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We present a universal approach to the investigation of the dynamics in generalized models. In these models the processes that are taken into account are not restricted to specific functional forms. Therefore a single generalized models can describe a class of systems which share a similar structure. Despite this generality, the proposed approach allows us to study the dynamical properties of generalized models efficiently in the framework of local bifurcation theory. The approach is based on a normalization procedure that is used to identify natural parameters of the system. The Jacobian in a steady state is then derived as a function of these parameters. The analytical computation of local bifurcations using computer algebra reveals conditions for the local asymptotic stability of steady states and provides certain insights on the global dynamics of the system. The proposed approach yields a close connection between modelling and nonlinear dynamics. We illustrate the investigation of generalized models by considering examples from three different disciplines of science: a socioeconomic model of dynastic cycles in china, a model for a coupled laser system and a general ecological food web
The question as to whether state-selective population of molecular vibrational levels by shaped infrared laser pulses is possible in a condensed phase environment is of central importance for such diverse fields as time-resolved spectroscopy, quantum computing, or "vibrationally mediated chemistry." This question is addressed here for a model system, representing carbon monoxide adsorbed on a Cu(100) surface. Three of the six vibrational modes are considered explicitly, namely, the CO stretch vibration, the CO-surface vibration, and a frustrated translation. Optimized infrared pulses for state-selective excitation of "bright" and "dark" vibrational levels are designed by optimal control theory in the framework of a Markovian open-system density matrix approach, with energy flow to substrate electrons and phonons, phase relaxation, and finite temperature accounted for. The pulses are analyzed by their Husimi "quasiprobability" distribution in time-energy space.
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 report that the performances of blue polymer electrophosphorescent devices are crucially depending on the choice of the electron transporting material incorporated into the emissive layer. Devices with 1,3-bis[(4-tert- butylphenyl)-1,3,4-oxidiazolyl]phenylene (OXD-7) doped at similar to 40 wt% into a poly(vinylcarbazole) matrix exhibited significantly higher efficiencies than those with 2-(4-biphenylyl)-5-(4-tert-butylphenyl)-1,3,4-oxadiazole (PBD), yielding maximum luminous and power efficiency values of 18.2 Cd/A and 8.8 lm/W, respectively. Time resolved photoluminescence measurements revealed a long lifetime phosphorescence component in layers with PBD, which we assign to significant triplet harvesting by this electron-transporting component. (c) 2006 American Institute of Physics
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.
High cw power using an external cavity for spectral beam combining of diode laser-bar emission
(2006)
In extension to known concepts of wavelength-multiplexing diode laser arrays, a new external cavity is presented. The setup simultaneously improves the beam quality of each single emitter of a standard 25 emitter broad-area stripe laser bar and spectrally superimposes the 25 beams into one. By using this external resonator in an "off-axis" arrangement, beam qualities of M-slow(2) < 14 and M-fast(2) < 3 with optical powers in excess of 10 W in cw operation are obtained.
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 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
An effective dynamical description of a general class of stochastic phase oscillators is presented. For this, the effective phase velocity is defined either by the stochastic phase oscillators invariant probability density or its first passage times. Using the first approach the effective phase exhibits the correct frequency and invariant distribution density, whereas the second approach models the proper phase resetting curve. The discrepancy of the effective models is most pronounced for noise-induced oscillations and is related to non-monotonicity of the stochastic phase variable due to fluctuations.
In this paper, a measuring technique is presented for the detection of radial oscillations of tube walls excited by changes in internal air pressure. On organ pipes, the oscillations were investigated by means of piezoelectric polymer films slightly tensioned around the pipe bodies. Employing sensors with patterned electrodes, the well-known elliptical oscillation of the cross section as well as an additional monopole breathing of the organ-pipe body were detected. For the monopole breathing, a close relationship between the pressure distribution of the air-column resonances inside the pipe and the circumference variations along the pipe was observed
Human comment is studied using data from 'tianya' which is one of the most popular on-line social systems in China. We found that the time interval between two consecutive comments on the same topic, called inter-event time, follows a power-law distribution. This result shows that there is no characteristic decay time on a topic. It allows for very long periods without comments that separate bursts of intensive comments. Furthermore, the frequency of a different ID commenting on a topic also follows a power-law distribution. It indicates that there are some "hubs" in the topic who lead the direction of the public opinion. Based on the personal comments habit, a model is introduced to explain these phenomena. The numerical simulations of the model fit well with the empirical results. Our findings are helpful for discovering regular patterns of human behavior in on-line society and the evolution of the public opinion on the virtual as well as real society.
The coherence length of the thermal electromagnetic field near a planar surface has a minimum value related to the nonlocal dielectric response of the material. We perform two model calculations of the electric energy density and the field's degree of spatial coherence. Above a polar crystal, the lattice constant gives the minimum coherence length. It also gives the upper limit to the near field energy density, cutting off its 1/z(3) divergence. Near an electron plasma described by the semiclassical Lindhard dielectric function, the corresponding length scale is fixed by plasma screening to the Thomas-Fermi length. The electron mean free path, however, sets a larger scale where significant deviations from the local description are visible
We develop an effective description of noise-induced oscillations based on deterministic phase dynamics. The phase equation is constructed to exhibit correct frequency and distribution density of noise-induced oscillations. In the simplest one-dimensional case the effective phase equation is obtained analytically, whereas for more complex situations a simple method of data processing is suggested. As an application an effective coupling function is constructed that quantitatively describes periodically forced noise-induced oscillations.
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.
Employing the chemically passive carbon reconstruction W(110)/C-R(15x3) as substrate for deposition of C-60 molecules, we have discovered by scanning tunneling microscopy two-dimensional self-assembly of fullerenes into uniform molecular nanoclusters with "magic" numbers. Our photoemission measurements determine van der Waals forces as the dominating interaction in this self-organizing two-dimensional molecular gas. Based on this, a theoretical determination of the cluster structures in the framework of the Girifalco model gives perfect agreement with the experiment
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
Superexponential droplet fractalization as a hierarchical formation of dissipative compactons
(2010)
We study the dynamics of a thin film over a substrate heated from below in a framework of a strongly nonlinear one-dimensional Cahn-Hilliard equation. The evolution leads to a fractalization into smaller and smaller scales. We demonstrate that a primitive element in the appearing hierarchical structure is a dissipative compacton. Both direct simulations and the analysis of a self-similar solution show that the compactons appear at superexponentially decreasing scales, which means vanishing dimension of the fractal.
We report time-dependent configuration interaction singles calculations for the ultrafast laser driven many- electron dynamics in a polyatomic molecule, N-methyl-6-quinolone. We employ optimal control theory to achieve a nearly state-selective excitation from the S-0 to the S-1 state, on a time scale of a few (approximate to 6) femtoseconds. The optimal control scheme is shown to correct for effects opposing a state-selective transition, such as multiphoton transitions and other, nonlinear phenomena, which are induced by the ultrashort and intense laser fields. In contrast, simple two-level pi pulses are not effective in state-selective excitations when very short pulses are used. Also, the dependence of multiphoton and nonlinear effects on the number of states included in the dynamical simulations is investigated.
The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions in terms of ensembles of epistemic states (symbols) with corresponding classical observables, it is shown that such observables are complementary to each other with respect to particular partitions unless those partitions are generating. This explains why symbolic descriptions based on an ad hoc partition of an underlying phase space description should generally be expected to be incompatible. Related approaches with different background and different objectives are discussed