Properties Of Solutions Research Articles

On a quenching problem of hyperbolic MEMS equation with a nonlocal term

We consider a nonlocal hyperbolic problem. It arises in the field of MEMS control. First, we review the stationary problem and state that there exists a unique and no solution for small and large parameter, respectively. Next, we introduce the results of global existence and dynamical properties of solution for the hyperbolic equation. Finally, we derive the result of the quenching behaviour. As proven in similar problems, we show that the quenching occurs for large parameter. This criterion is also expressed by means of the first eigenvalue of Laplace operator.

Weighted means and an analytic characterization of discs

Weighted means are obtained for solutions of the two-dimensional Helmholtz and modified Helmholtz equations and also for harmonic functions. The presence of a logarithmic weight reduces the coefficient in the last two mean value identities. A new theorem characterizing disks in the Euclidean plane R 2 \mathbb {R}^2 analytically is proved; it is based on the weighted mean value property of solutions to the modified Helmholtz equation.

Effect of triazolium-based ionic liquid (1, 4-dimethyl- 4H-1, 2, 4-triazolium iodide) on volumetric and ultrasonic properties of binary aqueous solutions of benzamide/benzylamine: experimental and computational study

ABSTRACT In the current investigation, effect of triazolium-based ionic liquid 1, 4-Dimethyl- 4 H-1,2,4-triazolium iodide (DMTI) on volumetric and ultrasonic properties of binary aqueous solutions of benzamide/benzylamine is analysed at four equidistant temperatures and atmospheric pressure. Molecular interactions of DMTI in binary aqueous solutions of benzylamine/benzamide are also interpreted using density (ρ) and speed of sound (u) data along with FT-IR measurements. Different volumetric and ultrasonic parameters were also computed by employing the experimental values of density (ρ) and speed of sound (u), and are further used to elucidate various kinds of interactions in the ternary system. Volumetric and acoustic transfer parameters were further used for the computation of interaction coefficients (pair and triplet). To analyse the outcomes of the estimated parameters, spectroscopic and density-functional theory (DFT) investigations have also been carried out.

On Asymptotic Properties of Solutions for Differential Equations of Neutral Type

On Asymptotic Properties of Solutions for Differential Equations of Neutral Type

Electrokinetic properties of NaCl solution via molecular dynamics simulations with scaled-charge electrolytes.

Scaling ionic charges has become an alternative to polarizable force fields for representing indirect charge transfer effects in molecular simulations. In our work, we apply molecular dynamics simulations to investigate the properties of NaCl aqueous solutions in homogeneous and confined media. We compare classical integer- and scaled-charge force fields for the ions. In the bulk, we validate the force fields by computing equilibrium and transport properties and comparing them with experimental data. Integer-charge ions overestimate dielectric saturation and ionic association. Both force fields present an excess in ion-ion correlation, which leads to a deviation in the ionic conductivity at higher ionic strengths. Negatively charged quartz is used to simulate the confinement effect. Electrostatic interactions dominate counter-ion adsorption. Full-charge ions have stronger and more defined adsorption planes. We obtain the electroosmotic mobility of the solution by combining the shear plane location from non-equilibrium simulations with the ionic distribution from equilibrium simulations. From the Helmholtz-Smoluchowski equation, the zeta potential and the streaming potential coupling coefficient are computed. From an atomic-scale perspective, our molecular dynamics simulations corroborate the hypothesis of maximum packing of the Stern layer, which results in a stable and non-zero zeta potential at high salinity. The scaled-charge model representation of both properties is in excellent qualitative and quantitative agreement with experimental data. With our work, we demonstrate how useful and precise simple scaled-charge models for electrolytes can be to represent complex systems, such as the electrical double layer.

