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A new globally uniform Lagrangian transport scheme for large ensembles of passive tracer particles is presented and applied to wind data from a coupled atmosphere-ocean climate model that includes interactive dynamical feedback with stratospheric chemistry. This feedback from the chemistry is found to enhance large-scale meridional air mass exchange in the northern winter stratosphere as well as intrusion of stratospheric air into the troposphere, where both effects are due to a weakened polar vortex.
Stripe-array diode lasers naturally operate in an anti-phase supermode. This produces a sharp double lobe far field at angles ña depending on the period of the array. In this paper a 40 emitter gain guided stripe-array laterally coupled by off-axis filtered feedback is investigated experimentally and numerically. We predict theoretically and confirm experimentally that at doubled feedback angle 2a a stable higher order supermode exists with twice the number of emitters per array period. The theoretical model is based on time domain traveling wave equations for optical fields coupled to the carrier density equation taking into account diffusion of carriers. Feedback from the external reflector is modeled using Fresnel integration.
Polymer composites are currently suggested for use as improved dielectric materials in many applications. Here, the effect of particle size and dispersion on the electrical properties of composites of rutile TiO2 and poly(styrene- ethylene-butadiene-styrene) (SEBS) are investigated. Both 15 and 300 nm particles are mixed with SEBS, with amounts of sorbitan monopalmitate surfactant from 0 to 3.3 vol%, and their dielectric and mechanical properties are measured. Composites with the 300 nm TiO2 particles result in increases of 170% in relative permittivity over the pure polymer, far above those predicted by standard theories, such as Bruggeman (140%) and Yamada (114%), and improving dispersion with surfactant has little effect. The composites with 15 nm particles showed surprisingly large relative permittivity increases (350%), but improving the dispersion by the addition of any surfactant causes the relative permittivity to decrease to 240% of the pure polymer value. We suggest that the increase is due to the formation of a highly conductive layer in the polymer around the TiO2 particles.
Nanocrystalline carbonitrides were performed by pulsed plasma electrolytic carbonitriding on hard chromium coating deposited on AISI 1035 substrate by electroplating. The electroplated samples were connected cathodically to a high-current pulsed power supply and biased to a negative voltage. The treatment times were 30, 60 and 60 min. A thick compound layer was formed on the surface of Cr coating with microhardness of about 1200 HV0.15. The nanostructure of the treated layers depends strongly on the applied voltage. The wear resistance of the treated layers depended on process parameters. Overall mechanical properties of treated samples show strong relation to morphology and distribution of complex carbonitride nanocrystallites.
We present conditions for the local and global synchronizations in coupled-map networks using the matrix measure approach. In contrast to many existing synchronization conditions, the proposed synchronization criteria do not depend on the solution of the synchronous state and give less limitation on the network connections. Numerical simulations of the coupled quadratic maps demonstrate the potentials of our main results.
In a 2D parameter space, by using nine experimental time series of a Clitia's circuit, we characterized three codimension-1 chaotic fibers parallel to a period-3 window. To show the local preservation of the properties of the chaotic attractors in each fiber, we applied the closed return technique and two distinct topological methods. With the first topological method we calculated the linking, numbers in the sets of unstable periodic orbits, and with the second one we obtained the symbolic planes and the topological entropies by applying symbolic dynamic analysis.
The annual cycle of extreme I-day precipitation events across the UK is investigated by developing a statistical model and fitting it to data from 689 rain gauges A generalized extrerne-value distribution (GEV) is fit to the time series of monthly maxima, across all months of the year simultaneously, by approximating, the annual cycles of the location and scale parameters by harmonic functions, while keeping the shape parameter constant throughout the year We average the shape parameter of neighbouring rain gauges to decrease uncertainties. and also Interpolate values of all model parameters to give complete coverage of (lie UK. The model reveals distinct spatial patterns the estimated parameters The annual mean of the location and scale parameter is highly correlated with orography. The annual cycle of the location parameter is strong in the northwest UK (peaking in late autumn or winter) and in East Anglia (where it peaks HI late summer), and low in the Midlands The annual cycle of the scale parameter exhibits a similar pattern with strongest amplitudes in East Anglia The spatial patterns of the annual cycle phase suggest that they are linked to the dominance of frontal precipitation for generating extreme precipitation in the west and convective precipitation in the southeast of the UK The shape parameter shows a gradient from Positive Values in the east to negative values in some areas of the west We also estimate 10-year and 100-year return levels at each rain gauge, and interpolated across the UK.
