A Cusp Catastrophe Model for Adolescent Alcohol Use: An Empirical Test

The current study was designed to assess the usefulness of a cusp catastrophe model in predicting adolescent alcohol use. The model suggests that dispositions should be viewed as a normal parameter in a cusp catastrophe model and situational pressure serves as a splitting parameter. This conceptualization predicts that as situational pressure increases a bimodal distribution in the underlying behavior should result. Statistical analyses revealed that the cusp model was a better predictor of alcohol use than the alternative linear models. These findings suggest that the modeling of situational pressure variables should be reexamined from within this new framework.     

Is research publication a catastrophic phenomenon among medical faculty?

Studies seeking to predict publication rates among faculty have found contradictory results. The purpose of this study was to determine whether short- or long-term research publications among family medicine faculty were better accounted for using cusp catastrophe modeling (CCM) rather than linear modeling. This secondary analysis of annual research publications used data collected from family medicine faculty in a university department. To predict the number of research publications, two service variables -- national service and administrative responsibility -- were used. There were three bifurcation variables: Scholarly Activity, Professional Status, and 'proportion of studies asprincipal investigator'. Research publications at two and five years were modeled using CCM as well as two linear models. Based upon the amount of variance explained, while linear models accounted for more variance in publications at -year intervals, CCM was superior at explaining publications for all three bifurcation variables at -year intervals. Entering all of the bifurcation variables into the models found that CCM explained more of the -year publication variance with Scholarly Activity and national service as significant predictors. In conclusion, short-term career planning needs to consider its irregular cusp behavior and to minimize the possible impact of bifurcation factors.     

基于突变理论的液化评估方法

作为众多突变类型的一种形式,尖点突变模型由于其优良的性质而广泛应用于生物学和社会科学,近年来又有越来越多的学者用尖点突变模型来研究工程实际问题。本文基于地震液化的基本机理和突变理论的特点,以土体的抗液化能力和土体得到的地震能量为控制变量,以孔隙水压力发展为状态变量,建立了地震诱导的孔隙水压力发展模型。宏观震害调查结果和本文的计算结果对比表明,本文建议的方法方便、可靠,是一种理想的液化评估方法。     

Instability leading to coal bumps and nonlinear evolutionary mechanisms for a coal-pillar-and-roof system

This paper studies the unstable mechanisms of the mechanical system that is composed of the stiff hosts (roof and floor) and the coal pillar using catastrophe theory. It is assumed that the roof is an elastic beam and the coal pillar is a strain-softening medium which can be described by the Weibull’s distribution theory of strength. It is found that the instability leading to coal bump depends mainly on the system’s stiffness ratio k, which is defined as the ratio of the flexural stiffness of the beam to the absolute value of the stiffness at the turning point of the constitutive curve of the coal pillar, and the homogeneity index m or shape parameter of the Weibull’s distribution for the coal pillar. The applicability of the cusp catastrophe is demonstrated by applying the equations to the Mentougou coal mine. A nonlinear dynamical model, which is derived by considering the time-dependent property of the coal pillar, is used to study the physical prediction of coal bumps. An algorithm of inversion for determining the parameters of the nonlinear dynamical model is suggested for seeking the precursory abnormality from the observed series of roof settlement. A case study of the Muchengjian coal mine is conducted and its nonlinear dynamical model is established from the observation series using the algorithm of inversion. An important finding is that the catastrophic characteristic index D (i.e., the bifurcation set of the cusp catastrophe model) drastically increases to a high peak value and then quickly drops close to instability. From the viewpoint of damage mechanics of coal pillar, a dynamical model of acoustic emission (AE) is established for modeling the AE activities in the evolutionary process of the system. It is revealed that the values of m and the evolutionary path (D = 0 or D ≠ 0) of the system have a great impact on the AE activity patterns and characters.     

Catastrophe fracture of thin-wall pressure tubes

Catastrophe theory was used to investigate the fracture behavior of thin-wall cylindrical tubes subjected to internal explosive pressure. Based on the energy theory and catastrophe theory, a cusp catastrophe model for the fracture was established, and a critical condition associated with the model is given. Contributed by YANG Gui-tong Biographies: WEI De-min (1955-); YANG Gui-tong (1931-)     

A predictive model for pressure fluctuations on sloping channels using support vector machine

In this study, support vector machine (SVM) is proposed as a new predictive model for pressure fluctuations beneath free jump occurring on sloping channels. The proposed model reproduces the pressure fluctuation intensity C′_p in terms of normalized flow and channel section characteristics. The model variables were derived from dimensional analysis. The proposed model is calibrated and validated by using a wide range of experimental data. The SVM predicted C′_p with a correlation of coefficient (CC) of 0.989 and a root mean square error (RMSE) of 0.004. Also, linear and nonlinear regression analyses are applied on the same experimental data set, and the SVM model is compared to the equations obtained from these regression analyses. CC, RMSE and average absolute deviation (D_i) are used in the evaluation of performance of each model. The SVM model predicted the measured pressure fluctuations better than conventional regression equations. The results of this study reveal that the proposed SVM model can be effectively used in predicting the pressure fluctuation beneath free jump. Copyright © 2010 John Wiley & Sons, Ltd.     