Qualitative properties of solutions to a nonlinear transmission problem for an elastic Bresse beam

We consider a nonlinear transmission problem for a Bresse beam, which consists of two parts, damped and undamped. The mechanical damping in the damping part is present in the shear angle equation only, and the damped part may be of arbitrary positive length. We prove the well-posedness of the corresponding system in energy space and establish the existence of a regular global attractor under certain conditions on the nonlinearities and coefficients of the damped part only. Besides, we study the singular limits of the problem under consideration when curvature tends to zero, or curvature tends to zero, and simultaneously shear moduli tend to infinity and perform numerical modeling for these processes.

On decay properties for solutions of the Zakharov–Kuznetsov equation

This work mainly focuses on spatial decay properties of solutions to the Zakharov–Kuznetsov equation. For the two- and three-dimensional cases, it was established that if the initial condition u0 verifies 〈σ⋅x〉ru0∈L2(σ⋅x≥κ), for some r∈N, κ∈R, being σ be a suitable non-null vector in the Euclidean space, then the corresponding solution u(t) generated from this initial condition verifies 〈σ⋅x〉ru(t)∈L2σ⋅x>κ−νt, for any ν>0. Additionally, depending on the magnitude of the weight r, it was also deduced some localized gain of regularity. In this regard, we first extend such results to arbitrary dimensions, decay power r>0 not necessarily an integer, and we give a detailed description of the gain of regularity propagated by solutions. The deduction of our results depends on a new class of pseudo-differential operators, which is useful for quantifying decay and smoothness properties on a fractional scale. Secondly, we show that if the initial data u0 has a decay of exponential type on a particular half space, that is, ebσ⋅xu0∈L2(σ⋅x≥κ), then the corresponding solution satisfies ebσ⋅xu(t)∈Hpσ⋅x>κ−t, for all p∈N, and time t≥δ, where δ>0. To our knowledge, this is the first study of such property. As a further consequence, we also obtain well-posedness results in anisotropic weighted Sobolev spaces in arbitrary dimensions.Finally, as a by-product of the techniques considered here, we show that our results are also valid for solutions of the Korteweg–de Vries equation.

Anti-turbulent efficiency of oil-soluble polymer solutions and colloid systems flowing through cylindrical channel

Relevance. The use of anti-turbulent additives for transporting hydrocarbon liquids through main pipelines allows reducing significantly the energy consumption of pumping power stations. Aim. Comparative analysis of the anti-turbulent efficiency of high-molecular polymers and compositions of surfactants. Methods. Laboratory-scale experimentation aimed to study the flow of dilute polymer solutions and dispersed surfactant systems through a cylindrical channel of a turbulent rheometer. Results. The author has carried out the comparative experimental studies of the anti-turbulent efficiency of extremely dilute solutions of polymers and colloidal systems. The results were obtained that suggest a higher anti-turbulent efficiency of high-molecular-weight polymers compared to micellar surfactant systems. Solutions of high molecular weight polybutadiene and aluminum polyhydroxydicarboxylates in gasoline were used as samples for the experimental comparison of hydrodynamic efficiency. The paper describes the laboratory setup, on which the studies were carried out, and introduces the formulas used for quantitative calculations. The structure of polymer solutions and colloidal systems is considered and a theoretical explanation is given for the preferential use in industrial practice of high-molecular polymers in extremely low concentrations in real pipelines. It was found out that the mechanisms of degradation of antiturbulent properties of polymer solutions and dispersed surfactant systems are different. This is due to the difference in the structure of macromolar coils of polymer with an immobilized solvent and that of micelles from low molecular amphiphilic compounds. The paper introduces the arguments that explain the degradation of the antiturbulent properties of polymers not by the destruction of carbon-chain macromolecules, but by decomposition in a turbulent flow of the original large associates, consisting of a large number of chains, into individual and smaller macromolecular coils with an immobilized solvent.

