Explicit Solutions for the Wave Equation on Homogeneous Trees

AbstractIn this paper we consider the discretized version of the wave equation, in which a manifold is replaced by a homogeneous tree and the time line is replaced by the natural numbers. We give two methods for finding a closed form of the solution. One of these methods is found by first solving the Radon transform of the solution, which has a much simpler form. We also find a simple formula for the Radon transformation of the solution to the heat equation on homogeneous trees

Effective Values of Komar Conserved Quantities and Their Applications

We calculate the effective Komar angular momentum for the Kerr-Newman (KN) black hole. This result is valid at any radial distance on and outside the black hole event horizon. The effcetive values of mass and angular momentum are then used to derive an identity ($K_{\chi^{\mu}}=2ST$) which relates the Komar conserved charge ($K_{\chi^{\mu}}$) corresponding to the null Killing vector ($\chi^{\mu}$) with the thermodynamic quantities of this black hole. As an application of this identity the generalised Smarr formula for this black hole is derived. This establishes the fact that the above identity is a local form of the inherently non-local generalised Smarr formula.Comment: v3, minor modifications over v2; LaTex, 9 pages, no figures, to appear in Int. Jour. Theo. Phy

Uniqueness of the electrostatic solution in Schwarzschild space

In this Brief Report we give the proof that the solution of any static test charge distribution in Schwarzschild space is unique. In order to give the proof we derive the first Green's identity written with p-forms on (pseudo) Riemannian manifolds. Moreover, the proof of uniqueness can be shown for either any purely electric or purely magnetic field configuration. The spacetime geometry is not crucial for the proof.Comment: 3 pages, no figures, uses revtex4 style file

Resuscitation-promoting factors possess a lysozyme-like domain

The novel bacterial cytokine family – resuscitation-promoting factors (Rpfs) – share a conserved domain of uncharacterized function. Predicting the structure of this domain suggests that Rpfs possess a lysozyme-like domain. The model highlights the good conservation of residues involved in catalysis and substrate binding. A lysozyme-like function makes sense for this domain in the light of experimental characterization of the biological function of Rpfs

Semiclassical force for electroweak baryogenesis: three-dimensional derivation

We derive a semiclassical transport equation for fermions propagating in the presence of a CP-violating planar bubble wall at a first order electroweak phase transition. Starting from the Kadanoff-Baym (KB) equation for the two-point (Wightman) function we perform an expansion in gradients, or equivalently in the Planck constant h-bar. We show that to first order in h-bar the KB equations have a spectral solution, which allows for an on-shell description of the plasma excitations. The CP-violating force acting on these excitations is found to be enhanced by a boost factor in comparison with the 1+1-dimensional case studied in a former paper. We find that an identical semiclassical force can be obtained by the WKB method. Applications to the MSSM are also mentioned.Comment: 19 page

Generation of the Baryon Asymmetry of the Universe within the Left--Right Symmetric Model

Fermions scattering off first-order phase transition bubbles, in the framework of $SU(2)_L\otimes SU(2)_R\otimes U(1)$ models, may generate the Baryon Asymmetry of the Universe (BAU), either at the $LR$-symmetry-breaking scale, or at the weak scale. In the latter case, the baryon asymmetry of the Universe is related to CP violation in the $K_0$--$\bar K_0$ system.Comment: 17 pages, CERN--TH 6747/92, ULB--TH--07/92, UAB-FT-298/9

Mixing-induced CP violating sources for electroweak baryogenesis from a semiclassical approach

The effects of flavor mixing in electroweak baryogenesis is investigated in a generalized semiclassical WKB approach. Through calculating the nonadiabatic corrections to the particle currents it is shown that extra CP violation sources arise from the off-diagonal part of the equation of motion of particles moving inside the bubble wall. This type of mixing-induced source is of the first order in derivative expansion of the Higgs condensate, but is oscillation suppressed. The numerical importance of the mixing-induced source is discussed in the Minimal Supersymmetric Standard Model and compared with the source term induced by semiclassical force. It is found that in a large parameter space where oscillation suppression is not strong enough, the mixing-induced source can dominate over that from the semiclassical force.Comment: 19 pp, 2 figs, 1 table, some comments added, to appear in Eur.Phys.J.

