D-instantons, Strings and M-theory

The R^4 terms in the effective action for M-theory compactified on a two-torus are motivated by combining one-loop results in type II superstring theories with the Sl(2,Z) duality symmetry. The conjectured expression reproduces precisely the tree-level and one-loop R^4 terms in the effective action of the type II string theories compactified on a circle, together with the expected infinite sum of instanton corrections. This conjecture implies that the R^4 terms in ten-dimensional string type II theories receive no perturbative corrections beyond one loop and there are also no non-perturbative corrections in the ten-dimensional IIA theory. Furthermore, the eleven-dimensional M-theory limit exists, in which there is an R^4 term that originates entirely from the one-loop contribution in the type IIA theory and is related by supersymmetry to the eleven-form C^{(3)}R^4. The generalization to compactification on T^3 as well as implications for non-renormalization theorems in D-string and D-particle interactions are briefly discussed.Comment: harvmac (b) 17 pages. v4: Some formulae corrected. Dimensions corrected for eleven-dimensional expression

Optimized trajectories to the nearest stars using lightweight high-velocity photon sails

New means of interstellar travel are now being considered by various research teams, assuming lightweight spaceships to be accelerated via either laser or solar radiation to a significant fraction of the speed of light (c). We recently showed that gravitational assists can be combined with the stellar photon pressure to decelerate an incoming lightsail from Earth and fling it around a star or bring it to rest. Here, we demonstrate that photogravitational assists are more effective when the star is used as a bumper (i.e. the sail passes "in front of" the star) rather than as a catapult (i.e. the sail passes "behind" or "around" the star). This increases the maximum deceleration at $\alpha$ Cen A and B and reduces the travel time of a nominal graphene-class sail (mass-to-surface ratio 8.6e-4 gram m$^{-2}$) from 95 to 75 yr. The maximum possible velocity reduction upon arrival depends on the required deflection angle from $\alpha$ Cen A to B and therefore on the binary's orbital phase. Here, we calculate the variation of the minimum travel times from Earth into a bound orbit around Proxima for the next 300 yr and then extend our calculations to roughly 22,000 stars within about 300 ly. Although $\alpha$ Cen is the most nearby star system, we find that Sirius A offers the shortest possible travel times into a bound orbit: 69 yr assuming 12.5% c can be obtained at departure from the solar system. Sirius A thus offers the opportunity of flyby exploration plus deceleration into a bound orbit of the companion white dwarf after relatively short times of interstellar travel.Comment: 14 pages, 7 figures (5 col, 2 b/w), 2 table

Statistical extraction of process zones and representative subspaces in fracture of random composite

We propose to identify process zones in heterogeneous materials by tailored statistical tools. The process zone is redefined as the part of the structure where the random process cannot be correctly approximated in a low-dimensional deterministic space. Such a low-dimensional space is obtained by a spectral analysis performed on pre-computed solution samples. A greedy algorithm is proposed to identify both process zone and low-dimensional representative subspace for the solution in the complementary region. In addition to the novelty of the tools proposed in this paper for the analysis of localised phenomena, we show that the reduced space generated by the method is a valid basis for the construction of a reduced order model.Comment: Submitted for publication in International Journal for Multiscale Computational Engineerin

Self-Stabilizing TDMA Algorithms for Dynamic Wireless Ad-hoc Networks

In dynamic wireless ad-hoc networks (DynWANs), autonomous computing devices set up a network for the communication needs of the moment. These networks require the implementation of a medium access control (MAC) layer. We consider MAC protocols for DynWANs that need to be autonomous and robust as well as have high bandwidth utilization, high predictability degree of bandwidth allocation, and low communication delay in the presence of frequent topological changes to the communication network. Recent studies have shown that existing implementations cannot guarantee the necessary satisfaction of these timing requirements. We propose a self-stabilizing MAC algorithm for DynWANs that guarantees a short convergence period, and by that, it can facilitate the satisfaction of severe timing requirements, such as the above. Besides the contribution in the algorithmic front of research, we expect that our proposal can enable quicker adoption by practitioners and faster deployment of DynWANs that are subject changes in the network topology

Jahn-Teller, polarity and insulator-to-metal transition in BiMnO3 at high pressure

The interaction of coexisting structural instabilities in multiferroic materials gives rise to intriguing coupling phenomena and extraordinarily rich phase diagrams, both in bulk materials and strained thin films. Here we investigate the multiferroic BiMnO3 with its peculiar 6s2 electrons and four interacting mechanisms: electric polarity, octahedra tilts, magnetism, and cooperative Jahn-Teller distortion. We have probed structural transitions under high pressure by synchrotron x-ray diffraction and Raman spectroscopy up to 60 GPa. We show that BiMnO3 displays under pressure a rich sequence of five phases with a great variety of structures and properties, including a metallic phase above 53 GPa and, between 37 and 53 GPa, a strongly elongated monoclinic phase that allows ferroelectricity, which contradicts the traditional expectation that ferroelectricity vanishes under pressure. Between 7 and 37 GPa, the Pnma structure remains remarkably stable but shows a reduction of the Jahn-Teller distortion in a way that differs from the behavior observed in the archetypal orthorhombic Jahn-Teller distorted perovskite LaMnO3.Comment: 5 pages, 3 figures + supplemental material included (3 pages, 1 figure, 3 tables

Polarized Fermi gases at finite temperature in the BCS-BEC crossover

We consider a polarized Fermi gas in the BCS-BEC crossover region above the critical temperature within a T matrix formalism. By treating the mean-field like shift of the quasiparticle energies in a self-consistent manner, we avoid the known pathological behavior of the standard Nozieres-Schmitt-Rink approach in the polarized case, i.e., the polarization has the right sign and the spin polarizability is positive. The momentum distributions of the correlated system are computed and it is shown that, in the zero-temperature limit, they satisfy the Luttinger theorem. Results for the phase diagram, the spin susceptibility, and the compressibility are discussed.Comment: 9 pages; v2: references and comparison with more recent experimental data added; v3: reference added and minor correction

Proof of a modular relation between 1-, 2- and 3-loop Feynman diagrams on a torus

The coefficients of the higher-derivative terms in the low energy expansion of genus-one graviton Type II superstring scattering amplitudes are determined by integrating sums of non-holomorphic modular functions over the complex structure modulus of a torus. In the case of the four-graviton amplitude, each of these modular functions is a multiple sum associated with a Feynman diagram for a free massless scalar field on the torus. The lines in each diagram join pairs of vertex insertion points and the number of lines defines its weight $w$, which corresponds to its order in the low energy expansion. Previous results concerning the low energy expansion of the genus-one four-graviton amplitude led to a number of conjectured relations between modular functions of a given $w$, but different numbers of loops $\le w-1$. In this paper we shall prove the simplest of these conjectured relations, namely the one that arises at weight $w=4$ and expresses the three-loop modular function $D_4$ in terms of modular functions with one and two loops. As a byproduct, we prove three intriguing new holomorphic modular identities.Comment: 38 pages, 9 figures, in version 2: Appendix D added and corrections made in section