Axially Uniform Magnetic Field-Modulation Excitation for Electron Paramagnetic Resonance in Rectangular and Cylindrical Cavities by Slot Cutting

In continuous-wave (CW) Electron Paramagnetic Resonance (EPR) a low-frequency time-harmonic magnetic field, called field modulation, is applied parallel to the static magnetic field and incident on the sample. Varying amplitude of the field modulation incident on the sample has consequences on spectral line-shape and line-height over the axis of the sample. Here we present a method of coupling magnetic field into the cavity using slots perpendicular to the sample axis where the slot depths are designed in such a way to produce an axially uniform magnetic field along the sample. Previous literature typically assumes a uniform cross-section and axial excitation due to the wavelength of the field modulation being much larger than the cavity. Through numerical analysis and insights obtained from the eigenfunction expansion of dyadic Green’s functions, it is shown that evanescent standing-wave modes with complex cross-sections are formed within the cavity. From this analysis, a W-band (94 GHz) cylindrical cavity is designed where modulation slots are optimized to present a uniform 100 kHz field modulation over the length of the sample

A moving boundary problem motivated by electric breakdown: I. Spectrum of linear perturbations

An interfacial approximation of the streamer stage in the evolution of sparks and lightning can be written as a Laplacian growth model regularized by a `kinetic undercooling' boundary condition. We study the linear stability of uniformly translating circles that solve the problem in two dimensions. In a space of smooth perturbations of the circular shape, the stability operator is found to have a pure point spectrum. Except for the zero eigenvalue for infinitesimal translations, all eigenvalues are shown to have negative real part. Therefore perturbations decay exponentially in time. We calculate the spectrum through a combination of asymptotic and series evaluation. In the limit of vanishing regularization parameter, all eigenvalues are found to approach zero in a singular fashion, and this asymptotic behavior is worked out in detail. A consideration of the eigenfunctions indicates that a strong intermediate growth may occur for generic initial perturbations. Both the linear and the nonlinear initial value problem are considered in a second paper.Comment: 37 pages, 6 figures, revised for Physica

Αριθμητική προσομοίωση της υδροελαστικής αλληλεπίδρασης κυμάτων tsunami με Μεγάλες Πλωτές Κατασκευές και στρώματα πάγου.

