has a reversible capacity of 729 mAhg-1, which exceeds traditional graphite anodes (372 mAhg-1). Furthermore, the material exhibits a capacity retention of up to 80 % as the current density is increased from 0.025 Ag-1 to 0.5 Ag-1. Thus, the synthesized Ni-silicate composite is a promising candidate material for LIB anode.