Oscillation-free method for semilinear diffusion equations under noisy initial conditions

Noise in initial conditions from measurement errors can create unwanted oscillations which propagate in numerical solutions. We present a technique of prohibiting such oscillation errors when solving initial-boundary-value problems of semilinear diffusion equations. Symmetric Strang splitting is applied to the equation for solving the linear diffusion and nonlinear remainder separately. An oscillation-free scheme is developed for overcoming any oscillatory behavior when numerically solving the linear diffusion portion. To demonstrate the ills of stable oscillations, we compare our method using a weighted implicit Euler scheme to the Crank-Nicolson method. The oscillation-free feature and stability of our method are analyzed through a local linearization. The accuracy of our oscillation-free method is proved and its usefulness is further verified through solving a Fisher-type equation where oscillation-free solutions are successfully produced in spite of random errors in the initial conditions.Comment: 19 pages, 9 figure

Numerical simulation of EHD flows using Discontinuous Galerkin Finite Element methods

The aim of this paper is to explore the capability of Discontinuous Galerkin Finite Element methods to solve numerically the charge transport equation in EHD convective flows, in both strong and weak injection regimes. These methods are especially suited to treat purely hyperbolic problems, as it is the charge transport equation in most EHD problems. We consider the 2D electroconvective flow between two parallel plates. We compare our com- putations with the analytical results in the hydrostatic regime, the linear and non-linear stability analysis, computing both the electric and velocity fields. The stability of the finite amplitude electroconvection is also anal- ysed. Comparisons are made with computations in the literature obtained with other numerical techniques. The results show that DG-FEM are a very good alternative to simulate numerically EHD convective flows

Eigenvector Model Descriptors for Solving an Inverse Problem of Helmholtz Equation: Extended Materials

We study the seismic inverse problem for the recovery of subsurface properties in acoustic media. In order to reduce the ill-posedness of the problem, the heterogeneous wave speed parameter to be recovered is represented using a limited number of coefficients associated with a basis of eigenvectors of a diffusion equation, following the regularization by discretization approach. We compare several choices for the diffusion coefficient in the partial differential equations, which are extracted from the field of image processing. We first investigate their efficiency for image decomposition (accuracy of the representation with respect to the number of variables and denoising). Next, we implement the method in the quantitative reconstruction procedure for seismic imaging, following the Full Waveform Inversion method, where the difficulty resides in that the basis is defined from an initial model where none of the actual structures is known. In particular, we demonstrate that the method is efficient for the challenging reconstruction of media with salt-domes. We employ the method in two and three-dimensional experiments and show that the eigenvector representation compensates for the lack of low frequency information, it eventually serves us to extract guidelines for the implementation of the method.Comment: 45 pages, 37 figure

Exploration of the functional consequences of fixational eye movements in the absence of a fovea.

A recent theory posits that ocular drifts of fixational eye movements serve to reformat the visual input of natural images, so that the power of the input image is equalized across a range of spatial frequencies. This "spectral whitening" effect is postulated to improve the processing of high-spatial-frequency information and requires normal fixational eye movements. Given that people with macular disease exhibit abnormal fixational eye movements, do they also exhibit spectral whitening? To answer this question, we computed the power spectral density of movies of natural images translated in space and time according to the fixational eye movements (thus simulating the retinal input) of a group of observers with long-standing bilateral macular disease. Just as for people with normal vision, the power of the retinal input at low spatial frequencies was lower than that based on the 1/f2 relationship, demonstrating spectral whitening. However, the amount of whitening was much less for observers with macular disease when compared with age-matched controls with normal vision. A mediation analysis showed that the eccentricity of the preferred retinal locus adopted by these observers and the characteristics of ocular drifts are important factors limiting the amount of whitening. Finally, we did not find a normal aging effect on spectral whitening. Although these findings alone cannot form a causal link between macular disease and spectral properties of eye movements, they suggest novel potential means of modifying the characteristics of fixational eye movements, which may in turn improve functional vision for people with macular disease

Heavy Quark Momentum Diffusion Coefficient from Lattice QCD

The momentum diffusion coefficient for heavy quarks is studied in a deconfined gluon plasma in the static approximation by investigating a correlation function of the color electric field using Monte Carlo techniques. The diffusion coefficient is extracted from the long distance behavior of such a correlator. For temperatures Tc < T <~ 2 Tc, our nonperturbative estimate of the diffusion coefficient is found to be very different from the leading order perturbation theory, and is in the right ballpark to explain the heavy quark flow seen by PHENIX at RHIC.Comment: Minor changes, version to appear in Physical Review

Color image segmentation using a spatial k-means clustering algorithm

This paper details the implementation of a new adaptive technique for color-texture segmentation that is a generalization of the standard K-Means algorithm. The standard K-Means algorithm produces accurate segmentation results only when applied to images defined by homogenous regions with respect to texture and color since no local constraints are applied to impose spatial continuity. In addition, the initialization of the K-Means algorithm is problematic and usually the initial cluster centers are randomly picked. In this paper we detail the implementation of a novel technique to select the dominant colors from the input image using the information from the color histograms. The main contribution of this work is the generalization of the K-Means algorithm that includes the primary features that describe the color smoothness and texture complexity in the process of pixel assignment. The resulting color segmentation scheme has been applied to a large number of natural images and the experimental data indicates the robustness of the new developed segmentation algorithm

Novel Findings about Double-Loaded Curcumin-in-HPβcyclodextrin-in Liposomes: Effects on the Lipid Bilayer and Drug Release

In this study, the encapsulation of curcumin (Cur) in “drug-in-cyclodextrin-in-liposomes (DCL)” by following the double-loading technique (DL) was proposed, giving rise to DCL–DL. The aim was to analyze the effect of cyclodextrin (CD) on the physicochemical, stability, and drug-release properties of liposomes. After selecting didodecyldimethylammonium bromide (DDAB) as the cationic lipid, DCL–DL was formulated by adding 2-hydroxypropyl-α/β/γ-CD (HPβCD)–Cur complexes into the aqueous phase. A competitive effect of cholesterol (Cho) for the CD cavity was found, so cholesteryl hemisuccinate (Chems) was used. The optimal composition of the DCL–DL bilayer was obtained by applying Taguchi methodology and regression analysis. Vesicles showed a lower drug encapsulation efficiency compared to conventional liposomes (CL) and CL containing HPβCD in the aqueous phase. However, the presence of HPβCD significantly increased vesicle deformability and Cur antioxidant activity over time. In addition, drug release profiles showed a sustained release after an initial burst effect, fitting to the Korsmeyer-Peppas kinetic model. Moreover, a direct correlation between the area under the curve (AUC) of dissolution profiles and flexibility of liposomes was obtained. It can be concluded that these “drug-in-cyclodextrin-in-deformable” liposomes in the presence of HPβCD may be a promising carrier for increasing the entrapment efficiency and stability of Cur without compromising the integrity of the liposome bilayer