Abstract:
This study focuses on modeling hydrological responses of shallow hillslope soil in a headwater catchment. The research is conducted using data from the experimental site Uhlí ská in Jizera Mountains, Czech Republic. To compare different approaches of runoff generation modeling, three models were used: (1) one-dimensional variably saturated flow model S1D, based on the dual-continuum formulation of Richards' equation; (2) zero-dimensional nonlinear morphological element model GEOTRANSF; and (3) semi-distributed model utilizing the topographic index similarity assumption - TOPMODEL. Hillslope runoff hydrographs and soil water storage variations predicted by the simplified catchment scale models (GEOTRANSF and TOPMODEL) were compared with the respective responses generated by the more physically based local scale model S1D. Both models, GEOTRANSF and TOPMODEL, were found to predict general trends of hydrographs quite satisfactorily; however their ability to correctly predict soil water storages and inter-compartment fluxes was limited.

Abstract:
a method for determining soil hydraulic properties of a weathered tropical soil (oxisol) using a medium-sized column with undisturbed soil is presented. the method was used to determine fitting parameters of the water retention curve and hydraulic conductivity functions of a soil column in support of a pesticide leaching study. the soil column was extracted from a continuously-used research plot in central oahu (hawaii, usa) and its internal structure was examined by computed tomography. the experiment was based on tension infiltration into the soil column with free outflow at the lower end. water flow through the soil core was mathematically modeled using a computer code that numerically solves the one-dimensional richards equation. measured soil hydraulic parameters were used for direct simulation, and the retention and soil hydraulic parameters were estimated by inverse modeling. the inverse modeling produced very good agreement between model outputs and measured flux and pressure head data for the relatively homogeneous column. the moisture content at a given pressure from the retention curve measured directly in small soil samples was lower than that obtained through parameter optimization based on experiments using a medium-sized undisturbed soil column.

Abstract:
The most significant problems of acoustic echo canceller (AEC) realizations are high computational complexity and insufficient convergence rate of the applied adaptive algorithms. From the analysis of the frequency domain block adaptive filter [2,3] realization and the modified subband acoustic echo canceller [6] the generalized frequency domain adaptive filter [8,9] has been derived. The result of simulations is demonstrated the efficiency of this algorithm for a stationary noise and real speech signal excitation.

Abstract:
This paper constructs perfectly matched layers (PML) for a system of 2D Coupled Nonlinear Schr\"odinger equations with mixed derivatives which arises in the modeling of gap solitons in nonlinear periodic structures with a non-separable linear part. The PML construction is performed in Laplace Fourier space via a modal analysis and can be viewed as a complex change of variables. The mixed derivatives cause the presence of waves with opposite phase and group velocities, which has previously been shown to cause instability of layer equations in certain types of hyperbolic problems. Nevertheless, here the PML is stable if the absorption function $\sigma$ lies below a specified threshold. The PML construction and analysis are carried out for the linear part of the system. Numerical tests are then performed in both the linear and nonlinear regimes checking convergence of the error with respect to the layer width and showing that the PML performs well even in many nonlinear simulations.

Abstract:
The paper studies asymptotics of moving gap solitons in nonlinear periodic structures of finite contrast ("deep grating") within the one dimensional periodic nonlinear Schr\"odinger equation (PNLS). Periodic structures described by a finite band potential feature transversal crossings of band functions in the linear band structure and a periodic perturbation of the potential yields new small gaps. Novel gap solitons with O(1) velocity despite the deep grating are presented in these gaps. An approximation of gap solitons is given by slowly varying envelopes which satisfy a system of generalized Coupled Mode Equations (gCME) and by Bloch waves at the crossing point. The eigenspace at the crossing point is two dimensional and it is necessary to select Bloch waves belonging to the two band functions. This is achieved by an optimization algorithm. Traveling solitary wave solutions of the gCME then result in nearly solitary wave solutions of PNLS moving at an O(1) velocity across the periodic structure. A number of numerical tests are performed to confirm the asymptotics.

