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The process of directional crystallization in the presence of a quasi-equilibrium two-phase region located between the solid material and the liquid phase is studied theoretically. The mathematical model of the process is based on heat and mass transfer equations in the solid, liquid and two-phase regions, as well as boundary conditions at the phase interfaces "solid phase" – "two-phase region" and "two-phase region" – "liquid phase", which are moving with a constant velocity. The process of directional crystallization is given by fixed temperature gradients in the solid and liquid phases, which determine a constant velocity of melt solidification. An exact analytical solution of the nonlinear problem with two moving boundaries of phase transformation is obtained, which is based on the transition to a new independent variable, the solid phase fraction, when integrating the nonlinear heat and mass transfer equations in the two-phase region. As a result of solving the problem, the distributions of temperature and concentration of dissolved impurity, the solid phase fraction in a two-phase region, the laws and velocities of motion of its interphase boundaries are determined. It is analytically shown that the impurity concentration and temperature in the two-phase region are only the functions of solid phase fraction, which, in turn, depends on the spatial coordinate. Analysis of the obtained solutions shows that the solid phase fraction in a two-phase region can be both a decreasing and increasing function of the spatial coordinate, which is directed from the solid material to the melt. This determines the internal structure of two-phase region, its permeability, average interdendritic spacing, distribution of dissolved impurity, crystallization velocity and laws of two-phase region boundaries. [ABSTRACT FROM AUTHOR]

In this study, the model of directional solidification with a quasiequilibrium two-phase (mushy) region is formulated in the presence of weak melt flow (convection). This model is analytically solved for the steady-state solidification scenario when phase transition boundaries of the two-phase region move with a constant velocity. The distributions of impurity concentration, temperature, and solid-phase fraction in the two-phase region as well as its thickness and crystallization velocity are found in the case of weak convection. A generalization of the Scheil–Brody–Flemings law for impurity concentration as a function of solid-phase fraction is derived for the diffusion of impurity and the steady-state motion of two-phase layer. The present theory coupled with the selection criterion of stable dendritic growth enables us to deduce the primary interdendritic spacing within a two-phase layer. The theory under consideration contains all previously known theories and is in agreement with the experimental data on solidification of the aluminum–copper melts. [ABSTRACT FROM AUTHOR]

We propose two iterative algorithms for solving two classes of quasi-equilibrium problems in Hilbert spaces: pseudomonotone and quasimonotone ones. The algorithms combine the subgradient method and the projection method with self-adaptive step sizes. Convergence of our proposed algorithms requires a condition that is milder than the one commonly used in the existing papers. Numerical experiments show that our algorithms are efficient and competitive to other extragradient-type, projection-type, and proximal point algorithms in solving the problem. [ABSTRACT FROM AUTHOR]

The notion of sharp minima, given by Polyak, is an important tool in studying the convergence analysis of algorithms designed to solve optimization problems. It has been studied extensively for variational inequality problems and equilibrium problems. In this paper, the convergence analysis of the sequence generated by proximal point method for quasi-equilibrium problem (QEP) will be established under sharp minima conditions. Further, the characterizations of weak sharp solution for QEP are provided. We also introduce an inexact proximal point method and demonstrate the convergence of the sequence for solving the QEP. Finally, we deduce the proximal point approximation for generalized Nash equilibrium problem. [ABSTRACT FROM AUTHOR]

Cells exert forces on each other and their environment, shaping the tissue. The resulting mechanical stresses can be determined experimentally or estimated computationally using stress inference methods. Over the years, mechanical stress inference has become a non-invasive, low-cost computational method for estimating the relative intercellular stresses and intracellular pressures of tissues. This mini-review introduces and compares the static and dynamic modalities of stress inference, considering their advantages and limitations. To date, most software has focused on static inference, which requires only a single microscopy image as input. Although applicable in quasi-equilibrium states, this approach neglects the influence that cell rearrangements might have on the inference. In contrast, dynamic stress inference relies on a time series of microscopy images to estimate stresses and pressures. Here, we discuss both static and dynamic mechanical stress inference in terms of their physical, mathematical, and computational foundations and then outline what we believe are promising avenues for in silico inference of the mechanical states of tissues. [ABSTRACT FROM AUTHOR]

Existence results are given for vector quasi-equilibrium problems whose objectives are described by the sum of two set-valued trifunctions with possibly different properties. The main results are established in the framework of topological vector spaces, without monotonicity-type assumptions. As applications, we obtain existence results for optimal control problems, where the state behaviors are given by vector quasi-equilibrium problems and the vector optimality criteria are understood in the sense of Kuroiwa. [ABSTRACT FROM AUTHOR]

Earth's tropics are characterized by quasi‐steady precipitation with small oscillations about a mean value, which has led to the hypothesis that moist convection is in a state of quasi‐equilibrium (QE). In contrast, very warm simulations of Earth's tropical convection are characterized by relaxation‐oscillator‐like (RO) precipitation, with short‐lived convective storms and torrential rainfall forming and dissipating at regular intervals with little to no precipitation in between. We develop a model of moist convection by combining a zero‐buoyancy model of bulk‐plume convection with a QE heat engine model, and we use it to show that QE is violated at high surface temperatures. We hypothesize that the RO state emerges when the equilibrium condition of the convective heat engine is violated, that is, when the heating rate times a thermodynamic efficiency exceeds the rate at which work can be performed. We test our hypothesis against one‐ and three‐dimensional numerical simulations and find that it accurately predicts the onset of RO convection. The proposed mechanism for RO emergence from QE breakdown is agnostic of the condensable, and can be applied to any planetary atmosphere undergoing moist convection. To date, RO states have only been demonstrated in three‐dimensional convection‐resolving simulations, which has made it seem that the physics of the RO state requires simulations that can explicitly resolve the three‐dimensional interaction of cloudy plumes and their environment. We demonstrate that RO states also exist in single‐column simulations of radiative‐convective equilibrium with parameterized convection, albeit in a different surface temperature range and with much longer storm‐free intervals. Plain Language Summary: Earth's tropics are characterized by steady rainfall, indicating that moist convection is a continuous process. However, in simulations of very warm conditions, a form of episodic convection emerges that is characterized by short bursts of intense rainfall followed by longer rain‐free intervals. We construct a simple model that represents convection as a heat engine, and use it to show that steady convection must break down in very warm conditions. We hypothesize that the essential condition for steady convection is the balanced conversion of heat into work, which is violated at high surface temperatures. We test our hypothesis against climate model simulations of increasing complexity—the first parameterizes convection and the second actually resolves it—and found that it accurately predicts when the steady climate state transitions to the episodic state. The simple model of convection isn't limited to Earth, and could be applied to planets with different atmospheric compositions. Finally, while it has seemed that episodic precipitation could only be obtained from model simulations that resolve convection, we've shown here that it can also occur in simpler climate models with parameterized convection. Key Points: A transition from quasi‐equilibrium (QE) to relaxation‐oscillator (RO) convection occurs at high surface temperatures on EarthQE breakdown is predicted by a simple model of a convective heat engine in radiative‐convective equilibrium where plumes have zero buoyancyQE breaks down when the equilibrium condition of the heat engine is violated, and this leads to RO emergence [ABSTRACT FROM AUTHOR]

