Mathematical Modelling of Molecular Separation Processes in Aggressive Solvent Systems

2018 ◽  
Vol 14 (2) ◽  
Author(s):  
Issara Sereewatthanawut ◽  
Supranee Lisawadi ◽  
Lapyote Prasittisopin
Keyword(s):  
Mathematical Models ◽  
Industrial Application ◽  
Organic Dyes ◽  
Experimental System ◽  
Process Models ◽  
Pressure Effects ◽  
Separation Processes ◽  
Molecular Separation ◽  
The Difference ◽  
General Transport

Abstract Research works on membrane technology, particularly molecular separation in solvent-based systems, has increased tremendously in recent years. In order to apply this technology at industrial scale, a suitable mathematical model for process design and optimisation must be developed. In the present study, mathematical models to describe process performance were developed with different levels of complexities. The models were developed based on two general transport mechanisms, pore-flow and solution-diffusion principles. Models with different complexity levels were developed, ranging from simple process models to a combination of transport, mass transfer and osmotic pressure effects. Series of molecular separation experiments were conducted to validate the models and to compare the difference among all models. The experimental system conducted in this study was a mixture of organic dyes in n-Dimethylformamide (DMF) solution, which mimics a typical industrial application where molecular purification in aggressive organic solvent is required. The filtration results obtained from any mathematical models are in good agreement with the experiments. The calculated purity of the organic dyes in the permeate ranging from 99.72 % to 100 % in comparison to 99.76 % from the experiments at 8000 s. The results obtained from this study can potentially be applied for industrial application as a prediction tool without conducting any excessive experiments.

Mathematical models of Gauss – Kruger projection for calculation of meridians conversion on the plane and scale of the image

2018 ◽  
Vol 934 (4) ◽  
pp. 2-7
Author(s):  
P.A. Medvedev ◽  
M.V. Novgorodskaya
Keyword(s):  
Mathematical Models ◽  
Analytical Methods ◽  
Theoretical Studies ◽  
Spherical Trigonometry ◽  
Cylindrical Projection ◽  
Rectangular Coordinates ◽  
In Series ◽  
Observational Errors ◽  
The Difference

This work contains continued research carried out on improving mathematical models of the Gauss-Krueger projection in accordance with the parameters of any ellipsoid with the removal of points from the axial meridian to l ≤ 6° . In terms of formulae earlier derived by the authors with improved convergence for the calculation of planar rectangular coordinates by geodesic coordinates, the algorithms for determining the convergence of meridians on the plane and the scale of the image are obtained. The improvement of the formulae represented in the form of series in powers of the difference in longitudes was accomplished by separating spherical terms in series and then replacing their approximate sums by exact expressions using the formulae of spherical trigonometry. As in previous works published in this journal [7, 8], determining the sums of the spherical terms was carried out according to the laws of the transverse-cylindrical projection of the sphere on the plane. Theoretical studies are given and formulae are proposed for estimating the observational errors in the results of the derived algorithms. The maximum of observational errors of convergence of meridians and scale, proceeding from the specified accuracy of the determined quantities was established through analytical methods.

Mathematical Models of Spacetime in Contemporary Physics and Essential Issues of the Ontology of Spacetime

1998 ◽  
pp. 1-5
Author(s):  
Maciej Gos
Keyword(s):  
Field Theory ◽  
Mathematical Models ◽  
Space Time ◽  
Theory Of Relativity ◽  
Time Arrow ◽  
Time Singularities ◽  
Time Quantum ◽  
Theory Of Gravitation ◽  
The Difference ◽  
Definition Of

The general theory of relativity and field theory of matter generate an interesting ontology of space-time and, generally, of nature. It is a monistic, anti-atomistic and geometrized ontology — in which the substance is the metric field — to which all physical events are reducible. Such ontology refers to the Cartesian definition of corporeality and to Plato's ontology of nature presented in the Timaeus. This ontology provides a solution to the dispute between Clark and Leibniz on the issue of the ontological independence of space-time from distribution of events. However, mathematical models of space-time in physics do not solve the problem of the difference between time and space dimensions (invariance of equations with regard to the inversion of time arrow). Recent research on space-time singularities and asymmetrical in time quantum theory of gravitation will perhaps allow for the solution of this problem based on the structure of space-time and not merely on thermodynamics.

