Quasi Equilibrium Research Articles

Quasi equilibrium approximations of the fixation index under neutrality: The finite and infinite island models

The fixation index FST and the coefficient of gene differentiation GST are analyzed for the finite island model under short time spans, ignoring mutations. Dividing the reproduction cycle into the three steps–gamete formation, fertilization, and migration–we develop a new approach for computing quasi equilibrium formulas for FST (and GST). Our formulas generalize earlier ones and reveal that the equilibrium value of FST is influenced not only by the migration rate and local effective population size, Ne, but also by the local census size N, particularly so when the migration rate is high. The order of migration and fertilization is found to have a smaller effect on FST. A major advantage compared to previous approaches is that stochastic allele frequency of migrants is easily accommodated, thereby avoiding underestimation of FST for large migration rates.

Interactions between Shallow and Deep Convection under a Finite Departure from Convective Quasi Equilibrium

Abstract The present paper presents a simple theory for the transformation of nonprecipitating, shallow convection into precipitating, deep convective clouds. To make the pertinent point a much idealized system is considered, consisting only of shallow and deep convection without large-scale forcing. The transformation is described by an explicit coupling between these two types of convection. Shallow convection moistens and cools the atmosphere, whereas deep convection dries and warms the atmosphere, leading to destabilization and stabilization, respectively. Consequently, in their own stand-alone modes, shallow convection perpetually grows, whereas deep convection simply damps: the former never reaches equilibrium, and the latter is never spontaneously generated. Coupling the modes together is the only way to reconcile these undesirable separate tendencies, so that the convective system as a whole can remain in a stable periodic state under this idealized setting. Such coupling is a key missing element in current global atmospheric models. The energy cycle description used herein is fully consistent with the original formulation by Arakawa and Schubert, and is suitable for direct implementation into models using a mass flux parameterization. The coupling would alleviate current problems with the representation of these two types of convection in numerical models. The present theory also provides a pertinent framework for analyzing large-eddy simulations and cloud-resolving modeling.

Adsorption of some cationic and anionic dyes on magnetite nanoparticles-modified activated carbon from aqueous solutions: equilibrium and kinetics study

In this study, magnetite nanoparticles-modified low-cost activated carbon (MMAC) was used as an adsorbent for the removal of the anionic and cationic dyes Congo red, reactive blue 19, thionine, janus green B, methylthymol blue and mordant Blue 29, from aqueous solutions. Batch studies were performed to address various experimental parameters like pH, contact time, temperature and adsorbent dosage for the removal of these dyes. Kinetic studies showed that the adsorption of dyes on MMAC was a rapid process. Quasi equilibrium was reached in 30 min. Pseudo-first order and pseudo-second order models were used to fit the experimental data. Pseudo-second order rate equation was able to provide realistic description of adsorption kinetics. Equilibrium isotherms were analyzed by Freundlich, Langmuir, Redliche–Peterson (R–P) and Sips equations using correlation coefficients and RMS error function. Sips equation is found to best represent the equilibrium data for dye–MMAC system. It was clear that affinity of synthesized adsorbent to cationic dyes is much higher than anionic dyes.

Analytical Framework for the Steady State Analysis of Wavelength-Dependent and Intensity-Dependent Interaction of Multiple Monochromatic Beams in Semiconductor Photonic Structures With Multiple Active and Passive Sections

The design, optimization, and parametric studies of photonic integrated circuits typically require steady state optical field profiles. Previously, a planewave-based eigenmode expansion and mode-matching analysis was shown to be an efficient method in calculating the steady-state optical field profile of a monochromatic beam in 2-D/3-D geometries with passive media. In this paper, we extend this approach for steady state analyses of photonic integrated circuits with both passive as well as active media, by enabling the interaction of multiple monochromatic beams with the medium via a self-consistent solution of the Maxwell's equations and a modified Bloch equations-based analytical framework. Through the Bloch equations-based framework, we treat the active medium as an ensemble of two-level Bloch atoms with varying density of states to characterize the bandstructure of semiconductors. This enables us to track carrier transitions between conduction and valence bands induced by the light-matter interaction over the entire bandwidth of excited carriers, and yield the correct quasi equilibrium Fermi-Dirac distributions. The numerical solution of obtaining the carrier distributions at each spatial location in active media is simplified by reducing the modified Bloch equations with multiple unknowns to a single equation with just one unknown, to enhance the computational efficiency of the approach. The calculated carrier distributions are then used to evaluate the spatial profile of the complex refractive index seen by each monochromatic beam along with its optical field profile. The applicability of the method to 2-D structures of complex geometry is demonstrated by obtaining the spatial profiles of refractive indices seen by two simultaneously interacting monochromatic beams along with their optical field profiles in a waveguide with multiple passive and active sections.