We introduce a framework of optomechanical systems that are driven with a mildly amplitude-modulated light field, but that are not subject to classical feedback or squeezed input light. We find that in such a system one can achieve large degrees of squeezing of a mechanical micromirror-signifying quantum properties of optomechanical systems- without the need of any feedback and control, and within parameters reasonable in experimental settings. Entanglement dynamics is shown of states following classical quasiperiodic orbits in their first moments. We discuss the complex time dependence of the modes of a cavity-light field and a mechanical mode in phase space. Such settings give rise to certifiable quantum properties within experimental conditions feasible with present technology.
A series of copolymers containing oxadiazole and fluorene cromophores was synthesized by polycondensation of a diacid chloride incorporating one diphenylsilane linkage and a mixture of aromatic diamines containing oxadiazole and fluorene moieties. The solubility, thermal behavior, and photoluminescence ability of the thin polymer films were studied and compared with related heterocyclic polymers. These polymers are semicrystalline and form plastic mesophases in the first heating run, which brings about new ordered melted state processing opportunities. They exhibited blue photoluminescence in nanometric films, thus being promising candidates for manufacturing electroluminescent devices.
Nonlinear force-free field (NLFFF) models are thought to be viable tools for investigating the structure, dynamics, and evolution of the coronae of solar active regions. In a series of NLFFF modeling studies, we have found that NLFFF models are successful in application to analytic test cases, and relatively successful when applied to numerically constructed Sun-like test cases, but they are less successful in application to real solar data. Different NLFFF models have been found to have markedly different field line configurations and to provide widely varying estimates of the magnetic free energy in the coronal volume, when applied to solar data. NLFFF models require consistent, force-free vector magnetic boundary data. However, vector magnetogram observations sampling the photosphere, which is dynamic and contains significant Lorentz and buoyancy forces, do not satisfy this requirement, thus creating several major problems for force-free coronal modeling efforts. In this paper, we discuss NLFFF modeling of NOAA Active Region 10953 using Hinode/SOT-SP, Hinode/XRT, STEREO/SECCHI-EUVI, and SOHO/MDI observations, and in the process illustrate three such issues we judge to be critical to the success of NLFFF modeling: (1) vector magnetic field data covering larger areas are needed so that more electric currents associated with the full active regions of interest are measured, (2) the modeling algorithms need a way to accommodate the various uncertainties in the boundary data, and (3) a more realistic physical model is needed to approximate the photosphere-to-corona interface in order to better transform the forced photospheric magnetograms into adequate approximations of nearly force-free fields at the base of the corona. We make recommendations for future modeling efforts to overcome these as yet unsolved problems.
Agglomeration in a fluid flow, when collisions of aggregates with channel walls are important is analyzed. We assume the diffusion-limited mechanism for clusters growth and the Stokes' force exerted on the agglomerates from the flow. Collisions of the particles with the channel walls are modeled by a random Poisson process. We develop an analytical theory for the size distribution of the aggregates and check the theoretical predictions by Monte Carlo simulations. The numerical data agree well with the analytical results.
We present an analysis of concentration switching times in microfluidic devices. The limits of rapid switching are analyzed based on the theory of dispersion by Taylor and Aris and compared to both experiments and numerical simulations. We focus on switching times obtained by photo-activation of caged compounds in a micro-flow (flow photolysis). The performance of flow photolysis is compared to other switching techniques. A flow chart is provided to facilitate the application of our theoretical analysis to microfluidic switching devices.
