scholarly journals Specific Mass Growth Rate of Sugar Crystals: Probabilistic Modeling

2021 ◽  
Vol 51 (1) ◽  
pp. 39-52
Author(s):  
Denis Arapov ◽  
Vladimir Kuritsyn ◽  
Sergey Petrov ◽  
Nadezda Podgornova ◽  
Mariya Zaitseva

Introduction. The present research featured industrial sugar crystallization. The article introduces a generalized mathematical model of specific growth rate of sugar crystals depending on temperature, solids, and the purity of solution, as well as on the concentration and average size of crystals. The model includes the probabilistic component of growth rate of monocrystals and the reduced adjustment of the constrained crystal growth depending on the abovementioned as-pects. Study objects and methods. The research focused on mass crystallization of sucrose, including the growth rate of monocrystals and the number of crystals in the fill mass. The obtained experimental data were processed using nonlinear programming. Results and discussion. 421 experiments made it possible to develop a probabilistic mathematical model of specific mass growth rate of sugar monocrystals and its dependence on the solution temperature, purity, and solids content. Model error: ± 11.3%. The model covers the temperature range, concentration of solids, and purity of the solution. The proximity of crystals was calculated according to the dependence of the growth rate on their concentration and the average size (error: ± 1.3%). The adjustment range: concentration of crystals = 5–60%, average size = 0.25–1.50 mm. Conclusion. The present generalized mathematical model of crystallization considered the temperature, as well as the purity and solids content in the fill mass, the concentration of sucrose crystals and their average size. The research compared the effect of linear size and concentration of sugar monocrystals on the calculated and experimental sizes of specific mass growth rate and the dimensionless adjustment of growth rate. The calculated sizes proved to be close to the ex-perimental data, which showed adequacy to the developed crystallization model. The research results can be used to optimize the process of mass sugar crystallization.

2011 ◽  
Vol 189-193 ◽  
pp. 2869-2874 ◽  
Author(s):  
Wen Zhong Song ◽  
Qi Fang ◽  
Hui Ping Ren ◽  
Zi Li Jin ◽  
Hui Chang

The solid solution of the second phase particle and austenite grain growth behavior of the high niobium-containing RE steel was studied by mathematical calculation and extraction replica technique. The purpose of the study was to investigate the effects of Rare Earth La on austenite grain growth and propose an empirical equation for predicting the austenite grain size of RE steel. Austenite grain grows in an exponential law with the increase of heating temperature, while approximately in a parabolic law with the increase of holding time. Results show that the RE steel has good anti-coarsening ability at elevated temperatures. When soaking temperature is lower than 1250°C , AGS and growth rate are small for high niobium steel, but soaking temperature is lower than 1220°C , AGS and growth rate are small for RE steel. RE La can promote solid solution of second-phase particles Nb(C, N), the solution temperature decrease 30°C than high niobium steel.


2019 ◽  
Vol 19 (3&4) ◽  
pp. 112
Author(s):  
Sanjeev Kumar Karlopia ◽  
Yahya Bakhtiyar ◽  
Seema Langer

The study was conducted to assess the growth and survival of <em>Macrobrachium rosenbergii</em> in earthen culture ponds in order to know about the growth potential of <em>M. rosenbergii</em> in mono as well as polyculture conditions in Jammu. Polyculture experiments of prawn with some selected carps Indian Major Carps (<em>Cirrhinus mrigala</em> and <em>Labeo rohita</em>) and Exotic Carps (<em>Cyprinus carpio</em>) were undertaken in 3 freshwater ponds for duration of 4 months. Under the monoculture conditions, prawns attained an average size of 10.40 ± 0.17 cm weighing 23.84 ± 0.32 g in 4 months and the survival rate was found to be more than 75%. The growth rate of prawns was found to increase steadily during the first half (upto mid-October) after which a decline in the growth rate was evident as the mean temperature reached below 18°C. In the polyculture ponds the prawns attained an average size of 10.10 ± 0.03 cm weighing 18.39 ± 0.89g (without<em> C. carpio</em>) and 8.4 ± 0.36 cm weighing 15.23 ± 0.36 g (with <em>C. carpio</em>) in 4 months and their survival rate was less than 70%. Prawns being benthic feeders utilized the leftover food (of the fishes) that settled at the bottom, therefore, saving the feed cost. It was observed that mean size of the fish attained in the polyculture practice was almost similar to that obtained in the monoculture. The ideal prawn polyculture should be practiced with fast growing compatible carps such as Rohu and grass carp. Bottom feeder carps such as Mrigal (<em>C. mrigala</em>) should be avoided in prawn polyculture practice as they compete with prawns in feeding.


