On gravitational fields of stars in f(R) gravity theories

Einstein's general relativity is a classical theory of gravitation: it is a postulate on the coupling between the four-dimensional, continuos spacetime and the matter fields in the universe, and it yields their dynamical evolution. It is believed that general relativity must be replaced by a quantum theory of gravity at least at extremely high energies of the early universe and at regions of strong curvature of spacetime, cf. black holes. Various attempts to quantize gravity, including conceptually new models such as string theory, have suggested that modification to general relativity might show up even at lower energy scales. On the other hand, also the late time acceleration of the expansion of the universe, known as the dark energy problem, might originate from new gravitational physics. Thus, although there has been no direct experimental evidence contradicting general relativity so far - on the contrary, it has passed a variety of observational tests - it is a question worth asking, why should the effective theory of gravity be of the exact form of general relativity? If general relativity is modified, how do the predictions of the theory change? Furthermore, how far can we go with the changes before we are face with contradictions with the experiments? Along with the changes, could there be new phenomena, which we could measure to find hints of the form of the quantum theory of gravity? This thesis is on a class of modified gravity theories called f(R) models, and in particular on the effects of changing the theory of gravity on stellar solutions. It is discussed how experimental constraints from the measurements in the Solar System restrict the form of f(R) theories. Moreover, it is shown that models, which do not differ from general relativity at the weak field scale of the Solar System, can produce very different predictions for dense stars like neutron stars. Due to the nature of f(R) models, the role of independent connection of the spacetime is emphasized throughout the thesis.

Applications of dimensional reduction to electroweak and QCD matter

When heated to high temperatures, the behavior of matter changes dramatically. The standard model fields go through phase transitions, where the strongly interacting quarks and gluons are liberated from their confinement to hadrons, and the Higgs field condensate melts, restoring the electroweak symmetry. The theoretical framework for describing matter at these extreme conditions is thermal field theory, combining relativistic field theory and quantum statistical mechanics. For static observables the physics is simplified at very high temperatures, and an effective three-dimensional theory can be used instead of the full four-dimensional one via a method called dimensional reduction. In this thesis dimensional reduction is applied to two distinct problems, the pressure of electroweak theory and the screening masses of mesonic operators in quantum chromodynamics (QCD). The introductory part contains a brief review of finite-temperature field theory, dimensional reduction and the central results, while the details of the computations are contained in the original research papers. The electroweak pressure is shown to converge well to a value slightly below the ideal gas result, whereas the pressure of the full standard model is dominated by the QCD pressure with worse convergence properties. For the mesonic screening masses a small positive perturbative correction is found, and the interpretation of dimensional reduction on the fermionic sector is discussed.

Data mining approaches to software fault diagnosis

Automatic identification of software faults has enormous practical significance. This requires characterizing program execution behavior and the use of appropriate data mining techniques on the chosen representation. In this paper, we use the sequence of system calls to characterize program execution. The data mining tasks addressed are learning to map system call streams to fault labels and automatic identification of fault causes. Spectrum kernels and SVM are used for the former while latent semantic analysis is used for the latter The techniques are demonstrated for the intrusion dataset containing system call traces. The results show that kernel techniques are as accurate as the best available results but are faster by orders of magnitude. We also show that latent semantic indexing is capable of revealing fault-specific features.

Stabilisation and characterisation of N,N′-dibenzylidene-o-phenylenediamine as a copper(I) perchlorate complex

QUITE OFTEN, metal ions profoundly affect the condensation of carbonyl compounds with primary amines to form Schiff bases as well as their subsequent reactions[I-4]. Condensation of benzaldehyde with o-phenylenediamine (opd) in glacial acetic acid[5] or in absolute alcohol[6] gives benzimidazole derivative, 1-benzyl-2-phenylbenzimidazole (bpbi). In this reaction, the Schiff base N,N'-dibenzylidene-o-phenylenedianfme (dbpd) has been postulated as an intermediate, which cyclises to give bpbi. It was found that the reaction of opd in presence of copperO1) perchlorate with benzaldehyde gave dbpd complex of copper(l) perchlorate instead of bpbi.

Dark solitons in holographic superfluids

We construct dark soliton solutions in a holographic model of a relativistic superfluid. We study the length scales associated with the condensate and the charge density depletion, and find that the two scales differ by a non-trivial function of the chemical potential. By adjusting the chemical potential, we study the variation of the depletion of charge density at the interface.

Cu(II) complexes of 1-benzyl-2-phenyl-benzimidazole

Copper(II) complexes of 1-benzyl-2-phenylbenzimidazole (BPBI) of the general formula Cu(BPBI)2X2, nH2O [X= Cl-, Br-, NO3 or OAc- (n = O) and X = NO3- or 1 2SO42-(n = 2H2O)] have been prepared. The complexes are found to be nonelectrolytes in nitrobenzene. Conductivity in nonaqueous media, magnetic susceptibilities and i.r. and electronic spectra of the complexes are reported. A tetragonally distorted octahedral structure has been suggested for these complexes.

