Model In Equilibrium Research Articles

Numerical simulation of foam displacement impacted by kinetic and equilibrium surfactant adsorption

This study explores the effectiveness of foam in reducing gas mobility in porous media impacted by surfactant adsorption in highly heterogeneous porous media. The research focuses on assessing the influence of kinetic and equilibrium adsorption during foam displacement on reservoir sweep efficiency, considering co-injection and SAG (Surfactant Alternating Gas) injection strategies. Including the surfactant on the liquid phase and considering the surfactant adsorption effects fitted by experimental data, the mathematical modeling combines Darcy’s law, fluid phase conservation, surfactant transport equations, and a non-Newtonian foam model in local equilibrium. The simulations utilize FOSSIL (FOam diSplacement SImuLator), an in-house software composed of a stable and conservative numerical algorithm with reduced numerical diffusion. These properties are achieved by combining a hybrid mixed finite element method to solve the Darcy system with a central-upwind finite volume scheme to approximate the transport equations and adopting an implicit adaptive method in time. The results reveal that while omitting adsorption phenomena enhances sweep efficiency due to reduced surfactant loss, differences between equilibrium and kinetic adsorption models are minor (up to 0.3% in production). Consequently, these results suggest using simple adsorption models, such as equilibrium isotherms, rather than more complex models, such as kinetics. Additionally, the SAG approach outperforms co-injection (up to 19% in production), despite the fact that the adsorption is detrimental to both of them, aligning with literature results and previous findings.

Linear Time-Invariant Models of a Large Cumulus Ensemble

Abstract Methods in system identification are used to obtain linear time-invariant state-space models that describe how horizontal averages of temperature and humidity of a large cumulus ensemble evolve with time under small forcing. The cumulus ensemble studied here is simulated with cloud-system-resolving models in radiative–convective equilibrium. The identified models extend steady-state linear response functions used in past studies and provide accurate descriptions of the transfer function, the noise model, and the behavior of cumulus convection when coupled with two-dimensional gravity waves. A novel procedure is developed to convert the state-space models into an interpretable form, which is used to elucidate and quantify memory in cumulus convection. The linear problem studied here serves as a useful reference point for more general efforts to obtain data-driven and interpretable parameterizations of cumulus convection.

Numerical MHD simulations of solar flares and their associated small-scale structures

ABSTRACT Using numerical simulations, we study the formation and dynamics of solar flares in a local region of the solar atmosphere. The magnetohydrodynamics (MHD) equations describe the dynamic evolution of flares, including space-dependent and anomalous magnetic resistivity and highly anisotropic thermal conduction on a 2.5 D slice. We adopt an initial solar atmospheric model in magnetohydrostatic equilibrium, with a magnetic configuration consisting of a vertical current sheet, which helps trigger the magnetic reconnection process. Specifically, we study three scenarios, two with only resistivity and the third with resistivity plus thermal conduction. The main results of the numerical simulations show differences in the global morphology of the flares, including the post-flare loops and the current sheet in three cases. In particular, localized resistivity produces more substructure around the post-flare loops that could be related to the Ritchmyer–Meshkov Instability (RMI). Furthermore, in the scenario of anomalous resistivity, we identify the formation of a plasmoid and a jet at coronal heights. On the other hand, in the scenario with resistivity plus thermal conduction, the post-flare loops are smooth, and no apparent substructures develop. Besides, in the z-component of the current density for the Res + TC case, we observe the development of multiple magnetic islands generated due to the Tearing instability in the non-linear regime.

The mathematical model and analysis of the nanoparticle-stabilized foam displacement

This work proposes a mathematical model to study the foam displacement in porous media stabilized by nanoparticles. We consider a simplification of the Stochastic Bubble Population balance model in local equilibrium, with nanoparticle dependence inspired by the experimental data from the literature. It consists of a non-strictly hyperbolic system of conservation laws, which is solved for the generic initial and injection conditions. We investigate the existence of a global solution as a sequence of waves following the Conservation Laws Theory. When the solution is composed of two or more waves, we present necessary and sufficient conditions to guarantee the compatibility of these wave sequences. The analytical solution for the nanoparticle-stabilized foam displacement in porous media allowed us to quantify the effect of nanoparticles on foam displacement, focusing on the breakthrough time and cumulative water production. In agreement with the literature, when only gas is injected, the breakthrough time and the water production increase with the nanoparticle concentration. Although, we also observe that the effect of nanoparticles is less pronounced for high nanoparticle concentration. Counterintuitively, during gas-water co-injection for a certain parameter range, adding nanoparticles changes the mathematical solution qualitatively, yielding a negligible effect on water production. We discuss the most favorable conditions to observe the action of nanoparticles in laboratory experiments.

