Properties Of Solutions Research Articles

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.

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 $ .

The Convexity of a Planar Domain Via Properties of Solutions to the Modified Helmholtz Equation

The Convexity of a Planar Domain Via Properties of Solutions to the Modified Helmholtz Equation

Liquid-phase microextraction approach using supramolecular solvent formed in aqueous systems based on di(2-ethylhexyl)phosphoric acid salt: Spectrophotometric determination of antipyrine in saliva

In this study, di(2-ethylhexyl)phosphoric acid salt was investigated as a double-chain anionic surfactant for supramolecular solvent formation in a liquid-phase microextraction procedure for the first time. Inorganic electrolytes (sodium salts) were shown to be coacervation agents, due to their salting-out property in solution of sodium di(2-ethylhexyl)phosphate, obtained by deprotonation of the acid. The physico-chemical properties of the newly synthesised solvents were studied. Sodium carbonate and sodium phosphate were found to be the most suitable coacervation agents, due to their alkaline nature and low viscosity of the supramolecular solvent phases they produce. The extraction ability of the novel solvent was demonstrated in liquid-phase microextraction of a colored derivative of antipyrine from saliva for further spectrophotometric determination. The extraction recovery was found to be 70 %. The proposed green sample preparation technique enabled the exclusion of traditional toxic solvents and reduction of reagent consumption. The satisfactory analytical performance of the procedure was validated with real sample analysis. The calibration graph was linear over the concentration range of 0.03 to 0.5 mmol/L. The limit of detection (3σ) and limit of quantification (10σ), calculated from blank tests, were 0.01 and 0.03 mmol/L, respectively.

Prebiotic membrane structures mimic the morphology of alleged early traces of life on Earth

Elucidating compositions of the first cell membranes requires experiments with molecules and chemical conditions representative of early Earth. The molecules used are described as ‘prebiotically plausible’, i.e., they could have formed through abiotic reactions before the emergence of biology. Similarly, the chemical properties of solutions in which these membranes are formed (e.g., pH, temperature, ionic strength) must represent early Earth environments. Here, using confocal and transmission electron microscopy combined with population morphometry, we show that prebiotically plausible molecules, in solutions representative of Hadean submarine alkaline hydrothermal vents, form microstructures with substantial morphological diversity. The microstructures hold the potential for use as analogues of prebiotic processes in the rock record. Additionally, many of the structures are morphologically similar to purported early microfossils, highlighting limitations of morphological interpretation in these studies. Detailed analyses of abiotic microstructures are essential for understanding the earliest life on Earth, and for interpretation of potential biosignatures from extra-terrestrial bodies.

Mitigation of oxidative stress and inflammatory factors, along with the antibrowning and antimicrobial effects of cassia seed microbial fermentation solution

IntroductionCassia seeds, originating from the mature seeds of leguminous cassia species, possess pharmacological effects attributed to their rich composition of various active ingredients, notably anthraquinones. While current research predominantly focuses on pharmaceutical extractions, there has been limited progress in fermentation studies.MethodsOur study aimed to enhance the content of active compounds such as anthraquinones, flavonoids, and polyphenols using microbial fermentation techniques. We specifically optimized a fermentation system through a single-factor experimental design.ResultsThe antioxidant properties of the fermentation solution were validated through assays involving HaCaT cells and zebrafish. We observed effective suppression of inflammatory reactions in both RAW264.7 cells and transgenic zebrafish by the fermentation solution. Moreover, significant inhibition of tyrosinase activity and melanin production was evident in B16-F10 cells and zebrafish. Positive outcomes were also obtained in antibacterial assays and chick embryo experiments.DiscussionThese findings highlight the potential of cassia seed fermentation solution as a safe and eco-friendly material in food chemistry and biomedical sciences.

Alloying strategy to stabilize monocrystalline zinc anode under high utilization and working capacity

Zn(002) has been proven as a dendrite-free anode for Zn batteries. However, stable Zn plating/stripping behavior at an areal capacity exceeding 5 mAh cm−2 has remained unfulfilled so far. In this study, we show that the planar deposit on pure Zn (002) substrate is loosely stacked with high corrosion tendency by the aqueous electrolyte, the key obstacle to achieving considerable efficiency under high-capacity working conditions. To mitigate the side reactions, we introduce an alloying approach by combining monocrystalline Zn(002) with eutectic Al and Cu. The alloying strategy enhances the electrostatic interaction between deposits and substrate, favoring a dense-packed deposition morphology with improved corrosion resistant ability. Solid solution property of Al and Cu in Zn matrix also ensures the structure stability during repeated plating/stripping cycles. As a result, significant extension in cycle life of Zn alloy (002)-based symmetric cells even under 50 mA cm−2 and 25 mAh cm−2 and performance with high utilization also achieves a leading level without extra methods on surface protection. The modified Zn alloy (002) anode induces high anode utilization, paving the way for Zn batteries to meet the requirements of practical applications.

