Strange—Nonchaotic—Attractor—Like Behaviors in Coupled Map SYstems

In a coupled map system,an attractor which seems to be strange nonchaotic attractor(SNA)is discovered for nonzero measure in parameter range,The attractor has nonpositive Lyapunov exponent(LE) and discrete structure.We call it strange-nonchaotic-attractor-like(SNA-like) behavior because the size of its size of its discrete structure decreases with the computing precision increasing and the true SNA does not change.The SNA-like behavior in the autonomous system is born when the truncation error of round-off is amplified to the size of the discrete part of the attractor during the long time interval of positive local LE.The SNA-like behavior is easily mistaken for a true SNA judging merely from the largest LE and the phase portrait in double precision computing.In non-autonomous system an SNA-like attractor is also found.     

Investigation of a slot nanoantenna in optical frequency range

Following the analogy of radio frequency slot antenna and its complementary dipole, we propose the implementation of a slot nanoantenna (SNA) in the optical frequency range. Using finite-difference time-domain (FDTD) method, we investigate the electromagnetic (EM) properties of a SNA formed in a thin gold film and compare the results with the properties of a gold dipole nanoantenna (DNA) of the same dimension as the slot. It is found that the response of the SNA is very similar to the DNA, like their counterparts in the radio frequency (RF) range. The SNA can enhance the near field intensity of incident field which strongly depends on its feedgap dimension. The resonance of the SNA is influenced by its slot length; for the increasing slot length, resonant frequency decreases whereas the sharpness of resonance increases. Besides, the resonance of the SNA is found sensitive to the thickness of metal film, when the latter is smaller than the skin depth. The effect of polarization of incident field on the EM response of the SNA was examined; the field enhancement is optimum when polarization is parallel to the feedgap. Finally, we calculate the radiation patterns of the DNA and SNA and compare them with those of the RF dipole antenna. The radiation pattern of the SNA is found to be independent of its slot length when excited at resonant frequency. To the best of our knowledge, this is the first study on a slot antenna in the optical frequency.     

Birth of strange nonchaotic attractors through formation and merging of bubbles in a quasiperiodically forced Chuaʼs oscillator

We have constructed a quasiperiodically forced Chua?s circuit and report the occurrence of strange nonchaos in it. The birth of SNA is not through the well known mechanisms reported in literature, but through a novel route which we christen as “Formation and merging of bubbles route”. This is so named because the Poincaré strands undergo a series of splittings and mergings in certain regions, giving bubbles like appearance. These bubbles coalesce as the control parameter is varied, resulting in the birth of SNA. This has been confirmed numerically using various statistical measures.     

Quasiperiodically driven Josephson junctions: strange nonchaotic attractors, symmetries and transport

We consider the dynamics of the overdamped Josephson junction under the influence of an external quasiperiodic driving field. In dependence on parameter values either a quasiperiodic motion or a strange nochaotic attractor (SNA) can be observed. The latter corresponds to a resistive state in the current-voltage characteristics while for quasiperiodic motion a finite superconducting current exists for zero voltage. It is shown that in the case of SNA a nonzero mean voltage across the junction can appear due to symmetry breakings. Based on this observation a detailed symmetry consideration of the generalized equation of motion is performed and symmetry conditions ensuring zero mean voltage across the junction are found. Received 16 August 2001 and Received in final form 22 January 2002     

Components of supercritical extracts of garlic and synthetic nonsymmetrical allyl disulfides as potential antimicrobial preparations

Extracts of garlic (Allium sativum L.) were obtained using supercritical carbon dioxide extraction and were separated into individual compounds using preparative high performance liquid and gas chromatography. A series of nonsymmetrical allyl disulfides with different substituents were synthesized. The compounds isolated from the supercritical garlic extract and the synthetic nonsymmetrical allyl disulfides (SNA) were tested as potential antimicrobial agents using a number of test objects: Candida utilis, Bacillus cereus, Pseudomonas aurantiaca, and Escherichia coli. It was shown that the SNA exhibit high antimicrobial activity, which was much higher that the activities of individual components of garlic and in some cases were comparable in efficiency with antibiotics of the floxacin series widely used in clinical practice. The data obtained suggest the potential for using SNA as antimicrobial agents.     