Contraction of fermionic operator circuits and the simulation of strongly correlated fermions
(2009)
A fermionic operator circuit is a product of fermionic operators of usually different and partially overlapping support. Further elements of fermionic operator circuits (FOCs) are partial traces and partial projections. The presented framework allows for the introduction of fermionic versions of known qudit operator circuits (QUOC), important for the simulation of strongly correlated d-dimensional systems: the multiscale entanglement renormalization ansaumltze (MERA), tree tensor networks (TTN), projected entangled pair states (PEPS), or their infinite-size versions (iPEPS etc.). After the definition of a FOC, we present a method to contract it with the same computation and memory requirements as a corresponding QUOC, for which all fermionic operators are replaced by qudit operators of identical dimension. A given scheme for contracting the QUOC relates to an analogous scheme for the corresponding fermionic circuit, where additional marginal computational costs arise only from reordering of modes for operators occurring in intermediate stages of the contraction. Our result hence generalizes efficient schemes for the simulation of d- dimensional spin systems, as MERA, TTN, or PEPS to the fermionic case.
We present time-dependent density matrix renormalization group simulations (t-DMRG) at finite temperatures. It is demonstrated how a combination of finite-temperature t-DMRG and time-series prediction allows for an easy and very accurate calculation of spectral functions in one-dimensional quantum systems, irrespective of their statistics for arbitrary temperatures. This is illustrated with spin structure factors of XX and XXX spin-1/2 chains. For the XX model we can compare against an exact solution, and for the XXX model (Heisenberg antiferromagnet) against a Bethe ansatz solution and quantum Monte Carlo data.
We investigate the propagation of information through one-dimensional nearest-neighbor interacting quantum spin chains in the presence of external fields which fluctuate independently on each site. We study two fundamentally different models: (i) a model with general nearest-neighbor interactions in a field which fluctuates in both strength and direction and (ii) the XX chain placed in a fluctuating field aligned in the z direction. In both cases we find that information propagation is suppressed in a way which is quite different from the suppression observed when the XX model is placed in a statically disordered field.
We report on the structural and electronic interface formation between ITO (indium-tin-oxide) and prototypical organic small molecular semiconductors, i.e., CuPc (copper phthalocyanine) and alpha-NPD (N,N'-di(naphtalen-1-yl)- N,N'-diphenyl-benzidine). In particular, the effects of in situ oxygen plasma pretreatment of the ITO surface on interface properties are examined in detail: Organic layer-thickness dependent Kelvin probe measurements revealed a good alignment of the ITO work function and the highest occupied electronic level of the organic material in all samples. In contrast, the electrical properties of hole-only and bipolar organic diodes depend strongly on the treatment of ITO prior to organic deposition. This dependence is more pronounced for diodes made of polycrystalline CuPc than for those of amorphous alpha-NPD layers. X-ray diffraction and atomic force microscopic (AFM) investigations of CuPc nucleation and growth evidenced a more pronounced texture of the polycrystalline film structure on the ITO substrate that was oxygen plasma treated prior to organic layer deposition. These findings suggest that the anisotropic electrical properties of CuPc crystallites, and their orientation with respect to the substrate, strongly affect the charge carrier injection and transport properties at the anode interface.
We perform a quantitative analysis of extensive chess databases and show that the frequencies of opening moves are distributed according to a power law with an exponent that increases linearly with the game depth, whereas the pooled distribution of all opening weights follows Zipf's law with universal exponent. We propose a simple stochastic process that is able to capture the observed playing statistics and show that the Zipf law arises from the self-similar nature of the game tree of chess. Thus, in the case of hierarchical fragmentation the scaling is truly universal and independent of a particular generating mechanism. Our findings are of relevance in general processes with composite decisions.
We present a technique for pulse recovery based on real-time measurement of the differential optical phase spectrum from spectral interference patterns. Using a phase retrieval algorithm we can obtain accurate all order polarization mode dispersion (PMD) information for the optical signal and correspondingly compensate the impairment in optical transmission lines. Linear PMD is accurately extracted from measurements, and analytical simulations show recovery of pulses distorted by higher order PMD.
When locally exciting a quantum lattice model, the excitation will propagate through the lattice. This effect is responsible for a wealth of nonequilibrium phenomena, and has been exploited to transmit quantum information. It is a commonly expressed belief that for local Hamiltonians, any such propagation happens at a finite "speed of sound". Indeed, the Lieb-Robinson theorem states that in spin models, all effects caused by a perturbation are essentially limited to a causal cone. We show that for meaningful translationally invariant bosonic models with nearest-neighbor interactions (addressing the challenging aspect of an experimental realization) this belief is incorrect: We prove that one can encounter accelerating excitations under the natural dynamics that allow for reliable transmission of information faster than any finite speed of sound. It also implies that the simulation of dynamics of strongly correlated bosonic models may be much harder than that of spin chains even in the low-energy sector.
