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Navier - Stokes results which assume incompressible fluids and divergence-free flows, i.e. ... = 0, obtained analytically for three dimensions in the literature, are expanded. For this purpose, numerical analyses were performed. In related studies, especially time-dependant viscosities µ(t) were investigated. Therefore, Poincare maps were obtained for µ(t) < 1/t. The Navier-Stokes equations are fundamental partial differential equations that mathematically describe the motion of fluids. These equations establish the relationship between velocity, pressure and density of a fluid. The first equation, known as the momentum equation, determines how the velocity of a fluid changes over time. The second equation, called the mass equation, expresses how the density of the fluid changes. The third equation, the energy equation, calculates the energy changes within the fluid. The fourth equation relates thermodynamic properties such as temperature and pressure. These coupled equations are crucial for understanding fluid dynamics and engineering applications. In this context, different assumptions for the viscosity are considered. Three different cases were examined. These assumptions include a time-dependent upper limit, time-dependent lower limit and constant lower limit of viscosity. In addition, evidence is presented that certain streams of literature-related solutions of the Beltrami equation which are vector fields parallel to their own curl do not have chaotic streaklines. For constant viscosities, this proves that the dynamics of Trkalian (exponentially decreasing with the time) flows are not chaotic. [ABSTRACT FROM AUTHOR]

Purpose: Throughout an aircraft development process, the conceptual design phase is an extremely important milestone; hence, the quality and success of this step directly affect the overall cost and lead time of the project. Because of this fact, the purpose of this study is to provide outputs and suggestions to the designing engineer regarding the requirements for reducing overall design time as well as costs and creating an ideal design at the early phases of the project by optimizing the aircraft development process. Design methodology approach: The system has been prepared parametrically and presents some performance specifications for the aircraft in the early phases of the design, for example, coefficients for lift CL as well as drag CD and weight as well as fuel estimations. The software uses a combination of well-known design techniques within just one platform in contrast to many other applications. Because of this feature, it is not needed to use different sub-platforms which would require an appropriate environment and even though would lead to complications with regard to the connectivity. The system also presents relevant information about the aircraft performance like velocity versus load factor (V-n) diagrams, maximum turn rate of climb, turn rate and climb angle graphs in contrast to many other open-source conceptual design platforms. Findings: In this study, authentic General Dynamics F-16 Fighting Falcon and McDonnell Douglas F-15 Eagle data were used as input to the system, and advanced geometric and/or performance graphs were obtained and compared to the literature where a good agreement of the results was observed. These results with regard to the aircraft performance are typically product specific and quite rare in the literature. These data obtained by use of the software during the aircraft design are, thus, of major interest, especially for the design of new aerospace platforms. In this study, all of these graphs (especially the remarkable V-n diagram) are obtained on one platform. Originality value: The aircraft conceptual design and analysis system software provides information and suggestions regarding the requirements for reducing the overall design time, reducing the design costs and creating an optimized design at the early phases of a project by optimizing the aircraft development process within just one convenient, that is, user friendly, platform, where it uses a combination of varying methodologies. Besides presenting one interface, which is quite typical for conceptual design tools, it allows applications of methods like vortex lattices and finite differences for obtaining aerodynamic performance parameters. [ABSTRACT FROM AUTHOR]

An analytical solution to the incompressible Navier--Stokes momentum equations for a divergence-free flow ... with time-dependent dynamic viscosity µ (t) is presented. The demonstrated methodology holds for the physically relevent three dimensions. The constructed flow velocities ... are eigenvectors of the vector operator curl. Moreover, vortex ..., helicity ..., enstrophy Ε(t) and enstrophy evolution dΕ(t)/dt are explicitly determined. [ABSTRACT FROM AUTHOR]

The ongoing coronavirus disease 2019 (COVID-19) pandemic poses a major threat to the worldwide health care. In this context, epidemic modelling is an integral part of containment strategies. Compartmental models are typically used for this purpose. Analytical solutions of the two distinct but connected Susceptible-Infectious-Recovered-Deceased (SIRD) and Susceptible-Infectious-Quarantine-Recovered (SIQR) models are presented in this study. Furthermore, the behaviour at the start of a disease outbreak is derived. This analysis shows that a combination of transmission, recovery and isolation rates dominates the behaviour at the start of an epidemic. In addition, the loss occurring due to quarantine and lockdown measures is investigated, where it can be observed that quarantine procedures lead to a smaller loss in comparison with lockdown regulations. Within this framework, optimized strategies that lead to a constant epidemic peak or a minimized loss are presented. [ABSTRACT FROM AUTHOR]