2002 ◽  
Vol 50 (12) ◽  
pp. 1633-1640 ◽  
Author(s):  
Massimo Derenzini ◽  
Lorenzo Montanaro ◽  
Alessandra Chillà ◽  
Elena Tosti ◽  
Claudio Ceccarelli ◽  
...  

In this study we investigated the relationship between thymidylate synthase (TS) protein expression, evaluated by Western blotting analysis and by immunohistochemistry (IHC), and growth rate in human colon xenograft tumors in nude mice. Human colon cancer cell lines were used to induce xenograft tumors and the tumor mass growth rate was calculated by measuring tumor size variations over time. TS 106 monoclonal antibody was used for both Western blotting and IHC TS detection. Tumor cell growth fraction was measured by Ki67/MIB1 immunolabeling and tumor cell growth rate by evaluating the mean nucleolar size in silver-stained sections. TS Western blotting values were related to tumor mass growth rate ( p<0.001) and cell growth rate ( p=0.002) but not to cell growth fraction ( p=0.676). The degree of the IHC staining showed only a trend to be associated with TS protein expression measured on Western blotting, and was not related either to tumor mass growth or cell proliferation rate. Tumor xenografts were also characterized for TS promoter tandem repeat and p53 status. No relationship was observed between these variables and TS expression evaluated by both Western blotting and IHC analysis. Our results demonstrate that TS expression evaluated by Western blotting analysis is directly related to the tumor mass growth rate and question the use of the IHC approach to obtain precise quantitative information on TS expression in tumor samples.


HortScience ◽  
2017 ◽  
Vol 52 (12) ◽  
pp. 1742-1747
Author(s):  
Martin P.N. Gent

Relative growth rate (RGR), the relative increase in weight per day, can analyze the effect of environment and nutrition on growth. I examined which of the parameters responding to plant growth scaled according to RGR for lettuce and spinach grown in heated greenhouses in hydroponics with control of the nutrient solution. The experiments for lettuce in 2006–08 included all times of year, high vs. low temperature, and effect of withdrawal of nitrogen. There were four parameters that were significant in multiple linear regression vs. RGR; irradiance divided by leaf area index if it was greater than one, or normalized daily light integral (NDLI), solution temperature, electrical conductivity (EC), and logarithm solution nitrate when it was between 3 and 55 mg·L−1 N. NDLI had the most significant coefficient, but the other parameters had regression coefficients more than three times se. For experiments on spinach in 2009–10, all the parameters mentioned previously were significant in multiple linear regression vs. RGR, except EC. The coefficient for NDLI in spinach was about half the value in lettuce. The coefficients for solution temperature and low nitrate were two and three times that in lettuce. In a third set of experiments on lettuce in 1996–98, solution temperature was the only significant parameter among those mentioned previously. The coefficient for solution temperature was similar to that for regression of lettuce in 2006–08.


2019 ◽  
Vol 29 (01) ◽  
pp. 1950009 ◽  
Author(s):  
Zonghong Feng ◽  
Xinxing Wu ◽  
Luo Yang

This paper studies a mathematical model for the interaction between tumor cells and Cytotoxic T lymphocytes (CTLs) under drug therapy. We obtain some sufficient conditions for the local and global asymptotical stabilities of the system by using Schur–Cohn criterion and the theory of Lyapunov function. In addition, it is known that the system without any treatment may undergo Neimark–Sacker bifurcation, and there may exist a chaotic region of values of tumor growth rate where the system exhibits chaotic behavior. So it is important to narrow the chaotic region. This may be done by increasing the intensity of the treatment to some extent. Moreover, for a fixed value of tumor growth rate in the chaotic region, a threshold value [Formula: see text] is predicted of the treatment parameter [Formula: see text]. We can see Neimark–Sacker bifurcation of the system when [Formula: see text], and the chaotic behavior for tumor cells ends and the system becomes locally asymptotically stable when [Formula: see text].