Our conceptual understanding of the tropical thermal structure is based on two complementary idealisations: one stemming from convective quasi‐equilibrium (QE) and the other being the weak temperature gradient (WTG) approximation. Through QE, moist convection provides a vertical control on the thermal structure, while, under WTG, wave dynamics are assumed to provide a non‐local horizontal control. While it is clear that moist convection plays an important role in setting the tropical mean stability through QE, the extent to which QE implies a local constraint on stability or whether the requirement for WTG effectively inhibits the influence of local conditions on stability remains debated. Here we hypothesise that a strong local vertical control of the thermal structure would imply a relationship between humidity and stability in the troposphere, as convection within moister regions would be less affected by entrainment of surrounding air. We utilise a combination of ERA5 reanalysis and observational data to examine the relationship between stability and local humidity across the Tropics. The results are compared with a prediction based upon a specific realisation of the theory of QE that incorporates entrainment through a simple plume model. We discover that, in convective regions, wave dynamics do not eliminate the effect of local conditions on stability, and that the resulting relationship between stability and humidity can be approximated well by the entraining plume model. Since QE is not applicable in the absence of convection, in non‐convective regions the WTG, and possibly other factors, acts to set stability in the region. These results may help us understand the controls on horizontal density gradients in the tropical troposphere and the associated overturning circulations. [ABSTRACT FROM AUTHOR]

Global approximations of scalar optimization problems in terms of variational convergence have been studied for several decades. However, there are very few results for vector models in the literature, which are limited to epi-convergence of vector functions, nothing has been obtained for vector bifunctions. This paper is the first attempt to consider approximations of vector optimization in terms of variational convergence of bifunctions. We first consider the vector quasi-equilibrium problem since it encompasses most optimization-related models. Then, we apply the obtained results to the vector Nash quasi-game (vector generalized non-cooperative game), which is one of the most important practical problems in applied mathematics. We approach to the vector problems in question via scalarization. Our scalarization tools are the Tammer and the Hiriart-Urruty scalarization functions. By scalarizing, we define types of vector variational convergence corresponding to some types of scalar variational convergence. We show that under these types of convergence of problems approximating the vector problems under consideration, approximate solutions of the former problems tend to solutions of the latter ones in the sense of set convergence. [ABSTRACT FROM AUTHOR]

The linear stability of quasi-equilibrium states of an inclined binary fluid layer subjected to the gravity field and high-frequency small-amplitude vibrations is studied in the presence of the prescribed vertical temperature and concentration gradients. The rigid boundaries of a layer are impermeable to a substance. The Soret and Dufour effects are neglected. The study is conducted in the average approach. The conditions for quasi-equilibrium state existence are found, and the linear stability of these states to the longwave and finite-wavelength perturbations is investigated. The results of the linear stability analysis are confirmed by the nonlinear modeling, which is carried out by the finite difference method. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the existence of solutions of set-valued quasiequilibrium problems in real Banach spaces. We introduce a concept of Brezis pseudomonotonicity for set-valued mappings. By constructing appropriate constraint conditions for the weak coercive function and the objective mapping, we obtain a solution-existence result for usual set-valued equilibrium problems. By a sequence of penalized set-valued equilibrium problems, we obtain a solution-existence result for set-valued quasi-equilibrium problems. These results do not require the assumption of compactness of the constraint set, and improve the corresponding ones in the literature. [ABSTRACT FROM AUTHOR]

The steepest-entropy-ascent quantum thermodynamic (SEAQT) framework is used to explore the influence of heating and cooling on polymer chain folding kinetics. The framework predicts how a chain moves from an initial non-equilibrium state to stable equilibrium along a unique thermodynamic path. The thermodynamic state is expressed by occupation probabilities corresponding to the levels of a discrete energy landscape. The landscape is generated using the Replica Exchange Wang–Landau method applied to a polymer chain represented by a sequence of hydrophobic and polar monomers with a simple hydrophobic-polar amino acid model. The chain conformation evolves as energy shifts among the levels of the energy landscape according to the principle of steepest entropy ascent. This principle is implemented via the SEAQT equation of motion. The SEAQT framework has the benefit of providing insight into structural properties under non-equilibrium conditions. Chain conformations during heating and cooling change continuously without sharp transitions in morphology. The changes are more drastic along non-equilibrium paths than along quasi-equilibrium paths. The SEAQT-predicted kinetics are fitted to rates associated with the experimental intensity profiles of cytochrome c protein folding with Rouse dynamics. [ABSTRACT FROM AUTHOR]