Observations of the Earth's magnetic field made in Edinburgh from 1670 to the present day

1994 ◽  
Vol 85 (4) ◽  
pp. 239-252 ◽  
Author(s):  
D. R. Barraclough
Keyword(s):  
Magnetic Field ◽  
Mathematical Models ◽  
Secular Variation ◽  
Geomagnetic Field ◽  
Upper Atmosphere ◽  
The Difference ◽  
Time Changes ◽  
Relative Measurements ◽  
Magnetic North ◽  
Made In

AbstractMagnetic observations made at the same site give valuable information about the time changes (the secular variation) of the geomagnetic field. This paper gives details of all known measurements of the geomagnetic field in and around Edinburgh since the earliest observation of magnetic declination (the difference between true and magnetic north) by George Sinclair in 1670. Early observations of the strength of the field were only relative measurements. Approximate conversion factors are derived to enable these data to be expressed in modern absolute units (nanoteslas). Observed values of declination, inclination and the horizontal intensity of the geomagnetic field are plotted and compared with values computed from mathematical models of the field covering the interval 1690 to 1990, inclusive. The earlier observations were not corrected for the effects of the rapidly varying magnetic fields caused by electric currents in the upper atmosphere. The consequences of this are estimated.

scholarly journals Electroporation can cause artefacts due to solubilization of cations from the electrode plates. Aluminum ions enhance conversion of inositol 1,3,4,5-tetrakisphosphate into inositol 1,4,5-trisphosphate in electroporated L1210 cells

1991 ◽  
Vol 277 (3) ◽  
pp. 883-885 ◽  
Author(s):  
J W Loomis-Husselbee ◽  
P J Cullen ◽  
R F Irvine ◽  
A P Dawson
Keyword(s):  
Experimental System ◽  
Experimental Medium ◽  
Assay Medium ◽  
L1210 Cells ◽  
Aluminum Ions ◽  
Inositol 1,4,5 Trisphosphate ◽  
The Difference ◽  
High Concentrations ◽  
As If ◽  
In Cells

1. In electroporated L1210 cells, Ins(1,3,4,5)P4 causes Ca2+ release, owing to its conversion into Ins(1,4,5)P3, but this does not happen in cells permeabilized by digitonin treatment [Cullen, Irvine, Drøbak & Dawson (1989) Biochem. J. 259, 931-933]. 2. If the assay medium is subjected to electroporation by using a commercially available electroporation apparatus and then the cells are added and permeabilized with digitonin, the cells behave as if they had been electroporated. 3. Electroporation causes the release of high concentrations of Al3+ into the experimental medium, and addition of these concentrations of Al3+ into the experimental medium mimics the effect of electroporation on the conversion of Ins(1,3,4,5)P4 into Ins(1,4,5)P3. 4. It is concluded that the difference between electroporated and digitonin-permeabilized L1210 cells in this experimental system can be attributed to dissolution of Al3+ from the electroporation cuvette. Al3+ contamination may thus be a serious problem when using this apparatus.

scholarly journals ON INTERACTION OF A LIQUID FILM WITH AN OBSTACLE

2002 ◽  
Vol 7 (2) ◽  
pp. 327-342 ◽  
Author(s):  
A. Zemitis
Keyword(s):  
Liquid Film ◽  
Mathematical Models ◽  
Numerical Experiments ◽  
Impinging Jets ◽  
Numerical Results ◽  
Qualitative Behavior ◽  
Different Shapes ◽  
The Wire ◽  
The Difference

