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We propose a new autonomous dynamical system of dimension N=4 that demonstrates the regime of stable two- frequency motions and period-doubling bifurcations of a two-dimensional torus. It is shown that the period-doubling bifurcation of the two-dimensional torus is not followed by the resonance phenomenon, and the two-dimensional ergodic torus undergoes a period-doubling bifurcation. The interaction of two generators is also analyzed. The phenomenon of external and mutual synchronization of two-frequency oscillations is observed, for which winding number locking on a two- dimensional torus takes place
We present the results of phase-referenced VLBA+Effelsberg observations at five frequencies of the double-image gravitational lens WAS B0218+357, made to establish the precise registration of the A and B lensed image positions. The motivation behind these observations is to investigate the anomalous variation of the image flux-density ratio (A[B) with frequency - this ratio changes by almost a factor of two over a frequency range from 1.65 GHz to 15.35 GHz. We investigate whether frequency dependent image positions, combined with a magnification gradient across the image field, could give rise to the anomaly. Our observations confirm the variation of image flux-density ratio with frequency. The results from Our phase-reference astrometry, taken together with the lens mass model of Wucknitz et al. (2004, MNRAS, 349, 14), show that shifts of the image peaks and centroids are too small to account for the observed frequency- dependent ratio
We study the overdamped version of two coupled anharmonic oscillators under the influence of both low- and high-frequency forces respectively and a Gaussian noise term added to one of the two state variables of the system. The dynamics of the system is first studied in the presence of both forces separately without noise. In the presence of only one of the forces, no resonance behaviour is observed, however, hysteresis happens there. Then the influence of the high-frequency force in the presence of a low-frequency, i.e. biharmonic forcing, is studied. Vibrational resonance is found to occur when the amplitude of the high-frequency force is varied. The resonance curve resembles a stochastic resonance-like curve. It is maximum at the value of g at which the orbit lies in one well during one half of the drive cycle of the low-frequency force and in the other for the remaining half cycle. Vibrational resonance is characterized using the response amplitude and mean residence time. We show the occurrence of stochastic resonance behaviour in the overdamped system by replacing the high-frequency force by Gaussian noise. Similarities and differences between both types of resonance are presented. (c) 2006 Elsevier B.V. All rights reserved.
An approach is presented for coupled chaotic systems with weak coherent motion, from which we estimate the upper bound value for the absolute phase difference in phase synchronous states. This approach shows that synchronicity in phase implies synchronicity in the time of events, a characteristic explored to derive an equation to detect phase synchronization, based on the absolute difference between the time of these events. We demonstrate the potential use of this approach for the phase coherent and the funnel attractor of the Rossler system, as well as for the spiking/bursting Rulkov map.
Experimental results show that the polymerization of pyrrole in the presence of beta-naphthalenesulfonic acid and different fluorosurfactants like perfluorooctanesulfonic acid, perfluorooctyldiethanolamide, and ammonium perfluorooctanoate leads to polypyrrole with special morphologies, such as rings or disks and rectangular frames or plates. The formation of these unusually shaped particles of polymer dispersions is explained by the chemical and colloidal peculiarities of the oxidative pyrrole polymerization with ammonium peroxodisulfate in aqueous medium.
Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in the connection strengths. Here we study synchronization in weighted complex networks and show that the synchronizability of random networks with a large minimum degree is determined by two leading parameters: the mean degree and the heterogeneity of the distribution of node's intensity, where the intensity of a node, defined as the total strength of input connections, is a natural combination of topology and weights. Our results provide a possibility for the control of synchronization in complex networks by the manipulation of a few parameters
Triplet energy back transfer in conjugated polymers with pendant phosphorescent iridium complexes
(2006)
The nature of Dexter triplet energy transfer between bonded systems of a red phosphorescent iridium complex 13 and a conjugated polymer, polyfluorene, has been investigated in electrophosphorescent organic light-emitting diodes. Red- emitting phosphorescent iridium complexes based on the [Ir(btp)2(acac)]fragment (where btp is 2-(2 '- benzo[b]thienyl)pyridinato and acac is acetylacetonate) have been attached either directly (spacerless) or through a - (CH2)(8)-chain (octamethylene-tethered) at the 9-position of a 9-octylfluorene host. The resulting dibromo- functionalized spacerless (8) or octamethylene-tethered (12) fluorene monomers were chain extended by Suzuki polycondensations using the bis(boronate)-terminated fluorene macromonomers 16 in the presence of end-capping chlorobenzene solvent to produce the statistical spacerless (17) and octamethylene-tethered ( 18) copolymers containing an even dispersion of the pendant phosphorescent fragments. The spacerless monomer 12 adopts a face-to-face conformation with a separation of only 3.6 angstrom between the iridium complex and fluorenyl group, as shown by X-ray analysis of a single crystal, and this facilitates intramolecular triplet energy transfer in the spacerless copolymers 17. The photo- and electroluminescence efficiencies of the octamethylene-tethered copolymers 18 are double those of the spacerless copolymers 17, and this is consistent with suppression of the back transfer of triplets from the red phosphorescent iridium complex to the polyfluorene backbone in 18. The incorporation of a -(CH2)(8)- chain between the polymer host and phosphorescent guest is thus an important design principle for achieving higher efficiencies in those electrophosphorescent organic light-emitting diodes for which the triplet energy levels of the host and guest are similar
We investigate the effects of a time-delayed all-to-all coupling scheme in a large population of oscillators with natural frequencies following a bimodal distribution. The regions of parameter space corresponding to synchronized and incoherent solutions are obtained both numerically and analytically for particular frequency distributions. In particular, we find that bimodality introduces a new time scale that results in a quasiperiodic disposition of the regions of incoherence.
We study thermally induced birefringence in crystalline Nd:YAG zigzag slab lasers and the associated depolarization losses. The optimum crystallographic orientation of the zigzag slab within the Nd:YAG boule and photoelastic effects in crystalline Nd:YAG slabs are briefly discussed. The depolarization is evaluated using the temperature and stress distributions, calculated using a finite element model, for realistically pumped and cooled slabs of finite dimensions. Jones matrices are then used to calculate the depolarization of the zigzag laser mode. We compare the predictions with measurements of depolarization, and suggest useful criteria for the design of the gain media for such lasers.
Fast, three-dimensional polarization mapping in piezoelectric sensor cables was performed by means of the novel thermal-pulse tomography (TPT) technique with a lateral resolution of 200 mum. The active piezoelectric cable material (a copolymer of polyvinylidene fluoride with trifluoroethylene) was electrically poled with a point-to-cable corona discharge. A focused laser was employed to heat the opaque outer electrode, and the short-circuit current generated by the thermal pulse was used to obtain 3D polarization maps via the scale transformation method. The article describes the TPT technique as a fast non-destructive option for studying cylindrical geometries.
Ferroelectrets are thin films of polymer foams, exhibiting piezoelectric properties after electrical charging. Ferroelectret foams usually consist of a cellular polymer structure filled with air. Polymer-air composites are elastically soft due to their high air content as well as due to the size and shape of the polymer walls. Their elastically soft composite structure is one essential key for the working principle of ferroelectrets, besides the permanent trapping of electric charges inside the polymer voids. The elastic properties allow large deformations of the electrically charged voids. However, the composite structure can also possibly limit the stability and consequently the range of applications because of, e. g., penetration of gas and liquids accompanied by discharge phenomena or because of a mechanical pre-load which may be required during the application. Here, we discuss various stability aspects related to the piezoelectric properties of polypropylene ferroelectrets. Near and below room temperature, the piezoelectric effect and the stability of the trapped charges are practically independent from humidity during long-time storage in a humid atmosphere or water, or from operating conditions, such as continuous mechanical excitation. Thermal treatment of cellular polypropylene above -10 degrees C leads to a softening of the voided structure which is apparent from the decreasing values of the elastic modulus. This decrease results in an increase of the piezoelectric activity. Heating above 60 degrees C, however, leads to a decrease in piezoelectricity
In this paper a perturbation-theory study of vibrational lifetimes for the bending and stretching modes of hydrogen adsorbed on a Si(100) surface is presented. The hydrogen-silicon interaction is treated with a semiempirical bond-order potential. Calculations are performed for H-Si clusters of different sizes. The finite lifetime is due to vibration-phonon coupling, which is assumed to be linear or bilinear in the phonon and nonlinear in the H-Si stretching and bending modes. Lifetimes and vibrational transition rates are evaluated with one- and two-phonon processes taken into account. Temperature effects are also discussed. In agreement with the experiment and previous theoretical treatment it is found that the H-Si (upsilon(s)=1) stretching vibration decays on a nanosecond timescale, whereas for the H-Si (upsilon(b)=1) bending mode a picosecond decay is predicted. For higher-excited vibrations, simple scaling laws are found if the excitation energies are not too large. The relaxation mechanisms for the excited H-Si stretching and the H-Si bending modes are analyzed in detail.