Chemical Composition and Properties of Water-Methanol Solution of Formaldehyde

By reacting paraform with methanol and water at concentrations of 10.8, 11.6 and 22.7 mol/l in the presence of catalytic quantities of monoethanolamine, a method was developed for obtaining a bactericide that, at a concentration of 500 mg/l, completely inhibits the formation of hydrogen sulfide in an accumulative culture of planktonic form of sulfate-reducing bacteria with a quantity of 106 cells/ml. The composition of the resulting bactericide, its effectiveness and corrosion properties were studied. Using scanning electron microscopy using a system for energy-dispersive microanalysis, it was shown that the corrosion products formed during the corrosive action of the bactericide on St-20 steel are iron oxides.

Stability of the Global Weak Axisymmetric Solution to the Quantum Euler System with Vorticity in Dimension d=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$d=2$\\end{document}

We consider the stability of the global weak solution of the Quantum Euler system in two space dimensions. More precisely, we establish compactness properties of global finite energy weak solution for large initial data provided that these are axisymmetric. The main novelty is that the initial velocity is not necessary irrotational when the density is not vanishing, our main argument is based on the Madelung transform which enables us to prove new Kato estimates on the irrotational part of the velocity.

Existence and properties of soliton solution for the quasilinear Schrödinger system

Abstract In this article, we consider the following quasilinear Schrödinger system: − ε Δ u + u + k 2 ε [ Δ ∣ u ∣ 2 ] u = 2 α α + β ∣ u ∣ α − 2 u ∣ v ∣ β , x ∈ R N , − ε Δ v + v + k 2 ε [ Δ ∣ v ∣ 2 ] v = 2 β α + β ∣ u ∣ α ∣ v ∣ β − 2 v , x ∈ R N , \left\{\begin{array}{ll}-\varepsilon \Delta u+u+\frac{k}{2}\varepsilon \left[\Delta \hspace{-0.25em}{| u| }^{2}]u=\frac{2\alpha }{\alpha +\beta }{| u| }^{\alpha -2}u{| v| }^{\beta },& x\in {{\mathbb{R}}}^{N},\\ -\varepsilon \Delta v+v+\frac{k}{2}\varepsilon \left[\Delta \hspace{-0.25em}{| v| }^{2}]v=\frac{2\beta }{\alpha +\beta }{| u| }^{\alpha }{| v| }^{\beta -2}v,& x\in {{\mathbb{R}}}^{N},\end{array}\right. where ε > 0 , k < 0 \varepsilon \gt 0,k\lt 0 are real constants, N ≥ 3 N\ge 3 , α , β \alpha ,\beta are integers multiple of constant 2. By using the Mountain Pass Theorem in a suitable Orlicz space proposed by Abbas Moameni [Existence of soliton solutions for a quasilinear Schrödinger equation involving critical exponent in R N {{\mathbb{R}}}^{N} , J. Differential Equations 229 (2006), 570–587], we proved the existence of soliton solution ( u ε , v ε ) \left({u}_{\varepsilon },{v}_{\varepsilon }) for the above system, and ( u ε ( x ) , v ε ( x ) ) → ( 0 , 0 ) ({u}_{\varepsilon }\left(x),{v}_{\varepsilon }\left(x))\to \left(0,0) as ∣ ε ∣ → 0 | \varepsilon | \to 0 .

New piperidinium surfactants with carbamate fragments as effective adjuvants in insecticide compositions based on imidacloprid.

