Resonance effects on the dynamics of dense granular beds: achieving optimal energy transfer in vibrated granular systems

Using a combination of experimental techniques and discrete particle method simulations, we investigate the resonant behaviour of a dense, vibrated granular system. We demonstrate that a bed of particles driven by a vibrating plate may exhibit marked differences in its internal energy dependent on the specific frequency at which it is driven, even if the energy corresponding to the oscillations driving the system is held constant and the acceleration provided by the base remains consistently significantly higher than the gravitational acceleration, g. We show that these differences in the efficiency of energy transfer to the granular system can be explained by the existence of resonances between the bed's bulk motion and that of the oscillating plate driving the system. We systematically study the dependency of the observed resonant behaviour on the system's main, controllable parameters and, based on the results obtained, propose a simple empirical model capable of determining, for a given system, the points in parameter space for which optimal energy transfer may be achieved

Spectral Orbits and Peak-to-Average Power Ratio of Boolean Functions with respect to the {I,H,N}^n Transform

We enumerate the inequivalent self-dual additive codes over GF(4) of blocklength n, thereby extending the sequence A090899 in The On-Line Encyclopedia of Integer Sequences from n = 9 to n = 12. These codes have a well-known interpretation as quantum codes. They can also be represented by graphs, where a simple graph operation generates the orbits of equivalent codes. We highlight the regularity and structure of some graphs that correspond to codes with high distance. The codes can also be interpreted as quadratic Boolean functions, where inequivalence takes on a spectral meaning. In this context we define PAR_IHN, peak-to-average power ratio with respect to the {I,H,N}^n transform set. We prove that PAR_IHN of a Boolean function is equivalent to the the size of the maximum independent set over the associated orbit of graphs. Finally we propose a construction technique to generate Boolean functions with low PAR_IHN and algebraic degree higher than 2.Comment: Presented at Sequences and Their Applications, SETA'04, Seoul, South Korea, October 2004. 17 pages, 10 figure

Inflation, quantum fields, and CMB anisotropies

Inflationary cosmology has proved to be the most successful at predicting the properties of the anisotropies observed in the cosmic microwave background (CMB). In this essay we show that quantum field renormalization significantly influences the generation of primordial perturbations and hence the expected measurable imprint of cosmological inflation on the CMB. However, the new predictions remain in agreement with observation, and in fact favor the simplest forms of inflation. In the near future, observations of the influence of gravitational waves from the early universe on the CMB will test our new predictions.Comment: 11 pages, 1 figure, Awarded with the fourth prize in the Gravity Research Foundation 2009 Essay Competitio

The Tensor to Scalar Ratio of Phantom Dark Energy Models

We investigate the anisotropies in the cosmic microwave background in a class of models which possess a positive cosmic energy density but negative pressure, with a constant equation of state w = p/rho < -1. We calculate the temperature and polarization anisotropy spectra for both scalar and tensor perturbations by modifying the publicly available code CMBfast. For a constant initial curvature perturbation or tensor normalization, we have calculated the final anisotropy spectra as a function of the dark energy density and equation of state w and of the scalar and tensor spectral indices. This allows us to calculate the dependence of the tensor-to-scalar ratio on w in a model with phantom dark energy, which may be important for interpreting any future detection of long-wavelength gravitational waves.Comment: 5 pages, 4 figure

Gyroid cuticular structures in butterfly wing scales: biological photonic crystals

We present a systematic study of the cuticular structure in the butterfly wing scales of some papilionids (Parides sesostris and Teinopalpus imperialis) and lycaenids (Callophrys rubi, Cyanophrys remus, Mitoura gryneus and Callophrys dumetorum). Using published scanning and transmission electron microscopy (TEM) images, analytical modelling and computer-generated TEM micrographs, we find that the three-dimensional cuticular structures can be modelled by gyroid structures with various filling fractions and lattice parameters. We give a brief discussion of the formation of cubic gyroid membranes from the smooth endoplasmic reticulum in the scale's cell, which dry and harden to leave the cuticular structure behind when the cell dies. The scales of C. rubi are a potentially attractive biotemplate for producing three-dimensional optical photonic crystals since for these scales the cuticle-filling fraction is nearly optimal for obtaining the largest photonic band gap in a gyroid structure