We present a detailed, realistic analysis of the implementation of a proposal for a quantum phase gate based on atomic vibrational states, specializing it to neutral rubidium atoms on atom chips. We show how to create a double-well potential with static currents on the atom chips, using for all relevant parameters values that are achieved with present technology. The potential barrier between the two wells can be modified by varying the currents in order to realize a quantum phase gate for qubit states encoded in the atomic external degree of freedom. The gate performance is analyzed through numerical simulations; the operation time is similar to 10 ms with a performance fidelity above 99.9%. For storage of the state between the operations the qubit state can be transferred efficiently via Raman transitions to two hyperfine states, where its decoherence is strongly inhibited. In addition we discuss the limits imposed by the proximity of the surface to the gate fidelity.
In planetary rings, binary collisions and mutual gravity are the predominant particle interactions. Based on a viscoelastic contact model we implement the concept of static adhesion. We discuss the collision dynamics and obtain a threshold velocity for restitution or agglomeration to occur. The latter takes place within a range of a few cm s(-1) for icy grains at low temperatures. The stability of such two-body agglomerates bound by adhesion and gravity in a tidal environment is discussed and applied to the saturnian system. A maximal agglomerate size for a given orbit location is obtained. In this way we are able to resolve the borderline of the zone where agglomerates can exist as a function of the agglomerate size and thus gain an alternative to the classical Roche limit. An increasing ring grain size with distance to Saturn as observed by the VIMS-experiment on board the Cassini spacecraft can be found by our estimates and implications for the saturnian system will be addressed.
Context. Very massive stars pass through the Wolf-Rayet (WR) stage before they finally explode. Details of their evolution have not yet been safely established, and their physics are not well understood. Their spectral analysis requires adequate model atmospheres, which have been developed step by step during the past decades and account in their recent version for line blanketing by the millions of lines from iron and iron-group elements. However, only very few WN stars have been re-analyzed by means of line-blanketed models yet. Aims. The quantitative spectral analysis of a large sample of Galactic WN stars with the most advanced generation of model atmospheres should provide an empirical basis for various studies about the origin, evolution, and physics of the Wolf-Rayet stars and their powerful winds. Methods. We analyze a large sample of Galactic WN stars by means of the Potsdam Wolf-Rayet (PoWR) model atmospheres, which account for iron line blanketing and clumping. The results are compared with a synthetic population, generated from the Geneva tracks for massive star evolution. Results. We obtain a homogeneous set of stellar and atmospheric parameters for the GalacticWN stars, partly revising earlier results. Conclusions. Comparing the results of our spectral analyses of the Galactic WN stars with the predictions of the Geneva evolutionary calculations, we conclude that there is rough qualitative agreement. However, the quantitative discrepancies are still severe, and there is no preference for the tracks that account for the effects of rotation. It seems that the evolution of massive stars is still not satisfactorily understood.
