Small- and waiting-time behaviour of the thin-film-equation

We consider the small-time behavior of interfaces of zero contact angle solutions to the thin-film equation. For a certain class of initial data, through asymptotic analyses, we deduce a wide variety of behavior for the free boundary point. These are supported by extensive numerical simulations. © 2007 Society for Industrial and Applied Mathematics

The Klein-Gordon equation on the half line: a Riemann-Hilbert approach

We solve an initial-boundary problem for the Klein-Gordon equation on the half line using the Riemann-Hilbert approach to solving linear boundary value problems advocated by Fokas. The approach we present can be also used to solve more complicated boundary value problems for this equation, such as problems posed on time-dependent domains. Furthermore, it can be extended to treat integrable nonlinearisations of the Klein-Gordon equation. In this respect, we briefly discuss how our results could motivate a novel treatment of the sine-Gordon equation.

A simple theoretical model for the intensification of tropical cyclones and polar lows

A simple theoretical model for the intensification of tropical cyclones and polar lows is developed using a minimal set of physical assumptions. These disturbances are assumed to be balanced systems intensifying through the WISHE (Wind-Induced Surface Heat Exchange) intensification mechanism, driven by surface fluxes of heat and moisture into an atmosphere which is neutral to moist convection. The equation set is linearized about a resting basic state and solved as an initial-value problem. A system is predicted to intensify with an exponential perturbation growth rate scaled by the radial gradient of an efficiency parameter which crudely represents the effects of unsaturated processes. The form of this efficiency parameter is assumed to be defined by initial conditions, dependent on the nature of a pre-existing vortex required to precondition the atmosphere to a state in which the vortex can intensify. Evaluation of the simple model using a primitive-equation, nonlinear numerical model provides support for the prediction of exponential perturbation growth. Good agreement is found between the simple and numerical models for the sensitivities of the measured growth rate to various parameters, including surface roughness, the rate of transfer of heat and moisture from the ocean surface, and the scale for the growing vortex.

Virtual reality Post Traumatic Stress Disorder (PTSD) exposure therapy results with active duty Iraq war combatants

Post Traumatic Stress Disorder (PTSD) is reported to be caused by traumatic events that are outside the range of usual human experience including (but not limited to) military combat, violent personal assault, being kidnapped or taken hostage and terrorist attacks. Initial data suggests that at least 1 out of 6 Iraq War veterans are exhibiting symptoms of depression, anxiety and PTSD. Virtual Reality (VR) delivered exposure therapy for PTSD has been used with reports of positive outcomes. The aim of the current paper is to present the rationale and brief description of a Virtual Iraq PTSD VR therapy application and present initial findings from its use with PTSD patients. Thus far, Virtual Iraq consists of a series of customizable virtual scenarios designed to represent relevant Middle Eastern VR contexts for exposure therapy, including a city and desert road convoy environment. User-centered design feedback needed to iteratively evolve the system was gathered from returning Iraq War veterans in the USA and from a system deployed in Iraq and tested by an Army Combat Stress Control Team. Results from an open clinical trial at San Diego Naval Medical Center of the first 18 treatment completers indicate that 14 no longer meet PTSD diagnostic criteria at post-treatment, with only one not maintaining treatment gains at 3 month follow-up. Clinical tests are also currently underway at Ft. Lewis, Emory University, Weill Cornell Medical College, Walter Reed Army Medical Center and 10 other sites. Other sites are preparing to use the application for a variety of PTSD and VR research purposes.

Virtual reality Post Traumatic Stress Disorder (PTSD) exposure therapy results with active duty OIF/OEF service members

Posttraumatic stress disorder (PTSD) is reported to be caused by exposure to traumatic events including (but not limited to) military combat, violent personal assault, being kidnapped or taken hostage and terrorist attacks. Initial data suggest that at least 1 out of 6 Iraq War veterans are exhibiting symptoms of depression, anxiety and PTSD. Virtual reality (VR) delivered exposure therapy for PTSD has been used with reports of positive outcomes. The aim of the current paper, is to present the rationale and brief description of a Virtual Iraq/Afghanistan PTSD VR therapy application and present initial findings from its use with PTSD patients. Thus far, Virtual Iraq/Afghanistan consists of a series of customizable virtual scenarios designed to represent relevant Middle Eastern VR contexts for exposure therapy, including a city and desert road convoy environment. User-centered design feedback, needed to iteratively evolve the system, was gathered from returning Iraq War veterans in the USA and from a system deployed in Iraq and tested by an Army Combat Stress Control Team. Results from an open clinical trial at San Diego Naval Medical Center of the first 20 treatment completers indicate that 16 no longer met PTSD screening criteria at post-treatment, with only one not maintaining treatment gains at 3 month follow-up.

