Saturated Equilibrium Research Articles

Epidemic models in well-mixed multiplex networks with distributed time delay

In this paper, we consider an epidemic model in well-mixed multiplex networks with distributed time delay. Specifically, the model consists of two layers of well-mixed networks in the physical and virtual worlds, respectively, where two diffusive processes interact and influence each other within the same individual. We assume that there is a distributed time delay for an individual to become infected, but no delay for an individual to transition from unawareness to awareness. Our main results are as follows: Let R0P and R0V represent the basic reproduction numbers in the physical and virtual worlds, respectively. First, we demonstrate that the disease will die out for any delay time, provided that R0P≤1 or 1<R0P≤R0V. The latter condition emphasizes the significance of effective information spreading in eradicating the disease. Secondly, in the case of R0P>max⁡{1,R0V}, we establish that the model exhibits an endemic and information saturated equilibrium, denoted as E3. Additionally, we show that the model is uniformly persistent, indicating the sustained outbreak of the disease.

Sequestration of chromium by Ananas comosus extract–coated nanotubes: synthesis, characterization, optimization, thermodynamics, kinetics, and antioxidant activities

AbstractHerein, a superior adsorbent was fabricated via immobilizing Ananas comosus juice extract on nanotubes (MWPJ) for the removal of chromium (VI) from simulated wastewater. The batch adsorption technique was used to establish the influence of solution pH, adsorbent dosage, solution temperature, initial Cr(VI) concentration, and contact time on the adsorption of chromium (VI). To comprehend the surface properties and to confirm chromium (VI) adsorption onto MWPJ and MWCNTs, TGA, SEM, and FTIR analyses were performed for MWPJ and MWCNTs before and after the adsorption process. These spectroscopic techniques revealed the temperature and surface characteristics responsible for the effectiveness of MWPJ. MWPJ and MWCNTs demonstrated optimum removal potential at solution pH 2, 0.05 g adsorbent dosage, and 180 min contact time. The MWPJ and MWCNTs had a maximum adsorption potential of 44.87 and 33.38 mg g−1 at 25 °C respectively. The reaction rate kinetics data for MWPJ and MWCNTs fitted well with Elovich and the pseudo-first-order kinetic model, respectively, while the saturated equilibrium data were best described by Freundlich isotherm. The thermodynamics analysis revealed that the uptake of Cr(VI) onto MWPJ and MWCNTs was a spontaneous and exothermic process. After five adsorption–desorption cycles of MWPJ, about 80% removal efficiency of Cr(VI) ions was sustained. Hence, MWPJ has demonstrated a superior capacity for practical applications in environmental remediation practice.

Particle deposition model for a fully developed turbulent channel flow

This study aims to develop a mathematical model for solid particle deposition under a fully-developed turbulent flow in a rectangular channel, considering the effect of the change in geometry over time. The present study introduces a mathematical approach to predict the equilibrium thickness/mass of the deposition, saturation and equilibrium times, and their corresponding non-dimensionalized parameters. Scaling analysis, and parametric study are reported. For a fixed Reynolds number Re, the particle deposition increases with non-dimensional relaxation time. In general, as more particles are deposited, the surface takes less time to become saturated and approach equilibrium faster. The saturation and equilibrium times decrease with an increase in non-dimensional particle relaxation time. For a fixed particle concentration, as the inlet velocity increases, the saturation and equilibrium time decreases, and the asymptotic deposited mass decreases.

Topological structures on saturated sets, optimal orbits and equilibrium states

In this paper, we investigate topological complexity of saturated set from the viewpoints of upper capacity entropy and packing entropy. We obtain that if a topological dynamical system $ (X, T) $ satisfies almost product property, then for each nonempty compact convex subset $ K $ of invariant measures, the following two formulas hold for the saturated set $ G_K $:$ \begin{equation*} h_{top}^{UC}(T, G_{K}) = h_{top}(T, X)\ \mathrm{and}\ h_{top}^{P}(T, G_{K}) = \sup\{h(T, \mu):\mu\in K\}, \end{equation*} $where $ h_{top}^{UC}(T, G_{K}) $ is the upper capacity entropy of $ T $ on $ G_{K}, $ $ h_{top}^{P}(T, G_{K}) $ is the packing entropy of $ T $ on $ G_{K}, $ and $ h(T, \mu) $ is the Kolmogorov-Sinai entropy of $ \mu $. As applications, for a transitive Anosov diffeomorphism on a compact manifold, we use the above results to quantify topological complexity of optimal orbits and equilibrium states for both real and matrix valued potentials.

