Behavior Of Solutions Research Articles

Local behavior for solutions to anisotropic weighted quasilinear degenerate parabolic equations

Local behavior for solutions to anisotropic weighted quasilinear degenerate parabolic equations

Neutral Emden–Fowler Differential Equation of Second Order: Oscillation Criteria of Coles Type

In this work, we study the asymptotic and oscillatory behavior of solutions to the second-order general neutral Emden–Fowler differential equation (avηxvz′v)′ + qvFxgv = 0, where v≥v0 and the corresponding function z = x + px∘h. Besides the importance of equations of the neutral type, studying the qualitative behavior of solutions to these equations is rich in analytical points and interesting issues. We begin by finding the monotonic features of positive solutions. The new properties contribute to obtaining new and improved relationships between x and z for use in studying oscillatory behavior. We present new conditions that exclude the existence of positive solutions to the examined equation, and then we establish oscillation criteria through the symmetry property between non-oscillatory solutions. We use the generalized Riccati substitution method, which enables us to apply the results to a larger area than the special cases of the considered equation. The new results essentially improve and extend previous results in the literature. We support this claim by applying the results to an example and comparing them with previous findings. Moreover, the reduction of our results to Euler’s differential equation introduces the well-known sharp oscillation criterion.

Unexpected tunable photoluminescence and emission mechanism during the gradual increase of cyclic glucose units

Excitation-dependent (λex-dependent) emission is one of the most common emission characteristics of nonconventional luminophores. Previously, we have reported D-xylose crystals has an obvious λex-dependent color tunable persistent room temperature phosphorescence (p-RTP) from blue to green, but its p-RTP emission at long wavelength is very weak. To further explore this attractive multicolor p-RTP behavior, and to enhance its tunability, the photoluminescence (PL) behavior of three common cyclodextrins (CDs), namely α-CD, β-CD and γ-CD, including solution and single crystals, were studied. Their single crystals demonstrate λex-dependent multicolor p-RTP properties in the order of β-CD>α-CD>γ-CD, rather than the strongest with the least glucose units (α-CD). Among them, the λex-dependent tunable p-RTP of β-CD and α-CD is superior to that of D-(+)-xylose single crystal. The above unexpected phenomena could be explained reasonably through detailed single crystal structure analysis and theoretical calculations. The emission behavior of solution and single crystals of CDs can be reasonably explained by the clustering-triggered emission (CTE) mechanism. Furthermore, CD-based covalent organic frameworks (COF) and supramolecules are readily fabricated, which own significantly enhanced p-RTP emission. Due to the intriguing PL property as well as hydrophilic rim and low biotoxicity of CDs, successful imaging of HCT116 cells and encryption applications were demonstrated. It is believed that the intrinsic PL properties of CDs, especially their regularly adjustable multicolor p-RTP that varies with the number of glucose units, have significant guidance for the development of a series of multicolor luminescent materials.

Biopolymer-enhanced delivery of reactive sulfide reagents for in-situ mercury remediation of heterogeneous contaminated soils