We consider theoretically the dynamics of an oscillated sessile drop of incompressible liquid and focus on the contact line hysteresis. We address the situation of the small-amplitude and high-frequency oscillations imposed normally to the substrate surface. We deal with the drop whose equilibrium surface is hemispherical and the equilibrium contact angle equals pi/2. We apply the dynamic boundary condition that involves an ambiguous dependence of the contact angle on the contact line velocity: The contact line starts to slide only when the deviation of the contact angle exceeds a certain critical value. As a result, the stick-slip dynamics can be observed. The frequency response of surface oscillations on the substrate and at the pole of the drop are analyzed. It is shown that novel features such as the emergence of antiresonant frequency bands and nontrivial competition of different resonances are caused by contact line hysteresis.
Aims: We present a study of Nv absorption systems at 1.5 less than or similar to z less than or similar to 2.5 in the spectra of 19 QSOs, based on data obtained with the VLT/UVES instrument. Our analysis includes both the absorbers arising from the intergalactic medium, as well as systems in the vicinity of the background quasar. Methods: We construct detailed photoionization models to study the physical conditions and abundances in the absorbers and to constrain the spectral hardness of the ionizing radiation. Results: The rate of incidence for intervening Nv components is dN/dz = 3.38 +/- 0.43, corresponding to dN/dX = 1.10 +/- 0.14. The column density distribution function is fitted by the slope beta = 1.89 +/- 0.22, consistent with measurements of CIV and OVI. The narrow line widths (b(Nv) similar to 6 kms(-1)) imply photoionization rather than collisions as the dominating ionization process. The column densities of CIV and NV are correlated but show different slopes for intervening and associated absorbers, which indicates different ionizing spectra. Associated systems are found to be more metal-rich, denser, and more compact than intervening absorbers. This conclusion is independent of the adopted ionizing radiation. For the intervening NV systems we find typical values of [C/H] similar to-0.6 and n(II) similar to 10-3.6 cm(-3) and sizes of a few kpc, while for associated Nv absorbers we obtain [C/H] similar to + 0.7, n(II) similar to 10(-2.8) cm(-3) and sizes of several 10 pc. The abundance of nitrogen relative to carbon [N/C] and alpha-elements like oxygen and silicon [N/alpha] is correlated with [N/H], indicating the enrichment by secondary nitrogen. The larger scatter in [N/alpha] in intervening systems suggests an inhomogeneous enrichment of the IGM. There is an anti-correlation between [N/alpha] and [alpha/C], which could be used to constrain the initial mass function of the carbon-and nitrogen-producing stellar population.
Epitaxial ferroelectric PbZr0.2Ti0.8O3 thin films were grown by pulsed laser deposition. PbZr0.2Ti0.8O3 was doped with Cr acting as acceptor ion. Microstructural characterization was performed by (high resolution) transmission electron microscopy. The voltage dependence of polarization, dielectric constant, and leakage current were measured with respect to the Cr content. To derive the electronic properties, PZT was considered as a wide-gap semiconductor which allows treating the metal-PZT interface as a Schottky contact. The Cr was found to facilitate the elastic relaxation of the film. Furthermore, the leakage current was increased through a reduction of the Schottky barrier.
Recent efforts have applied quantum tomography techniques to the calibration and characterization of complex quantum detectors using minimal assumptions. In this work, we provide detail and insight concerning the formalism, the experimental and theoretical challenges and the scope of these tomographical tools. Our focus is on the detection of photons with avalanche photodiodes and photon-number resolving detectors and our approach is to fully characterize the quantum operators describing these detectors with a minimal set of well-specified assumptions. The formalism is completely general and can be applied to a wide range of detectors.
