Boundary Asymptotic Analysis for an Incompressible Viscous Flow: Navier Wall Laws

We consider a new way of establishing Navier wall laws. Considering a bounded domain $\Omega$ of R N , N=2,3, surrounded by a thin layer $\Sigma \epsilon$, along a part $\Gamma$2 of its boundary $\partial \Omega$, we consider a Navier-Stokes flow in $\Omega \cup \partial \Omega \cup \Sigma \epsilon$ with Reynolds' number of order 1/$\epsilon$ in $\Sigma \epsilon$. Using $\Gamma$-convergence arguments, we describe the asymptotic behaviour of the solution of this problem and get a general Navier law involving a matrix of Borel measures having the same support contained in the interface $\Gamma$2. We then consider two special cases where we characterize this matrix of measures. As a further application, we consider an optimal control problem within this context

Evaluating the impact of Hymenoscyphus fraxineus in Trentino (Alps, Northern Italy): first investigations

The spread of Hymenoscyphus fraxineus has been causing great concern regarding the survival of European ash (Fraxinus excelsior) throughout Europe since the 1990s. The disease was first recorded in Trentino (southern Alps, Italy) in 2012 and has spread throughout the mountain landscape, where ash trees are scattered in small and isolated stands in different valleys. The status of the disease was checked by monitoring the damage to natural regeneration and adult trees in 90 sites spread over the whole region. The survey confirmed the complete colonization by the pathogen of the whole investigated area, with high levels of damage to both young and adult ash trees. Regeneration (both seedlings and saplings) was observed to be affected by the fungus in 88 plots out of 90. Out of 4486 examined young European ashes, 2261 (50.4%) were affected and 789 (17.6%) were already dead. Ten of the 384 assayed flowering ashes (Fraxinus ornus) showed symptoms on branches and apical stems, similar to those observed for European ash. Isolation and molecular analysis proved the presence of the fungus on both symptomatic European and flowering ashes. The examined 386 adult trees showed different levels of damage, sometimes reaching more than 75% of the crown. Some individual trees (42) growing close to severely damaged trees appeared fully healthy, which suggests the possible existence of some resistant/tolerant individuals in the examined populations

Contribution of mixing in the ABL to new particle formation based on observations

The connection between new particle formation and micro- and mesoscale meteorology was studied based on measurements at SMEAR II station in Southern Finland. We analyzed turbulent conditions described by sodar measurements and utilized these combined with surface layer measurements and a simple model to estimate the upper boundary layer conditions. Turbulence was significantly stronger on particle formation days and the organic vapor saturation ratio increase due to large eddies was stronger on event than nonevent days. We examined which variables could be the best indicators of new particle formation and concluded that the formation probability depended on the condensation sink and temporal temperature change at the top of the atmospheric boundary layer. Humidity and heat flux may also be good indicators for particle formation

On weak convergence of locally periodic functions

We prove a generalization of the fact that periodic functions converge weakly to the mean value as the oscillation increases. Some convergence questions connected to locally periodic nonlinear boundary value problems are also considered.Comment: arxiv version is already officia

On the competitive harvesting of marine resources

The paper is concerned with the optimal harvesting of a marine resource, described by an elliptic equation with Neumann boundary conditions and a nonlinear source term. We first consider a single agent, whose harvesting effort at various locations is described by a positive Radon measure. Necessary conditions for optimality are derived, complementing the existence result proved in [A. Bressan, G. Coclite, and W. Shen, SIAM J. Control Optim., 51 (2013), pp. 1186--1202]. The second part of the paper deals with a competitive scenario, where several groups of fishermen, from different coastal towns and hence with different cost functions, harvest the same marine resource. We prove the existence of a Nash equilibrium, which is characterized in terms of a suitable variational inequality.publishe

Power calculation for gravitational radiation: oversimplification and the importance of time scale

A simplified formula for gravitational-radiation power is examined. It is shown to give completely erroneous answers in three situations, making it useless even for rough estimates. It is emphasized that short timescales, as well as fast speeds, make classical approximations to relativistic calculations untenable.Comment: Three pages, no figures, accepted for publication in Astronomische Nachrichte

Leanness as early marker of cancer of the oral cavity and pharynx

Summary Background: It is not clear whether the purported association of leanness with cancer of the oral cavity and pharynx was due to cancer-related weight loss or to the influence of factors associated with leanness. Patients and methods: Seven hundred fifty-four incident cases of cancers of the oral cavity and pharynx and 1775 controls, admitted to hospital for acute, non-neoplastic diseases, in Italy and Switzerland. Questionnaire included height, lifetime history of weight and of physical activity, waist and hip measurements, and a validated food-frequency section. Results: Leanness at diagnosis was associated with elevated risk in men (adjusted odds ratio, OR for 5-unit decrease in body-mass index, BMI = 1.9; 95% confidence interval (CI): 1.6-2.2 in men). Male cases were significantly leaner than control subjects at the age of 30 and of 50. Thinner women also had an increased risk, but the inverse association with BMI was non linear. In both sexes, the association with leanness was restricted to smokers and moderate/heavy drinkers, but was not accounted for by drinking and smoking habits, nor by differences in physical activity or dietary habits. Conclusions: Leanness appears to be an early marker of some unknown biological effect of smoking and/or of alcohol abuse, which may contribute to the prediction of cancers of the oral cavity and pharynx. Cessation of smoking and substantial reduction of alcohol intake may improve nutritional status, besides stopping carcinogen exposur

Some homogenization and corrector results for nonlinear monotone operators

This paper deals with the limit behaviour of the solutions of quasi-linear equations of the form \ \ds -\limfunc{div}\left(a\left(x, x/{\varepsilon _h},Du_h\right)\right)=f_h on $\Omega$ with Dirichlet boundary conditions. The sequence $(\varepsilon _h)$ tends to $0$ and the map $a(x,y,\xi )$ is periodic in $y$, monotone in $\xi$ and satisfies suitable continuity conditions. It is proved that $u_h\rightarrow u$ weakly in $H_0^{1,2}(\Omega )$, where $u$ is the solution of a homogenized problem \ -\limfunc{div}(b(x,Du))=f on $\Omega$. We also prove some corrector results, i.e. we find $(P_h)$ such that $Du_h-P_h(Du)\rightarrow 0$ in $L^2(\Omega ,R^n)$

Coupling techniques for nonlinear hyperbolic equations. III. The well-balanced approximation of thick interfaces

We continue our analysis of the coupling between nonlinear hyperbolic problems across possibly resonant interfaces. In the first two parts of this series, we introduced a new framework for coupling problems which is based on the so-called thin interface model and uses an augmented formulation and an additional unknown for the interface location; this framework has the advantage of avoiding any explicit modeling of the interface structure. In the present paper, we pursue our investigation of the augmented formulation and we introduce a new coupling framework which is now based on the so-called thick interface model. For scalar nonlinear hyperbolic equations in one space variable, we observe that the Cauchy problem is well-posed. Then, our main achievement in the present paper is the design of a new well-balanced finite volume scheme which is adapted to the thick interface model, together with a proof of its convergence toward the unique entropy solution (for a broad class of nonlinear hyperbolic equations). Due to the presence of a possibly resonant interface, the standard technique based on a total variation estimate does not apply, and DiPerna's uniqueness theorem must be used. Following a method proposed by Coquel and LeFloch, our proof relies on discrete entropy inequalities for the coupling problem and an estimate of the discrete entropy dissipation in the proposed scheme.Comment: 21 page