A series of novel platinum-containing carbazole monomers and polymers was synthesized and fully characterized by UV-VIS absorption, luminescence, and photoinduced absorption studies. In these compounds, a carbazole unit is incorporated into the main chain via either a para- or a meta-linkage. We discuss the effects of linkage and polymerization on the energy levels of S-1, T-1, and T-n. The S-1-T-1 splitting observed for the meta-linked monomer (0.4 eV) is only half of that in the para-linked monomer (0.8 eV). Upon polymerization, the exchange energy in the para- linked compound reduces, yet still remains larger than in the meta-linked polymer. We attribute the difference in exchange energy to the difference in wave function overlap between electron and hole in these compounds. (c) 2006 American Institute of Physics
We present a straightforward comparison of model calculations for the alpha-effect, helicities, and magnetic field line twist in the solar convection zone with magnetic field observations at atmospheric levels. The model calculations are carried out in a mixing-length approximation for the turbulence with a profile of the solar internal rotation rate obtained from helioseismic inversions. The magnetic field data consist of photospheric vector magnetograms of 422 active regions for which spatially-averaged values of the force-free twist parameter and of the current helicity density are calculated, which are then used to determine latitudinal profiles of these quantities. The comparison of the model calculations with the observations suggests that the observed twist and helicity are generated in the bulk of the convection zone, rather than in a layer close to the bottom. This supports two-layer dynamo models where the large-scale toroidal field is generated by differential rotation in a thin layer at the bottom while the alpha-effect is operating in the bulk of the convection zone. Our previous observational finding was that the moduli of the twist factor and of the current helicity density increase rather steeply from zero at the equator towards higher latitudes and attain a certain saturation at about 12 - 15 degrees. In our dynamo model with algebraic nonlinearity, the increase continues, however, to higher latitudes and is more gradual. This could be due to the neglect of the coupling between small-scale and large-scale current and magnetic helicities and of the latitudinal drift of the activity belts in the model
New amphiphilic compounds 1-9 that feature a construction with dendronized hydrophilic and hydrophobic segment groups connected to a specific aromatic or aliphatic spacer unit have been synthesized, following a modular building block strategy. The hydrophilic dendrons are typically branched elements with peripheral carboxylic groups, unlike the hydrophobic dendrons that contain peripheral alkyl chains as part of respective amide functions. The hydrophilic dendrons are in different generations of branching, while the hydrophobic dendrons are all in the first generation of branching (three terminal branching), but differ in the length of the alkyl chains, thus giving rise to designed structure and amphiphilic properties in the new compounds. The resulting surfactants are capable of forming well-defined Langmuir films of remarkable stability when spread from a solution onto an aqueous subphase. Nevertheless, specific packing behaviour and orientation of the amphiphilic molecules were found, depending on the molecular structure, as determined using analysis of the surface pressure-area (pi-A) isotherms. Langmuir-Blodgett transfer of the first monolayer from a pure water subphase to a clean silicon wafer proved possible for the amphiphiles of peripheral alkyl chain length C-12, while the amphiphiles with the longer alkyl chains failed, possibly due to the more rigid monolayers they form, impeding the transfer.
We present experimental and numerical evidence of synchronization of burst events in two different modulated CO2 lasers. Bursts appear randomly in each laser as trains of large amplitude spikes intercalated by a small amplitude chaotic regime. Experimental data and model show the frequency locking of bursts in a suitable interval of coupling strength. We explain the mechanism of this phenomenon and demonstrate the inhibitory properties of the implemented coupling.
We report measurements on the synchronization properties of organ pipes. First, we investigate influence of an external acoustical signal from a loudspeaker on the sound of an organ pipe. Second, the mutual influence of two pipes with different pitch is analyzed. In analogy to the externally driven, or mutually coupled self-sustained oscillators, one observes a frequency locking, which can be explained by synchronization theory. Further, we measure the dependence of the frequency of the signals emitted by two mutually detuned pipes with varying distance between the pipes. The spectrum shows a broad '' hump '' structure, not found for coupled oscillators. This indicates a complex coupling of the two organ pipes leading to nonlinear beat phenomena.
In the present paper, two kinds of dynamical complex networks are considered. The first is that elements of every node have different time delays but all nodes in Such networks have the same time-delay vector. The second is that different nodes have different time-delay vectors, and the elements of each node also have different time delays. Corresponding synchronization theorems are established. Numerical examples show the efficiency of the derived theorems.
