scholarly journals Systematic interpolation method predicts protein chromatographic elution from batch isotherm data without a detailed mechanistic isotherm model

2015 ◽  
Vol 10 (9) ◽  
pp. 1400-1411 ◽  
Author(s):  
Arch Creasy ◽  
Gregory Barker ◽  
Yan Yao ◽  
Giorgio Carta
Keyword(s):  
Interpolation Method ◽  
Isotherm Model ◽  
Chromatographic Elution

Ab initio band theory approach to electron energy loss near edge structures

1988 ◽  
Vol 46 ◽  
pp. 506-507
Author(s):  
Xudong Weng ◽  
O.F. Sankey ◽  
Peter Rez
Keyword(s):  
Ab Initio ◽  
Local Density ◽  
Interpolation Method ◽  
Atomic Orbital ◽  
Plane Waves ◽  
Large Set ◽  
Theory Approach ◽  
Band Theory ◽  
Atomic Orbitals ◽  
Pseudopotential Calculations

Single electron band structure techniques have been applied successfully to the interpretation of the near edge structures of metals and other materials. Among various band theories, the linear combination of atomic orbital (LCAO) method is especially simple and interpretable. The commonly used empirical LCAO method is mainly an interpolation method, where the energies and wave functions of atomic orbitals are adjusted in order to fit experimental or more accurately determined electron states. To achieve better accuracy, the size of calculation has to be expanded, for example, to include excited states and more-distant-neighboring atoms. This tends to sacrifice the simplicity and interpretability of the method.In this paper. we adopt an ab initio scheme which incorporates the conceptual advantage of the LCAO method with the accuracy of ab initio pseudopotential calculations. The so called pscudo-atomic-orbitals (PAO's), computed from a free atom within the local-density approximation and the pseudopotential approximation, are used as the basis of expansion, replacing the usually very large set of plane waves in the conventional pseudopotential method. These PAO's however, do not consist of a rigorously complete set of orthonormal states.

Competitive adsorption of organic solvents using modified and unmodified calcium bentonite clay mineral

2019 ◽  
Author(s):  
Chem Int
Keyword(s):  
Adsorption Isotherm ◽  
Adsorption Capacity ◽  
Organic Solvents ◽  
Competitive Adsorption ◽  
Correlation Factor ◽  
Isotherm Model ◽  
Isotherm Models ◽  
High Concentration ◽  
Dual Purpose ◽  
Calcium Bentonite

Dodecyltrimethylammonium bromide (DTAB)–modified and unmodified calcium bentonite were both used for the competitive adsorption of aromatics (xylene, ethylbenzene and toluene) and petroleum products (gasoline, dual purpose kerosene and diesel) from their aqueous solution. Infrared spectroscopy (IR) and expansion tests (adsorption capacity and Foster swelling) measurement were performed in order to evaluate the performance of the adsorbents. The Foster swelling index and adsorption capacity of the DTAB modified calcium bentonite in the organic solvents follow the trend: xylene > ethylbenzene > toluene > gasoline > dual purpose kerosene (DPK) > diesel > water. However, the adsorption capacity of the adsorbent in diesel outweighed the adsorption capacity in DPK at high concentration of DTAB indicating that diesel has higher affinity for high DTAB concentration than DPK. The percentage removal of the solvent is directly proportional to the concentration of DTAB used in modifying the bentonite as well as the contact time between the adsorbent and the solvent, hence modified calcium bentonite adsorbed a higher percentage of organic solvents than the unmodified calcium bentonite. The adsorption characteristics of both adsorbents improved remarkably after proper agitation of the organic solvents, the unmodified calcium bentonite however adsorbed more water than the modified bentonite. Data obtained from adsorption isotherm models confirms that Freundlich adsorption isotherm model was favored more than Langmuir adsorption isotherm model with the correlation factor (R2) of the former tending more towards unity. The adsorption of ethylbenzene using DTAB modified and unmodified calcium bentonites follow a pseudo second order kinetics mechanism, suggesting that the rate determining step of adsorption involves both the adsorbent and the organic solvent.

A cell-based smoothed point interpolation method (CS-PIM) for 2D thermoelastic problems

2017 ◽  
Vol 27 (6) ◽  
pp. 1249-1265 ◽  
Author(s):  
Yijun Liu ◽  
Guiyong Zhang ◽  
Huan Lu ◽  
Zhi Zong
Keyword(s):  
Thermal Stresses ◽  
Interpolation Method ◽  
Content Type ◽  
Novel Approach ◽  
Convergence Results ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Thermoelastic Problems ◽  
Gradient Smoothing ◽  
Practical Implications

Purpose Due to the strong reliance on element quality, there exist some inherent shortcomings of the traditional finite element method (FEM). The model of FEM behaves overly stiff, and the solutions of automated generated linear elements are generally of poor accuracy about especially gradient results. The proposed cell-based smoothed point interpolation method (CS-PIM) aims to improve the results accuracy of the thermoelastic problems via properly softening the overly-stiff stiffness. Design/methodology/approach This novel approach is based on the newly developed G space and weakened weak (w2) formulation, and of which shape functions are created using the point interpolation method and the cell-based gradient smoothing operation is conducted based on the linear triangular background cells. Findings Owing to the property of softened stiffness, the present method can generally achieve better accuracy and higher convergence results (especially for the temperature gradient and thermal stress solutions) than the FEM does by using the simplest linear triangular background cells, which has been examined by extensive numerical studies. Practical implications The CS-PIM is capable of producing more accurate results of temperature gradients as well as thermal stresses with the automated generated and unstructured background cells, which make it a better candidate for solving practical thermoelastic problems. Originality/value It is the first time that the novel CS-PIM was further developed for solving thermoelastic problems, which shows its tremendous potential for practical implications.

Sign in / Sign up

Export Citation Format

Share Document