Abstract In this article, we considered a nonlinear compartmental mathematical model that assesses the effect of treatment on the dynamics of HIV/AIDS and pneumonia (H/A-P) co-infection in a human population at different infection stages. Understanding the complexities of co-dynamics is now critically necessary as a consequence. The aim of this research is to construct a co-infection model of H/A-P in the context of fractional calculus operators, white noise and probability density functions, employing a rigorous biological investigation. By exhibiting that the system possesses non-negative and bounded global outcomes, it is shown that the approach is both mathematically and biologically practicable. The required conditions are derived, guaranteeing the eradication of the infection. Furthermore, adequate prerequisites are established, and the configuration is tested for the existence of an ergodic stationary distribution. For discovering the system’s long-term behavior, a deterministic-probabilistic technique for modeling is designed and operated in MATLAB. By employing an extensive review, we hope that the previously mentioned approach improves and leads to mitigating the two diseases and their co-infections by examining a variety of behavioral trends, such as transitions to unpredictable procedures. In addition, the piecewise differential strategies are being outlined as having promising potential for scholars in a range of contexts because they empower them to include particular characteristics across multiple time frame phases. Such formulas can be strengthened via classical techniques, power law, exponential decay, generalized Mittag-Leffler kernels, probability density functions and random procedures. Furthermore, we get an accurate description of the probability density function encircling a quasi-equilibrium point if the effect of H/A-P minimizes the propagation of the co-dynamics. Consequently, scholars can obtain better outcomes when analyzing facts using random perturbations by implementing these strategies for challenging issues. Random perturbations in H/A-P co-infection are crucial in controlling the spread of an epidemic whenever the suggested circulation is steady and the amount of infection eliminated is closely correlated with the random perturbation level.

Although surface plasmon (SP) coupling has been widely used for enhancing the emission efficiency of an InGaN/GaN quantum well (QW) structure, the interplay of the carrier transport behavior in the QW with SP coupling, which is a crucial mechanism controlling the SP-coupling induced QW emission enhancement, is still an issue not well explored yet. To understand the effects of SP coupling on the radiative and non-radiative recombination behaviors of carriers in a QW structure, the temperature-dependent time-resolved photoluminescence spectroscopies of two QW samples of different indium contents with surface Ag nanoparticles are studied. A two-single-exponential model is used for calibrating their radiative and non-radiative decay times. The SP coupling process, which transfers carrier energy from a QW into the SP resonance mode for effective radiation and increases the effective radiative recombination rate, produces energy-dependent carrier depletion and, hence, disturbs the quasi-equilibrium condition of carrier distribution. In this situation, a strong carrier transport process occurs targeting a new quasi-equilibrium condition that enhances non-radiative recombination and, hence, reduces the benefit of using the SP coupling technique. To alleviate this problem of SP-coupling induced energy loss, a weak energy-dependent or broad-spectrum SP coupling process is recommended. [ABSTRACT FROM AUTHOR]

The charge-transfer resistance R1 as a function of the electrode potential Е for the hydrogen evolution reaction passing by the Volmer–Heyrovsky mechanism involving atomic hydrogen adsorbed according to Temkin isotherm is studied. For a quasiequilibrium Volmer reaction, logR1,E-curves have a minimum and a maximum. With the increasing of the surface nonuniformity factor f the minimum has been shifted toward lower electrode potentials, the minimum region in the voltammogram is widened. The half-width of the minimum region allowed determining the f value. At the lowest and highest values of the surface coverage, the logR1,E-dependence demonstrated the same regularities as the Langmuir isotherm. [ABSTRACT FROM AUTHOR]

In this article, we considered a nonlinear compartmental mathematical model that assesses the effect of treatment on the dynamics of HIV/AIDS and pneumonia (H/A-P) co-infection in a human population at different infection stages. Understanding the complexities of co-dynamics is now critically necessary as a consequence. The aim of this research is to construct a co-infection model of H/A-P in the context of fractional calculus operators, white noise and probability density functions, employing a rigorous biological investigation. By exhibiting that the system possesses non-negative and bounded global outcomes, it is shown that the approach is both mathematically and biologically practicable. The required conditions are derived, guaranteeing the eradication of the infection. Furthermore, adequate prerequisites are established, and the configuration is tested for the existence of an ergodic stationary distribution. For discovering the system's long-term behavior, a deterministic-probabilistic technique for modeling is designed and operated in MATLAB. By employing an extensive review, we hope that the previously mentioned approach improves and leads to mitigating the two diseases and their co-infections by examining a variety of behavioral trends, such as transitions to unpredictable procedures. In addition, the piecewise differential strategies are being outlined as having promising potential for scholars in a range of contexts because they empower them to include particular characteristics across multiple time frame phases. Such formulas can be strengthened via classical techniques, power law, exponential decay, generalized Mittag-Leffler kernels, probability density functions and random procedures. Furthermore, we get an accurate description of the probability density function encircling a quasi-equilibrium point if the effect of H/A-P minimizes the propagation of the co-dynamics. Consequently, scholars can obtain better outcomes when analyzing facts using random perturbations by implementing these strategies for challenging issues. Random perturbations in H/A-P co-infection are crucial in controlling the spread of an epidemic whenever the suggested circulation is steady and the amount of infection eliminated is closely correlated with the random perturbation level. [ABSTRACT FROM AUTHOR]

In the Markov relaxation and locally quasi-equilibrium distribution approximation, analogues of Onzager's relations for the response functions of the spin current in the nonlinear by intense mechanical and thermodynamic effects regime were obtained by the Kubo method. [ABSTRACT FROM AUTHOR]

The proposed method is a development of the well-known one, based on the determination of the sensor's transducers impedance parameters according to the three-element equivalent circuit at two frequencies. The increase in accuracy is achieved due to the step-by-step refinement of parameter values using the values obtained in the previous step using simplified mathematical expressions. Mathematical expressions for calculating the specified parameters are presented. Comparative results of calculations based on known and proposed methods using a computer model are presented, which showed the possibility of significantly reducing the influence of changes in the background electrical conductivity of the solution compared to the known method. References 9, figures 2, tables 1 [ABSTRACT FROM AUTHOR]

In this paper, the Schauder conjecture for set-valued mappings is studied by using suitable conditions. Also, an existence theorem for a solution of quasi-equilibrium problem in the setting of topological vector spaces is provided. [ABSTRACT FROM AUTHOR]

