Slow Mixing Rates Research Articles

Fast Computer Model Calibration using Annealed and Transformed Variational Inference

Computer models play a crucial role in numerous scientific and engineering domains. To ensure the accuracy of simulations, it is essential to properly calibrate the input parameters of these models through statistical inference. While Bayesian inference is the standard approach for this task, employing Markov chain Monte Carlo methods often encounters computational hurdles due to the costly evaluation of likelihood functions and slow mixing rates. Although variational inference (VI) can be a fast alternative to traditional Bayesian approaches, VI has limited applicability due to boundary issues and local optima problems. To address these challenges, we propose flexible VI methods based on deep generative models that do not require parametric assumptions on the variational distribution. We embed a surjective transformation in our framework to avoid posterior truncation at the boundary. Additionally, we provide theoretical conditions that guarantee the success of the algorithm. Furthermore, our temperature annealing scheme and fine-tuning can prevent being trapped in local optima through a series of intermediate posteriors and weight adjustment. We apply our method to infectious disease models and a geophysical model, illustrating that the proposed method can provide fast and accurate inference compared to its competitors.

Atomic insights into shock-induced alloying reaction of premixed Ni/Al nanolaminates.

In material processing and handling processes, premixed interlayer often replace the ideal Ni/Al interface, which would become a new origin of alloying reaction. This work investigates shock-induced reaction mechanism and kinetics of premixed Ni/Al nanolaminates with molecular dynamics simulations and theoretical analysis. The reaction is found to be driven by the crystallization evolution in premixed interlayer and the diffusion of premixed atoms. Among them, multi-stage reaction patterns are strongly manifested by the crystallization evolution characteristics. Specifically, "crystallization-dissolution-secondary growth" and "crystallization-dissolution" of B2 phase respectively correspond to the solid-state and solid-liquid reaction cases, where crystallizations are fitted well by Johnson-Mehl-Avrami kinetics model. Interestingly, the different growth mechanisms of B2 grain are revealed, namely nuclei coalescence and atomic diffusion. Moreover, the analysis of microscopic diffusion theory indicates a certain non-random diffusion nature for solid-state reaction initiation, but near-purely random diffusion for solid-liquid reaction initiation. The diffused Al atoms possess a limited diffusion coefficient and enhanced diffusion correlation, resulting in extremely slow mixing rate in Ni layer. In addition, the influence law of Ni concentration in premixed interlayer on reactivity parameters can be quantitatively described by a quadratic function.

Maximal large deviations and slow recurrences in weakly chaotic systems

We prove a maximal-type large deviation principle for dynamical systems with arbitrarily slow polynomial mixing rates. Also several applications, particularly to billiard systems, are presented.

Enhancing Mixing During Groundwater Remediation via Engineered Injection‐Extraction: The Issue of Connectivity

AbstractIn the context of in situ groundwater remediation, mixing is vital for a successful outcome. A slow mixing rate between the contaminated groundwater and the injected treatment solution can severely weaken the effective degradation rate. Engineered Injection‐Extraction (EIE) has been proposed as a means to accelerate dilution within the porous medium. However, existing studies on the subject have not considered the potential impact of connectivity and preferential flow‐paths. Neglecting connectivity can lead to an overestimation of EIE's capabilities, since the fluid may in reality be carried mainly through a few high‐permeability channels, thus hampering mixing and reaction. Due to the fact that channeling can be found in many actual sites, in this work we aim to evaluate EIE methods in both poorly connected (represented as Multigaussian fields) and well‐connected fields (represented as non‐Multigaussians). The approach is to identify, for each given medium, a stirring protocol—defined by a specific combination of rotation angle and rotation rate—which maximizes mixing. To that end, metrics are proposed in order to (a) quantify both the mixing and the containment of the treatment solution within a given remediation volume, and (b) characterize the particle trajectories to explicitly evaluate if preferential paths are broken. The results obtained from these metrics are quite similar for both types of fields, proving that the enhancing of mixing by means of EIE is effective regardless of the presence of preferential flow paths. This study demonstrates that EIE via rotating dipoles diminishes the remediation outcome uncertainty induced by medium heterogeneity.

