Dispersive Approach Research Articles

High-fidelity simulation of blade vortex interaction of helicopter rotor based upon TENO scheme

Numerical simulation methods for unsteady vortex field of helicopter rotor with high resolution and low dissipation TENO8-AA primitive variables reconstruction schemes are established based on moving-embedded grid and Navier-Stokes equations. Firstly, the Targeted Essentially Non-Oscillatory (TENO) scheme are developed by employing ENO-like candidate stencil selection strategy, and the candidate stencil is adopted with optimal weight in smooth region while it is discarded completely in discontinuous region, which reduces the dissipation and dispersion errors and approaches better spectral properties. Then, the aerodynamic characteristics of Helishape-7A model rotor in Blade Vortex Interaction (BVI) state and the flowfield of Lynx rotor in hover are simulated, which validates that the blade tip vortex trajectory with larger wake age and more details of vortex can be captured by TENO8-AA scheme with only a quarter of grid points and half time comparing to WENO-JS scheme. Moreover, the simulation accuracy of thrust coefficient is improved by up to 36%. Finally, the analyses for BVI and aeroacoustic characteristics of Operational Loads Survey (OLS) rotor are conducted, and the different forms of interaction mechanism are explored, such as oblique and parallel interactions. The results indicate that TENO scheme not only ensures the resolution of simulation in discontinuous region, but also minimizes the numerical dissipation in smooth region dominated by blade tip vortex. Therefore, the acoustic pressure peak prediction error of rotor in BVI state is significantly reduced to 5.6% and 0.8% at two microphone locations, respectively.

Soft, Stretchable, and Conductive Hydrogel Based on Liquid Metal for Accurately Facial Expression Monitoring

AbstractSoft electronics have emerged as a prominent research domain, with diverse applications from medical monitoring to soft robotics. Liquid metal (LM) has emerged as a promising material for soft electronics due to its high electrical conductivity (3.4 × 106 S m−1) and fluidity at room temperature. However, the dispersion of LM nanoparticles and the performance of LM composites in soft electronics applications have not been extensively explored. In this study, a novel approach for the direct dispersion of LM nanoparticles in biocompatible hyaluronic acid (HA) to create multifunctional LM/HA hydrogels is presented. The LM/HA hydrogel displays remarkable electromechanical properties, including high stretchability (2,700%) and conductivity (116 S m−1), as well as excellent sensitivity (GF = 4.8) as a sensing material. Specifically, a facial expression monitoring system is developed utilizing the LM/HA hydrogel as the sensing material, along with a microcontroller, signal‐processing circuits, and a Bluetooth transceiver. The LM/HA hydrogel adheres closely to the skin surface to ensure the accuracy of facial expression monitoring. In summary, this study not only advances the understanding of the properties of LM but also expands the potential application scenarios of multifunctional LM hydrogels in soft robotics and implantable sensors.

Light-cone sum rules for S-wave B → Kπ form factors

We derive a set of light-cone sum rules relating the S-wave B → Kπ hadronic form factors to the B-meson light-cone distribution amplitudes (LCDAs), taking into account the complete set of LCDAs up to and including twist four. These results complement the sum rules for the P-wave B → Kπ form factors obtained earlier. We then use the new sum rules to estimate the S-wave contributions to B → Kπℓℓ decays as a function of the Kπ invariant mass. We pay particular attention to the fact that the S-wave Kπ spectrum cannot be modelled by a sum of Breit-Wigner resonances, and employ a more consistent dispersive coupled-channel approach. We compare our predictions for branching ratios and angular observables with LHCb measurements in two different kinematic regions, around K∗(892) and {K}_0^{ast }(1430) . We observe an overall compatibility and discuss possible improvements of our model to obtain a better description of the B → Kπ form factors over a large kinematic range.

Formulation and Characterization of Solid Dispersion of Oxcarbazepine

The purpose of the current study was to use the solid dispersion approach to improve the solubility of the medication oxcarbazepine, which is only moderately water soluble. The antiepileptic medication oxcarbazepine is used to treat seizures. Due to its high permeability and low water solubility, it falls under BCS class II. To prevent issues of this nature, it was imperative to increase the solubility of oxcarbazepine in accordance with British Pharmacopoeia (BP) solubility criteria since pure oxcarbazepine falls under the category of being only very slightly soluble. Solid dispersion technique has been used to try and increase the solubility of pure oxcarbazepine. Oxcarbazepine is also extensively metabolized by the liver. Attempt has been made to formulate solid dispersions containing oxcarbazepine to improve its solubility and dissolution rate to avoid first pass metabolism; to avoid difficulty.