The physical basis of osmosis.

Osmosis is an important force in all living organisms, yet the molecular basis of osmosis is widely misunderstood as arising from diffusion of water across a membrane separating solutions of differing osmolarities, and hence different water concentrations. In 1923, Peter Debye proposed a physical model for a semipermeable membrane emphasizing the repulsive forces between solute molecules and membrane that prevent the solute from entering the membrane. His work was hardly noticed at the time and slipped out of view. We show that Debye's analysis of van 't Hoff's law for osmotic equilibrium also provides a consistent and plausible mechanism for osmotic flow. A difference in osmolyte concentrations in solutions separated by a semipermeable membrane leads to different pressures at the two water-membrane interfaces because the total repulsive force between solute molecules and the membrane is different at the two interfaces. Water is therefore driven through the membrane for exactly the same reason that pure water flows in response to an imposed hydrostatic pressure difference. In this paper, we present the Debye model in both equilibrium and flow conditions. We point out its applicability regardless of the nature of the membrane with examples ranging from the predominantly convective flow of water through synthetic membranes and capillary walls to the purely diffusive flow of independent water molecules through a lipid bilayer and the flow of a single-file column of water molecules in narrow protein channels.

Gyro orbit simulations of neutral beam injection in Wendelstein 7-X

Simulations exploring neutral beam operation in Wendelstein 7-X (W7-X) at reduced magnetic field are performed using a newly implemented gyro orbit model in the BEAMS3D code. Operation at field strengths below the nominal 2.5 T are seen as a path to explore both high beta plasmas and as a means to access magnetic configurations not possible at 2.5 T. As the field strength becomes smaller, the gyro radius for 55 keV fast protons grows from at 2.5 T to at 0.75 T in a device with minor radius bringing into question the applicability of the gyro center approximation. To address this a gyro orbit model was implemented in the BEAMS3D code. Agreement is found between the gyro center and gyro orbit models in a circular cross section tokamak equilibrium at high field. A set of W7-X equilibria are assessed with fixed density and temperature profiles but decreasing magnetic field strength (increasing plasma beta). Neutral beam deposition is found to be mostly unaffected with changes in the core of the plasma associated with the Shafranov-shift. In general good agreement is found between gyro orbit and gyro center simulations at 2.5 T. Both models indicate increasing losses with decreasing magnetic field strength with the gyro orbit losses being higher at all field strengths. Gyro orbit simulations to the first wall of W7-X show a change in loss pattern with decreasing magnetic field strength. A preliminary assessment of losses to fast ion loss detectors are made.

A climate–economy model in a stochastic differential equilibrium with fractional Brownian motions and Poisson jumps

A climate–economy model in a stochastic differential equilibrium with fractional Brownian motions and Poisson jumps

Integrating macroeconomics and economic geography: the neoclassical growth model in spatial general equilibrium

ABSTRACT The neoclassical growth model and the Roback model of spatial general equilibrium (SGE) are integrated to study the joint determination of macroeconomic phenomena (gross domestic product (GDP) and the rate of interest) and spatial economic phenomena (the spatial distribution of gross regional product (GRP), employment and capital). If internal capital mobility is perfect and regional savings rates are homogeneous, GDP depends on SGE, but SGE does not depend on GDP. If saving rates are spatially heterogeneous, GDP and the rate of interest depend on SGE, but SGE does not depend on the rate of interest and GDP. If in addition capital is imperfectly mobile, macroeconomic outcomes such as GDP, the rate of interest and SGE are jointly determined. In general, therefore, the dichotomy between macroeconomics and economic geography breaks down.

Effects of informative advertising on the formation of market structures

Information overload is a common phenomenon in the advertising dynamics of the twenty-first century, this not only causes inefficiencies in terms of advertising spending, but also, its management affects firms’ potential market power. This article builds a model in which firms compete by sending informative ads to passive consumers with reduced attention. Ads are sent through different transmission technologies, distinguished by their levels of information on consumer preferences. In equilibrium, sender strategies from firms with better-informed transmission technologies dominate sender strategies from firms with worse-informed transmission technologies, generating latent market power as a result of higher efficiency in ad location. This contribution is contrary to pro-competitive effects stated by current literature on strictly informative advertising. For context and simplicity, an iterative simulation of the model in equilibrium is carried out for the case of two transmission technologies, with the best-informed transmission technology belonging to an intermediary monopolist: the segmentation agent. The simulation yields consistent evidence of market power and industrial concentration in favor of firms that resort to intermediation by the segmentation agent. Our findings can be applied to suggest state intervention policies towards segmentation monopolists/oligopolists in information markets, to promote competition and diminish information overload.

