826 research outputs found
Inverse problem for wave equation with sources and observations on disjoint sets
We consider an inverse problem for a hyperbolic partial differential equation
on a compact Riemannian manifold. Assuming that and are
two disjoint open subsets of the boundary of the manifold we define the
restricted Dirichlet-to-Neumann operator . This
operator corresponds the boundary measurements when we have smooth sources
supported on and the fields produced by these sources are observed
on . We show that when and are disjoint but
their closures intersect at least at one point, then the restricted
Dirichlet-to-Neumann operator determines the
Riemannian manifold and the metric on it up to an isometry. In the Euclidian
space, the result yields that an anisotropic wave speed inside a compact body
is determined, up to a natural coordinate transformations, by measurements on
the boundary of the body even when wave sources are kept away from receivers.
Moreover, we show that if we have three arbitrary non-empty open subsets
, and of the boundary, then the restricted
Dirichlet-to-Neumann operators for determine the Riemannian manifold to an isometry. Similar result is proven
also for the finite-time boundary measurements when the hyperbolic equation
satisfies an exact controllability condition
Dynamics of viscous dissipative gravitational collapse: A full causal approach
The Misner and Sharp approach to the study of gravitational collapse is
extended to the viscous dissipative case in, both, the streaming out and the
diffusion approximations. The dynamical equation is then coupled to causal
transport equations for the heat flux, the shear and the bulk viscosity, in the
context of Israel--Stewart theory, without excluding the thermodynamics
viscous/heat coupling coefficients. The result is compared with previous works
where these later coefficients were neglected and viscosity variables were not
assumed to satisfy causal transport equations. Prospective applications of this
result to some astrophysical scenarios are discussed.Comment: 22 pages Latex. To appear in Int. J. Mod. Phys. D. Typos correcte
Some analytical models of radiating collapsing spheres
We present some analytical solutions to the Einstein equations, describing
radiating collapsing spheres in the diffusion approximation. Solutions allow
for modeling physical reasonable situations. The temperature is calculated for
each solution, using a hyperbolic transport equation, which permits to exhibit
the influence of relaxational effects on the dynamics of the system.Comment: 17 pages Late
Inverse problem by Cauchy data on arbitrary subboundary for system of elliptic equations
We consider an inverse problem of determining coefficient matrices in an
-system of second-order elliptic equations in a bounded two dimensional
domain by a set of Cauchy data on arbitrary subboundary. The main result of the
article is as follows: If two systems of elliptic operators generate the same
set of partial Cauchy data on an arbitrary subboundary, then the coefficient
matrices of the first-order and zero-order terms satisfy the prescribed system
of first-order partial differential equations. The main result implies the
uniqueness of any two coefficient matrices provided that the one remaining
matrix among the three coefficient matrices is known
Fourier, hyperbolic and relativistic heat transfer equations: a comparative analytical study
[EN] Parabolic heat equation based on Fourier's theory (FHE), and hyperbolic heat equation (HHE), has been used to mathematically model the temperature distributions of biological tissue during thermal ablation. However, both equations have certain theoretical limitations. The FHE assumes an infinite thermal energy propagation speed, whereas the HHE might possibly be in breach of the second law of thermodynamics. The relativistic heat equation (RHE) is a hyperbolic-like equation, whose theoretical model is based on the theory of relativity and which was designed to overcome these theoretical impediments. In this study, the three heat equations for modelling of thermal ablation of biological tissues (FHE, HHE and RHE) were solved analytically and the temperature distributions compared. We found that RHE temperature values were always lower than those of the FHE, while the HHE values were higher than the FHE, except for the early stages of heating and at points away from the electrode. Although both HHE and RHE are mathematically hyperbolic, peaks were only found in the HHE temperature profiles. The three solutions converged for infinite time or infinite distance from the electrode. The percentage differences between the FHE and the other equations were larger for higher values of thermal relaxation time in HHE.This work received financial support from the Spanish Government (Ministerio de Ciencia e Innovacion, Ref. TEC2011-27133-C02-01).López Molina, JA.; Rivera Ortun, MJ.; Berjano, E. (2014). Fourier, hyperbolic and relativistic heat transfer equations: a comparative analytical study. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 470:1-16. https://doi.org/10.1098/rspa.2014.0547S11647
Pore-size dependence of the thermal conductivity of porous silicon : a phonon hydrodynamic approach
Phononhydrodynamics is used to analyze the influence of porosity and of pore size on reduction in thermal conductivity in porous silicon, with respect to crystalline silicon. The expressions predict that the thermal conductivity is lower for higher porosity and for smaller pore radius, as a consequence of phononballisticeffects. The theoretical results describe experimental data better than the assumption that they only depend on porosity
Organics in comet 67P – a first comparative analysis of mass spectra from ROSINA–DFMS, COSAC and Ptolemy
The ESA Rosetta spacecraft followed comet 67P at a close distance for more than 2 yr. In addition, it deployed the lander Philae on to the surface of the comet. The (surface) composition of the comet is of great interest to understand the origin and evolution of comets. By combining measurements made on the comet itself and in the coma, we probe the nature of this surface material and compare it to remote sensing observations. We compare data from the double focusing mass spectrometer (DFMS) of the ROSINA experiment on ESA's Rosetta mission and previously published data from the two mass spectrometers COSAC (COmetary Sampling And Composition) and Ptolemy on the lander. The mass spectra of all three instruments show very similar patterns of mainly CHO-bearing molecules that sublimate at temperatures of 275 K. The DFMS data also show a great variety of CH-, CHN-, CHS-, CHO2- and CHNO-bearing saturated and unsaturated species. Methyl isocyanate, propanal and glycol aldehyde suggested by the earlier analysis of the measured COSAC spectrum could not be confirmed. The presence of polyoxymethylene in the Ptolemy spectrum was found to be unlikely. However, the signature of the aromatic compound toluene was identified in DFMS and Ptolemy data. Comparison with remote sensing instruments confirms the complex nature of the organics on the surface of 67P, which is much more diverse than anticipated
Immunoproteasome Overexpression Underlies the Pathogenesis of Thyroid Oncocytes and Primary Hypothyroidism: Studies in Humans and Mice
BACKGROUND:Oncocytes of the thyroid gland (Hürthle cells) are found in tumors and autoimmune diseases. They have a unique appearance characterized by abundant granular eosinophilic cytoplasm and hyperchromatic nucleus. Their pathogenesis has remained, thus far, unknown. METHODOLOGY/PRINCIPAL FINDINGS:Using transgenic mice chronically expressing IFNgamma in thyroid gland, we showed changes in the thyroid follicular epithelium reminiscent of the human oncocyte. Transcriptome analysis comparing transgenic to wild type thyrocytes revealed increased levels of immunoproteasome subunits like LMP2 in transgenics, suggesting an important role of the immunoproteasome in oncocyte pathogenesis. Pharmacologic blockade of the proteasome, in fact, ameliorated the oncocytic phenotype. Genetic deletion of LMP2 subunit prevented the development of the oncocytic phenotype and primary hypothyroidism. LMP2 was also found expressed in oncocytes from patients with Hashimoto thyroiditis and Hürthle cell tumors. CONCLUSIONS/SIGNIFICANCE:In summary, we report that oncocytes are the result of an increased immunoproteasome expression secondary to a chronic inflammatory milieu, and suggest LMP2 as a novel therapeutic target for the treatment of oncocytic lesions and autoimmune hypothyroidism
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