In this paper are discussed mathematical models for the liquid film generated by impinging jets. These models describe only the film shape under special assumptions about processes. Attention is stressed on the interaction of the liquid film with some obstacle. The idea is to generalize existing models and to investigate qualitative behavior of liquid film using numerical experiments. G.I. Taylor [Proc. R. Soc. London Ser. A 253, 313 (1959)] found that the liquid film generated by impinging jets is very sensitive to properties of the wire which was used as an obstacle. The aim of this presentation is to propose a modification of the Taylor's model, which allows to simulate the film shape in cases when the angle between jets is different from 180°. Numerical results obtained by discussed models give two different shapes of the liquid film similar as in Taylors experiments. These two shapes depend on the regime: either droplets are produced close to the obstacle or not. The difference between two regimes becomes larger if the angle between jets decreases. Existence of such two regimes can be very essential for some applications of impinging jets, if the generated liquid film can have a contact with obstacles.

Distance Measures for Surgical Process Models

2013 ◽  
Vol 52 (05) ◽  
pp. 422-431 ◽  
Author(s):  
U. Bühligen ◽  
T. Neumuth ◽  
S. Schumann
Keyword(s):  
Graph Matching ◽  
Surgical Techniques ◽  
Process Models ◽  
Distance Measures ◽  
Levenshtein Distance ◽  
Data Sets ◽  
Distance Measurements ◽  
Surgical Interventions ◽  
The Difference ◽  
The Impact

SummaryBackground: The development of new resources, such as surgical techniques and approaches, results in continuous modification of surgery. To assess these modifications, it is necessary to use measures that quantify the impact of resources on surgical processes.Objectives: The objective of this work is to introduce and evaluate distance measurements that are able to represent differences in the courses of surgical interventions as processes.Methods: Hence, we present four different distance measures for surgical processes: the Jaccard distance, Levenshtein distance, Adjacency distance, and Graph matching distance. These measures are formally introduced and evaluated by applying them to clinical data sets from laparoscopic training in pediatric surgery.Results: We analyzed the distances of 450 surgical processes using these four measures with a focus on the difference in surgical processes performed by novices and by experienced surgeons. The Levenshtein and Adjacency distances were best suited to measure distances between surgical processes.Conclusion: The measurement of distances between surgical processes is necessary to estimate the benefit of new surgical techniques and strategies.

Nuclear matrix generation during reactivation of avian erythrocyte nuclei: an analysis of the protein traffic in cybrids

1986 ◽  
Vol 84 (1) ◽  
pp. 105-127
Author(s):  
C.L. Woodcock ◽  
H. Woodcock
Keyword(s):  
Nuclear Matrix ◽  
Specific Activity ◽  
Nuclear Periphery ◽  
Experimental System ◽  
Cell Nuclei ◽  
Electron Microscopic ◽  
Electron Microscopic Autoradiography ◽  
Protein Traffic ◽  
L Cell ◽  
The Difference

It has previously been shown that an internal nuclear matrix is generated during the reactivation of the chick erythrocyte nucleus in mouse L-cell cytoplasts. This experimental system has now been used to identify the major polypeptides that migrate into the nucleus during the reactivation process. Mouse L-cells were prelabelled with [35S]methionine, enucleated using cytochalasin B, and fused with 14- to 17-day embryonic chick erythrocytes. Sixteen hours post-fusion, the redistribution of the labelled proteins was examined by electron microscopic autoradiography, and two-dimensional polyacrylamide gel fluorography of the isolated nuclei was used to identify the major imported species. After allowing for cytoplasmic contamination, 15 nucleus-associated polypeptides were identified, two of which also matched with counterparts in the L-cell nuclear preparation. Five of the nucleus-associated polypeptides were tentatively identified (on the basis of one-dimensional gel matches) as nuclear matrix proteins; these five included the two that had counterparts in L-cell nuclei. The autoradiographic results showed that 16 h post-fusion, the specific activity (silver grains/unit area) of the reactivated nucleus was about half that of the cytoplasm, with no evidence for an accumulation of labelled protein at the nuclear periphery. When well-reactivated nuclei were distinguished from poorly reactivated nuclei on the basis of the extent of chromatin decondensation, it was found that their specific activities were quite similar, but because of the difference in size, the well-reactivated nuclei contained about twice as much labelled protein. Estimates of the protein traffic based upon the autoradiographic data indicated that the nuclei had increased in mass by 10–20% during the 16 h reactivation period.