Design and construction of Prussian blue analogue combined by Na2WO4 toward high-performance cathode materials for Li-ion battery

Prussian blue analogues have been considered as one of hopeful cathode materials of Li-ion batteries (LIBs) because of their tunable composition, low cost and simple synthesis method, but the high volume variation and electrical resistance during cycling limit the wide application. In this work, Na1.06Fe[Fe(CN)6]·2.8H2O/Na2WO4 (PBA/NW) composites with high performance are successfully synthesized by a hydrothermal route following through a simple solution dispersion approach. The Na2WO4 coating will not alter the structure and morphology of PBA sample. Na2WO4 coating improves the structure stability and Li+ insertion/extraction reversibility, and decreases the charge transfer resistance, then promotes the transfer of Li+. The PBA-NW2 indicates an outstanding reversible discharge capacity of 134.9 mAh g−1 at 1C after 1000 cycles, but the pure PBA only performs a discharge capacity of 108 mAh g−1. In addition, PBA-NW2 also indicates superior rate property with discharge capacity of 150.3, 145.1, 140.0, 132.5, 132.32, 105.3, 91.9 mAh g−1 at 0.1, 0.3, 0.5, 1, 2, 5 and 10C, respectively. This work offers a facile and easy synthesis method to construct high-performance Prussian blue analogues cathode material for low-cost LIBs.

Dispersion relations for hadronic light-by-light scattering in triangle kinematics

We present a new strategy for the dispersive evaluation of the hadronic light-by-light contribution to the anomalous magnetic moment of the muon aμ. The new approach directly applies in the kinematic limit relevant for aμ: one of the photons is treated as an external electromagnetic field with vanishing momentum, so that the kinematics corresponds to a triangle. We derive expressions for the relevant single-particle intermediate states, as well as the tensor decompositions of the two-pion sub-processes that appear in addition to those needed in the established dispersive approach. The existing approach is based on a set of dispersion relations for the hadronic light-by-light tensor in four-point kinematics. At present it is not known how to consistently include in this framework resonant intermediate states of spin 2 or larger, due to the appearance of kinematic singularities that can be traced back to the redundancy of the tensor decomposition. We show that our new approach circumvents this problem and enables dispersion relations in the limit of triangle kinematics that are manifestly free from kinematic singularities, paving the way towards a data-driven evaluation of all relevant exclusive hadronic intermediate states.

Additive manufacturing of metal matrix nanocomposites: Novel approach for nanoparticles dispersion by electromagnetic three-dimensional vibration

A novel electromagnetic three-dimensional vibration approach was employed for powder feedstock preparation oriented to additive manufacturing of metal matrix nano-composites (MMNCs). The efficiency of this promising mixing technique was validated by laser powder bed fusion (LPBF) of AlSi10Mg reinforced with 3 wt% of B4C nanopowder. Scanning electron microscopy (SEM) analysis revealed that a uniform dispersion of B4C was achieved on the AlSi10Mg powder surface, while retaining its original spherical morphology. The modified powder recycling had no influence on the adherence of nanoparticles to the powder surface. The LPBF-processed samples exhibited good homogeneity in the nano B4C distribution, resulting in an increase in hardness compared to unmodified AlSi10Mg. This high-productivity and cost-efficient approach provides a remedy for the process chain bottleneck in the additive manufacturing of MMNC.

