Volume Integral Equation Method Solution for Spheroidal Inclusion Problem

In this paper, the volume integral equation method (VIEM) is introduced for the numerical analysis of an infinite isotropic solid containing a variety of single isotropic/anisotropic spheroidal inclusions. In order to introduce the VIEM as a versatile numerical method for the three-dimensional elastostatic inclusion problem, VIEM results are first presented for a range of single isotropic/orthotropic spherical, prolate and oblate spheroidal inclusions in an infinite isotropic matrix under uniform remote tensile loading. We next considered single isotropic/orthotropic spherical, prolate and oblate spheroidal inclusions in an infinite isotropic matrix under remote shear loading. The authors hope that the results using the VIEM cited in this paper will be established as reference values for verifying the results of similar research using other analytical and numerical methods.

Electron-energy-loss spectroscopy and cathodoluminescence for particles inside substrate

To simulate the interaction of a nanoparticle with an electron beam, we previously developed a theoretical description for the general case of a particle fully embedded in an infinite arbitrary host medium. The theory is based on the volume-integral variant of frequency-domain Maxwell’s equations and, therefore, is naturally applicable in the discrete-dipole approximation. The fully-embedded approximation allows fast numerical simulations of the experiments for particles inside a substrate since the host medium discretization is not needed. In this work, we study how applicable the fully-embedded approach is for realistic scenarios with relatively thin substrates. In particular, we performed test simulations for a silver sphere both inside an infinite host medium and inside a finite box or sphere. For the host medium, we considered two non-absorbing cases (the denser one causes Cherenkov radiation), as well as an absorbing case. The peak positions in the obtained spectra approximately agree between substrates a few times thicker than the sphere and the infinite one. However, a much thicker substrate (of the order of μm) would be required to have a qualitative agreement for absolute peak amplitudes. The developed algorithm is implemented in the open-source code ADDA, allowing one to rigorously and efficiently simulate electron-energy-loss spectroscopy and cathodoluminescence by particles of arbitrary shape and internal structure embedded into any homogeneous host medium.

Electromagnetic fields and applications for anisotropic / photonic structures

Το πρώτο μέρος αφορά τoν σχεδιασμό κεραίας με σκοπό την εμφύτευση της σε περιβάλλον ανθρώπινου ιστού. Πιο συγκεκριμένα, η κεραία προορίζεται για την ενσωμάτωση της σε εφαρμογές τύπου βηματοδότη, δηλαδή σε εφαρμογές που έχουν ως περιβάλλον την μορφολογία του ανθρώπινου στήθους. Επιπλέον πραγματοποιείται εκτενής συγκριτική μελέτη όλων των συνδυασμών των τεχνικών σμίκρυνσης που αναφέρονται στην βιβλιογραφία, προκειμένου να εξαχθεί ένας οδηγός για τους σχεδιαστές εμφυτεύσιμων κεραιών, όσον αφορά τις δυνατότητες σμίκρυνσης που προσφέρει ο κάθε συνδυασμός και επομένως να διευκολύνει την διαδικασία σχεδίασης.Το δεύτερο, και κύριο μέρος, της διδακτορικής διατριβής πραγματεύεται την επίλυση ηλεκτρομαγνητικών (ΗΜ) προβλημάτων διαφόρων τύπων. Αρχικά, αναπτύχθηκε μια μέθοδος με σκοπό τον υπολογισμό του σκεδαζόμενου ηλεκτρομαγνητικού πεδίου από κυλινδρικούς σκεδαστές, με άπειρο μήκος κατά μήκος του άξονα του κυλίνδρου. Κύριος πυλώνας της μεθόδου αυτής αποτέλεσε η χρήση των Coupled Fields Volume Integral Equations (CFVIEs), καθώς και η ανάπτυξη των άγνωστων πεδίων σε αναπτύγματα τύπου Dini. Η μέθοδος αυτή μπορεί να χειριστεί με ευκολία ηλεκτρικά μεγάλες διατάξεις, οι οποίες αποτελούνται από ισοτροπικά/ανισοτροπικά υλικά, ακόμη και με υψηλή ανομοιογένεια. Στην συνέχεια, αναπτύχθηκε υπολογιστική μέθοδος για την εξαγωγή των κυματαριθμών αποκοπής για την περίπτωση του κυλινδρικού κυματοδηγού κυκλικής διατομής, με μεταλλικά τοιχώματα. Η μέθοδος αυτή, επίσης, στηρίχθηκε στις CFVIEs καθώς και στα αναπτύγματα τύπου Dini. Τέλος, αναπτύχθηκε ασυμπτωτική μέθοδος για τον υπολογισμό των μιγαδικών συντονισμών των Whispering Gallery Modes (WGM) για την περίπτωση κυλινδρικού συντονιστή. Για την εξαγωγή των ασυμπτωτικών εκφράσεων χρησιμοποιήθηκε η συνάρτηση Airy.

Volume Integral Equation Method (VIEM)

A number of analytical techniques are available for the stress analysis of inclusion problems when the geometries of inclusions are simple (e.g., cylindrical, spherical or ellipsoidal) and when they are well separated [9, 41, 52]. However, these approaches cannot be applied to more general problems where the inclusions are anisotropic and arbitrary in shape, particularly when their concentration is high. Thus, stress analysis of heterogeneous solids or analysis of elastic wave scattering problems in heterogeneous solids often requires the use of numerical techniques based on either the finite element method (FEM) or the boundary integral equation method (BIEM). However, these methods become problematic when dealing with elastostatic problems or elastic wave scattering problems in unbounded media containing anisotropic and/or heterogeneous inclusions of arbitrary shapes. It has been demonstrated that the volume integral equation method (VIEM) can overcome such difficulties in solving a large class of inclusion problems [6,10,20,21,28–30]. One advantage of the VIEM over the BIEM is that it does not require the use of Green’s functions for anisotropic inclusions. Since the elastodynamic Green’s functions for anisotropic media are extremely difficult to calculate, the VIEM offers a clear advantage over the BIEM. In addition, the VIEM is not sensitive to the geometry or concentration of the inclusions. Moreover, in contrast to the finite element method, where the full domain needs to be discretized, the VIEM requires discretization of the inclusions only.

Minimally deformed wormholes

This work is devoted to the study of wormhole solutions in the framework of gravitational decoupling by means of the minimal geometric deformation scheme. As an example, to analyze how this methodology works in this scenario, we have minimally deformed the well-known Morris–Thorne model. The decoupler function f(r) and the $$\theta $$ θ -sector are determined considering the following approaches: (i) the most general linear equation of state relating the $$\theta _{\mu \nu }$$ θ μ ν components is imposed and (ii) the generalized pseudo-isothermal dark matter density profile is mimicked by the temporal component of the $$\theta $$ θ -sector. It is found that the first approach leads to a non-asymptotically flat space-time with an unbounded mass function. To address this issue we have matched both the wormhole and the Schwarzschild vacuum solutions, via a thin-shell at the junction surface. Using the second approach, it can be seen that, on one hand, the solution for $$\gamma =1$$ γ = 1 does not give place to a bounded mass and it presents a topological defect at large distances; on the other hand, the wormhole manifold is asymptotically flat in the $$\gamma =2$$ γ = 2 case. In order to satisfy the flare-out condition, we have found restrictions on the value of the $$\alpha $$ α parameter, which is related with the amount of exotic matter distribution. Finally, the averaged weak energy condition has been analyzed by using the volume integral quantifier.