Josef Voldřich

Frictionally Excited Thermoelastic Instability and the Suppression of Its Exponential Rise in Disc Brakes

This paper deals with processes of thermoelastic instability occurring on brake systems that become evident as a non-uniform distribution of temperature with hot spots on contact surfaces. Thermoelastic instability is accompanied by the exponential rising of temperature amplitudes of hot spots during its initial linear phase. The authors discuss different mechanisms of interruption of the growth, based on experimental and computational results. An example of experimental data is presented for the case of a disc brake.

Raman thermometry: Effective temperature of the nonuniform temperature field induced by a Gaussian laser

Raman spectroscopy is a widely applied analytical technique with numerous applications that is based on inelastic scattering of monochromatic light, which is typically provided by a laser. Irradiation of a sample by a laser beam is always accompanied by an increase in the sample temperature, which may be unwanted or may be beneficial for studying temperature-related effects and determining thermal parameters. This work reports analyses of the temperature field induced by a Gaussian laser to calculate the Raman scattered intensity related to each temperature value of the nonuniform field present on the sample. The effective temperature of the probed field, calculated as an average weighted by the laser intensity, is demonstrated to be about 70% of the maximum temperature irrespective of the absorption coefficient or the laser focus. Finally, using crystalline silicon as a model material, it is shown that this effective value closely approximates the temperature value identified from the thermally related peak shift.

Averaging over N-dimensional balls and Cauchy problem for equations of mathematical physics

Abstract In this paper, we deal with averaging over balls in E N and derive an equality describing a relation between scale and space dependence of the average function. We also show connections with equations of mathematical physics.

Neumann problem for elliptic equation in Sobolev power weighted spaces

The Neumann problem for an elliptic equation in a bounded domain Ω ⊂ RN and for external forces with degenerations or singularities relating to the m-dimensional variety M ⊂ δ Ω are considered. The underlying ideas of proof of the existence of the considered problem solution are given for the remaining cases of N - m = 1 and N - m =2.