Nonlinear dynamics of coupled transverse-rotational waves in granular chains

The nonlinear dynamics of coupled waves in one-dimensional granular chains with and without a substrate is theoretically studied accounting for quadratic nonlinearity. The multiple time scale method is used to derive the nonlinear dispersion relations for infinite granular chains and to obtain the wave solutions for semiinfinite systems. It is shown that the sum-frequency and difference-frequency components of the coupled transverse-rotational waves are generated due to their nonlinear interactions with the longitudinal wave. Nonlinear resonances are not present in the chain with no substrate where these frequency components have low amplitudes and exhibit beating oscillations. In the chain positioned on a substrate two types of nonlinear resonances are predicted. At resonance, the fundamental frequency wave amplitudes decrease and the generated frequency component amplitudes increase along the chain, accompanied by the oscillations due to the wave numbers asynchronism. The results confirm the possibility of a highly efficient energy transfer between the waves of different frequencies, which could find applications in the design of acoustic devices for energy transfer and energy rectification

No black hole information puzzle in a relational universe

The introduction of a relational time in quantum gravity naturally implies that pure quantum states evolve into mixed quantum states. We show, using a recently proposed concrete implementation, that the rate at which pure states naturally evolve into mixed ones is faster than that due to collapsing into a black hole that later evaporates. This is rather remarkable since the fundamental mechanism for decoherence is usually very weak. Therefore the ``black hole information puzzle'' is rendered de-facto unobservable.Comment: 4 pages, no figures, revte

Spin dependent point potentials in one and three dimensions

We consider a system realized with one spinless quantum particle and an array of $N$ spins 1/2 in dimension one and three. We characterize all the Hamiltonians obtained as point perturbations of an assigned free dynamics in terms of some ``generalized boundary conditions''. For every boundary condition we give the explicit formula for the resolvent of the corresponding Hamiltonian. We discuss the problem of locality and give two examples of spin dependent point potentials that could be of interest as multi-component solvable models.Comment: 15 pages, some misprints corrected, one example added, some references modified or adde

Super-roughening versus intrinsic anomalous scaling of surfaces

In this paper we study kinetically rough surfaces which display anomalous scaling in their local properties such as roughness, or height-height correlation function. By studying the power spectrum of the surface and its relation to the height-height correlation, we distinguish two independent causes for anomalous scaling. One is super-roughening (global roughness exponent larger than or equal to one), even if the spectrum behaves non anomalously. Another cause is what we term an intrinsically anomalous spectrum, in whose scaling an independent exponent exists, which induces different scaling properties for small and large length scales (that is, the surface is not self-affine). In this case, the surface does not need to be super-rough in order to display anomalous scaling. In both cases, we show how to extract the independent exponents and scaling relations from the correlation functions, and we illustrate our analysis with two exactly solvable examples. One is the simplest linear equation for molecular beam epitaxy , well known to display anomalous scaling due to super-roughening. The second example is a random diffusion equation, which features anomalous scaling independent of the value of the global roughness exponent below or above one.Comment: 9 pages, 6 figures, Revtex (uses epsfig), Phys. Rev. E, submitte

Strong anisotropy in two-dimensional surfaces with generic scale invariance: Gaussian and related models

Among systems that display generic scale invariance, those whose asymptotic properties are anisotropic in space (strong anisotropy, SA) have received a relatively smaller attention, specially in the context of kinetic roughening for two-dimensional surfaces. This is in contrast with their experimental ubiquity, e.g. in the context of thin film production by diverse techniques. Based on exact results for integrable (linear) cases, here we formulate a SA Ansatz that, albeit equivalent to existing ones borrowed from equilibrium critical phenomena, is more naturally adapted to the type of observables that are measured in experiments on the dynamics of thin films, such as one and two-dimensional height structure factors. We test our Ansatz on a paradigmatic nonlinear stochastic equation displaying strong anisotropy like the Hwa-Kardar equation [Phys. Rev. Lett. 62, 1813 (1989)], that was initially proposed to describe the interface dynamics of running sand piles. A very important role to elucidate its SA properties is played by an accurate (Gaussian) approximation through a non-local linear equation that shares the same asymptotic properties

