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We study localized traveling waves and chaotic states in strongly nonlinear one-dimensional Hamiltonian lattices. We show that the solitary waves are superexponentially localized and present an accurate numerical method allowing one to find them for an arbitrary nonlinearity index. Compactons evolve from rather general initially localized perturbations and collide nearly elastically. Nevertheless, on a long time scale for finite lattices an extensive chaotic state is generally observed. Because of the system's scaling, these dynamical properties are valid for any energy.
We describe the concept, the fabrication, and the most relevant properties of a piezoelectric-polymer system: Two fluoroethylenepropylene (FEP) films with good electret properties are laminated around a specifically designed and prepared polytetrafluoroethylene (PTFE) template at 300 degrees C. After removing the PTFE template, a two-layer FEP film with open tubular channels is obtained. For electric charging, the two-layer FEP system is subjected to a high electric field. The resulting dielectric barrier discharges inside the tubular channels yield a ferroelectret with high piezoelectricity. d(33) coefficients of up to 160 pC/N have already been achieved on the ferroelectret films. After charging at suitable elevated temperatures, the piezoelectricity is stable at temperatures of at least 130 degrees C. Advantages of the transducer films include ease of fabrication at laboratory or industrial scales, a wide range of possible geometrical and processing parameters, straightforward control of the uniformity of the polymer system, flexibility, and versatility of the soft ferroelectrets, and a large potential for device applications e.g., in the areas of biomedicine, communications, production engineering, sensor systems, environmental monitoring, etc.
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.
Periodically forced ensemble of nonlinearly coupled oscillators : from partial to full synchrony
(2009)
We analyze the dynamics of a periodically forced oscillator ensemble with global nonlinear coupling. Without forcing, the system exhibits complicated collective dynamics, even for the simplest case of identical phase oscillators: due to nonlinearity, the synchronous state becomes unstable for certain values of the coupling parameter, and the system settles at the border between synchrony and asynchrony, what can be denoted as partial synchrony. We find that an external common forcing can result in two synchronous states: (i) a weak forcing entrains only the mean field, whereas the individual oscillators remain unlocked to the force and, correspondingly, to the mean field; (ii) a strong forcing fully synchronizes the system, making the phases of all oscillators identical. Analytical results are confirmed by numerics.
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 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 investigate the sensitivity of a coarse resolution coupled climate model to the representation of the overflows over the Greenland-Scotland ridge. This class of models suffers from a poor representation of the water mass exchange between the Nordic Seas and the North Atlantic, a crucial part of the large-scale oceanic circulation. We revisit the explicit representation of the overflows using a parameterisation by hydraulic constraints and compare it with the enhancement of the overflow transport by artificially deepened passages over the Greenland-Scotland ridge, a common practice in coarse resolution models. Both configurations increase deep water formation in the Nordic Seas and represent the large-scale dynamics of the Atlantic realistically in contrast to a third model version with realistic sill depths but without the explicit overflow transport. The comparison of the hydrography suggests that for the unperturbed equilibrium the Nordic Seas are better represented with the parameterised overflows. As in previous studies, we do not find a stabilising effect of the overflow parameterisation on the Atlantic meridional overturning circulation but merely on the overflow transport. As a consequence the surface air temperature in the Nordic Seas is less sensitive to anomalous surface fresh water forcing. Special attention is paid to changes in the subpolar gyre circulation. We find it sensitive to the overflow transport and the density of these water masses through baroclinic adjustments. The analysis of the governing equations confirms the presence of positive feedbacks inherent to the subpolar gyre and allows us to isolate the influence of the overflows on its dynamics.
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 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.