A cusp catastrophe model analysis of changes in adolescent substance use: assessment of behavioural intention as a bifurcation variable

Behavioural intention was advanced as an alternative bifurcation variable to peer pressure in the context of a cusp catastrophe model of changes in adolescent substance use (Clair, 1998; Byrne, Mazanov & Gregson, 2001). Three sets of models were tested using data from a 12 month longitudinal study of adolescent smoking in Australia: the first with peer pressure only as the bifurcation term, the second with behavioural intention only and the third with both. In isolation both bifurcation variables performed similarly (adjusted-R2 and beta). In the third model, peer pressure edged out behavioural intention as an indicator of catastrophic change. Post hoc analysis revealed the polynomial and simple terms of initial conditions were more important than the bifurcation variable to explain change in smoking behaviour. This provoked a call for more work on finding an appropriately complex (non-straight line), theoretically justifiable mathematical model of adolescent substance use. Overall, behavioural intention was considered equivalent to peer pressure as a bifurcation variable although further research is needed to confirm this result.     

The nonlinear dynamical hypothesis in science education problem solving: a catastrophe theory approach

The current study tests the nonlinear dynamical hypothesis in science education problem solving by applying catastrophe theory. Within the neo-Piagetian framework a cusp catastrophe model is proposed, which accounts for discontinuities in students' performance as a function of two controls: the functional M-capacity as asymmetry and the degree of field dependence/independence as bifurcation. The two controls have functional relation with two opponent processes, the processing of relevant information and the inhibitory process of dis-embedding irrelevant information respectively. Data from achievement scores of freshmen at a technological college were measured at two points in time, and were analyzed using dynamic difference equations and statistical regression techniques. The cusp catastrophe model proved superior (R(2)=0.77) comparing to the pre-post linear counterpart (R(2)=0.46). Besides the empirical evidence, theoretical analyses are provided, which attempt to build bridges between NDS-theory concepts and science education problem solving and to neo-Piagetian theories as well. This study sets a framework for the application of catastrophe theory in education.     

Global stability for infinite-delay,dispersive Lotka-Volterra systems: Weakly interacting populations in nearly identical patches

A Lotka-Volterra-like model ofm interacting species which can disperse amongn discrete habitats and where species interaction terms involve general unbounded delays is shown to possess a globally stable equilibrium when the undelayed intraspecific competition term dominates interspecific interactions as well as the delayed intraspecific competition effect and when then habitats are nearly identical.     

ON THE CRITICAL POINTS OF THE MAP Fp:X→‖AXB-C‖pp

Suppose A,B and C are the bounded linear operators on a Hilbert space H, when A has a generalized inverse A^- such that (AA^-)^*=AA^- and B has a generalized inverse B^- such that (B^-B)^*=B^-B,the general characteristic forms for the critical points of the map F_p:X^→‖AXB-C‖_p^p(1p=2. Similarly, the same question has been discussed for several operators.     

Long-range prediction of epileptic seizures with nonlinear dynamics

Patients with uncontrolled epilepsy have some significant problems with planning life routines, and thus one goal of the present study was to explore the viability of predicting seizures in time intervals of one week. The second goal was to utilize the principle of dynamic diseases and to assess the viability of a cusp catastrophe model for seizure onset that was proposed by Cerf (2006). A seizure history of 124 weeks from one adult male patient fit both the cusp and fold catastrophe models (R2 = .92 and .88 respectively) reasonably well using the pdf method and more accurately than counterpart linear models. Prediction of future states was possible, but somewhat compromised because of the nonstationary nature of the data and uncertainties regarding the control variables in the catastrophe models. Analyses of lag functions, however, revealed some surprising elements, suggesting that the precursory conditions for a seizure could be building up over a period of several weeks and that a self-correcting effect within the nervous system could have been occurring.     