Operator mixing and three-point functions in N=4 SYM

We study the three-point functions between two BPS and one non-BPS local gauge invariant operators in N=4 Super Yang-Mills theory. In particular we show, in explicit 1-loop examples, that the operator mixing discussed in arXiv:0810.0499 plays an important role in the computations of the correlators and is necessary to cancel contributions that would violate the constraints following from the superconformal and the bonus U(1)_Y symmetries. We analyse the same type of correlators also at strong coupling by using the BMN limit of the AdS_5xS^5 string theory. Again the mixing between states with different types of impurities is crucial to ensure the cancellation of various amplitudes that would violate the constraints mentioned above. However, on the string side, we also find some examples of interactions between one non-BPS and two BPS states that do not satisfy expectations based on the superconformal and the bonus U(1)_Y symmetries.Comment: 28 pages, 5 figure

Power Allocation, Relay Selection, and User Pairing for Cooperative NOMA Systems with Rate Fairness

Funding Information: This research was partially funded by Fundac¸ão para a Ciência e Tecnologia under the Projects CoSHARE (PTDC/EEI-TEL/30709/2017), UIDB/04111/2020, IF/00325/2015, and UIDB/50008/2020.Assuming a cooperative non-orthogonal multiple access (NOMA) system with rate fairness in a scenario with multiple users and arbitrary relays, this paper investigates adaptive power allocation (PA), relay selection (RS), and user pairing (UP) policies. Specifically, two adaptive PA optimization problems are formulated, one at the base station (BS) and another at the selected relays. Closed-form expressions for the power allocation factors are derived as well as an algorithm that provides the optimal solution at the BS. In order to show the superiority of the proposed study, our results are compared with other benchmark schemes in terms of outage probability, Jain's fairness index, and average sum rate.publishersversionpublishe

The large cosmological constant approximation to classical and quantum gravity: model examples

We have recently introduced an approach for studying perturbatively classical and quantum canonical general relativity. The perturbative technique appears to preserve many of the attractive features of the non-perturbative quantization approach based on Ashtekar's new variables and spin networks. With this approach one can find perturbatively classical observables (quantities that have vanishing Poisson brackets with the constraints) and quantum states (states that are annihilated by the quantum constraints). The relative ease with which the technique appears to deal with these traditionally hard problems opens several questions about how relevant the results produced can possibly be. Among the questions is the issue of how useful are results for large values of the cosmological constant and how the approach can deal with several pathologies that are expected to be present in the canonical approach to quantum gravity. With the aim of clarifying these points, and to make our construction as explicit as possible, we study its application in several simple models. We consider Bianchi cosmologies, the asymmetric top, the coupled harmonic oscillators with constant energy density and a simple quantum mechanical system with two Hamiltonian constraints. We find that the technique satisfactorily deals with the pathologies of these models and offers promise for finding (at least some) results even for small values of the cosmological constant. Finally, we briefly sketch how the method would operate in the full four dimensional quantum general relativity case.Comment: 21 pages, RevTex, 2 figures with epsfi

Sea anemones may thrive in a high CO2 world

Increased seawater pCO 2, and in turn 'ocean acidification' (OA), is predicted to profoundly impact marine ecosystem diversity and function this century. Much research has already focussed on calcifying reef-forming corals (Class: Anthozoa) that appear particularly susceptible to OA via reduced net calcification. However, here we show that OA-like conditions can simultaneously enhance the ecological success of non-calcifying anthozoans, which not only play key ecological and biogeochemical roles in present day benthic ecosystems but also represent a model organism should calcifying anthozoans exist as less calcified (soft-bodied) forms in future oceans. Increased growth (abundance and size) of the sea anemone (Anemonia viridis) population was observed along a natural CO 2 gradient at Vulcano, Italy. Both gross photosynthesis (P G) and respiration (R) increased with pCO 2 indicating that the increased growth was, at least in part, fuelled by bottom up (CO 2 stimulation) of metabolism. The increase of P G outweighed that of R and the genetic identity of the symbiotic microalgae (Symbiodinium spp.) remained unchanged (type A19) suggesting proximity to the vent site relieved CO 2 limitation of the anemones' symbiotic microalgal population. Our observations of enhanced productivity with pCO 2, which are consistent with previous reports for some calcifying corals, convey an increase in fitness that may enable non-calcifying anthozoans to thrive in future environments, i.e. higher seawater pCO 2. Understanding how CO 2-enhanced productivity of non- (and less-) calcifying anthozoans applies more widely to tropical ecosystems is a priority where such organisms can dominate benthic ecosystems, in particular following localized anthropogenic stress. © 2012 Blackwell Publishing Ltd