The behavior of weakly coupled self-sustained oscillators can often be well described by phase equations. Here we use the paradigm of Kuramoto phase oscillators which are coupled in a network to calculate first- and second-order corrections to the frequency of the fully synchronized state for nonidentical oscillators. The topology of the underlying coupling network is reflected in the eigenvalues and eigenvectors of the network Laplacian which influence the synchronization frequency in a particular way. They characterize the importance of nodes in a network and the relations between them. Expected values for the synchronization frequency are obtained for oscillators with quenched random frequencies on a class of scale-free random networks and for a Erdoumls-Reacutenyi random network. We briefly discuss an application of the perturbation theory in the second order to network structural analysis.
The Kuramoto phase-diffusion equation is a nonlinear partial differential equation which describes the spatiotemporal evolution of a phase variable in an oscillatory reaction-diffusion system. Synchronization manifests itself in a stationary phase gradient where all phases throughout a system evolve with the same velocity, the synchronization frequency. The formation of concentric waves can be explained by local impurities of higher frequency which can entrain their surroundings. Concentric waves in synchronization also occur in heterogeneous systems, where the local frequencies are distributed randomly. We present a perturbation analysis of the synchronization frequency where the perturbation is given by the heterogeneity of natural frequencies in the system. The nonlinearity in the form of dispersion leads to an overall acceleration of the oscillation for which the expected value can be calculated from the second-order perturbation terms. We apply the theory to simple topologies, like a line or sphere, and deduce the dependence of the synchronization frequency on the size and the dimension of the oscillatory medium. We show that our theory can be extended to include rotating waves in a medium with periodic boundary conditions. By changing a system parameter, the synchronized state may become quasidegenerate. We demonstrate how perturbation theory fails at such a critical point.
Femtosecond x-ray diffraction provides direct insight into the ultrafast reversible lattice dynamics of materials with a perovskite structure. Superlattice (SL) structures consisting of a sequence of nanometer-thick layer pairs allow for optically inducing a tailored stress profile that drives the lattice motions and for limiting the influence of strain propagation on the observed dynamics. We demonstrate this concept in a series of diffraction experiments with femtosecond time resolution, giving detailed information on the ultrafast lattice dynamics of ferroelectric and ferromagnetic superlattices. Anharmonically coupled lattice motions in a SrRuO3/PbZr0.2Ti0.8O3 (SRO/ PZT) SL lead to a switch-off of the electric polarizations on a time scale of the order of 1 ps. Ultrafast magnetostriction of photoexcited SRO layers is demonstrated in a SRO/SrTiO3 (STO) SL.
We investigate the dielectric properties and electric breakdown strength of subpercolative composites of conductive carbon black particles in a rubber insulating matrix. A significant increase in the permittivity in the vicinity of the insulator to conductor transition was observed, with relatively low increases in dielectric loss; however, a rapid decrease in electric breakdown strength was inevitable. A steplike feature was ascribed to agglomeration effects. The low ultimate values of the electric field strength of such composites appear to prohibit practical use.
We study the effects of parametric noise on a lattice network, which is locally modeled by a two-dimensional Rulkov map. We conclude that at some intermediate noise intensity, parametric noise can induce ordered circular patterns, which indicates the appearance of spatiotemporal coherence resonance in the studied lattice. With the observation of coherence-like manner in linear spatial cross-correlation, the coherence phenomena can be analyzed quantitatively.
We consider the dynamics of monodisperse bubbly liquid confined by two plane solid walls and subject to small- amplitude high-frequency transverse oscillations. The period of these oscillations is assumed small in comparison with typical relaxation times for a single bubble but comparable with the period of volume eigenoscillations. The time- averaged description accounting for the two-way coupling between the liquid and the bubbles and for the diffusivity of bubbles is applied. We find nonuniform steady states with the liquid quiescent on average. At relatively low frequencies, accumulation of bubbles either at the walls or in planes parallel to the walls is detected. These one- dimensional states are shown to be unstable. At relatively high frequencies, this accumulation is found at the central plane and the solution is stable.
