Cop and robber game and hyperbolicity

In this note, we prove that all cop-win graphs G in the game in which the robber and the cop move at different speeds s and s' with s'<s, are \delta-hyperbolic with \delta=O(s^2). We also show that the dependency between \delta and s is linear if s-s'=\Omega(s) and G obeys a slightly stronger condition. This solves an open question from the paper (J. Chalopin et al., Cop and robber games when the robber can hide and ride, SIAM J. Discr. Math. 25 (2011) 333-359). Since any \delta-hyperbolic graph is cop-win for s=2r and s'=r+2\delta for any r>0, this establishes a new - game-theoretical - characterization of Gromov hyperbolicity. We also show that for weakly modular graphs the dependency between \delta and s is linear for any s'<s. Using these results, we describe a simple constant-factor approximation of the hyperbolicity \delta of a graph on n vertices in O(n^2) time when the graph is given by its distance-matrix

Cosmological Simulations of Normal-Branch Braneworld Gravity

We introduce a cosmological model based on the normal branch of DGP braneworld gravity with a smooth dark energy component on the brane. The expansion history in this model is identical to LambdaCDM, thus evading all geometric constraints on the DGP cross-over scale r_c. This model can serve as a first approximation to more general braneworld models whose cosmological solutions have not been obtained yet. We study the formation of large scale structure in this model in the linear and non-linear regime using N-body simulations for different values of r_c. The simulations use the code presented in (F.S., arXiv:0905.0858) and solve the full non-linear equation for the brane-bending mode in conjunction with the usual gravitational dynamics. The brane-bending mode is attractive rather than repulsive in the DGP normal branch, hence the sign of the modified gravity effects is reversed compared to those presented in arXiv:0905.0858. We compare the simulation results with those of ordinary LambdaCDM simulations run using the same code and initial conditions. We find that the matter power spectrum in this model shows a characteristic enhancement peaking at k ~ 0.7 h/Mpc. We also find that the abundance of massive halos is significantly enhanced. Other results presented here include the density profiles of dark matter halos, and signatures of the brane-bending mode self-interactions (Vainshtein mechanism) in the simulations. Independently of the expansion history, these results can be used to place constraints on the DGP model and future generalizations through their effects on the growth of cosmological structure.Comment: 17 pages, 10 figures; v2: minor changes; v3: references added; v4: added appendix on comparison with previous results; matches published version; v5: corrected Eqs. (2.4-2.5) and Fig. 1 following Ref. [28]; all following results unchange

Giant Thermomechanical Bandgap Engineering in Quasi-two-dimensional Tellurium

Mechanical straining-induced bandgap modulation in two-dimensional (2D) materials has been confined to volatile and narrow modulation due to substrate slippage and poor strain transfer. We report the thermomechanical modulation of the inherent bandgap in quasi-2D tellurium nanoflakes (TeNFs) via non-volatile strain induction during hot-press synthesis. We leveraged the coefficient of thermal expansion (CTE) mismatch between TeNFs and growth substrates by maintaining a high-pressure enforced non-slip condition during thermal relaxation (623 to 300K) to achieve the optimal biaxial compressive strain of -4.6 percent in TeNFs/sapphire. This resulted in an enormous bandgap modulation of 2.3 eV, at a rate of up to ~600 meV/%, which is two-fold larger than reported modulation rate. Strained TeNFs display robust band-to-band radiative excitonic blue photoemission with an intrinsic quantum efficiency (IQE) of c.a. 79.9%, making it promising for energy efficient blue LEDs and nanolasers. Computational studies reveal that biaxial compressive strain inhibits exciton-exciton annihilation by evading van-Hove singularities, hence promoting radiative-recombination. Bandgap modulation by such nonvolatile straining is scalable to other 2D semiconductors for on-demand nano(opto)-electronics

Relative Locations

The fact that physical laws often admit certain kinds of space-time symmetries is often thought to be problematic for substantivalism --- the view that space-time is as real as the objects it contains. The most prominent alternative, relationism, avoids these problems but at the cost of giving abstract objects (rather than space-time points) a pivotal role in the fundamental metaphysics. This incurs related problems concerning the relation of the physical to the mathematical. In this paper I will present a version of substantivalism that respects Leibnizian theses about space-time symmetries, and argue that it is superior to both relationism and the more orthodox form of substantivalism

Triple crossing positivity bounds, mass dependence and cosmological scalars: Horndeski theory and DHOST

Scalars are widely used in cosmology to model novel phenomena such as the late-time cosmic acceleration. These are effective field theories with highly nonlinear interactions, including Horndeski theory/generalized galileon and beyond. We use the latest fully crossing symmetric positivity bounds to constrain these cosmological EFTs. These positivity bounds, based on fundamental principles of quantum field theory such as causality and unitarity, are able to constrain the EFT coefficients both from above and below. We first map the mass dependence of the fully crossing symmetric bounds, and find that a nonzero mass generically enlarges the positivity regions. We show that fine-tunings in the EFT construction can significantly reduce the viable regions and sometimes can be precarious. Then, we apply the positivity bounds to several models in the Horndeski class and beyond, explicitly listing the ready-to-use bounds with the model parameters, and discuss the implications for these models. The new positivity bounds are found to severely constrain some of these models, in which positivity requires the mass to be parametrically close to the cutoff of the EFT, effectively ruling them out. The examples include massive galileon, the original beyond Horndeski model, and DHOST theory with unity speed of gravity and nearly constant Newton's coupling.Comment: 45 pages, 16 figures, 1 table. To appear in JCA