High vacuum packaging is the key manufacturing technology of passive vacuum devices. The inherent characteristics of narrow and long space and large surface-to-volume ratio make it challenging to effectively remove the desorption gas inside the device. To this end, the pressure distribution of two standard packaging methods during the pump-down process is investigated using the two-dimensional diffusion equation. Experiments and simulations show that a pressure gradient persists within the slit even when pumping reaches the quasi-equilibrium state. In addition, a Monte Carlo method based on the cosine law reveals that the high-frequency collisions of gas molecules with the walls impede the pumping process. Furthermore, the results indicate that for tube pumping, the number of collisions of gas molecules with the wall during transport within the gap is inversely proportional to the gap height. For edge pumping, the number of collisions is inversely proportional to the square of the gap height. This provides a theoretical basis for efficient high vacuum packaging and long-term pressure maintenance for passive vacuum devices. [ABSTRACT FROM AUTHOR]

Quasi-equilibrium states that can be prepared in solids through Nuclear Magnetic Resonance (NMR) techniques are out-of-equilibrium states that slowly relax towards thermodynamic equilibrium with the lattice. In this work, we use the quantum discord dynamics as a witness of the quantum correlation in this kind of state. The studied system is a set of dipole interacting spin pairs whose initial state is prepared with the NMR Jeener–Broekaert pulse sequence, starting from equilibrium at high temperature and high external magnetic field. It then evolves as an open quantum system within two consecutive dynamic scenarios: adiabatic decoherence driven by the coupling of the pairs to a common phonon field, described within a non-Markovian approach, and spin–lattice relaxation represented by the high-temperature limit of the Born–Markov master equation, and driven by thermal fluctuations. In this way, the studied model is endowed with the dynamics of a realistic solid sample. The quantum discord rapidly increases during the preparation of the initial state, escalating several orders of magnitude compared with thermal equilibrium at room temperature. During decoherence—despite the decay of coherences—the quantum discord oscillates upon this high value, holding the same value as the initial state. Finally, the quantum discord dissipates within a time scale shorter than but comparable to spin–lattice relaxation. [ABSTRACT FROM AUTHOR]

The chemistry of H2O, CO, and other small molecular species in an isolated pre-stellar core, L1544, has been assessed in the context of a comprehensive gas-grain chemical model, coupled to an empirically constrained physical/dynamical model. Our main findings are (i) that the chemical network remains in near equilibrium as the core evolves towards star formation and the molecular abundances change in response to the evolving physical conditions. The gas-phase abundances at any time can be calculated accurately with equilibrium chemistry, and the concept of chemical clocks is meaningless in molecular clouds with similar conditions and dynamical time-scales, and (ii) A comparison of the results of complex and simple chemical networks indicates that the abundances of the dominant oxygen and carbon species, H2O, CO, C, and C+ are reasonably approximated by simple networks. In chemical equilibrium, the time-dependent differential terms vanish, and a simple network reduces to a few algebraic equations. This allows rapid calculation of the abundances most responsible for spectral line radiative cooling in molecular clouds with long dynamical time-scales. The dust ice mantles are highly structured and the ice layers retain a memory of the gas-phase abundances at the time of their deposition. A complex (gas-phase and gas-grain) chemical structure therefore exists, with cosmic-ray induced processes dominating in the inner regions. The inferred H2O abundance profiles for L1544 require that the outer parts of the core and also any medium exterior to the core are essentially transparent to the interstellar radiation field. [ABSTRACT FROM AUTHOR]

By using the quasi-equilibrium Helmholtz energy, which is defined as the thermodynamic work in a quasi-static process, we investigate the thermal properties of both an isothermal process and a transition process between the adiabatic and isothermal states (adiabatic transition). Here, the work is defined by the change in energy from a steady state to another state under a time-dependent perturbation. In particular, the work for a quasi-static change is regarded as thermodynamic work. We employ a system–bath model that involves time-dependent perturbations in both the system and the system–bath interaction. We conduct numerical experiments for a three-stroke heat machine (a Kelvin–Planck cycle). For this purpose, we employ the hierarchical equations of motion (HEOM) approach. These experiments involve an adiabatic transition field that describes the operation of an adiabatic wall between the system and the bath. Thermodynamic–work diagrams for external fields and their conjugate variables, similar to the P–V diagram, are introduced to analyze the work done for the system in the cycle. We find that the thermodynamic efficiency of this machine is zero because the field for the isothermal processes acts as a refrigerator, whereas that for the adiabatic wall acts as a heat engine. This is a numerical manifestation of the Kelvin–Planck statement, which states that it is impossible to derive the mechanical effects from a single heat source. These HEOM simulations serve as a rigorous test of thermodynamic formulations because the second law of thermodynamics is only valid when the work involved in the operation of the adiabatic wall is treated accurately. [ABSTRACT FROM AUTHOR]

Landscapes are sculpted by a complex response of surface processes to external forcings, such as climate and tectonics. Several major river captures have been documented in the Hengduan Mountains, leading to the hypothesis that the region experiences exceptionally high rates of drainage reorganization driven by horizontal shortening and propagating uplift. Here we determine the prevalence, intensity, and spatial patterns of ongoing drainage reorganization in the Hengduan Mountains and evaluate the relative timescales of this transience by comparing drainage divide asymmetry for four geomorphic metrics that operate at different spatial and temporal scales. Specifically, we calculate the migration direction and the divide asymmetry index (DAI) for drainage divides using catchment-restricted topographic relief (CRR), hillslope gradient (HSG), normalized channel steepness (ksn), and normalized channel distance (χ). ksn and χ are both precipitation-corrected to account for the strong precipitation gradient across the region. The different spatial scales of these geomorphic metrics allow us to establish the relative timescales of observed landscape transience in the Hengduan Mountains, where local-scale metrics measure short-term change and integral quantities measure long-term disequilibrium. We find a high incidence of strongly asymmetric divides in all metrics across the Hengduan Mountain region. Although the magnitude of asymmetry varies significantly between metrics, possibly due to a combination of metric-specific thresholds and varying proxy relationships with erosion rate, a majority of divides agree on divide migration direction. Agreement in divide migration direction indicates an actively responding landscape when asymmetry is high and a state of quasi-equilibrium when asymmetry is low. Disagreements between the integral quantity, χ , and the other geomorphic metrics can be explained by different timescales of the underlying geomorphic processes, with χ reflecting a long-term response and CRR, HSG, and ksn capturing short-term perturbations to catchment structure. These perturbations include various transient mechanisms, such as differential tectonic uplift or erodibility, glacial alteration, and river captures. Our work confirms the high incidence of drainage reorganization across the Hengduan Mountains and highlights both transient and stable areas in the landscape with high resolution. We also offer valuable insights into the application of geomorphic metrics that can be generalized and applied to the study of landscape transience and drainage divide asymmetry in other settings. [ABSTRACT FROM AUTHOR]

