The enclosure method for the heat equation

This paper shows how the enclosure method which was originally introduced for elliptic equations can be applied to inverse initial boundary value problems for parabolic equations. For the purpose a prototype of inverse initial boundary value problems whose governing equation is the heat equation is considered. An explicit method to extract an approximation of the value of the support function at a given direction of unknown discontinuity embedded in a heat conductive body from the temperature for a suitable heat flux on the lateral boundary for a fixed observation time is given.Comment: 12pages. This is the final versio

Probe method and a Carleman function

A Carleman function is a special fundamental solution with a large parameter for the Laplace operator and gives a formula to calculate the value of the solution of the Cauchy problem in a domain for the Laplace equation. The probe method applied to an inverse boundary value problem for the Laplace equation in a bounded domain is based on the existence of a special sequence of harmonic functions which is called a {\it needle sequence}. The needle sequence blows up on a special curve which connects a given point inside the domain with a point on the boundary of the domain and is convergent locally outside the curve. The sequence yields a reconstruction formula of unknown discontinuity, such as cavity, inclusion in a given medium from the Dirichlet-to-Neumann map. In this paper, an explicit needle sequence in {\it three dimensions} is given in a closed form. It is an application of a Carleman function introduced by Yarmukhamedov. Furthermore, an explicit needle sequence in the probe method applied to the reduction of inverse obstacle scattering problems with an {\it arbitrary} fixed wave number to inverse boundary value problems for the Helmholtz equation is also given.Comment: 2 figures, final versio

An inverse source problem for the heat equation and the enclosure method

An inverse source problem for the heat equation is considered. Extraction formulae for information about the time and location when and where the unknown source of the equation firstly appeared are given from a single lateral boundary measurement. New roles of the plane progressive wave solutions or their complex versions for the backward heat equation are given.Comment: 23page

Linear sampling method for identifying cavities in a heat conductor

We consider an inverse problem of identifying the unknown cavities in a heat conductor. Using the Neumann-to-Dirichlet map as an input data, we develop a linear sampling type method for the heat equation. A new feature is that there is a freedom to choose the time variable, which suggests that we have more data than the linear sampling methods for the inverse boundary value problem associated with EIT and inverse scattering problem with near field data

The enclosure method for inverse obstacle scattering problems with dynamical data over a finite time interval II. Obstacles with a dissipative boundary or finite refractive index and back-scattering data

In this paper a wave is generated by an initial data whose support is localized at the outside of unknown obstacles and observed in a limited time on a known closed surface or the same position as the support of the initial data. The observed data in the latter process are nothing but the back-scattering data. Two types of obstacles are considered. One is obstacles with a dissipative boundary condition which is a generalization of the sound-hard obstacles; another is obstacles with a finite refractive index, so-called, transparent obstacles. For each type of obstacles two formulae which yield explicitly the distance from the support of the initial data to unknown obstacles are given.Comment: 34 pages, submitted to Inverse Problems on 13 July 201

Radiating and non-radiating sources in elasticity

In this work, we study the inverse source problem of a fixed frequency for the Navier's equation. We investigate that nonradiating external forces. If the support of such a force has a convex or non-convex corner or edge on their boundary, the force must be vanishing there. The vanishing property at corners and edges holds also for sufficiently smooth transmission eigenfunctions in elasticity. The idea originates from the enclosure method: The energy identity and new type exponential solutions for the Navier's equation.Comment: 17 page

Reconstruction of Inclusions for the Inverse Boundary Value Problem with Mixed Type Boundary Condition

We consider an inverse boundary value problem for identifying the inclusion inside a known anisotropic conductive medium. We give a reconstruction procedure for identifying the in­clusion from the Dirichlet-Neumann map or the Neumann-Dirichlet map associated with the mixed type boundary condition

Initial structure development in the CO2 laser-heated drawing of poly(trimethylene terephthalate) fiber