Chicken Eggshell as an Innovative Bioflocculant in Harvesting Biofloc for Aquaculture Wastewater Treatment

Implementation of biofloc technology (BFT) system in aquaculture industry shows high productivity, low feed conversion ratio, and an optimum culture environment. This study was divided into two phases. The first phase involved maintaining the water quality using the optimum carbon-to-nitrogen ratio by manipulating pH in culture water. The second phase examined the performance of harvesting biofloc (remaining phytoplankton and suspended solids in the system) using chicken eggshell powder (CESP). This study showed that pH 7 to 8 were the best biofloc performance with high removal percentage of ammonia (>99%) with a remaining ammonia concentration of 0.016 mg L−1 and 0.018 mg L−1 , respectively. The second phase of this study was performed to determine the optimal formulation and conditions of using CESP as a bio-flocculant in harvesting excess biofloc. The use of eggshell showed a higher harvesting efficiency of more than 80% under the following treatment conditions: 0.25 g L−1 of eggshell dosage; with rapid and slow mixing rates of 150 and 30 rpm, respectively; 30 min of settling time; settling velocity of 0.39 mm s−1 and pH of 6 to 7. Therefore, the results indicated that biofloc would be the best green technology approach for sustainable aquaculture wastewater and the CESP is an organic matrix that environmental-friendly bio-coagulant for biofloc harvesting.

Taguchi Grey Relational Analysis for Multi-Response Optimization of Bacillus Bacteria Flocculation Recovery from Fermented Broth by Chitosan to Enhance Biocontrol Efficiency.

Degradation of environment is a challenge to crop production around the world. Biological control of various plant diseases using antagonistic bacteria is an encouraging alternative to traditionally used chemical control strategies. Chitosan as a well-known natural flocculation agent also exhibits antimicrobial activity. The goal of this study was to investigate a dual nature of chitosan in flocculation of Bacillus sp. BioSol021 cultivation broth intended for biocontrol applications. Experiments were performed based on L18 standard Taguchi orthogonal array design with five input parameters (chitosan type and dosage, pH value, rapid and slow mixing rates). In this study, the grey relational analysis was used to perform multi-objective optimization of the chosen responses, i.e., flocculation efficiency and four inhibition zone diameters against the selected phytopathogens. The results have indicated a great potential of a highly efficient method for removal of the Bacillus bacteria from the cultivation broth using chitosan. The good flocculation efficiency and high precipitate antimicrobial activity against the selected phytopathogens were achieved. It has been shown that multiple flocculation performance parameters were improved, resulting in slightly improved response values.

Effect of micro-impeller geometries on mixing in a continuous flow active microreactor

Microreactors are widely reported for performing chemical reactions of all kinds. Chemical reactions should possess attributes like complete mixing with a faster rate to obtain a high-quality product. Usually, microreactors mix the liquid passively and thus suffer from slow mixing rates due to longer channels. Moreover, it is challenging to achieve complete mixing of fluids in passive microreactors as they are predominantly diffusion dependent. An active microreactor is suitable to enhance the rate of mixing and its efficiency. In the present work, we have utilized the magnetic field to rotate a micro-impeller in an active microreactor. The active microreactor and micro-impellers (iron oxide nanoparticles embedded in PDMS matrix) of various geometry (triangle, square, rectangle, and rhombus) were fabricated using soft lithography. These differently shaped micro-impellers were evaluated theoretically and experimentally for mixing in a continuous flow active microreactor. Simulation studies using Comsol Multiphysics revealed approximately equivalent mixing efficiency for all the shapes; however, rhombus micro-impeller excelled. Further, experimental studies showed better mixing efficiency of rhombus micro-impeller as compared to other micro-impellers. 97% mixing efficiency for rhombus micro-impeller can be attributed to the shape and its stability in continuous flow. Finally, the rhombus micro-impeller was used to synthesize Prussian blue nanoparticles in a continuous flow active microreactor.