This paper has two parts. In the mathematical part, we present two inexact versions of the proximal point method for solving quasi-equilibrium problems (QEP) in Hilbert spaces. Under mild assumptions, we prove that the methods find a solution to the quasi-equilibrium problem with an approximated computation of each iteration or using a perturbation of the regularized bifunction. In the behavioral part, we justify the choice of the new perturbation, with the help of the main example that drives quasi-equilibrium problems: the Cournot duopoly model, which founded game theory. This requires to exhibit a new QEP reformulation of the Cournot model that will appear more intuitive and rigorous. It leads directly to the formulation of our perturbation function. Some numerical experiments show the performance of the proposed methods. [ABSTRACT FROM AUTHOR]

Humans have influenced the sediment transport of rivers on a centurial scale. Our goal was to use the rate of lateral channel processes as a proxy to reconstruct sediment budget (SB) changes of a lowland river (Middle Tisza, Hungary) on a historical scale (1838–2017). The gross sediment budget (GSB) refers to the total area of eroded and accumulated surfaces, and the net sediment budget (NSB) indicates the sediment sink or source characteristics. At the beginning (1838–1890), the artificial cut-offs increased the slope and channel erosion, but the eroded sediment deposited in the oxbows, so the reach acted as a sediment sink (NSB: +0.1–0.8 m2/m/y). Then (1890–1929), a quasi-equilibrium state developed (NSB: −0.2 m2/m/y to +0.4 m2/m/y). Later (1929–1976), the bank protections impeded lateral erosion, so the system became a sediment sink again (NSB: +0.1–0.7 m2/m/y). Finally (1976–2017), the erosional processes accelerated due to dam construction and revetment collapses, and now the river is a sediment source (NSB: −0.03 to −0.08 m2/m/y). This study proved that (1) the actual SB could not be projected in the long term, as it was heavily modified, and (2) lateral channel changes could be used as a proxy to estimate long-term SB. [ABSTRACT FROM AUTHOR]

Target-mediated drug disposition (TMDD) is a phenomenon characterized by a drug's high-affinity binding to a target molecule, which significantly influences its pharmacokinetic profile within an organism. The comprehensive TMDD model delineates this interaction, yet it may become overly complex and computationally demanding in the absence of specific concentration data for the target or its complexes. Consequently, simplified TMDD models employing quasi-steady state approximations (QSSAs) have been introduced; however, the precise conditions under which these models yield accurate results require further elucidation. Here, we establish the validity of three simplified TMDD models: the Michaelis-Menten model reduced with the standard QSSA (mTMDD), the QSS model reduced with the total QSSA (qTMDD), and a first-order approximation of the total QSSA (pTMDD). Specifically, we find that mTMDD is applicable only when initial drug concentrations substantially exceed total target concentrations, while qTMDD can be used for all drug concentrations. Notably, pTMDD offers a simpler and faster alternative to qTMDD, with broader applicability than mTMDD. These findings are confirmed with antibody-drug conjugate real-world data. Our findings provide a framework for selecting appropriate simplified TMDD models while ensuring accuracy, potentially enhancing drug development and facilitating safer, more personalized treatments. Author summary: Target-mediated drug disposition (TMDD) is a phenomenon characterized by the high-affinity binding of a drug to its target molecule. The TMDD model can describe the process to elucidate the binding of the drug to its target and its elimination from the body. However, when target or complex concentrations are not available, simpler models of the TMDD model need to be used to avoid over-parameterization and to improve computational efficiency and analysis. Several simplified TMDD models based on quasi-equilibrium, Michaelis-Menten (MM), or quasi-steady-state (QSS) approximation have been proposed. However, their validity conditions have not been fully investigated. In this study, we derive the validity conditions for the approximations of the TMDD model, providing insights into the appropriate use of simplified models. We also propose a first-order approximation of the QSS model, which is faster than the QSS model and more accurate than the MM model. We also applied the simplified models to antibody-drug conjugate real-world data and obtained the same results. Our work provides clear guidance on the use of the simplified TMDD models, potentially leading to improved drug development and safer, more tailored treatments for patients. [ABSTRACT FROM AUTHOR]

This study aims to achieve the computational results for the oxidation of carbon monoxide using the spectral quasi-equilibrium manifold and the intrinsic low-dimensional manifold techniques, enabling the identification of the slow invariant manifold and subsequent simulation of the solutions. In addition, the application of Gibbs' rule facilitates the reduction of the system, thereby effectively transforming higher dimensions into lower dimensions, ultimately revealing the underlying 1D manifold dynamics. This research serves to elucidate the intricacies of phase-shifting behaviors in the context of key species within the overarching and interconnected multi-step reaction mechanisms, contributing significantly to the advancement of understanding in this complex field. [ABSTRACT FROM AUTHOR]

Simulating the complexity in its entirety proves highly challenging, to examine both the local and global stability of the model, as well as its positivity, recognizing the overall instability. To address this challenge, a strategy of splitting down the multi-route complex reactions into its independent sub-routes is employed. For the validation of sub-routes, the stability and positivity of each individual route were comprehensively analyzed. In addition, we employ techniques to simplify our models by considering factors such as reaction speed and thermodynamic properties, ensuring their accuracy. Furthermore, we integrate the Spectral Quasi-Equilibrium Manifold to obtain a deeper understanding of the sequential advancement of reactions, focusing on the slowest eigenvector. A comprehensive examination of the mathematical underpinnings of these reaction steps and diverse pathways is conducted. We also investigate the temporal behavior of these pathways, yielding fresh perspectives. Our findings suggest the feasibility of independently evaluating each pathway rather than treating the entire mechanism as a singular entity. To enhance our analysis, we conduct a local sensitivity assessment using the SimBiology toolbox in MATLAB of each route and compare calculation periods for TRM (Total Relative Motion). Furthermore, we employ the short-time Fourier transform graph to capture time–frequency information regarding the steady state of compounds in various routes, revealing spectral variations over time. [ABSTRACT FROM AUTHOR]