Starting from an initial wiring of connections, we show that the synchronizability of a network can be significantly improved by evolving the graph along a time dependent connectivity matrix. We consider the case of connectivity matrices that commute at all times, and compare several approaches to engineer the corresponding commutative graphs. In particular, we show that synchronization in a dynamical network can be achieved even in the case in which each individual commutative graphs does not give rise to synchronized behavior
We present two different approaches to detect and quantify phase synchronization in the case of coupled non- phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the Rossler system in the funnel regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data from a population of 64 electrochemical oscillators
Crystal structures of four different di-aryl-1,3,4-oxadiazole compounds (aryl = 2-pyridyl-, 3-pyridyl-, 2-aminophenyl-, 3-aminophenyl-) are determined. Crystallization of di(2-pyridyl)-1,3,4-oxadiazole yielded monoclinic and triclinic polymorphs. The structures are characterized by the occurrence of pi-pi interactions. Additionally, in case of the aminophenyl compounds intra- as well as intermolecular hydrogen bonds are found that influence the packing motif as well. Since these molecules are often used as ligands in metal-organic complexes similarities and differences of the molecular conformation between the molecules in the pure crystals and that of the ligands in the complexes are discussed. (c) 2006 Elsevier B.V. All rights reserved.
To develop and investigate detailed mathematical models of metabolic processes is one of the primary challenges in systems biology. However, despite considerable advance in the topological analysis of metabolic networks, kinetic modeling is still often severely hampered by inadequate knowledge of the enzyme-kinetic rate laws and their associated parameter values. Here we propose a method that aims to give a quantitative account of the dynamical capabilities of a metabolic system, without requiring any explicit information about the functional form of the rate equations. Our approach is based on constructing a local linear model at each point in parameter space, such that each element of the model is either directly experimentally accessible or amenable to a straightforward biochemical interpretation. This ensemble of local linear models, encompassing all possible explicit kinetic models, then allows for a statistical exploration of the comprehensive parameter space. The method is exemplified on two paradigmatic metabolic systems: the glycolytic pathway of yeast and a realistic-scale representation of the photosynthetic Calvin cycle.
Structural and spectroscopical study of a 2,5-diphenyl-1,3,4-oxadiazole polymorph under compression
(2006)
The x-ray pattern and the Raman and luminescence spectra of crystalline 2,5-diphenyl-1,3,4-oxadiazole in one of its polymorphic forms (DPO II) have been investigated under pressure up to 5 GPa. The behaviour of the lattice parameters under compression was determined and it was found that the Murnaghan equation of state provides a good description of the volume-pressure relationship of DPO II. The values for the bulk modulus and its pressure derivative are K-0 = 8.6 GPa and K-0' = 7.2. The analysis of the Raman spectrum under compression clearly shows the pressure- induced shift of the Raman modes to higher frequencies. The mode Gruneisen parameters for the lattice modes were determined. Additionally, it was found that the emission spectrum of DPO II moves to lower energies and that the luminescence intensity decreases when pressure is applied
To test the consequences of decreased diversity and exclusion of keystone species, we compared the planktonic food webs in two acidic (pH <= 3), species-poor mining lakes with those in two species-rich, neutral lakes. The ratio of heterotrophic to autotrophic biomass (HIA) was similar in acidic and neutral lakes with comparable productivity. However, food webs in both acidic lakes were largely restricted to two trophic levels in contrast to the four levels found in neutral lakes. This restriction in food chain length was attributed to the absence of efficient secondary consumers, rather than to productivity or lake size which resulted in unusually low predator-prey weight ratios, with small top predators hardly exceeding their pry in size. In contrast to the neutral lakes, plankton biomass size spectra of acidic lakes were discontinuous due to a lack of major functional groups. The unique size-dependence of feeding modes in pelagic food webs, with bacteria in the smallest size classes followed by autotrophs, herbivores and carnivores, was maintained for bacteria but the other feeding modes strongly overlapped in size. Thus, their characteristic succession along the size gradient was roughly preserved under extreme conditions but the flow of energy along the size gradient was truncated in the acidic lakes. For most but not all attributes studied, differences were larger between acidic and neutral lakes than between neutral lakes of different trophic state
Recent research using the complex network approach has revealed a rich and complicated network topology in the cortical connectivity of mammalian brains. It is of importance to understand the implications of such complex network structures in the functional organization of the brain activities. Here we study this problem from the viewpoint of dynamical complex networks. We investigate synchronization dynamics on the corticocortical network of the cat by modeling each node (cortical area) of the network with a sub-network of interacting excitable neurons. We find that the network displays clustered synchronization behavior, and the dynamical clusters coincide with the topological community structures observed in the anatomical network. Our results provide insights into the relationship between the global organization and the functional specialization of the brain cortex.