Mercury pollution from natural and anthropogenic sources demands effective remediation. This study focuses on optimizing a chemical stabilization approach using sulfur-containing compounds to create stable mercury sulfide (HgS) and immobilize elemental mercury in polluted soils. We propose using xanthan gum biopolymer to enhance the in-situ delivery of sulfide microparticles, overcoming soil heterogeneities due to its non-Newtonian behavior. Stability tests indicated that increased biopolymer concentration enhances particle stability due to the viscous and shear-thinning behavior of the polymer solutions. Various combinations (12 solutions) of xanthan polymer, pyrite microparticles, and sulfide-containing reagents were tested in batch experiments. Pyrite microparticles slightly reduced the xanthan solution's viscosity while retaining its non-Newtonian character. All solutions effectively transformed liquid mercury droplets into cinnabar, demonstrating successful mercury stabilization. Notably, solutions containing PIAX and SIPX, xanthate organosulfur compounds, significantly reduced the dissolved concentration of elemental mercury. Column experiments demonstrated xanthan gum's superior performance for in-situ injection of pyrite microparticles and sulfide mixtures into the soil compared to conventional water injection. At a polymer concentration of 4 g/L, a stable displacement front and an 88 % recovery of the initially injected particle-suspension density were achieved. The combined effects of xanthate's floating behavior and xanthan gum's shear-thinning nature substantially enhanced the delivery of pyrite microparticles in porous media for soil mercury remediation. This combination reduced the aqueous elemental mercury concentration in artificially polluted sand by up to 97 %, particularly with the xanthate organosulfur compound, PIAX. Xanthate has a higher potential to react with elemental mercury to form cinnabar compared to sodium thiosulfate. Additionally, the pyrite microparticles, rendered hydrophobic in xanthate solutions, integrated into the mercury droplets, forming a black paste. This study introduces a promising approach for efficient elemental mercury stabilization in contaminated soils by integrating biopolymers, reactive soluble compounds, and pyrite microparticles for sustainable decontamination.

Dynamic behavior of vector solutions of a class of 2-D neutral differential systems

Dynamic behavior of vector solutions of a class of 2-D neutral differential systems

Evaluating Imide-Based Mass Spectrometry-Cleavable Cross-Linkers for Structural Proteomics Studies.

Disuccinimidyl dibutyric urea (DSBU) is a mass spectrometry (MS)-cleavable cross-linker that has multiple applications in structural biology, ranging from isolated protein complexes to comprehensive system-wide interactomics. DSBU facilitates a rapid and reliable identification of cross-links through the dissociation of its urea group in the gas phase. In this study, we further advance the structural capabilities of DSBU by remodeling the urea group into an imide, thus introducing a novel class of cross-linkers. This modification preserves the MS cleavability of the amide bond, granted by the two acyl groups of the imide function. The central nitrogen atom enables the introduction of affinity purification tags. Here, we introduce disuccinimidyl disuccinic imide (DSSI) as a prototype of this class of cross-linkers. It features a phosphonate handle for immobilized metal ion affinity chromatography enrichment. We detail DSSI synthesis and describe its behavior in solution and in the gas phase while cross-linking isolated proteins and human cell lysates. DSSI and DSBU cross-links are compared at the same enrichment depth to bridge these two cross-linker classes. We validate DSSI cross-links by mapping them in high-resolution structures of large protein assemblies. The cross-links observed yield insights into the morphology of intrinsically disordered proteins and their complexes. The DSSI linker might spearhead a novel class of MS-cleavable and enrichable cross-linkers.

Insights into mechanisms of MALT1 allostery from NMR and AlphaFold dynamic analyses

Mucosa-associated lymphoid tissue lymphoma-translocation protein 1 (MALT1) is an attractive target for the development of modulatory compounds in the treatment of lymphoma and other cancers. While the three-dimensional structure of MALT1 has been previously determined through X-ray analysis, its dynamic behaviour in solution has remained unexplored. We present here dynamic analyses of the apo MALT1 form along with the E549A mutation. This investigation used NMR 15N relaxation and NOE measurements between side-chain methyl groups. Our findings confirm that MALT1 exists as a monomer in solution, and demonstrate that the domains display semi-independent movements in relation to each other. Our dynamic study, covering multiple time scales, along with the assessment of conformational populations by Molecular Dynamic simulations, Alpha Fold modelling and PCA analysis, put the side chain of residue W580 in an inward position, shedding light at potential mechanisms underlying the allosteric regulation of this enzyme.

GCMe: Efficient Implementation of the Gaussian Core Model with Smeared Electrostatic Interactions for Molecular Dynamics Simulations of Soft Matter Systems.