Curved passive mixing structures: a robust design to obtain efficient mixing and mass transfer in microfluidic channels

Analyte mixing and delivery to a functionalized sensor surface are important to realize several advantages associated with biosensors integrated with microfluidic channels. Here, we present a comparison between a herringbone structure (HBS) and a curved passive mixing structure of their efficiency at facilitating mixing and surface saturation using fluorescein included in one of the inlets of a Y-channel microfluidic device. We performed a large parametric study to assess the effects of varying the height of the microfluidic channel as well as the height, width, and spacing of the passive mixing structures. Scanning confocal microscopy combined with a custom-designed image-analysis procedure were utilized to visualize and quantify the observed changes in efficiency in inducing solute mixing by the different designs. The flow patterns within the channels were found to vary significantly with changes in the geometry of the passive mixing structures, which in turn affected the efficiency of the channel at mixing the fluid and saturating the surface opposite the mixing structures. The solute mixing as a function of the channel length was also determined; an initial slow mixing rate does not always coincide with a low mixing index (MI). We found that the range of MIs for the curved mixing structure 1 cm downstream from the inlet was 0.85–0.99 whilst for our HBS it was 0.74–0.98, depending on the design parameters of the passive mixing structures. Overall, this study shows that the curved passive mixing structure family is more robust in inducing efficient mixing than the HBSs.

Mixed culture microalgae removal for water quality improvement using chitosan

The presence of microalgae affects water quality and beneficial uses of surface freshwaters. Chitosan with proven potential for harvesting specific microalgae species from their culture medium to produce biofuels and bioproducts also appears promising for efficient removal of mixed microalgae species from surface freshwaters. The main focus of the present study was on removal of mixed microalgae species using chitosan as a coagulant to help improve water quality. Important operational parameters were optimized for economical microalgae removal. The microalgae cells, chlorophyll-a, total nitrogen, and total phosphorous removal efficiency were 82.06%, 89.90%, 69.32%, and 44.01%, respectively, at an optimum chitosan dose of 10 mg/L, pH 8, slow mixing time 7 min, slow mixing rate 30 rpm, and settling time of 15 min. The results show that chitosan coagulation efficiently removed mixed microalgae species from surface freshwater with significant improvement in water quality and recovery of algal biomass for other beneficial applications.

Preparation of Quaternized Lignin Derived from Oil Palm Empty Fruit Bunches and its Flocculation Properties

Quaternized lignin-based flocculant (QL) was prepared by a single-step reaction of an extracted lignin (EL) derived from oil palm empty fruit bunches (OPEFB) with 3-chloro-2-hydroxypropyl trimethylammonium chloride (CHPTAC) under alkaline condition. The performance of QLs was studied for various β values (molar ratios of CHPTAC to phenylpropanoid unit of lignin), flocculant dosages, pH values, kaolin concentrations, slow mixing rates and sedimentation times. The QL10 achieved the highest turbidity removal efficiency (εt) with increasing flocculant dosage, pH and kaolin concentration to the optimal conditions of 5 mg L−1, pH 7 and 1000 mg L−1, and required 20 min of sedimentation time at all the mixing rates tested. The flocculation kinetics agreed well with the particle collision model. The QL10 has good sludge dewatering properties compared to the alum. It also showed encouraging results in water quality analysis for sewage wastewater flocculation in comparison to that of the alum. This indicates the potential application of QL in treating water and wastewater.