Two well known phenomena associated with erupting filaments are the transient coronal holes that form on each side of the filament channel and the bright post-event arcade with its expanding double row of footpoints. Here we focus on a frequently overlooked signature of filament eruptions: the spike- or fan-shaped brightenings that appear to mark the far endpoints of the filament. From a sample of non-active-region filament events observed with the Extreme- Ultraviolet Imaging Telescope on the Solar and Heliospheric Observatory, we find that these brightenings usually occur near the outer edges of the transient holes, in contrast to the post-event arcades, which define their inner edges. The endpoints are often multiple and are rooted in and around strong network flux well outside the filament channel, a result that is consistent with the axial field of the filament being much stronger than the photospheric field inside the channel. The extreme ultraviolet brightenings, which are most intense at the time of maximum outward acceleration of the filament, can be used to determine unambiguously the direction of the axial field component from longitudinal magnetograms. Their location near the outer boundary of the transient holes suggests that we are observing the footprints of the current sheet formed at the leading edge of the erupting filament, as distinct from the vertical current sheet behind the filament which is the source of the post-event arcade.
Komplexe Systeme reichen von "harten", physikalischen, wie Klimaphysik, Turbulenz in Fluiden oder Plasmen bis zu so genannten "weichen", wie man sie in der Biologie, der Physik weicher Materie, Soziologie oder Ökonomie findet. Die Ausbildung von Verständnis zu einem solchen System beinhaltet eine Beschreibung in Form von Statistiken und schlussendlich mathematischen Gleichungen. Moderne Datenanalyse stellt eine große Menge von Werkzeugen zur Analyse von Komplexität auf verschiedenen Beschreibungsebenen bereit. In diesem Kurs werden statistische Methoden mit einem Schwerpunkt auf dynamischen Systemen diskutiert und eingeübt. Auf der methodischen Seite werden lineare und nichtlineare Ansätze behandelt, inklusive der Standard-Werkzeuge der deskriptiven und schlussfolgernden Statistik, Wavelet Analyse, Nichtparametrische Regression und der Schätzung nichtlinearer Maße wie fraktaler Dimensionen, Entropien und Komplexitätsmaßen. Auf der Modellierungsseite werden deterministische und stochastische Systeme, Chaos, Skalierung und das Entstehen von Komplexität durch Wechselwirkung diskutiert - sowohl für diskrete als auch für ausgedehnte Systeme. Die beiden Ansätze werden durch Systemanalyse jeweils passender Beispiele vereint.
Komplexe Systeme reichen von "harten", physikalischen, wie Klimaphysik, Turbulenz in Fluiden oder Plasmen bis zu so genannten "weichen", wie man sie in der Biologie, der Physik weicher Materie, Soziologie oder Ökonomie findet. Die Ausbildung von Verständnis zu einem solchen System beinhaltet eine Beschreibung in Form von Statistiken und schlussendlich mathematischen Gleichungen. Moderne Datenanalyse stellt eine große Menge von Werkzeugen zur Analyse von Komplexität auf verschiedenen Beschreibungsebenen bereit. In diesem Kurs werden statistische Methoden mit einem Schwerpunkt auf dynamischen Systemen diskutiert und eingeübt. Auf der methodischen Seite werden lineare und nichtlineare Ansätze behandelt, inklusive der Standard-Werkzeuge der deskriptiven und schlussfolgernden Statistik, Wavelet Analyse, Nichtparametrische Regression und der Schätzung nichtlinearer Maße wie fraktaler Dimensionen, Entropien und Komplexitätsmaßen. Auf der Modellierungsseite werden deterministische und stochastische Systeme, Chaos, Skalierung und das Entstehen von Komplexität durch Wechselwirkung diskutiert - sowohl für diskrete als auch für ausgedehnte Systeme. Die beiden Ansätze werden durch Systemanalyse jeweils passender Beispiele vereint.
Komplexe Systeme reichen von "harten", physikalischen, wie Klimaphysik, Turbulenz in Fluiden oder Plasmen bis zu so genannten "weichen", wie man sie in der Biologie, der Physik weicher Materie, Soziologie oder Ökonomie findet. Die Ausbildung von Verständnis zu einem solchen System beinhaltet eine Beschreibung in Form von Statistiken und schlussendlich mathematischen Gleichungen. Moderne Datenanalyse stellt eine große Menge von Werkzeugen zur Analyse von Komplexität auf verschiedenen Beschreibungsebenen bereit. In diesem Kurs werden statistische Methoden mit einem Schwerpunkt auf dynamischen Systemen diskutiert und eingeübt. Auf der methodischen Seite werden lineare und nichtlineare Ansätze behandelt, inklusive der Standard-Werkzeuge der deskriptiven und schlussfolgernden Statistik, Wavelet Analyse, Nichtparametrische Regression und der Schätzung nichtlinearer Maße wie fraktaler Dimensionen, Entropien und Komplexitätsmaßen. Auf der Modellierungsseite werden deterministische und stochastische Systeme, Chaos, Skalierung und das Entstehen von Komplexität durch Wechselwirkung diskutiert - sowohl für diskrete als auch für ausgedehnte Systeme. Die beiden Ansätze werden durch Systemanalyse jeweils passender Beispiele vereint.
