A kind of extended Korteweg-de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system

This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. It just focuses on the weakly non-linear small amplitude waves by introducing two small independent parameters: the nonlinearity ratio epsilon, represented by the ratio of amplitude to depth, and the dispersion ratio mu, represented by the square of the ratio of depth to wave length, which quantify the relative importance of nonlinearity and dispersion. It derives an extended KdV equation of the interfacial waves using the method adopted by Dullin et al in the study of the surface waves when considering the order up to O(mu(2)). As expected, the equation derived from the present work includes, as special cases, those obtained by Dullin et al for surface waves when the surface tension is neglected. The equation derived using an alternative method here is the same as the equation presented by Choi and Camassa. Also it solves the equation by borrowing the method presented by Marchant used for surface waves, and obtains its asymptotic solitary wave solutions when the weakly nonlinear and weakly dispersive terms are balanced in the extended KdV equation.

Magnetic resonance water proton relaxation in protein solutions and tissue: T(1rho) dispersion characterization.

BACKGROUND: Image contrast in clinical MRI is often determined by differences in tissue water proton relaxation behavior. However, many aspects of water proton relaxation in complex biological media, such as protein solutions and tissue are not well understood, perhaps due to the limited empirical data. PRINCIPAL FINDINGS: Water proton T(1), T(2), and T(1rho) of protein solutions and tissue were measured systematically under multiple conditions. Crosslinking or aggregation of protein decreased T(2) and T(1rho), but did not change high-field T(1). T(1rho) dispersion profiles were similar for crosslinked protein solutions, myocardial tissue, and cartilage, and exhibited power law behavior with T(1rho)(0) values that closely approximated T(2). The T(1rho) dispersion of mobile protein solutions was flat above 5 kHz, but showed a steep curve below 5 kHz that was sensitive to changes in pH. The T(1rho) dispersion of crosslinked BSA and cartilage in DMSO solvent closely resembled that of water solvent above 5 kHz but showed decreased dispersion below 5 kHz. CONCLUSIONS: Proton exchange is a minor pathway for tissue T(1) and T(1rho) relaxation above 5 kHz. Potential models for relaxation are discussed, however the same molecular mechanism appears to be responsible across 5 decades of frequencies from T(1rho) to T(1).

Asymptotic behavior at infinity of solutions of multidimensional second kind integral equations

We consider second kind integral equations of the form x(s) - (abbreviated x - K x = y ), in which Ω is some unbounded subset of Rn. Let Xp denote the weighted space of functions x continuous on Ω and satisfying x (s) = O(|s|-p ),s → ∞We show that if the kernel k(s,t) decays like |s — t|-q as |s — t| → ∞ for some sufficiently large q (and some other mild conditions on k are satisfied), then K ∈ B(XP) (the set of bounded linear operators on Xp), for 0 ≤ p ≤ q. If also (I - K)-1 ∈ B(X0) then (I - K)-1 ∈ B(XP) for 0 < p < q, and (I- K)-1∈ B(Xq) if further conditions on k hold. Thus, if k(s, t) = O(|s — t|-q). |s — t| → ∞, and y(s)=O(|s|-p), s → ∞, the asymptotic behaviour of the solution x may be estimated as x (s) = O(|s|-r), |s| → ∞, r := min(p, q). The case when k(s,t) = к(s — t), so that the equation is of Wiener-Hopf type, receives especial attention. Conditions, in terms of the symbol of I — K, for I — K to be invertible or Fredholm on Xp are established for certain cases (Ω a half-space or cone). A boundary integral equation, which models three-dimensional acoustic propaga-tion above flat ground, absorbing apart from an infinite rigid strip, illustrates the practical application and sharpness of the above results. This integral equation mod-els, in particular, road traffic noise propagation along an infinite road surface sur-rounded by absorbing ground. We prove that the sound propagating along the rigid road surface eventually decays with distance at the same rate as sound propagating above the absorbing ground.

Efficient solutions to factored MDPs with imprecise transition probabilities

When modeling real-world decision-theoretic planning problems in the Markov Decision Process (MDP) framework, it is often impossible to obtain a completely accurate estimate of transition probabilities. For example, natural uncertainty arises in the transition specification due to elicitation of MOP transition models from an expert or estimation from data, or non-stationary transition distributions arising from insufficient state knowledge. In the interest of obtaining the most robust policy under transition uncertainty, the Markov Decision Process with Imprecise Transition Probabilities (MDP-IPs) has been introduced to model such scenarios. Unfortunately, while various solution algorithms exist for MDP-IPs, they often require external calls to optimization routines and thus can be extremely time-consuming in practice. To address this deficiency, we introduce the factored MDP-IP and propose efficient dynamic programming methods to exploit its structure. Noting that the key computational bottleneck in the solution of factored MDP-IPs is the need to repeatedly solve nonlinear constrained optimization problems, we show how to target approximation techniques to drastically reduce the computational overhead of the nonlinear solver while producing bounded, approximately optimal solutions. Our results show up to two orders of magnitude speedup in comparison to traditional ""flat"" dynamic programming approaches and up to an order of magnitude speedup over the extension of factored MDP approximate value iteration techniques to MDP-IPs while producing the lowest error of any approximation algorithm evaluated. (C) 2011 Elsevier B.V. All rights reserved.

