Wigner Functions versus WKB-Methods in Multivalued Geometrical Optics

We consider the Cauchy-problem for a class of scalar linear dispersive equations with rapidly oscillating initial data. The problem of high-frequency asymptotics of such models is reviewed,in particular we highlight the difficulties in crossing caustics when using (time-dependent) WKB-methods. Using Wigner measures we present an alternative approach to such asymptotic problems. We first discuss the connection of the naive WKB solutions to transport equations of Liouville type (with mono-kinetic solutions) in the prebreaking regime. Further we show that the Wigner measure approach can be used to analyze high-frequency limits in the post-breaking regime, in comparison with the traditional Fourier integral operator method. Finally we present some illustrating examples.Comment: 38 page

On two-temperature problem for harmonic crystals

We consider the dynamics of a harmonic crystal in $d$ dimensions with $n$ components,$d,n \ge 1$. The initial date is a random function with finite mean density of the energy which also satisfies a Rosenblatt- or Ibragimov-Linnik-type mixing condition. The random function converges to different space-homogeneous processes as $x_d\to\pm\infty$, with the distributions $\mu_\pm$. We study the distribution $\mu_t$ of the solution at time $t\in\R$. The main result is the convergence of $\mu_t$ to a Gaussian translation-invariant measure as $t\to\infty$. The proof is based on the long time asymptotics of the Green function and on Bernstein's `room-corridor' argument. The application to the case of the Gibbs measures $\mu_\pm=g_\pm$ with two different temperatures $T_{\pm}$ is given. Limiting mean energy current density is $- (0,...,0,C(T_+ - T_-))$ with some positive constant $C>0$ what corresponds to Second Law

Inverse modeling of soil characteristics from surface soil moisture observations: potential and limitations

International audienceLand surface models (LSM) are widely used as scientific and operational tools to simulate mass and energy fluxes within the soil vegetation atmosphere continuum for numerous applications in meteorology, hydrology or for geobiochemistry studies. A reliable parameterization of these models is important to improve the simulation skills. Soil moisture is a key variable, linking the water and energy fluxes at the land surface. An appropriate parameterisation of soil hydraulic properties is crucial to obtain reliable simulation of soil water content from a LSM scheme. Parameter inversion techniques have been developed for that purpose to infer model parameters from soil moisture measurements at the local scale. On the other hand, remote sensing methods provide a unique opportunity to estimate surface soil moisture content at different spatial scales and with different temporal frequencies and accuracies. The present paper investigates the potential to use surface soil moisture information to infer soil hydraulic characteristics using uncertain observations. Different approaches to retrieve soil characteristics from surface soil moisture observations is evaluated and the impact on the accuracy of the model predictions is quantified. The results indicate that there is in general potential to improve land surface model parameterisations by assimilating surface soil moisture observations. However, a high accuracy in surface soil moisture estimates is required to obtain reliable estimates of soil characteristics

Treatment of Obesity in Mentally Retarded Persons: The Rehabilitator\u27s Role

Obesity is a common problem for the mentally retarded and nonretarded populations. Prevalence estimates ranging from 40 to 80 million obese Americans have been reported. The relationship between obesity and cardiovascular disease, diabetes mellitus, and other health related problems is strong. Also, the greater the degree of obesity, the higher the risk of medical problems. In addition to the health problems associated with obesity, the obese mentally retarded person is likely to be the object of increased social prejudice and nonacceptance as a result of being mentally retarded and obese. Fortunately, this solution does not need to be an intractable one. Van Itallie cited studies reporting a positive influence for weight reduction on health. Another treatment goal has been enhanced self-esteem. Given these promising outcomes for weight reduction, the field of obesity has witnessed an explosion of diet programs and exercise regimes to promote weight loss. These programs have varied in their initial success but nearly all have failed to produce long-term maintenance of weight loss. The application of behavioral procedures to the problem of obesity has produced more promising results. This approach has also been successfully extended to the mentally retarded population. This article describes the treatment rationale and procedures for a behavioral self-control package that has been developed for the obese retarded population. Implications of this approach for professionals concerned with rehabilitation efforts for mentally retarded persons will be delineated

Inverse modeling of soil characteristics from surface soil moisture observations: potential and limitations

Land surface models (LSM) are widely used as scientific and operational tools to simulate mass and energy fluxes within the soil vegetation atmosphere continuum for numerous applications in meteorology, hydrology or for geobiochemistry studies. A reliable parameterization of these models is important to improve the simulation skills. Soil moisture is a key variable, linking the water and energy fluxes at the land surface. An appropriate parameterisation of soil hydraulic properties is crucial to obtain reliable simulation of soil water content from a LSM scheme. Parameter inversion techniques have been developed for that purpose to infer model parameters from soil moisture measurements at the local scale. On the other hand, remote sensing methods provide a unique opportunity to estimate surface soil moisture content at different spatial scales and with different temporal frequencies and accuracies. The present paper investigates the potential to use surface soil moisture information to infer soil hydraulic characteristics using uncertain observations. Different approaches to retrieve soil characteristics from surface soil moisture observations is evaluated and the impact on the accuracy of the model predictions is quantified. The results indicate that there is in general potential to improve land surface model parameterisations by assimilating surface soil moisture observations. However, a high accuracy in surface soil moisture estimates is required to obtain reliable estimates of soil characteristics