The long view of triadic resonance instability in finite-width internal gravity wave beams

This article presents our exploration into how a finite-width internal gravity wave beam is modified by triadic resonance instability. We present both experimental and weakly nonlinear modelling to examine this instability mechanism, in which a primary wave beam generates two secondary wave beams of lower frequencies and shorter length scales. Through a versatile experimental set-up, we examine how this instability evolves over hundreds of buoyancy periods. Unlike predictions from previous zero-dimensional weakly nonlinear theory, we find that the wave does not monotonically approach a saturated equilibrium of triadic interactions; rather, the amplitudes and structures of the constituent beams continue to modulate without ever reaching a steady equilibrium. To understand this behaviour, we develop a weakly nonlinear approach to account for the spatiotemporal evolution of the amplitudes and structures of the beams over slow time scales and long distances, and explore the consequences using a numerical scheme to solve the resulting equations. Through this approach, we establish that the evolution of the instability is remarkably sensitive to the spatiotemporal triadic configuration for the system and how part of the observed modulations can be attributed to a competition between the linear growth rate of the secondary wave beams and the finite residence time of the triadic perturbations within the underlying primary beam.

Global R&D Location Strategy of Multinational Enterprises: an Agent-Based Simulation Modeling Approach

The global research and development (R&D) location strategy of multinational enterprises (MNEs) is examined using agent-based simulation (ABS) modeling. This study focuses on the positioning strategy of MNEs to understand the impact of their R&D location strategy. In ABS modeling, agents search for knowledge owners or universities in the global host market using Hotelling’s location model algorithm. We measure the result of increasing the number of entry agents from 2 to 121. Three types of equilibria are found in our agent-based simulation model: pure equilibrium, saturated equilibrium, and quasi-saturated equilibrium. Core locations attract MNEs, while peripheral countries in the global market are the least preferred. As a result, peripheral countries experience a paucity of foreign R&D investments. Even though emerging economies absorb foreign direct investment (FDI) inflows from MNEs, least-less developed countries (LLDC) may experience a dearth in FDI. Thus, the optimal location strategy of MNEs leads to economic disparities between the core and peripheral countries. This study suggests the need for developing official assistance to attract FDI inflows to LLDCs so that peripheral countries emerge as attractive global market destinations for MNEs.

Solid-liquid phase equilibrium of SOV-I2 in various pure and binary mixed solvents: Solubility determination, solvent effect, preferential solvation and model correlation

