We consider the perturbation of an electric potential due to an insulating inclusion with corners. This perturbation is known to admit a multipole expansion whose coefficients are linear combinations of generalized polarization tensors. We define new geometric factors of a simple planar domain in terms of a conformal mapping associated with the domain. The geometric factors share properties of the generalized polarization tensors and are the Fourier series coefficients of a generalized external angle of the inclusion boundary. Since the generalized external angle contains the Dirac delta singularity at corner points, we can determine a criteria for the existence of corner points on the inclusion boundary in terms of the geometric factors. We illustrate and validate our results with numerical examples computed to a high degree of precision using integral equation techniques, the Nyström discretization, and recursively compressed inverse preconditioning.involving the Neumann-Poincaré (NP) operator. Furthermore, the boundary integral equation framework admits a multipole expansion of u − h whose coefficients are linear combinations of the generalized polarization tensors (GPTs), which can also be expressed in terms of boundary integrals.The GPTs are a sequence of real-valued tensors that are associated with Ω and they generalize the classical polarization tensors [28]. They can be obtained from multistatic measurements, where a high signal-to-noise ratio is needed to acquire high-order terms [2]. They have been used as building blocks when solving imaging problems for inclusions with smooth boundaries [4,5]. The GPTs contain sufficient geometric information to determine Ω uniquely [5]. One can suitably approximate the conductivity, location, and shape of an inclusion, or several inclusions, using the first few leading terms of the GPTs by adopting an optimization framework [4,9].An inclusion with corners generally induces strong scattering close to corner points (vertices). The understanding and application of such corner effects is a subject of great interest. Detection methods for inclusions, from boundary measurements, have been developed in [22]. The gradient blow-up of the electrical potential for a bow-tie structure, which has two closely located domains with corners, was investigated in [25]. It has been shown that the spectral features of the NP operator of a domain with corners is significantly different from that of a smooth domain [11,17,19,21,27]. It is worth mentioning that the spectrum of the NP operator has recently drawn significant attention in relation to plasmonic resonances [1,24,32].This paper analyzes the effects of inclusion corners on the perturbation of an electric potential. We present new geometric factors that clearly reveal the boundary information of an inclusion, including the existence of corner points. They satisfy mutually equivalent relations with the GPTs, so that one can compute them from the GPTs and vice versa. The geometric factors form an infinite sequence of complex numbers....

In the last few decades, an average method which is regulated by ISO 9869-1 has been used to evaluate the in situ thermal transmittance (U-value) and thermal resistance (R-value) of building envelopes obtained from onsite measurements and to verify the validity of newly proposed methods. Nevertheless, only a few studies have investigated the test duration required to obtain reliable results using this method and the convergence characteristics of the results. This study aims to evaluate the convergence characteristics of the in situ values analyzed using the average method. The criteria for determining convergence (i.e., end of the test) using the average method are very strict, mainly because of the third condition, which compares the deviation of two values derived from the first and last periods of the same duration. To shorten the test duration, environmental variables should be kept constant throughout the test or an appropriate period should be selected. The convergence of the in situ U-value and R-value is affected more by the length of the test duration than by the temperature difference if the test environment meets literature-recommended conditions. Furthermore, there is no difference between the use of the U-value and R-value in determining the end of the test.

There are several methods to obtain the in situ thermal transmittance value (U-value) of building envelopes from on-site data, including the three approaches of the progressive average method, average method considering the thermal storage effect, and dynamic method for deriving the U-value from heat flowmeter (HFM) measurements and the four methods with different formulas to analyze infrared thermography (IRT) measurement data. Since each of these methods considers different parameters and the non-steady characteristics of the heat transfer in building walls in their own way, discrepancies may occur among the obtained results. This study evaluates and compares the in situ U-values by using various methods of analyzing HFM and IRT measurement data. Further, by investigating buildings with similar materials and identical stratigraphies, but with different construction years, we analyze the discrepancy between the designed and measured values caused by material deterioration and evaluate the errors according to the analysis method. The percentage deviation between the U-values obtained by the three methods from the HFM data is found to be satisfactory, being within 10%. When compared with the results of the progressive average method, the deviations for the four different IRT-measurement-based methods vary greatly, being in the range of 6-43%.

This paper is concerned with the inverse problem of reconstructing small and local perturbations of a planar surface using the field interaction between a known plasmonic particle and the planar surface. The aim is to perform a super-resolved reconstruction of these perturbations from shifts in the plasmonic frequencies of the particle-surface system. In order to analyze the interaction between the plasmonic particle and the planar surface, a well chosen conformal mapping, which transforms the particle-surface system into a coated structure, is used. Then the even Fourier coefficients of the transformed domain are related to the shifts in the plasmonic resonances of the particle-surface system. A direct reconstruction of the perturbations of the planar surface is proposed. Its viability and limitations are documented by numerical examples.Mathematics Subject Classification (MSC2000): 35R30, 35C20.

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