Brownian Carnot engine

The Carnot cycle imposes a fundamental upper limit to the efficiency of a macroscopic motor operating between two thermal baths. However, this bound needs to be reinterpreted at microscopic scales, where molecular bio-motors and some artificial micro-engines operate. As described by stochastic thermodynamics, energy transfers in microscopic systems are random and thermal fluctuations induce transient decreases of entropy, allowing for possible violations of the Carnot limit. Despite its potential relevance for the development of a thermodynamics of small systems, an experimental study of microscopic Carnot engines is still lacking. Here we report on an experimental realization of a Carnot engine with a single optically trapped Brownian particle as working substance. We present an exhaustive study of the energetics of the engine and analyze the fluctuations of the finite-time efficiency, showing that the Carnot bound can be surpassed for a small number of non-equilibrium cycles. As its macroscopic counterpart, the energetics of our Carnot device exhibits basic properties that one would expect to observe in any microscopic energy transducer operating with baths at different temperatures. Our results characterize the sources of irreversibility in the engine and the statistical properties of the efficiency -an insight that could inspire novel strategies in the design of efficient nano-motors.Comment: 7 pages, 7 figure

Numerical Studies of Cosmic Ray Injection and Acceleration

A numerical scheme that incorporates a thermal leakage injection model into a combined gas dynamics and cosmic ray (CR, hereafter) diffusion-convection code has been developed. The particle injection is followed numerically by filtering the diffusive flux of suprathermal particles across the shock to the upstream region according to a velocity-dependent transparency function that controls the fraction of leaking particles. We have studied CR injection and acceleration efficiencies during the evolution of CR modified planar shocks for a wide range of initial shock Mach numbers, $M_0$, assuming a Bohm-like diffusion coefficient. The injection process is very efficient when the subshock is strong, leading to fast and significant modification of the shock structure. As the CR pressure increases, the subshock weakens and the injection rate decreases accordingly, so that the subshock does not disappear. Although some fraction of the particles injected early in the evolution continue to be accelerated to ever higher energies, the postshock CR pressure reaches an approximate time-asymptotic value due to a balance between fresh injection/acceleration and advection/diffusion of the CR particles away from the shock. We conclude that the injection rates in strong parallel shocks are sufficient to lead to rapid nonlinear modifications to the shock structures and that self-consistent injection and time-dependent simulations are crucial to understanding the non-linear evolution of CR modified shocks.Comment: 28 pages, To appear in ApJ November 1, 2002 issu

Optically levitated nanoparticle as a model system for stochastic bistable dynamics

Nano-mechanical resonators have gained an increasing importance in nanotechnology owing to their contributions to both fundamental and applied science. Yet, their small dimensions and mass raises some challenges as their dynamics gets dominated by nonlinearities that degrade their performance, for instance in sensing applications. Here, we report on the precise control of the nonlinear and stochastic bistable dynamics of a levitated nanoparticle in high vacuum. We demonstrate how it can lead to efficient signal amplification schemes, including stochastic resonance. This work contributes to showing the use of levitated nanoparticles as a model system for stochastic bistable dynamics, with applications to a wide variety of fields.inancial support from the ERC- QnanoMECA (Grant No. 64790), the Spanish Ministry of Economy and Competitiveness, under grant FIS2016-80293-R and through the ‘Severo Ochoa’ Programme for Centres of Excellence in R&D (SEV-2015-0522), Fundació Privada CELLEX and from the CERCA Programme/Generalitat de Catalunya. J.G. has been supported by H2020-MSCA-IF-2014 under REA grant Agreement No. 655369. L.R. acknowledges support from an ETH Marie Curie Cofund Fellowship