Herding behavior in integrated financial markets: the case of MILA

PurposeIt has been argued in the literature that structural changes in the financial markets, such as integration, have the potential to cause herding behavior or correlated behavioral patterns in traders. The purpose of this study is to investigate whether there is any financial herding behavior in the Latin American Integrated Market (MILA), a transnational stock market composed of Chile, Peru, Colombia and Mexico stock exchanges and whether there is any ARCH or GARCH effect in the herding behavior models.Design/methodology/approachThis study uses the modified return dispersion approach on daily index return data. The sample period is from January 03, 2002 to May 07, 2019. The data are obtained from the MILA database. To count time-varying volatilities in herding models, the authors run ARCH family regression with GARCH (1,1) settings. Hwang and Salmon (2004) model is used as a robustness test.FindingsThe authors found strong herding behavior under the general market conditions and moderate and partial herding behavior under some specified markets circumstances, such as bull and bear markets and high-low volatility states. Moreover, the pre-MILA period exhibits more herding behavior than the post-MILA period. The empirical results show that most of the ARCH and GARCH effects are statistically significant, implying that the past information of stock returns and market volatility significantly affect the volatility of following periods, which can also explain the formation of herding tendency among investors. Finally, the results of the robustness tests (Hwang and Salmon, 2004) confirm herding in all periods, except full sample period for Mexico and post-MILA period for Mexico and Colombia.Research limitations/implicationsThis study investigates the herding behavior in the MILA market in terms of market return, volatility and timing. A limitation of the paper is that the authors have not included other factors on the formation of herding behavior, such as macroeconomic factors, effects of regional or international markets and policy influences. The authors will explore the issue in the extension of the paper.Practical implicationsAs MILA is the first virtual integration of stock exchanges without merging, the study provides useful findings and draws good inferences of herding behavior in the MILA market in terms of market return, volatility and timing which are useful for academics, investors and policymakers in their investment and decision makings.Social implicationsThe paper provides useful findings and draws good inferences of herding behavior in the MILA market in terms of market return, volatility and timing which are not only useful in practical implications, but also in social implications.Originality/valueThis study contributes to the herding literature by examining four different hypotheses in respect of the unique case of transnational stock exchange without fusions or corporate mergers, where each market maintains its independence and regulatory autonomy. The authors also contribute to the literature by including both ARCH and GARCH effects in the herding behavioral models along the Hwang and Salmon (2004) approach.

GOVERNING MIGRATION THROUGH SMALL TOWNS: Dispersal and the Production of Spaces of Transit

AbstractBased on qualitative long‐term fieldwork conducted in a peripherally located small town in East Germany, this article compares the dispersal of repatriates from the former Soviet Union with that of recent refugee arrivals. It shows that in this small town the dispersal and local governance of refugees builds on previous approaches to dealing with repatriates. Such approaches repeatedly result in cycles of localized distribution and subsequent small‐scale segregation, short‐term integration activities, the detachment of both groups from the town and, finally, migrants’ subsequent outmigration and relocation to other (mostly larger) cities. To make sense of this path dependency in terms of its specific patterns and characteristics, and to explore the relationships between dispersal, local policy framings, and in‐ and outmigration to and from small towns, I apply a studying through dispersal approach. This approach reveals that dispersal is an important factor in making and unmaking local migration policies. It can turn small towns into productive sites for migration governance, often transforming them into mere waiting zones and transit spaces. This not only continues migrants’ experiences of displacement but also impacts on the image of the small town, where migrants themselves may not want to reside permanently.

Detection of genes with differential expression dispersion unravels the role of autophagy in cancer progression.

The majority of gene expression studies focus on the search for genes whose mean expression is different between two or more populations of samples in the so-called "differential expression analysis" approach. However, a difference in variance in gene expression may also be biologically and physiologically relevant. In the classical statistical model used to analyze RNA-sequencing (RNA-seq) data, the dispersion, which defines the variance, is only considered as a parameter to be estimated prior to identifying a difference in mean expression between conditions of interest. Here, we propose to evaluate four recently published methods, which detect differences in both the mean and dispersion in RNA-seq data. We thoroughly investigated the performance of these methods on simulated datasets and characterized parameter settings to reliably detect genes with a differential expression dispersion. We applied these methods to The Cancer Genome Atlas datasets. Interestingly, among the genes with an increased expression dispersion in tumors and without a change in mean expression, we identified some key cellular functions, most of which were related to catabolism and were overrepresented in most of the analyzed cancers. In particular, our results highlight autophagy, whose role in cancerogenesis is context-dependent, illustrating the potential of the differential dispersion approach to gain new insights into biological processes and to discover new biomarkers.

