Probability symmetry broken upon rapid period-doubling bifurcation

A quadratic one-dimensional mapping with noise is used to model the phenomenon of violation of the equal probability of variants in the postbifurcation system evolution upon a fast change of the control parameter. The case of a period-doubling bifurcation, after which only one of the two types of oscillations with different phases may occur in the system, is analyzed. The laws of the phenomenon are considered and its possible mechanism is discussed.     

Interior symmetry and local bifurcation in coupled cell networks

A coupled cell system is a network of dynamical systems, or 'cells', coupled together. Such systems can be represented schematically by a directed graph whose nodes correspond to cells and whose edges represent couplings. A symmetry of a coupled cell system is a permutation of the cells and edges that preserves all internal dynamics and all couplings. It is well known that symmetry can lead to patterns of synchronized cells, rotating waves, multirhythms, and synchronized chaos. Recently, the introduction of a less stringent form of symmetry, the 'symmetry groupoid', has shown that global group-theoretic symmetry is not the only mechanism that can create such states in a coupled cell system. The symmetry groupoid consists of structure-preserving bijections between certain subsets of the cell network, the input sets. Here, we introduce a concept intermediate between the groupoid symmetries and the global group symmetries of a network: 'interior symmetry'. This concept is closely related to the groupoid structure, but imposes stronger constraints of a group-theoretic nature. We develop the local bifurcation theory of coupled cell systems possessing interior symmetries, by analogy with symmetric bifurcation theory. The main results are analogues for 'synchrony-breaking' bifurcations of the Equivariant Branching Lemma for steady-state bifurcation, and the Equivariant Hopf Theorem for bifurcation to time-periodic states.     

Phenomena in the bifurcation of unsymmetric composite plates

The phenomena observed in the large scale bifurcation of unsymmetric composite plates are characterized. Such plates can exhibit more than one stable geometry and can be ‘snapped’ from one geometry to another. It is convenient to think of this process as providing sufficient strain energy to overcome an energy maximum and is analogous to an activation energy. To describe the snap-through process, 2-ply, [0, 90] unsymmetric plates were forced from one state to the other in rigid test rigs such that great control could be achieved over the process and loads and deformations were monitored throughout the bifurcation. A hitherto unrecognised phenomenon was noted in that the snap-through process was seen to take place not as a single bifurcation but as two closely coupled bifurcations, as first one side snaps through and then the other. The experimental approach taken here, coupled with the simple energy analysis, should be of value in understanding practical structures of multiple stable states, such as might be used in morphing or adaptive aircraft.     

Essential instabilities of fronts: bifurcation, and bifurcation failure

Various instability mechanisms of fronts in reaction-diffusion systems are analysed; the emphasis is on instabilities that have the potential to create modulated (i.e. time-periodic) waves near the primary front. Hopf bifurcations caused by point spectrum with associated localized eigenfunctions provide an example of such an instability. A different kind of instability occurs if one of the asymptotic rest states destabilizes: these instabilities are caused by essential spectrum. It is demonstrated that, if the rest state ahead of the front destabilizes, then modulated fronts are created that connect the rest state behind the front with small spatially periodic patterns ahead of the front. These modulated fronts are stable provided the spatially periodic patterns are stable. If, on the other hand, the rest state behind the front destabilizes, then modulated fronts that leave a spatially periodic pattern behind do not exist.     

On the Persistence of Researchers in Technological Development

This paper examines several factors that might influence a researcher'slikelihood of continuing with a particular avenue of researchand development. Using the literature as a source of data tomeasure researcher contribution spans in the development ofcochlear implants, specific hypotheses regarding the determinantsof persistence are develped and empircally tested. The resultsnot only provide the basis for developing a theory of researcherpersitence, but also provide a means to track the emergenceof technologies and shape their evolution.     

Phase diagrams beyond the critical point

Following a path in the usual p‐T‐diagrams of one‐component systems via the supercritical region it seems that one can make a transition from the liquid to the gas phase (and in reverse) without traversing a phase boundary curve, whereas in the sub‐critical region one clearly has to pass a phase boundary curve. To solve this paradox situation, the phase diagrams of one‐component systems are analyzed with respect to the phase transition from the liquid to the gas state in the sub‐ and supercritical range. It is shown that the critical point is not an isolated point or an end point on the phase boundary curve between the gaseous and the liquid phase in a p‐T‐diagram. Instead, it marks on the boundary curve just the transition between the section of a first order phase transition in the sub‐critical range and the section of a second or higher order phase transition in the supercritical range. Thus, the present phase diagrams of one‐component systems are incomplete with respect to the phase boundary curve between liquid and gas in the supercritical region. The result is illustrated using the model of a van der Waals gas.     

Dynamic crack bifurcation in PMMA

An investigation of the branching characteristics of small PMMA single edge notched tensile (SENT) specimens is presented. The influence of notch depth and specimen thickness was examined and it was found that branching only occurred for thicker specimens and very short notch depths. The location at which successful branching occurred was very consistent for a given notch depth. Subsequently, however, a statistical variation of branching patterns was observed.A series of simulations was then performed to provide further insight into these tests and in particular to examine the evolution of the fracture process region ahead of the running crack. A finite volume/cohesive zone formulation was used to model micro-crack nucleation and dynamic interaction in the process zone. The cohesive strength and fracture resistance were estimated from unnotched tensile tests and the application of LEFM to the notch test data. Even though a very simple criterion was used to govern the insertion and subsequent behaviour of the cohesive surfaces in the model, many of the experimental observations were reproduced, including high frequency oscillations in crack velocity, the substantial increase in the fracture surface area due to the formation of subsurface micro-cracks, and the location at which successful branching took place.     