Impact of misspecified residual correlation structure on the parameter estimates in a shared spatial frailty model

ABSTRACTIn practice, survival data are often collected over geographical regions. Shared spatial frailty models have been used to model spatial variation in survival times, which are often implemented using the Bayesian Markov chain Monte Carlo method. However, this method comes at the price of slow mixing rates and heavy computational cost, which may render it impractical for data-intensive application. Alternatively, a frailty model assuming an independent and identically distributed (iid) random effect can be easily and efficiently implemented. Therefore, we used simulations to assess the bias and efficiency loss in the estimated parameters, if residual spatial correlation is present but using an iid random effect. Our simulations indicate that a shared frailty model with an iid random effect can estimate the regression coefficients reasonably well, even with residual spatial correlation present, when the percentage of censoring is not too high and the number of clusters and cluster size are not too low. Therefore, if the primary goal is to assess the covariate effects, one may choose the frailty model with an iid random effect; whereas if the goal is to predict the hazard, additional care needs to be given due to the efficiency loss in the parameter(s) for the baseline hazard.

3-Dimensional Numerical Simulation of Pollution Dispersion in an Urban Street Canyon

Pollution dispersion mechanism in an urban street canyon has been studied using numerical simulations. Street canyon of aspect ratio “one” with perpendicular wind flow direction and pollutant line source has been modelled using ANSYS FLUENT 16.2 software code. RNG, k-ε turbulence model and species transport model were applied in this numerical study. Pollutant mass fractions at various locations of street canyon have been studied and discussed. The numerical results show significant variations of pollutant due to existence of unsteady vortex in street canyon. Pollutant concentrations were observed higher on leeward side compared to windward side. Slow mixing rate of pollutant with fresh air leads to higher pollutant accumulation in street canyon. It has been observed that pollutant concentrations were higher at pedestrian level and decreased along the height of the street canyon.

Harvesting of microalgae Desmodesmus sp. F51 by bioflocculation with bacterial bioflocculant

The small particulate size of microalgae cells and the extremely dilute concentrations of microalgae cultures continue to be major challenges to effective harvesting. In an attempt to find a cost-effective and environmentally friendly harvesting technique, the bioflocculant poly (γ-glutamic acid) (γ-PGA) produced by Bacillus licheniformis CGMCC 2876 was used to concentrate freshwater microalgae Desmodesmus sp. F51. Experimental results showed that the flocculation efficiency was dependent on the initial culture pH. The flocculation efficiency increased from 43.8±1.6% to 98.2±0.1% when the initial culture pH was changed from ~7.2, as the original culture pH, to 3. With the optimum operating parameters of bioflocculant dosage of 2.5mL/L, flash mixing rate of 150rpm for 1min, and slow mixing rate of 80rpm for 2min, a flocculation efficiency of 99% was achieved. Microscopic photos of the harvested microalgae cells showed no cell damage and hence no premature release of intracellular contents during the process. The bioflocculation process is easy to operate, cost-efficient, environmentally friendly and as effective as chemical flocculation processes applied industrially. The γ-PGA bioflocculant produced by B. licheniformis CGMCC 2876 demonstrated high performance for optimal microalgae recovery and can be applied in commercial-scale microalgae harvesting.

Determination of optimum conditions for color and COD removal of Reactive Blue 19 by Fenton oxidation process

In this study, Taguchi method was used to determine the optimum parametric conditions such as initial pH, Fe2+ and H2O2 concentrations, initial dye concentration, slow mixing rate (SMR) and rapid mixing rate (RMR) for Fenton oxidation process performance. The main objective of the study is to provide maximum color and chemical oxygen demand (COD) removals by using optimal levels for Fenton reaction parameters. The orthogonal array L25 was selected as experimental matrix to determine of the optimum parametric levels. It was also, the contribution ratios of each factor were determined by the analysis of variance analysis, separately. Thus, the most effective parameter manages to the process was determined in terms of color and COD removals. Consequently, the optimum color removal conditions for the initial pH, Fe2+ and H2O2 concentrations, initial dye concentration, SMR and RMR are 3, 500 mg/l, 150 mg/l, 250 mg/l, 60 rpm, 90 rpm, respectively, and 3, 400 mg/l, 150 mg/l, 250 mg/l, 60 rpm and 15 rpm for the initial pH, Fe2+ and H2O2 concentrations, initial dye concentration, SMR and RMR to the COD removal, respectively. Under these optimum conditions, 98.90% color and 100% COD removals were achieved by Fenton oxidation process.

