Rheological properties of large particulate-liquid model food systems were studied by using the BMS （ball measuring system）. The model food systems were composed of alginate gel particles （-10mm） and a gelatinised...Rheological properties of large particulate-liquid model food systems were studied by using the BMS （ball measuring system）. The model food systems were composed of alginate gel particles （-10mm） and a gelatinised starch solution with 1% w/w sodium chloride as a liquid phase. The effects of particle phase volume （Ф, 0-0.60）, particle shapes （cube, sphere, rod and disc） and starch concentrations （3% and 5% w/w starch） were investigated. The power law model was successfully applied to characterize the flow properties of each system and the consistency K and power law index n were obtained. The K increased and n decreased with increasing # for samples at all particle shapes at 3% w/w starch in the liquid phase. The particle effect on the viscosity is further analysed by means of the Krieger-Dougherty model and the maximum packing fraction #,, and the intrinsic viscosity [η] were obtained in each system. The Фm, depended on the particle shape, as expected. The [7] value depended on particle shape and was largely in the order of 4.04 （cube）, 3.28 （disc）, 2.56 （sphere） and 2.32 （rod） at 3% w/w starch. The [η] also depended on starch concentration and was 1.1 at 5%,6 w/w starch in the liquid phase with spherical particles. The present results show successful application of BMS to study the rheological properties of large particulate liquid food systems at relatively small scale experiment （-0.5 L） and also that existing models for suspension rheology are applicable for such food systems to a great extend.展开更多
In this paper,a deterministic and stochastic fractional-order model of the tri-trophic food chain model incorporating harvesting is proposed and analysed.The interaction between prey,middle predator and top predator p...In this paper,a deterministic and stochastic fractional-order model of the tri-trophic food chain model incorporating harvesting is proposed and analysed.The interaction between prey,middle predator and top predator population is investigated.In order to clarify the characteristics of the proposed model,the analysis of existence,uniqueness,non-negativity and boundedness of the solutions of the proposed model are examined.Some sufficient conditions that ensure the local and global stability of equilibrium points are obtained.By using stability analysis of the fractional-order system,it is proved that if the basic reproduction number R_(0)<1,the predator free equilibrium point E_(1) is globally asymptotically stable.The occurrence of local bifurcation near the equilibrium points is investigated with the help of Sotomayor’s theorem.Some numerical examples are given to illustrate the theoretical findings.The impact of harvesting on prey and themiddle predator is studied.We conclude that harvesting parameters can control the dynamics of the middle predator.A numerical approximation method is developed for the proposed stochastic fractional-order model.展开更多
In this paper a dynamic food chain model for Hong Kong which simulates the transfer of radioactive substances from a fallout deposition via the food chain into the human bodies is built. The model is based on the RADF...In this paper a dynamic food chain model for Hong Kong which simulates the transfer of radioactive substances from a fallout deposition via the food chain into the human bodies is built. The model is based on the RADFOOD model and the BirchallJames algorithm. The radionuclides 13if and 90Sr representing the short-term and long-term risk situations have been studied as sample cases. Various types of crops,and the dietary pattern of the public have been collsidered. The resulting internal radiation doses have been calculated. The results are obtained for food consumption starting at various time after the fallout deposition and for different consumption durations.展开更多
In this paper,we have analyzed a tri-trophic food chain model consisting of phytoplankton,zooplankton and fish population in an aquatic environment.Here,the pelagic water column is divided into two layers namely,the u...In this paper,we have analyzed a tri-trophic food chain model consisting of phytoplankton,zooplankton and fish population in an aquatic environment.Here,the pelagic water column is divided into two layers namely,the upper layer and the lower layer.The zooplankton population makes a diel vertical migration(DVM)from lower portion to upper portion and vice-versa to trade-off between food source and fear from predator(Fish).Here,mathematical model has been developed and analyzed in a rigorous way.Apart from routine calculations like boundedness and positivity of the solution,local stability of the equilibrium points,we performed Hopf bifurcation analysis of the interior equilibrium point of our model system in a systematic way.It is observed that the migratory behavior of zooplankton plays a crucial role in the dynamics of the model system.Both the upward and downward migration rates of DVM leads the system into Hopf bifurcation.The upward migration rate of zooplankton deteriorates the stable coexistence of all the species in the system,whereas the downward migration rate enhance the stability of the system.FYirther,we analyze the non-autonomous version of the system to capture seasonal effect of environmental variations.We have shown that under certain parametric restrictions periodic coexistence of all the species of our system is possible.Finally,extensive numerical simulation has been performed to support our analytical findings.展开更多