Komplexe Systeme reichen von "harten", physikalischen, wie Klimaphysik, Turbulenz in Fluiden oder Plasmen bis zu so genannten "weichen", wie man sie in der Biologie, der Physik weicher Materie, Soziologie oder Ökonomie findet. Die Ausbildung von Verständnis zu einem solchen System beinhaltet eine Beschreibung in Form von Statistiken und schlussendlich mathematischen Gleichungen. Moderne Datenanalyse stellt eine große Menge von Werkzeugen zur Analyse von Komplexität auf verschiedenen Beschreibungsebenen bereit. In diesem Kurs werden statistische Methoden mit einem Schwerpunkt auf dynamischen Systemen diskutiert und eingeübt. Auf der methodischen Seite werden lineare und nichtlineare Ansätze behandelt, inklusive der Standard-Werkzeuge der deskriptiven und schlussfolgernden Statistik, Wavelet Analyse, Nichtparametrische Regression und der Schätzung nichtlinearer Maße wie fraktaler Dimensionen, Entropien und Komplexitätsmaßen. Auf der Modellierungsseite werden deterministische und stochastische Systeme, Chaos, Skalierung und das Entstehen von Komplexität durch Wechselwirkung diskutiert - sowohl für diskrete als auch für ausgedehnte Systeme. Die beiden Ansätze werden durch Systemanalyse jeweils passender Beispiele vereint.
Komplexe Systeme reichen von "harten", physikalischen, wie Klimaphysik, Turbulenz in Fluiden oder Plasmen bis zu so genannten "weichen", wie man sie in der Biologie, der Physik weicher Materie, Soziologie oder Ökonomie findet. Die Ausbildung von Verständnis zu einem solchen System beinhaltet eine Beschreibung in Form von Statistiken und schlussendlich mathematischen Gleichungen. Moderne Datenanalyse stellt eine große Menge von Werkzeugen zur Analyse von Komplexität auf verschiedenen Beschreibungsebenen bereit. In diesem Kurs werden statistische Methoden mit einem Schwerpunkt auf dynamischen Systemen diskutiert und eingeübt. Auf der methodischen Seite werden lineare und nichtlineare Ansätze behandelt, inklusive der Standard-Werkzeuge der deskriptiven und schlussfolgernden Statistik, Wavelet Analyse, Nichtparametrische Regression und der Schätzung nichtlinearer Maße wie fraktaler Dimensionen, Entropien und Komplexitätsmaßen. Auf der Modellierungsseite werden deterministische und stochastische Systeme, Chaos, Skalierung und das Entstehen von Komplexität durch Wechselwirkung diskutiert - sowohl für diskrete als auch für ausgedehnte Systeme. Die beiden Ansätze werden durch Systemanalyse jeweils passender Beispiele vereint.
Recent efforts have applied quantum tomography techniques to the calibration and characterization of complex quantum detectors using minimal assumptions. In this work, we provide detail and insight concerning the formalism, the experimental and theoretical challenges and the scope of these tomographical tools. Our focus is on the detection of photons with avalanche photodiodes and photon-number resolving detectors and our approach is to fully characterize the quantum operators describing these detectors with a minimal set of well-specified assumptions. The formalism is completely general and can be applied to a wide range of detectors.
