Bifurcation and Turing Pattern Formation in a Diffusion Modified Leslie-Gower Predator-Prey Model with Crowley-Martin Functional Response

In this paper, we study a modified Leslie-Gower predator-prey model with Smith growth subject to homogeneous Neumann boundary condition, in which the functional response is the Crowley-Martin functional response term. Firstly, for ODE model, the local stability of equilibrium point is given. And by using bifurcation theory and selecting suitable bifurcation parameters, we find many kinds of bifurcation phenomena, including Transcritical bifurcation and Hopf bifurcation. For the reaction-diffusion model, we find that Turing instability occurs. Besides, it is proved that Hopf bifurcation exists in the model. Finally, numerical simulations are presented to verify and illustrate the theoretical results.

A Modified Model for Calculating Theoretical Flame Temperature in Blast Furnace and Its Application

The theoretical flame temperature （TFT） before tuyere, always highly concerned by blast furnace （BF） operators, is one of the most important parameters for evaluating the thermal state of hearth. However, some influ- encing parameters, for example, the SiO2 reduction by carbon, were always neglected or inaccurate when calculating the TFT. According to the definition of TFT, the temperature of coke into raceway and the reduction rate of SiO2 in ash of coke and pulverized coal were obtained by analyzing the samples before tuyere in blast furnace. Taking full ac- count of different factors, a modified model for calculating the TFT in blast furnace was established. The effects of the oxygen enrichment rate, the reduction rate of SiO2 in raceway, the ash content in coke and pulverized coal and the pulverized coal injection （PCI） rate on TFT were determined quantitatively. The modified model was applied to selecting the used coal for PCI in blast furnace. Considering the different SiO2 contents of mixed coal, the calculated TFT remained a stable level. This showed that the selected coal could be suitable for PCI in blast furnace.

Multivariable Fuzzy Predictive Control Based on the Modified CPN Model

Through modifying the CPN model, a kind of multivariable fuzzy model is put forward, and the matching fuzzy multistep predictive control algorithm is deduced based on the model. The modified model works in a competitive output manner which results in its local representation property. While studying on line, only a few parameters need to be regulated. So the model has the merits of fast learning and on line self organizing modeling. The control algorithm is simple, adaptive and useful in multivariable and time delay systems. Applying the algorithm in a paper making system, simulation shows its good effect.

Numerical simulation of residual stress field in green power metallurgy compacts by modified Drucker-Prager Cap model

Compaction process simulation and residual stress prediction of green PM compact were carried out with elasto-plastic 3D FEA based on the modified Drueker-Prager Cap model in Abaqus. The model parameters of the investigated powder Distaloy AE were determined as functions of relative density through typical mechanical property tests of powder. The model was implemented as a user subroutine USDFLD. Single sided compaction of a d20 ram^5 mm disk green compact of Distaloy AE was simulated, and the residual stress of the disk after ejection was predicted with FEA. The FEA results of the compaction process and the residual stress of the disk show good agreement with compaction experiments and X-ray diffraction measurements, which validates the model and its parameters. The results indicate that the compressive residual stresses exist mainly in a thin layer on the side surface, but the residual stresses are very small on the top and bottom surfaces.

Study of Rheological Characterization of Fenugreek Gum with Modified Maxwell Model

Taking into account the viscoelasticity of the fenugreek gum, a modified Maxwell model in terms of fractional derivatives is developed. Using this model, it is observed that the fenugreek gums with at least two different concentrations obey the Cox-Merz rule.

A modified constitutive model and hot compression instability behavior of Cu-Ag alloy

The hot compressive deformation behaviors of Cu-6wt.%Ag alloy were studied experimentally in the temperature range of 973.1123 K and the strain rate range of 0.01.10 s^-1.The stress increases and reaches the maximum value when the true strain is very small,and then the stress changes slowly and tends to be stable under the action of work hardening,dynamic recovery and recrystallization.The material parameters of the conventional Arrhenius constitutive model are only related to strain under different deformation conditions,and the prediction error is large,which cannot accurately characterize the hot deformation behavior of the alloy.To describe the hot deformation behavior of the alloy accurately,a modified constitutive model was established by considering the simultaneous influence of forming temperature,strain rate and strain.The results indicate that correlation coefficient(R)and the average absolute relative error(AARE)are 0.993 and 4.2%,respectively.The modified constitutive model can accurately describe the hot deformation behavior of Cu-6wt.%Ag alloy.

