Behavior Of Solutions Research Articles

Note on the diffusive prey-predator model with variable coefficients and degenerate diffusion

It is of interest to understand effects of variable coefficients and degenerate diffusion on the longtime behaviors of solutions of reaction diffusion equations. Recently, Yang and Yao (2024) studied a classical prey-predator model and proved that the degradation of the diffusion coefficient of the prey and variable coefficients satisfying the appropriate conditions will not affect dynamical properties. In this note we shall simplify the proof of Yang and Yao (2024) and delete the condition (4).

High-Speed Fluctuation Analysis of Silver-Nanoparticle SERS in Solutions.

We analyzed the fluctuation of surface-enhanced Raman spectra with a temporal resolution of 25 ms using a conventional electron-multiplying charge-coupled device camera experimental setup. The signal-to-noise ratio of the spectra was improved using density-based spatial cluster analysis with noise. Silver nanoparticles (AgNPs) with different sizes were dispersed as surface-enhanced Raman spectroscopy platforms in violet aqueous solutions. The movement of AgNPs and the fluctuation of the spectra were characterized. The fluctuation (signal ON and OFF) was evaluated on the basis of the time intervals between ON and OFF timing. The behavior of each AgNP solution was explained by a two-dimensional random walk model, which means that the phenomenon was mainly governed by the Brownian motion of the AgNPs in the solution. The fluctuation was also compared among three different Raman modes, one of which showed anomalous behavior.

Small scale model for predicting transportation-induced particle formation in biotherapeutics

Understanding protein adsorption and aggregation at the air-liquid interfaces of protein solutions is an important open challenge in biopharmaceutical, medical, and biotechnological applications, among others. Proteins, being amphiphilic, adsorb at the surface, partially unfold, and form a viscoelastic film through non-covalent interactions. Mechanical agitation of the surface can break this film up, releasing insoluble protein particles into the solution. These aggregates are usually highly undesirable and even toxic in cases, such as for biopharmaceutical application. Therefore, it is imperative to be able to predict the behavior of such solutions undergoing surface agitation during handling, usually transport or mixing. We apply the findings on the viscoelastic protein film, formed at the air-liquid interface, to the prediction of surface mediated aggregation in selected protein solutions of direct biopharmaceutical relevance. Our broad study of Brewster angle microscopy and aggregation monitoring across multiple size ranges by micro-flow imaging, light scattering, and size exclusion chromatography shows that formation of protein particles is driven by the adsorption rate as compared to the rate of surface turnover and that surface film dynamics in the quiescent phase directly affect aggregation. We demonstrate how these learnings can be directly applied to the design of a novel small scale biopharmaceutical stability study, simulating relevant transport conditions. More generally, we show the impact of adsorption dynamics at the air-liquid interface on the stability of a distinct protein solution, as a general contribution to understanding different colloidal and biological interfacial systems.

Unlocking the charge efficiency of γ’-V2O5 for Na-ion battery through a solution synthesis technique

In this study, the γ’-V2O5 cathode material was prepared through a solution synthesis technique leading to homogeneous, fine and porous particles 100–200 nm in size. This successful preparation allows to overcome the huge drawback of the microsized material in terms of charge efficiency and to take benefit of the attractive Na insertion properties of γ’-V2O5, i. e. a significant available capacity of 145 mAh g- 1, a high working potential of about 3.25 V vs. Na+/Na, an excellent charge efficiency, a high-rate capability and good cycle life. A detailed structural study upon Na insertion/extraction shows that the proposed nanosizing approach promotes a homogeneous Na solubility and solid solution behavior in a wider composition range (0.4 < x ≤ 1 in γ-NaxV2O5) compared to the results previously reported for solid-state synthesized γ’-V2O5. Furthermore, highly reversible structural changes are evidenced. Key kinetic parameters governing the Na insertion-extraction reaction are discussed thanks to an impedance spectroscopy study revealing a faster Na diffusivity in the one-phase region. The obtained results allow a comprehensive understanding of the enhanced performance exhibited by the present sub-micronic γ’-V2O5 material.

Multi-objective grounding system optimisation using NSGA-II

This study investigates the optimisation of grounding infrastructure in substations by implementing the philosophy of the multi-objective algorithm NSGA-II Elite. A complete description of the operating scheme and the characteristic mechanisms that support the behaviour and development of optimal Pareto solutions is provided. A detailed comparison was made with the optimisation method used in the GMAT program of Aplicaciones Tecnológicas, based on a semi-optimization process derived from the correlation of semi-precision optimisation solutions. The results show that multi-objective optimisation using NSGA-II results in a significant cost reduction compared to the semi-optimization method, although the computational time required to reach the final solution increases significantly. This approach allows a more adequate understanding of optimising the terrestrial substation grid. It highlights its ability to generate more cost-effective and performance-efficient solutions by carefully considering the computing time required.