The effect of residual stresses on hardness measurements

The RockwellC hardness,RC, was measured as a function of position on steel rings with different residual-stress profiles through the thickness. An experimental correlation between residual stress andRC was obtained. A relationship between the average pressurep of a spherical indenter, the yield strengthS _y and the residual stress of the material was conceived and used in fitting the experimental data. In order to model the effects of residual stresses on the measured hardness, the von Mises-Hencky (power) yield criterion was utilized, together with an adaptation for residual stresses of the expression for the stress state under a spherical indenter, given in Shaw, Hoshi and Henry. A parameter α was introduced in our calculations to account for the effect of the nonperpendicularity of the residual stresses to the pressurep of the spherical indenter. The proposed model in large measure fits experimental hardness versus residual stress data, and results are consistent with different samples. This model can be used as a basis for the measurement of residual stresses in steel or other materials.     

Pore-scale Network Modeling of Three-Phase Flow Based on Thermodynamically Consistent Threshold Capillary Pressures. II. Results

We use the model described in Zolfaghari and Piri (Transp Porous Media, 2016) to predict two- and three-phase relative permeabilities and residual saturations for different saturation histories. The results are rigorously validated against their experimentally measured counterparts available in the literature. We show the relevance of thermodynamically consistent threshold capillary pressures and presence of oil cusps for significantly improving the predictive capabilities of the model at low oil saturations. We study systems with wetting and spreading oil layers and cusps. Three independent experimental data sets representing different rock samples and fluid systems are investigated in this work. Different disordered networks are used to represent the pore spaces in which different sets of experiments were performed, i.e., Berea, Bentheimer, and reservoir sandstones. All three-phase equilibrium interfacial tensions used for the simulation of three-phase experimental data are measured and used in the model’s validation. We use a fixed set of parameters, i.e., the input network (to represent the pore space) and contact angles (to represent the wettability state), for all experiments belonging to a data set. Incorporation of the MSP method for capillary pressure calculations and cusp analysis significantly improves the agreement between the model’s predictions of relative permeabilities and residual oil saturations with experimental data.     

Cross-cultural generalizability of a cusp catastrophe model for binge drinking among college students

We examined whether a cusp catastrophe model for binge alcohol consumption by college students that was reported earlier (Smerz & Guastello, 2008) could generalize to another culture. Participants were 130 undergraduates enrolled in economics courses at a private urban Japanese university. They completed the same questionnaire items that were used in the previous US study. For some analyses, a stratified random subsample was taken from the earlier US data that was comparable in number, age, and gender proportions (N = 132). Results for the combined sample showed essentially the same results that were obtained from the US sample: Binge drinking can be modeled as a cusp catastrophe with two stable states of behavior - low to moderate consumption and binge level consumption. The two control parameters were peer influence (bifurcation) and attitude toward alcohol use (asymmetry). The nonlinear models (average R2 = .74) accounted for considerably more variance in binge drinking and other alcohol consumption indices than the comparison linear models (average r2 = .18 ). There were some subtle differences between the two samples of students, however.     

Numerical simulation of axisymmetric turbulent flow in combustors and diffusers

Numerical studies of turbulent flow in an axisymmetric 45° expansion combustor and bifurcated diffuser are presented. The Navier-Stokes equations incorporating a k–? model were solved in a non-orthogonal curvillinear co-ordinate system. A zonal grid method, wherein the flow field was divided into several subsections, was developed. This approach permitted different computational schemes to be used in the various zones. In addition, grid generation was made a more simple task. However, treatment of the zonal boundaries required special handling. Boundary overlap and interpolating techniques were used and an adjustment of the flow variables was required to assure conservation of mass flux. Three finite differencing methods—hybrid, quadratic upwind and skew upwind—were used to represent the convection terms. Results were compared with existing experimental data. In general, good agreement between predicted and measured values was obtained.     

Calculation of turbulent combustion of propane in furnaces

An evaluation of some numerical methods for turbulent reacting flows in furnace-like geometries is carried out. The Reynolds averaged Navier–Stokes equations and the two-equation k–? model together with either finite-rate or infinite-rate reaction models are solved numerically. Either single- or multiple-step reactions together with the ‘eddy dissipation concept’ (EDC) are used to model reacting flows with finite reaction rates. The numerical scheme is finite difference based, together with a multi-grid method and a local grid refinement technique. These methods have been used to calculate the combustion of propane in a single- and multiple-burner configurations. In the former case, the sensitivity of the solution to variations in some model parameters (determining the reaction rate) and numerical parameters (mesh spacing) has been studied. It is noted that different dependent variables exhibit different levels of sensitivity to the variation in model parameters. Thus, calibration and validation of models for reacting flows require that one compares the most sensitive variables. For engineering purposes, on the other hand, one may calibrate and validate models with respect to the most relevant variables. Our conclusion is that since sensitivity of the temperature distribution is relatively mild, one can still use EDC-like methods in engineering applications where details of the temperature field are of minor importance.     