The solubility knowledge is important in the field of separation and purification of chemicals as well as quality control of drugs. In this work, the saturated phase equilibrium of SOV-I2 in ethanol, 1-butanol, acetone, methanol, 1-propanol, acetonitrile, toluene, 2-propanol, ethyl acetate, water, ethanol + water and acetone + water at a series of temperature of 278.15 K-318.15 K was constructed and the solubility data was measured by using isothermal saturation methods. The solvent effect evaluation, preferential solvation discussion and model correlation were used to explore the solubility behavior of SOV-I2. The solubility of SOV-I2 in mole fraction increased with the increasing of temperature. The experimental solubility data of SOV-I2 in mole fraction showed a subsequence in acetone > ethyl acetate > toluene > acetonitrile > methanol > ethanol > 1-propanol > 2-propanol > 1-butanol > water. For SOV-I2 + aqueous mixtures systems, the solubility data raised with the adding of co-solvents and no co-solvency phenomenon appeared in the dissolution process of SOV-I2 in two aqueous mixtures. The solvent effect was analyzed by KAT-LSER model which suggested that interaction of nonspecific dipolarity/polarizability played a dominant role in SOV-I2 dissolution. The solute–solvent interactions, accounted for>60%, were very important in dissolution of SOV-I2. Furthermore, the preferential solvation mechanism of SOV-I2 in two aqueous mixtures was discussed by IKBI method. The negative preferential solvation parameter (δx1,3) exhibited in the region of < x1 < 0.24 for ethanol (1) + water (2) mixtures and 0 < x1 < 0.21 for acetone (1) + water (2) mixtures. It suggested that SOV-I2 (3) was dissolved by water (2) preferentially in water-rich region. However, in other regions, the δx1,3 values were positive which indicated that SOV-I2 (3) was dissolved by co-solvents (1, ethanol or acetone) preferentially. In addition, the classical Apelblat, λh, Jouyban-Acree and Apelblat-Jouyban-Acree models were used to correlate the solubility data of SOV-I2. The correlation results showed that the greatest values of RAD and RMSD were 0.94% and 0.68 × 10-4 for pure solvent systems, and 2.10% and 2.14 × 10-4 for two aqueous mixtures systems, respectively. The evaluation indexes were quite small. In brief, these models showed a good applicability to experimental solubility data of SOV-I2.

Screen-Printed Gold Electrodes as Passive Samplers and Voltammetric Platforms for the Determination of Gaseous Elemental Mercury.

We present a methodology for the determination of gaseous elemental mercury (GEM). It is based on passive sampling of Hg on screen-printed gold electrodes (SPGEs), followed by the measurement of amalgamated mercury by square wave anodic stripping voltammetry. We have explored in detail the behavior of the SPGE electrode surface during the sampling process (by time-of-flight secondary ion mass spectrometry), the stability of the voltammetric signals, and the inter-electrode reproducibility, and obtained acceptable results. Adsorption of mercury onto the SPGE follows a nearly linear behavior until the sorbent becomes saturated (equilibrium phase) for different mercury concentrations, allowing to select a sampling time of 30 min for calibration. The theoretical behavior of the sampling system was modeled, considering the changes in the diffusive path length between the porous diffusive barrier and the adsorbed surface, L. Finally, we have tested two GEM calibration protocols. The first one is based on the measurement of the mercury stripping peak area, AHg, and the second one is based on the measurement of the mass of mercury, mHg, by standard additions. We found good correlation coefficients between the GEM concentration for both AHg (R2 = 0.9591) and mHg (R2 = 9615) in the range of 5.82 to 59.29 ng dm–3 GEM. Detection limits were 5.32 and 5.22 ng dm–3 for AHg and mHg, respectively. Our results open a new line of electroanalytical strategies for the determination of GEM in atmospheric samples.

An Analysis of Saturated Conditions in Hydrogen Peroxide Decontamination Applications.

This article discusses theoretical aspects of saturated vapor-liquid equilibrium for a hydrogen peroxide-water system at temperatures between 16°C and 30°C and humidities between 20% relative humidity to 65% relative humidity, common in pharmaceutical isolator decontamination applications. A discrepancy is pointed out between two competing sets of empirical relations published in the literature that are used to calculate saturated parameters. It is shown how the two published sets can result in four combinations of equations. The four sets of equations were compared to existing published data as well as new data from experiments conducted in this study, and it is shown that one set of relations consistently provided the best match to the experimental data. This set came from a hybrid combination of the previously published equations. This has practical implications for hydrogen peroxide sensors that rely on saturated theory for calibration. In addition, new empirical relations aimed at simplifying the calculation of relevant parameters such as hydrogen peroxide concentration, mole fraction of hydrogen peroxide in the condensed liquid, and relative humidity are presented. The concept of relative saturation is discussed and a new procedure for calculating this parameter during a decontamination cycle is presented, incorporating the results from our experiments. Together the updated theoretical framework and simplified empirical relationships can be used to estimate in a simple, direct, and accurate manner where a decontamination cycle is operating in relation to the 100% saturation level, at which point condensation is likely to form in the isolator. This provides a repeatable and objective measure, useful for monitoring and comparing decontamination cycles.