In recent years, molecular dynamics (MD) simulations have emerged as an essential tool for understanding the structure, dynamics, and phase behavior of charged soft matter systems. To explore phenomena across greater length and time scales in MD simulations, molecules are often coarse-grained for better computational performance. However, commonly used force fields represent particles as hard-core interaction centers with point charges, which often overemphasizes the packing effect and short-range electrostatics, especially in systems with bulky deformable organic molecules and systems with strong coarse-graining. This underscores the need for an efficient soft-core model to physically capture the effective interactions between coarse-grained particles. To this end, we implement a soft-core model uniting the Gaussian core model with smeared electrostatic interactions that is phenomenologically equivalent to recent theoretical models. We first parametrize it generically using water as the model solvent. Then, we benchmark its performance in the OpenMM toolkit for different boundary conditions to highlight a computational speedup of up to 34 × compared to commonly used force fields and existing implementations. Finally, we demonstrate its utility by investigating how boundary polarizability affects the adsorption behavior of a polyelectrolyte solution on perfectly conducting and nonmetal boundaries.

Analytical solution of fractional oscillation equation with two Caputo fractional derivatives

Analytical solution of initial value problem for the fractional oscillation equation with two Caputo fractional derivatives , where the coefficients and orders satisfy and , is investigated by using the Laplace transform and complex inverse integral method on the principal Riemann surface. It is proved by using the argument principle that the characteristic equation has a pair of conjugated simple complex roots with a negative real part on the principal Riemann surface under the assumption that and are not both integers. Then three fundamental solutions, the unit impulse response, the unit initial displacement response, and the unit initial rate response, are derived analytically. Each of these solutions is expressed into a superposition of a classical damped oscillation decaying exponentially and a real Laplace integration decaying in a negative power law. Finally, the asymptotic behaviors of these analytical solutions for sufficiently large are determined as monotonous decays in a power of negative exponent.

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.

Oscillatory behavior of solutions of second-order non-linear differential equations with mixed non-linear neutral terms

This study primarily seeks to expand upon these developments by encompassing neutral differential equations of mixed type, incorporating both delay and advanced terms, particularly in the case of the canonical operator. The presented results are derived from the application of the comparison method, Riccati transformation, and integral averaging technique. These methodologies lead to substantial improvements and extensions of existing results found in the literature. Additionally, illustrative examples are provided to demonstrate the practical implications of the developed criteria.

The ion-activated attractive patchy particle model and its application to the liquid-vapor phase transitions.

Patchy particles are an intriguing subject of study and indeed a model system in the field of soft matter physics. In recent years, patchy particle models have been applied to describe a wide variety of systems, including colloidal crystals, macromolecular interactions, liquid crystals, and nanoparticle assemblies. Given the importance of the topic, rationalizing and capturing the basic features of these models is crucial to their correct application in specific systems. In this study, we extend the ion-activated attractive patchy particles model previously employed to elucidate the phase behavior of protein solutions in the presence of trivalent salts. Our extension incorporates the effect of repulsion between unoccupied and occupied binding sites, depicted as patches. Furthermore, we examine the influence of model parameters on the liquid-vapor coexistence region within the phase diagram, employing numerical methods. A deeper understanding of this model will facilitate a better comprehension of the effects observed in experiments.

Asymptotic behavior of Riemann solutions for the one-dimensional mean-field games in conservative form with the logarithmic coupling term

Construction of Riemann solutions for a hyperbolic system in conservative form arising from the one-dimensional mean-field games with the quadratic Hamiltonian and the logarithmic coupling term are provided in detail. Moreover, the delta shock formation is concretely analyzed from the limit of double-shock-solution as well as the emergence of vacuum state is also specifically discussed from the limit of double-rarefaction-solution when the coupling coefficient drops to zero. Accordingly, the remarkable cavitation and concentration phenomena can be closely observed and explored. Additionally, the numerical experiments are also presented in correspondence to authenticate the theoretical analysis results.

