Nonequilibrium statistical mechanics of shear flow: invariant quantities and current relations

In modeling nonequilibrium systems one usually starts with a definition of the microscopic dynamics, e.g., in terms of transition rates, and then derives the resulting macroscopic behavior. We address the inverse question for a class of steady state systems, namely complex fluids under continuous shear flow: how does an externally imposed shear current affect the microscopic dynamics of the fluid? The answer can be formulated in the form of invariant quantities, exact relations for the transition rates in the nonequilibrium steady state, as discussed in a recent letter [A. Baule and R. M. L. Evans, Phys. Rev. Lett. 101, 240601 (2008)]. Here, we present a more pedagogical account of the invariant quantities and the theory underlying them, known as the nonequilibrium counterpart to detailed balance (NCDB). Furthermore, we investigate the relationship between the transition rates and the shear current in the steady state. We show that a fluctuation relation of the Gallavotti-Cohen type holds for systems satisfying NCDB.Comment: 24 pages, 11 figure

Spontaneous Breaking of Translational Invariance in One-Dimensional Stationary States on a Ring

We consider a model in which positive and negative particles diffuse in an asymmetric, CP-invariant way on a ring. The positive particles hop clockwise, the negative counterclockwise and oppositely-charged adjacent particles may swap positions. Monte-Carlo simulations and analytic calculations suggest that the model has three phases; a "pure" phase in which one has three pinned blocks of only positive, negative particles and vacancies, and in which translational invariance is spontaneously broken, a "mixed" phase with a non-vanishing current in which the three blocks are positive, negative and neutral, and a disordered phase without blocks.Comment: 7 pages, LaTeX, needs epsf.st

Mode-Dependent nonequilibrium temperature in aging systems

We introduce an exactly solvable model for glassy dynamics with many relaxational modes, each one characterized by a different relaxational time-scale. Analytical solution of the aging dynamics at low temperatures shows that a nonequilibrium or effective temperature can be associated to each time-scale or mode. The spectrum of effective temperatures shows two regions that are separated by an age dependent boundary threshold. Region I is characterized by partially equilibrated modes that relax faster than the modes at the threshold boundary. Thermal fluctuations and time-correlations for modes in region I show that those modes are in mutual thermal equilibrium at a unique age-dependent effective temperature $\Theta (s)$. In contrast, modes with relaxational timescales longer than that of modes at the threshold (region II) show diffusive properties and do not share the common temperature $\Theta (s)$. The shift of the threshold toward lower energy modes as the system ages, and the progressive shrinking of region II, determines how the full spectrum of modes equilibrates. As is usually done in experiments, we have defined a frequency-dependent effective temperature and we have found that all modes in region I are mutually equilibrated at the temperature $\Theta (s)$ independently of the probing frequency. The present model aims to explain transport anomalies observed in supercooled liquids in terms of a collection of structurally disordered and cooperative rearranging mesoscopic regions.Comment: 26 pages, 11 figure

A census of massive stars in NGC 346. Stellar parameters and rotational velocities

Spectroscopy for 247 stars towards the young cluster NGC 346 in the Small Magellanic Cloud has been combined with that for 116 targets from the VLT-FLAMES Survey of Massive Stars. Spectral classification yields a sample of 47 O-type and 287 B-type spectra, while radial-velocity variations and/or spectral multiplicity have been used to identify 45 candidate single-lined systems, 17 double-lined systems, and one triple-lined system. Atmospheric parameters (T$_eff$ and log$g$) and projected rotational velocities ($v_e$sin$i$) have been estimated using TLUSTY model atmospheres; independent estimates of $v_e$sin$i$ were also obtained using a Fourier Transform method. Luminosities have been inferred from stellar apparent magnitudes and used in conjunction with the T$_eff$ and $v_e$sin$i$ estimates to constrain stellar masses and ages using the BONNSAI package. We find that targets towards the inner region of NGC 346 have higher median masses and projected rotational velocities, together with smaller median ages than the rest of the sample. There appears to be a population of very young targets with ages of less than 2 Myr, which have presumably all formed within the cluster. The more massive targets are found to have lower $v_e$sin$i$ consistent with previous studies. No significant evidence is found for differences with metallicity in the stellar rotational velocities of early-type stars, although the targets in the SMC may rotate faster than those in young Galactic clusters. The rotational velocity distribution for single non-supergiant B-type stars is inferred and implies that a significant number have low rotational velocity ($\simeq$10\% with $v_e$<40 km/s), together with a peak in the probability distribution at $v_e \simeq$300 km/s. Larger projected rotational velocity estimates have been found for our Be-type sample and imply that most have rotational velocities between 200-450 km/s.Comment: Accepted by A&