Industrial Applications

2015 ◽  
pp. 503-537
Keyword(s):  
Structural Analysis ◽  
Mathematical Models ◽  
Industrial Application ◽  
Safety Assessment ◽  
Damage Mechanics ◽  
Industrial Applications ◽  
Analysis Techniques ◽  
Engineering Problems ◽  
The Subject ◽  
Earthquake Safety

The application of structural analysis techniques to solve real engineering problems is an entirely independent discipline by itself that cannot be properly presented in a book of structural mechanics. However, it is important to give an overview of how mathematical models can help make engineering decisions. This is the subject of the current chapter. The context of the presentation is that of earthquake safety assessment. Of course, this is not the only industrial application of the fracture and damage mechanics of frames, but it is a very representative one and a good example of it. The chapter is organized as follows. First, the problem is presented and a protocol to solve it is described in Section 13.1. Then, an academic software that can be accessed via Internet is described in Section 13.2. This program is used to solve some examples of real structures in the last section of the chapter.

Use of Partial Molar Volumes of Model Compounds in the Interpretation of High-Pressure Effects on Proteins

1996 ◽  
Author(s):  
Kenneth E. Prehoda ◽  
John L. Markley
Keyword(s):  
Volume Change ◽  
Atmospheric Pressure ◽  
Protein Unfolding ◽  
Partial Molar Volumes ◽  
Bulk Water ◽  
Pressure Effects ◽  
Molar Volumes ◽  
Positive Term ◽  
Full Characterization ◽  
The Difference

The transfer of liquid hydrocarbons into water is accompanied by a large decrease in volume at 25 °C and atmospheric pressure, with typical values for ΔV°tr of — 2.0 ml mol methylene−1. Considering the large amount of apolar surface that is exposed when a globular protein unfolds, the hydrocarbon transfer results imply that the change in volume accompanying the unfolding process (ΔV°obs) should be highly negative under these conditions. However, experimental data on the pressure denaturation of proteins typically yield relatively small values of ΔV°obs at atmospheric pressure and 25 °C. We analyze this apparent inconsistency in terms of a simple thermodynamic dissection of the partial molar volume. This approach allows the volume effects that result from solute-solvent interactions to be determined from experimental partial molar volumes. The use of absolute quantities (partial molar volumes) circumvents assumptions associated with the use of results from transfer experiments. An important finding is that hydration of apolar species is less dense than bulk water. This discovery leads to the conclusion that the contribution to ΔV°obs for protein unfolding from the hydration of apolar surfaces is highly positive, contrary to predictions based on transfer data. Further, hydration of polar surfaces makes a positive contribution to ΔV°obs. The large, positive term from the differential hydration of the folded and unfolded states is compensated by the difference in free volume of the protein in the two states. This finding provides a new framework for interpreting pressure effects on macromolecules. The full characterization of a macromolecular system requires knowledge of the effect of pressure on the system. The thermodynamic information obtained from using pressure as a perturbation is a volume change for the particular reaction being studied. The observed volume change, ΔV°obs, for protein unfolding may provide insight into the mechanisms that determine the three-dimensional structure of the folded state. Pressure denaturation experiments have been demonstrated for a number of proteins, including ribonuclease A (Gill & Glogovsky, 1965; Brandts et al., 1970), chymotrypsinogen (Hawley, 1971), metmyoglobin (Zipp & Kauzmann, 1973), and, more recently, lysozyme (Samarasinghe et al., 1992) and staphylococcal nuclease (Royer et al., 1993).

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