A Note on Diogmitae

published or submitted for publicatio

The J-Box Problem

The study group was presented with the problem of determining the behaviour of a web of wet cellulose fibres - called a tow - as it passes through part of the manufacturing process. The name of the problem derives from the fact that on its passage down the production line the tow passes through a J-shaped box, whose purpose is to provide a buffer where the tow is stored long enough and hot enough for certain chemical reactions to take place, mainly concerned with giving the right quality to the fibre surface. (The production line in fact involves two J-boxes, one containing wet tow, the other dry, and we are here entirely concerned with the first of these, the wet J-box.) Three aspects of the tow behaviour were proposed for investigation: 1. What is the mechanical behaviour of the tow within the J-box ? Specifically, how do the time spent within the J-box and the shape of the tow outlet column depend on the J- box geometry, tow density and compressibility, flow rate, friction coefficients etc. 2. What is the temperature history, and hence the chemical history, of the tow within the J-box? 3. Why do dislocations and loops occur within the tow? We first give typical parameters and other details of the process, and then further details of these three questions

Μαρτυρία для Аполлония Тианского

Автор ставит задачу проанализировать одно из т.н. писем Аполлония Тианского. Исследователь доказывает, что письмо это точно соответствует форме официального "свидетельства о заслугах", и делает попытку подтвердить существующее в историографии наблюдение, что автором письма был не император Клавдий, а некий римский гражданин, имя которого было вычеркнуто из текста

Inflation on Fractional Branes: D--Brane Inflation as D--Term Inflation

We describe a D--brane inflation model which consists of two fractional D3 branes separated on a transverse $T^2 \times K3$. Inflation arises due to the resolved orbifold singularity of $K3$ which corresponds to an anomalous D--term on the brane. We show that D--brane inflation in the bulk corresponds to D--term inflation on the brane. The inflaton and the trigger field parametrize the interbrane distances on $T^2$ an $K3$ respectively. After inflation the branes reach a supersymmetric configuration in which they are at the origin of $T^2$ but separated along the $K3$ directions.Comment: 15 pages in phyzzx.tex; minor corrections including all factors of 2\pi; v3: more minor correction

Cosmology and two-body problem of D-branes

In this paper, we investigate the dynamics and the evolution of the scale factor of a probe Dp-brane which move in the background of source Dp-branes. Action of the probe brane is described by the Born-Infeld action and the interaction with the background R-R field. When the probe brane moves away from the source branes, it expands by power law, whose index depends on the dimension of the brane. If the energy density of the gauge field on the brane is subdominant, the expansion is decelerating irrespective of the dimension of the brane. On the other hand, when the probe brane is a Nambu-Goto brane, the energy density of the gauge field can be dominant, in which case accelerating expansion occurs for $p \leq 4$. The accelerating expansion stops when the brane has expanded sufficiently so that the energy density of the gauge field become subdominant.Comment: 6 pages, 7 figures, reference added, accepted for publication in PR

The Effective Potential, the Renormalisation Group and Vacuum Stability

We review the calculation of the the effective potential with particular emphasis on cases when the tree potential or the renormalisation-group-improved, radiatively corrected potential exhibits non-convex behaviour. We illustrate this in a simple Yukawa model which exhibits a novel kind of dimensional transmutation. We also review briefly earlier work on the Standard Model. We conclude that, despite some recent claims to the contrary, it can be possible to infer reliably that the tree vacuum does not represent the true ground state of the theory.Comment: 23 pages; 5 figures; v2 includes minor changes in text and additional reference

Inflation in Realistic D-Brane Models

We find successful models of D-brane/anti-brane inflation within a string context. We work within the GKP-KKLT class of type IIB string vacua for which many moduli are stabilized through fluxes, as recently modified to include `realistic' orbifold sectors containing standard-model type particles. We allow all moduli to roll when searching for inflationary solutions and find that inflation is not generic inasmuch as special choices must be made for the parameters describing the vacuum. But given these choices inflation can occur for a reasonably wide range of initial conditions for the brane and antibrane. We find that D-terms associated with the orbifold blowing-up modes play an important role in the inflationary dynamics. Since the models contain a standard-model-like sector after inflation, they open up the possibility of addressing reheating issues. We calculate predictions for the CMB temperature fluctuations and find that these can be consistent with observations, but are generically not deep within the scale-invariant regime and so can allow appreciable values for $dn_s/d\ln k$ as well as predicting a potentially observable gravity-wave signal. It is also possible to generate some admixture of isocurvature fluctuations.Comment: 39 pages, 21 figures; added references; identified parameters combining successful inflation with strong warping, as needed for consistency of the approximation

The universality of the shift of the Chern-Simons parameter for a general class of BRS invariant regularizations

We consider a biparametric family of BRS invariant regularization methods of SU(N) Chern-Simons theory (the parameters defining the family taking arbitrary values in \RR^2) and show that the shift $k\to k + sign(k) N$ of the Chern-Simons parameter $k$ occurs for arbitrary values of the family defining parameters. This supports irrefutably the conjecture that the shift of $k$ is universal for BRS invariant regulators.Comment: phyzzx, 7 pages (no figures

Adatoms and nanoengineering of carbon

We present a new and general mechanism for inter-conversion of carbon structures via a catalytic exchange process, which operates under conditions of Frenkel pair generation. The mechanism typically lowers reaction barriers by a factor of four compared to equivilent uncatalysed reactions. We examine the relevance of this mechanism for fullerene growth, carbon onions and nanotubes, and dislocations in irradiated graphite.Comment: 3 Figures, 5 Page letter accepted for publication in Chemical Physics Letter

Regular S-Brane Backgrounds

We construct time-dependent S-brane solutions to the supergravity field equations in various dimensions which (unlike most such geometries) do not contain curvature singularities. The configurations we consider are less symmetric than are earlier solutions, with our simplest solution being obtained by a simple analytical continuation of the Kerr geometry. We discuss in detail the global structure and properties of this background. We then generalize it to higher dimensions and to include more complicated field configurations - like non vanishing scalars and antisymmetric tensor gauge potentials - by the usual artifice of applying duality symmetries.Comment: 22 pages, 3 figures. Typos in eq.(2.6) correcte