We develop a model of stochastic radiation pressure for rotating non-spherical particles and apply the model to circumplanetary dynamics of dust grains. The stochastic properties of the radiation pressure are related to the ensemble-averaged characteristics of the rotating particles, which are given in terms of the rotational time-correlation function of a grain. We investigate the model analytically and show that an ensemble of particle trajectories demonstrates a diffusion-like behaviour. The analytical results are compared with numerical simulations, performed for the motion of the dusty ejecta from Deimos in orbit around Mars. We find that the theoretical predictions are in a good agreement with the simulation results. The agreement however deteriorates at later time, when the impact of non-linear terms, neglected in the analytic approach, becomes significant. Our results indicate that the stochastic modulation of the radiation pressure can play an important role in the circumplanetary dynamics of dust and may in case of some dusty systems noticeably alter an optical depth. (c) 2006 Elsevier Ltd. All rights reserved.
In this paper we show that delay embedding produces spurious structures in a recurrence plot (RP) that are not present in the real attractor. We analyze typical sets of simulated data, such as white noise and data from the chaotic Rossler system to show the relevance of this effect. In the second part of the paper we show that the second order Renyi entropy and the correlation dimension are dynamical invariants that can be estimated from Recurrence Plots with arbitrary embedding dimension and delay
Clear-water phase (CWP) is an important event in seasonal plankton succession. We examined the influence of all herbivorous zooplankton on its initiation under different weather and climatic conditions using up to 19 years of observations from the large, deep Lake Constance (Europe) and estimates of relative clearance rates. A CWP occurred regularly, even if daphnid biomass was still very low. CWP was attributed to strong grazing either by a daphnid- dominated zooplankton community or by a diverse assemblage consisting of micro- and meso-zooplankton. Both types of zooplankton communities occurred with approximately the same frequency. The timing of the CWP was unrelated to the North Atlantic Oscillation (NAO) but correlated with the wind-dependent intensity of deep vertical mixing 3 months earlier, during early spring. Less mixing enabled early growth of phytoplankton, ciliates and rotifers despite low temperatures, which prevented daphnid development at this time. This resulted in enhanced grazing of ciliates and rotifers, which increased the importance of phytoplankton less edible for most ciliates, rotifers and daphnids. Ciliates clearly dominated the grazing pressure on phytoplankton throughout spring, maintaining high biomasses together with the phytoplankton for up to 2 months. A CWP was observed when herbivores grazing on larger phytoplankton developed in addition to ciliates
Spatial recurrence plots
(2006)
We propose an extension of the recurrence plot concept to perform quantitative analyzes of roughness and disorder of spatial patterns at a fixed time. We introduce spatial recurrence plots (SRPs) as a graphical representation of the pointwise correlation matrix, in terms of a two-dimensional spatial return plot. This technique is applied to the study of complex patterns generated by coupled map lattices, which are characterized by measures of complexity based on SRPs. We show that the complexity measures we propose for SRPs provide a systematic way of investigating the distribution of spatially coherent structures, such as synchronization domains, in lattice profiles. This approach has potential for many more applications, e.g., in surface roughness analyzes
The development of surface relief and density patterns in azobenzene polymer films was studied by diffraction at two different wavelengths. We used x-ray diffraction of synchrotron radiation at 0.124 nm in combination with visible light diffraction at a wavelength of 633 nm. In contrast to visible light scattering x-ray diffraction allows the separation of a surface relief and a density grating contribution due to the different functional dependence of the scattering power. Additionally, the x-ray probe is most sensitive for the onset of the surface grating formation
We investigate the bifurcation structures in a two-dimensional parameter space (PS) of a parametrically excited system with two degrees of freedom both analytically and numerically. By means of the Renyi entropy of second order K-2, which is estimated from recurrence plots, we uncover that regions of chaotic behavior are intermingled with many complex periodic windows, such as shrimp structures in the PS. A detailed numerical analysis shows that, the stable solutions lose stability either via period doubling, or via intermittency when the parameters leave these shrimps in different directions, indicating different bifurcation properties of the boundaries. The shrimps of different sizes offer promising ways to control the dynamics of such a complex system.