Application of modified k-ω model to predicting cavitating flow in centrifugal pump

Considering the compressibility of the cavity in the cavitating flow, this paper presents a modified k-ω model for predicting the cavitating flow in a centrifugal pump, in which the modified k-ω model and Schnerr-Sauer cavitation model were combined with ANSYS CFX. To evaluate the modified and standard k-co models, numerical simulations were performed with these two models, respectively, and the calculation results were compared with the experimental data. Numerical simulations were executed with three different values of the flow coefficient, and the simulation results of the modified k-ω model showed agreement with most of the experimental data. The cavitating flow in the centrifugal pump obtained by the modified k-ω model at the design flow coefficient of 0.102, was analyzed. When the cavitation number decreases, the cavity initially generates on the suction side of the blade near the leading edge and then expands to the outlet of the impeller, and the decrease of the total pressure coefficient mainly occurs upstream of the impeller passage, while the downstream remains almost unaffected by the development of cavitation.

Numerical simulation of solidification morphologies of Cu-0.6Cr casting alloy using modified cellular automaton model

The purpose of this study is to predict the morphologies in the solidification process for Cu-0.6Cr(mass fraction,%)alloy by vacuum continuous casting(VCC)and verify its accuracy by the observed experimental results.In numerical simulation aspect, finite difference(FD)method and modified cellular automaton(MCA)model were used to simulate the macro-temperature field, micro-concentration field,nucleation and grain growth of Cu-0.6Cr alloy using real data from actual casting operations.From the observed casting experiment,the preliminary grain morphologies are the directional columnar grains by the VCC process.The solidification morphologies by MCAFD model are in agreement with the result of actual casting experiment well.

Relationship between modified homeostasis model assessment/correlative serum factors and diabetic retinopathy among type 2 diabetics with insulin therapy in Guangzhou, China

AIM:To explore the related risk factors for diabetic retinopathy(DR)in type 2 diabetes with insulin therapy.METHODS:We studied the relationships among blood glucose,serum C-peptide,plasma insulin,beta-cell function and the development of DR.Beta-cell function was assessed by a modified homeostasis model assessment(modified HOMA)which was gained by using C-peptide to replace insulin in the homeostasis model assessment(HOMA)of beta-cell function.We also studied the relationships between modified HOMA index and serum C-peptide response to 100 g tasteless steamed bread to determine the accuracy of modified HOMA.RESULTS:Our study group consisted of 170 type 2diabetic inpatients with DR(age:58.35±13.87y,mean±SD)and 205 type 2 diabetic inpatients with no DR(NDR)(age:65.52±11.59y).DR patients had higher age,longer diabetic duration,higher hypertension grade,higher postprandial plasma glucose,higher fluctuation level of plasma glucose,lower body mass index(BMI),lower postprandial serum insulin and C-peptide,lower fluctuation level of serum insulin and C-peptide(P【0.05).In our logistic regression model,duration of diabetes,hypertension grade,fasting plasma insulin and glycosylated hemoglobin(HbA1C)were significantly associated with the presence of DR after adjustment for confounding factors(P【0.05).CONCLUSION:Our results suggested although modified HOMA showed significant correlation to the occurrence of DR on Spearman’s rank-correlationanalysis,logistic regression showed no significant association between these two variables after adjustment for relevant confounding factors(such as age,sex,duration of diabetes,BMI,hypertension grade,HbA1C,plasma insulin).Duration of diabetes,hypertension grade,fasting plasma insulin and HbA1C were independently associated with the development of DR in Chinese type 2 diabetics.

A modified discrete element model for sea ice dynamics

Considering the discontinuous characteristics of sea ice on various scales,a modified discrete element model（DEM） for sea ice dynamics is developed based on the granular material rheology.In this modified DEM,a soft sea ice particle element is introduced as a self-adjustive particle size function.Each ice particle can be treated as an assembly of ice floes,with its concentration and thickness changing to variable sizes under the conservation of mass.In this model,the contact forces among ice particles are calculated using a viscous-elastic-plastic model,while the maximum shear forces are described with the Mohr-Coulomb friction law.With this modified DEM,the ice flow dynamics is simulated under the drags of wind and current in a channel of various widths.The thicknesses,concentrations and velocities of ice particles are obtained,and then reasonable dynamic process is analyzed.The sea ice dynamic process is also simulated in a vortex wind field.Taking the influence of thermodynamics into account,this modified DEM will be improved in the future work.