Evolution of isotropic and anisotropic spatial distribution of large ion clouds during the onset of quasi state equilibrium condition in a Paul trap

A study of variation of large ion cloud spatial density distribution with the applied potential, in a three dimensional (3-d) Paul trap has been conducted. Large ion clouds (ion numbers >106) have been trapped using a combination of static field (DC) and radiofrequency (RF) electric fields and are cooled using buffer gas. Laser scanning across the trap in the x and z directions yielded the spatial density distribution at different applied trap potential well depths. The spatial density distribution of the ion cloud exhibited a good Gaussian fit for all the three set of operating parameters chosen, enabling the study of a near; spherical, oblate and prolate distributions. Using Monte Carlo code theoretical simulations for 1000 ions were carried out and the spatial density distribution of the ion cloud is compared with the experimental values.

Recombinative dissociation and the evolution of a molecular ultracold plasma

We present a kinetic model based on coupled rate-equation simulations that accounts for state-detailed rate processes in the evolution of a molecular Rydberg gas to plasma. Calculations support a steady-state picture of Rydberg predissociation and its contribution to plasma dissipation. Inelastic collisions of electrons with Rydberg states efficiently transfer energy from and to the thermal bath of free electrons, giving rise to quasi equilibria of relatively high temperature. Dissipative effects that remove low-n population change the time course of this heating. Including statistically sampled channels of Rydberg predissociation with n- and ℓ-dependent lifetimes slows the relaxation to quasi equilibrium and retards the initial electron temperature increase. At later times, the dissociative loss of low-n population displaces this quasi equilibrium leading to continuous electron heating. Dissociation products appear at a rate that is controlled initially by the rate of Rydberg relaxation to quasi equilibrium. Thereafter, the overall rate at which the total dissociation consumes neutral molecules determines the decay rate for all levels. Simulations predict a total predissociation rate that is smaller than the initial rate of direct electron–ion dissociative recombination. At later times, residual predissociation displays an apparent first-order decay with a rate constant that fits well with experimental observations.

Bi-dust solitary waves

Propagations of non linear solitary waves in bi-dust plasma systems is analyzed. In the present treatment, one of the dust particles is assumed to be much smaller than other one, in such a way that there is enough time for this particle to reach quasi thermal equilibrium. Maxwell-Boltzmann factors are therefore applied for the density distribution of electrons, ions and light dust grains. The treatment of the problem can now be made by the method of the pseudo-potential taking into account temperature effects as function of the density of the heavy grain. In the limit where the light grain density tends to zero the effects found by other authors when only one kind of grains is re-obtained. Several numerical calculations for different values of the characteristic parameters will be shown.

Enzymatic synthesis of fructooligosaccharides by levansucrase from Bacillus amyloliquefaciens: specificity, kinetics, and product characterization

► B. amyloliquefaciens levansucrase (LS) has one of the highest turnover numbers for the catalysis of the transfructosylation reaction. ► A shift of the transfructosylation reaction further towards the polymerization side was observed in the presence of raffinose donor as compared to sucrose. ► LS synthesized a variety of hetero-fructooligosaccharides from various fructosyl acceptors with disaccharides being the best ones. ► The formation of polymer fructans (Gal-(Fru)n-Fru, n > 18) was the most abundant in the galactose-acceptor reaction. ► The oligomers (Xyl-(Fru)n-Fru, n < 18) were the dominant transfructosylation products in the xylose-acceptor reaction. The kinetic parameters and the product spectra of purified Bacillus amyloliquefaciens levansucrase (LS) were investigated in the present study. LS was highly transfructosylic than hydrolytic with high k cat value of 1136.5 s −1 for its transfructosylation activity. Contrary to the hydrolytic activity, the kinetic of the transfructosylation activity of LS was best fitted to the Hill model with low Hill coefficients ( n H , 0.74), indicating the negative binding cooperativity of substrates. These results reveal the competition of sucrose with the growing (oligo)polymer chain as a fructosyl acceptor. A shift of the transfructosylation reaction further towards the polymerization side was observed in the presence of raffinose as a fructosyl donor as compared to sucrose. The acceptor specificity studies reveal the ability of LS to synthesize a variety of hetero-fructooligosaccharides from various saccharides as fructosyl acceptors. Disaccharides were more favourable fructosyl acceptors as compared to monsaccharides. Contrary to disaccharides acceptor reactions, LS-catalyzed transfructosylation of monosaccharides did not yield a quasi equilibrium state. Contrary to lactose, galactose, xylose and glucose acceptor reactions, a lower accumulation of levan was detected in the presence of maltose. When sucrose and raffinose coexisted, they were both used as fructosyl donor, revealing the low acceptor specificity of LS towards raffinose. The structures of products were analysed NMR and MS.