We analytically describe the complex scenario of homoclinic bifurcations in the Chua’s circuit. We obtain a general scaling law that gives the ratio between bifurcation parameters of different nearby homoclinic orbits. As an application of this theoretical approach, we estimate the number of higher order subsidiary homoclinic orbits that appear between two consecutive lower order subsidiary orbits. Our analytical finds might be valid for a large class of dynamical systems and are numerically confirmed in the parameter space of the Chua’s circuit.
Shilnikov homoclinic orbits are trajectories that depart from a fixed saddle-focus point, with specific eigenvalues, and return to it after an infinite amount of time (that is also true to time reversal evolution). That results in an orbit that is unstable and has an infinite period. These two main characteristics contribute in the hardness for its observation in a dynamical system as well as in nature. However, its presence reveals fundamental characteristics of the system involved, as the existence of unstable periodic orbits embedded in a chaotic set. Once the unstable periodic orbits give invariants quantities of this set,1 the Shilnikov homoclinic orbits are also related to the characteristics of the chaotic set. Their connection with the fundamental dynamical properties is verified in a wide variety of systems. A series of numerical and experimental investigations reveal how Shilnikov homoclinic orbits, in the vicinity of a chaotic attractor, determine its dynamical and topological properties.4 Thus, the Shilnikov orbits are related to the returning time of the trajectory of a CO2 laser,5 also to the topology of a glow-discharge system.6 Moreover, some class of spiking neurons are modeled by chaos governed by such orbits,7,8 and their presence are connected to the intermittence present in rabbit arteries.9 These orbits are shown to be behind the mechanism of noise-induced phenomena,10 and they are also responsible for the dynamics of an electrochemical oscillator.11 In this work, we contribute to the understanding of how Shilnikov homoclinic orbits appear on the parameter space of systems as the ones above mentioned, by showing that these orbits are not only distributed following an universal rule but also exist for large parameter variations. We then confirm our previsions in the Chua’s circuit system
In this Letter, we show that coherence and phase synchronization analysis are sensitive but not specific in detecting the correct class of underlying dynamics. We propose procedures to increase specificity and demonstrate the power of the approach by application to paradigmatic dynamic model systems. (c) 2006 Elsevier B.V. All rights reserved
The results of the theoretical consideration of stochastic resonance in overdamped bistable oscillators are given. These results are founded not on the model of two states as in [McNamara B, Wiesenfeld K. Theory of stochastic resonance. Phys Rev A 1989;39:4854-69], but on splitting of motion into regular and random and the rigorous solution of the Fokker-Planck equation for the random component. We show that this resonance is caused by a change, under the influence of noise, of the system's effective stiffness and damping factor contained in the equation for the regular component. For a certain value of the noise intensity the effective stiffness is minimal, and this fact causes non-monotonic change of the output signal amplitude as the noise intensity changes. It is important that the location of the minimum and its value depend essentially on the signal frequency.
