Dynamical Evolution of the Extra Dimension in Brane Cosmology

The evolution of the extra dimension is investigated in the context of brane world cosmology. New cosmological solutions are found. In particular, solutions in the form of waves travelling along the extra dimension are identified.Comment: Latex file, 10 page

The derivative notion revised: The fractional case

In this paper the historical origins of fractional calculus are explored with respect to non-conformable derivatives. Implications are made for the teaching and learning of calculus and for mathematics education

Towards a microscopic construction of flavour vacua from a space-time foam model

The effect on flavour oscillations of simple expanding background space-times, motivated by some D-particle foam models, is calculated for a toy-model of bosons with flavour degrees of freedom. The presence of D-particle defects in the space-time, which can interact non trivially (via particle capture) with flavoured particles in a flavour non-preserving way, generates mixing in the effective field theory of low-energy string excitations. Moreover, the recoil of the D-particle defect during the capture/scattering process implies Lorentz violation, which however may be averaged to zero in isotropic D-particle populations, but implies non-trivial effects in correlators. Both features imply that the flavoured mixed state sees a non-trivial flavour (Fock-space) vacuum of a type introduced earlier by Blasone and Vitiello in a generic context of theories with mixing. We discuss the orthogonality of the flavour vacua to the usual Fock vacua and the effect on flavour oscillations in these backgrounds. Furthermore we analyse the equation of state of the Flavour vacuum, and find that, for slow expansion rates induced by D particle recoil, it is equivalent to that of a cosmological constant. Some estimates of these novel non-perturbative contribution to the vacuum energy are made. The contribution vanishes if the mass difference and the mixing angle of the flavoured states vanish.Comment: 27 pages RevTex, 2 eps figures incorporate

Time and "angular" dependent backgrounds from stationary axisymmetric solutions

Backgrounds depending on time and on "angular" variable, namely polarized and unpolarized $S^1 \times S^2$ Gowdy models, are generated as the sector inside the horizons of the manifold corresponding to axisymmetric solutions. As is known, an analytical continuation of ordinary $D$-branes, $iD$-branes allows one to find $S$-brane solutions. Simple models have been constructed by means of analytic continuation of the Schwarzchild and the Kerr metrics. The possibility of studying the $i$-Gowdy models obtained here is outlined with an eye toward seeing if they could represent some kind of generalized $S$-branes depending not only on time but also on an ``angular'' variable.Comment: 24 pages, 5 figures, corrected typos, references adde

Variant N=(1,1) Supergravity and (Minkowski)_4 x S^2 Vacua

We construct the fermionic sector and supersymmetry transformation rules of a variant N=(1,1) supergravity theory obtained by generalized Kaluza-Klein reduction from seven dimensions. We show that this model admits both (Minkowski)_4 x S^2 and (Minkowski)_3 x S^3 vacua. We perform a consistent Kaluza-Klein reduction on S^2 and obtain D=4, N=2 supergravity coupled to a vector multiplet, which can be consistently truncated to give rise to D=4, N=1 supergravity with a chiral multiplet.Comment: Latex, 17 pages. Version appearing in Classical and Quantum Gravit

Spall And Dynamic Yielding Of Aluminum And Aluminum Alloys At Strain Rates Of 3X10(6) S(-1)

We have explored the role that grain size, impurity particles and alloying in aluminum play in dynamic yielding and spall fracture at tensile strain rates of similar to 3x10(6) We achieved these strain rates shocking the aluminum specimens via laser ablation using the Z-Beamlet Laser at Sandia National Laboratories. The high purity aluminum and 1100 series aluminum alloy produced very different spall strengths and nearly the same yield strengths. In contrast, various grain-sized Al + 3 wt. % Mg specimens presented the lowest spall strength, but the greatest dynamic yield strength. Fracture morphology results and particle analysis are presented along with hydrodynamic simulations to put these results in context. Impurity particles appeared to play a vital role in spall fracture at these fast strain rates. Alloying elements such as Mg seem to be the dominant factor in the dynamic yield results.Mechanical Engineerin

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

Numerical experiments with p F- and q D-strings: the formation of (p,q) bound states

We investigate the behaviour of (p,q) string networks, focusing on two aspects: (1) modelling more realistic (p,q) string networks than the Z_N networks used so far and (2) investigating the effect of long-range interactions on the evolution of the network. We model the network with no long-range interactions using two sets of fields, complex scalars coupled to gauge fields, with a potential chosen such that the two types of strings will form bound states. This way we can model junctions of 3 strings with different tension; in Z_N models used so far in simulations all the strings have identical tensions. In order to introduce long-range interactions we also study a network in which one of the scalars forms global strings. We observe that in the absence of long-range interactions the formation of bound states has a significant influence on the evolution of the network. When long-range interactions are turned on the bound states are short-lived and have a minimal effect on the network evolution.Comment: 17 pages, 8 figures, JCAP styl

Holography and Brane-bulk Energy Exchange

The five-dimensional description of generalized Randall-Sundrum cosmology is mapped via holography to a generalization of the Starobinsky model. This provides a holographic dual description of the cosmological brane-bulk energy exchange processes studied previously. Some simple solutions are presented in four dimensions.Comment: 41 pages, LaTe