Quasi steady state and partial equilibrium approximations: their relation and their validity

The quasi steady state and partial equilibrium approximations are analysed in the context of a system of nonlinear differential equations exhibiting multiscale behaviour. Considering systems in the most general and dimensional form , it is shown that both approximations are limiting cases of leading-order asymptotics. Algorithmic conditions are established which guarantee that the accuracy and stability delivered by the two approximations are equivalent to those obtained with leading-order asymptotics. It is shown that the quasi steady state approximation is a limiting case of the partial equilibrium approximation. Algorithms are reported for the identification of the variables in quasi steady state and/or of the processes in partial equilibrium.

Fischer–Tropsch synthesis using H2/CO/CO2 syngas mixtures: A comparison of paraffin to olefin ratios for iron and cobalt based catalysts

Fischer–Tropsch synthesis (FTS) using H2/CO/CO2 syngas mixtures over cobalt and iron based catalysts was carried out in a fixed-bed reactor. CO2 rich feeds produce products that are mostly light hydrocarbons with higher molar paraffin to olefin (P/O) ratio, whereas CO rich feeds shift the product composition to an FT type product with higher olefin product selectivity over both iron and cobalt based catalysts. Although the P/O ratio for FTS is strongly dependent on the operating conditions, the experimental evidence shows that the linear relationship between P(n+1)/O(n+1) and P(n)/O(n) holds for a large number of experiments. It is also shown to be independent of the type of the reactor, the composition of the syngas, reaction conditions and the kind of catalyst. Two features about the ratio of ξ=[P(n+1)/O(n+1)]/[P(n)/O(n)] for the FT products have been identified: (1) with n>2, the experimental values of ξn>2 are higher than 1, fairly constant and independent of chain length n; (2) with chain length n=2, the ratio of P3/O3 to P2/O2 (ξn=2) is significantly different, and shows that ξn=2≪ξn>2. An equilibrium hypothesis is considered in an attempt to explain this experimental phenomenon.A simple vapor–liquid equilibrium (VLE) model indicates that the ratio of P(n+1)/O(n+1) to P(n)/O(n) changes in a range of (1, 1/β), where β is the variation of the vapor pressure coefficient, which is related to the incremental energy of vaporization per CH2 unit of the hydrocarbon chain. Our experimental results support the expression when the chain length n>2. But with chain length n=2, this expression is unable to explain the relationship between P3/O3 and P2/O2. Another model, based on quasi reaction equilibrium, is developed to explain the linear relationship between P(n+1)/O(n+1) and P(n)/O(n). We assume that the reaction of Cn+1H2n+2+CnH2n+2=Cn+1H2n+4+CnH2n reaches quasi-equilibrium. Because the experimental results are quite close to the equilibrium calculations, we postulate that the product distribution might be determined by considering reaction equilibrium.

Atmospheric Circulation Response to an Instantaneous Doubling of Carbon Dioxide. Part I: Model Experiments and Transient Thermal Response in the Troposphere*

AbstractThis study aims to understand the dynamical mechanisms driving the changes in the general circulation of the atmosphere due to increased carbon dioxide (CO2) by looking into the transient step-by-step adjustment of the circulation. The transient atmospheric adjustment is examined using the National Center for Atmospheric Research Community Atmosphere Model, version 3, coupled to a slab ocean model, and the CO2 concentration in the atmosphere is uniformly and instantaneously doubled. The thermal structure and circulation response is well established after one year of integration, with the magnitudes gradually increasing afterward toward quasi equilibrium. Tropical upper-tropospheric warming occurs in the first month. The expansion of the warming in the mid- and upper troposphere to the subtropics occurs later and is found to be primarily dynamically driven due to the intensification of transient eddy momentum flux convergence and resulting anomalous descending motion in this region. The poleward displacement of the midlatitude tropospheric jet streams occurs together with the change in eddy momentum flux convergence, but only after the intensification of the subpolar westerlies in the stratosphere. The results demonstrate the importance of the tropospheric eddies in setting up the extratropical tropospheric response to global warming.