This paper discusses the application of the Nash strategy to a quasi-linear parabolic equation and a quasi-linear parabolic equation with a semilinear term. First, we demonstrate the existence of a Nash quasi-equilibrium for both equations using the fixed point method. Subsequently, we establish that the functionals are convex, ensuring that the Nash quasiequilibrium is, in fact, a Nash equilibrium. Additionally, in conjunction with the theoretical results, numerical techniques are developed for each problem. To describe the iterative algorithms, the Newton's Method is utilized in combination with the Finite Element Method and Finite Difference Method. All algorithms are implemented using the Freefem++ software, and various results are presented through figures and comparative graphics. [ABSTRACT FROM AUTHOR]

We extend gap functions to quasi-equilibrium problems by using the duality results. In particular, we obtain new results for quasi-equilibrium problems known earlier for equilibrium problems and mixed quasi-variational inequalities. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present new existence results for solutions to a generalized quasi-equilibrium problem with set-valued mappings and moving cones. The key to this approach is a new Browder-type fixed point theorem, which permits working in a new direction with the milder condition of transfer open-valued mapping and considering weaker assumptions on the coving cone. These results are applied to some generalized vector quasi-equilibrium problems with trifunctions and to a vector quasi-equilibrium problem with fuzzy mappings in a fuzzy environment. [ABSTRACT FROM AUTHOR]

We developed a macroscopic description of the evolutionary dynamics by following the temporal dynamics of the total Shannon entropy of sequences, denoted by S, and the average Hamming distance between them, denoted by H. We argue that a biological system can persist in the so-called quasi-equilibrium state for an extended period, characterized by strong correlations between S and H, before undergoing a phase transition to another quasi-equilibrium state. To demonstrate the results, we conducted a statistical analysis of SARS-CoV-2 data from the United Kingdom during the period between March 2020 and December 2023. From a purely theoretical perspective, this allowed us to systematically study various types of phase transitions described by a discontinuous change in the thermodynamic parameters. From a more-practical point of view, the analysis can be used, for example, as an early warning system for pandemics. [ABSTRACT FROM AUTHOR]

A continuous quasi-equilibrium phase diagram δ(pO2, T) of a nonstoichiometric oxide La2NiO4 + δ with the layered perovskite-like Ruddlesden–Popper structure is obtained by the method of quasi-equilibrium oxygen release. The thermodynamic parameters are determined as a function of the oxide nonstoichiometry δ. Calculations are carried out within the framework of the localized-electron and itinerant-electron models which are used for description of the defect structure of ferrites and cobaltites, respectively. It is shown that the specific features of the phase diagram can be related to the electronic density of states near the Fermi level. [ABSTRACT FROM AUTHOR]

Triaxial neutron stars can be sources of continuous gravitational radiation detectable by ground-based interferometers. The amplitude of the emitted gravitational wave can be greatly affected by the state of the hydrodynamical fluid flow inside the neutron star. In this work, we examine the most triaxial models along two sequences of constant rest mass, confirming their dynamical stability. We also study the response of a triaxial figure of quasiequilibrium under a variety of perturbations that lead to different fluid flows. Starting from the general relativistic compressible analog of the Newtonian Jacobi ellipsoid, we perform simulations of Dedekind-type flows. We find that in some cases the triaxial neutron star resembles a Riemann-S-type ellipsoid with minor rotation and gravitational wave emission as it evolves towards axisymmetry. The present results highlight the importance of understanding the fluid flow in the interior of a neutron star in terms of its gravitational wave content. [ABSTRACT FROM AUTHOR]

This study investigates the emergence of hurricane-like vortices in idealized simulations of rotating moist convection. A Boussinesq atmosphere with simplified thermodynamics for phase transitions is forced by prescribing the temperature and humidity at the upper and lower boundaries. The governing equations are solved numerically using a variable-density incompressible Navier-Stokes solver with adaptive mesh refinement to explore the behavior of moist convection under a broad range of conditions. In the absence of rotation, convection aggregates into active patches separated by large unsaturated regions. Rotation modulates this statistical equilibrium state so that the self-aggregated convection organizes hurricane-like vortices. The warm and saturated air converges to the center of the vortices, and the latent heat released through the upwelling, forms the warm core structure. These hurricane-like vortices share characteristics similar to tropical cyclones in the earth's atmosphere. The hurricane-like vortices occur under conditionally unstable conditions where the potential energy given at the boundaries is large enough, corresponding to a moderate rate of rotation. This regime shares many similar characteristics to the tropical atmosphere indicating that the formation of intense meso-scale vortices is a general characteristic of rotating moist convection. The model used here does not include any interactions with radiation, wind-evaporation feedback, or cloud microphysics, indicating that, while these processes may be relevant for tropical cyclogenesis in the Earth atmosphere, they are not its primary cause. Instead, our results confirm that the formation and maintenance of hurricane-like vortices involve a combination of atmospheric dynamics under the presence of rotation and of phase transitions.