Development of an efficient dispersive liquid-liquid microextraction approach combined with spectrophotometry for determination of antiviral drug, valacyclovir HCl in pharmaceutical formulations

ABSTRACT. A new, fast, sensitive, simple, and green dispersive liquid–liquid microextraction (DLLME)-based spectrophotometric method for the determination of valacyclovir HCl (VAL) in pure form and pharmaceutical formulations has been developed and validated. The developed method is based on the formation of a coloured product through the reaction of VAL and 1,2-naphthoquine-4-sulfonate (NQS) at pH = 9. The important experimental parameters affecting the extraction efficiency were investigated and optimized. The tiny organic droplets had a wavelength of l = 505 nm. At the optimum conditions, linearity ranged from 0.06 to 2.0 μg/mL, with a linear correlation coefficient of 0.9995. The limits of detection and quantification were 0.02, and 0.06 μg/mL, respectively. The enhancement factor was 36.87. Good recovery as accuracy (99.50%) and relative standard deviation (RSD) as precision were 1.20%, respectively. The developed DLLME method was successfully applied to the determination of VAL in pharmaceutical formulations, and the validity was assessed by applying the standard addition technique. The results obtained by the proposed method for the pure VAL and commercial tablets agreed well with those obtained by the official method.
 
 KEY WORDS: Valacyclovir HCl, Spectrophotometry, 1-2-Naphthoquine-4-sulfonate, Dispersive liquid–liquid microextraction, Pharmaceutical formulations
 
 Bull. Chem. Soc. Ethiop. 2023, 37(3), 579-592. 
 DOI: https://dx.doi.org/10.4314/bcse.v37i3.4

Vehicle Pollutant Dispersion in the Urban Atmospheric Environment: A Review of Mechanism, Modeling, and Application

In recent years, vehicle emissions have become one of the important pollutant sources of the urban atmosphere. Scholars and decision-makers are constantly expected to accurately grasp the dispersion of vehicle pollutants to formulate a series of policies and strategies which can facilitate a friendly and sustainable urban environment, such as controlling the total number of vehicles, requiring higher emission standards, promoting new energy vehicles, improving public transit service, and optimizing non-motorized transportation systems. This paper provides a review of the mechanism research methods and mathematical modeling approaches for urban vehicle pollutant dispersion. The mechanism research methods reviewed include field measurements, wind tunnel experiments, and numerical simulations. The modeling approaches involve two kinds of popular models: Box models (STREET, CPBM, AURORA, PBM) and Gaussian models (CALINE, HIWAY, OSPM, CALPUFF, R-LINE, ADMS series, EPISODE, CityChem, SIRANE, MUNICH). Moreover, this paper clarifies the basic assumption, fundamental principle, related research, applicable conditions, and limitations of these mechanism research methods and modeling approaches.

Emergence of heavy quark spin symmetry breaking in heavy quarkonium decays

Heavy-quark spin symmetry (HQSS) implies that in the direct decay of a heavy quarkonium with spin $S$, only lower lying heavy quarkonia with the same spin $S$ can be produced. However, this selection rule, expected to work very well in the $b$-quark sector, can be overcome if multiquark intermediate states are involved in the decay chain, allowing for transitions to the final-state heavy quarkonia with a different spin ${S}^{\ensuremath{'}}$. In particular, the measured decays $\mathrm{\ensuremath{\Upsilon}}(10860)\ensuremath{\rightarrow}\ensuremath{\pi}{Z}_{b}^{(\ensuremath{'})}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}\mathrm{\ensuremath{\Upsilon}}(nS)$ ($n=1$, 2, 3) and $\mathrm{\ensuremath{\Upsilon}}(10860)\ensuremath{\rightarrow}\ensuremath{\pi}{Z}_{b}^{(\ensuremath{'})}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}{h}_{b}(mP)$ ($m=1$, 2) appear to have nearly equal strengths, which is conventionally explained by a simultaneous presence of both ${S}_{b\overline{b}}=0$ and ${S}_{b\overline{b}}=1$ components in the wave functions of the ${Z}_{b}\mathrm{s}$ in equal shares. Meanwhile, the destructive interference between the contributions of the ${Z}_{b}$ and ${Z}_{b}^{\ensuremath{'}}$ to the decay amplitude for a $\ensuremath{\pi}\ensuremath{\pi}{h}_{b}$ final state kills the signal to zero in the strict HQSS limit. In this paper, we discuss how the HQSS violation needs to be balanced by the narrowness of the ${Z}_{b}^{(\ensuremath{'})}$ states in the physical case to allow for equal transition strengths into final states with different total heavy quark spins, and how spin symmetry is restored as a result of a subtle interplay of the scales involved, when the mass of a heavy quark becomes infinite. Moreover, we demonstrate how similar branching fractions of the decays into $\ensuremath{\pi}\ensuremath{\pi}{h}_{b}$ and $\ensuremath{\pi}\ensuremath{\pi}\mathrm{\ensuremath{\Upsilon}}$ can be obtained and how the mentioned HQSS breaking can be reconciled with the dispersive approach to the $\ensuremath{\pi}\ensuremath{\pi}/K\overline{K}$ interaction in the final state and matched with the low-energy chiral dynamics in both final states.