2005 ◽  
Vol 1 (5) ◽  
Author(s):  
Ms. Aamarpali Ratna Puri ◽  
S. Kaur

Sucrose Crystallization is a mass transfer process. Sucrose molecule's migration from solution to crystal is driven by concentration difference between the mother liquor and the crystal surface; the coefficient of super saturation is the most important parameter for the process. Supersaturation of sugar solution depends on the purity and brix of the mother liquor. It has large influence on product's quantity and quality (crystal yield, crystal size and size distribution) and on the cost of production i.e output/hour and energy consumption. However there is still no generally applicable theory, which permits an accurate prediction of the effects of all the factors that govern the industrial processes of crystallization from solution. The crystal growth depends on the viscosity, which further depends on the nature and amount of impurities. If the local conditions are favourable, localized layers of molecules of impurity can statistically remain on the surface for a period of time. On the other hand, if the interaction between the impurity and the layer is weak, then there will be competition between impurity and sucrose molecules thus affecting the sucrose crystal growth rate. In the present study, the growth rate of sugar crystals was studied, using two-litre automatic laboratory vacuum pan, under controlled conditions in the presence of impurities. The effect of phosphate and silica (adding one at time) on the growth rate of sugar crystals was studied at two different temperatures 328 and 338K and with two different seed sizes of sucrose (850 and 600µm). The growth rate was studied at two degrees of supersaturation (1.10 and 1.15). The growth rate of sucrose crystals (with or without added impurities) showed significant increase with the 10°C rise in temperature. The growth rate of sucrose crystals increased with the increase in the level of phosphate but decreased with the increase in the level of silica in sugar solution.


1981 ◽  
Vol 38 (12) ◽  
pp. 1636-1656 ◽  
Author(s):  
W. E. Ricker

Of the five species of Pacific salmon in British Columbia, chinook salmon (Oncorhynchus tshawytscha) and coho salmon (O. kisutch) are harvested during their growing seasons, while pink salmon (O. gorbuscha), chum salmon (O. keta), and sockeye salmon (O. nerka) are taken only after practically all of their growth is completed. The size of the fish caught, of all species, has decreased, but to different degrees and over different time periods, and for the most part this results from a size decrease in the population. These decreases do not exhibit significant correlations with available ocean temperature or salinity series, except that for sockeye lower temperature is associated with larger size. Chinook salmon have decreased greatly in both size and age since the 1920s, most importantly because nonmaturing individuals are taken by the troll fishery; hence individuals that mature at older ages are harvested more intensively, which decreases the percentage of older ones available both directly and cumulatively because the spawners include an excess of younger fish. Other species have decreased in size principally since 1950, when the change to payment by the pound rather than by the piece made it profitable for the gill-netters to harvest more of the larger fish. Cohos and pinks exhibit the greatest decreases, these being almost entirely a cumulative genetic effect caused by commercial trolls and gill nets removing fish of larger than average size. However, cohos reared in the Strait of Georgia have not decreased in size, possibly because sport trolling has different selection characteristics or because of the increase in the hatchery-reared component of the catch. The mean size of chum and sockeye salmon caught has changed much less than that of the other species. Chums have the additional peculiarity that gill nets tend to take smaller individuals than seines do and that their mean age has increased, at least between 1957 and 1972. That overall mean size has nevertheless decreased somewhat may be related to the fact that younger-maturing individuals grow much faster than older-maturing ones; hence excess removal of the smaller younger fish tends to depress growth rate. Among sockeye the decrease in size has apparently been retarded by an increase in growth rate related to the gradual cooling of the ocean since 1940. However, selection has had two important effects: an increase in the percentage of age-3 "jacks" in some stocks, these being little harvested, and an increase in the difference in size between sockeye having three and four ocean growing seasons, respectively.Key words: Pacific salmon, age changes, size changes, fishery, environment, selection, heritability


Blood ◽  
2020 ◽  
Vol 136 (Supplement 1) ◽  
pp. 21-21
Author(s):  
Koichi Miyamura ◽  
Masahide Osaki ◽  
Tatsunori Goto ◽  
Takanobu Morishita ◽  
Yukiyasu Ozawa

