A procedure for the reconstruction of a stochastic stationary temperature field

An iterative procedure is proposed for the reconstruction of a temperature field from a linear stationary heat equation with stochastic coefficients, and stochastic Cauchy data given on a part of the boundary of a bounded domain. In each step, a series of mixed well-posed boundary-value problems are solved for the stochastic heat operator and its adjoint. Well-posedness of these problems is shown to hold and convergence in the mean of the procedure is proved. A discretized version of this procedure, based on a Monte Carlo Galerkin finite-element method, suitable for numerical implementation is discussed. It is demonstrated that the solution to the discretized problem converges to the continuous as the mesh size tends to zero.

Some Fractional Extensions of the Temperature Field Problem in Oil Strata

This survey is devoted to some fractional extensions of the incomplete lumped formulation, the lumped formulation and the formulation of Lauwerier of the temperature field problem in oil strata. The method of integral transforms is used to solve the corresponding boundary value problems for the fractional heat equation. By using Caputo’s differintegration operator and the Laplace transform, new integral forms of the solutions are obtained. In each of the different cases the integrands are expressed in terms of a convolution of two special functions of Wright’s type.

On (b,c)-system at finite temperature in thermo field approach

We construct the finite temperature field theory of the two-dimensional ghost-antighost system within the framework of thermo field theory. (C) 2000 Elsevier B.V. B.V. All rights reserved.

Effect of cold wire inclination on temperature fluctuation measurements in a heated jet

Hot-wire anemometers at low operating currents are used as fast response resistance thermometers for the study of heated turbulent flows. Simultaneous measurement of temperature and velocity is generally performed with multi-wire arrays. In order to give good spatial resolution a new layout has been tested which uses an inclined temperature wire positioned parallel to the nearest inclined velocity wire. This leads to an asymmetric wire arrangement relative to the mean flow direction. As expected, a reduction in thermal interference from the velocity wires results when compared with an array containing a temperature wire placed normal to the flow. However, measurement of higher order moments of fluctuating quantities in an axisymmetric jet shows considerable distortion of radial distributions which is traced to alteration of the temperature field sensed by the temperature wire. When inclined velocity sensitive wires contain a temperature component, the latter may be affected by the same phenomenon.

Influence of ohmic heating on the flow field in thin-layer electrodeposition

In thin-layer electrodeposition the dissipated electrical energy leads to a substantial heating of the ion solution. We measured the resulting temperature field by means of an infrared camera. The properties of the temperature field correspond closely with the development of the concentration field. In particular, we find that the thermal gradients at the electrodes act similar to a weak additional driving force to the convection rolls driven by concentration gradients.

Stochastic quantization of real-time thermal field theory

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A numerical study of temperature effects on hot wire measurements inside turbulent channel flows

A way to investigate turbulence is through experiments where hot wire measurements are performed. Analysis of the in turbulence of a temperature gradient on hot wire measurements is the aim of this thesis work. Actually - to author's knowledge - this investigation is the first attempt to document, understand and ultimately correct the effect of temperature gradients on turbulence statistics. However a numerical approach is used since instantaneous temperature and streamwise velocity fields are required to evaluate this effect. A channel flow simulation at Re_tau = 180 is analyzed to make a first evaluation of the amount of error introduced by temperature gradient inside the domain. Hot wire data field is obtained processing the numerical flow field through the application of a proper version of the King's law, which connect voltage, velocity and temperature. A drift in mean streamwise velocity profile and rms is observed when temperature correction is performed by means of centerline temperature. A correct mean velocity pro�le is achieved correcting temperature through its mean value at each wall normal position, but a not negligible error is still present into rms. The key point to correct properly the sensed velocity from the hot wire is the knowledge of the instantaneous temperature field. For this purpose three correction methods are proposed. At the end a numerical simulation at Re_tau =590 is also evaluated in order to confirm the results discussed earlier.

Temperature measured in permafrost borehole at ICDP site 5011-3 in El'gygytgyn Crater, 2008-2011

This study focuses on the temperature field observed in boreholes drilled as part of interdisciplinary scientific campaign targeting the El'gygytgyn Crater Lake in NE Russia. Temperature data are available from two sites: the lake borehole 5011-1 located near the center of the lake reaching 400 m depth, and the land borehole 5011-3 at the rim of the lake, with a depth of 140 m. Constraints on permafrost depth and past climate changes are derived from numerical simulation of the thermal regime associated with the lake-related talik structure. The thermal properties of the subsurface needed for these simulations are based on laboratory measurements of representative cores from the quaternary sediments and the underlying impact-affected rock, complemented by further information from geophysical logs and data from published literature. The temperature observations in the lake borehole 5011-1 are dominated by thermal perturbations related to the drilling process, and thus only give reliable values for the lowermost value in the borehole. Undisturbed temperature data recorded over more than two years are available in the 140 m deep land-based borehole 5011-3. The analysis of these observations allows determination of not only the recent mean annual ground surface temperature, but also the ground surface temperature history, though with large uncertainties. Although the depth of this borehole is by far too insufficient for a complete reconstruction of past temperatures back to the Last Glacial Maximum, it still affects the thermal regime, and thus permafrost depth. This effect is constrained by numerical modeling: assuming that the lake borehole observations are hardly influenced by the past changes in surface air temperature, an estimate of steady-state conditions is possible, leading to a meaningful value of 14 ± 5 K for the post-glacial warming. The strong curvature of the temperature data in shallower depths around 60 m can be explained by a comparatively large amplitude of the Little Ice Age (up to 4 K), with low temperatures prevailing far into the 20th century. Other mechanisms, like varying porosity, may also have an influence on the temperature profile, however, our modeling studies imply a major contribution from recent climate changes.

A procedure for the temperature reconstruction in corner domains from Cauchy data

An iterative procedure is proposed for the reconstruction of a stationary temperature field from Cauchy data given on a part of the boundary of a bounded plane domain where the boundary is smooth except for a finite number of corner points. In each step, a series of mixed well-posed boundary value problems are solved for the heat operator and its adjoint. Convergence is proved in a weighted L2-space. Numerical results are included which show that the procedure gives accurate and stable approximations in relatively few iterations.

An iterative method for reconstruction of temperature

An iterative method for the reconstruction of a stationary three-dimensional temperature field, from Cauchy data given on a part of the boundary, is presented. At each iteration step, a series of mixed well-posed boundary value problems are solved for the heat operator and its adjoint. A convergence proof of this method in a weighted L 2-space is include

Thermal instability in a gravity-like scalar theory

We study the question of stability of the ground state of a scalar theory which is a generalization of the phi(3) theory and has some similarity to gravity with a cosmological constant. We show that the ground state of the theory at zero temperature becomes unstable above a certain critical temperature, which is evaluated in closed form at high temperature.