Computer modelling of phase diagrams

Abstract

An investigation has been made of the tensile behaviour between 20 and 600°C of two ultrahigh boron steels (Fe–2·2B and Fe–4·9B), consolidated by hot isostatic pressing at temperatures ranging from 700 to 1100°C. Tensile tests showed plastic deformation only in the Fe–2·2B alloy. A decrease in yield and ultimate tensile stresses occurred when the consolidation temperature was increased. This was accompanied by an increase in the elongation to failure. This alloy satisfies the Hall–Petch relation for all testing temperatures. The slope of the yield stress versus d^?1/2 curve (d is grain size) decreases as the temperature increases, indicating that the mechanism controlling plastic deformation becomes independent of grain size at high testing temperatures. The fracture mode observed was brittle at room temperature and ductile, shown by the presence of dimples, at temperatures above 400°C.

MST/2050     

Computer calculations of phase diagrams

The thermodynamic route of establishing phase diagrams is a relatively recent activity, considering that till about the fifties most phase diagrams were determined by the measurement of certain physical property or quantitative microscopy using light optics or x-ray diffraction. The thermodynamic formalism used by Kaufman and Bernstein is explained and illustrated with examples of the development of hypothetical binary phase diagrams. The calculation of ternary phase diagrams can begin with the binary phase diagram data as a first approximation. However, to calculate a reasonably accurate ternary phase diagram a certain amount of ternary solution data is necessary. Various empirical equations have been proposed in the literature to express ternary thermodynamic data. Calculation of simple ternary isothermal sections is illustrated with the examples of Mo-V-W and Cd-Sn-Pb systems. The numerical techniques which involve the differentiation of thermodynamic parameters with respect to composition get more involved with the number of components becoming 3 or more. A simpler approach has been applied recently to find the minimum position on the Gibbs free energy surface.     

Parameter diagrams for the fractional fourier transform

Abstract

A simple diagram illustrates the relations between six parameters of the generalized FRT. The diagram is developed to illustrate a variety of equations which have appeared in the literature, particularly in relation to free-space propagation, Gaussian beams, optical filtering experiments, and the ABCD matrix. Analysis of the effect of imperfect collimation and of the production of a Radon-Wigner spectrum using a varifocal lens are given as examples of the technique.     

Phase diagrams of model magnetofluids

A model of ferrofluids is treated analytically and numerically in order to discuss the phase diagrams. Magnetic particles are supposed to sit on a lattice and to interact through a magnetic Kac potential and through a short range potential between nearest neighbours. The equation of state and the phase diagrams of such one and two dimensional ferrofluids are presented and discussed.     

Usage of symmetry in the simulation of interdigital transducers

This paper discusses the application of the finite element method to the simulation of surface acoustic wave generation on piezoelectric substrates and the possibility of reducing the number of computations by taking into account the symmetry of the problem. It is shown that the computations can be performed in only one half of the structure provided that the substrate assumes particular orientations. The class of allowed orientations encompasses the majority of crystal cuts used in practice. A test computation of the electric admittance agrees well with experimental results. The perfectly matched layer method is implemented to truncate the computational domain.     

磁悬浮控制系统的稳定性及Hopf分岔的研究

研究了反馈增益系数对非线性磁悬浮控制系统稳定性的影响,给出了系统保持稳定时设计参数的取值范围。通过引入Hopf分岔的检验函数分析了磁悬浮控制系统动态Hopf分岔的产生条件,从而避免了分析系统稳定性时求解全部特征值的大量计算。以速度反馈增益为参量,运用规范型法和中心流形法,解析地确定出表征磁悬浮系统中Hopf分岔方向、周期解的稳定性及周期变化的特征量,以便通过向分岔的反方向调节反馈增益系数而实现系统的稳定。最后通过数值模拟验证了主要结果的可靠性。     

Equilibrium phase diagrams of isolated nano-phases

 Materials processing and fabrication shows a strong trend toward manipulation of materials at ever decreasing sizes. This is especially true in microelectronics. Once the size of a material extends below the sub-micrometer level significant changes in the properties and behavior of materials emerges. It is sometimes difficult to determine if the changes observed at this nano-scale are a result of the process variables or are inherent to material because of its small size. In order to address this difficulty with regard to crystal structure and composition, phase diagrams as a function of size would be particularly useful. In the present paper experimental data on phase equilibria are presented as well as a thermodynamical analysis based on capillarity effects from surface curvature. The analysis and experimental data for binary phase diagrams agree with one another and show that isolated particles of less than 100 nm exhibit substantial decreases in liquidus temperature, factors of more than 10 increase in solubility, and narrowing of the two-phase fields. The details of the thermodynamic model and its predictive powers are presented along with a three-dimensional phase diagram which has temperature-composition-size as its axes. Received: 10 August 1998 / Reviewed and accepted: 27 September 1998     

On the symmetry of phosphorous doped ZnSe

The site symmetry of P doped ZnSe is analysed in detail here, as the recent experiments suggest two possible symmetriesT _d andC _3V. The reduction toC _3V is attributed to the presence of natural impurity, Ga. Our calculations based on molecular model and Green’s functions suggest that the symmetryC _3V is possible with ZnSe : P when Jahn Teller distortion of about ～ 0.2 Å (towards one of Zn atom) is assumed. This has been supported by other experiments.