Two-species model for nonlinear flow of wormlike micelle solutions. Part I: Model

We develop a rheological model to approximate the nonlinear rheology of wormlike micelles using two constitutive models to represent a structural transition at high shear rates. The model is intended to describe the behavior of semidilute wormlike micellar solutions over a wide range of shear rates whose parameters can be determined mainly from small-amplitude equilibrium measurements. Length evolution equations are incorporated into reactive Rolie-Poly entangled-polymer rheology and dilute reactive-rod rheology, with a kinetic exchange between the two models. Although the micelle length is remarkably reduced during flow, surprisingly, we propose that they are not shortened by stress-enhanced breakage, which remains thermally driven. Instead, we hypothesize that stretching energy introduces a linear potential that decreases the rate of recombination and reduces the mean micelle length. This stress-hindered recombination approach accurately describes transient stress-growth upon start-up shear flow, and it predicts a transition of shear viscosity and alignment response observed at high shear rates. The proposed mechanism applies only when self-recombination occurs frequently. The effect of varying the relative rate of self-recombination on the rheology of wormlike micelles at high shear rates is yet to be explored.

Existence and Uniqueness of Homogeneous Linear Equation Solutions in Supertropical Algebra

This research investigates the existence and uniqueness of solutions to homogeneous linear equations in supertropical algebra. We analyze the structure of supertropical matrices to identify the conditions in which nontrivial solutions exist for the system of equations A⊗𝒙 ⊨ 𝜀, where A is a matrix over a supertropical semiring and x is a vector. By applying determinant-based criteria, we demonstrate how tropical and supertropical values influence the solution space. The research applies theorems that determine the presence of trivial and nontrivial solutions and uses examples to illustrate practical methods for solving homogeneous matrix systems. This highlights the distinct characteristics of supertropical algebra compared to classical linear algebra. Our findings provide a deeper insight into solution behaviors in supertropical systems, paving the way for further research in tropical mathematics.

Type-2 fuzzy initial value problems under granular differentiability

This article investigates type-2 fuzzy initial value problems and introduces a novel strategy that capitalises on granular differentiability. Incorporating type-2 fuzzy numbers to depict the problem’s uncertainty may be advantageous from a practical standpoint. This work employs triangularly perfect quasi type-2 fuzzy numbers (TPQT2FNs) and defines the granular differentiability of TPQT2FN-valued functions. In addition, the solution approach for initial value problems with type-2 fuzzy initial conditions is discussed in the context of granular differentiability by transforming the type-2 fuzzy problem into a type-1 fuzzy problem using the lower membership function (LMF) and upper membership function (UMF) concepts. A couple of numerical examples are then examined to determine the applicability of the proposed method, and comparisons are made with existing type-2 fuzzy results and, in a special case, type-1 fuzzy results. In order to aid readers’ comprehension and study the behaviour of the numerical solution, three-dimensional graphical results are also shown.

Global existence and asymptotic behavior of affine solutions to Navier–Stokes equations in ℝN with degenerate viscosity and free boundary

Global existence and asymptotic behavior of affine solutions to Navier–Stokes equations in ℝN with degenerate viscosity and free boundary

A singular system involving mixed local and non-local operators

This article sets forth results on the existence, non-existence, uniqueness, and regularities properties, as well as boundary behavior of solutions for singular systems involving mixed local and non-local elliptic operators (see System (S) below). More precisely, we first establish a new weak comparison principle for a singular equation. Afterward, we discuss the non-existence of positive classical solutions, as well as construct suitable ordered pairs of sub-solutions and super-solutions. This allows us to obtain the existence of a pair of positive weak solutions for System (S) by employing Schauder’s fixed-point theorem in the associated conical shell. Finally, we adapt a method of Krasnoselsky to establish the uniqueness of such a positive pair of solutions.

Investigation of pitting corrosion of 304L stainless steel in algerian manufacturing

Stainless steel structures are subjected to gradual deterioration of their fundamental qualities when subjected to both mechanical stress and harsh conditions. The objective of this work is to examine the influence of tension-induced cold deformation on the localized roughness corrosion of 304L steel in a 3% NaCl solution, which mimics the conditions of saltwater. The samples underwent corrosion testing using standardized and deformed tensile specimens of algerian industrial manufacturing at different deformation rates: 2.18%, 3.63%, 10.90%, and 16.36%. The results, which encompassed corrosion susceptibility, pitting tendencies, and repassivation potentials, were compared and examined in relation to the deformation rate. The findings suggest that when the deformation rates increase, all of these potentials decrease, except for the roughness potential, which shows a considerable decrease. This decline indicates a reduction in the material's ability to resist corrosion. The main reasons why stainless-steel samples exposed to the phenomenon of corroded pits fail in Algerian industrial manufacturing are directly related to their resistance and strength characteristics, which in turn affect the mechanical behavior of 304L steel and its electrochemical behavior in aggressive solutions.

