Motion of a droplet for the mass-conserving stochastic Allen-Cahn equation

We study the stochastic mass-conserving Allen-Cahn equation posed on a bounded two-dimensional domain with additive spatially smooth space-time noise. This equation associated with a small positive parameter describes the stochastic motion of a small almost semicircular droplet attached to domain's boundary and moving towards a point of locally maximum curvature. We apply It\^o calculus to derive the stochastic dynamics of the droplet by utilizing the approximately invariant manifold introduced by Alikakos, Chen and Fusco for the deterministic problem. In the stochastic case depending on the scaling, the motion is driven by the change in the curvature of the boundary and the stochastic forcing. Moreover, under the assumption of a sufficiently small noise strength, we establish stochastic stability of a neighborhood of the manifold of droplets in $L^2$ and $H^1$, which means that with overwhelming probability the solution stays close to the manifold for very long time-scales

Existence and regularity of solution for a Stochastic CahnHilliard / Allen-Cahn equation with unbounded noise diffusion

The Cahn-Hilliard/Allen-Cahn equation with noise is a simplified mean field model of stochastic microscopic dynamics associated with adsorption and desorption-spin flip mechanisms in the context of surface processes. For such an equation we consider a multiplicative space-time white noise with diffusion coefficient of linear growth. Applying technics from semigroup theory, we prove local existence and uniqueness in dimensions d = 1,2,3. Moreover, when the diffusion coefficient satisfies a sub-linear growth condition of order α bounded by 1 3, which is the inverse of the polynomial order of the nonlinearity used, we prove for d = 1 global existence of solution. Path regularity of stochastic solution, depending on that of the initial condition, is obtained a.s. up to the explosion time. The path regularity is identical to that proved for the stochastic Cahn-Hilliard equation in the case of bounded noise diffusion. Our results are also valid for the stochastic Cahn-Hilliard equation with unbounded noise diffusion, for which previous results were established only in the framework of a bounded diffusion coefficient. As expected from the theory of parabolic operators in the sense of Petrovsk˘ıı, the bi-Laplacian operator seems to be dominant in the combined model

Musculoskeletal disorders in shipyard industry: prevalence, health care use, and absenteeism

BACKGROUND: It is unclear whether the well-known risk factors for the occurrence of musculoskeletal disorders (MSD) also play an important role in the determining consequences of MSD in terms of sickness absence and health care use. METHODS: A cross-sectional study was conducted among 853 shipyard employees. Data were collected by questionnaire on physical and psychosocial workload, need for recovery, perceived general health, occurrence of musculoskeletal complaints, and health care use during the past year. Retrospective data on absenteeism were also available from the company register. RESULTS: In total, 37%, 22%, and 15% of employees reported complaints of low back, shoulder/neck, and hand/wrist during the past 12 months, respectively. Among all employees with at least one MSD, 27% visited a physician at least once and 20% took at least one period of sick leave. Various individual and work-related factors were associated with the occurrence of MSD. Health care use and absenteeism were strongest influenced by chronicity of musculoskeletal complaints and comorbidity with other musculoskeletal complaints and, to a lesser extent, by work-related factors. CONCLUSION: In programmes aimed at preventing the unfavourable consequences of MSD in terms of sickness absence and health care use it is important to identify the (individual) factors that determine the development of chronicity of complaints. These factors may differ from the well-know risk factors for the occurrence of MSD that are targeted in primary prevention

Measuring the burden of herpes zoster and post herpetic neuralgia within primary care in rural Crete, Greece

<p>Abstract</p> <p>Background</p> <p>Research has indicated that general practitioners (GPs) have good clinical judgment in regards to diagnosing and managing herpes zoster (HZ) within clinical practice in a country with limited resources for primary care and general practice. The objective of the current study was to assess the burden of HZ and post herpetic neuralgia (PHN) within rural general practices in Crete, Greece.</p> <p>Methods</p> <p>The current study took place within a rural setting in Crete, Greece during the period of November 2007 to November 2009 within the catchment area in which the Cretan Rural Practice-based Research Network is operating. In total 19 GP's from 14 health care units in rural Crete were invited to participate, covering a total turnover patient population of approximately 25, 000 subjects. For the purpose of this study an electronic record database was constructed and used as the main tool for monitoring HZ and PHN incidence. Stress related data was also collected with the use of the Short Anxiety Screening Test (SAST).</p> <p>Results</p> <p>The crude incidence rate of HZ was 1.4/1000 patients/year throughout the entire network of health centers and satellite practices, while among satellite practices alone it was calculated at 1.3/1000 patients/year. Additionally, the standardised incidence density within satellite practices was calculated at 1.6/1000 patients/year. In regards to the stress associated with HZ and PHN, the latter were found to have lower levels of anxiety, as assessed through the SAST score (17.4 ± 3.9 vs. 21.1 ± 5.7; <it>p </it>= 0.029).</p> <p>Conclusions</p> <p>The implementation of an electronic surveillance system was feasible so as to measure the burden of HZ and PHN within the rural general practice setting in Crete.</p

