Properties Of Solutions Research Articles

On the heat kernel of the Rumin complex and Calderón reproducing formula

Abstract We derive several properties of the heat equation with the Hodge operator associated with the Rumin’s complex on Heisenberg groups and prove several properties of the fundamental solution. As an application, we use the heat kernel for Rumin’s differential forms to construct a Calderón reproducing formula on Rumin’s forms.

Some Asymptotic Properties of Solutions to Triharmonic Equations

Some Asymptotic Properties of Solutions to Triharmonic Equations

Novel Solid‐state Fluorophores, a Series of Cyanostilbene‐based Amorphous Molecular Materials

We have designed and synthesized a novel series of cyanostilbene‐based amorphous molecular materials with different methylene chain lengths, BMAC‐n (n=3,4,5,6), and investigated their emitting properties in solution and various solid states. All BMAC‐n molecules showed solvatochromic fluorescence in solutions. Emission spectra of BMAC‐n molecules in the same solution were identical to one another irrespective of the methylene chain length while the spectra in crystalline states depended on their methylene chain length. As in solutions, emission spectra of their spin‐coated amorphous films were identical to each other irrespective of the methylene chain length. Emission spectra of rubbed amorphous films prepared by grinding their crystals were identical to those for spin‐coated amorphous films; however, comparative studies between spin‐coated and rubbed amorphous films indicated that fluorescence quantum yields and photochemical reactivity depend on the preparation method.

Effect of Annealing Temperature on Microstructure and Properties of Solid Solution Extruded Mg–2.0Zn–1.0Y–0.5Zr Alloys

In this investigation, the effects of different annealing temperatures (180, 200, 220, 240, 260, and 280 °C) on the microstructure evolution and properties of an extruded Mg–2.0Zn–1.0Y–0.5Zr (wt%) magnesium alloys were determined. Optical microscopy (OM), scanning electron microscopy (SEM), immersion corrosion, electrochemical corrosion experiments, and tensile testing were performed. Research has found that combining hot extrusion with subsequent low-temperature annealing significantly improves the strength, plasticity, and corrosion resistance of alloys due to grain refinement and a reduced dislocation density. The alloy was completely recrystallized at an annealing temperature of 240 °C for 4 h after solid solution extrusion, and the grains were fine and uniform, demonstrating the best comprehensive properties. Its corrosion rate, ultimate tensile strength, yield strength, and elongation were 0.454 ± 0.023 mm/y, 346.7 ± 8.9 MPa, 292.4 ± 6.9 MPa, and 19.0 ± 0.4%, respectively. The corrosion mechanism of the specimens under extruded and annealed conditions was analyzed. After annealing at 240 °C for 4 h, the dislocation and bimodal grain structure of the samples were almost eliminated, resulting in uniform and fine grains, which were conducive to the formation of a more uniform and denser oxide film, thus improving the corrosion resistance of the alloy.

Analytical Properties and Numerical Preservation of an Age-Group Susceptible-Infected-Recovered Model: Application to the Diffusion of Information

Abstract This paper analyzes an age-group susceptible-infected-recovered (SIR) model. Theoretical results concerning the conservation of the total population, the positivity of the analytical solution, and the final size of the epidemic are derived. Since the model is a nonlinear system of ordinary differential equations (ODEs), a numerical approximation is considered, based on Standard and non-Standard Finite Difference methods, and on a Modified Patankar-Runge–Kutta (MPRK) method. The numerical preservation of the qualitative properties of the analytical solution is studied. The obtained results are applied to the diffusion of information in social networks, and the effectiveness of the different numerical approaches is shown through several numerical tests on real data.

Synthesis, Optical Performance Characterization, and Durability of Electrospun PTFE-PEO Materials for Space Applications.