Abstract:
The addition of an aqueous extract from fruitbodies of Tylopilus felleus to tissue cultures of Holarrhena antidysenterica (Apocynaceae) caused the accumulation of an unknown compound in the culture medium. The compound was isolated and identified as 5-hydroxymethyl-2-furancarboxaldehyde (1). Moreover, biosynthesis of phenolic compounds was stimulated in response to the stress agents of the fungal preparation. Methyl ferulate (2) was the major phenolic constituent.

Abstract:
Gap solitons near a band edge of a spatially periodic nonlinear PDE can be formally approximated by solutions of Coupled Mode Equations (CMEs). Here we study this approximation for the case of the 2D Periodic Nonlinear Schr\"{o}dinger / Gross-Pitaevskii Equation with a non-separable potential of finite contrast. We show that unlike in the case of separable potentials [T. Dohnal, D. Pelinovsky, and G. Schneider, J. Nonlin. Sci. {\bf 19}, 95--131 (2009)] the CME derivation has to be carried out in Bloch rather than physical coordinates. Using the Lyapunov-Schmidt reduction we then give a rigorous justification of the CMEs as an asymptotic model for reversible non-degenerate gap solitons and even potentials and provide $H^s$ estimates for this approximation. The results are confirmed by numerical examples including some new families of CMEs and gap solitons absent for separable potentials.

Abstract:
Many physical systems can be described by nonlinear eigenvalues and bifurcation problems with a linear part that is non-selfadjoint e.g. due to the presence of loss and gain. The balance of these effects is reflected in an antilinear symmetry, like e.g. the PT-symmetry, of the problem. Under this condition we show that the nonlinear eigenvalues bifurcating from real linear eigenvalues remain real and the corresponding nonlinear eigenfunctions remain symmetric. The abstract results are applied in a number of physical models of Bose-Einstein condensation, nonlinear optics and superconductivity, and further numerical analysis is performed.

Abstract:
The nonlinear Schr\"{o}dinger equation with a linear periodic potential and a nonlinearity coefficient $\Gamma$ with a discontinuity supports stationary localized solitary waves with frequencies inside spectral gaps, so called surface gap solitons (SGSs). We compute families of 1D SGSs using the arclength continuation method for a range of values of the jump in $\Gamma$. Using asymptotics, we show that when the frequency parameter converges to the bifurcation gap edge, the size of the allowed jump in $\Gamma$ converges to 0 for SGSs centered at any $x_c\in \R$. Linear stability of SGSs is next determined via the numerical Evans function method, in which the stable and unstable manifolds corresponding to the 0 solution of the linearized spectral ODE problem need to be evolved. Zeros of the Evans function coincide with eigenvalues of the linearized operator. Far from the SGS center the manifolds are spanned by exponentially decaying/increasing Bloch functions. Evolution of the manifolds suffers from stiffness but a numerically stable formulation is possible in the exterior algebra formulation and with the use of Grassmanian preserving ODE integrators. Eigenvalues with positive real part above a small constant are then detected using the complex argument principle and a contour parallel to the imaginary axis. The location of real eigenvalues is found via a straightforward evaluation of the Evans function along the real axis and several complex eigenvalues are located using M\"{u}ller's method. The numerical Evans function method is described in detail. Our results show the existence of both unstable and stable SGSs (possibly with a weak instability), where stability is obtained even for some SGSs centered in the domain half with the less focusing nonlinearity. Direct simulations of the PDE for selected SGS examples confirm the results of Evans function computations.

Abstract:
We demonstrate existence of waves localized at the interface of two nonlinear periodic media with different coefficients of the cubic nonlinearity via the one-dimensional Gross--Pitaevsky equation. We call these waves the surface gap solitons (SGS). In the case of smooth symmetric periodic potentials, we study analytically bifurcations of SGS's from standard gap solitons and determine numerically the maximal jump of the nonlinearity coefficient allowing for the SGS existence. We show that the maximal jump vanishes near the thresholds of bifurcations of gap solitons. In the case of continuous potentials with a jump in the first derivative at the interface, we develop a homotopy method of continuation of SGS families from the solution obtained via gluing of parts of the standard gap solitons and study existence of SGS's in the photonic band gaps. We explain the termination of the SGS families in the interior points of the band gaps from the bifurcation of linear bound states in the continuous non-smooth potentials.