We introduce a class of variational states to describe quantum many-body systems. This class generalizes matrix product states which underlie the density-matrix renormalization-group approach by combining them with weighted graph states. States within this class may (i) possess arbitrarily long-ranged two-point correlations, (ii) exhibit an arbitrary degree of block entanglement entropy up to a volume law, (iii) be taken translationally invariant, while at the same time (iv) local properties and two-point correlations can be computed efficiently. This variational class of states can be thought of as being prepared from matrix product states, followed by commuting unitaries on arbitrary constituents, hence truly generalizing both matrix product and weighted graph states. We use this class of states to formulate a renormalization algorithm with graph enhancement and present numerical examples, demonstrating that improvements over density-matrix renormalization-group simulations can be achieved in the simulation of ground states and quantum algorithms. Further generalizations, e.g., to higher spatial dimensions, are outlined.
Stripe-array diode lasers naturally operate in an anti-phase supermode. This produces a sharp double lobe far field at angles +/-alpha depending on the period of the array. In this paper a 40 emitter gain guided stripe-array laterally coupled by off-axis filtered feedback is investigated experimentally and numerically. We predict theoretically and confirm experimentally that at doubled feedback angle 2 alpha a stable higher order supermode exists with twice the number of emitters per array period. The theoretical model is based on time domain traveling wave equations for optical fields coupled to the carrier density equation taking into account diffusion of carriers. Feedback from the external reflector is modeled using Fresnel integration.
The search for experimental demonstration of the quantum behavior of macroscopic mechanical resonators is a fast growing field of investigation and recent results suggest that the generation of quantum states of resonators with a mass at the microgram scale is within reach. In this chapter we give an overview of two important topics within this research field: cooling to the motional ground state and the generation of entanglement involving mechanical, optical, and atomic degrees of freedom. We focus on optomechanical systems where the resonator is coupled to one or more driven cavity modes by the radiation-pressure interaction. We show that robust stationary entanglement between the mechanical resonator and the output fields of the cavity can be generated, and that this entanglement can be transferred to atomic ensembles placed within the cavity. These results show that optomechanical devices are interesting candidates for the realization of quantum memories and interfaces for continuous variable quantum-communication networks.
The influence of molecular architecture on light-induced SRG formation was investigated. Polymers with different degree of branching were synthesized by ATRP and functionalized with azobenzene chromophores. The polymers differ only in their architecture - linear, 4-, 6-, or 12-arms stars. The photo-induced dichroism as well as the efficiency of SRG formation was similar for all polymers of this series. New consideration for the origin of the driving force was used to explain this behavior. The comparable SRG inscription rate in differently branched polymers can be rationalized by assuming that azobenzene acts as an internal molecular motor and can cause a non-turbulent motion on a scale smaller than that on which normal entanglement restriction forces act.
It is often argued that entanglement is at the root of the speedup for quantum compared to classical computation, and that one needs a sufficient amount of entanglement for this speedup to be manifest. In measurement- based quantum computing, the need for a highly entangled initial state is particularly obvious. Defying this intuition, we show that quantum states can be too entangled to be useful for the purpose of computation, in that high values of the geometric measure of entanglement preclude states from offering a universal quantum computational speedup. We prove that this phenomenon occurs for a dramatic majority of all states: the fraction of useful n-qubit pure states is less than exp(-n(2)). This work highlights a new aspect of the role entanglement plays for quantum computational speedups.
We present accurate electromechanical measurements on a balanced push-pull dielectric elastomer actuator, demonstrating submicrometer accurate position control. An analytical model based on a simplified pure-shear dielectric elastomer film with prestretch is found to capture the voltage-displacement behavior, with reduced output due to the boundary conditions. Two complementary experiments show that actuation coefficients of 0.5-1 nm/V-2 are obtainable with the demonstrated device, enabling motion control with submicrometer accuracy in a voltage range below 200 V.
Detuning-dependent dominance of oscillation death in globally coupled synthetic genetic oscillators
(2009)
We study dynamical regimes of globally coupled genetic relaxation oscillators in the presence of small detuning. Using bifurcation analysis, we find that under strong coupling via the slow variable, the detuning can eliminate standard oscillatory solutions in a large region of the parameter space, providing the dominance of oscillation death. This result is substantially different from previous results on oscillation quenching, where for homogeneous populations, the coexistence of oscillation death and limit cycle oscillations is always present. We propose further that this effect of detuning-dependent dominance could be a powerful regulator of genetic network's dynamics.