Passive heat management is crucial in space, especially for extended missions involving protection from sunlight. Thermal coatings with desirable optical properties can drastically reduce the power consumed by active cooling systems, thereby reserving more resources for other critical systems onboard. Specifically, materials with wavelength-dependent reflectance and emittance are desirable for managing incident sunlight and self-cooling by thermal emission. This study demonstrates the use of polymer nanofibers, specifically poly(tetrafluoroethylene) (PTFE), for passive temperature control in space applications. This study describes the electrospinning fabrication process to create nanofibers and how process parameters can be varied to control the fiber geometry. We combine poly(tetrafluoroethylene) (PTFE) and poly(ethylene oxide) (PEO) polymers to fabricate highly reflective thermal control materials by electrospinning. To understand the role of material and fiber geometry, we measure spectral reflectance, absorptance, and transmittance using spectrophotometers interfaced with integrating spheres. We control the materials' fiber geometry and solar reflectance by modifying the solution properties, flow rate, rotating collector speed, and fabrication time. With 220-1560 μm thick electrospun nanofiber materials, we demonstrate an average solar reflectance of 94.73-99.75%, with values approaching 99.9% for thicker samples, which is among the highest for space applications. Meanwhile, a thermal emittance of 81.4% was observed at 300 K for a 3360 μm thick sample. The durability of these samples was also tested under ultraviolet light and atomic oxygen. Compared to the state-of-the-art materials, the electrospun PTFE-PEO fibers present a new paradigm for passive thermal management in space applications.

Physicochemical Properties of Lithium Bis(trifluoromethanesulfonyl)imide Solutions in Sulfolane

Abstract A study is performed of the physicochemical properties (ionic conductivity, viscosity, and density in the 30–50°C range of temperatures) and the electrochemical and thermal stability of lithium bis(trifluoromethanesulfonyl)imide solutions in sulfolane in the 0.001–1.89 M range of concentrations. It is shown that lithium bis(trifluoromethanesulfonyl)imide solutions in sulfolane exhibit high electrochemical stability (5.75 V vs. Li/Li+) and moderate ionic conductivity (2.75 × 10−3 Ω−1 cm−1 at 30°C for a 1 M solution), which are comparable to the respective parameters of sulfolane solutions of lithium hexafluorophosphate. The structure and transport properties of sulfolane solutions of lithium bis(trifluoromethanesulfonyl)imide are determined by their concentrations. In dilute solutions, lithium bis(trifluoromethanesulfonyl)imide is weakly associated. The degree of electrolytic dissociation of LiN(SO2CF3)2 initially falls and then rises upon an increase in its concentration. The electrolytic dissociation of lithium bis(trifluoromethanesulfonyl)imide rises along with its concentration, due to the formation of ion triplets and more complex ion associates. The constant of association and limit equivalent conductivity of LiN(SO2CF3)2 in sulfolane rise along with temperature, due to a drop in the degree of self-association and the degradation of the solvent’s structure. A specific feature of sulfolane solutions of lithium bis(trifluoromethanesulfonyl)imide is their tendency to form stable supercooled solutions.

Highly Efficient Luminescent Solar Concentrators Based on BODIPY Derivatives

AbstractThree new chromophores based on difluoroborondipyrromethene dyes (Bodipy‐1, Bodipy‐2, and Bodipy‐3) are used as precursors to prepare luminescent solar concentrators (LSC) based on poly‐acrylate, following a thermally activated polymerization involving lauryl methacrylate as monomer, ethyl glycol dimethacrylate as cross‐linking agent, and lauroyl peroxide as initiator. The new dyes exhibit typical BODIPY absorption and emission properties in dichloromethane fluid solution, assigned to the lower‐lying singlet π–π∗ level, which in the case of Bodipy‐2 and Bodipy‐3, both containing diamino‐substituted styryl subunits in their structure, has a strong charge transfer contribution. The LSCs obtained starting from each of the three Bodipys are interfaced to silicon photovoltaic (PV) cells, and the PV light‐to‐energy conversion efficiencies ηopt for the three systems are calculated. The results yield ηopt of 4.53% for LSC‐Bodipy‐1, 5.26% for LSC‐Bodipy‐2, and 8.23% for LSC‐Bodipy‐3. The optical efficiency for LSC‐Bodipy‐3 is a remarkable value among the LSC based on organic dyes.

Global Dynamics of a Social Hierarchy-Stratified Malaria Model: Insight from Fractional Calculus

In this study, a mathematical model for the transmission dynamics of malaria among different socioeconomic groups in the human population interacting with a susceptible-infectious vector population is presented and analysed using a fractional-order derivative of the Caputo type. The total human population is stratified into two distinguished classes of lower and higher income individuals, with each class further subdivided into susceptible, infectious, and recovered populations. The socio hierachy-structured fractional-order malaria model is analyzed through the application of different dynamical system tools. The theory of positivity and boundedness based on the generalized mean value theorem is employed to investigate the basic properties of solutions of the model, while the Banach fixed point theory approach is used to prove the existence and uniqueness of the solution. Furthermore, unlike the existing related studies, comprehensive global asymptotic dynamics of the fractional-order malaria model around both disease-free and endemic equilibria are explored by generalizing the usual classical methods for establishing global asymptotic stability of the steady states. The asymptotic behavior of the trajectories of the system are graphically illustrated at different values of the fractional (noninteger) order.