Sand Erosion in Axial Flow Conditions

A mathematical model of sand erosion in axial flow conditions is presented. The basic mass balance equations and sand erosion constitutive equation were given in Vardoulakis et al. (1996). As opposed to reference Vardoulakis et al. (1996), we consider here the extreme case where convection is null and hydrodynamic dispersion dominates. In addition, Brinkman's extension of Darcy's law is adopted to account for a smooth transition between channel flow and Darcian flow. The set of governing PDE's is presented in dimensionless form and is solved numerically. In concordance with the basic constitutive equation for erosion kinetics, the analysis shows that erosion progresses in time as a front of high transport concentration. This result is justified by the highly non-linear character of the erosion source term which dominates in the diffusion-like governing equation.     

Growth and structure of nematic spherulites under shallow thermal quenches

The growth kinetics, shape, interfacial and internal orientation texture of a submicron nematic spherulite arising during the isotropic-to-nematic liquid crystal phase transformation under shallow thermal quenches is analyzed using theory, scaling, and numerical simulations based on the Landau – de Gennes model (The Physics of Liquid Crystals, 2nd edn. Clarendon, Oxford). The numerical computations from this model yield interfacial cusp formation that relaxes through the nucleation of two disclination lines of topological charge +1/2 and subsequently leads to intra-droplet texturing and a net topological charge within the spherulite of +1. The timing of these events suggests that cusp formation at the interface is intimately associated with the interfacial defect shedding mechanism (J. Chem. Phys. 124:244902, 2006) for shallow quenches. These results are different than predictions for deep quenches (J. Chem. Phys. 124:244902, 2006) where interfacial defect shedding leads to four defects and a net topological charge of +2. A liquid crystal dynamic shape equation is derived from the Landau – de Gennes model to account for the interface shape changes in terms of surface viscosity, the driving forces due to the uniaxial nematic-isotropic free energy difference, capillary forces, and friction forces, and used to semi-quantitatively show that during cusp formation and defect shedding, gradient elasticity, capillary forces and friction play significant roles in decelerating and accelerating the surface. An interfacial eigenvalue analysis shows that during the shallow quench, disclination lines nucleate within the interface itself and then texturize the nematic droplet as they migrate from within the interface to the bulk of the growing nematic droplet. After defect shedding, the spherulite is nearly circular and grows with constant velocity, in agreement with experiments. The results shed new light on intra-spherulite texturing mechanisms in phase ordering under weak driving forces.      

A spectral/hp least‐squares finite element analysis of the Carreau–Yasuda fluids

A least‐squares finite element model with spectral/hp approximations was developed for steady, two‐dimensional flows of non‐Newtonian fluids obeying the Carreau–Yasuda constitutive model. The finite element model consists of velocity, pressure, and stress fields as independent variables (hence, called a mixed model). Least‐squares models offer an alternative variational setting to the conventional weak‐form Galerkin models for the Navier–Stokes equations, and no compatibility conditions on the approximation spaces used for the velocity, pressure, and stress fields are necessary when the polynomial order (p) used is sufficiently high (say, p > 3, as determined numerically). Also, the use of the spectral/hp elements in conjunction with the least‐squares formulation with high p alleviates various forms of locking, which often appear in low‐order least‐squares finite element models for incompressible viscous fluids, and accurate results can be obtained with exponential convergence. To verify and validate, benchmark problems of Kovasznay flow, backward‐facing step flow, and lid‐driven square cavity flow are used. Then the effect of different parameters of the Carreau–Yasuda constitutive model on the flow characteristics is studied parametrically. Copyright © 2016 John Wiley & Sons, Ltd.     

Nonlinear models for the adoption and diffusion of innovations for industrial energy conservation

Four different theoretical models for explaining the diffusion of innovation were compared for 13 energy-related innovations--the Theory of Planned Behavior, the S-curve for Diffusion of Innovations, the power law distribution, and the cusp catastrophe. The substantive concern was to explore the roles of facilitative and obstructive factors in diffusing industrial and commercial innovations. Participants were 102 industrial plant and facilities managers from sites that were among the top users of electrical energy and natural gas in the United States. They completed a survey that contained measurements of positive attitudes toward innovation, organizational resistance to innovation, and the extent to which they had investigated or adopted each of the target innovations. Seven of the 13 innovations exhibited strong cusp catastrophe models (via nonlinear regression, average R2 = .91) compared to linear alternative models (average R2 = .31) for those innovations; the S-curve for diffusion was regarded as a simplified version of the cusp. One innovation was characterized best by a power law distribution (R2 = .94), and the remaining five were characterized best by a linear model that was based on the Theory of Planned Behavior (R2 = .41). Different underlying dynamics for the various innovations were implied by these results.