Surfactants, particularly non-ionic ones, are widely used as adjuvants in pesticide formulations due to their ability to maintain pesticide effectiveness without changing solution properties, such as pH. While non-ionic surfactants are generally low-toxic, stable, and excellent dispersants with high solubilization capabilities, they may be less effective than cationic surfactants, which offer superior surface activity, transport properties, and antimicrobial action. This study investigates the efficacy of new piperidinium surfactants with carbamate fragments as adjuvants in insecticide formulations containing imidacloprid. The efficacy of these formulations is being assessed against greenhouse whitefly, a pest known to harm cultivated and ornamental flowering plants. The aggregation behavior of piperidinium surfactants containing carbamate fragments was investigated, and their wetting effect was evaluated. Synthesized surfactants have lower CMC values compared to their methylpiperidinium analogue. The effect of piperidinium surfactants on the insecticide concentration on the surface and inside tomato leaves was assessed using spectrophotometric methods. It was found that the introduction of piperidinium surfactants with carbamate fragment at a concentration of 0.1% wt. allows for decrease in lethal concentration of imidacloprid up to 10 times, thereby testifying the marked increase in the effectiveness of imidacloprid against the greenhouse whitefly insect pest (Trialeurodes vaporariorum). It was shown that the main factors responsible for the enhanced efficacy of the insecticide were the ability of the surfactant to increase the concentration of imidacloprid on the leaf surfaces and improve their penetration into the plant. The presented work employed a comprehensive approach, which significantly increases the generalizability of the results obtained and provides the ability to predict the effect and target selection of adjuvants. © 2024 Society of Chemical Industry.

Rogue wave, lump, kink, periodic and breather-like solutions of the (2+1)-dimensional KdV equation

In this paper, the ([Formula: see text])-dimensional KdV equation is investigated by using the bilinear neural network method (BNNM). We construct six neural network models, extending beyond single hidden layer models to create deeper and broader network structures (e.g. [3-3-1], [3-4-1], [3-1-3-1], [3-4-1-1], [3-2-2-1] and [3-2-3-1-1] models). Introducing specific activation functions into the neural network model enables the generation of various test functions, resulting in novel solutions for equations that include rogue wave solutions, lump-kink solutions, periodic soliton solution, breather-like solutions and lump solutions. The physical properties of these novel solutions are vividly depicted through three-dimensional plots, density plots, and curve plots. The findings contribute to a better understanding of the propagation behavior of shallow water waves.

Concentration of solutions for non-autonomous double-phase problems with lack of compactness

The present paper is devoted to the study of the following double-phase equation -div(|∇u|p-2∇u+με(x)|∇u|q-2∇u)+Vε(x)(|u|p-2u+με(x)|u|q-2u)=f(u)inRN,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} -\ ext {div}(|\ abla u|^{p-2}\ abla u+\\mu _{\\varepsilon }(x)|\ abla u|^{q-2}\ abla u)+V_{\\varepsilon }(x)(|u|^{p-2}u+\\mu _{\\varepsilon }(x)|u|^{q-2}u)=f(u)\\quad \ ext{ in }\\quad \\mathbb {R}^{N}, \\end{aligned}$$\\end{document}where N≥2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N\\ge 2$$\\end{document}, 1<p<q<N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1<p<q<N$$\\end{document}, q<p∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q<p^{*}$$\\end{document} with p∗=NpN-p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p^{*}=\\frac{Np}{N-p}$$\\end{document}, μ:RN→R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu :\\mathbb {R}^{N}\\rightarrow \\mathbb {R}$$\\end{document} is a continuous non-negative function, με(x)=μ(εx)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu _{\\varepsilon }(x)=\\mu (\\varepsilon x)$$\\end{document}, V:RN→R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V:\\mathbb {R}^{N}\\rightarrow \\mathbb {R}$$\\end{document} is a positive potential satisfying a local minimum condition, Vε(x)=V(εx)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V_{{{\\,\\mathrm{\\varepsilon }\\,}}}(x)=V({{\\,\\mathrm{\\varepsilon }\\,}}x)$$\\end{document}, and the nonlinearity f:R→R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f:\\mathbb {R}\\rightarrow \\mathbb {R}$$\\end{document} is a continuous function with subcritical growth. Under natural assumptions on μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu $$\\end{document}, V and f, by using penalization methods and Lusternik–Schnirelmann theory we first establish the multiplicity of solutions, and then, we obtain concentration properties of solutions.

Synergistic effects of selenium and zinc on Bletilla striata (Thunb.) Reichb. F. growth and polysaccharide antioxidation.