Actinium chelation and crystallization in a macromolecular scaffold

Targeted alpha therapy (TAT) pairs the specificity of antigen targeting with the lethality of alpha particles to eradicate cancerous cells. Actinium-225 [225Ac; t1/2 = 9.920(3) days] is an alpha-emitting radioisotope driving the next generation of TAT radiopharmaceuticals. Despite promising clinical results, a fundamental understanding of Ac coordination chemistry lags behind the rest of the Periodic Table due to its limited availability, lack of stable isotopes, and inadequate systems poised to probe the chemical behavior of this radionuclide. In this work, we demonstrate a platform that combines an 8-coordinate synthetic ligand and a mammalian protein to characterize the solution and solid-state behavior of the longest-lived Ac isotope, 227Ac [t1/2 = 21.772(3) years]. We expect these results to direct renewed efforts for 225Ac-TAT development, aid in understanding Ac coordination behavior relative to other +3 lanthanides and actinides, and more broadly inform this element’s position on the Periodic Table.

Phase separation behavior and CO2 absorption kinetic analysis of DETA/DEA/DMAC biphasic absorbent

Lower regeneration energy and superior cyclic capacity have enabled biphasic absorbents great potential in the area of flue gas CO2capture. The liquid film mass transfer coefficient(kL) is a vital parameter in the development of absorbents with efficient CO2 absorption mass transfer performance, while the phase separation behavior of biphasic solutions could be an essential factor for the absorption mass transfer and the stability of absorber. However, systemic kinetic research towards biphasic absorbents, especially the impact of phase separation behavior, is limited. In this study, a typical amide-based biphasic absorbent diethylenetriamine(DETA)/diethanolamine(DEA)/N, N-dimethylacetamide(DMAC) which has achieved great reduction in regeneration energy, was selected as the subject of kinetic investigation in a wetted wall column. The CO2 overall mass transfer coefficient(KG) of DETA/DEA/DMAC exceeded other biphasic solvents, blended amine solution, and 40% K2CO3 solution, with 3 times that of 40% K2CO3 solution. Moreover, various operational conditions including absorption temperature, gas flow rate, and water content of solution were taken into account to build a multiple-condition kinetic mechanism to offer guidance for biphasic absorbents. Furthermore, phase separation behavior was revealed as the main blame for the deterioration in the liquid film chemical mass transfer process of biphasic solvents in the CO2 absorption process, resulting in the kL of DETA/DEA/DMAC before phase separation decreased by 75.3% at the phase separation stage. Therefore, it is crucial to ensure that the CO2 loading of the solution entering absorber is lower than the phase separation point in applications. After phase separation, DETA/DEA/DMAC split into the organic and aqueous phases, the kL of the aqueous phase gradually exceeded that of the organic phase as CO2 loading increased for its higher chemical enhancement factor(E).

Dynamics of a delayed nonlocal reaction–diffusion heroin epidemic model in a heterogenous environment

To study the consumption of heroin in a heterogeneous environment, we propose and analyze a spatiotemporal model with a distributed delay. Using the spectral theory, we determine the basic reproduction number , which serves a threshold role. If , then the addiction‐free steady state is globally asymptotically stable while if , then there is at least one addictive steady state. Moreover, when , if one of the dispersal coefficients is zero, then there is only one addictive steady state, and it is globally asymptotically stable; if both diffusions of susceptible and addicted individuals are present, we cannot identify the temporal behavior of solutions, and hence, we study the asymptotic profile of addictive steady states when one of the dispersal coefficients tend to zero.

Gold-Thiolate Nanocluster Dynamics and Intercluster Reactions Enabled by a Machine Learned Interatomic Potential.

