A catastrophe model for the impact torsional buckling of elastic cylindrical shell

The catastrophe theory is used to study the impact buckling of elastic structures. A criterion for impact buckling is established based on the proposed catastrophe system, in whose bifurcation set the critical step load is located. By the present theory, the impact torsional buckling for a clamped cylindrical shell is studied and the critical step torques for different imperfections are given. Also, the static critical torque is given, and it is shown that the critical step torque is smaller than the critical static torque.The project is supported by National Natural Science Foundation of China     

A swallowtail catastrophe model for the emergence of leadership in coordination-intensive groups

This research extended the previous studies concerning the swallowtail catastrophe model for leadership emergence to coordination-intensive groups. Thirteen 4-person groups composed of undergraduates played in Intersection coordination (card game) task and were allowed to talk while performing it; 13 other groups worked nonverbally. A questionnaire measured leadership emergence at the end of the game along with other social contributions to the groups' efforts. The swallowtail catastrophe model that was evident in previous leadership emergence phenomena in creative problem solving and production groups was found here also. All three control parameters were identified: a general participation variable that was akin to K in the rugged landscape model of self-organization, task control, and whether the groups worked verbally or nonverbally. Several new avenues for future research were delineated.     

Cusp catastrophe model for binge drinking in a college population

A cusp catastrophe model for binge drinking behavior was developed and tested with attitude toward alcohol consumption and peer influence as the two control parameters. Similar models were also developed for frequency and quantity of alcohol use. Participants were 1,247 students who completed the Long Form of the Core Alcohol and Drug Survey. The results were strongest for the binge drinking criterion (R(2) = .90), compared to a linear model (R(2) = .34) that is usually associated with the Theory of Planned Behavior or Theory of Reasoned Action. The results have numerous implications for the development of interventions and for future research.     

An example of applications of the elementary catastrophe theory in Hamiltonian systems

The convection in atmosphere discussed in ref. [1] is rigorously treated by considering the variation of environmental temperature with the height. This represents an example of applications of the elementary catastrophe theory in Hamiltonian systems.     

A fuzzy blue sky catastrophe

In this paper, a blue sky catastrophe of limit cycles of a Van der Pol system with fuzzy disturbances is studied by means of the fuzzy generalized cell mapping (FGCM) method. The blue sky catastrophe happens when a fuzzy limit cycle collides with a fuzzy saddle on the basin boundary as the intensity of fuzzy noise reaches a critical value. The fuzzy limit cycle, characterized by its global topology and membership function, suddenly loses stability and disappears into the blue sky after the collision. We illustrate this bifurcation event by considering the Van der Pol system under the multiplicative fuzzy noise. Such a bifurcation is a fuzzy noise-induced effect which cannot be seen in deterministic systems.     

Triple mode alignment in a canonical model of the blue-sky catastrophe

The blue-sky catastrophe (BSC) is a homoclinic bifurcation of a saddle node periodic orbit of codimension one, which has been found to occur in a number of physically relevant dynamics systems. The onset and termination of the BSC in a chaotic system is shown to coincide with the occurrence of triple mode alignment in a canonical model undergoing the BSC when the model is recast as an oscillator system. Typically, such behavior is only seen in hyperchaotic systems of dimension greater than three. Hence, in the case of three dimensional chaotic systems, competitive modes may under some circumstances be used in the prediction of the blue-sky catastrophe. Limitations to this approach are also discussed.     

Analysis of main shock of thrust fault earthquake by catastrophe theory

The relationship between work and energy increment of a thrust fault system with quasi-static deformation can be decomposed into two parts: volume strain energy and deviation stress energy. The relationship between work and energy increment of the deviation stress of a simplified thrust fault system is analyzed based on the catastrophe theory. The research indicates that the characteristics displayed by the fold catastrophe model can appropriately describe the condition of earthquake generation, the evolvement process of main shock of thrust fault earthquake, and some important aftershock properties. The bigger the surrounding press of surrounding rock is, the bigger the maximum principal stress is, the smaller the incidences of the potential thrust fault surface are, and the smaller the ratio between the tangential stiffness of surrounding rock and the slope is, which is at the inflexion point on the softened zone of the fault shearing strength curve. Thus, when earthquake occurrs, the larger the elastic energy releasing amount of surrounding rock is, the bigger the earthquake magnitude is, the larger the half distance of fault dislocation is, and the larger the displacement amplitude of end face of surrounding rock is. Fracturing and expanding the fault rock body and releasing the volume strain energy of surrounding rock during the earthquake can enhance the foregoing effects together.     

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.     

Relative velocity difference model for the car-following theory

To explore and evaluate the impacts of relative velocity difference (RVD) with memory on the dynamic characteristics and fuel economy of traffic flow in the intelligent transportation environment, we first analyze the linkage between RVD with different-step memory and the following car’s behaviors with the measured car-following (CF) data in cities by using the gray correlation analysis method and then present a RVD model based on the previous CF models in the literatures and calibrate it. Finally, we conduct several numerical simulations in the adaptive cruise control (ACC) strategy to explore how RVD with memory affects car’s velocity fluctuation and fuel consumptions, and find that the RVD model can describe the phase transition of traffic flow and estimate the evolution of traffic congestion, and that considering RVD with memory in modeling CF behaviors and designing the advanced ACC strategy can improve the stability and fuel economy of traffic flow.     