Preparation of lower oxide of sulphur

RECENT work on the lower oxide of sulphur1,2 has established that disulphur monoxide (S2O) or its polymeric form is produced when sulphur is burnt in oxygen under reduced pressure. It has now been shown that it is possible to make use of an oxide of a heavy metal as a source of limited supply of oxygen to prepare the disulphur monoxide. For example, when a mixture of finely powdered cupric oxide and sulphur (1 : 5 by weight) is heated under vacuum in a glass tube gaseous products are evolved. which, on cooling in a trap surrounded by liquid air, will give an orange-red condensate (S2O)x. This condensate also gives off sulphur dioxide in stages as the temperature is raised, finally leaving a residue of elemental sulphur. Copper sulphide and excess of sulphur are left behind in the reaction tube.

Nitrosation of N,N′-ethylenebis-(acetylacetoneimine) complexes of copper (II) and nickel(II) and characterization of the products

Isonitroso derivatives of copper(II) and nickel(II) complexes of N,N′-ethylenebis(acetylacetoneimine) have been prepared by nitrosation of the respective complexes using nitric oxide as well as nitrite ion. The condensation of isonitrosoacetylacetone in the presence and in the absence of nickel(II) has been investigated. The i.r. and electronic spectra and magnetic moment of the nickel(II) and copper(II) complexes have been studied. The nature of bonding of the ligand to the metal ion is discussed. The complexes have planar structures.

Nickel(II) complexes of 1-benzyl-2-phenylbenzimidazole

Nickel(II) complexes of 1-benzyl-2-phenylbenzimidazole (BPBI) of the general formula [Ni(BPBI)2X2](X=Cl-, Br-, NCS- or NO3-) have been prepared and their magnetic moments, i.r. and electronic spectra studied. [Ni(BPBI)2Cl2] has a pseudotetrahedral structure while [Ni(BPBI)2 Br2] exists as square planar and speudotetrahedral isomers. [Ni(BPBI)2I2] and [NI(BPBI)2(NCS)2] have square planar stereochemistry. The nitrato complex [Ni(BPBI)2(NO)3)2] exists in two different octahedral modifications in the solid state.

Interfacial microrheology as a tool to study viscoelastic transitions in nanoconfined soft matter

We present a method to perform in situ microrheological measurements on monolayers of soft materials undergoing viscoelastic transitions under compression. Using the combination of a Langmuir trough mounted on the inverted microscope stage of a laser scanning confocal microscope we track the motion of individual fluorescent quantum dots partly dispersed in monolayers spread at the air-water interface. From the calculated mean square displacement of the probe particles and extending a well established scheme of the generalized Stokes-Einstein relation in bulk to the interface we arrive at the viscoelastic modulus for the respective monolayers as a function of surface density. Measurements on monolayers of glassy as well as nonglassy polymers and a standard fatty acid clearly show sensitivity of our technique to subtle variations, in the viscoelastic properties of the highly confined materials under compression. Evidence for possible spatial variations of such viscoelastic properties at a given surface density for the fatty acid monolayer is also provided.

Interfacial microrheology as a tool to study viscoelastic transitions in nanoconfined soft matter

We present a method to perform in situ microrheological measurements on monolayers of soft materials undergoing viscoelastic transitions under compression. Using the combination of a Langmuir trough mounted on the inverted microscope stage of a laser scanning confocal microscope we track the motion of individual fluorescent quantum dots partly dispersed in monolayers spread at the air-water interface. From the calculated mean square displacement of the probe particles and extending a well established scheme of the generalized Stokes-Einstein relation in bulk to the interface we arrive at the viscoelastic modulus for the respective monolayers as a function of surface density. Measurements on monolayers of glassy as well as nonglassy polymers and a standard fatty acid clearly show sensitivity of our technique to subtle variations, in the viscoelastic properties of the highly confined materials under compression. Evidence for possible spatial variations of such viscoelastic properties at a given surface density for the fatty acid monolayer is also provided.

A possible mechanism for high-temperature superconductivity: Application to Bi and Tl compounds

We applied our previous theory of high temperature superconductivity to Bi and Tl compounds in this paper. The theory involves the role of electron pairs in the spin singlet of species Xequal-or-greater, slanted (Bi3+ (6S2), Tl(6S2) etc.) and their virtual excited state X0 (Bi5+ (6s0), Tl3+ (6s0), etc.) in the pairing interaction of quasiholes. Bi and Tl species provide additional channels of kind (Xequal-or-greater, slanted left angle bracket X0) owing to the charge fluctuations. We treated the two states of these species like a two-level Bose system. We used the pseudospin formalism to calculate the expression for the critical temperature in this paper. We also calculated numerically the value of Tc for Bi and Tl compounds and found a good agreement between theory and experiment.