A numerical investigation into the influence of the surfactant injection technique on the foam flow in heterogeneous porous media

We propose a sequential algorithm to investigate the influence of surfactant injection on foam-induced mobility reduction in two-phase liquid–gas flows in highly heterogeneous porous media. A foam model in local equilibrium is adopted in this context, assuming non-Newtonian foam behavior. A fractional flow formulation based on global pressure that includes the surfactant in the liquid phase is adopted, resulting in a system that couples elliptic and hyperbolic equations. These equations are split into two sub-systems that group equations of the same kind and are solved employing a sequential numerical algorithm that combines a locally conservative hybrid finite element method to approximate the hydrodynamics of the system with a central-upwind finite volume method for the transport equations. The resulting spatial discretized system is approximated in time by applying a multi-step, implicit finite difference method. The hydrodynamics and hyperbolic problems are solved using a staggered algorithm in different time scales. Through comparison with experimental data and classical numerical methods, we validated the proposed methodology and demonstrated its ability to produce stable approximations with reduced numerical dissipation and computational cost. Then, we apply the sequential algorithm to compare the co-injection of the water–gas–surfactant with the Surfactant Alternating Gas (SAG) technique in two-dimensional flows in highly heterogeneous media. The numerical results suggest a better sweep efficiency using the SAG injection technique when compared with the co-injection approach for the equivalent amount of injected surfactant.

Dynamic phase transitions on the kagome Ising ferromagnet.

We perform extensive Monte Carlo simulations to investigate the dynamic phase transition properties of the two-dimensional kinetic Ising model on the kagome lattice in the presence of square-wave oscillating magnetic field. Through detailed finite-size scaling analysis, we study universality aspects of the nonequilibrium phase transition. Obtained critical exponents indicate that the two-dimensional kagome-lattice kinetic Ising model belongs to the same universality class with the corresponding Ising model in equilibrium. Moreover, dynamic critical exponent of the local moves used in simulations is determined with high precision. Our numerical results are compatible with the previous ones on kinetic Ising models.

An appreciative theorizing approach to gazelle enterprises assisted by the Arica Business Center

The role played by gazelles in economic development processes is a topic of growing interest in the scientific and business community. Empirical evidence agrees that gazelles and fast-growing firms are innovative, transformative economic structures with capabilities to promote economic growth. This paper examines the role of a group of gazelle firms assisted in Arica that positively weigh the cost-benefit ratio of the Business Center program in Chile. This path poses an exercise in “appreciative theorizing” —as Richard Nelson (2018) calls it— and examines various factors of growth that cannot be explained by economic models in equilibrium.

Resolving ambiguities in core size determination of magnetic nanoparticles from magnetic frequency mixing data

Frequency mixing magnetic detection (FMMD) has been widely utilized as a measurement technique in magnetic immunoassays. It can also be used for the characterization and distinction (also known as “colourization”) of different types of magnetic nanoparticles (MNPs) based on their core sizes. In a previous work, it was shown that the large particles contribute most of the FMMD signal. This leads to ambiguities in core size determination from fitting since the contribution of the small-sized particles is almost undetectable among the strong responses from the large ones. In this work, we report on how this ambiguity can be overcome by modelling the signal intensity using the Langevin model in thermodynamic equilibrium including a lognormal core size distribution fL(dc,d0,σ) fitted to experimentally measured FMMD data of immobilized MNPs. For each given median diameter d0, an ambiguous amount of best-fitting pairs of parameters distribution width σ and number of particles Np with R2 > 0.99 are extracted. By determining the samples’ total iron mass, mFe, with inductively coupled plasma optical emission spectrometry (ICP-OES), we are then able to identify the one specific best-fitting pair (σ, Np) one uniquely. With this additional externally measured parameter, we resolved the ambiguity in core size distribution and determined the parameters (d0, σ, Np) directly from FMMD measurements, allowing precise MNPs sample characterization.

On the Origin of Hemoglobin Cooperativity under Non-equilibrium Conditions.