IV‐VI/I‐V‐VI2 Thermoelectrics: Recent Progress and Perspectives

AbstractThermoelectric energy conversion technology is considered as one of the most promising solutions for recovering waste heat generated by fossil fuel combustion. As typical types of thermoelectric materials in the middle and high‐temperature range (500–900 K), binary IV‐VI (IV = Ge, Sn, Pb; VI = Se, Te) compounds are extensively studied. Lately, the obtained high‐performance thermoelectric solid solutions between IV‐VI and I‐V‐VI2 (I = Li, Na, K, Ag, Cu; V = Sb, Bi; VI = S, Se, Te) compounds have brought those complex chalcogenides back to the central point of thermoelectric community due to the emerging rich physical phenomena. Profiting from this effective approach, unveiling the underlying mechanism and understanding of alloying effect on the transport properties of these solid solutions becomes particularly significant. This review presents the latest progress in designing high‐performance IV‐VI/I‐V‐VI2 solid solutions and the underlining physical mechanisms, in which detailed discussion about the role of I‐V‐VI2 compounds play in optimizing individual properties of IV‐VI materials is made. This comprehensive review highlights the multiple effects of I‐V‐VI2 alloying on thermoelectric properties of IV‐VI compounds and will drive the related research interests aiming at developing new‐generation thermoelectric compounds in this family.

Defect/disorder correlated modification of transport properties from hopping to tunneling processes in BaTiO3–LaFeO3 solid solution

Crystal structure, bandgap, and the changes in the charge conduction mechanisms in ceramics are interrelated, and the underlying physics unifies all these different phenomena. The experimental and theoretical evaluation of the electronic properties of the solid solution of (1 − x)BaTiO3–(x)LaFeO3 (x = 0, 0.015, 0.031, 0.062) is attempted in this work. Bandgap was observed to be tunable with La/Fe doping from 3.2 eV (x = 0) to 2.6 eV (x = 0.06), while the lattice disorder was found to increase. A theoretical assessment confirms a considerable shift of valence band maxima and conduction band minima with an introduction of additional defect states within the bandgap. Electron localization was also confirmed theoretically with doping. Such changes in the electronic properties were experimentally confirmed from dielectric/AC - conductivity/impedance spectroscopy studies. From different transportation models, hopping is a preferred mechanism in the less distorted BaTiO3. However, a large polaron tunneling process can be justified for the doped samples at lower temperatures. Only at higher temperatures, a small polaron tunneling can be justified for the doped samples. The transportation is affected by the grain boundaries as much as the grains themselves. A complete analysis using Nyquist plots reveals the competing contributions of these regions to the transportation mechanism and is correlated to the disorder/distortions in the lattice in terms of the formation of oxygen vacancies.

Responsive cellulose nanocrystal / acrylamide / poly (ethylene glycol) photonic films with chiral nematic structures by co-assembly and photopolymerization

Cellulose nanocrystals (CNCs), acrylamide (AAm) and poly (ethylene glycol) (PEG) can be co-assembled and photopolymerized into responsive, patterned photonic films with chiral nematic (N*) structures. Here, we report stimuli-responsive CNC/AAm/ PEG composite films (CFs) for use in humidity sensing. With the increase of AAm content, the CFs had an increased helical pitch and showed a red shift. With the adding of PEG, the CFs can quickly capture or release water molecules in air, which resulted in the changes of the helical pitch in N* structures and the structural color. After photopolymerization, the elastic modulus, hardness by nanomechanical testing and tensile strength of polymer films (PFs) were improved compared with CFs. The elastic modulus and hardness of PFs increased with the increase of AAm content. PFs and CFs showed different swelling properties in solutions with different EtOH / H2O ratio. Due to the swelling properties difference between CFs and PFs, partial photopolymerized photonic film showed photonic pattern. This research provides a new method to prepare photonic films with sensitive color response to humidity and photonic pattern, which has potential applications in the fields of sensing, anti-counterfeiting, and decoration.