The asymptotic behavior of constant sign and nodal solutions of [formula omitted]-Laplacian problems as [formula omitted] goes to 1

In this paper we study the asymptotic behavior of solutions to the (p,q)-equation −Δpu−Δqu=f(x,u)inΩ,u=0on∂Ω,as p→1+, where N≥2, 1<p<q<1∗≔N/(N−1) and f is a Carathéodory function that grows superlinearly and subcritically. Based on a Nehari manifold treatment, we are able to prove that the (1,q)-Laplace problem given by −div∇u|∇u|−Δqu=f(x,u)inΩ,u=0on∂Ω,has at least two constant sign solutions and one sign-changing solution, whereby the sign-changing solution has least energy among all sign-changing solutions. Furthermore, the solutions belong to the usual Sobolev space W01,q(Ω) which is in contrast with the case of 1-Laplacian problems, where the solutions just belong to the space BV(Ω) of all functions of bounded variation. As far as we know this is the first work dealing with (1,q)-Laplace problems even in the direction of constant sign solutions.

Using microfluidics to assess the elongational behavior of low concentration Carbopol solutions upon addition of polyethylene oxide

Using microfluidics to assess the elongational behavior of low concentration Carbopol solutions upon addition of polyethylene oxide

Predictive potentialities of the Quasi-Random Lattice model for electrolyte solutions, discussion and improvement strategies

This article focuses on the predictive potentialities of the Quasi-Random Lattice (QRL) model, developed for describing the activity behaviour of electrolytic solutions, and elaborates strategies for their improvement.First, the study critically discusses the computational-experimental procedure (previously published) for determining the QRL parameterization, whose convergence within few iterations is counterbalanced by known experimental issues concerning, in particular, the mean activity coefficient. An alternative procedure is proposed, that makes use of osmotic data at medium-high concentrations, so as to make QRL more interesting from a practical point of view.Second, the study explores the applicability of the model beyond the concentration ranges earlier considered. To this purpose, the solution density is evaluated in detail. Its thermodynamic relationship with the mean activity coefficient yields a parametric Abel Equation of the Second Kind valid in the medium-high range of concentrations. A further density equation is formulated, useful in the low-medium range, based on a classical power-series combined with appropriate analytical constraints to improve estimation and prediction methods.QRL theory, methods and procedures are applied to binary aqueous solutions at 25°C.

Characterization of macrocyclic peptide drug interactions with bile salts and biorelevant colloids via single amino acid mutations and 1H nuclear magnetic resonance (NMR) spectroscopy

There is growing interest in the oral delivery of poorly permeable peptide drugs; however, the effect of biorelevant colloids found in the aqueous gastrointestinal environment on peptide drug solution behavior has been largely understudied. In this work, we detail the molecular level interactions between octreotide, a water-soluble macrocyclic peptide drug, and biorelevant colloids, i.e. bile salt micelles and bile salt-phospholipid mixed micelles, via dialysis membrane flux experiments and proton nuclear magnetic resonance (1H NMR) spectroscopy. A modified alanine scan was employed to generate eight mutated octreotide analogs; the impact of individual amino acid mutations on peptide dialysis membrane flux rates in micellar (trihydroxy and dihydroxy) bile salt solutions as well as fasted state simulated intestinal fluid (FaSSIF) and fed state simulated intestinal fluid (FeSSIF) was evaluated and compared against the parent peptide, octreotide. We show that octreotide interacts more strongly with dihydroxy bile salt micelles than trihydroxy bile salt micelles in solution, and in FaSSIF/FeSSIF media, octreotide mainly interacts with the phospholipid component. These interactions are largely mediated by hydrophobic interactions of octreotide's aromatic residues as well as electrostatic interactions between octreotide's basic Lys residue and terminal amine.

The existences and asymptotic behavior of solutions to stochastic semilinear generalized Rayleigh–Stokes equation with delays

We consider a functional stochastic delay semilinear Rayleigh–Stokes equation involving Riemann–Liouville derivative. Our aim is using the resolvent theory, fixed point argument to prove the global solvability and gives some sufficient conditions to ensure the asymptotic stability of mild solutions in the mean square moment.