Abnormal hemoglobins can have major consequences for tissue delivery of oxygen. Correct diagnosis of hemoglobinopathies with altered oxygen affinity requires a determination of hemoglobin oxygen dissociation curve, which relates the hemoglobin oxygen saturation to the partial pressure of oxygen in the blood. Determination of the oxygen dissociation curve of human hemoglobin is typically carried out under conditions in which hemoglobin is in equilibrium with O2 at each partial pressure. However, in the human body due to the fast transit of red blood cells through tissues hemoglobin oxygen exchanges occur under non-equilibrium conditions. We describe the determination of non-equilibrium oxygen dissociation curve and show that under these conditions the true nature of hemoglobin cooperativity is revealed as emerging solely from the consecutive binding of oxygen to each one of the four subunits of hemoglobin until the entire tetramer is saturated. We call this form of cooperativity the sequential cooperativity of hemoglobin and define the simplest model that includes it as the minimalist model of hemoglobin. A single instantiation of this model accounts for ~70% of hemoglobin cooperativity under non-equilibrium conditions. The total cooperativity of hemoglobin can be viewed more correctly as the summation of two instantiations of the minimalist model (each one corresponding to a tetramer of low and high affinity for O2, respectively) in equilibrium with each other, as in the Monod-Wyman-Changeux model of hemoglobin. In addition to offering new insights on the nature of hemoglobin reaction with oxygen, the methodology described here for the determination of hemoglobin non-equilibrium oxygen dissociation curve provides a simple, fast, low-cost alternative to complex spectrophotometric methods, which is expected to be particularly valuable in regions where hemoglobinopathies are a significant public health problem, but where highly specialized laboratories capable of determining a traditional oxygen dissociation curve are not easily accessible.

Bridging Theories for Ecosystem Stability Through Structural Sensitivity Analysis of Ecological Models in Equilibrium

Ecologists are challenged by the need to bridge and synthesize different approaches and theories to obtain a coherent understanding of ecosystems in a changing world. Both food web theory and regime shift theory shine light on mechanisms that confer stability to ecosystems, but from different angles. Empirical food web models are developed to analyze how equilibria in real multi-trophic ecosystems are shaped by species interactions, and often include linear functional response terms for simple estimation of interaction strengths from observations. Models of regime shifts focus on qualitative changes of equilibrium points in a slowly changing environment, and typically include non-linear functional response terms. Currently, it is unclear how the stability of an empirical food web model, expressed as the rate of system recovery after a small perturbation, relates to the vulnerability of the ecosystem to collapse. Here, we conduct structural sensitivity analyses of classical consumer-resource models in equilibrium along an environmental gradient. Specifically, we change non-proportional interaction terms into proportional ones, while maintaining the equilibrium biomass densities and material flux rates, to analyze how alternative model formulations shape the stability properties of the equilibria. The results reveal no consistent relationship between the stability of the original models and the proportionalized versions, even though they describe the same biomass values and material flows. We use these findings to critically discuss whether stability analysis of observed equilibria by empirical food web models can provide insight into regime shift dynamics, and highlight the challenge of bridging alternative modelling approaches in ecology and beyond.

Spectrum synthesis for radially pulsating stars with shocked atmospheres

ABSTRACT spec_puls describes a suite of computer programs to simulate the emergent spectrum from a radially pulsating star. It combines a Christy-type non-linear pulsation code with classical stellar atmosphere codes. The principal aim is to interpret the dynamical spectrum of the radially pulsating extreme helium star V652 Herculis (V652 Her), which shows a strong shock at minimum radius. The components are general enough to treat other classes of radial pulsation. The theoretical spectrum from a shocked pulsation model shows line doubling, with the blue component emerging at standstill velocity and accelerating blueward. The doubling phase depends on line depth and parent ion. The behaviour of line cores post-shock points to a drop in the ionization temperature, although the gas temperature in the model remains high. Shock compression leads to phase-dependent strengthening of Stark-broadened line wings, with the far wings responding first. With velocity-, temperature-, and pressure-sensitive diagnostics, detailed tomography of the pulsation-driven shock in V652 Her seems possible. Even when no shock is present, the dynamical spectrum is significantly different from a model in hydrostatic equilibrium. Using the quasi-static approximation (e.g. at maximum radius) may lead to a considerable underestimate of the star’s mean effective temperature and surface gravity.

Anisotropic compact objects with Finch–Skea geometry in EGB gravity

We present a new class of relativistic anisotropic stellar models with spherically symmetric matter distribution in Einstein Gauss–Bonnet (EGB) gravity. A higher dimensional Finch–Skea geometry in the theory is taken up here to construct stellar models in hydrostatic equilibrium. The Gauss–Bonnet term is playing an important role in accommodating neutron stars. We study the physical features namely, the energy density, the radial and tangential pressures and the suitability of the models. It is found that the equation of state of such stars are non-linear which is determined for a given mass and radius of known stars. The stability of the stellar models are also explored for a wide range of values of the model parameters.