On the construction of the Stokes flow in a domain with cylindrical ends

Based on existence results for the Stokes operator and its solution properties in manifolds with cylindrical ends by Große et al. and Kohr et al., the Stokes flow in a three‐dimensional compact domain with circular openings through which the fluid enters and leaves through unbounded cylindrical pipes the Stokes flow is modeled as a mixed boundary value problem whereas in the cylindrical ends, the velocities and pressures are constant on every straight line in the cylindrical directions with initial values from the openings of . These values equal the velocities and pressures which are obtained from the mixed boundary values' solution in at the openings .

Well‐posedness and time decay of fractional Keller–Segel–Navier‐Stokes equations in homogeneous Besov spaces

AbstractIn this paper, we consider the parabolic–elliptic Keller–Segel system, which is coupled to the incompressible Navier–Stokes equations through transportation and friction. It is shown that when the system is diffused by Lévy motion, the well‐posedness of the mild solution to the corresponding Cauchy problem in homogeneous Besov spaces is established by means of the Banach fixed point theorem. Furthermore, we prove the Lorentz regularity in time direction and the maximal regularity of solutions. In addition, we obtain the additional regularity and explore the time decay property of global mild solutions.

Turbulent System Dynamics: An Introduction to Spectral Decomposition and External Forcing in Sobolev Spaces

Turbulent systems represent a complex and ubiquitous phenomenon in various natural and engineered environments. This study investigates the dynamics of turbulent systems through the lens of four fundamental theorems. The first theorem establishes a spectral decomposition of the velocity correlation function, shedding light on the coherent and incoherent structures within turbulent flows. The second theorem delves into the energy distribution in Sobolev spaces, providing insights into the regularity and properties of turbulent solutions. Expanding on these findings, the third theorem explores the influence of external forcing on energy distribution, elucidating how external factors shape turbulent behavior. Building upon these insights, the fourth theorem integrates the concepts from the previous theorems, describing the interplay between spectral decomposition, energy distribution, and external forcing effects in turbulent systems. This comprehensive analysis offers a deeper understanding of turbulent dynamics, with implications for fields such as fluid mechanics, atmospheric science, and engineering. By elucidating the underlying mechanisms governing turbulent behavior, this study paves the way for improved modeling, prediction, and control of turbulent systems in various practical applications.

The properties of chitosan and paracetamol in acidic water mixture by viscosity study for pharmaceutical and biomedical applications

ABSTRACT Paracetamol (PC), the active ingredient in Efferalgan, is an effervescent tablet medicine used in the treatment of mild-to-moderate pain. Chitosan (CH) is a biopolymer having immense structural possibilities for chemical and mechanical modifications to generate novel properties, functions and applications, especially in the pharmaceutical area. The dynamic viscosities, η, have been measured, and investigated for the mixture of CH in acidic water and paracetamol aqueous solutions over the entire range of the temperature 20–65°C, and concentrations of 1–10 g/l. The main objective of our research described here was to determine the viscometric properties of biopolymer solutions of CH in PC, as a function of the volume fraction fCH in the CH and PC mixture and temperatures. We identified three main concentration regimes, corresponding to a dilute regime, a critical regime and the semi-dilute regime. Our results showed that the CH/PC is a promising mixture for use in pharmaceutical and antibacterial applications. The chitosan shows antimicrobial activity against various microorganisms, including bacteria.

Infinitely degenerate slowly rotating solutions in f(R) gravity

Abstract This work tests the no-hair conjecture in f(R) gravity models. No-hair conjecture asserts that all black holes in General Relativity coupled to any matter must be Kerr–Newman type. However, the conjecture fails in some cases with non-linear matter sources. Here, we address this by explicitly constructing multiple slow-rotating black hole solutions, up to second order in rotational parameter, for a class of f(R) models ( f(R) =(\alpha_{0} + \alpha_{1}\,R)^{p}, p > 1). Such an f(R) includes all higher-powers of R. We analytically show that multiple vacuum solutions satisfy the field equations up to the second order in the rotational parameter. In other words, we show that the multiple vacuum solutions depend on arbitrary constants, which depend on the coupling parameters of the model. Hence, our results indicate that the no-hair theorem for modified gravity theories merits extending to include the coupling constants. The uniqueness of our result stems from the fact that these are obtained directly from metric formalism without conformal transformation. We discuss the kinematical properties of these black hole solutions and compare them with slow-rotating Kerr. Specifically, we show that the circular orbits for the black holes in f(R) are smaller than that of Kerr. This implies that the inner-most stable circular orbit for black holes in f(R) is smaller than Kerr's; hence, the shadow radius might also be smaller. Finally, we discuss the implications of our results for future observations.