Coupled hydro-mechanical analysis of slope under rainfall using modified elasto-plastic model for unsaturated soils

Two modifications for the basic Barcelona model(BBM) are present. One is the replacement of the net stress by the average skeleton stress in unsaturated soil modeling, and the other is the adoption of an expression for the load-collapse(LC) yield surface that can match flexibly the normal compression lines at different suctions. The predictions of the modified BBM for the controlled-suction triaxial test on the unsaturated compacted clay are presented and compared with the experimental results. A good agreement between the predicted and experimental results demonstrates the reasonability of the modified BBM. On this basis, the coupled processes of groundwater flow and soil deformation in a homogeneous soil slope under a long heavy rainfall are simulated with the proposed elasto-plastic model. The numerical results reveal that the failure of a slope under rainfall infiltration is due to both the reduction of soil suction and the significant rise in groundwater table. The evolution of the displacements is greatly related to the change of suction. The maximum collapse deformation happens near the surface of slope where infiltrated rainwater can quickly reach. The results may provide a helpful reference for hazard assessment and control of rainfall-induced landslides.

A Modified Monte Carlo Model of Speckle Tracking of Shear Wave Induced by Acoustic Radiation Force for Acousto-Optic Elasticity Imaging

A modified Monte Carlo model of speckle tracking of shear wave propagation in scattering media is proposed. The established Monte Carlo model mainly concerns the variations of optical electric field and speckle. The two- dimensional intensity distribution and the time evolution of speckles in different probe locations are obtained. The fluctuation of speckle intensity tracks the acoustic-radiation-force shear wave propagation, and especially the reduction of speckle intensity implies attenuation of shear wave. Then, the shear wave velocity is estimated quantitatively on the basis of the time-to-peak algorithm and linear regression processing. The results reveal that a smaller sampling interval yields higher estimation precision and the shear wave velocity is estimated more efficiently by using speckle intensity difference than by using speckle contrast difference according to the estimation error. Hence, the shear wave velocity is estimated to be 2.25 m/s with relatively high accuracy for the estimation error reaches the minimum （0.071）.

Vacancies and Antisites in B2 FeAl and DO_3 Fe_3Al with a Modified Analytic EAM Model

A simple modified analytic EAM model for bcc Fe and fcc Al was used to calculate the lattice constant and elastic constants of B2 FeAl and DO3 Fe3Al alloys. The formation energies of vacancy and antisite were also calculated. The present calculations are in agreement with the experimental data and the theoretical results obtained by other authors.

A Modified Logvinovich Model For Hydrodynamic Loads on an Asymmetric Wedge Entering Water with a Roll Motion

The water entry problem of an asymmetric wedge with roll motion was analyzed by the method of a modified Logvinovich model (MLM). The MLM is a kind of analytical model based on the Wagner method, which linearizes the free surface condition and body boundary condition. The difference is that the MLM applies a nonlinear Bernoulli equation to obtain pressure distribution, which has been proven to be helpful to enhance the accuracy of hydrodynamic loads. The Wagner condition in this paper was generalized to solve the problem of the water entry of a wedge body with rotational velocity. The comparison of wet width between the MLM and a fully nonlinear numerical approach was given, and they agree well with each other. The effect of angular velocity on the hydrodynamic loads of a wedge body was investigated.

The modified temperature term on Johnson-Cook constitutive model of AZ31 magnesium alloy with {0002} texture

The dynamic compression experiments with Split-Hopkinson Pressure Bar(SHPB)were performed on AZ31 magnesium alloy rolled sheet specimens in the normal direction(AZ31-ND)with{0002}texture at the temperature of 293-523 K and the strain rate of 0.001-2200 s^−1.The temperature term in Johnson-Cook(JC)constitutive model had been reasonably modified.This advantage made constitutive model promising for decribing the dynamic deformation behavior of AZ31-ND with{0002}texture more accurately.The obtained true stress-true plastic strain curves agreed well with the measured results in a wide range of strain rates and temperatures.The thermal softeninging,strain and strain rate hardening effect on the AZ31-ND with{0002}texture were discussed.The adiabatic shear band(ASB)of AZ31-ND with{0002}texture hat shaped specimen was successfully predicted by combining modified JC constitutive model and numerical simulation,which was also validated by Electron Back-Scattered Diffraction(EBSD)map under the same boundary condition.