Modeling and experiment for effective diffusion coefficient of gas in water-saturated coal

The diffusion of gas in water-saturated porous media plays a significant role in CO2 geological sequestration and mine gas prevention and control. However, it is lack of an accurate model to calculate the effective diffusion coefficient of gas in a water-saturated coal core. In this work, an improved model was constructed to calculate the effective diffusion coefficient of gas in a water-saturated coal core by considering both the gas adsorption in residual pore and the gas dissolution in pore water. By using a PVT (Pressure-Volume-Temperature) test method, the calculation results of improved model are in the range of 1.03 × 10−12 ~ 30.40 × 10−12m2/s, which are 5 ~ 6 orders of magnitude lower than those calculated by traditional model, because the traditional model only considers the gas dissolution in pore water. Therefore, the results of improved model are more in line with the actual situation. Furthermore, the saturated moisture, equilibrium moisture and NMR experiments were carried out. Results shows that, the saturated moisture and equilibrium moisture decreases with the rising coal rank. The pore size changes from micropore/mesopore-dominated to micropores-dominated as the coal rank rise. In addition, the proportion of open porosity gradually reduces with the rising coal rank, while the closed porosity increases, indicating that the pore connectivity decreases with the growing coal rank. Finally, the influences of adsorbability, pore structure, pressure and liquid properties on the effective diffusion coefficient were analyzed.

State of uranyl arsenates MIAsUO6·nH2O (MI–H+, Li+, Na+, K+, Rb+, Cs+, NH4+) in aqueous solution

The state of uranyl arsenates with general formula MIAsUO6·nH2O, MI = H+, Li+, Na+, K+, Rb+, Cs+, NH4+ have been investigated in aqueous solutions. The pH ranges of existence of these compounds in aqueous solutions, transformation products and solubility of MIAsUO6·nH2O have been established. Solubility products, standard Gibbs free energies of the uranyl arsenates formation, speciation diagrams for uranium (VI) and arsenic (V) in saturated aqueous solutions and equilibrium solids have been calculated on the basis of the experimental data.

Experimental measurements of saturated vapor pressure and isothermal vapor-liquid equilibria for 1,1,1,2-Tetrafluoroethane (HFC-134a) + 3,3,3-trifluoropropene (HFO-1243zf) binary system

This work investigated saturated vapor pressure and isothermal vapor-liquid equilibrium (VLE) for 1,1,1,2-Tetrafluoroethane (HFC-134a) + 3,3,3-trifluoropropene (HFO-1243zf) binary system. The saturated vapor pressures of HFC-134a and HFO-1243zf ranging from (273.17–353.13) K, and VLE data at four temperatures (283.15, 293.15, 313.15, 323.14) K for the HFC-134a + HFO-1243zf system were measured by a static-analytical apparatus. The vapor pressure data of HFO-1243zf were regressed by a Wagner type equation and compared with existing literature data. The experimental VLE data of HFC-134a + HFO-1243zf system were correlated by Peng-Robinson (PR) equation of state (EOS) combined with van der Waals (vdW) mixing rules. The binary interaction parameters were obtained, and correlation deviation was acceptable. Azeotropic behavior can be found for the HFC-134a + HFO-1243zf system at measured temperatures. Our work provides fundamental thermodynamic properties of new mixed refrigerants which are crucial to evaluate their cycle performance and optimize the design of refrigeration system.

Highly efficient [C8mim][Cl] ionic liquid accompanied with magnetite nanoparticles and different salts for interfacial tension reduction