Strange Non-Chaotic Attractors in Quasiperiodically Forced Circle Maps

The occurrence of strange non-chaotic attractors (SNA) in quasiperiodically forced systems has attracted considerable interest over the last two decades, in particular since it provides a rich class of examples for the possibility of complicated dynamics in the absence of chaos. Their existence was first described by Millions̆c̆ikov (and later by Vinograd and also Herman) for quasiperiodic -cocycles and by Grebogi et al (and later Keller) for so-called pinched skew products. However, except for these two particular classes there are still hardly any rigorous results on the topic, despite a large number of numerical studies confirming the widespread existence of SNA in quasiperiodically forced systems. Here, we prove the existence of SNA in quasiperiodically forced circle maps under rather general conditions, which can be stated in terms of -estimates. As a consequence, we obtain the existence of SNA for parameter sets of positive measure in suitable parameter families. These SNA carry the unique physical measure of the system, which determines the behaviour of Lebesgue-almost all initial conditions. Finally, we show that the dynamics are minimal in the considered situations. The results apply in particular to a forced version of the Arnold circle map. For this example, we also describe how the first Arnold tongue collapses and looses its regularity due to the presence of strange non-chaotic attractors and a related unbounded mean motion property.     

A special type of attractor and transitions in a delayed system

We discuss strange nonchaotic attractors (SNAs) in addition to chaotic and regular attractors in a quasiperiodically driven system with time delays. A route and the associated mechanism are described for a special type of attractor called strange-nonchaotic-attractor-like (SNA-like) through T² torus bifurcation. The type of attractor can be observed in large parameter domains and it is easily mistaken for a true SNA judging merely from the phase portrait, power spectrum and the largest Lyapunov exponent. SNA-like attractor is not strange and has no phase sensitivity. Conditions for Neimark-Sacker bifurcation are obtained by theoretical analysis for the unforced system. Complicated and interesting dynamical transitions are investigated among the different tongues.     

Prediction of verbal communication in noise—A development of generalized SIL curves and the quality of communication (Part 2)

The prediction of verbal communication is absolutely necessary for workplaces and living quarters disturbed by high noise levels. The methods to predict speech intelligibility (SIL, AI, STI, SNA) are assessed, taking into account both the speaker's sound level and the speech intelligibility at the hearer's position (Part 1). On the basis of this survey the development of generalized SIL curves is described and new SIL curves are proposed. Furthermore a method to determine the communication quality is described, which includes both the speaker's effort and the intelligibility reduction at the hearer's position (Part 2).     

Prediction of Verbal Communication is Noise— A review: Part 1

The prediction of verbal communication is absolutely necessary for workplaces and living quarters disturbed by high noise levels. The methods of predicting speech intelligibility (SIL, AI, STI, SNA) are assessed, taking into account both the speaker's sound level and the speech intelligibility at the hearer's position (part 1). On the basis of this survey, the development of generalized SIL curves is described and new SIL curves are proposed. Furthermore, a method of determining the quality of communication is described which includes both the speaker's effort and the reduction in intelligibility at the hearer's position (part 2).     

On Nodal Sets for Dirac and Laplace Operators

We prove that the nodal set (zero set) of a solution of a generalized Dirac equation on a Riemannian manifold has codimension 2 at least. If the underlying manifold is a surface, then the nodal set is discrete. We obtain a quick proof of the fact that the nodal set of an eigenfunction for the Laplace-Beltrami operator on a Riemannian manifold consists of a smooth hypersurface and a singular set of lower dimension. We also see that the nodal set of a Δ-harmonic differential form on a closed manifold has codimension 2 at least; a fact which is not true if the manifold is not closed. Examples show that all bounds are optimal. Received: 28 October 1996 / Accepted: 3 March 1997     

Limit Sets of Cellular Automata Associated to Probability Measures

We introduce the concept of limit set associated to a cellular automaton (CA) and a shift invariant probability measure. This is a subshift whose forbidden blocks are exactly those, whose probabilities tend to zero as time tends to infinity. We compare this probabilistic concept of limit set with the concepts of attractors, both in topological and measure-theoretic sense. We also compare this notion with that of topological limit set in different dynamical situations.     

