Instability of steady states for nonlinear wave and heat equations

We consider time-independent solutions of hyperbolic equations such as \d_{tt}u -\Delta u= f(x,u) where $f$ is convex in $u$. We prove that linear instability with a positive eigenfunction implies nonlinear instability. In some cases the instability occurs as a blow up in finite time. We prove the same result for parabolic equations such as \d_t u -\Delta u= f(x,u). Then we treat several examples under very sharp conditions, including equations with potential terms and equations with supercritical nonlinearities

Towards the quantization of the non-relativistic D2-brane in the Pure Spinor Formalism

An attempt is made to apply the pure spinor formalism to the non-relativistic IIA D2-brane. The fermionic constraints corresponding to the rescaled fermionic coordinates are given. Two commuting spinor fields are introduced, each one corresponding to a fermionic constraint. A BRST charge is constructed via the ansatz proposed by N. Berkovits. The nilpotency of the BRST charge leads to a set of constraints for the two spinor fields including pure spinor constraints. A novel non-trivial solution is given for one of the spinor fields which can be written as a sum of two pure spinors.Comment: 23 pages in latex, no figures; discussion added, some typos corrected, more references adde

String Thermalization in Static Spacetimes

We study the evolution, the transverse spreading and the subsequent thermalization of string states in the Weyl static axisymmetric spacetime. This possesses a singular event horizon on the symmetry axis and a naked singularity along the other directions. The branching diffusion process of string bits approaching the singular event horizon provides the notion of temperature that is calculated for this process. We find that the solution of the Fokker-Planck equation in the phase space of the transverse variables of the string, can be factored as a product of two thermal distributions, provided that the classical conjugate variables satisfy the uncertainty principle. We comment on the possible physical significance of this result.Comment: 16 pages, no figures, Late

Strengthening of existing reinforced concrete structures using ultra high performance fiber reinforced concrete

Most of the new Reinforced Concrete (RC) structures which are built nowadays have a high safety level. Nevertheless, we cannot claim the same for structures built in the past. Many of these were designed without any regulations, or are based on those which have proved to be inadequate. Additionally, it seems that many old structures have reached the end of their service life and, in many cases, were designed to carry loads significantly lower than the current needs specify. Therefore, the structural evaluation and intervention are considered necessary, so they can meet the same requirements as the structures which are built today. Existing techniques for the strengthening and retrofitting of RC structures present crucial disadvantages which are mainly related to the ease of application, the high cost, the time it takes to be applied, the relocation of the tenants during the application of the technique and the poor performance. Research is now focused on new techniques which combine strength, cost effectiveness and ease of application. The superior mechanical properties of Ultra High Performance Fiber Reinforced Concrete (UHPFRC) compared to conventional concrete, together with the ease of preparation and application of the material, make the application of UHPFRC in the field of strengthening of RC structures attractive. The present research aims to investigate the effectiveness of UHPFRC as a strengthening material, and to examine if the material is able to increase the load carrying capacity of existing RC elements. This has been achieved through an extensive experimental and numerical investigation. The first part of the present research is focused on the experimental investigation of the properties of the material which are missing from the literature and the development of a mixture design which can be used for strengthening applications. The second part is focused on the realistic application of the material for the strengthening of existing RC elements using different strengthening configurations. Finally, in the last part, certain significant parameters of the examined technique, which are mainly related to the design of the technique, are investigated numerically. From the experimental and numerical investigation of the present research it was clear that UHPFRC is a material with enhanced properties and the strengthening with UHPFRC is a well promising technique. Therefore, in all the examined cases, the performance of the strengthened elements was improved. Finally, an important finding of the present research was that the bonding between UHPFRC and concrete is effective with low values of slip at the interface

2-Imidazolines in Annulation Studies.

This thesis will describe attempts to use suitably substituted 2-imidazolines in Diels-Alder reactions. In order to synthesise these target 2-imidazolines a new and reliable method for the synthesis of 2-alkyl and 2-alkenyl-2-imidazolines has been developed. Metallation at C(2a) of l-ferf-butyloxycarbonyl-2-methyl-2-imidazoline, followed by reaction with a range of electrophiles and deprotection with TFA reliably afforded N(l)- unsubstituted 2-substituted 2-imidazolines; P- or Se-electrophiles led to 2-alkenyl-2- imidazolines via Wadsworth-Emmons reaction or selenoxide elimination. In an attempt to prepare N-butadienyl-2-imidazolines via the reaction of 2-alkyl-2-imidazolines and ɑ,ß-unsaturated aldehydes or ketones, tetrahydroimidazo[1,2-a]pyridines have been synthesised via conjugate addition of the heterocycle N(l) nitrogen atom followed by enamine-aldol condensation at C(2ɑ). 2-Imidazolines reacted with ß-ketoesters to give tetrahydroimidazo[1,2-a]pyridin- 5-ones. Whilst examining the reactions of 2-alkyl-2-imidazolines with alkyne diesters, a new annulation was uncovered that is based on N(l) conjugate addition followed by C(2ɑ) The reaction of 2-imidazolines with dialkyl acetylenedicafboxylate afforded tetrahydropyrrolo[1,2-a]imidazole-5,6-diones. None of the 2-imidazolines synthesised that contained diene functionalities underwent either intra or intermolecular Diels-Alder reactions

Application of the canonical quantization of systems with curved phase space to the EMDA theory

The canonical quantization of dynamical systems with curved phase space introduced by I.A. Batalin, E.S. Fradkin and T.E. Fradkina is applied to the four-dimensional Einstein-Maxwell Dilaton-Axion theory. The spherically symmetric case with radial fields is considered. The Lagrangian density of the theory in the Einstein frame is written as an expression with first order in time derivatives of the fields. The phase space is curved due to the nontrivial interaction of the dilaton with the axion and the electromagnetic fields.Comment: 23 pages in late

3-D Registration on Carotid Artery imaging data: MRI for different timesteps

A common problem which is faced by the researchers when dealing with arterial carotid imaging data is the registration of the geometrical structures between different imaging modalities or different timesteps. The use of the "Patient Position" DICOM field is not adequate to achieve accurate results due to the fact that the carotid artery is a relatively small structure and even imperceptible changes in patient position and/or direction make it difficult. While there is a wide range of simple/advanced registration techniques in the literature, there is a considerable number of studies which address the geometrical structure of the carotid artery without using any registration technique. On the other hand the existence of various registration techniques prohibits an objective comparison of the results using different registration techniques. In this paper we present a method for estimating the statistical significance that the choice of the registration technique has on the carotid geometry. One-Way Analysis of Variance(ANOVA) showed that the p-values were <0.0001 for the distances of the lumen from the centerline for both right and left carotids of the patient case that was studied.Comment: 4 pages, 4 figures, 1 table, preprint submitted to IEEE-EMBC 201