Numerical experiments to help understand cause and effect in massive star evolution

ABSTRACT The evolution of massive stars is affected by a variety of physical processes, including convection, rotation, mass-loss, and binary interaction. Because these processes modify the internal chemical abundance profiles in multiple ways simultaneously, it can be challenging to determine which properties of the stellar interior are primarily driving the overall evolution. Building on previous work, we develop a new modelling approach called snapshot that allows us to isolate the key features of the internal abundance profile that drive the evolution of massive stars. Using our approach, we compute numerical stellar structure models in thermal equilibrium covering key phases of stellar evolution. For the main sequence, we demonstrate that models with the same mass and very similar surface properties can have different internal distributions of hydrogen and convective core masses. We discuss why massive stars expand after the main sequence and the fundamental reasons for why they become red, blue or yellow supergiants. For the post-main sequence, we demonstrate that small changes in the abundance profile can cause very large effects on the surface properties. We also discuss the effects that produce blue supergiants and the cause of blue loops. Our models show that massive stars with lower metallicity tend to be more compact due to the combined effect of lower CNO abundances in the burning regions and lower opacity in the envelope.

Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production.

Many complex fluids can be described by continuum hydrodynamic field equations, to which noise must be added in order to capture thermal fluctuations. In almost all cases, the resulting coarse-grained stochastic partial differential equations carry a short-scale cutoff, which is also reflected in numerical discretisation schemes. We draw together our recent findings concerning the construction of such schemes and the interpretation of their continuum limits, focusing, for simplicity, on models with a purely diffusive scalar field, such as ‘Model B’ which describes phase separation in binary fluid mixtures. We address the requirement that the steady-state entropy production rate (EPR) must vanish for any stochastic hydrodynamic model in a thermal equilibrium. Only if this is achieved can the given discretisation scheme be relied upon to correctly calculate the nonvanishing EPR for ‘active field theories’ in which new terms are deliberately added to the fluctuating hydrodynamic equations that break detailed balance. To compute the correct probabilities of forward and time-reversed paths (whose ratio determines the EPR), we must make a careful treatment of so-called ‘spurious drift’ and other closely related terms that depend on the discretisation scheme. We show that such subtleties can arise not only in the temporal discretisation (as is well documented for stochastic ODEs with multiplicative noise) but also from spatial discretisation, even when noise is additive, as most active field theories assume. We then review how such noise can become multiplicative via off-diagonal couplings to additional fields that thermodynamically encode the underlying chemical processes responsible for activity. In this case, the spurious drift terms need careful accounting, not just to evaluate correctly the EPR but also to numerically implement the Langevin dynamics itself.

Enhancing Students’ Academic Interest Using Two Instructional Models in Chemical Equilibrium In Benue State, Nigeria

The study investigated the effects of 4As and 5Es instructional models on senior secondary II students’ interest in chemical equilibrium in Benue State. Two research questions guided the study, while two hypotheses were formulated and tested. The study adopted quasi-experimental, non-randomized control group pretest and posttest design. The population of the study comprised 8,864 SSII Chemistry students. Samples of 194 SSII students from six Government grant aided secondary schools in Benue Education Zone C were selected using multistage sampling techniques. Instrument for the study was Chemical Equilibrium Students’ Interest Rating Questionnaire (CESIRQ) with reliability coefficient of 0.70. Analysis using mean, standard deviation and mean gain scores were used to answer the research questions while Analysis of Covariance (ANCOVA) was used to test the hypotheses at 0.05 level of significance. The findings of the study revealed that there was a significant difference in the mean interest rating of students taught chemical equilibrium using 4As, 5Es instructional models and modified lecture method [ F 2,193 = 89.995; P = 0.000< 0.05]. There is no significant difference in the mean interest rating of male and female students taught chemical equilibrium using 4As instructional model [ F 1,62 = 2.339; P = 0131< 0.05]. There is no significant difference in the mean interest rating of male and female students taught chemical equilibrium using 4As instructional model [ F 1,63 = 3.173; P = 0.080< 0.05].There is no significant interaction effects between instructional models and gender on students interest [F2, 193 = .262; P = .769 > 0.05] when taught chemical equilibrium concepts. The study concludes that 5Es and 4As instructional models have greater effects on students’ academic interest in Chemical Equilibrium than Modified Lecture Method on SS II students in Benue Education Zone C. Based on the findings, it was recommended among others that Ministry of Education through Chemistry teachers should emphases the use of 5Es and 4As instructional models in teaching to enhance the academic interest of students in Chemistry.