Stagnation of a gas puff Z pinch

Simulations of a gas puff Z pinch were performed, using an appropriately modified version of the M3D code [Park et al., Phys. Plasmas 6, 1796 (1999)]. The simulations investigated the stagnation process, including the effects of the shock driven by the magnetic piston and the influence of the Rayleigh Taylor instability. The results compare favorably with recent experimental measurements. The stagnated plasma reaches a quasi equilibrium with approximate balance of plasma pressure and magnetic pressure, measured by β≤1. The dependence of the stagnation radius on β and radiative energy loss are calculated, using a simple radiation model.

Beyond Spacetime Geometry—The Death of Philosophy and Its Quantum Reincarnation

Contrary to the “end” and “death” assertions on philosophy, this paper predicts an equilibrium-based and harmony-centered scientific reincarnation of philosophy. Logically, the reincarnation is backed by a formal system and a background independent geometry that transcends spacetime. Physically, it is supported by definable quantum causality and bipolar logical unifications of matter and antimatter, particle and wave, big bang and black hole, relativity and quantum entanglement. Philosophically, it is distinguished from Western metaphysics and dialectics as well as the Dao of Laozi. It is named a quantum reincarnation for its central claim that YinYang bipolar quantum entanglement is the source of causality for the Being of beings following the 2nd law of thermodynamics. Thus, it presents a modest unification of science and philosophy for their reciprocal interaction (Note: Equilibrium subsumes non-equilibrium and quasi—equilibrium as local non-equilibriums can form global equilibrium or quasi-equilibrium).

Static Studies of a Steel Chain Ropeway Section Using Msc Adams

This paper describes work that has been done on an innovative use of a steel chain as a cable in chain ropeway system developed for use in the mountain orchards of china. This work focuses on the use of Msc Adams in describing the quasi static behavior of the configuration of the chain ropeway. A model was built in solid works and then transferred to Msc Adams which was used to predict the profile of the chain and the tension for various loads. From this study it has been shown that Msc Adams can be a valuable tool in solving problems related to the quasi static and equilibrium state of the chain rope way system and getting an in depth behavior of its dynamics. There is now a foundation to proceed on the dynamic investigation of the chain ropeway system.

Validity of the Einstein Relation in Disordered Organic Semiconductors

It is controversial whether energetic disorder in semiconductors is already sufficient to violate the classical Einstein relation, even in the case of thermal equilibrium. We demonstrate that the Einstein relation is violated only under nonequilibrium conditions due to deeply trapped carriers, as in diffusion-driven current measurements on organic single-carrier diodes. Removal of these deeply trapped carriers by recombination unambiguously proves the validity of the Einstein relation in disordered semiconductors in thermal (quasi)equilibrium.

Quantifying the limits of convective parameterizations

[1] Quasi-equilibrium (QE) closure is an approximation that is expected to apply to a large ensemble of clouds under slowly changing weather conditions. It breaks down under rapidly changing conditions or when the domain size is too small to provide an adequate sample of the cloud field. We explore fluctuations about an equilibrium state as simulated by a three-dimensional cloud-resolving model. An ensemble of simulations is used to determine how the response to prescribed periodic large-scale forcing changes with the period of the forcing and the size of the averaging domain. The vertical profile of the forcing is loosely based on GATE data. Results are compared with those from constant forcing simulations. In the constant forcing simulations, the noise-to-signal ratio is nearly independent of forcing magnitude. With time-varying forcing, a considerable range of responses is found. As expected, the more slowly the forcing varies, the better the response is approximated by QE. Errors become large when the period of the forcing is less than 30 h, suggesting that the diurnal cycle cannot be accurately simulated with a QE closure. Nondeterministic variability becomes more significant with smaller domain sizes. For the cases studied, a domain width of at least 180 km is needed to obtain an adequate sample of the cloud population.

Theoretical investigations of localized, semi-localized and unified models of thermally stimulated luminescence: a review

Localized transitions, which represent sub-conduction recombination, have been investigated comprehensively using localized recombination model (LRM) of thermally stimulated luminescence (TSL). The study reveals the following results: (i) The conventional quasi-equilibrium (QE) approximation criteria do not hold in LRM and new criteria for QE approximation is proposed. (ii) The glow peak temperature “Tm” is always independent of the radiation dose.