113 σ.Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) “Υπολογιστική Μηχανική”Οι συνέπειες τηςκλιματικής αλλαγής τόσοστο περιβάλλον, όσο και στην ανθρώπινη δραστηριότητα αποτελεί αντικείμενοεντατικής έρευνας.Με την αύξησητηςθερμοκρασίας, το ενδιαφέρον στρέφεται στιςΠολικές ζώνες και στην ευπαθή ισσορροπία τους.Ως ρυθμιστέςτου παγκόσμιου κλίματος, οι Αρκτικέςζώνες επηρεάζουν την θερμοκρασία και την ωκεάνια κυκλοφορία.Τηνίδια στιγμή, ο καταγεγραμμένος ‘κατακερματισμός’των στρωμάτων πάγου (ice shelves) ή παγετώνων στηνΑνταρκτική και η σημαντική μείωση του θαλάσσιου πάγου στην Αρκτική, φαίνονται να επηρεάζουνάμεσα τιςεμπορικές δραστηριότητες και να επιβεβαιώνουν την αρχή μιας σειράςκλιματικών διαταραχών. Η κυματική διέγερση τωνστρωμάτων πάγου έχει συνδεθείμε τα φαινομενα απόσχισηςσωμάτων πάγων και τοσχηματισμό ροών (ice floes). Η παλιρροιακή δράση και η συνεχής καταπόνηση των κυμάτων, σε συνδιασμό με τις εγγενείς ατέλειες του πάγου οδηγεί σε καμπτική αστοχία και τηντελική απόσχισητμημάτων πάγου. Οιμεγάλεςοριζόντιεςδιαστάσεις, σεσχέσημετο πάχοςτωνστρωμάτων πάγου, καθιστάτιςελαστικές παραμορφώσεις κυρίαρχες των κινήσεων στερεού σώματος. Επομένως, η μελέτητης απόκρισηςστρωματών πάγων υπο κυματική καταπόνιση εμπίπτει στη περιοχή της υδροελαστικότητας. Ανθρώπινες κατασκευές που μοιράζονται τα ίδια χαρακτηριστικάμε τα στρώματα πάγου, όπως οι Μεγάλες Πλώτες Κατασκευές (Very Large Floating Structures, VLFS) αποτελούνεφαρμογές της υδροελαστικότητας.Συνεπώς, η υδροελαστική ανάλυση πλωτών στρωμάτων υπο κυματική καταπόνισηείναι κοινόέδαφος για εφαρμογές τοσοστηγεωφυσικήόσο και στημηχανική κλίμακα. Στην παρούσα εργασία εξετάζεται η απόκριση πλωτώνστρωμάτων ύπο την καταπόνηση μακρών κυμάτων.Για την ανάλυση, επιδιώκεται η μονοδιάστατη σύζευξητουμοντέλουλεπτής, ελαστικής δοκού Euler Bernoulli και τωνγραμμικοποιημένων εξισώσεωνρηχώνυδάτων.Ορίζονται δύοξεχωριστά προβλήματα.Το πρώτο πρόβλημα αφοράμια πλωτή πλάκα μεένα πακτωμέμο άκρο ενώ το δεύτερο εξετάζει μια ελεύθερη πλωτή πλάκα. Στησυνέχεια παρουσιάζεται η ανάλυση ευστάθειας της ισχυρήςδιατύπωσης τωνδύο προβλήματων και μελετάται η αρχήτηςδιατήρησης τηςενέργειας για κάθε σύστημα.Στησυνέχεια, για την επίλυση γίνεται χρήση της μεθόδου των πεπερασμένων στοιχείων.Ειδικά πεπερασμένα στοιχεία κατασκευάζονται μεδιαφορους πολυωνυμικούς βαθμούς, για την προσεγγιση της λύσηςστις περιοχέςτηςυδροελαστικής σύζευξης.Επιπλέον παρατίθεται και η εκτίμησησφάλματος για τηνημι-διακριτή μορφήστοχώρο.Στησυνέχεια η λύσητωνπεπερασμένων στοιχείων συγκρίνεται με διαφορετική μέθοδο (Sturova 2009) που βασίζεται στην ανάπτυξη της ανύψωσης ελεύθερης επιφάνειας σειδιοσυναρτήσεις τηςδοκού in vacuo. Τέλος, παρουσιάζονται δύο παραδείγματα για τοκάθεένα απο τα προβλήματα καθώς και το παράδειγμα τουστρώματος Sulzberger.Επίσης, δίνονται αποτελέσματα που παρουσιάστηκαν στο European Geosciences Union Assembly 2014, μεσυμμετοχήτηςσυγγραφέα.Η ανάλυση επιβεβαιώνειτην επίδραση του πάχουςτης πλάκας στηδιασπορά τουυδροελαστικού κύματος καθώς και στην κατανομήτωνροπών και τεμνουσών.Η απόσταση της μέγιστης ροπής απο το ελευθερο άκρο φαίνεται να εξαρταται απο το πάχος αλλά όχι απο τομήκοςκύματος της καταπόνησης.Ice caps act as climate controllers, regulating temperature, ocean circulation and affecting global weather patterns. The disintegration of ice shelves and sea ice in recent years has gathered scientific attention as the stability of ice formations is being re-evaluated. The detrimental interaction between ice sheets and long waves has been recently advocated, showing the need for a thorough investigation of the phenomenon. Simultaneous technological advancements in marine engineering provide a different motivation for the study of the transient response of Very Large Floating Structures (VLFS) under long wave excitation. In the present thesis, the elastic Euler Bernoulli beam model and the shallow water equations are coupled in order to derive a 1-D hydroelastic system. Two specific problems are defined, the one of a floating cantilever, a fixed-edge plate, able to simulate an ice shelf or moored VLFS, and one of a freely floating plate approximating the configuration of an ice floe or a pontoon VLFS. Stability estimates of the variational form of the governing equations and the energy conservation principle are studied for both problems. The finite element method is employed for the solution of the problems in question. Special hydroelastic elements incorporating various polynomial degrees are developed in order to cater for the coupling in the hydroelasticity dominated regions of the problem. In addition, error estimates for the semi-discrete form are derived. The finite element solution is compared against the eigenfunction expansion method of Sturova (2009). Finally, two examples are explored for each of the problems along with a geophysical case study based on the Sulzberger Ice Shelf calving event in 2011. Additionally, results presented as collaboration, by the author, at the European Geosciences General Assembly 2014 are given. The presence of the fixed boundary and its effect on the bending moment and shear force distributions are explored. Thickness variations are shown to have an effect on shear force distribution while the distance from the free edge of a cantilever plate where the maximum bending moment appears is relatively insensitive of the incoming tsunami wavelength.Αγγελική Ε. Καρπεράκ

