Production of primordial gravitational waves in a simple class of running vacuum cosmologies

The problem of cosmological production of gravitational waves is discussed in the framework of an expanding, spatially homogeneous and isotropic FRW type Universe with time-evolving vacuum energy density. The gravitational wave equation is established and its modified time-dependent part is analytically resolved for different epochs in the case of a flat geometry. Unlike the standard $\Lambda$CDM cosmology (no interacting vacuum), we show that gravitational waves are produced in the radiation era even in the context of general relativity. We also show that for all values of the free parameter, the high frequency modes are damped out even faster than in the standard cosmology both in the radiation and matter-vacuum dominated epoch. The formation of the stochastic background of gravitons and the remnant power spectrum generated at different cosmological eras are also explicitly evaluated. It is argued that measurements of the CMB polarization (B-modes) and its comparison with the rigid $\Lambda$CDM model plus the inflationary paradigm may become a crucial test for dynamical dark energy models in the near future.Comment: 13 pages, 12 figure

Numerical Simulation of Nano Scanning in Intermittent-Contact Mode AFM under Q control

We investigate nano scanning in tapping mode atomic force microscopy (AFM) under quality (Q) control via numerical simulations performed in SIMULINK. We focus on the simulation of whole scan process rather than the simulation of cantilever dynamics and the force interactions between the probe tip and the surface alone, as in most of the earlier numerical studies. This enables us to quantify the scan performance under Q control for different scan settings. Using the numerical simulations, we first investigate the effect of elastic modulus of sample (relative to the substrate surface) and probe stiffness on the scan results. Our numerical simulations show that scanning in attractive regime using soft cantilevers with high Qeff results in a better image quality. We, then demonstrate the trade-off in setting the effective Q factor (Qeff) of the probe in Q control: low values of Qeff cause an increase in tapping forces while higher ones limit the maximum achievable scan speed due to the slow response of the cantilever to the rapid changes in surface profile. Finally, we show that it is possible to achieve higher scan speeds without causing an increase in the tapping forces using adaptive Q control (AQC), in which the Q factor of the probe is changed instantaneously depending on the magnitude of the error signal in oscillation amplitude. The scan performance of AQC is quantitatively compared to that of standard Q control using iso-error curves obtained from numerical simulations first and then the results are validated through scan experiments performed using a physical set-up

Primordial Gravitational Waves in Running Vacuum Cosmologies

We investigate the cosmological production of gravitational waves in a nonsingular flat cosmology powered by a "running vacuum" energy density described by $\rho_{\Lambda}\equiv\rho_{\Lambda}(H)$, a phenomenological expression potentially linked with the renormalization group approach in quantum field theory in curved spacetimes. The model can be interpreted as a particular case of the class recently discussed by Perico et al. (Phys. Rev. D {\bf 88}, 063531, 2013) which is termed complete in the sense that the cosmic evolution occurs between two extreme de Sitter stages (early and late time de Sitter phases). {The gravitational wave equation is derived and its time-dependent part numerically integrated since the primordial de Sitter stage. The generated spectrum of gravitons is also compared with the standard calculations where an abrupt transition, from the early de Sitter to the radiation phase, is usually assumed.} It is found that the stochastic background of gravitons is very similar to the one predicted by the cosmic concordance model plus inflation except at higher frequencies ($\nu \gtrsim 100$ kHz). This remarkable signature of a "running vacuum" cosmology combined with the proposed high frequency gravitational wave detectors and measurements of the CMB polarization (B-modes) may provide a new window to confront more conventional models of inflation.Comment: 13 pages, 4 figures, uses latex, title changed. Other corrections in agreement with the accepted version in Astroparticle Physic

Comment on ``Theory of Spinodal Decomposition''

I comment on a paper by S. B. Goryachev [PRL vol 72, p.1850 (1994)] that presents a theory of non-equilibrium dynamics for scalar systems quenched into an ordered phase. Goryachev incorrectly applies only a global conservation constraint to systems with local conservation laws.Comment: 2 pages LATeX (REVTeX macros), no figures. REVISIONS --- more to the point. microscopic example added, presentation streamlined, long-range interactions mentioned, to be published in Phys. Rev. Let

Entropy Production of Brownian Macromolecules with Inertia

We investigate the nonequilibrium steady-state thermodynamics of single Brownian macromolecules with inertia under feedback control in isothermal ambient fluid. With the control being represented by a velocity-dependent external force, we find such open systems can have a negative entropy production rate and we develop a mesoscopic theory consistent with the second law. We propose an equilibrium condition and define a class of external forces, which includes a transverse Lorentz force, leading to equilibrium.Comment: 10 pages, 1 figur

Non-equilibrium Phase-Ordering with a Global Conservation Law

In all dimensions, infinite-range Kawasaki spin exchange in a quenched Ising model leads to an asymptotic length-scale $L \sim (\rho t)^{1/2} \sim t^{1/3}$ at $T=0$ because the kinetic coefficient is renormalized by the broken-bond density, $\rho \sim L^{-1}$. For $T>0$, activated kinetics recovers the standard asymptotic growth-law, $L \sim t^{1/2}$. However, at all temperatures, infinite-range energy-transport is allowed by the spin-exchange dynamics. A better implementation of global conservation, the microcanonical Creutz algorithm, is well behaved and exhibits the standard non-conserved growth law, $L \sim t^{1/2}$, at all temperatures.Comment: 2 pages and 2 figures, uses epsf.st

A very low current scanning tunneling microscope

The applications of the scanning tunneling microscope (STM) in air are usually restricted to good conducting materials as clean metals, doped and passivated semiconductors, or to some molecular adsorbates deposited onto graphite. In order to study poor conducting materials as biological molecules, we have built a very low current STM. This instrument can routinely be operated at 0.1 pA while having a bandwidth of 7 kHz. The advantages of using very low currents are illustrated by imaging 5-nm-thick purple membranes. These membranes can only be imaged at currents smaller than 2 pA. © 1995 American Institute of Physics.DGICYT Nº.PB94-0016 .Peer Reviewe