A proper generalized decomposition approach for optical flow estimation

This paper introduces the use of the proper generalized decomposition (PGD) method for the optical flow (OF) problem in a classical framework of Sobolev spaces, ie, optical flow methods including a robust energy for the data fidelity term together with a quadratic penalizer for the regularization term. A mathematical study of PGD methods is first presented for general regularization problems in the framework of (Hilbert) Sobolev spaces, and their convergence is then illustrated on OF computation. The convergence study is divided in two parts: (a) the weak convergence based on the Brézis-Lieb decomposition and (b) the strong convergence based on a growth result on the sequence of descent directions. A practical PGD-based OF implementation is then proposed and evaluated on freely available OF data sets. The proposed PGD-based OF approach outperforms the corresponding non-PGD implementation in terms of both accuracy and computation time for images containing a weak level of information, namely, low image resolution and/or low signal-to-noise ratio (SNR).     

Solving nonlinear reaction–diffusion problem in electrostatic interaction with reaction-generated pH change on the kinetics of immobilized enzyme systems using Taylor series method

A mathematical model of electrostatic interaction with reaction-generated pH change on the kinetics of immobilized enzyme is discussed. The model involves the coupled system of non-linear reaction–diffusion equations of substrate and hydrogen ion. The non-linear term in this model is related to the Michaelis–Menten reaction of the substrate and non-Michaelis–Menten kinetics of hydrogen ion. The approximate analytical expression of concentration of substrate and hydrogen ion has been derived by solving the non-linear reactions using Taylor’s series method. Reaction rate and effectiveness factor are also reported. A comparison between the analytical approximation and numerical solution is also presented. The effects of external mass transfer coefficient and the electrostatic potential on the overall reaction rate were also discussed.

     

Analysis of lumps,single-stripe,breather-wave,and two-wave solutions to the generalized perturbed-KdV equation by means of Hirota’s bilinear method

In this paper, we implement the Hirota’s bilinear method to extract diverse wave profiles to the generalized perturbed-KdV equation when the test function approaches are taken into consideration. Several novel solutions such as lump-soliton, lump-periodic, single-stripe soliton, breather waves, and two-wave solutions are obtained to the proposed model. We conduct some graphical analysis including 2D and 3D plots to show the physical structures of the recovery solutions. On the other hand, this work contains a correction of previous published results for a special case of the perturbed KdV. Moreover, we investigate the significance of the nonlinearity, perturbation, and dispersion parameters being acting on the propagation of the perturbed KdV. Finally, our obtained solutions are verified by inserting them into the governing equation.

     

An exact Block–Newton algorithm for solving fluid–structure interaction problems

In this Note, we introduce a partitioned Newton based method for solving nonlinear coupled systems arising in the numerical approximation of fluid–structure interaction problems. The originality of this Schur–Newton algorithm lies in the exact Jacobians evaluation involving the fluid–structure linearized subsystems which are here fully developed. To cite this article: M.Á. Fernández, M. Moubachir, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Multilayer polarizing grating mirror used for the generation of radial polarization in Yb:YAG thin-disk lasers

The design, fabrication and characterization of a multilayer polarizing grating mirror developed for an Yb:YAG thin-disk laser resonator are reported. The potential of the proposed solution is discussed together with the first demonstration of a radially polarized Yb:YAG thin-disk laser.     

On the difference equationx_{n + 1} = \alpha + \frac{{x_n^p }}{{x_{n - 1}^p }}

We study, firstly, the dynamics of the difference equation $x_{n + 1} = \alpha + \frac{{x_n^p }}{{x_{n - 1}^p }}$ , withp ∈ (0,1) and α∈ [0, ∞). Then, we generalize our results to the (k + 1)th order difference equation $x_{n + 1} = \alpha + \frac{{x_n^p }}{{x_{n - k}^p }}$ ,k = 2, 3,... with positive initial conditions.     

Node-weighted measures for complex networks with spatially embedded,sampled, or differently sized nodes

When network and graph theory are used in the study of complex systems, a typically finite set of nodes of the network under consideration is frequently either explicitly or implicitly considered representative of a much larger finite or infinite region or set of objects of interest. The selection procedure, e.g., formation of a subset or some kind of discretization or aggregation, typically results in individual nodes of the studied network representing quite differently sized parts of the domain of interest. This heterogeneity may induce substantial bias and artifacts in derived network statistics. To avoid this bias, we propose an axiomatic scheme based on the idea of node splitting invariance to derive consistently weighted variants of various commonly used statistical network measures. The practical relevance and applicability of our approach is demonstrated for a number of example networks from different fields of research, and is shown to be of fundamental importance in particular in the study of spatially embedded functional networks derived from time series as studied in, e.g., neuroscience and climatology.     

Enhanced performance of thin-disk lasers by pumping into the zero-phonon line

Pumping Yb:YAG or Yb:LuAG into the zero-phonon line at 969?nm instead of using the common pump wavelength of 940?nm reduces the heat generation by 32%. In addition to the 3% increase of the Stokes efficiency, this significantly reduces the diffraction losses caused by the thermally induced phase distortions leading to a remarkable increase of the overall efficiency especially of fundamental-mode thin-disk lasers. Using this pumping scheme in an Yb:LuAG thin-disk laser, we achieved 742?W of nearly diffraction limited (M²≈1.5) output power at an unprecedented high optical efficiency of 58.5%. For multimode operation (M²≈15) the maximum optical efficiency of an Yb:YAG thin-disk laser was increased to 72%.     

Geometric detection of coupling directions by means of inter-system recurrence networks

We introduce a geometric method for identifying the coupling direction between two dynamical systems based on a bivariate extension of recurrence network analysis. Global characteristics of the resulting inter-system recurrence networks provide a correct discrimination for weakly coupled Rössler oscillators not yet displaying generalised synchronisation. Investigating two real-world palaeoclimate time series representing the variability of the Asian monsoon over the last 10,000 years, we observe indications for a considerable influence of the Indian summer monsoon on climate in Eastern China rather than vice versa. The proposed approach can be directly extended to studying K>2$K>2$ coupled subsystems.     

Through-bond and through-space interactions of substituents and the nonlinearity of X-C≡Y Linkages

Ab initio SCF calculations using the split valence basis sets 3–21G, 4–21G, 4–31G, 5–31G, and 3–321G, which were augmented by a set of polarization functions on the nonhydrogen atoms, were performed on a series of propynes, nitriles, isonitriles, and geminal dinitriles. Substituent effects on the structures of these molecules have been interpreted via appropriate concepts. In contrast to widespread opinion, the CC triple bond may be highly sensitive to effects of substituents, particularly when these effects are associated with -bonding interaction. This is reflected, for instance, by the appreciable contraction of the CC bond length in 1 -fluoropropyne (1 -FP) of 1.173 Å in comparison to the same bond in cyanopropyne, 1.183 Å. One of the interesting results of the present work is the markedly short C-F bond distance of 1.275 Å in 1-FP. The most acceptable rationale for this bonding behavior is provided by electrostatic arguments. The geometric results of both F₂C(CN)₂ and CF₃NC, particularly the short C-F bond distance of 1.323 Å and 1.306 Å, respectively, indicate the presence of fluorine negative hyperconjugation (anomeric effect). The characteristic nonlinearity of the C-CN chain in several geminally substituted dinitriles, YC(CN)₂, has been discussed. It appears that a relationship exists between the direction of bending of the C-CN moieties and the electronegativity of Y.