应用问题教学法改革材料力学的课堂教学模式

依据高等教育学中问题教学法的相关理论,用问题教学法改革材料力学的课堂教学,利于教学质量的提高和学生思维能力的培养。     

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.     

A question of constant strain

A condition under which more than one state of constant strain (contorted aeolotropy) is possible in a two dimensional solid crystal body is derived and some results are presented on the propagation of weak waves in such inhomogeneous elastic solids.     

Elastoplastic model and theory of slipping for the three-dimensional stress state

On the basis of concepts of the Batdorf-Budyanskii theory of slipping, we construct a model of elastoplastic medium for the case of three-dimensional stress state. The slipping conditions on the unit site take into account the local yield criterion and the local loading criterion. Under certain assumptions, one can integrate the increments of plastic shears over all possible sites of slipping in the case of an arbitrary three-dimensional stress state and obtain the constitutive relations for the elastoplastic model, which is a version of the theory of plastic flow.     

A dynamic slip velocity model for molten polymers based on a network kinetic theory

In this paper the slip phenomenon is considered as a stochastic process where the polymer segments (taken as Hookean springs) break off the wall due to the excessive tension imposed by the bulk fluid motion. The convection equation arising in network theories is solved for the special case of a polymer/wall interface to determine the time evolution of the configuration distribution function (Q, t). The stress tensor and the slip velocity are calculated by averaging the proper relations over a large number of polymer segments. Due to the fact that the model is probabilistic and time dependent, dynamic slip velocity calculations become possible for the first time and therefore some new insight is gained on the slip phenomenon. Finally, the model predictions are found to match macroscopic experimental data satisfactorily.Nomenclature rate of creation of polymer segments - g(Q) constant of rate of creation of polymer segments - rate of loss of polymer segments - h(Q) constant of rate of loss of polymer segments - h(Q) constant of rate of loss of polymer segments due to destruction of its B-link - H Hookean spring constant - k Boltzmann's constant - n unit vector normal to the polymer/wall interface - n ₀ number density of polymer segments - n ₀ surface number density of polymer segments - Q vector defining the size and orientation of a polymer segment - Q ^* critical length of a segment beyond which the tension may overcome the W _adh - t time - t _h howering time of broken polymer segments - T absolute temperature - W _adh work of adhesion Greek Letters _n nominal strain - strain - _n nominal shear rate - shear rate - dimensionless constant in the expressions of h(Q), g(Q) - viscosity - ^T velocity gradient tensor - ₀ time constant - standard deviation of vectors Q at equilibrium - _w wall shear stress - stress tensor - ₀ equilibrium configuration distribution function of Q - configuration distribution function of Q     

Linear viscoelastic model for elongational viscosity by control theory

Flows involving different types of chain branches have been modelled as functions of the uniaxial elongation using the recently generated constitutive model and molecular dynamics for linear viscoelasticity of polymers. Previously control theory was applied to model the relationship between the relaxation modulus, dynamic and shear viscosity, transient flow effects, power law and Cox–Merz rule related to the molecular weight distribution (MWD) by melt calibration. Temperature dependences and dimensions of statistical chain tubes were also modelled. The present study investigated the elongational viscosity. We introduced earlier the rheologically effective distribution (RED), which relates very accurately and linearly to the viscoelastic properties. The newly introduced effective strain-hardening distribution (RED_H) is related to long-chain branching. This RED_H is converted to real long-chain branching distribution by melt calibration and a simple relation formula. The presented procedure is very effective at characterizing long-chain branches, and also provides information on their structure and distribution. Accurate simulations of the elongational viscosities of low-density polyethylene, linear low-density polyethylene and polypropylene, and new types of MWDs are presented. Models are presented for strain-hardening that includes the monotonic increase and overshoot effects. Since the correct behaviour at large Hencky strains is still unclear, these theoretical models may aid further research and measurements.     

Streamline bifurcations and scaling theory for a multiple-wake model

We investigate the interaction between multiple arrays of (reverse) von Kármán streets as a model for the mid-wake regions produced by schooling fish. There exist configurations where an infinite array of vortex streets is in relative equilibrium, that is, the streets move together with the same translational velocity. We examine the topology of the streamline patterns in a frame moving with the same translational velocity as the streets. Fluid is advected along different paths depending on the distance separating two adjacent streets. When the distance between the streets is large enough, each street behaves as a single von Kármán street and fluid moves globally between two adjacent streets. When the streets get closer to each other, the number of streets that enter into partnership in transporting fluid among themselves increases. This observation motivates a bifurcation analysis which links the distance between streets to the maximum number of streets transporting fluid among themselves. We describe a scaling law relating the number of streets that enter into partnership as a function of the three main parameters associated with the system, two associated with each individual street (determining the aspect ratio of the street), and a third associated with the distance between neighboring streets. In the final section we speculate on the timescale associated with the lifetime of the coherence of this mid-wake scaling regime.     

A constitutive theory for ferrofluids

A constitutive theory for paramagnetic ferrofluids based on a rational thermodynamic theory with Lagrange multipliers is developed. It is shown that the 44 scalar coefficients of a general constitutive theory are reduced to 20 scalar coefficients through the exploitation of the entropy principle. By imposing: i) that the thermomechanical quantities are decoupled from the magnetic quantities; and ii) that the magnetization contributes only to the antisymmetrical part of the stress tensor, the 20 scalar coefficients are reduced to five e. g. the coefficients of thermal conductivity, shear and bulk viscosity and two relaxation times related to magnetic relaxation effects of the ferrofluid. Received May 1, 1999