Several recent studies have highlighted differences in simulated properties of El Niño–Southern Oscillation (ENSO) under transient and equilibrium responses to increasing CO2. However, the reasons behind these disparate responses and the extent to which they are robust to different scales of CO2 forcing remain unclear. In this study, we adopt a climate system model with reduced SST bias in the eastern tropical Pacific and incrementally apply abrupt increases in CO2, analyzing outputs after each simulation reaches quasi-equilibrium with the imposed forcing. The results suggest that ENSO activity under quasi-equilibrium first increases and then decreases with increasing CO2, peaking in simulations with CO2 concentrations similar to the present day. Bjerknes–Jin stability analysis indicates that changes in the ENSO growth rate result primarily from changes in the thermocline feedback and thermodynamic damping terms. While thermodynamic damping increases monotonically with increasing CO2, the positive thermocline feedback varies within the range of internal variability up to twice the preindustrial value of CO2 and then weakens sharply with further increases. The mechanisms behind these changes include weaker mean ocean upwelling and weaker dynamical coupling between the atmosphere and subsurface ocean associated with substantial near-surface freshening at higher levels of CO2. These changes steepen the thermodynamic barrier to mixing between the surface and subsurface, weakening the east–west temperature gradient in the mean state and suppressing variability in the cold tongue. Analysis of similar model simulations from the Coupled Model Intercomparison Project (CMIP6) archive indicates that changes in the Bjerknes–Jin stability index are robust but do not establish a consensus as to the mechanisms behind them. Significance Statement: This study investigates how El Niño–Southern Oscillation changes with increasing CO2 forcing by using a global model with improved tropical Pacific climate. The simulations roughly correspond to scenarios in which emissions are reduced to maintain CO2 concentrations at near-constant values over a long period, with levels ranging from about 2/3 to more than 5 times the present-day concentration. Analysis of these simulations suggests that ENSO activity is strongest when CO2 concentrations are similar to the present-day and becomes substantially weaker when CO2 is more than double its present-day value. Reduced ENSO activity with further increases in CO2 is caused by weaker interactions between the atmosphere and the subsurface ocean. Both the amplitude of warm (El Niño) events and the occurrence frequency of warm and cold (La Niña) events decrease as ENSO events become first more difficult to grow and then more difficult to trigger with increasing CO2. [ABSTRACT FROM AUTHOR]

The present study reports the effects of two pharmaceutical excipients of differing natures—non-ionic surfactant pluronic F127 (F127) and anionic sulfobutylether-β-cyclodextrin (SBE-β-CD)—on the permeation of the model compound, carbamazepine (CBZ). The permeability coefficients of CBZ at three concentrations of the excipients were measured through two different artificial barriers: hydrophilic cellulose membrane (RC) and lipophilic polydimethylsiloxane–polycarbonate membrane (PDS). The equilibrium solubility of CBZ in F127 and SBE-β-CD solutions was determined. The micellization, complexation, and aggregation tendencies were investigated. Systemically increasing the solubility and the reduction of permeation upon the excipients' concentration growth was revealed. The quantitative evaluation of the permeability tendencies was carried out using a Pratio parameter, a quasi-equilibrium mathematical mass transport model, and a correction of permeability coefficients for the free drug concentration ("true" permeability values). The results revealed the mutual influence of the excipient properties and the membrane nature on the permeability variations. [ABSTRACT FROM AUTHOR]

Cave carbonate minerals are an important terrestrial paleoclimate archive. A few studies have explored the potential for applying carbonate clumped isotope thermometry to speleothems as a tool for constraining past temperatures. To date, most papers utilizing this method have focused on mass-47 clumped isotope values (Δ 47) at a single location and reported that cave carbonate minerals rarely achieve isotopic equilibrium, with kinetic isotope effects (KIEs) attributed to CO 2 degassing. More recently, studies have shown that mass-47 and mass-48 CO 2 from acid digested carbonate minerals (Δ 47 and Δ 48) can be used together to assess equilibrium and probe KIEs. Here, we examined 44 natural and synthetic modern cave carbonate mineral samples from 13 localities with varying environmental conditions (ventilation, water level, pCO 2 , temperature) for (dis)equilibrium using Δ 47 -Δ 48 values, in concert with traditional stable carbon (δ13C) and oxygen (δ18O) isotope ratios. Data showed that 19 of 44 samples exhibited Δ 47 -Δ 48 values indistinguishable from isotopic equilibrium, and 18 (95 %) of these samples yield Δ 47 -predicted temperatures within error of measured modern temperatures. Conversely, 25 samples exhibited isotopic disequilibria, 13 of which yield erroneous temperature estimates. Within some speleothem samples, we find Δ 47 -Δ 48 values consistent with CO 2 degassing effects, however, the majority of samples with KIEs are consistent with other processes being dominant. We hypothesize that these values reflect isotopic buffering effects on clumped isotopes that can be considerable and cannot be overlooked. Using a Raleigh Distillation Model, we examined carbon and oxygen isotope exchange trajectories and their relationships with dual clumped isotope disequilibria. Carbon isotope exchange is associated with depletion of both Δ 47 and Δ 48 relative to equilibrium, while oxygen isotope exchange is associated with enrichment of both Δ 47 and Δ 48 relative to equilibrium. Cave rafts collected from proximate locations in Mexico exhibit the largest average departures from equilibrium ( Δ Δ 47 ¯ = −0.032 ± 0.007, Δ Δ 48 ¯ = −0.104 ± 0.035, where ΔΔ i is the measured value – the equilibrium value). This study shows how the Δ 47 -Δ 48 dual carbonate clumped isotope framework can be applied to a variety of tcave carbonate mineral samples, enabling identification of isotopic equilibria and therefore quantitative application of clumped isotope thermometry for paleoclimate reconstruction, or alternatively, constraining the mechanisms of kinetic effects. [ABSTRACT FROM AUTHOR]

In this paper, we intend to investigate the dynamics of the Circular Restricted Three-Body Problem. Here we assumed the primaries as the source of radiation and have variable mass. The gravitational perturbation from disk-like structure are also considered in this study. There exist five equilibrium points in this system. By considering the combined effect of disk-like structure and the mass transfer, we found that the classical collinear equilibrium points depart from the x-axis. We called these equilibrium points as quasi-collinear equilibrium points. Meanwhile, this combined effect also breaks the symmetry of triangular equilibrium point positions. We noted that the quasi-equilibrium points are unstable whereas the triangular equilibrium points are stable if the mass ratio μ is smaller than critical mass µc. Besides the mass ratio, the stability of triangular equilibrium points depend on time. [ABSTRACT FROM AUTHOR]

The polymer translocation through a nanopore from a donor space (or named cis side) to a receiver space (trans side) in the chaperone-induced crowded environment has attracted increasing attention in recent years due to its significance in biological systems and technological applications. In this work, we mainly focus on the effects of chaperone concentration and chaperone-polymer interaction on the polymer translocation. By assuming the polymer translocation to be a quasi-equilibrium process, the free energy F of the polymer can be estimated by Rosenbluth-Rosenbluth method and then the translocation time τ can be calculated by Fokker-Plank equation based on the obtained free energy landscape. Our calculation results show that the translocation time can be controlled by independently tuning the chaperone concentration and chaperone-polymer interaction at the cis side or the trans side. There exists a critical chaperone-polymer attraction ε*=−0.2 at which the volume exclusion and interaction effects of the chaperone can balance each other. Additionally, we also find that at large chaperone-polymer attraction, the translocation time is mainly governed by the diffusion coefficient of the polymer. [ABSTRACT FROM AUTHOR]