Relaxation processes at the glass transition in polyamide 11: From rigidity to viscoelasticity
(2006)
Relaxation processes associated with the glass transition in nonferroelectric and ferroelectric polyamide (PA) 11 are investigated by means of differential scanning calorimetry, dynamic mechanical analysis, and dielectric relaxation spectroscopy (DRS) in order to obtain information about the molecular mobility within the amorphous phase. In particular, the effects of melt quenching, cold drawing, and annealing just below the melting region are studied with respect to potential possibilities and limitations for improving the piezoelectric and pyroelectric properties of PA 11. A relaxation map is obtained from DRS that shows especially the crossover region where the cooperative alpha relaxation and the local beta relaxation merge into a single high-temperature process. No fundamental difference between quenched, cold-drawn, and annealed films is found, though in the cold-drawn (ferroelectric) film the alpha relaxation is suppressed and slowed down, but it is at least partly recovered by subsequent annealing. It is concluded that there exists an amorphous phase in all structures, even in the cold-drawn film. The amorphous phase can be more rigid or more viscoelastic depending on preparation. Cold drawing not only leads to crystallization in a ferroelectric form but also to higher rigidity of the remaining amorphous phase. Annealing just below the melting region after cold drawing causes a stronger phase separation between the crystalline phase and a more viscoelastic amorphous phase.
Relaxation processes at the glass transition in polyamide 11 : From rigidity to viscoelasticity
(2006)
Recurrence plot analyses suggest a novel reference system involved in newborn spontaneous movements
(2006)
The movements of newborns have been thoroughly studied in terms of reflexes, muscle synergies, leg coordination, and target-directed arm/hand movements. Since these approaches have concentrated mainly on separate accomplishments, there has remained a clear need for more integrated investigations. Here, we report an inquiry in which we explicitly concentrated on taking such a perspective and, additionally, were guided by the methodological concept of home base behavior, which Ilan Golard developed for studies of exploratory behavior in animals. Methods from nonlinear dynamics, such as symbolic dynamics and recurrence plot analyses of kinematic data received from audiovisual newborn recordings, yielded new insights into the spatial and temporal organization of limb movements. In the framework of home base behavior, our approach uncovered a novel reference system of spontaneous newborn movements.
Le rayonnement électromagnétique produit par un corps à température T est généralement considéré comme l'exemple type du rayonnement incohérent que l'on oppose au rayonnement laser. L'un est quasi isotrope tandis que l'autre est très directionnel, l'un a un large spectre tandis que l'autre est quasi-monochromatique. Aussi surprenant que cela puisse paraître, le rayonnement thermique de bon nombre de corps est cohérent lorsque l'on se place à une distance inférieure à la longueur d'onde de la surface émettrice. Nous verrons que ces effets peuvent être prédits à l'aide d'une approche électromagnétique du rayonnement thermique. Plusieurs expériences récentes ont confirmé ces propriétés inattendues.
We study the spontaneous emission of a single emitter close to a metallic nanoparticle, with the aim to clarify the distance dependence of the radiative and non-radiative decay rates. We derive analytical formulas based on a dipole- dipole model, and show that the nonradiative decay rate follows a R-6 dependence at short distance, where R is the distance between the emitter and the center of the nanoparticle, as in Forster's energy transfer. The distance dependence of the radiative decay rate is more subtle. It is chiefly dominated by a R-3 dependence, a R-6 dependence being visible at plasmon resonance. The latter is a consequence of radiative damping in the effective dipole polarizability of the nanoparticle. The different distance behavior of the radiative and non-radiative decay rates implies that the apparent quantum yield always vanishes at short distance. Moreover, non-radiative decay is strongly enhanced when the emitter radiates at the plasmon-resonance frequency of the nanoparticle.
Recent progress towards a quantum theory of laser-induced desorption and related phenomena is reviewed, for specific examples. These comprise the photodesorption of NO from Pt(111), the scanning tunnelling microscope and laser- induced desorption and switching of H at Si(100), and the electron stimulated desorption and dissociation of CO at Ru(0001). The theoretical methods used for nuclear dynamics range from open-system density matrix theory over nonadiabatically coupled multi-state models to electron-nuclear wavepackets. Also, aspects of time-dependent spectroscopy to probe ultrafast nonadiabatic processes at surfaces will be considered for the example of two-photon photoemission of solvated electrons in ice layers on Cu(111)