Front Motion in the One-Dimensional Stochastic Cahn-Hilliard Equation

In this paper, we consider the one-dimensional Cahn-Hilliard equation perturbed by additive noise and study the dynamics of interfaces for the new stochastic model. The noise is smooth in space and is defined as a Fourier series with independent Brownian motions in time. Motivated by the work of Bates & Xun on slow manifolds for the integrated Cahn-Hilliard equation, our analysis reveals the significant difficulties and differences in comparison with the deterministic problem. New higher order terms, that we estimate, appear due to Itô calculus and stochastic integration dominating the exponentially slow deterministic dynamics of the interfaces. We derive a first order linear system of stochastic ordinary differential equations approximating the equations of front motion. Furthermore, we prove stochastic stability for the approximate slow manifold of solutions on a very long time scale and evaluate the noise effect

The Sharp Interface Limit for the Stochastic Cahn-Hilliard Equation

We study the two and three dimensional stochastic Cahn-Hilliard equation in the sharp interface limit, where the positive parameter ε tends to zero, which measures the width of transition layers generated during phase separation. We also couple the noise strength to this parameter. Using formal asymptotic expansions, we identify the limit. In the right scaling we indicate that the solutions of stochastic Cahn-Hilliard converge to a solution of a Hele-Shaw problem with stochastic forcing. In the case when the noise is sufficiently small, we rigorously prove that the limit is a deterministic Hele-Shaw problem. Finally, we discuss which estimates are necessary in order to extend the rigorous result to larger noise strength

EXISTENCE AND REGULARITY OF SOLUTION FOR A STOCHASTIC CAHN-HILLIARD/ALLEN-CAHN EQUATION WITH UNBOUNDED NOISE DIFFUSION

Abstract. The Cahn-Hilliard/Allen-Cahn equation with noise is a simplified mean field model of stochastic microscopic dynamics associated with adsorption and desorption-spin flip mechanisms in the context of surface processes. For such an equation we consider a multiplicative space-time white noise with diffusion coefficient of sub-linear growth. Using technics from semigroup theory, we prove existence, and path regularity of stochastic solution depending on that of the initial condition. Our results are also valid for the stochastic Cahn-Hilliard equation with unbounded noise diffusion, for which previous results were established only in the framework of a bounded diffusion coefficient. We prove that the path regularity of stochastic solution depends on that of the initial condition, and are identical to those proved for the stochastic Cahn-Hilliard equation and a bounded noise diffusion coefficient. If the initial condition vanishes, they are strictly less than 2 − d 2 in time. As expected from the theory of parabolic operators in the sense of Petrovskĭı, the bi-Laplacian operator seems to be dominant in the combined model. in space and 1

The multi-dimensional stochastic Stefan financial model for a portfolio of assets

From Crossref journal articles via Jisc Publications RouterPublication status: Published&lt;p style='text-indent:20px;'&gt;The financial model proposed involves the liquidation process of a portfolio through sell / buy orders placed at a price &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$x\in\mathbb{R}^n$\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;, with volatility. Its rigorous mathematical formulation results to an &lt;inline-formula&gt;&lt;tex-math id="M3"&gt;\begin{document}$n$\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;-dimensional outer parabolic Stefan problem with noise. The moving boundary encloses the areas of zero trading. We will focus on a case of financial interest when one or more markets are considered. We estimate the areas of zero trading with diameter approximating the minimum of the &lt;inline-formula&gt;&lt;tex-math id="M4"&gt;\begin{document}$n$\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; spreads for orders from the limit order books. In dimensions &lt;inline-formula&gt;&lt;tex-math id="M5"&gt;\begin{document}$n = 3$\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;, for zero volatility, this problem stands as a mean field model for Ostwald ripening, and has been proposed and analyzed by Niethammer in [&lt;xref ref-type="bibr" rid="b25"&gt;25&lt;/xref&gt;], and in [&lt;xref ref-type="bibr" rid="b7"&gt;7&lt;/xref&gt;]. We propose a spherical moving boundaries approach where the zero trading area consists of a union of spherical domains centered at portfolios various prices with radii representing the half of the minimum spread. We apply Itô calculus and provide second order formal asymptotics for the stochastic dynamics of the spreads that seem to disconnect the financial model from a large diffusion assumption on the liquidity coefficient of the Laplacian that would correspond to an increased trading density. Moreover, we solve the approximating systems numerically.&lt;/p&gt