Printability and mechanical properties of solution impregnated continuous jute yarn reinforced acrylonitrile butadiene styrene composites fabricated by fused deposition modeling

AbstractThis work aimed to check the influence of solution impregnated (SIP) jute yarn on printability and mechanical properties of 3D printed continuous jute yarn reinforced biocomposites. Acrylonitrile butadiene styrene (ABS) was employed as the matrix and the biocomposites were fabricated by in‐nozzle melt impregnation fused deposition modeling (FDM). The thermoplasic polyurethane (TPU), polystyrene (PS) and ABS solutions with the concentration of 2 and 10 wt% were prepared for making the SIP jute yarn. The best tensile strength and pull‐out results were obtained for the single strand composed of ABS and jute in which the yarn was impregnated with the solution containing 2 wt% TPU (TPU2%) before processing. The three printing parameters of layer height, print speed and nozzle diameter were changed to compare the process window of the composite specimens fabricated using the solution unimpregnated (SUIP) and SIP jute yarn with TPU2%. The results indicated that the print speed could be higher for the SIP one than that of its counterpart. The tensile and short beam shear tests of the non‐dried (ABS/NDJ) and dried ABS/Jute (ABS/DJ) composites revealed that the influence of drying was more obvious on the tensile properties results than those of on the short beam shear test. In addition, the yield stress, elastic modulus and tensile strength of ABS/DJ were 24, 17 and 12% higher than for ABS/NDJ, respectively. However, the highest tensile properties and short beam shear test results were acquired for the composites fabricated by jute yarn SIP with TPU2%.Highlights Printability of ABS/impregnated continuous jute yarn composites was studied by FDM TPU, PS and ABS of 2 and 10 wt% solutions were used to impregnate the jute yarn Three printing parameters were altered to find the process window for FDM process Best mechanical properties was obtained for ABS/Jute filament impregnated by TPU2% Process window was wider for the impregnated than that for unimpregnated composite

Machine Learning for Polymer Design to Enhance Pervaporation-Based Organic Recovery.

Pervaporation (PV) is an effective membrane separation process for organic dehydration, recovery, and upgrading. However, it is crucial to improve membrane materials beyond the current permeability-selectivity trade-off. In this research, we introduce machine learning (ML) models to identify high-potential polymers, greatly improving the efficiency and reducing cost compared to conventional trial-and-error approach. We utilized the largest PV data set to date and incorporated polymer fingerprints and features, including membrane structure, operating conditions, and solute properties. Dimensionality reduction, missing data treatment, seed randomness, and data leakage management were employed to ensure model robustness. The optimized LightGBM models achieved RMSE of 0.447 and 0.360 for separation factor and total flux, respectively (logarithmic scale). Screening approximately 1 million hypothetical polymers with ML models resulted in identifying polymers with a predicted permeation separation index >30 and synthetic accessibility score <3.7 for acetic acid extraction. This study demonstrates the promise of ML to accelerate tailored membrane designs.

SUMMABILITY AND ASYMPTOTICS OF POSITIVE SOLUTIONS OF AN EQUATION OF WOLFF TYPE

Abstract We use potential analysis to study the properties of positive solutions of a discrete Wolff-type equation $$ \begin{align*} w(i)=W_{\beta,\gamma}(w^q)(i), \quad i \in \mathbb{Z}^n. \end{align*} $$ Here, $n \geq 1$ , $\min \{q,\beta \}&gt;0$ , $1&lt;\gamma \leq 2$ and $\beta \gamma &lt;n$ . Such an equation can be used to study nonlinear problems on graphs appearing in the study of crystal lattices, neural networks and other discrete models. We use the method of regularity lifting to obtain an optimal summability of positive solutions of the equation. From this result, we obtain the decay rate of $w(i)$ when $|i| \to \infty $ .