Reheating after f(R) inflation

The reheating dynamics after the inflation induced by $R^2$-corrected $f(R)$ model is considered. To avoid the complexity of solving the fourth order equations, we analyze the inflationary and reheating dynamics in the Einstein frame and its analytical solutions are derived. We also perform numerical calculation including the backreaction from the particle creation and compare the results with the analytical solutions. Based on the results, observational constraints on the model are discussed.Comment: 16 pages, 11 figure

Theory of radiation trapping by the accelerating solitons in optical fibers

We present a theory describing trapping of the normally dispersive radiation by the Raman solitons in optical fibers. Frequency of the radiation component is continuously blue shifting, while the soliton is red shifting. Underlying physics of the trapping effect is in the existence of the inertial gravity-like force acting on light in the accelerating frame of reference. We present analytical calculations of the rate of the opposing frequency shifts of the soliton and trapped radiation and find it to be greater than the rate of the red shift of the bare Raman soliton. Our findings are essential for understanding of the continuous shift of the high frequency edge of the supercontinuum spectra generated in photonic crystal fibers towards higher frequencies.Comment: Several misprints in text and formulas corrected. 10 pages, 9 figures, submitted to Phys. Rev.

Model-independent test of gravity with a network of ground-based gravitational-wave detectors

The observation of gravitational waves with a global network of interferometric detectors such as advanced LIGO, advanced Virgo, and KAGRA will make it possible to probe into the nature of space-time structure. Besides Einstein's general theory of relativity, there are several theories of gravitation that passed experimental tests so far. The gravitational-wave observation provides a new experimental test of alternative theories of gravity because a gravitational wave may have at most six independent modes of polarization, of which properties and number of modes are dependent on theories of gravity. This paper proposes a method to reconstruct the independent modes of polarization in time-series data of an advanced detector network. Since the method does not rely on any specific model, it gives model-independent test of alternative theories of gravity

A note on q-Euler numbers and polynomials

The purpose of this paper is to construct q-Euler numbers and polynomials by using p-adic q-integral equations on Zp. Finally, we will give some interesting formulae related to these q-Euler numbers and polynomials.Comment: 6 page

Digital microscopy: A useful technique for measuring root elongation in solution

Decreased root elongation and rupture of outer cells, major effects of soluble aluminum (Al), may be studied using digital microscopy with little interference by the experimental technique. Single roots of 3-d-old mungbean (Vigna radiata L.) or soybean (Glycine max (L.) Merr.) seedlings were marked with activated charcoal particles and grown for ca. 2 h in 500 mL 1 mM CaCl solution at pH 6, followed by the imposition of an Al treatment. A digital image at 25-time magnification was recorded every 5 min for up to 7 h. Examination of the digital images showed that Al exerted its rhizotoxic effects rapidly (ca. 20-50 min) by reducing cell expansion in the elongation zone. Rupture of epidermal and outer cortical cells occurred later (after≥4 h) and closer to the root tip. Digital microscopy has a number of inherent benefits and problems, but is overall a valuable technique that may find wide use in studies on root growth

A manifesto for researching entrepreneurial ecosystems

Entrepreneurial ecosystems are the focus of government economic policies around the world for their potential to generate entrepreneur-led economic development. The paper identifies key research questions and challenges to building effective public policy: (i) the limitations of existing data sources, (ii) the need to balance findings from quantitative and qualitative studies, (iii) the danger that entrepreneurial ecosystems will be just a policy fad, (iv) the narrow focus of policy and research on high tech firms and scale-ups, and (v) the need to balance research approaches between simplified models and a complex systems approach. There is a need for a better understanding of the diversity of policy contexts (level of government, country context) and model of ecosystem governance. A more granulated understanding of ecosystem thinking is required, with greater consideration of the diversity of actors and the institutional context, with more attention given to the heterogeneous nature of places and complex interactions between actors and networks. Looking to the future, the potential of new data sources and methodologies is identified. Future research should give greater consideration to the institutional context to understand how policy can better support entrepreneurial activity and the extent to which specific policies can be replicated elsewhere

Thermodynamic properties of ferromagnetic mixed-spin chain systems

Using a combination of high-temperature series expansion, exact diagonalization and quantum Monte Carlo, we perform a complementary analysis of the thermodynamic properties of quasi-one-dimensional mixed-spin systems with alternating magnetic moments. In addition to explicit series expansions for small spin quantum numbers, we present an expansion that allows a direct evaluation of the series coefficients as a function of spin quantum numbers. Due to the presence of excitations of both acoustic and optical nature, the specific heat of a mixed-spin chain displays a double-peak-like structure, which is more pronounced for ferromagnetic than for antiferromagnetic intra-chain exchange. We link these results to an analytically solvable half-classical limit. Finally, we extend our series expansion to incorporate the single-ion anisotropies relevant for the molecular mixed-spin ferromagnetic chain material MnNi(NO$_{2}$)$_{4}$(ethylenediamine)$_{2}$, with alternating spins of magnitude 5/2 and 1. Including a weak inter-chain coupling, we show that the observed susceptibility allows for an excellent fit, and the extraction of microscopic exchange parameters.Comment: 8 pages including 7 figures, submitted to Phys. Rev. B; series extended to 29th. QMC adde

Testing metric-affine f(R)-gravity by relic scalar gravitational waves

We discuss the emergence of scalar gravitational waves in metric-affine f(R)-gravity. Such a component allows to discriminate between metric and metric-affine theories The intrinsic meaning of this result is that the geodesic structure of the theory can be discriminated. We extend the formalism of cross correlation analysis, including the additional polarization mode, and calculate the detectable energy density of the spectrum for cosmological relic gravitons. The possible detection of the signal is discussed against sensitivities of VIRGO, LIGO and LISA interferometers.Comment: 12 pages, 4 figure

Optimal Location of Two Laser-interferometric Detectors for Gravitational Wave Backgrounds at 100 MHz

Recently, observational searches for gravitational wave background (GWB) have been developed and given constraints on the energy density of GWB in a broad range of frequencies. These constraints have already resulted in the rejection of some theoretical models of relatively large GWB spectra. However, at 100 MHz, there is no strict upper limit from direct observation, though an indirect limit exists due to He4 abundance due to big-bang nucleosynthesis. In our previous paper, we investigated the detector designs that can effectively respond to GW at high frequencies, where the wavelength of GW is comparable to the size of a detector, and found that the configuration, a so-called synchronous-recycling interferometer is best at these sensitivity. In this paper, we investigated the optimal location of two synchronous-recycling interferometers and derived their cross-correlation sensitivity to GWB. We found that the sensitivity is nearly optimized and hardly changed if two coaligned detectors are located within a range 0.2 m, and that the sensitivity achievable in an experiment is far below compared with the constraint previously obtained in experiments.Comment: 17 pages, 6 figure