1,137 research outputs found
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 is convex in . 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
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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
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