The effect of disinfectant solutions on the hardness of acrylic resin denture teeth

This investigation studied the effects of disinfectant solutions on the hardness of acrylic resin denture teeth. The occlusal surfaces of 64 resin denture teeth were ground flat with abrasives up to 400-grit silicon carbide paper. Measurements were made after polishing and after the specimens were stored in water at 37 degreesC for 48 h. The specimens were then divided into four groups and immersed in chemical disinfectants (4% chlorhexidine; 1% sodium hypochlorite and sodium perborate) for 10 min. The disinfection methods were performed twice to simulate clinical conditions and hardness measurements were made. Specimens tested as controls were immersed in water during the same disinfection time. Eight specimens were produced for each group. After desinfection procedures, testing of hardness was also performed after the samples were stored at 37 degreesC for 7, 30, 60, 90 and 120 days. Data were analysed using two-way analysis of variance (anova) and Tukey's test at 95% confidence level. According to the results, no significant differences were found between materials and immersion solutions (P > 0.05). However, a continuous decrease in hardness was noticed after ageing (P < 0.05). It was conclude that the surfaces of both acrylic resin denture teeth softened upon immersion in water regardless the disinfecting solution.

Transient non-Darcy forced convective heat transfer from a flat plate embedded in a fluid-saturated porous medium

Transient non-Darcy forced convection on a flat plate embedded in a porous medium is investigated using the Forchheimer-extended Darcy law. A sudden uniform pressure gradient is applied along the flat plate, and at the same time, its wall temperature is suddenly raised to a high temperature. Both the momentum and energy equations are solved by retaining the unsteady terms. An exact velocity solution is obtained and substituted into the energy equation, which then is solved by means of a quasi-similarity transformation. The temperature field can be divided into the one-dimensional transient (downstream) region and the quasi-steady-state (upstream) region. Thus the transient local heat transfer coefficient can be described by connecting the quasi-steady-state solution and the one-dimensional transient solution. The non-Darcy porous inertia works to decrease the velocity level and the time required for reaching the steady-state velocity level. The porous-medium inertia delays covering of the plate by the steady-state thermal boundary layer. © 1990.

Exposed Collagen In Resin Bonds to Caries-affected Dentin After Dentin Treatment with Aqueous and Alcoholic Chlorhexidine Solutions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Twinlike models for kinks and compactons in flat and warped spacetime

This work deals with the presence of twinlike models in scalar field theories. We show how to build distinct scalar field theories having the same extended solution, with the same energy density and linear stability. Here, however, we start from a given but generalized scalar field theory, and we construct the corresponding twin model, which also engenders generalized dynamics. We investigate how the twinlike models arise in both flat and curved spacetimes. In the curved spacetime, we consider a braneworld model with the warp factor controlling the spacetime geometry with a single extra dimension of infinite extent. In particular, we study linear stability in both flat and curved spacetimes, and in the case of curved spacetime-in both the gravity and the scalar field sectors-for the two braneworld models. DOI: 10.1103/PhysRevD.86.125021

Solutions to common issues in widefield microscopy: vignetting, mosaicing and depth of focus

In this thesis we have developed solutions to common issues regarding widefield microscopes, facing the problem of the intensity inhomogeneity of an image and dealing with two strong limitations: the impossibility of acquiring either high detailed images representative of whole samples or deep 3D objects. First, we cope with the problem of the non-uniform distribution of the light signal inside a single image, named vignetting. In particular we proposed, for both light and fluorescent microscopy, non-parametric multi-image based methods, where the vignetting function is estimated directly from the sample without requiring any prior information. After getting flat-field corrected images, we studied how to fix the problem related to the limitation of the field of view of the camera, so to be able to acquire large areas at high magnification. To this purpose, we developed mosaicing techniques capable to work on-line. Starting from a set of overlapping images manually acquired, we validated a fast registration approach to accurately stitch together the images. Finally, we worked to virtually extend the field of view of the camera in the third dimension, with the purpose of reconstructing a single image completely in focus, stemming from objects having a relevant depth or being displaced in different focus planes. After studying the existing approaches for extending the depth of focus of the microscope, we proposed a general method that does not require any prior information. In order to compare the outcome of existing methods, different standard metrics are commonly used in literature. However, no metric is available to compare different methods in real cases. First, we validated a metric able to rank the methods as the Universal Quality Index does, but without needing any reference ground truth. Second, we proved that the approach we developed performs better in both synthetic and real cases.

Functional and structural mapping of human cerebral cortex: Solutions are in the surfaces

The human cerebral cortex is notorious for the depth and irregularity of its convolutions and for its variability from one individual to the next. These complexities of cortical geography have been a chronic impediment to studies of functional specialization in the cortex. In this report, we discuss ways to compensate for the convolutions by using a combination of strategies whose common denominator involves explicit reconstructions of the cortical surface. Surface-based visualization involves reconstructing cortical surfaces and displaying them, along with associated experimental data, in various complementary formats (including three-dimensional native configurations, two-dimensional slices, extensively smoothed surfaces, ellipsoidal representations, and cortical flat maps). Generating these representations for the cortex of the Visible Man leads to a surface-based atlas that has important advantages over conventional stereotaxic atlases as a substrate for displaying and analyzing large amounts of experimental data. We illustrate this by showing the relationship between functionally specialized regions and topographically organized areas in human visual cortex. Surface-based warping allows data to be mapped from individual hemispheres to a surface-based atlas while respecting surface topology, improving registration of identifiable landmarks, and minimizing unwanted distortions. Surface-based warping also can aid in comparisons between species, which we illustrate by warping a macaque flat map to match the shape of a human flat map. Collectively, these approaches will allow more refined analyses of commonalities as well as individual differences in the functional organization of primate cerebral cortex.

Proposed flat-topped pulses bursts generation using all-pass multi-cavity structures

We propose a simple lossless method for the generation of flat-topped intensity pulses bursts from a single utrashort pulse. We have found optimum solutions corresponding to different numbers of cavities and burst pulses, showing that the proposed all-pass structures of optical cavities, properly designed, can generate close to flat-topped pulse busts.