Calculation of Activity Coefficient from Immiscible Binary Alloy Phase Diagram by Means of Modified Sub-regular Solution Model

The modified sub regular solution model was used for a calculation of the activity coefficient of immiscible binary alloy systems. The parameters needed for the calculation are the interaction parameters, λ 1 and λ 2, which are represented as a linear function of temperature, T . The molar excess Gibbs free energy, G m E, can be written in the form G m E= x A x B[( λ 11 + λ 12 T )+( λ 21 + λ 22 T ) x B ] The calculation is carried out numerically for three immiscible binary alloy systems, Al Pb, Cu Tl and In V. The agreement between the calculated and experimentally determined values of activity coefficient is excellent.

Simulation based on a modified social force model for sensitivity to emergency signs in subway station

The subway is the primary travel tool for urban residents in China. Due to the complex structure of the subway and high personnel density in rush hours, subway evacuation capacity is critical. The subway evacuation model is explored in this work by combining the improved social force model with the view radius using the Vicsek model. The pedestrians are divided into two categories based on different force models. The first category is sensitive pedestrians who have normal responses to emergency signs. The second category is insensitive pedestrians. By simulating different proportions of the insensitive pedestrians, we find that the escape time is directly proportional to the number of insensitive pedestrians and inversely proportional to the view radius. However, when the view radius is large enough, the escape time does not change significantly, and the evacuation of people in a small view radius environment tends to be integrated. With the improvement of view radius conditions, the escape time changes more obviously with the proportion of insensitive pedestrians. A new emergency sign layout is proposed, and the simulations show that the proposed layout can effectively reduce the escape time in a small view radius environment. However, the evacuation effect of the new escape sign layout on the large view radius environment is not apparent. In this case, the exit setting emerges as an additional factor affecting the escape time.

Suppression of Spiral Wave in Modified Orengonator Model

In this paper, a spatial perturbation scheme is proposed to suppress the spiral wave in the modified Orengonator model, which is used to describe the chemical reaction in the light-sensitive media. The controllable external illumination Ф is perturbed with a spatial linear function. In our numerical simulation, the scheme is investigated by imposing the external controllable illumination on the space continuously and/or intermittently. The numerical simulation results confirm that the stable rotating spiral wave still can be removed with the scheme proposed in this paper even if the controllable Ф changed vs. time and space synchronously. Then the scheme is also used to control the spiral wave and turbulence in the modified Fitzhugh-Nagumo model. It is found that the scheme is effective to remove the sable rotating and meandering spiral wave but it costs long transient period and intensity of the gradient parameter to eliminate the soiral turbulence.

Modified magnetomechancial model in the constant and low intensity magnetic field based on J-A theory

The existing magnetomechancial models cannot explain the different experimental phenomena when the ferromagnetic specimen is respectively subjected to tension and compression stress in the constant and low intensity magnetic field,especially in the compression case. To promote the development of magnetomechancial theory, the energy conservation equation, effective magnetic field equation, and anhysteretic magnetization equation of the original Jiles-Atherton（J-A）theory are elucidated and modified, an equation of the local equilibrium status is employed and the differential expression of the modified magnetomechancial model based on the modified J-A theory is established finally. The effect of stress and plastic deformation on the magnetic parameters is analyzed. An excellent agreement is achieved between the theoretic predictions by the present modified model and the previous experimental results. Comparing with the calculation results given by the existing models and experimental results, it is seen indeed that the modified magnetomechanical model can describe the different magnetization features during tension-release and compression-release processes much better, and is the only one which can accurately reflect the experimental observation that the magnetic induction intensity reverses to negative value with the increase of the compressive stress and applied field.

Modified Observation Model in Tightly-Coupled INS/GPS Integration

The conventional Kalman filter（CKF）is widely used in tightly-coupled INS/GPS integrated navigation systems.The linearization accuracy of the CKF observation model is one of the decisive factors of the estimation accuracy and therefore navigation accuracy.Additionally,the conventional observation model（COM）used by the filter may be divergent,which would result into some terrible accuracies of INS/GPS integration navigation in some cases.To improve the navigation accuracy,the linearization accuracy of the COM still needs further improvement.To deal with this issue,the observation model is modified with the linearization of the range and range rate equations in this paper.Compared with COM,the modified observation model（MOM）further considers the difference between the real user position and the position calculated by SINS.To verify the advantages of this model,INS/GPS integrated navigation simulation experiments are conducted with the usage of COM and MOM respectively.According to the simulation results,the positions（velocities）calculated using COM are divergent over time while the others using MOM are convergent,which demonstrates the higher linearization accuracy of MOM.