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.

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.

Morphology prediction of dihydroxylammonium 5,5'-bistetrazole-1,1'-diolate (TKX-50) crystal in different solvent systems using modified attachment energy model

In order to theoretically study the growth morphology of dihydroxylammonium 5,5’-bistetrazole-1,1’-dio late(TKX-50)crystal in different solvent systems,crystal–solvent models were established,and then molecular dynamics(MD)methods were adopted as a means to simulate particle motion.Modified attachment energy(MAE)model was employed to calculate the growth morphology of TKX-50.The simulation results demonstrate that COMPASS force field and RESP charge are suitable for molecular dynamics simulation of TKX-50.The morphologically dominant growth surfaces of TKX-50 in vacuum are(020),(011),(11–1),(100)and(120),respectively.In water(H_(2)O)and N,N-dimethylformamide(DMF)solvents,the(11–1)face is the largest in the habit face,the growth rate of(020)face becomes faster.With the increase of temperature,the aspect ratios of TKX-50 crystal in DMF solvent increase,and the areas of the(120)faces decrease.In ethylene glycol/H_(2)O mixed solvent system with volume ratio of 1/1,aspect ratio of TKX-50 is relatively small.In formic acid/H_(2)O mixed solvents with different volume ratios(1/4,1/3,1/2,1/1 and 2/1),aspect ratio of TKX-50 is relatively small when volume ratio is 1/2.

Evaluating Model Effectiveness for Soil Infiltration Attribute: Comparison of Green-Ampt, Horton and Modified Green-Ampt Infiltration Models

Soil infiltration is a very important concept in hydrology as well as irrigation, which plays a vital role in estimating surface runoff and groundwater recharge. It is a complicated process that varies with numerous factors. Accurate estimation of soil infiltration is required for future irrigation, and many other purposes. To estimate the infiltration process, there are numerous models. The majority of them have some presumptions, a unique calculation method, and some limitations. The purpose of the paper was to assess the model’s performance for a similar hypothetical scenario involving soil infiltration. It compared the infiltration rate, runoff rate, and incremental infiltration versus time for three different infiltration models: the Green-Ampt model (GA), the Horton model and the Modified Green-Ampt (MGA) model. A spreadsheet was used to calculate the Horton model, and HYDROL-INF (V 5.03) was used to simulate the other two models. Among those three models, the MGA model outperformed those three models, while the GA model produced greater infiltration rate than rainfall, which was insensible. The study showed that the MGA model, which provides useful infiltration predictions, outperformed the other two infiltration models. Since the Horton model does not consider ponding conditions, it is only applicable when the effective rainfall intensity exceeds the final infiltration capacity. Moreover, the GA model’s initial infiltration rate is irrational because it disregards the intensity of the rainfall. The results of this study will assist in selecting the most accurate method for estimating soil infiltration for agricultural purposes.

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.

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.

A modified Johnson–Cook model for 7N01 aluminum alloy under dynamic condition

Tensile tests at different strain rates(0.0002, 0.002, 0.02, 1000 and 3000 s^(-1)) were carried out for 7N01 aluminum alloy. Low strain rate experiments(0.0002, 0.002 and 0.02 s^(-1)) were conducted using an electronic mechanical universal testing machine, while high strain rate experiments(1000, 3000 s^(-1)) were carried out through a split Hopkinson tensile bar. The experimental results showed that 7N01 aluminum alloy is strain rate sensitive. By introducing a correction scheme of the strain rate hardening coefficient, a modified Johnson–Cook model was proposed to describe the flow behaviors of 7N01 aluminum alloy. The proposed model fitted the experimental data better than the original Johnson–Cook model in plastic flow under dynamic condition. Numerical simulations of the dynamic tensile tests were performed using ABAQUS with the modified Johnson–Cook model. Digital image correlation was used together with high-speed photography to study the mechanical characters of specimen at high strain rate. Good correlations between the experiments results, numerical predictions and DIC results are achieved. High accuracy of the modified Johnson-Cook model was validated.

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.

A modified multi-group model of angular and momentum distribution of cosmic ray muons for thickness measurement and material discrimination of slabs

Muon tomography is a capable imaging technique to measure the geometry of high-Z objects. However,most existed algorithms used in muon tomography have obscured the effects of angular distribution and momentum spectra of cosmic ray muons and reduced the spatial resolution. We present a modified multi-group model that takes into account these effects and calibrates the model by the material of lead. Performance tests establish that the model is capable of measuring the thickness of a Pb slab and identifying the material of an unknown slab on a reasonable exposure timescale, in both cases of complete and incomplete angular data. Results show that the modified multi-group model is helpful for improvements in image resolution in real applications.