Selenium (Se) is a beneficial trace element for plants, while zinc (Zn) is a vital micronutrient. Bletilla striata (Thunb.) Reichb. F. is widely recognized as a medicinal herb. In this study, Se and Zn were introduced to determine the medicinal properties of B. striata. The plant's biomass, polysaccharides, Se and Zn contents, and the antioxidant properties of polysaccharide solutions were all examined. A notable increase in polysaccharide synthesis in B. striata tubers was observed following the application of 0.2 kg ha-1 of Se, and 1.0 kg ha-1 of Zn, either individually or in combination. Se and Zn content in polysaccharides were 3.33 to 3.77 mg kg-1 and 82.82 to 121.78 mg kg-1, at 1.0 kg ha-1 Se and 10.0 kg ha-1 Zn treatments, respectively. These values were 2.1-3.1 times and 1.8-2.8 times higher than those observed in control samples. Polysaccharide antioxidation has resulted in an increase in antioxidant activity as the concentration of polysaccharide solutions increased. The largest scavenging of 1, 1-diphenyl-2-picrylhydrazyl (DPPH) radicals and the most excellent reducingpower of the polysaccharide solutions were observed when a mixture of Se and Zn was applied at a rate of 1.0 kg ha-1 and 10.0 kg ha-1. The individual application of Se at 1.0 kg ha-1 and Zn at 10.0 kg ha-1 also resulted in significant DPPH radicals scavenging and reduced power. These data suggested that Se-Zn enriched B. striata is a new source of Se and Zn supplementation and an antioxidant resource.

Solid Solutions of Plastic/Ferroelectric Crystals: Toward Tailor-Made Functional Materials.

Plastic crystals that show ferroelectricity are highly promising materials for a wide range of applications. Their inherent remarkable malleability and highly symmetric cubic structures in the plastic crystal phase ensure that their ferroelectricity and related properties are retained in their bulk polycrystals. To develop functional materials based on such plastic/ferroelectric crystals, methods to tune their properties for specific applications are required. Here, we report the preparation of solid solutions of plastic/ferroelectric ionic crystals by mixing crystals with a common anion but different cations, or crystals with a common cation but different anions, which allows a continuous modification of the Curie temperature of the ferroelectric system over a range of 100 K. This adjustment of the Curie temperature allows the flexible tuning of the pyroelectric properties of the solid solutions, including a significant enhancement of room-temperature performance. The solid solutions also exhibit morphotropic phase boundaries in the composition-temperature phase diagrams, which shows an abrupt change in crystal structures with a variation of composition. This study showcases a simple and versatile property-tuning method that can be expected to pave the way for major progress in the development of materials based on plastic/ferroelectric crystals, which will eventually advance to the stage of pursuing tailor-made functional materials with desired properties.

Novel Solid‐State Fluorophores, a Series of Cyanostilbene‐Based Amorphous Molecular Materials

AbstractWe 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.

Impact of hydroxyethyl headgroup on long-chain quaternary ammonium cationic surfactants: Solubility, surface activities, self-assembly behaviors, and rheological properties

The incorporation of hydroxy groups into long-chain quaternary ammonium surfactants can enhance their solubility and confer other desirable properties; however, the systematic investigation on the solution properties and the influence of molecular structures was less documented. In this work, two saturated C18-tailed quaternary ammonium surfactants with dual hydroxyethyl moieties, namely N,N-bis(2-hydroxyethyl)-N-methyloctadecan-1-aminium iodide (HEOAI) and N,N-bis(2-hydroxypropyl)-N-methyloctadecan-1-aminium iodide (HPOAI), were designed and synthesized. We investigated and compared their Krafft temperature (Tk), surface activities, self-assembly behaviors, and rheological properties. Our findings demonstrate that the introduction of hydroxyethyl groups dramatically improves the solubility and surface activities. The Tk of HEOAI and HPOAI is approximately 50 °C lower than that of the corresponding surfactant octadecyl trimethylammonium iodide. Both surfactants exhibit lower critical micelle concentration and equilibrium surface tension compared to those of corresponding conventional quaternary ammonium surfactant. This should be ascribed to the formation of hydrogen bonds between hydroxyl groups and water molecules. Moreover, HPOAI shows even better solubility and surface activities than HEOAI does. Additionally, the presence of two more methyl groups for HPOAI enhances its ability to form worm-like micelles in pure water. However, HEOAI shows better salt and temperature resistance for maintaining stability of worm-like micelles. A solution containing 50 mM HEOAI with 10 % NaCl exhibits temperature tolerance up to around 80 °C, indicating potential application as fracturing fluid for shallow and medium oil/gas reservoirs. These findings contribute to designing surfactants with improved solubility and diverse properties.