The formalism for an efficient scheme for spin-rotational symmetric matrix-product states (MPSs), also known as tensor trains (TTs), is presented. The methodology is applied for the study of ground-state energy and correlation properties of the isotropic spin-1 bilinear-biquadratic quantum Heisenberg chain with nearest-neighbor interactions and periodic boundary conditions as an example. The mathematical framework can be used for arbitrary spin-rotational invariant spin-S chains. [ABSTRACT FROM AUTHOR]

The formalism for an efficient scheme for spin-rotational symmetric matrix-product states (MPSs), also known as tensor trains (TTs), is presented. The methodology is applied for the study of ground-state energy and correlation properties of the isotropic spin-1 bilinear-biquadratic quantum Heisenberg chain with nearest-neighbor interactions and periodic boundary conditions as an example. The mathematical framework can be used for arbitrary spin-rotational invariant spin-S chains. [ABSTRACT FROM AUTHOR]

An analytical solution to the Navier–Stokes momentum equations for a compressible flow with volume and small shear viscosities as well as external friction is presented while the dynamic viscosity is set to zero. The demonstrated methodology holds in d dimensions. However, in this study, the three-dimensional case is considered in detail. The analytical solution blows up at finite times T , which is determined by a cubic relation if the initial flow velocity is not divergence-free. The existence of T is a necessary and sufficient condition for implementing a singularity. Nonetheless, for external friction μ e > T − 1 , all analytical expressions are smooth while the averaged expressions are smooth for all times. [ABSTRACT FROM AUTHOR]

Electron field emission experiments of carbon nanotubes (CNT) show that due to heat CNTs breakdown faster under applied voltage than expected. Therefore, different systems with varying temperature distributions are considered analytically and numerically by use of the heat conduction equation. This methodology yields a phenomenological understanding and description of the thermoelectric behavior of CNTs under applied voltages. [ABSTRACT FROM AUTHOR]

Usage of thermoplastic composites with low densities is increasing, with lightness coming to the fore especially in the aerospace industry while various sectors like automotive, electronics, sport etc. are also following the trend. Important factors for the preference of thermoplastics are the increase in the amount of waste of conventional materials in addition with increasing product requirements. Composite wastes are accumulated in certain composite collection centers in the world and disposed by incineration. Until at least 2025, studies on recycling are carried out in the European Union. Within this regard, the most important feature of thermoplastics is that they can be melted and shaped again at high temperatures. In this way, recycling of fibers and matrices is possible. Mainly thermal and chemical methods are preferred for obtaining fibers while mechanical methods are preferred for obtaining the matrix. Hence, it is aimed to use both open and closed loop recycling in order to reduce wastes, energy consumption, fossil fuel consumption, and the carbon footprint. Note that these recycling approaches are also of significance for the circular economy concept. Correspondingly, this review thematizes current recycling methods for thermoplastic composites. [ABSTRACT FROM AUTHOR]

Delamination due to an inferior adhesion between reinforcement material and matrix in carbon fiber-reinforced thermoplastic (CFRTP) composites is a crucial problem to be solved. To this end, this study aims to overcome poor wettability between reinforcing phase, i.e., carbon fiber (CF), and thermoplastic matrix, i.e., polyetherether ketone (PEEK). Herein, CF's surface was tailored by application of different polymeric sizing agents which have different chemical structures. Morphology and topology analyses were performed by Scanning Electron Microscope and 3D laser scanning, respectively. Later, a variety of wettability results were obtained by the sessile drop method used in Contact Angle (CA) measurements for CFs throughout application of each sizing agent applied by dip coating. Sizing materials were designed such that the chemical structure of CF's surface could exhibit compatibility with the matrix itself. Consequently, complete wettability (CA: 0°) was achieved for CFs sized by HPEEK (CF/hydroxylated PEEK (HPEEK)) and the surface free energy (SFE) of CF was enhanced from 5.43 to 72.8 mJ/m2 while the SFE of the PEEK matrix is 40.1 mJ/m2. Moreover, sizing by HPEEK improved the average surface roughness of CF by 32% which enables optimized adhesion. Afterward, repetitive tensile tests were carried out to observe effects of improved interfacial interlocking on the mechanical properties of the final CFRTP composite. Stress–strain curves revealed that the tensile strength of CFRTP improved from 473 to 508 MPa through the sizing of CF by HPEEK whereas pristine PEEK has a much smaller tensile strength (98 MPa) than the aforementioned CF-reinforced composites. The sizing of carbon fiber's surface by HPEEK resulted in an enhanced adhesion with the PEEK matrix. Since the chemical structure and physical properties of sizing agent and matrix are compatible, potential debonding between them was eliminated. Thus, the improved wettability led to a substantial increase in the mechanical strength of the final TP composite. [ABSTRACT FROM AUTHOR]

