Dynamics of piecewise linear interval maps with hysteresis

We study a special case of multistate maps, piecewise linear interval maps with hysteresis. The main object of study is the global attractor. We find the conditions for it to be lower semicontinuous. We also prove that it coincides with the non-wandering set and prove several facts about omega-limit sets of the discontinuity points of the map.     

On the asymptotic properties of piecewise contracting maps

We are interested in the phenomenology of the asymptotic dynamics of piecewise contracting maps. We consider a wide class of such maps and we give sufficient conditions to ensure some general basic properties, such as the periodicity, the total disconnectedness or the zero Lebesgue measure of the attractor. These conditions show in particular that a non-periodic attractor necessarily contains discontinuities of the map. Under this hypothesis, we obtain numerous examples of attractors, ranging from finite to connected and chaotic, contrasting with the (quasi-)periodic asymptotic behaviours observed so far.     

A counterexample to the multifractal rigidity conjecture of piecewise linear Markov maps of the interval

A multifractal rigidity is the phenomena that the coincidence with the two multifractal spectra implies more strong relation between the given two dynamical systems. For the dimension spectrum of a Bernoulli measure defined on a repeller of a piecewise linear Markov map, Barreira, Pesin and Schmeling proved that a rigidity holds if the repeller is modelled by the full shift of two symbols. It was an open problem whether this rigidity holds in the case of three or more symbols. We give a negative answer to this problem by constructing a counter-example and we show that our counter-example is the unique one in the case of three symbols.     

Topology of attractors from two-piece expanding maps

In this paper we study the topology of the invariant sets derived from two-piece expanding maps. We classify the conditions under which the invariant sets are topological attractors, and show that the set of attractors is open and dense in the set of invariant sets derived by two-piece expanding maps.     

Simultaneously non-dense orbits under different expanding maps

Given a point and an expanding map on the unit interval, we consider the set of points for which the forward orbit under this map is bounded away from the given point. It is well-known that in many cases such sets have full Hausdorff dimension. We prove that such sets have a large intersection property, i.e. countable intersections of such sets also have full Hausdorff dimension. This result applies to a class of maps including multiplication by integers modulo 1 and x ? 1/x modulo 1. We prove that the same properties hold for multiplication modulo 1 by a dense set of non-integer numbers between 1 and 2.     

Piecewise linear elastic–plastic analysis

The purpose of this paper is to show that a mathematical programming method, due to Maier and his co-workers, of nonlinear structural analysis can be rerformulated so that greater computational efficiences are achived. The methods are designed for a class of elastic–plastic structures under ‘piecewise linear’ assumptions and solve among others the problem of determining the stresses and strains in the structure. The reformulation gives rise to a class of mathematical programming problems calles a ‘n by dn linear complementarity problem’, for which the author has developed an efficient algorithm. It will be explained why and by how much the proposed method (the reformulation and its solution by the author's algorithm) solves the structural problems more efficiently than the existing one. Results of a systematic computer experiment supporting the efficiency of the proposed method are also presented.     

形状记忆合金超弹性分段线性模型及其阻尼特性

建立简单有效的本构关系模型是形状记忆合金（SMA）工程应用和理论分析的一个必要条件。考虑相变过程中马氏体含量的影响,对SMA非线性本构关系进行简化,建立了SMA超弹性应力应变关系的分段线性模型。以此为基础,给出了损耗因子等特性参数计算表达式,并探讨了特性参数随应变幅值、温度等变化的规律,最后应用于一种常见的振动模型,考察了影响其隔振性能的因素。结果表明：应变幅值是影响SMA耗能能力的主要因素;并联弹簧的刚度会对SMA的作用效果产生影响。     

Unsteady flow of a dilute suspension in a semi-infinite contracting or expanding pipe

In the present paper an exact similar solution of the Navier-Stokes equation for unsteady flow of a dilute suspension in a semi-infinite contracting or expanding circular pipe is presented. The effects of the Schmidt number (Sc), Reynolds number (|?|), the volume fraction (α) and the relaxation time (τ) of the particulate phase on the flow characteristics are examined. The presence of the solid particles has been observed to influence the flow behaviour significantly. These solutions are valid down to the state of a completely collapsed pipe, since the nonlinearity is retained fully. The results may help understanding the flow near the heart and certain forced contractions or expansions of valved veins.     

Recurrence determinism and Li–Yorke chaos for interval maps

Recurrence determinism, one of the fundamental characteristics of recurrence quantification analysis, measures predictability of a trajectory of a dynamical system. It is tightly connected with the conditional probability that, given a recurrence, following states of the trajectory will be recurrences. In this paper, we study recurrence determinism of interval dynamical systems. We show that recurrence determinism distinguishes three main types of ω-limit sets of zero entropy maps: finite, solenoidal without non-separable points, and solenoidal with non-separable points. As a corollary, we obtain characterizations of strongly non-chaotic and Li–Yorke (non-)chaotic interval maps via recurrence determinism. For strongly non-chaotic maps, recurrence determinism is always equal to one. Li–Yorke non-chaotic interval maps are those for which recurrence determinism is always positive. Finally, Li–Yorke chaos implies the existence of a Cantor set of points with zero determinism.     