Abstract The 1-octyl-3-methylimidazolium chloride, [C8mim][Cl] ionic liquid (IL) was used as a novel surfactant in n-heptane/water system. The interfacial tensions (IFT) were measured and corresponding variations were investigated. An IFT reduction of 80.8% was appropriate under the IL CMC of about 0.1 mol·L−1 and stronger effects were achieved when magnetite nanoparticles and salts were present profoundly under alkaline pHs. The equilibrium IFT data were accurately simulated with the Frumkin adsorption model. Hereafter, the saturated surface concentration, equilibrium constant and interaction parameter were obtained and their variations were demonstrated. Further, emulsion stability and contact angle of oil/water interface over quartz surface were studied. The oil/water emulsion stability was hardly changed with nanoparticles; however, the stability of oil/water + IL emulsions was significantly improved. It was also revealed that the presence of sodium and calcium chloride electrolytes fortifies the IL impact, whereas sodium sulfate weakens. From dynamic IFT data and fitting with kinetic models, it was found that the IL migration toward interface follows the mixed diffusion–kinetic control model. Consequently, the IL diffusion coefficient and the appropriate activation energy were determined.

Attractivity of saturated equilibria for Lotka-Volterra systems with infinite delays and feedback controls

In this paper, we apply a Lyapunov functional approach to Lotka-Volterra systems with infinite delays and feedback controls and establish that the feedback controls have no influence on the attractivity properties of a saturated equilibrium. This improves previous results by the authors and others, where, while feedback controls were used mostly to change the position of a unique saturated equilibrium, additional conditions involving the controls had to be assumed in order to preserve its global attractivity. The situation of partial extinction is further analysed, for which the original system is reduced to a lower dimensional one which maintains its global dynamics features.

Global stability for epidemic models on multiplex networks.

In this work, we consider an epidemic model in a two-layer network in which the dynamics of susceptible-infected-susceptible process in the physical layer coexists with that of a cyclic process of unaware-aware-unaware in the virtual layer. For such multiplex network, we shall define the basic reproduction number [Formula: see text] in the virtual layer, which is similar to the basic reproduction number [Formula: see text] defined in the physical layer. We show analytically that if [Formula: see text] and [Formula: see text], then the disease and information free equilibrium is globally stable and if [Formula: see text] and [Formula: see text], then the disease free and information saturated equilibrium is globally stable for all initial conditions except at the origin. In the case of [Formula: see text], whether the disease dies out or not depends on the competition between how well the information is transmitted in the virtual layer and how contagious the disease is in the physical layer. In particular, it is numerically demonstrated that if the difference in [Formula: see text] and [Formula: see text] is greater than the product of [Formula: see text], the deviation of [Formula: see text] from 1 and the relative infection rate for an aware susceptible individual, then the disease dies out. Otherwise, the disease breaks out.

Simulations of natural transition in viscoelastic channel flow

Orderly, or natural, transition to turbulence in dilute polymeric channel flow is studied using direct numerical simulations of a FENE-P fluid. Three Weissenberg numbers are simulated and contrasted to a reference Newtonian configuration. The computations start from infinitesimally small Tollmien–Schlichting (TS) waves and track the development of the instability from the early linear stages through nonlinear amplification, secondary instability and full breakdown to turbulence. At the lowest elasticity, the primary TS wave is more unstable than the Newtonian counterpart, and its secondary instability involves the generation of $\unicode[STIX]{x1D6EC}$-structures which are narrower in the span. These subsequently lead to the formation of hairpin packets and ultimately breakdown to turbulence. Despite the destabilizing influence of weak elasticity, and the resulting early transition to turbulence, the final state is a drag-reduced turbulent flow. At the intermediate elasticity, the growth rate of the primary TS wave matches the Newtonian value. However, unlike the Newtonian instability mode which reaches a saturated equilibrium condition, the instability in the polymeric flow reaches a periodic state where its energy undergoes cyclical amplification and decay. The spanwise size of the secondary instability in this case is commensurate with the Newtonian $\unicode[STIX]{x1D6EC}$-structures, and the extent of drag reduction in the final turbulent state is enhanced relative to the lower elasticity condition. At the highest elasticity, the exponential growth rate of the TS wave is weaker than the Newtonian flow and, as a result, the early linear stage is prolonged. In addition, the magnitude of the saturated TS wave is appreciably lower than the other conditions. The secondary instability is also much wider in the span, with weaker ejection and without hairpin packets. Instead, streamwise-elongated streaks are formed and break down to turbulence via secondary instability. The final state is a high-drag-reduction flow, which approaches the Virk asymptote.