Three‐dimensional spatial point computation in fringe projection profilometry

The demodulated phase in fringe projection profilometry (FPP) provides information about the (x,y,z)-coordinates of points of the observed object. However, the phase-to-coordinate conversion employing multiple cameras and projectors with different imaging models is not straightforward. This paper presents the following two contributions. First, a theoretical framework to investigate the triangulation problem in FPP is established. Seven representative triangulation methods commonly used in FPP are reviewed. Second, a generalized triangulation method is proposed for single-axis fringe projection supporting multiple cameras and projectors with lens distortion. The performance of the eight investigated triangulation methods is evaluated in terms of noise robustness and computation time by computer simulations and an experimental fringe projection optical setup. The results demonstrate that the mean dispersion approach yields the best performance, but vertical and horizontal fringes must be projected, while the new method is the most appropriate for single-axis fringe projection using multiple devices with lens distortion.

Isolation of DNA from plant tissues using a miniaturized matrix solid-phase dispersion approach featuring ionic liquid and magnetic ionic liquid solvents

The isolation of high-quality plant genomic DNA is a major prerequisite in many plant biomolecular analyses involving nucleic acid amplification. Conventional plant cell lysis and DNA extraction methods involve lengthy sample preparation procedures that often require large amounts of sample and chemicals, high temperatures and multiple liquid transfer steps which can introduce challenges for high throughput applications. In this study, a simple, rapid, miniaturized ionic liquid (IL)-based extraction method was developed for the isolation of genomic DNA from milligram fragments of Arabidopsis thaliana plant tissue. This method is based on a modification of vortex-assisted matrix solid-phase dispersion (VA-MSPD) in which the trihexyl(tetradecyl)phosphonium bis(trifluoromethylsulfonyl)imide ([P6,6,6,14+][NTf2-]) IL or trihexyl(tetradecyl)phosphonium tris(hexafluoroacetylaceto)nickelate(II) ([P6,6,6,14+][Ni(hfacac)3-]) magnetic IL (MIL) was directly applied to treated plant tissue (∼1.5 mg) and dispersed in an agate mortar to facilitate plant cell lysis and DNA extraction, followed by recovery of the mixture with a qPCR compatible co-solvent. This study represents the first approach to use ILs and MILs in a MSPD procedure to facilitate plant cell lysis and DNA extraction. The DNA-enriched IL- and MIL-cosolvent mixtures were directly integrated into the qPCR buffer without inhibiting the reaction while also circumventing the need for additional purification steps prior to DNA amplification. Under optimum conditions, the IL and MIL yielded 2.87 ± 0.28 and 1.97 ± 0.59 ng of DNA/mg of plant tissue, respectively. Furthermore, the mild extraction conditions used in the method enabled plant DNA in IL- and MIL-cosolvent mixtures to be preserved from degradation at room temperature.

Additive Manufacturing of Metal Matrix Nanocomposites: Novel Approach for Nanoparticles Dispersion by Electromagnetic Three-Dimensional Vibration

Additive Manufacturing of Metal Matrix Nanocomposites: Novel Approach for Nanoparticles Dispersion by Electromagnetic Three-Dimensional Vibration

Imaging near-surface S-wave velocity and attenuation models by full-waveform inversion with distributed acoustic sensing-recorded surface waves