Piecewise linear approach to an archetypal oscillator for smooth and discontinuous dynamics

In a recent paper we examined a model of an arch bridge with viscous damping subjected to a sinusoidally varying central load. We showed how this yields a useful archetypal oscillator which can be used to study the transition from smooth to discontinuous dynamics as a parameter, alpha, tends to zero. Decreasing this smoothness parameter (a non-dimensional measure of the span of the arch) changes the smooth load-deflection curve associated with snap-buckling into a discontinuous sawtooth. The smooth snap-buckling curve is not amenable to closed-form theoretical analysis, so we here introduce a piecewise linearization that correctly fits the sawtooth in the limit at alpha=0. Using a Hamiltonian formulation of this linearization, we derive an analytical expression for the unperturbed homoclinic orbit, and make a Melnikov analysis to detect the homoclinic tangling under the perturbation of damping and driving. Finally, a semi-analytical method is used to examine the full nonlinear dynamics of the perturbed piecewise linear system. A chaotic attractor located at alpha=0.2 compares extremely well with that exhibited by the original arch model: the topological structures are the same, and Lyapunov exponents (and dimensions) are in good agreement.     

Robust controllability of linear time-invariant interval systems

The robust controllability problem for linear time-invariant interval systems is studied in this article. The rank preservation problem is converted to a non-singularity analysis problem of the minors of the matrix in discussion. Based on some essential properties of matrix measures, a new, sufficient, algebraically elegant criterion for the robust controllability of linear time-invariant interval systems is established. A numerical example is given to illustrate the application of the proposed sufficient algebraic criterion, and to show that the proposed sufficient condition can obtain less conservative results than the existing ones reported recently in the literature.     

Renormalization in a class of interval translation maps of d branches

Bruin and Troubetzkoy's 2003 results are generalized to a class of interval translation maps with arbitrarily many pieces. It is shown that there is an uncountable set of parameters leading to type ∞ interval translation maps (ITMs), but that the Lebesgue measure of these parameters is 0. Furthermore, conditions are given that imply that the ITMs have multiple ergodic invariant measures.     

Dynamic reliability analysis model for structure with both random and interval uncertainties

International Journal of Mechanics and Materials in Design - Aiming at analyzing the safety of the dynamic structure involving both input random variables and the interval ones, a new dynamic...     

New CPW-fed monopole antennas with both linear and circular polarisations

A low-profile, planar, circularly polarised monopole antenna with a shorting sleeve strip fed using a coplanar-waveguide transmission line for wireless communication in the digital communication system and the global positioning system bands is studied. By utilising the coupling effect between the monopole antenna and sleeve, two excited resonant modes, including the monopole and travelling-wave modes, cover the 1.57- and 1.8-GHz bands. Through modification with antennas of various geometrical parameters, the proposed antenna exhibits the wide bandwidth in the desired frequency bands, which has a bandwidth of 45% at 1.6%GHz for an input reflection coefficient of less than %10%dB. Meanwhile, the antenna has a 3-dB axial ratio bandwidth of 5%. Details of the design considerations for the proposed antennas are described, and the results of the antenna performances obtained are presented and discussed.     

Polarimetric investigation of materials with both linear and circular anisotropy

Abstract

We investigate light propagation through materials with both linear and circular anisotropy and find the relation of the amplitude and polarization transfer functions to the four anisotropic characteristics: linear circular birefringence, and linear and circular dichroism. We determine these four characteristics of anisotropic samples by measuring the output intensity and polarization corresponding to different input polarization azimuths and fitting the theoretical and experimental results. In our experiments we have used films of side-chain azobenzene polyesters in which optical anisotropy had been previously induced on illumination with elliptically polarized light.     

Laser linear encoder with both high fabrication and head-to-scale tolerances

We introduce a new configuration for the optical head of a newly developed diffractive laser encoder system. This configuration has a high manufacturing tolerance and a high head-to-scale alignment tolerance, both of which can enhance the wider potential applicability of this newly designed laser encoder. The measurement principles of the encoder are discussed and detailed. We optimized the grating shape and analyzed the impact of the optical components and their arrangement on the measurement error. The head-to-scale alignment tolerance and the arrangement of components in the encoder were also determined. Finally, the measurement performance was evaluated and analyzed. Under nonenvironmentally controlled conditions, the measurement accuracy was found to be 37.3 nm with a standard deviation of 25.4 nm.     

On the unsteady flow of a fairly concentrated suspension due to contracting or expanding walls of a tube

Consummating our earlier work [1], the unsteady flow of a fairly concentrated suspension due to a single contraction or expansion of the walls of a tube is studied. A comparison of the results obtained by using two different formulae for the additional drag terms in the governing equations has been made. A region of circulation in the flow field is observed when the volume fraction Z ? 0.3, the Schmidt number Sc < 1 andthedensityratio (densityoftheparticulatephase/densityofthefluidphase) > 1.     

Robust interval linear programming for environmental decision making under uncertainty

In this study, a robust interval linear programming (RILP) method is developed for dealing with uncertainties expressed as intervals with deterministic boundaries. An enhanced two-step method (ETSM) is also advanced to solve the RILP model. The developed RILP improves upon the conventional interval linear programming (ILP) method since it can generate solution intervals within a larger feasible zone. The decision space based on ETSM contains all feasible solutions, such that no useful information is neglected. Moreover, the RILP can guarantee the stability of the optimization model due to no violation for the best-case constraints. The results also suggest that the RILP is effective for practical environmental and engineering problems that involve uncertainties.     

测量仪器校准间隔的动态灰色线性回归预测

根据测量仪器的实际状态进行校准间隔的预测,可有效地避免不足校准和过剩校准。该文分析了历史校准数据的特征,对于既含有线性因素又含有指数因素的历史校准数据序列,建立动态灰色线性回归预测模型,预测测量仪器的校准间隔。动态灰色线性回归模型有机地将灰色GM(1,1)模型和线性模型组合起来,通过新老数据的新陈代谢,更加真实地反映系统的特征。通过实验对预测模型进行验证,结果表明:动态灰色线性回归模型的拟合与预测精度高于单纯的灰色GM(1,1)模型及新陈代谢GM(1,1)模型。