SNA’s in the Quasi-Periodic Quadratic Family

We rigorously show that there can exist Strange Nonchaotic Attractors (SNA) in the quasi-periodically forced quadratic (or logistic) map

On the integration of a three-wave set of equations

It is shown that a certain set of equations describing the evolution of a three-wave system can be derived from a hamiltonian. We show that this set has three integrals of motion which are in involution, so that the system is integrable. We then show how the equations can be integrated.     

Polarization transformers for optical anisotropy: II. Transformation of properties of optical anisotropy of reciprocal and nonreciprocal elements

The methods of transformation of an arbitrary phase optical anisotropy using a set of quarter-wave plates are considered. For this purpose, we use a formal analogy between the Jones matrices of these anisotropic elements and the matrices of transformation of the polarization basis states. We consider all types of reciprocal and nonreciprocal optical phase anisotropy. We show that the minimum set of anisotropic elements sufficient for such a transformation is a set of four quarter-wave plates. For nonreciprocal systems, this set should be complemented with Faraday rotators, whose number depends on the initial and final type of the nonreciprocity.     

Optimized local basis set for Kohn–Sham density functional theory

We develop a technique for generating a set of optimized local basis functions to solve models in the Kohn–Sham density functional theory for both insulating and metallic systems. The optimized local basis functions are obtained by solving a minimization problem in an admissible set determined by a large number of primitive basis functions. Using the optimized local basis set, the electron energy and the atomic force can be calculated accurately with a small number of basis functions. The Pulay force is systematically controlled and is not required to be calculated, which makes the optimized local basis set an ideal tool for ab initio molecular dynamics and structure optimization. We also propose a preconditioned Newton–GMRES method to obtain the optimized local basis functions in practice. The optimized local basis set is able to achieve high accuracy with a small number of basis functions per atom when applied to a one dimensional model problem.     

Redistancing by flow of time dependent eikonal equation

Construction of signed distance to a given interface is a topic of special interest to level set methods. There are currently, however, few algorithms that can efficiently produce highly accurate solutions. We introduce an algorithm for constructing an approximate signed distance function through manipulation of values calculated from flow of time dependent eikonal equations. We provide operation counts and experimental results to show that this algorithm can efficiently generate solutions with a high order of accuracy. Comparison with the standard level set reinitialization algorithm shows ours is superior in terms of predictability and local construction, which, for example, are critical in local level set methods. We further apply the same ideas to extension of values off interfaces. Together, our proposed approaches can be used to advance the level set method for fast and accurate computations of the latest scientific problems.     

Proper Effect Algebras Admitting No States

We show that there is even a finite proper effect algebra admitting no states. Further, every lattice effect algebra with an ordering set of valuations is an MV effect algebra (consequently it can be organized into an MV algebra). An example of a regular effect algebra admitting no ordering set of states is given. We prove that an Archimedean atomic lattice effect algebra is an MV effect algebra iff it admits an ordering set of valuations. Finally we show that every nonmodular complete effect algebra with trivial center admits no order-continuous valuations.     

Derivation of classical capacity of a quantum channel for a discrete information source

We prove that the classical capacity of a quantum channel for M symmetric states is achieved by a uniform distribution on a priori probabilities. We also investigate nonsymmetric cases such as a ternary amplitude shift keyed signal set and a 16-ary quadrature amplitude modulated signal set in coherent states.     

Conditions for common-noise-induced synchronization in time-delay systems

We studied synchronization induced by a common external noise in scalar time-delay systems. We have found a set of sufficient conditions for the synchronization. This set of conditions shows that the synchronization occurs in a wide class of time-delay systems. Numerical evidence for the analytically obtained conditions is also presented.     

Markov partition in non-hyperbolic interval dynamics

We considerC ² unimodal mapsf such that all periodic points are hyperbolic, the critical point is non-degenerated and non-recurrent, and the Julia set does not contain intervals. We construct a Markov partition for a big part of the Julia set. Then we use it to estimate the limit capacity and Hausdorff dimension of the Julia set.Partially supported by CNPq, S.C.T.-Brazil