Border effect corrections for diagonal line based recurrence quantification analysis measures

Recurrence Quantification Analysis (RQA) defines a number of quantifiers, which base upon diagonal line structures in the recurrence plot (RP). Due to the finite size of an RP, these lines can be cut by the borders of the RP and, thus, bias the length distribution of diagonal lines and, consequently, the line based RQA measures. In this letter we investigate the impact of the mentioned border effects and of the thickening of diagonal lines in an RP (caused by tangential motion) on the estimation of the diagonal line length distribution, quantified by its entropy. Although a relation to the Lyapunov spectrum is theoretically expected, the mentioned entropy yields contradictory results in many studies. Here we summarize correction schemes for both, the border effects and the tangential motion and systematically compare them to methods from the literature. We show that these corrections lead to the expected behavior of the diagonal line length entropy, in particular meaning zero values in case of a regular motion and positive values for chaotic motion. Moreover, we test these methods under noisy conditions, in order to supply practical tools for applied statistical research.     

Solitary Roll Vortices in the Mixed Convection of a Vertical Fluid Layer

Some earlier experimental and numerical findings from convection in vertical channels suggest that localized convection rolls could play a role in the transition process of free or mixed convection. In the present work solitary convection roll vortices for a vertical fluid layer with stable stratification, differential shear and differentially heated side-walls have been obtained numerically for a fluid of unit Prandtl number. The solutions appear through saddle-node bifurcations and in certain parameter ranges they do also exist for linearly stable basic flow. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of quantum many-body systems with strings of operators and Monte Carlo tensor contractions

We introduce string-bond states, a class of states obtained by placing strings of operators on a lattice, which encompasses the relevant states in quantum information. For string-bond states, expectation values of local observables can be computed efficiently using Monte Carlo sampling, making them suitable for a variational algorithm which extends the density matrix renormalization group to higher dimensional and irregular systems. Numerical results demonstrate the applicability of these states to the simulation of many-body systems.     

Investigating the formation of an adduct of formamide with dioxane by means of Raman spectroscopy

Raman experiments of formamide (FA) and p‐dioxane (DX) mixtures at different compositions were carried out. A red shift of the C O stretching band of DX was observed upon dilution, while blue shifts were observed for the C H stretching and C O C bending bands. In this latter region, the new band at ∼441 cm⁻¹, whose intensity shows large dependence on the FA concentration, has been assigned to an FA–DX adduct and it is reported for the first time in the literature. The spectral changes observed in the C O C bending region allowed to determine a proportion of 4:1 FA–DX and this experimental evidence is also presented for the first time by Raman spectroscopy. The present work shows an excellent agreement with our previous investigation, where the 2:1 FA—THF (tetrahydrofuran) adduct was characterized. Copyright © 2008 John Wiley & Sons, Ltd.     

Generation of Monodisperse Micron‐Sized Droplets using Free Adjustable Signals

This paper describes the generation of small water droplets in the size range down to a few microns. Commercially available inkjet printing devices are not suitable for producing such droplets since they produce satellite droplets. Furthermore, standard drop‐on‐demand devices are normally restricted to the generation of droplets with the same size as the orifice diameter. Using a new and more sophisticated computer‐based signal generation system, smaller‐sized droplets can be generated from the same orifice. A key feature of the design is the generation of freely definable pulses. This enables the generation of acoustic modes within the fluid of the droplet generator, which leads to the generation of droplets without satellites. Only very few pulse forms enable the generation of suitable acoustic modes. Therefore, it is necessary to look for the specific pulse corresponding to the chosen droplet generator. Flexible pulse form generation appears to be more suitable than simple pulse forms for the generation of such droplets.     

Computational difficulty of finding matrix product ground states

We determine the computational difficulty of finding ground states of one-dimensional (1D) Hamiltonians, which are known to be matrix product states (MPS). To this end, we construct a class of 1D frustration-free Hamiltonians with unique MPS ground states and a polynomial gap above, for which finding the ground state is at least as hard as factoring. Without the uniqueness of the ground state, the problem becomes NP complete, and thus for these Hamiltonians it cannot even be certified that the ground state has been found. This poses new bounds on convergence proofs for variational methods that use MPS.     

Basic design scheme for wave rotors

Pressure wave devices use shock waves to transfer energy directly between fluids without additional mechanical components, thus having the potential for increased efficiency. The wave rotor is a promising technology which uses shock waves in a self-cooled dynamic pressure exchange between fluids. For high-pressure, high-temperature topping cycles, it results in increased engine overall pressure and temperature ratio, which in turn generates higher efficiency and lower specific fuel consumption. Designing a wave rotor mainly focuses on predicting the behavior of shock and expansion waves. The extant literature presents numerous examples of wave rotor designs, but most of them rely on complicated numerical analyses as well as computer code developed specifically for this application. This paper presents an initial scheme used for designing wave rotors employing thermodynamic and gasdynamic analysis as well as computational fluid dynamic analysis. Basic theory and a simplified model of the wave rotor are used to predict the travel time and strength of waves. The model is then refined using a more advanced numerical scheme on the basis of the Lax–Wendroff method and FLUENT, a commercial CFD code.

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Research was conducted while F. Iancu was a Ph.D. candidate at Michigan State University.