INVESTIGATION OF HYDROELASTIC BEHAVIOR OF A PONTOON-TYPE VLFS DURING UNSTEADY EXTERNAL LOADS IN WAVE CONDITION USING A HYBRID FINITE ELEMENT-BOUNDARY ELEMENT (FE-ME) METHOD

The hydroelastic behaviour of a pontoon-type VLFS subjected to unsteady external loads in wave condition is investigated in the context of the time-domain modal expansion theory, in which the boundary element method (BEM) based on time domain Kelvin sources is used for hydrodynamic forces and the finite element method (FEM) is adopted for solving the deflections of the VLFS. In this analysis, the interpolation-tabulation scheme is applied to assess rapidly and accurately the free-surface Green function in finite water depth, and the boundary integral equation of a quarter VLFS model is further established taking advantage of symmetry of flow field and structure. The VLFS is modelled as an equivalent solid plate based on the Mindlin plate theory. The coupled plate-water model is performed to determine the wave-induced responses and transient behaviour under external loads such as a huge mass impact onto the structure and moving loads of an airplane, respectively. These results are verified with existing numerical results and experimental test. Then, the developed numerical tools are used in the study of the combined action taking into account of the mass drop/airplane landing as well as forward or reverse incident wave action. The deflections of the runway, the time history of vertical positions and the trajectory of the airplane are also presented through a systematic time-domain simulation, which illustrates the usefulness of the presently developed numerical solutions

Local and global instabilities of flow in a flexible-walled channel

We consider laminar high-Reynolds-number flow through a long finite-length planar channel, where a segment of one wall is replaced by a massless membrane held under longitudinal tension. The flow is driven by a fixed pressure difference across the channel and is described using an integral form of the unsteady boundary-layer equations. The basic flow state, for which the channel has uniform width, exhibits static and oscillatory global instabilities, having distinct modal forms. In contrast, the corresponding local problem (neglecting boundary conditions associated with the rigid parts of the system) is found to be convectively, but not absolutely, unstable to small-amplitude disturbances in the absence of wall damping. We show how amplification of the primary global oscillatory instability can arise entirely from wave reflections with the rigid parts of the system, involving interacting travelling wave flutter and static-divergence modes that are convectively stable; alteration of the mean flow by oscillations makes the onset of this primary instability subcritical. We also show how distinct mechanisms of energy transfer differentiate the primary global mode from other modes of oscillatory instability

Analytical and Numerical Approaches to Initiation of Excitation Waves

This thesis studies the problem of initiation of propagation of excitation waves in one- dimensional spatially extended excitable media. In a study which set out to determine an analytical criteria for the threshold conditions, Idris and Biktashev [68] showed that the linear approximation of the (center-)stable manifold of a certain critical solution yields analytical approximation of the threshold curves, separating initial (or boundary) conditions leading to propagation wave solutions from those leading to decay solutions. The aim of this project is to extend this method to address a wider class of ex- citable systems including multicomponent reaction-diffusion systems, systems with non-self-adjoint linearized operators and in particular, systems with moving critical solutions (critical fronts and critical pulses). In the case of one-component excitable systems where the critical solution is the critical nucleus, we also extend the theory to a quadratic approximation for the purpose of improving the accuracy of the linear approximation. The applicability of the approach is tested through five test problems with either traveling front such as Biktashev model, a simplified cardiac excitation model or traveling pulse solutions including Beeler-Reuter model, near realistic cardiac excitation model. Apart from some exceptional cases, it is not always possible to obtain explicit solution for the essential ingredients of the theory due to the nonlinear nature of the problem. Thus, this thesis also covers a hybrid method, where these ingredients are found numerically. Another important finding of the research is the use of the perturbation theory to find the approximate solution of the essential ingredients of FitzHugh-Nagumo system by using the exact analytical solutions of its primitive ver- sion, Zeldovich-Frank-Kamenetsky equation

Super-convergence of Discontinuous Galerkin Method Applied to the Navier-Stokes Equations

The practical benefits of the hyper-accuracy properties of the discontinuous Galerkin method are examined. In particular, we demonstrate that some flow attributes exhibit super-convergence even in the absence of any post-processing technique. Theoretical analysis suggest that flow features that are dominated by global propagation speeds and decay or growth rates should be super-convergent. Several discrete forms of the discontinuous Galerkin method are applied to the simulation of unsteady viscous flow over a two-dimensional cylinder. Convergence of the period of the naturally occurring oscillation is examined and shown to converge at 2p+1, where p is the polynomial degree of the discontinuous Galerkin basis. Comparisons are made between the different discretizations and with theoretical analysis