Low Reynolds number hydrodynamics of asymmetric, oscillating dumbbell pairs

Active dumbbell suspensions constitute one of the simplest model system for collective swimming at low Reynolds number. Generalizing recent work, we derive and analyze stroke-averaged equations of motion that capture the effective hydrodynamic far-field interaction between two oscillating, asymmetric dumbbells in three space dimensions. Time-averaged equations of motion, as those presented in this paper, not only yield a considerable speed-up in numerical simulations, they may also serve as a starting point when deriving continuum equations for the macroscopic dynamics of multi-swimmer suspensions. The specific model discussed here appears to be particularly useful in this context, since it allows one to investigate how the collective macroscopic behavior is affected by changes in the microscopic symmetry of individual swimmers.Comment: 10 pages, to appear in EPJ Special Topic

Stationarity, soft ergodicity, and entropy in relativistic systems

Recent molecular dynamics simulations show that a dilute relativistic gas equilibrates to a Juettner velocity distribution if ensemble velocities are measured simultaneously in the observer frame. The analysis of relativistic Brownian motion processes, on the other hand, implies that stationary one-particle distributions can differ depending on the underlying time-parameterizations. Using molecular dynamics simulations, we demonstrate how this relativistic phenomenon can be understood within a deterministic model system. We show that, depending on the time-parameterization, one can distinguish different types of soft ergodicity on the level of the one-particle distributions. Our analysis further reveals a close connection between time parameters and entropy in special relativity. A combination of different time-parameterizations can potentially be useful in simulations that combine molecular dynamics algorithms with randomized particle creation, annihilation, or decay processes.Comment: 4 page

A System for Series Magnetic Measurements of the LHC Main Quadrupoles

More than 400 twin aperture lattice quadrupoles are needed for the Large Hadron Collider (LHC) which is under construction at CERN. The main quadrupole is assembled with correction magnets in a common cryostat called the Short Straight Section (SSS). We plan to measure all SSS's in cold conditions with an unprecedented accuracy: integrated gradient of the field within 150 ppm, harmonics in a range of 1 to 5 ppm, magnetic axis of all elements within 0.1 mm and their field direction within 0.2 mrad. In this paper we describe the automatic measurement system that we have designed, built and calibrated. Based on the results obtained on the two first prototypes of the SSS's (SSS3 and SSS4) we show that this system meets all above requirements

Establishing the substantive interpretation of the GFP by considering evidence from research on personality disorders and Animal Personality

In research on individual differences, various structural models aim at providing a comprehensive description of personality. These models assume multiple, mostly independent personality dimensions. More recently, the so-called General Factor of Personality (GFP) has become a proliferous, but contentious, topic. The notion of the GFP is based on the observations that personality dimensions are not independent, but in fact show consistent inter-correlations, leading to a relevant proportion of shared variance among them (Figueredo et al., 2006). The GFP seems to capture the socially desirable ends of personality scales, and, in terms of the Big Five model, high-GFP individuals score relatively high on openness, conscientiousness, extraversion (mainly the sociability-facet), agreeableness, and emotional stability (Rushton and Irwing, 2009; van der Linden et al., 2010a). Some authors have suggested that the GFP simply reflects methodological artifacts (Ashton et al., 2009; Backstrom et al., 2009; Hopwood et al., 2011b; Pettersson et al., 2012). However, much of this criticism has been addressed (Rushton and Erdle, 2010; Loehlin, 2012; Dunkel and van der Linden, 2014; van der Linden et al., 2014a). The objective of the present work is not to reiterate these issues, as they have been discussed extensively elsewhere (Irwing, 2013; van der Linden et al., 2016). Instead, we contend that criticism mostly offered within the specialty of personality psychology misses the bigger picture. More specific, evidence in favor of the GFP as a substantive and theoretically coherent construct has been provided in other research fields long before it became a contentious issue in personality psychology. Here we introduce two lines of evidence that may further corroborate the substantive interpretation of the GFP, specifically, findings from personality pathology as well as from animal personality. Looking at the GFP from a different perspective may help to overcome the current debates within personality psychology. In the following we will first briefly introduce work on the GFP and its theoretical foundation as social effectiveness. Afterwards we outline research from psychiatric nosology and animal ecology and discuss these in context

First order and stable relativistic dissipative hydrodynamics

Relativistic thermodynamics is derived from kinetic equilibrium in a general frame. Based on a novel interpretation of Lagrange multipliers in the equilibrium state we obtain a generic stable but first order relativistic dissipative hydrodynamics. Although this was believed to be impossible, we circumvent this difficulty by a specific handling of the heat flow.Comment: revised, 11 pages, accepted for publication in PL

Non-analytic microscopic phase transitions and temperature oscillations in the microcanonical ensemble: An exactly solvable 1d-model for evaporation