Naturaliste plateau: constraints on the timing and evolution of the Kerguelen Large Igneous Province and its role in Gondwana breakup

Volcanism associated with the Kerguelen Large Igneous Province is found scattered in southwestern Australia (the ca 136 to ca 130 Ma Bunbury Basalts, and ca 124 Ma Wallaby Plateau), India (ca 118 Ma Rajmahal Traps and Cona Basalts), and Tibet (the ca 132 Ma Comei Basalts), but apart from the ∼70 000 km2 Wallaby Plateau, these examples are spatially and volumetrically minor. Here, we report dredge, geochronological and geochemical results from the ∼90 000 km2 Naturaliste Plateau, located ∼170 to ∼500 km southwest of Australia. Dredged lavas and intrusive rocks range from mafic to felsic compositions, and prior geophysical analyses indicate these units comprise much of the plateau substrate. 40Ar/39Ar plagioclase ages from mafic units and U–Pb zircon ages from silicic rocks indicate magmatic emplacement from 130.6 ± 1.2 to 129.4 ± 1.3 Ma for mafic rocks and 131.8 ± 3.9 to 128.2 ± 2.3 Ma for silicic rocks (2σ). These Cretaceous Naturaliste magmas incorporated a significant component of continental crust, with relatively high 87Sr/86Sr (up to 0.78), high 207Pb/204 Pb ratios (15.5–15.6), low 143Nd/144Nd (0.511–0.512) and primitive-mantle normalised Th/Nb of 11.3 and La/Nb of 3.97. These geochemical results are consistent with the plateau being underlain by continental basement, as indicated by prior interpretations of seismic and gravity data, corroborated by dredging of Mesoproterozoic granites and gneisses on the southern plateau flank. The Cretaceous Naturaliste Plateau igneous rocks have signatures indicative of extraction from a depleted mantle, with trace-element and isotopic values that overlap with Kerguelen Plateau lavas reflect crustal contamination. Our chemical and geochronological results therefore show the Naturaliste Plateau contains evidence of an extensive igneous event representing some of the earliest voluminous Kerguelen hotspot magmas. Prior work reports that contemporaneous correlative volcanic sequences underlie the nearby Mentelle Basin, and the Enderby Basin and Princess Elizabeth Trough in the Antarctic. When combined, the igneous rocks in the Naturaliste, Mentelle, Wallaby, Enderby, Princess Elizabeth, Bunbury and Comei-Cona areas form a 136–124 Ma Large Igneous Province covering >244 000 km2

A sticky business: the status of the conjectured viscosity/entropy density bound

There have been a number of forms of a conjecture that there is a universal lower bound on the ratio, eta/s, of the shear viscosity, eta, to entropy density, s, with several different domains of validity. We examine the various forms of the conjecture. We argue that a number of variants of the conjecture are not viable due to the existence of theoretically consistent counterexamples. We also note that much of the evidence in favor of a bound does not apply to the variants which have not yet been ruled out.Comment: 23 pages, 4 figures, added references, corrected typos, added subsection in response to Son's comments in arXiv:0709.465

Colonisation-induced protection against Streptococcus pneumoniae disease

Streptococus pneumoniae is an important human pathogen, yet in most individuals it establishes only transient nasopharyngeal colonisation without causing disease. Using murine models, this thesis explores the hypothesis that colonisation induces acquired immune responses which protect against subsequent pneumonia. Colonisation models with wild-type (WT) and mutant S. pneumoniae were established in outbred CD1 mice. Mutants lacked either capsule or lipoproteins, or were auxotrophs unable to replicate in vivo. WT colonisation protected against subsequent pneumonia. Mutants were cleared more rapidly than WT, were not immunogenic and did not protect. When the auxotroph was supplemented, colonisation, immunogenicity and protection were improved, suggesting duration of a colonisation event is an important factor in determining immunogenicity. This may be one factor explaining the poor immunogenicity of the other mutants. The mechanism by which previous colonisation protected against subsequent lethal pneumonia was then defined in a series of studies in inbred CBA/Ca mice. Colonisation induced both mucosal and systemic antibody responses to bacterial surface antigens but not capsule. There was also evidence of more robust cytokine production during subsequent pneumonia, including systemic and mucosal IL-17 responses dependant on the presence of CD4-cells. Protection was primarily against systemic invasion following pneumonia. Passive transfer studies and experiments using genetically modified mice demonstrated that systemic antibody was both necessary and sufficient to protect, and in vitro and in vivo models showed this to be via opsonophagocytosis and bloodstream clearance of bacteria. Antigenic protein targets of protective serum were defined using Western blotting and multiplex bead immunoassay techniques. Overall this thesis demonstrates that nasopharyngeal colonisation can protect against lethal pneumonia in mice via opsonophagocytic antibody against surface proteins thus preventing bacteraemia