Dynamic interplay: unveiling inelastic breather collisions and modulation instability enhancement in a periodically gained inhomogeneous fiber optic communication system across temporal frequencies

Examining the impact of inhomogeneity on the propagation of femtosecond ultrafast optical pulses in fiber, we delve into the realm of the modified Hirota nonlinear Schrödinger equation (NLS) with inhomogeneity of variable coefficients (MIH-vc). Employing the Hirota bilinear method, we derive two soliton solutions for the modified Hirota NLS equation and analyze the effect of variable coefficients. The dynamical properties of these soliton solutions come to light as we meticulously analyze the corresponding plots. In our exploration, a noteworthy revelation unfolds as we witness the inelastic collision between two breathers, unleashing profound changes in the trajectory of femtosecond pulses. Furthermore, we showcase a detailed modulation instability analysis, unraveling the gain spectrum for our theoretical model. Through graphical illustrations, we elucidate how inhomogeneous functions intricately shape the modulation instability (MI) gain spectrum. A groundbreaking observation surfaces as, for the first time, we discern the periodic gain enhancement in relation to Group Velocity Dispersion along the fiber and its dynamic interactions.

Analysis of cryopreservation media thermophysical characteristics after ultra-rapid cooling through differential scanning calorimetry

Cryoprotective agents play a critical role in minimizing cell damage caused by ice formation during cryopreservation. However, high concentrations of CPAs are toxic to cells and tissues. Required concentrations of CPAs can be reduced by utilizing higher cooling and warming rates, but insight into the thermophysical properties of biological solutions in the vitrification method is necessary for the development of cryopreservation protocols. Most studies on thermophysical properties under ultra-rapid cooling conditions have been qualitatively based on visualization. Differential scanning calorimetry methods are ideal for studying the behavior of biomaterials in various freezing conditions quantitatively and accurately, though previous studies have been predominantly restricted to slower cooling rates. Here, we developed an ultra-rapid cooling method for DSC that can achieve minimal cooling rates exceeding 2000 °C/min. We investigated the thermophysical vitrification behavior of ternary solutions of phosphate buffer saline (1X), dimethyl sulfoxide or glycerol and ice blocking polymers (X-1000 or Z-1000). We quantified the impact of solute concentration on ice crystal formation during rapid cooling. Our findings support the expectation that increasing the solute concentration reduces the amount of ice formation, including devitrification. Devitrification increases from 0 % to 40 % (v/v) Me2SO and then reduces significantly. The relative amounts of devitrification to the total ice formation are 0 %, 60 %, 0 % in 20 %, 40 %, 60 % (v/v) Me2SO, and 2 %, 48 %, 49 % in 20 %, 40 %, 60 % (v/v) glycerol, respectively. The results suggest that at low concentrations, such as below 20 % (v/v) for Me2SO or glycerol, increasing the warming rate after ultra-rapid freezing is not essential to eliminate devitrification. Furthermore, ice blocking polymers do not reduce ice formation substantially and cannot eliminate devitrification under ultra-rapid cooling conditions. In conclusion, our results provide insights into the impact of solute concentration on ice formation and devitrification during rapid cooling, which can be practical for optimizing cryopreservation protocols.