Traveling waves in a model of calcium ions influx via mechanically stimulated membrane channels

We consider the problem of existence and properties of pulse solutions to a system of equations modeling fast calcium waves in long cells. These waves have the speed up to 1000 m/s. They propagate via the inflow of calcium ions from the extracellular space through the mechanically stimulated membrane channels. The channels open due to mechano‐chemical interaction, in which stretching of the cell's membrane at a point opens the calcium channels at neighboring points due to the forces exerted by the actomyosin network. The existence of homoclinic solutions is based on the celebrated exchange lemma, which cannot be applied straightforwardly due to some specificities of the model equations.

Solutions with moving singularities for a one-dimensional nonlinear diffusion equation

AbstractThe aim of this paper is to study singular solutions for a one-dimensional nonlinear diffusion equation. Due to slow diffusion near singular points, there exists a solution with a singularity at a prescribed position depending on time. To study properties of such singular solutions, we define a minimal singular solution as a limit of a sequence of approximate solutions with large Dirichlet data. Applying the comparison principle and the intersection number argument, we discuss the existence and uniqueness of a singular solution for an initial-value problem, the profile near singular points and large-time behavior of solutions. We also give some results concerning the appearance of a burning core, convergence to traveling waves and the existence of an entire solution.

Synergistic effects of nonionic surfactants ethoxylated alkylamines and sodium dodecyl sulfate in mixed systems

HypothesisIn general, the performance of surfactant hybrid systems is better than that of single surfactants, so surfactant hybrid systems are widely used in various industries. As a very important class of nonionic surfactants, ethoxylated alkylamines have been widely used in industries such as washing, coating, and pesticide, but little research has been conducted on their mixed systems. In order to improve the utilization efficiency of surfactants and reduce wastage, the surface properties and aggregation behavior of ethoxylated alkylamine mixed systems should be further explored. ExperimentIn this study, the nonionic surfactant ethoxylated dodecylamine (AC-1202) and the anionic surfactant sodium dodecyl sulfate (SDS) were used to form a mixed system. The static surface tension and interaction parameters of the mixed system under the influence of inorganic salt ions were investigated using a KRÜSS K12 surface tensiometer. The diffusion process of the mixed system was investigated using a KRÜSS bubble pressure tensiometer. At the same time, the aggregate behavior of the mixed system was studied by particle size analyzer. In addition, the contact angle and rheological properties of the mixed solution were also investigated. FindingsThe SDS/AC-1202 mixture system formed a synergistic effect that could reduce the CMC value to 24.20 mN/m and the CMC value was as low as 22.89 mN/m after the addition of inorganic salts. The mixed system conforms to the kinetic mechanism of mixing and diffusion and the Ostwald de model for non-Newtonian fluids. Finally, there is a good aggregation pattern in the mixed system, and the stronger synergistic effect will lead to the reduction of the average particle size of the mixture to 45.41 nm.

D-π-A chromophores based on novel macroacceptors - Fused (azinylmethylene)malononitriles: Linear and nonlinear optical properties in solution and in poled polymer films

D-π-A chromophores based on novel macroacceptors − fused azinylmethylenemalononitriles (fused azine = pyrido [2,3-b]pyrazine, quinoline, quinoxaline and quinoxalin-2-one) − have been synthesized and their linear and nonlinear optical properties in gas, solution and in poled PMMA-based films have been investigated by DFT, UV–vis and second harmonic generation technique. The transition from chromophores with an azine acceptor to ones with azinylmethylenemalononitrile acceptors leads to a 10-fold increase in calculated μβ values. Poled polymer films doped with studied chromophores at 25 wt% load exhibit quadratic nonlinear optical activity with d33 values up to 42 pm/V.

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

Abstract This paper analyzes an age-group SIR (Susceptible-Infected-Recovered) 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, a numerical approximation is considered, based on Standard and non Standard Finite Difference methods, and on the Modified Patankar Euler 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. The effectiveness of the different numerical approaches is shown through several numerical tests on real data.

Anionic Effects on Concentrated Aqueous Lithium Ion Dynamics.

The dynamics, orientational anisotropy, diffusivity, viscosity, and density were measured for concentrated lithium salt solutions, including lithium chloride (LiCl), lithium bromide (LiBr), lithium nitrite (LiNO2), and lithium nitrate (LiNO3), with methyl thiocyanate as an infrared vibrational probe molecule, using two-dimensional infrared spectroscopy (2D IR), nuclear magnetic resonance (NMR) spectroscopy, and viscometry. The 2D IR, NMR, and viscosity results show that LiNO2 exhibits longer correlation times, lower diffusivity, and nearly 4 times greater viscosity compared to those of the other lithium salt solutions of the same concentration, suggesting that nitrite anions may strongly facilitate structure formation via strengthening water-ion network interactions, directly impacting bulk solution properties at sufficiently high concentrations. Additionally, the LiNO2 and LiNO3 solutions show significantly weakened chemical interactions between the lithium cations and the methyl thiocyanate when compared with those of the lithium halide salts.