Optimization of chemical coagulation of real textile wastewater using Taguchi experimental design method

In the present study, optimal coagulation conditions, such as pH, coagulant dosage, slow mixing rate, rapid mixing rate, and initial concentration, were determinated using the Taguchi experimental design method. Color and turbidity were considered as performance statistics. An L25 (55) orthogonal array was selected as the experimental plan for the five parameters mentioned above. Performance measure analysis was followed by performing a variance analysis, in order to determine the optimum levels and relative magnitude of the effect of parameters. The obtained results allowed concluding that the optimal conditions in terms of color and turbidity removals were initial pH of the wastewater of 9, coagulant dosage of 200 and 400 mg Al3+/l, slow mixing rate of 15 and 30 rpm, rapid mixing rate of 150, and initial concentration of wastewater of Co/4, respectively. At the end of the experimental studies, obtained color and turbidity removal results for real textile wastewater were 99.43 and 99.22%, respectively, at these optimum conditions.

Application of Endwall Contouring to Transonic Turbine Cascades: Experimental Measurements at Design Conditions

An experimental investigation of the endwall flows in two high-turning turbine cascades was presented by Taremi et al. (2010, “Measurements of Endwall Flows in Transonic Linear Turbine Cascades: Part II—High Flow Turning,” ASME Conf. Proc., GT2010-22760, pp. 1343–1356). Endwall contouring was subsequently implemented in these cascades to control the secondary flows and reduce the total pressure losses. The current paper presents experimental results from these cascades to assess the effectiveness of endwall contouring in the transonic flow regime. The results include blade loadings, total pressure losses, streamwise vorticity and secondary kinetic energy distributions. In addition, surface flow visualization results are presented in order to interpret the endwall limiting streamlines within the blade passages. The flat-endwall and contoured-endwall cascades produce very similar midspan loading distributions and profile losses, but exhibit different secondary flows. The endwall surface flow visualization results indicate weaker interaction between the secondary flows and the blade suction surface boundary layers in the contoured cascades. Overall, the implementation of endwall contouring results in smaller and less intense vortical structures, and the reduction of the associated secondary kinetic energy (SKE) and exit flow angle variations. However, the mass-averaged losses at the main measurement plane, located 40% axial chord lengths downstream of the cascade (1.4CX), do not corroborate the numerically predicted improvements for the contoured cascades. This is in part attributed to slower mixing rates of the secondary flows in the compressible flow regime. The mass-averaged results at 2.0CX, on the other hand, show smaller losses for the contoured configurations associated with smaller SKE dissipation downstream of the cascades. Accordingly, the mixed-out row losses also show improvements for the contoured cascades.