A series of experimental and numerical studies were carried out on the mechanical and geometric performance of an aerostructural part produced by a material out-of-autoclave stamp forming process using unidirectional (UD) carbon fiber (CF) reinforced polyetherketoneketone (PEKK), which provides advantages like reshaping, recycling, welding, and low serial manufacturing costs. As a novelty, initial part geometry, different types of springs, and their attachment type were examined experimentally and compared with simulations. Compression tests were performed to determine mechanical strengths which reach levels up to 550 MPa. In addition, differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) were conducted to determine the crystallinity which occurs depending on the cooling regimes of the material. The crystallinity has been observed to vary regionally ranging from 16 to 21%. However, the crystallinity of the part towards the cold mold region decreased from 20 to 17%. In addition, simulations were performed to observe and control the occurrence of wrinkles and other defects. [ABSTRACT FROM AUTHOR]

The aerospace industry has progressively grown its use of composites. Electrically conductive nanocomposites are among important modern materials for this sector. We report on a bulk composite containing silver nanowires (AgNW) and an aerospace grade epoxy for use in carbon fiber reinforced polymers (CFRPs). AgNWs' surfaces were also modified to enhance their ability to be dispersed in epoxy. Composites were obtained by use of three-roll milling which is of major interest for industrial applications, especially for the aerospace sector, since the process is scalable and works for aerospace grade resins with high curing temperatures. Our main objective is to improve the electromagnetic interference (EMI) shielding performance of CFRPs via improving the properties of the resin material. The addition of AgNWs did not considerably alter the flexural strength of the epoxy, however the composite with surface-modified AgNWs has a 46 % higher flexural strength. Adding AgNWs over a low threshold concentration of 0.05 wt% significantly enhanced the electrical conductivity. Conductivities above the percolation threshold lie around 102 S/m. At a concentration of 5 wt% AgNW, the EMI shielding efficiency (SE) of epoxy increased from 3.49 to 12.31 dB. Moreover, the thermal stability of the epoxy was unaffected by AgNWs. As a result, it was discovered that (surface modified) AgNWs improved the (multifunctional) capabilities of the aerospace grade epoxy resin which might be used in CFRPs to further enhance properties of composites parts, demonstrating suitability of AgNWs' as a reinforcement material in aerospace applications. [ABSTRACT FROM AUTHOR]

As a result of the widespread use of composite materials in primary structures of aerospace platforms, composite joining became more crucial. This study addresses the effect of joining methods on the strength of composite joints experimentally, numerically and analytically. Single lap joint shear strengths of carbon fiber reinforced epoxy composite parts joined by mechanical fastening with a pop and solid rivet, secondary bonding with a paste adhesive, co-curing and co-bonding techniques were compared. In addition, the effect of adhesive thicknesses (0.2, 0.4, 0.6, 0.76 mm) on the single lap shear strength was investigated. Carbon fiber reinforced composite (CFRP) samples were produced according to the ASTM 5868 standard. After the production of samples with varying joining methods, single lap shear tests were implemented. Moreover, the interface damage in the composites was examined by use of a scanning electron microscope (SEM) for the purpose of studying the damage mechanism. Fracture mechanisms corresponding with bonding methods were also assessed by examining the fracture surface of the composite samples. Furthermore, results were analyzed by Hypermesh, ABAQUS and ESAComp. For instance, the co-bonded sample with an adhesive film exhibits an experimental shear strength of 24.03 MPa which deviates only 3 % from the numerical expectation. [ABSTRACT FROM AUTHOR]

Dispersion and distribution of graphene nanoplatelets (GNPs) and carbon nanotubes (CNTs) in polymer matrices without the use of any functionalization and application of conventional procedures such as mixing or sonication does not display the full potential of the fillers due to agglomeration which limits the use of the corresponding nanomaterials. Contrarily, varying GNP and CNT based fillers were integrated to an aerospace grade epoxy resin, which has a high curing temperature of 180 °C and is commonly used as matrix to manufacture structural parts, by use of three-roll milling in this study. This procedure is of major interest for industrial applications, especially for the aerospace sector, since the process is scalable and works for resins with high curing temperatures. Microstructure and thermal properties of the nanocomposites were investigated. Moreover, mechanical and electrical performances were studied. Results show that certain fillers yield multifunctional properties, i.e. enhanced flexural strength up to 64 ± 41 % in combination with low electrical resistivity with orders of magnitude of ∼ 10 − 1 − 10 − 2 Ω m in comparison to the electrical resistivity of the epoxy being 10 9 Ω m. [Display omitted] • Aerospace grade epoxy was reinforced with various carbonaceous fillers. • Electrical conductivity was increased 10 10 fold. • Flexural strength was increased by 64 %. • Industrial methodology compatible with standard manufacturing methods. • Aerostructure which carries static loads was manufactured by this approach. [ABSTRACT FROM AUTHOR]