Maximum principles for elliptic operators in unbounded Riemannian domains

The necessity of a Maximum Principle arises naturally when one is interested in the study of qualitative properties of solutions to partial differential equations. In general, to ensure the validity of these kinds of principles one has to consider some additional assumptions on the ambient manifold or on the differential operator. The present work aims to address, using both of these approaches, the problem of proving Maximum Principles for second order, elliptic operators acting on unbounded Riemannian domains under Dirichlet boundary conditions. Hence there is a natural division of this article in two distinct and standalone sections.

Block and Statistical Copolymers of Methacrylate Monomers with Dimethylamino and Diisopropylamino Groups on the Side Chains: Synthesis, Chemical Modification and Self-Assembly in Aqueous Media.

The synthesis of amphiphilic diblock and statistical (random) copolymers of poly(dimethylamino ethyl methacrylate) and poly((2-(diisopropylamino) ethyl methacrylate) using the reversible addition-fragmentation chain transfer polymerization technique (RAFT polymerization) is reported. The precursor copolymers were chemically modified to create derivative copolymers of polyelectrolyte and polyampholyte nature with novel solution properties. Moreover, their molecular and physicochemical characteristics, as well as their self-assembly in aqueous media as a function of molecular architecture and composition, are investigated by using size exclusion chromatography, spectroscopic characterization techniques and light scattering techniques. Furthermore, the behavior and properties of the obtained micelles and aggregates were studied, depending on the pH, temperature and ionic strength of the aqueous solutions. The response of the systems to changes in these parameters shows interesting behavior and new properties that are useful for their utilization as nanocarriers of pharmaceutical compounds.

Experimental study on flow characteristics of falling film over horizontal tubes under countercurrent gas flow

Open-absorption heat pump serves as an important means of industrial waste heat recovery, and the overall performance of the heat pump system depends on the absorber’s performance. Horizontal-tube–falling-film absorption refers to a complex process involving the coupling of fluid flow, heat transfer, and mass transfer. For the complete understanding of the intertube flow characteristics of horizontal-tube falling film under countercurrent gas flow (We), Visual experimental studies on falling-film flow were conducted using high-speed photography. The critical Reynolds number (Re) was quantitatively characterized to represent the transition of different flow patterns between tubes. The experiment was conducted to investigate the variation in the critical Re under the coupling effects of various factors and establish an experimental prediction correlation formula for the critical Re and solution properties, We, s, and d with an error margin of less than 10%.The influence of single factors was characterized qualitatively and then subjected to sensitivity analysis. The factors affecting the critical Re in descending order of magnitude were as follows: solution mass fraction > s > d > countercurrent gas flow (We). A reduction of approximately 50% in the critical Re for every 10% increase in the solution mass fraction.

Reaction calorimetry and structural crystal properties of non-ideal binary rhabdophane solid solutions (Ce1−xREExPO4·nH2O)

Rhabdophane is a hydrous phosphate that commonly replaces monazite as a weathering product in critical mineral deposits during the alteration of rare earth elements (REE) bearing carbonatites and alkaline igneous complexes. It is an important host to the light (L)REE (i.e., La to Gd) but the stability and structure of binary solid solutions between the Ce and the other LREE endmembers have not yet been determined experimentally. Here we present room temperature calorimetric experiments that were used to measure the enthalpy of precipitation of rhabdophane (Ce1−xREExPO4·nH2O; REE = La, Pr, Nd, Sm, Eu, and Gd). The solids were characterized using X-ray diffraction, scanning electron microscopy, Raman spectroscopy, and the role of water in the rhabdophane structure was further determined using thermogravimetric analysis coupled with differential scanning calorimetry. The calorimetric experiments indicate a non-ideal behavior for all of the binary solid solutions investigated with an excess enthalpy of mixing (ΔHex) described by a 2- to 3-term Guggenheim parameters equation. The solid solutions were categorized into three groups: 1) binary Ce-La and Ce-Pr which display positive ΔHex values with a slight asymmetry; 2) binary Ce-Nd and Ce-Sm which display negative ΔHex values with a nearly symmetric shape; 3) Ce-Eu and Ce-Gd which display both negative and positive ΔHex values with nearly symmetric shape. The excess Gibbs energy (ΔGex) of the solid solutions was further investigated using a thermodynamic analysis approach of aqueous-solid solution equilibria and the optimization programs GEMS and GEMSFITS. The resulting ΔGex values combined with the calorimetric ΔHex values indicate that there is likely an excess entropy contribution implying important short-range structural modifications in the solid solutions dependent on the deviation of the REE ionic radii from the size of Ce3+. These observations corroborate with the trends in the Raman v1 stretching bands of the PO4-site. The excess molar volumes determined from X-ray diffraction analysis further indicate an overall asymmetric behavior in all of the studied binary solid solutions, which becomes increasingly important from La to Gd. The pronounced short-range order–disorder occurring in groups 2 and 3 solid solutions mimics some of the behavior observed from previous studies in anhydrous monazite solid solutions. This study highlights the potential to use the chemistry and the structural modifications of rhabdophane as potential indicators of formation conditions in geologic systems and permits improving our modeling capabilities of REE partitioning in critical minerals systems.