Analytical calculation of saturated polarization and equilibrium composition near tetragonal-rhombohedral morphotropic phase boundary of polycrystalline ferroelectrics

In this study, the saturated polarization and equilibrium composition near tetragonal-rhombohedral morphotropic phase boundary (MPB) of polycrystalline ferroelectrics have been analytically calculated. A generalized inverse-pole-figure (IPF) method has been suggested to estimate saturated polarization and composition of polycrystalline ferroelectrics. On the other hand, saturated polarization of monoclinic polycrystalline ferroelectrics has been analytically calculated by the generalized IPF. The results can support the results from the experimental studies which maintained that monoclinic symmetry can appear at tetragonal-rhombohedral MPB and the saturated polarization is enhanced at a certain composition.

Modelling of saturated soil slopes equilibrium with an account of the liquid phase bearing capacity

The paper presents an original method of solving the problem of uniformly distributed load action on a two-phase elastic half-plane with the use of a kinematic model. The kinematic model (Maltsev L.E.) of two-phase medium is based on two new hypotheses according to which the stress and strain state of the two-phase body is described by a system of linear elliptic equations. These equations differ from the Lame equations of elasticity theory with two terms in each equation. The terms describe the bearing capacity of the liquid phase or a decrease in stress in the solid phase. The finite element method has been chosen as a solution method.

Nitrobenzene-adsorption capacity of NaOH-modified spent coffee ground from aqueous solution

Adsorption of nitrobenzene (NB) on the NaOH-modified spent coffee ground (NaOH-SCG) was examined and the effects of contact time and adsorbent dose were investigated. The adsorption isotherm of NB on NaOH-SCG was compared with that of untreated SCG. The results from our study showed that the removal efficiencies of NB (25mg/L) on SCG and NaOH-SCG after 2h were 91.8% and 98.2%, respectively. The adsorption rate was very quick with the equilibrium of adsorption being achieved within about 30 min. The values of parameters obtained for NB from the Langmuir isotherm saturated adsorption amount and adsorption equilibrium constant were 117.2mg/g, 0.0753L/mg for SCG and 169.4mg/g, 0.1815L/mg for NaOH-SCG. NaOH-SCG (0.44mmol/g) has fewer acidic functional groups than SCG (1.49mmol/g). Therefore, the surface polarity of NaOH-SCG is low, thus makes this material more hydrophobic. The strong hydrophobicity of the NaOH-SCG surface might explain the high adsorption capacity for NB. As a result, this study has found that the NaOH-modified spent coffee ground has high adsorption ability for NB.

Poly(glycidyl methacrylate)-grafted hydrophobic charge-induction agarose resins with 5-aminobenzimidazole as a functional ligand.

Hydrophobic charge-induction chromatography is a new technology for antibody purification. To improve antibody adsorption capacity of hydrophobic charge-induction resins, new poly(glycidyl methacrylate)-grafted hydrophobic charge-induction resins with 5-aminobenzimidazole as a functional ligand were prepared. Adsorption isotherms, kinetics, and dynamic binding behaviors of the poly(glycidyl methacrylate)-grafted resins prepared were investigated using human immunoglobulin G as a model protein, and the effects of ligand density were discussed. At the moderate ligand density of 330 μmol/g, the saturated adsorption capacity and equilibrium constant reached the maximum of 140 mg/g and 25 mL/mg, respectively, which were both much higher than that of non-grafted resin with same ligand. In addition, effective pore diffusivity and dynamic binding capacity of human immunoglobulin G onto the poly(glycidyl methacrylate)-grafted resins also reached the maximum at the moderate ligand density of 330 μmol/g. Dynamic binding capacity at 10% breakthrough was as high as 76.3 mg/g when the linear velocity was 300 cm/h. The results indicated that the suitable polymer grafting combined with the control of ligand density would be a powerful tool to improve protein adsorption of resins, and new poly(glycidyl methacrylate)-grafted hydrophobic charge-induction resins have a promising potential for antibody purification applications.