Results of high-temperature oxygen desorption from SrCoO3 – δ-oxide with mixed conductivity composed of obtained using an original quasi-equilibrium oxygen release technique are shown. The measurements are carried out with a characterized powder sample in a tubular reactor. The equilibrium phase diagram of the oxide in the 600–850°C temperature range and partial pressure of oxygen 0.2–6 × 10–5 atm is constructed. With the help of literature data, a correlation of phase diagram regions with their corresponding structures is obtained. [ABSTRACT FROM AUTHOR]

A proof of reciprocity relations for nonlinear systems in inhomogeneous variable electric and magnetic fields in the presence of unsteady spin currents, thermodynamic flows and mechanical disturbances is obtained by the Kubo method in the approximation of Markov relaxation and locally quasi-equilibrium distribution. [ABSTRACT FROM AUTHOR]

The external voltage-driven polymer translocation through a conical pore (with a large opening at the entry and a small tip at the exit) is studied by using the Langevin dynamics simulation in this paper. The entire translocation process is divided into an approaching stage and a threading stage. First, the approaching stage starts from the polymer entering the large opening and ends up at a terminal monomer reaching the pore tip. In this stage, the polymer will undergo the conformation adjustment to fit the narrowed cross-sectional area of the pore, leading to three approaching modes: the non-stuck mode with a terminal monomer arriving at the pore tip smoothly, the weak-stuck mode for the polymer stuck inside the pore for a short duration with minor conformational adjustments, and the strong-stuck mode with major conformational changes and a long duration. The approaching times (the duration of the approaching stage) of the three approaching modes show different behavior as a function of the pore apex angle. Second, the threading stage describes that the polymer threads through the pore tip with a linear fashion. In this stage, an increase in the apex angle causes the reduction of the threading time (the duration of the threading stage) due to the increase in the driving force with the apex angle at the tip. Moreover, we also find that with the increase in the apex angle or the polymer length, the polymer threading dynamics will change from the quasi-equilibrium state to the non-equilibrium state. [ABSTRACT FROM AUTHOR]

The effect of reversible modifiers on the initial rate of enzyme catalysed reactions has been investigated in a quasi-equilibrium approximation using the general modifier mechanism of Botts and Morales. It has been shown that, when investigating the dependence of the initial rate on the modifier concentration at a fixed substrate concentration, the kinetics of enzyme titration by reversible modifiers can generally be described using two kinetic constants. Just as the dependence of the initial rate on the substrate concentration (at a fixed modifier concentration) is described using two kinetic constants: the Michaelis constant K m and the limiting rate V m. Only one constant M 50 is needed to describe the kinetics of linear inhibition, and in the case of nonlinear inhibition and activation, along with M 50 the constant Q M is also needed. Knowing the values of the constants M 50 and Q M , it is possible to unambiguously determine the modification efficiency, that is, to calculate how many times the initial rate of the enzyme catalysed reaction will change when a certain modifier concentration is added to the incubation medium. The properties of these fundamental constants have been analysed in detail and the dependence of these constants on other parameters of the Botts-Morales model have been shown. Equations describing the dependence of relative reaction rates on the modifier concentration using these kinetic constants are presented. Various ways of linearising these equations for calculating the kinetic constants M 50 and Q M from experimental data are also presented. • The general modifier mechanism has been studied under quasi-equilibrium assumption. • The dependence of the initial rate on the modifier concentration has been analysed. • Only one constant (M 50) is needed to describe the kinetics of linear inhibition. • Two constants (M 50 , Q M) is needed to describe the kinetics of nonlinear inhibition. • These fundamental constants unambiguously determine the modification efficiency. [ABSTRACT FROM AUTHOR]

Landscapes are sculpted by a complex response of surface processes to external forcings, such as climate and tectonics. Several major river captures have been documented in the Hengduan Mountains, leading to the hypothesis that the region experiences exceptionally high rates of drainage reorganization driven by horizontal shortening and propagating uplift. Here we determine the prevalence, intensity, and spatial patterns of ongoing drainage reorganization in the Hengduan Mountains and evaluate the relative time scales of this transience by comparing drainage divide asymmetry for four geomorphic metrics that operate at different spatial and temporal scales. Specifically, we calculate the migration direction and the divide asymmetry index (DAI) drainage divide asymmetry in catchment-restricted topographic relief (CRR), hillslope gradient (HSG), normalized channel steepness (ksn), and normalized channel distance (χ). ksn and χ are both precipitation-corrected to account for the strong precipitation gradient across the region. The different spatial scales of these geomorphic metrics allow us to establish the relative timescales of observed landscape transience in the Hengduan Mountains, where local scale metrics measure short-term change and integral quantities measure long-term disequilibrium. We find a high incidence of strongly asymmetric divides in all metrics across the Hengduan Mountain region. Although the magnitude of asymmetry varies significantly between metrics, possibly due to a combination of metric-specific thresholds and varying proxy relationships with erosion rate, a majority of divides agree on divide migration direction. Agreement in divide migration direction indicates active landscape response when asymmetry is high and a state of quasi-equilibrium when asymmetry is low. Disagreements between the integral quantity, χ, and the other geomorphic metrics can be explained by different timescales of the underlying geomorphic processes, with χ reflecting a long-term response and CRR, HSG, and ksn capturing short-term perturbations to catchment structure. These perturbations include various transient mechanisms, such as differential tectonic uplift or erodibility, glacial alteration, and river captures. Our work confirms the high incidence of drainage reorganization across the Hengduan Mountains and highlights both transient and stable areas in the landscape with high resolution. We also offer valuable insights on the application of geomorphic metrics that can be generalized and applied to the study of landscape transience and drainage divide asymmetry in other settings. [ABSTRACT FROM AUTHOR]