From short-range barotropic modelling to extended-range global weather prediction: a 40-year perspective

At the end of the 20th century, we can look back on a spectacular development of numerical weather prediction, which has, practically uninterrupted, been going on since the middle of the century. High-resolution predictions for more than a week ahead for any part of the globe are now routinely produced and anyone with an Internet connection can access many of these forecasts for anywhere in the world. Extended predictions for several seasons ahead are also being done — the latest El Niño event in 1997/1998 is an example of such a successful prediction. The great achievement is due to a number of factors including the progress in computational technology and the establishment of global observing systems, combined with a systematic research program with an overall strategy towards building comprehensive prediction systems for climate and weather. In this article, I will discuss the different evolutionary steps in this development and the way new scientific ideas have contributed to efficiently explore the computing power and in using observations from new types of observing systems. Weather prediction is not an exact science due to unavoidable errors in initial data and in the models. To quantify the reliability of a forecast is therefore essential and probably more so the longer the forecasts are. Ensemble prediction is thus a new and important concept in weather and climate prediction, which I believe will become a routine aspect of weather prediction in the future. The limit between weather and climate prediction is becoming more and more diffuse and in the final part of this article I will outline the way I think development may proceed in the future.

Instantaneous gelation in Smoluchowski’s coagulation equation revisited

We study the solutions of the Smoluchowski coagulation equation with a regularization term which removes clusters from the system when their mass exceeds a specified cutoff size, M. We focus primarily on collision kernels which would exhibit an instantaneous gelation transition in the absence of any regularization. Numerical simulations demonstrate that for such kernels with monodisperse initial data, the regularized gelation time decreasesas M increases, consistent with the expectation that the gelation time is zero in the unregularized system. This decrease appears to be a logarithmically slow function of M, indicating that instantaneously gelling kernels may still be justifiable as physical models despite the fact that they are highly singular in the absence of a cutoff. We also study the case when a source of monomers is introduced in the regularized system. In this case a stationary state is reached. We present a complete analytic description of this regularized stationary state for the model kernel, K(m1,m2)=max{m1,m2}ν, which gels instantaneously when M→∞ if ν>1. The stationary cluster size distribution decays as a stretched exponential for small cluster sizes and crosses over to a power law decay with exponent ν for large cluster sizes. The total particle density in the stationary state slowly vanishes as [(ν−1)logM]−1/2 when M→∞. The approach to the stationary state is nontrivial: Oscillations about the stationary state emerge from the interplay between the monomer injection and the cutoff, M, which decay very slowly when M is large. A quantitative analysis of these oscillations is provided for the addition model which describes the situation in which clusters can only grow by absorbing monomers.

On the structure of infinity-harmonic maps

Let H ∈ C 2(ℝ N×n ), H ≥ 0. The PDE system arises as the Euler-Lagrange PDE of vectorial variational problems for the functional E ∞(u, Ω) = ‖H(Du)‖ L ∞(Ω) defined on maps u: Ω ⊆ ℝ n → ℝ N . (1) first appeared in the author's recent work. The scalar case though has a long history initiated by Aronsson. Herein we study the solutions of (1) with emphasis on the case of n = 2 ≤ N with H the Euclidean norm on ℝ N×n , which we call the “∞-Laplacian”. By establishing a rigidity theorem for rank-one maps of independent interest, we analyse a phenomenon of separation of the solutions to phases with qualitatively different behaviour. As a corollary, we extend to N ≥ 2 the Aronsson-Evans-Yu theorem regarding non existence of zeros of |Du| and prove a maximum principle. We further characterise all H for which (1) is elliptic and also study the initial value problem for the ODE system arising for n = 1 but with H(·, u, u′) depending on all the arguments.