Indirect Impact of Atmospheric Aerosols in Idealized Simulations of Convective–Radiative Quasi Equilibrium. Part II: Double-Moment Microphysics

AbstractThis paper extends the previous cloud-resolving modeling study concerning the impact of cloud microphysics on convective–radiative quasi equilibrium (CRQE) over a surface with fixed characteristics and prescribed solar input, both mimicking the mean conditions on earth. The current study applies sophisticated double-moment warm-rain and ice microphysics schemes, which allow for a significantly more realistic representation of the impact of aerosols on precipitation processes and on the coupling between clouds and radiative transfer. Two contrasting cloud condensation nuclei (CCN) characteristics are assumed, representing pristine and polluted conditions, as well as contrasting representations of the effects of entrainment and mixing on the mean cloud droplet size. In addition, four sets of sensitivity simulations are also performed with changes that provide a reference for the main simulation set.As in the previous study, the CRQE mimics the estimates of globally and annually averaged water and energy fluxes across the earth’s atmosphere. There are some differences from the previous study, however, consistent with the slightly lower water vapor content in the troposphere and significantly reduced lower-tropospheric cloud fraction in current simulations. There is also a significant reduction of the difference between the pristine and polluted cases, from ∼20 to ∼4 W m−2 at the surface from ∼20 to ∼9 W m−2 at the top of the atmosphere (TOA). The difference between the homogeneous and extremely inhomogeneous mixing scenarios, ∼20 W m−2 in the previous study, is reduced to a mere 2 (1) W m−2 at the surface (TOA). An unexpected difference between the previous and current simulations is the lower Bowen ratio of the surface heat flux, the partitioning of the total flux into sensible and latent components. It is shown that most of the change comes from the difference in the representation of rain evaporation in the subcloud layer in the single- and double-moment microphysics schemes. The difference affects the mean air temperature and humidity near the surface, and thus the Bowen ratio. The differences between the various simulations are discussed, contrasting the process-level approach with the impact of cloud microphysics on the quasi-equilibrium state with a more appropriate system dynamics approach. The key distinction is that the latter includes the interactions among all the processes in the modeled system.

Study of aggregate formation of caffeine in water by molecular dynamics simulation

The driving force of assembly formation of caffeine in water has been studied using molecular dynamics (MD) as the tool. A total of 340 ns long MD simulations were conducted with different caffeine concentrations in aqueous solutions. For the study of concentration dependence of aggregate formation all the simulations were performed in isothermal isobaric ensembles, where, pressure was maintained at 1 bar and temperature was kept at 300 K. The thermodynamics of aggregate formation were investigated at 1 bar by varying the temperature from 300 to 325 K. A previously developed potential model for caffeine [J. Mol. Struct. THEOCHEM 944 (2010) 116–123] was further validated by comparing solubility limit and also with experimental diffusion coefficients which show excellent agreements. Solvent accessible surface area, radial distribution functions and preferential interaction parameter of caffeine for itself over solvent water clearly indicate the aggregate formation of caffeine in aqueous solutions when the concentration exceeds the solubility limit. It was found that formation of aggregates is driven primarily by the enthalpy of the system. Within the temperature range considered here, aggregate formation shows a quasi equilibrium and the equilibrium constant (hence the standard free energy change) shows a linear relationship to the temperature (Δ G 0 (J mol −1) = −3790 + 12.8 × T). Caffeine aggregates show stacking arrangements with considerable overlapping of aromatic rings and a relative orientation of about 98°, which agree very well with the results of NMR studies. Caffeine exhibits a preference for urea over water with a preferential interaction parameter of ∼2. This preferred interaction could be the driving force for dissociation of caffeine aggregates in 8 M urea solution.

Adsorption studies of methylene blue dye on tunisian activated lignin

Activated carbon prepared from natural lignin, providing from a geological deposit, was used as the adsorbent for the removal of methylene blue (MB) dye from aqueous solutions. Batch adsorption studies were conducted to evaluate various experimental parameters like pH and contact time for the removal of this dye. Effective pH for MB removal was 11. Kinetic study showed that the adsorption of dye was gradual process. Quasi equilibrium reached in 4 h. Pseudo-first-order, pseudo-second-order were used to fit the experimental data. Pseudo-second-order rate equation was able to provide realistic description of adsorption kinetics. The experimental isotherms data were also modelled by the Langmuir and Freundlich equation of adsorption. Equilibrium data fitted well with the Langmuir model with maximum monolayer adsorption capacity of 147 mg/g. Activated lignin was shown to be a promising material for adsorption of MB from aqueous solutions.