Investigation of solution behavior of Differential Equations by Sumudu methods of random complex Partial Differential Equations

In this study, solutions of random complex partial differential equations were found using the two-dimensional Sumudu transformation method(STM). The initial conditions of a deterministic equation or the non-homogeneous part of the equation are transformed into random variables to obtain a random complex partial differential equation. With the help of the properties of two-dimensional Sumudu and inverse Sumudu transformation, an approximate analytical solution of a complex partial differential equation with random constant coefficients was obtained by selecting a random variable with an initial condition of Normal and Gamma distribution. The probability characteristics of the resulting solutions, such as expected value and variance, were obtained and graphically shown with the help of the Maple package program.

Determinants of adoption of climate resilient agricultural solutions

CONTEXTClimate change poses significant challenges to agricultural productivity, crop yield and overall resilience of farming system, particularly in mountainous regions. In a mountainous coutry like Nepal, where agriculture is a crucial livelihood for a substantial population, the Climate Resilient Agricultural (CRA) solutions are imperative. These solutions aim to enhance the sustainability of water, reduce reliance on pesticides and chemical fertilizers, and increase farm productivity and income. However, understanding the factors influencing farmers' decisions to adopt or reject such solutions remains a critical knowledge gap. OBJECTIVESThis study investigates the socio-psychological and socio-demographic determinants affecting the adoption of climate-resilient agricultural solutions. METHODSThis study uses the theory of planned behavior and a mixed-method approach to conduct household surveys with farmers, Key Informant Interviews with experts and implementing partners, and Focus Group Discussions with farmers' groups. Responses to behavior-related questions were analyzed using Partial Least Square Structural Equation Modeling (PLS-SEM), and the factors influencing the farmers' adoption behavior were identified using binary logistic regression. RESULTS AND CONCLUSIONSThe result based on a limited sample size indicates that farm characteristics and farmers' perceived behavior control significantly influence the adoption and continuation behavior of CRA solutions. In conclusion, fostering awareness, capacity building, and skill development and establishing both market and non-market incentives are essential for improving the adoption of new solutions for climate resilience in agriculture, however, the in-depth research is recommended to better understand the adoption behavior within specific farming systems. SIGNIFICANCEThe findings of this research offer valuable insights for policymakers and development practitioners striving to promote the widespread adoption of CRA solutions in farming communities. It will help to develop targeted strategies and policies that effectively support the integration of these solutions into agricultural practices, ultimately enhancing the resilience of the farming system in the face of climate change.

On examining the predictive capabilities of two variants of the PINN in validating localized wave solutions in the generalized nonlinear Schrödinger equation

We introduce a novel neural network structure called strongly constrained theory-guided neural network (SCTgNN), to investigate the behaviour of the localized solutions of the generalized nonlinear Schrödinger (NLS) equation. This equation comprises four physically significant nonlinear evolution equations, namely, the NLS, Hirota, Lakshmanan–Porsezian–Daniel and fifth-order NLS equations. The generalized NLS equation demonstrates nonlinear effects up to quintic order, indicating rich and complex dynamics in various fields of physics. By combining concepts from the physics-informed neural network and theory-guided neural network (TgNN) models, the SCTgNN aims to enhance our understanding of complex phenomena, particularly within nonlinear systems that defy conventional patterns. To begin, we employ the TgNN method to predict the behaviour of localized waves, including solitons, rogue waves and breathers, within the generalized NLS equation. We then use the SCTgNN to predict the aforementioned localized solutions and calculate the mean square errors in both the SCTgNN and TgNN in predicting these three localized solutions. Our findings reveal that both models excel in understanding complex behaviour and provide predictions across a wide variety of situations.

On the analysis and deeper properties of the fractional complex physical models pertaining to nonsingular kernels.

This study solves the coupled fractional differential equations defining the massive Thirring model and the Kundu Eckhaus equation using the Natural transform decomposition method. The massive Thirring model is a dynamic component of quantum field theory, consisting of a coupled nonlinear complex differential equations. Initially, we study the suggested equations under the fractional derivative of Caputo-Fabrizio. The Atangana-Baleanu derivative is then used to evaluate the comparable equations. The results are significant and necessary for exploring a range of physical processes. This paper uses modern approach and the fractional operators in this situation to develop satisfactory approximations to the offered problems. The proposed approach combines the natural transform technique with the efficient Adomian decomposition scheme. Obtaining numerical findings in the form of a fast-converge series significantly improves the scheme's accuracy. Some graphical plot distributions are presented to show that the present approach is very simple and straightforward. We performed a fractional order analysis of assumed phenomena to demonstrate and validate the effectiveness of the future technique. The behaviour of the approximate series solution for several fractional orders is shown visually. Additionally, the nature of the derived outcome has been observed for various fractional orders. The derived results demonstrate how simple and efficient the proposed method is to apply for analysing the behaviour of fractionally-order complex nonlinear differential equations that arise in related fields of engineering and science.