Discontinuous local semiflows for Kurzweil equations leading to LaSalle`s invariance principle for differential systems with impulses at variable times

In this paper, we consider an initial value problem for a class of generalized ODEs, also known as Kurzweil equations, and we prove the existence of a local semidynamical system there. Under certain perturbation conditions, we also show that this class of generalized ODEs admits a discontinuous semiflow which we shall refer to as an impulsive semidynamical system. As a consequence, we obtain LaSalle`s invariance principle for such a class of generalized ODEs. Due to the importance of LaSalle`s invariance principle in studying stability of differential systems, we include an application to autonomous ordinary differential systems with impulse action at variable times. (C) 2011 Elsevier Inc. All rights reserved.

Internal validity of the Swedish Maternal Health Care Register

Background: The Swedish Maternal Health Care Register (MHCR) is a national quality register that has been collecting pregnancy, delivery, and postpartum data since 1999. A substantial revision of the MHCR resulted in a Web-based version of the register in 2010. Although MHCR provides data for health care services and research, the validity of the MHCR data has not been evaluated. This study investigated degree of coverage and internal validity of specific variables in the MHCR and identified possible systematic errors. Methods: This cross-sectional observational study compared pregnancy and delivery data in medical records with corresponding data in the MHCR. The medical record was considered the gold standard. The medical records from nine Swedish hospitals were selected for data extraction. This study compared data from 878 women registered in both medical records and in the MHCR. To evaluate the quality of the initial data extraction, a second data extraction of 150 medical records was performed. Statistical analyses were performed for degree of coverage, agreement and correlation of data, and sensitivity and specificity. Results: Degree of coverage of specified variables in the MHCR varied from 90.0% to 100%. Identical information in both medical records and the MHCR ranged from 71.4% to 99.7%. For more than half of the investigated variables, 95% or more of the information was identical. Sensitivity and specificity were analysed for binary variables. Probable systematic errors were identified for two variables. Conclusions: When comparing data from medical records and data registered in the MHCR, most variables in the MHCR demonstrated good to very good degree of coverage, agreement, and internal validity. Hence, data from the MHCR may be regarded as reliable for research as well as for evaluating, planning, and decision-making with respect to Swedish maternal health care services.

Multivariate analysis for the classification and differentiation of Madeira wines according to main grape varieties

In order to differentiate and characterize Madeira wines according to main grape varieties, the volatile composition (higher alcohols, fatty acids, ethyl esters and carbonyl compounds) was determined for 36 monovarietal Madeira wine samples elaborated from Boal, Malvazia, Sercial and Verdelho white grape varieties. The study was carried out by headspace solid-phase microextraction technique (HS-SPME), in dynamic mode, coupled with gas chromatography–mass spectrometry (GC–MS). Corrected peak area data for 42 analytes from the above mentioned chemical groups was used for statistical purposes. Principal component analysis (PCA) was applied in order to determine the main sources of variability present in the data sets and to establish the relation between samples (objects) and volatile compounds (variables). The data obtained by GC–MS shows that the most important contributions to the differentiation of Boal wines are benzyl alcohol and (E)-hex-3-en-1-ol. Ethyl octadecanoate, (Z)-hex-3-en-1-ol and benzoic acid are the major contributions in Malvazia wines and 2-methylpropan-1-ol is associated to Sercial wines. Verdelho wines are most correlated with 5-(ethoxymethyl)-furfural, nonanone and cis-9-ethyldecenoate. A 96.4% of prediction ability was obtained by the application of stepwise linear discriminant analysis (SLDA) using the 19 variables that maximise the variance of the initial data set.

Unicidade e discretização para problemas de valor inicial

This paper has two objectives: (i) conducting a literature search on the criteria of uniqueness of solution for initial value problems of ordinary differential equations. (ii) a modification of the method of Euler that seems to be able to converge to a solution of the problem, if the solution is not unique

A mass-transportation approach to a one dimensional fluid mechanics model with nonlocal velocity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

High precision GPS network with precise ephemerides and earth body tide model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Avaliação clínica e microbiológica da irrigação subgengival com iodo-povidine 10% como adjunto à terapia periodontal não-cirúrgica

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)