Triaxial strength behaviour of rockmass satisfying Modified Mohr-Coulomb and Generalized Hoek-Brown criteria

The triaxial strength of twenty rockmass types was predicted using two non-linear triaxial strength criteria for rockmass i.e. Modified Mohr-Coulomb(MMC) criterion and Generalized Hoek-Brown(GHB)criterion. Four different rockmass classification systems were used for the calculation of MMC criterion parameters while only GSI classification system has been used for calculation of GHB parameters. The representative value of the uniaxial compressive strength and elastic modulus of rockmass have been estimated using probabilistic approach. A hypothetical case of an unsupported tunnel has been analyzed considering both MMC and GHB criteria. The analysis was done using the convergence-confinement method with two different approaches. The first approach predicts the tunnel response using GHB criterion directly. The second approach predicts the tunnel response using equivalent Mohr-Coulomb parameters obtained by linearization of triaxial data points obtained from MMC and GHB criteria. The tunnel response has been estimated in terms of radius of plastic zone, tunnel convergence and tunnel convergence strain. For very poor rockmasses the tunnel response predicted by MMC criterion is less than that predicted by GHB criterion. For poor and fair rockmass, the tunnel response estimated considering both the criteria are comparable except for few cases. Squeezing condition in rockmass has been also evaluated.

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.

An approximate nonlinear modified Mohr-Coulomb shear strength criterion with critical state for intact rocks

In this paper, the Mohr-Coulomb shear strength criterion is modified by mobilising the cohesion and internal friction angle with normal stress, in order to capture the nonlinearity and critical state concept for intact rocks reported in the literature. The mathematical expression for the strength is the same as the classical form, but the terms of cohesion and internal friction angle depend on the normal stress now,leading to a nonlinear relationship between the strength and normal stress. It covers both the tension and compression regions with different expressions for cohesion and internal friction angle. The strengths from the two regions join continuously at the transition of zero normal stress. The part in the compression region approximately satisfies the conditions of critical state, where the maximum shear strength is reached. Due to the nonlinearity, the classical simple relationship between the parameters of cohesion, internal friction angle and uniaxial compressive strength from the linear Mohr-Coulomb criterion does not hold anymore. The equation for determining one of the three parameters in terms of the other two is supplied. This equation is nonlinear and thus a nonlinear equation solver is needed. For simplicity, the classical linear relationship is used as a local approximation. The approximate modified Mohr-Coulomb criterion has been implemented in a fracture mechanics based numerical code FRACOD,and an example case of deep tunnel failure is presented to demonstrate the difference between the original and modified Mohr-Coulomb criteria. It is shown that the nonlinear modified Mohr-Coulomb criterion predicts somewhat deeper and more intensive fracturing regions in the surrounding rock mass than the original linear Mohr-Coulomb criterion. A more comprehensive piecewise nonlinear shear strength criterion is also included in Appendix B for those readers who are interested. It covers the tensile, compressive, brittle-ductile behaviour transition and the critical state, and gives smooth transitions.

Numerical Investigation of Penetration in Ceramic/Aluminum Targets Using Smoothed Particle Hydrodynamics Method and Presenting a Modified Analytical Model

Radius of ceramic cone can largely contribute into final solution of analytic models of penetration into ceramic/metal targets.In the present research,a modified model based on radius of ceramic cone was presented for ceramic/aluminum targets.In order to investigate and evaluate accuracy of the presented analytic model,obtained results were compared against the results of the Florence’s analytic model and also against numerical modeling results.The phenomenon of impact onto ceramic/aluminum composites were modeled using smoothed particle hydrodynamics(SPH)implemented utilizing ABAQUS Software.Results indicated that,with increasing initial velocity and ceramic thickness and decreasing support layer thickness,the radius of ceramic cone decreases;this ends up increasing residual velocity of the projectile and penetration time and extending the area across which the pressure is distributed.These findings indicate enhanced levels of target energy absorption and the required energy for bending and tensioning the target.As such,it can be observed that,at the same thickness and areal density,the ceramic target has its efficiency enhanced with increasing ceramic thickness and decreasing the support layer thickness.Finally,the results revealed that the associated data with SPH confirm the modified analytic model at higher accuracy than the Florence’s analytic model.

Restoring-force model of modified RAC columns with silica fume and hybrid fiber

In order to establish a restoring-force model for modified concrete columns with recycled aggregates concrete(RAC), cyclic loading tests were carried out on five concretes with RAC columns and ordinary concrete frame columns under the combined influence with different admixtures and admixtures ratios(silica fume and hybrid fiber). The expressions for characteristic nodes of the skeleton curve were given by the analysis and numerical regression of the test results. In addition, the hysteretic rules of the restoring-force model and the expression for unloading stiffness were presented. Finally, we summed up the complete calculation method of the hysteretic restoring force, whose results were in good agreement with experiment. The results demonstrated that the proposed model could simulate and reflect the corresponding hysteretic behaviors, and the calculation method can provide the theoretical basis for the engineering application.

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.

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.

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.

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.