Distributed acoustic sensing (DAS) technology is, increasingly, the seismic acquisition mode of choice for its high spatial sampling rate, low cost, and nonintrusive deployability. It is being widely evaluated as an enabler of seismic monitoring for [Formula: see text] sequestration in building subsurface time-lapse images and in characterizing near-surface environments. To advance this evaluation, field seismic surveys with optical fibers have been conducted at the Containment and Monitoring Institute’s Field Research Station (CaMI.FRS) in Newell County, Alberta, Canada. In comparison to the standard geophones, optical fibers deployed in surface trenches at CaMI.FRS have recorded high-quality surface waves, rich in low frequencies and exhibiting limited spatial aliasing. These benefits have motivated us to apply the full-waveform inversion (FWI) approach to image the S-wave velocity ([Formula: see text]) and attenuation (quality factor [Formula: see text]) models at shallow site using the surface waves recorded by optical fibers. Compared to the conventional surface-wave dispersion approach, FWI can intrinsically incorporate fundamental and high-order modes and produce [Formula: see text] model with high spatial resolution that resolves horizontal variations. The low-frequency components below 10 Hz measured in the DAS recordings are helpful to overcome the cycle-skipping problem of FWI. Following the adjoint-state method, [Formula: see text] sensitivity kernel can be calculated efficiently with memory strain variables. The [Formula: see text] model is iteratively estimated with a new misfit function measuring root-mean-square amplitude differences, which helps to reduce the trade-off artifacts. The synthetic data obtained from the inverted models are consistent with the observed data in amplitude and phase. The inversion results provide valuable information to characterize the near-surface environments at CaMI.FRS and are expected to support seismic imaging in deeper [Formula: see text] injection zones.

Comparison of two compounding techniques for carbon nanotubes filled natural rubbers through microscopic and dynamic mechanical characterizations

Natural rubber used in wave energy converters requires higher fatigue life and better energy harvesting efficiency to make it inexpensive compared to other renewable energy resources. Carbon nanotubes (CNTs) were extensively used to enhance the mechanical properties of natural rubber, however, its performance in a double-bonded shear condition was rarely investigated. In addition, the state of CNT dispersion was a critical factor for better energy harvesting efficiency and fatigue life. Therefore, this study was aimed to compare two different dispersion approaches in CNT synthesis so that better dynamic mechanical properties and lower hysteresis loss were achieved. One approach was done in the liquid state whereas the other one was carried out in dry condition. Although the former manifested a better CNT dispersion, no significant differences in terms of dynamic mechanical properties and dissipation losses compared to the latter compounding were obtained.

Comparison of conventional and dispersive solid phase extraction clean-up approaches for the simultaneous analysis of tetracyclines and sulfonamides in a variety of fresh vegetables

The extensive use of antibiotics in agriculture has led to the occurrence of residual drugs in different vegetables frequently consumed by humans. This could pose a potential threat to human health, not only because of the possible effects after ingestion but also because the transmission of antibiotic-resistant genes could occur. In this work, two accurate sample preparation procedures were developed and validated for the simultaneous analysis of sulfonamides (SAs) and tetracyclines (TCs) in four of the most widely consumed vegetables (lettuce, onion, tomato, and carrot) in Europe. The evaluated protocols were based on QuECHERS for extraction and subsequent clean-up by SPE (solid phase extraction) or dispersive SPE. Parameters affecting both extraction and clean-up were carefully evaluated and selected for accuracy of results and minimal matrix effect. Overall, apparent recoveries were above 70% for most of the target analytes with both analytical procedures, and adequate precision (RSD<30%) was obtained for all the matrices. The procedural limits of quantification (LOQPRO) values for SPE clean-up remained below 4.4 μg kg−1 for TCs in all vegetables except for chlortetracycline (CTC) in lettuce (11.3 μg kg−1) and 3.0 μg kg−1 for SAs, with the exception of sulfadiazine (SDZ) in onion (3.9 μg kg−1) and sulfathiazole (STZ) in carrot (5.0 μg kg−1). Lower LOQPRO values (0.1–3.7 μg kg−1) were obtained, in general, when dSPE clean-up was employed. Both methods were applied to twenty-five market vegetable samples from ecological and conventional agriculture and only sulfamethazine (SMZ) and sulfapyridine (SPD) were detected in lettuce at 1.2 μg kg−1 and 0.5 μg kg−1, respectively.

Reactive extraction evaluation for vanadium (V) removal in the MRDC column using axial dispersion and central composition approach

Reactive extraction evaluation for vanadium (V) removal in the MRDC column using axial dispersion and central composition approach