Monolayer protected metal clusters comprise a rich class of molecular systems and are promising candidate materials for a variety of applications. While a growing number of protected nanoclusters have been synthesized and characterized in crystalline forms, their dynamical behavior in solution, including prenucleation cluster formation, is not well understood due to limitations both in characterization and first-principles modeling techniques. Recent advancements in machine-learned interatomic potentials are rapidly enabling the study of complex interactions such as dynamical behavior and reactivity on the nanoscale. Here, we develop an Au-S-C-H atomic cluster expansion (ACE) interatomic potential for efficient and accurate molecular dynamics simulations of thiolate-protected gold nanoclusters (Aun(SCH3)m). Trained on more than 30,000 density functional theory calculations of gold nanoclusters, the interatomic potential exhibits ab initio level accuracy in energies and forces and replicates nanocluster dynamics including thermal vibration and chiral inversion. Long dynamics simulations (up to 0.1 μs time scale) reveal a mechanism explaining the thermal instability of neutral Au25(SR)18 clusters. Specifically, we observe multiple stages of isomerization of the Au25(SR)18 cluster, including a chiral isomer. Additionally, we simulate coalescence of two Au25(SR)18 clusters and observe series of clusters where the formation mechanisms are critically mediated by ligand exchange in the form of [Au-S]n rings.

Heat equation on the hypergraph containing vertices with given data

This paper is concerned with a multivalued ordinary differential equation governed by the hypergraph Laplacian, which describes the diffusion of “heat” or “particles” on the vertices of hypergraph. We consider the case where the heat on several vertices is manipulated internally by the observer, namely, are fixed by some given functions. This situation can be reduced to a nonlinear evolution equation associated with a time-dependent subdifferential operator, whose solvability has been investigated in numerous previous researches. In this paper, we give an alternative proof of the solvability in order to avoid some complicated calculations arising from the chain rule for the time-dependent subdifferential. As for results which cannot be assured by the known abstract theory, we also discuss the continuous dependence of solution on the given data and the time-global behavior of solution.

Long‐time asymptotics of solution for the fifth‐order modified KdV equation in the presence of discrete spectrum

AbstractWe investigate the Cauchy problem of an integrable focusing fifth‐order modified Korteweg–de Vries (KdV) equation, which contains the fifth‐order dispersion and relevant higher order nonlinear terms. The long‐time asymptotics of solution is established in the case of initial conditions that lie in some low regularity weighted Sobolev spaces and allow for the presence of discrete spectrum. Our method is based on a generalization of the nonlinear steepest descent method of Deift and Zhou. We show that the solution decomposes in the long time into three main regions: (i) an expanding oscillatory region where solitons and breathers travel with positive velocities, the leading order term has the form of a multisoliton/breather and soliton/breather–radiation interactions; (ii) a Painlevé region, which does not have traveling solitons and breathers, the asymptotics can be characterized with the solution of a fourth‐order Painlevé II equation; (iii) a region of breathers traveling with negative velocities. Employing a global approximation via PDE techniques, the asymptotic behavior of solution is extended to lower regularity spaces with weights.

Two-Dimensional Cu-Based MOF for Selective Staining of the Cellular Nucleus through Fluorescence Imaging and Selective Sorption of Dye Molecules in Aqueous Medium.

A two-dimensional copper-based metal-organic framework, [Cu(C23H14O6)(C10H8N2)2]·H2O·DMSO, 1, was synthesized using pamoic acid (C23H16O6) and 4,4'-bipyridine (C10H8N2) as an organic ligand and Cu(II) as a metal ion. Single-crystal structure X-ray diffraction studies of the as-synthesized compound showed a two- dimensional structure with free hydroxyl groups. Upon excitation at 370 nm, the aqueous dispersion of [Cu(C23H14O6)(C10H8N2)2]·H2O·DMSO, 1, showed emission centered at 525 nm resulting from the intraligand energy transfer. Fluorescence microscopic experiments using a human epithelioid cervix carcinoma HeLa cell line were carried out, clearly showing that our compound selectively stained the cellular nucleus. To utilize the porous nature of [Cu(C23H14O6)(C10H8N2)2]·H2O·DMSO, 1, its dye sorption behavior in aqueous solution was determined, and a high affinity for methylene blue (MB) dye was confirmed. Our synthesized compound sorbed 88% MB dye with an initial concentration of 32 mg L-1, and its sorption capacity for MB was found to be 29.79 mg g-1. The possible mechanism of the dye sorption behavior was discussed in terms of the size and charge of dye molecules with respect to molecular-level interactions between the framework and the dye molecules.