Background In Ph+ALL patients, prophylactic/maintenance administrations of TKI are used after the protocol treatment. Unlike Chronic myelogenous leukemia (CML), after TKI stopped, there is no consensus about how often to monitor to detect molecular relapse. In the current study, from clinical data of 31 patients we tried to determine the optimal frequency of MRD monitor for better prognosis using a mathematical model. Methods Doubling time (DT) and Growth rate (GR) were retrospectively calculated by the increase of BCR-ABL from 99 kinetic data from 31 patients with Ph+ALL at molecular relapse. Measurement of amount BCR-ABL was performed by RQ-PCR. Mimicking CML, we defined BCR-ABL/ABL ratio of 0.1% as "MR3 (Major molecular response)" and undetectable levels of BCR-ABL transcript as "MR5 (Complete molecular response)". In order to investigate the relationship between tumor burden (BCR/ABL) at the time of MRD detection and prognosis, it was divided into 3 groups, BCR/ABL&lt;0.1% (MR3), 0.1%&lt;BCR/ABL&lt;1% (MR2) and BCR/ABL&gt;1% (MR1). This study was approved by the institutional review committee. Results The doubling time was 1.3 days (GR 0.7%/day) to 95.4 days (70.8%/day) with a median of 12.3 days (5.8%). The rate of increase was compared by three groups of tumor burden. The DT among patients in MR1 was shorter than those in MR3 and MR2 (7.7 days vs 15.2 days in median, t-test p&lt;0.01). There were no differences of DT in sex, age, treatments and BCR/ABL mutation. Most patient had multiple kinetic data and the smallest amount of BCR/ABL was used in each patient. Among 8 patients who showed MR3 (MR3pt) and 11 who showed MR2 (MR2pt), 14 are alive at this analysis, while among 10 patients who showed MR1 (MR1pt), only 1 patient is alive.(Log-rank test, p&lt;0.1) (Figure) Median survival time is 882 days, 330 days and 16 days in MR3pt, Mr2pt and MR1pt, respectively. All patients died of progression of the disease. Finding molecular relapse before MR2 may related to better results. Optimal interval of MRD detection We set several hypotheses to determine the optimal frequency to detect early recurrence of leukemia. We estimated that patients with MR2 and MR5 have 1010 and 107 Ph+ cells in body, respectively. We defined "MR2" and "MR5" as "optimal intervention threshold" and "detection threshold". From our clinical data, we tentatively determined that doubling time of leukemia growth is distributed between 1 day (GR 100%/day) and 100days (0.7%). Also, we assumed that single cell has a relapse potency and the GR is constant during observation in each patient. The number of Ph+ cells in a MR5 patient who would potentially relapse might be distributed between 1 cell and 1 x 107 (MR5). "Success" was defined as if molecular relapse is detected between M5 and MR2 and "Failure" was defined as if detected more than MR2. According to the daily clinical practice, the optimal examination interval is tentatively every 7 days, every 14 days, every 28 days, every 56 days, every 84 days, every 6 months, and every year. First, in order to calculate the growth rate that would be successful at 7-day intervals, the rate of 168%/day for 1 cell to increase 107 (MR5) in 7 days was calculated. This rate is faster than the maximum rate of 100%/day in this study, so an interval of 7 days is good for the initial period. Similarly, at 14-day intervals, 68%/day is calculated, and in this case, it requires 32 days to increase 107 (MR5) from 1 cell. As a result, after 32.7 days, 14-day intervals are acceptable. Similarly, the calculated results for 28 days, 56 days, 84 days, 6 months, and 1 year are shown in the Table. MRD can be found before M3 (success) with 28-day intervals after 65 days, 56-day intervals after 131 days, 84-day intervals after 196 days, 6-month intervals after 419 days and 1-year intervals after 852 days. Conclusion Taken together, soon after stop of TKI, more frequent monitoring of MRD than in "treatment free remission" in CML is needed. The interval can be prolonged with the passage of time. In several patients, hematopoietic stem cell transplantation (HSCT) was possible due to early intervention by changing TKI and chemotherapy. After HSCT, TKI combined with rapid reduction of immune-suppressants and donor lymphocyte infusion successfully related with long term survival. (data will be shown in ASH) Thus, the tight monitoring according to the mathematical model is important. The current strategy may be applied to other leukemia in which MRD monitoring by PCR is established. Disclosures Miyamura: Bristol-Myers Squibb Co., Ltd.:Honoraria;Celgene Co., Ltd.:Honoraria;Daiichi-Sankyo Co., Ltd.:Honoraria;Otsuka Co., Ltd.:Honoraria;Pfizer Co., Ltd.:Honoraria;Novartis Co., Ltd.:Honoraria.Goto:Takeda Pharmaceutical Co., Ltd:Honoraria;Novartis Pharma Co., Ltd.:Honoraria.Morishita:Bristol-Myers Squibb Co., Ltd.:Honoraria.Ozawa:Novartis Co., Ltd.:Honoraria.


2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Chunlei Ruan ◽  
Chuntai Liu ◽  
Guoqiang Zheng

Monte Carlo method is used to capture the evolution of spherulites and shish-kebabs and to predict the crystallization kinetics in isothermal polymer crystallization. Effects of nucleation density and growth rate of spherulites, nucleation density, and length growth rate of shish-kebabs, respectively, on crystallization are investigated. Results show that nucleation densities of both spherulites and shish-kebabs strongly affect crystallization rate as well as morphology. An increase in nucleation density of either spherulites or shish-kebabs leads to a quicker crystallization rate and a smaller average spherulite size. It is also shown that nucleation density of shish-kebabs has a stronger impact on crystallization rate. Growth rate of spherulites and length growth rate of shish-kebabs also have significant effect on crystallization rate and morphology. An increase in growth rate of spherulites or length growth rate of shish-kebabs also speeds up the crystallization rate; additionally, a decrease in growth rate of spherulites or an increase in length growth rate of shish-kebabs results in a more highly anisotropic shish-kebab structure and a smaller average size of spherulites. Results also show that the effect of growth rate of spherulites is more important than the effect of length growth rate of shish-kebabs on crystallization.


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