文摘Rheological properties of large particulate-liquid model food systems were studied by using the BMS （ball measuring system）. The model food systems were composed of alginate gel particles （-10mm） and a gelatinised starch solution with 1% w/w sodium chloride as a liquid phase. The effects of particle phase volume （Ф, 0-0.60）, particle shapes （cube, sphere, rod and disc） and starch concentrations （3% and 5% w/w starch） were investigated. The power law model was successfully applied to characterize the flow properties of each system and the consistency K and power law index n were obtained. The K increased and n decreased with increasing # for samples at all particle shapes at 3% w/w starch in the liquid phase. The particle effect on the viscosity is further analysed by means of the Krieger-Dougherty model and the maximum packing fraction #,, and the intrinsic viscosity [η] were obtained in each system. The Фm, depended on the particle shape, as expected. The [7] value depended on particle shape and was largely in the order of 4.04 （cube）, 3.28 （disc）, 2.56 （sphere） and 2.32 （rod） at 3% w/w starch. The [η] also depended on starch concentration and was 1.1 at 5%,6 w/w starch in the liquid phase with spherical particles. The present results show successful application of BMS to study the rheological properties of large particulate liquid food systems at relatively small scale experiment （-0.5 L） and also that existing models for suspension rheology are applicable for such food systems to a great extend.
基金The authors gratefully acknowledge Qassim University,represented by the Deanship of Scientific Research,on the financial support under the number(cosao-bs-2019-2-2-I-5469)during the academic year 1440 AH/2019 AD.
文摘In this paper,a deterministic and stochastic fractional-order model of the tri-trophic food chain model incorporating harvesting is proposed and analysed.The interaction between prey,middle predator and top predator population is investigated.In order to clarify the characteristics of the proposed model,the analysis of existence,uniqueness,non-negativity and boundedness of the solutions of the proposed model are examined.Some sufficient conditions that ensure the local and global stability of equilibrium points are obtained.By using stability analysis of the fractional-order system,it is proved that if the basic reproduction number R_(0)<1,the predator free equilibrium point E_(1) is globally asymptotically stable.The occurrence of local bifurcation near the equilibrium points is investigated with the help of Sotomayor’s theorem.Some numerical examples are given to illustrate the theoretical findings.The impact of harvesting on prey and themiddle predator is studied.We conclude that harvesting parameters can control the dynamics of the middle predator.A numerical approximation method is developed for the proposed stochastic fractional-order model.
文摘In this paper a dynamic food chain model for Hong Kong which simulates the transfer of radioactive substances from a fallout deposition via the food chain into the human bodies is built. The model is based on the RADFOOD model and the BirchallJames algorithm. The radionuclides 13if and 90Sr representing the short-term and long-term risk situations have been studied as sample cases. Various types of crops,and the dietary pattern of the public have been collsidered. The resulting internal radiation doses have been calculated. The results are obtained for food consumption starting at various time after the fallout deposition and for different consumption durations.
基金Department of Science and Technology(No.DST/Inspire Fellowship/2015/IF150653),Govt,of India.
文摘In this paper,we have analyzed a tri-trophic food chain model consisting of phytoplankton,zooplankton and fish population in an aquatic environment.Here,the pelagic water column is divided into two layers namely,the upper layer and the lower layer.The zooplankton population makes a diel vertical migration(DVM)from lower portion to upper portion and vice-versa to trade-off between food source and fear from predator(Fish).Here,mathematical model has been developed and analyzed in a rigorous way.Apart from routine calculations like boundedness and positivity of the solution,local stability of the equilibrium points,we performed Hopf bifurcation analysis of the interior equilibrium point of our model system in a systematic way.It is observed that the migratory behavior of zooplankton plays a crucial role in the dynamics of the model system.Both the upward and downward migration rates of DVM leads the system into Hopf bifurcation.The upward migration rate of zooplankton deteriorates the stable coexistence of all the species in the system,whereas the downward migration rate enhance the stability of the system.FYirther,we analyze the non-autonomous version of the system to capture seasonal effect of environmental variations.We have shown that under certain parametric restrictions periodic coexistence of all the species of our system is possible.Finally,extensive numerical simulation has been performed to support our analytical findings.