Because rapid and uniform laser heating can fix the neck-drawing point in continuous drawing of PTT fiber, we have successfully analyzed the fiber structure development in the continuous drawing process by in-situ measurement with a time resolution of less than 1 ms. In this study, we investigated fiber structure development for PTT around the neck point controlled with a CO2 laser-heated apparatus during continuous drawing, through on-line measurements of WAXD, SAXS, and fiber temperature. Fiber temperature attained by laser radiation initiated a rise around −3 mm in relation to the neck point at 0 mm, and increased to about 90 °C, which is past the 45 °C Tg for PTT. The instantaneous increase in fiber temperature continued with a vertical ascent, with plastic deformation around the neck point. The crystalline diffraction pattern was revealed initially at the elapsed time of 0.415 ms immediately after necking, and remained fairly constant with elapsed time. The ultimate crystalline diffraction pattern for a completely drawn fiber showed little difference from that at the initial stage. In PET a two-dimensionally ordered structure in the form of a mesophase was detected immediately after the necking, whereas in PTT the phenomenon was not observed. With elapsed time, the d spacing of (002) plane decreased gradually due to transformation of the initial all-trans conformation into trans-gauche-gauche-trans conformation, and ultimately the PTT molecular chain could favorably adopt the trans-gauche-gauche-trans conformation. SAXS pattern immediately after the necking revealed an X-shape; the scattering intensity concentrated on meridian directions due to individual crystal development, and at 2 ms two-pointed scattering started to appear. Past 8 ms, the typical two-pointed scattering pattern was prominent and its intensity increased with elapsed time. Long period decreased with increasing elapsed time, but the crystallite size of meridian (002) plane hardly changed. The decrease in long period might be caused by chain relaxation in the amorphous region.ArticlePolymer. 49(26):5705-5713 (2008)journal articl

Computing Volume Bounds of Inclusions by EIT Measurements

The size estimates approach for Electrical Impedance Tomography (EIT) allows for estimating the size (area or volume) of an unknown inclusion in an electrical conductor by means of one pair of boundary measurements of voltage and current. In this paper we show by numerical simulations how to obtain such bounds for practical application of the method. The computations are carried out both in a 2D and a 3D setting.Comment: 20 pages with figure

FGF23 and Fetuin-A Interaction in the Liver and in the Circulation

Recently it has been demonstrated that Fetuin-A, an anti-inflammatory protein synthesized by the liver, is produced also in bone by an FGF23-regulated pathway. FGF23 has been also demonstrated to induce inflammatory cytokine production in the liver. This study aimed to explore if FGF23 plays a role in the Fetuin-A production in the liver cells too and the possible relationships with FGF23 pro-inflammatory effects.FGF23 and Fetuin-A were studied in liver, kidney and in plasma with immunochemistry, immunoprecipitation, western blot, chromatin immunoprecipitation, duolink, ELISA, qrtPCR methodology.FGF23 is produced, but not secreted by the liver cells. In hepatocytes and circulation, FGF23 was present only strictly linked to Fetuin-A, while Fetuin-A was found also in unbounded form. No link was observed in the kidney. FGF23 up to 600 pg/ml stimulates, while, at higher concentrations, reduces Fetuin-A expression.Notably, overall the range of concentrations, FGF23 stimulates Fetuin-A promoter, TNF alpha and IL6 expression.In the nucleus, FGF23 seems to act as a direct transcription factor of Fetuin-A promoter. These results suggest that FGF23 played a direct regulatory role in Fetuin-A expression in liver cells with a biphasic effect: Fetuin-A progressively increases when FGF23 increases up to 400-600 pg/mL, and declines at higher FGF23 concentrations.These results lead us to hypothesize: a) a possible epigenetic post-transcriptional regulation; b) a possible counter-regulatory effect of FGF23 induced inflammatory cytokines (TNF alpha/NF-kappa B mechanism). This study could add an additional key for the interpretation of the possible mechanisms linking FGF23, Fetuin-A and inflammation in CKD patients and suggests a role for FGF23 as transcription factor