Efficient Resolution of Anisotropic Structures

We highlight some recent new delevelopments concerning the sparse representation of possibly high-dimensional functions exhibiting strong anisotropic features and low regularity in isotropic Sobolev or Besov scales. Specifically, we focus on the solution of transport equations which exhibit propagation of singularities where, additionally, high-dimensionality enters when the convection field, and hence the solutions, depend on parameters varying over some compact set. Important constituents of our approach are directionally adaptive discretization concepts motivated by compactly supported shearlet systems, and well-conditioned stable variational formulations that support trial spaces with anisotropic refinements with arbitrary directionalities. We prove that they provide tight error-residual relations which are used to contrive rigorously founded adaptive refinement schemes which converge in $L_2$. Moreover, in the context of parameter dependent problems we discuss two approaches serving different purposes and working under different regularity assumptions. For frequent query problems, making essential use of the novel well-conditioned variational formulations, a new Reduced Basis Method is outlined which exhibits a certain rate-optimal performance for indefinite, unsymmetric or singularly perturbed problems. For the radiative transfer problem with scattering a sparse tensor method is presented which mitigates or even overcomes the curse of dimensionality under suitable (so far still isotropic) regularity assumptions. Numerical examples for both methods illustrate the theoretical findings

Effects of Cooling During Exercise on Thermoregulatory Responses of Men With Paraplegia.

BACKGROUND: People with spinal cord injury (SCI) have an altered afferent input to the thermoregulatory center, resulting in a reduced efferent response (vasomotor control and sweating capacity) below the level of the lesion. Consequently, core body temperature rises more rapidly during exercise in individuals with SCI compared with people who are able-bodied. Cooling strategies may reduce the thermophysiological strain in SCI. OBJECTIVE: The aim of this study was to examine the effects of a cooling vest on the core body temperature response of people with a thoracic SCI during submaximal exercise. METHODS: Ten men (mean age=44 years, SD=11) with a thoracic lesion (T4-T5 or below) participated in this randomized crossover study. Participants performed two 45-minute exercise bouts at 50% maximal workload (ambient temperature 25°C), with participants randomized to a group wearing a cooling vest or a group wearing no vest (separate days). Core body temperature and skin temperature were continuously measured, and thermal sensation was assessed every 3 minutes. RESULTS: Exercise resulted in an increased core body temperature, skin temperature, and thermal sensation, whereas cooling did not affect core body temperature. The cooling vest effectively decreased skin temperature, increased the core-to-trunk skin temperature gradient, and tended to lower thermal sensation compared with the control condition. LIMITATIONS: The lack of differences in core body temperature among conditions may be a result of the relative moderate ambient temperature in which the exercise was performed. CONCLUSIONS: Despite effectively lowering skin temperature and increasing the core-to-trunk skin temperature gradient, there was no impact of the cooling vest on the exercise-induced increase in core body temperature in men with low thoracic SCI

The lumping of heat transfer parameters in cooled packed beds: effect of the bed entry

The lumping of the heat transfer parameters of the one- and the two-dimensional pseudo-homogeneous model of a cooled fixed bed were compared. It appeared that the lumping of the two-dimensional parameters, being the effective radial conductivity h-eff and the heat transfer coefficient at the wall (alpha)w, into the one-dimensional overall heat transfer coefficient U results in a length dependence of U. It is shown that the ratio (alpha)w/U develops from unity at the bed inlet to a final value. The magnitude of this final value depends on the Biot number, whereas the length of this transition section is affected by the Peclet number. A new relation to lump the effective conductivity and the heat transfer coefficient at the wall into an overall heat transfer coefficient which depends on the values of the Biot number and the Peclet number is presented. This relation accounts for both the magnitude and the transition length of the ratio (alpha)w/U