Solar Polar Fields During Cycles 21 --- 23: Correlation with Meridional Flows

We have examined polar magnetic fields for the last three solar cycles, {$\it{viz.}$}, cycles 21, 22 and 23 using NSO Kitt Peak synoptic magnetograms. In addition, we have used SoHO/MDI magnetograms to derive the polar fields during cycle 23. Both Kitt Peak and MDI data at high latitudes (78${^{\circ}}$--90${^{\circ}}$) in both solar hemispheres show a significant drop in the absolute value of polar fields from the late declining phase of the solar cycle 22 to the maximum of the solar cycle 23. We find that long term changes in the absolute value of the polar field, in cycle 23, is well correlated with changes in meridional flow speeds that have been reported recently. We discuss the implication of this in influencing the extremely prolonged minimum experienced at the start of the current cycle 24 and in forecasting the behaviour of future solar cycles.Comment: 4 Figures 11 pages; Revised version under review in Solar Physic

Cosmology with a long range repulsive force

We consider a class of cosmological models in which the universe is filled with a (non-electric) charge density that repels itself by means of a force carried by a vector boson with a tiny mass. When the vector's mass depends upon other fields, the repulsive interaction gives rise to an electromagnetic barrier which prevents these fields from driving the mass to zero. This can modify the cosmology dramatically. We present a very simple realization of this idea in which the vector's mass arises from a scalar field. The electromagnetic barrier prevents this field from rolling down its potential and thereby leads to accelerated expansion.Comment: 15 pages, 8 figures, LaTeX (version accepted for publication in PRD). 3 new figures, extended discussion of observational consequence

Current Helicity and Twist as Two Indicators of The Mirror Asymmetry of solar Magnetic Fields

A comparison between the two tracers of magnetic field mirror asymmetry in solar active regions, twist and current helicity, is presented. It is shown that for individual active regions these tracers do not possess visible similarity while averaging by time over the solar cycle, or by latitude, reveals similarities in their behaviour. The main property of the dataset is anti-symmetry over the solar equator. Considering the evolution of helical properties over the solar cycle we find signatures of a possible sign change at the beginning of the cycle, though more systematic observational data are required for a definite confirmation. We discuss the role of both tracers in the context of the solar dynamo theory.Comment: 14 pages, 6 figure

Mutated hybrid inflation in f(R,□R)f(R,{\Box}R)-gravity

A new hybrid inflationary scenario in the context of $f(R,{\Box}R)$-gravity is proposed. Demanding the waterfall field to 'support the potential from below' [unlike the original proposal by Stewart in Phys. Lett. B345, 414 (1995)], we demonstrate that the scalar potential is similar to that of the large-field chaotic inflation model proposed by Linde in Phys. Lett. B129, 177 (1983). Inflationary observables are used to constrain the parameter space of our model; in the process, an interesting limit on the number of e-folds N is found.Comment: 9 pages, 2 figures, LaTeX2e, v2: Sec.3 expanded and improved, 1 Fig. added, a new result included, some Eqs. corrected, 2 References adde

Quenching of Meridional Circulation in Flux Transport Dynamo Models

Guided by the recent observational result that the meridional circulation of the Sun becomes weaker at the time of the sunspot maximum, we have included a parametric quenching of the meridional circulation in solar dynamo models such that the meridional circulation becomes weaker when the magnetic field at the base of the convection zone is stronger. We find that a flux transport solar dynamo tends to become unstable on including this quenching of meridional circulation if the diffusivity in the convection zone is less than about 2 * 10^{11} cm^2/s. The quenching of alpha, however, has a stabilizing effect and it is possible to stabilize a dynamo with low diffusivity with sufficiently strong alpha-quenching. For dynamo models with high diffusivity, the quenching of meridional circulation does not produce a large effect and the dynamo remains stable. We present a solar-like solution from a dynamo model with diffusivity 2.8 * 10^{12} cm^2/s in which the quenching of meridional circulation makes the meridional circulation vary periodically with solar cycle as observed and does not have any other significant effect on the dynamo.Comment: Consistent with the published version. Solar Physics, in pres