We calculate exactly both the microcanonical and canonical thermodynamic functions (TDFs) for a one-dimensional model system with piecewise constant Lennard-Jones type pair interactions. In the case of an isolated $N$-particle system, the microcanonical TDFs exhibit (N-1) singular (non-analytic) microscopic phase transitions of the formal order N/2, separating N energetically different evaporation (dissociation) states. In a suitably designed evaporation experiment, these types of phase transitions should manifest themselves in the form of pressure and temperature oscillations, indicating cooling by evaporation. In the presence of a heat bath (thermostat), such oscillations are absent, but the canonical heat capacity shows a characteristic peak, indicating the temperature-induced dissociation of the one-dimensional chain. The distribution of complex zeros (DOZ) of the canonical partition may be used to identify different degrees of dissociation in the canonical ensemble.Comment: version accepted for publication in PRE, minor additions in the text, references adde

Formation of the planet around the millisecond pulsar J1719-1438

Context. Recently the discovery of PSR J1719-1438, a 5.8 ms pulsar with a companion in a 2.2 hr orbit, was reported. The combination of this orbital period and the very low mass function is unique. The discoverers, Bailes et al., proposed an ultracompact X-ray binary (UCXB) as the progenitor system. However, the standard UCXB scenario would not produce this system as the time required to reach this orbital period exceeds the current estimate of the age of the Universe. The detached state of the system aggravates the problem. Aims. We want to understand the evolutionary history of PSR J1719-1438, and determine under which circumstances it could have evolved from an UCXB. Methods. We model UCXB evolution varying the donor size and investigate the effect of a wind mass loss from the donor, and compare the results with the observed characteristics of PSR J1719-1438. Results. An UCXB can reach a 2.2 hr orbit within the age of the Universe, provided that 1) the millisecond pulsar can significantly heat and expand the donor by pulsar irradiation, or 2) the system loses extra orbital angular momentum, e.g. via a fast wind from the donor. Conclusions. The most likely scenario for the formation of PSR J1719-1438 is UCXB evolution driven by angular momentum loss via the usual gravitational wave emission, which is enhanced by angular momentum loss via a donor wind of ~3x10^-13 Msun/yr. Depending on the size of the donor during the evolution, the companion presently probably has a mass of ~1-3 Jupiter masses, making it a very low mass white dwarf as proposed by Bailes et al. Its composition can be either helium or carbon-oxygen. A helium white dwarf companion makes the long (for an UCXB) orbital period easier to explain, but the required inclination makes it a priori less likely than a carbon-oxygen white dwarf.Comment: 5 pages, 4 figures. Accepted for publication in Astronomy and Astrophysics. v2: Updated a referenc

Resource Competition on Integral Polymatroids

We study competitive resource allocation problems in which players distribute their demands integrally on a set of resources subject to player-specific submodular capacity constraints. Each player has to pay for each unit of demand a cost that is a nondecreasing and convex function of the total allocation of that resource. This general model of resource allocation generalizes both singleton congestion games with integer-splittable demands and matroid congestion games with player-specific costs. As our main result, we show that in such general resource allocation problems a pure Nash equilibrium is guaranteed to exist by giving a pseudo-polynomial algorithm computing a pure Nash equilibrium.Comment: 17 page

Relative entropy, Haar measures and relativistic canonical velocity distributions

The thermodynamic maximum principle for the Boltzmann-Gibbs-Shannon (BGS) entropy is reconsidered by combining elements from group and measure theory. Our analysis starts by noting that the BGS entropy is a special case of relative entropy. The latter characterizes probability distributions with respect to a pre-specified reference measure. To identify the canonical BGS entropy with a relative entropy is appealing for two reasons: (i) the maximum entropy principle assumes a coordinate invariant form; (ii) thermodynamic equilibrium distributions, which are obtained as solutions of the maximum entropy problem, may be characterized in terms of the transformation properties of the underlying reference measure (e.g., invariance under group transformations). As examples, we analyze two frequently considered candidates for the one-particle equilibrium velocity distribution of an ideal gas of relativistic particles. It becomes evident that the standard J\"uttner distribution is related to the (additive) translation group on momentum space. Alternatively, imposing Lorentz invariance of the reference measure leads to a so-called modified J\"uttner function, which differs from the standard J\"uttner distribution by a prefactor, proportional to the inverse particle energy.Comment: 15 pages: extended version, references adde

The Simple Non-degenerate Relativistic Gas: Statistical Properties and Brownian Motion

This paper shows a novel calculation of the mean square displacement of a classical Brownian particle in a relativistic thermal bath. The result is compared with the expressions obtained by other authors. Also, the thermodynamic properties of a non-degenerate simple relativistic gas are reviewed in terms of a treatment performed in velocity space.Comment: 6 pages, 2 figure