Efficiency of Nonlinear Particle Acceleration at Cosmic Structure Shocks

We have calculated the evolution of cosmic ray (CR) modified astrophysical shocks for a wide range of shock Mach numbers and shock speeds through numerical simulations of diffusive shock acceleration (DSA) in 1D quasi- parallel plane shocks. The simulations include thermal leakage injection of seed CRs, as well as pre-existing, upstream CR populations. Bohm-like diffusion is assumed. We model shocks similar to those expected around cosmic structure pancakes as well as other accretion shocks driven by flows with upstream gas temperatures in the range $T_0=10^4-10^{7.6}$K and shock Mach numbers spanning $M_s=2.4-133$. We show that CR modified shocks evolve to time-asymptotic states by the time injected particles are accelerated to moderately relativistic energies (p/mc \gsim 1), and that two shocks with the same Mach number, but with different shock speeds, evolve qualitatively similarly when the results are presented in terms of a characteristic diffusion length and diffusion time. For these models the time asymptotic value for the CR acceleration efficiency is controlled mainly by shock Mach number. The modeled high Mach number shocks all evolve towards efficiencies $\sim 50$%, regardless of the upstream CR pressure. On the other hand, the upstream CR pressure increases the overall CR energy in moderate strength shocks ($M_s \sim {\rm a few}$). (abridged)Comment: 23 pages, 12 ps figures, accepted for Astrophysical Journal (Feb. 10, 2005

Modelling the spectral evolution of classical double radio sources

The spectral evolution of powerful double radio galaxies (FR II's) is thought to be determined by the acceleration of electrons at the termination shock of the jet, their transport through the bright head region into the lobes and the production of the radio emission by synchrotron radiation in the lobes. Models presented to date incorporate some of these processes in prescribing the electron distribution which enters the lobes. We have extended these models to include a description of electron acceleration at the relativistic termination shock and a selection of transport models for the head region. These are coupled to the evolution of the electron spectrum in the lobes under the influence of losses due to adiabatic expansion, by inverse Compton scattering on the cosmic background radiation and by synchrotron radiation. The evolutionary tracks predicted by this model are compared to observation using the power/source-size (P-D) diagram. We find that the simplest scenario, in which accelerated particles suffer adiabatic losses in the head region which become more severe as the source expands produces P-D-tracks which conflict with observation, because the power is predicted to decline too steeply with increasing size. Agreement with observation can be found by assuming that adiabatic losses are compensated during transport between the termination shock and the lobe by a re-acceleration process distributed throughout the head region.Comment: 14 pages, 6 figures, accepted for publication in Astronomy and Astrophysic

Connecting remote and in situ observations of shock-accelerated electrons associated with a coronal mass ejection

One of the most prominent sources for energetic particles in our solar system are huge eruptions of magnetised plasma from the Sun called coronal mass ejections (CMEs), which usually drive shocks that accelerate charged particles up to relativistic energies. In particular, energetic electron beams can generate radio bursts through the plasma emission mechanism, for example, type II and accompanying herringbone bursts. Here, we investigate the acceleration location, escape, and propagation directions of various electron beams in the solar corona and compare them to the arrival of electrons at spacecraft. To track energetic electron beams, we use a synthesis of remote and direct observations combined with coronal modelling. Remote observations include ground-based radio observations from the Nancay Radioheliograph (NRH) combined with space-based extreme-ultraviolet and white-light observations from the Solar Dynamics Observatory (SDO), the Solar Terrestrial Relations Observatory (STEREO) and Solar Orbiter (SolO). We also use direct observations of energetic electrons from the STEREO and Wind spacecraft. These observations are then combined with a three-dimensional (3D) representation of the electron acceleration locations that combined with results from magneto-hydrodynamic models of the solar corona is used to investigate the origin and link of electrons observed remotely at the Sun to in situ electrons. We observed a type II radio burst followed by herringbone bursts that show single-frequency movement through time in NRH images. The movement of the type II burst and herringbone radio sources seems to be influenced by the regions in the corona where the CME is more capable of driving a shock. We also found similar inferred injection times of near-relativistic electrons at spacecraft to the emission time of the type II and herringbone bursts.Comment: 16 pages, 15 figure