Stresses in lipid membranes

The stresses in a closed lipid membrane described by the Helfrich hamiltonian, quadratic in the extrinsic curvature, are identified using Noether's theorem. Three equations describe the conservation of the stress tensor: the normal projection is identified as the shape equation describing equilibrium configurations; the tangential projections are consistency conditions on the stresses which capture the fluid character of such membranes. The corresponding torque tensor is also identified. The use of the stress tensor as a basis for perturbation theory is discussed. The conservation laws are cast in terms of the forces and torques on closed curves. As an application, the first integral of the shape equation for axially symmetric configurations is derived by examining the forces which are balanced along circles of constant latitude.Comment: 16 pages, introduction rewritten, other minor changes, new references added, version to appear in Journal of Physics

Probing molecular free energy landscapes by periodic loading

Single molecule pulling experiments provide information about interactions in biomolecules that cannot be obtained by any other method. However, the reconstruction of the molecule's free energy profile from the experimental data is still a challenge, in particular for the unstable barrier regions. We propose a new method for obtaining the full profile by introducing a periodic ramp and using Jarzynski's identity for obtaining equilibrium quantities from non-equilibrium data. Our simulated experiments show that this method delivers significant more accurate data than previous methods, under the constraint of equal experimental effort.Comment: 4 pages, 3 figure

The Arches cluster revisited: II. A massive eclipsing spectroscopic binary in the Arches cluster

We have carried out a spectroscopic variability survey of some of the most massive stars in the Arches cluster, using K-band observations obtained with SINFONI on the VLT. One target, F2, exhibits substantial changes in radial velocity; in combination with new KMOS and archival SINFONI spectra, its primary component is found to undergo radial velocity variation with a period of 10.483+/-0.002 d and an amplitude of ~350 km/s-1. A secondary radial velocity curve is also marginally detectable. We reanalyse archival NAOS-CONICA photometric survey data in combination with our radial velocity results to confirm this object as an eclipsing SB2 system, and the first binary identified in the Arches. We model it as consisting of an 82+/-12 M⊙ WN8-9h primary and a 60+/-8 M⊙ O5-6 Ia+ secondary, and as having a slightly eccentric orbit, implying an evolutionary stage prior to strong binary interaction. As one of four X-ray bright Arches sources previously proposed as colliding-wind massive binaries, it may be only the first of several binaries to be discovered in this cluster, presenting potential challenges to recent models for the Arches' age and composition. It also appears to be one of the most massive binaries detected to date; the primary's calculated initial mass of >~120 M⊙ would arguably make this the most massive binary known in the Galaxy

Validation of the Jarzynski relation for a system with strong thermal coupling: an isothermal ideal gas model

We revisit the paradigm of an ideal gas under isothermal conditions. A moving piston performs work on an ideal gas in a container that is strongly coupled to a heat reservoir. The thermal coupling is modeled by stochastic scattering at the boundaries. In contrast to recent studies of an adiabatic ideal gas with a piston [R.C. Lua and A.Y. Grosberg, J. Phys. Chem. B 109, 6805 (2005); I. Bena et al., Europhys. Lett. 71, 879 (2005)], the container and piston stay in contact with the heat bath during the work process. Under this condition the heat reservoir as well as the system depend on the work parameter lambda and microscopic reversibility is broken for a moving piston. Our model is thus not included in the class of systems for which the nonequilibrium work theorem has been derived rigorously either by Hamiltonian [C. Jarzynski, J. Stat. Mech. (2004) P09005] or stochastic methods [G.E. Crooks, J. Stat. Phys. 90, 1481 (1998)]. Nevertheless the validity of the nonequilibrium work theorem is confirmed both numerically for a wide range of parameter values and analytically in the limit of a very fast moving piston, i.e., in the far nonequilibrium regime