CHEMICAL TIMESCALES IN THE ATMOSPHERES OF HIGHLY ECCENTRIC EXOPLANETS

Close-in exoplanets with highly eccentric orbits are subject to large variations in incoming stellar flux between periapse and apoapse. These variations may lead to large swings in atmospheric temperature, which in turn may cause changes in the chemistry of the atmosphere from higher CO abundances at periapse to higher CH4 abundances at apoapse. Here we examine chemical timescales for CO<->CH4 interconversion compared to orbital timescales and vertical mixing timescales for the highly eccentric exoplanets HAT-P-2b and CoRoT-10b. As exoplanet atmospheres cool, the chemical timescales for CO<->CH4 tend to exceed orbital and/or vertical mixing timescales, leading to quenching. The relative roles of orbit-induced thermal quenching and vertical quenching depend upon mixing timescales relative to orbital timescales. For both HAT-P-2b and CoRoT-10b, vertical quenching will determine disequilibrium CO<->CH4 chemistry at faster vertical mixing rates (Kzz > 10^7 cm^2 s^-1), whereas orbit-induced thermal quenching may play a significant role at slower mixing rates (Kzz < 10^7 cm^2 s^-1). The general abundance and chemical timescale results - calculated as a function of pressure, temperature, and metallicity - can be applied for different atmospheric profiles in order to estimate the quench level and disequilibrium abundances of CO and CH4 on hydrogen-dominated exoplanets. Observations of CO and CH4 on highly eccentric exoplanets may yield important clues to the chemical and dynamical properties of their atmospheres.

PolyDADMAC and polyacrylamide as a hybrid flocculation system in the treatment of pulp and paper mills waste water

The flocculation performance of polydiallydimethylammonium chloride (polyDADMAC) coupled with polyacrylamide for treating pulp and paper mill wastewaters was studied. The flocculation performance tests were carried out in jars with polyDADMAC and polyacrylamide (PAM) dosages of 0.4–2.0 mg L −1 and 0.4–8.0 mg L −1, respectively. The tests were conducted at a rapid mixing rate of 200 rpm for 2 min, followed by a slow mixing rate at 30 rpm for 10 min, and settling time of 5 min. Polyacrylamide was introduced into the wastewater samples 45 s after the addition of polyDADMAC. The reduction efficiency of turbidity, chemical oxygen demand (COD) and total suspended solids (TSS) were the main evaluating parameters. It was found that poyDADMAC incorporated with PAM was efficient in treating pulp and paper mills wastewater. Increasing dosages of polyDADMAC increased the destabilization of particles and produced small flocs, while the addition and increasing of PAM increased the size of flocs for a better synergistic flocculation process.

Effect of floc structure and strength on membrane permeability in the hybrid coagulation-microfiltration process

The relative importance of floc property on microfiltration and fouling mechanism remains a field of arguments. The effects of floc structure and strength on fouling rate of coagulation-microfiltration were investigated in dead-end microfiltration. Flocs varying in size, fractal structure and strength were prepared by AlCl3 and PACl (Polyaluminum Chloride) coagulation at various dosages followed by different slow mixing rates and filtration without any sedimentation step. The rates of flux decline for flocs formed under same coagulant dosage but different shear conditions showed only limited size and compactness dependence. However, the floc strength effect on membrane filtration performance was observed clearly with the floc strength constant exhibiting a strong positive linear correlation with the resulted cake compressibility index.

Comparative study of the effects of experimental variables on growth rates of aluminum and iron hydroxide flocs during coagulation and their structural characteristics

In this study, the dimensions of over six thousand flocs were analyzed to quantitatively and comparatively investigate the effects of several experimental variables on the growth rate of aluminum (Al) and ferric (Fe) hydroxide flocs. Results show that Fe hydroxide flocs have faster growth rate than Al hydroxide flocs; and the average size of the former is larger than that of the latter. Increasing the concentration of the bivalent sulfate ion (SO 4 2−), initial turbidity, or slow mixing rate, was able to increase the growth rate of both kinds of flocs. On the other hand, steady floc sizes were found to decrease with the increase in SO 4 2− concentration, initial turbidity, or shear rate. Fe hydroxide flocs are more prone to be influenced by the changes in the variables than Al hydroxide flocs. While the steady floc sizes became smaller when initial turbidity or slow mixing speed increased, the roundness and smoothness of flocs were found to increase, indicating that higher initial turbidity or larger slow mixing rate produces flocs with more regular and round shape. Furthermore, at a fixed shear rate, Fe hydroxide flocs are stronger than Al hydroxide flocs. However, Fe hydroxide floc sizes are much easier to decrease with the increase in slow mixing intensity.