Introduction to Systems Approach

Main aspects of systems theory are outlined. Emphasis is on the interface of between time and systems - natural or artificial

Negative association in uniform forests and connected graphs

We consider three probability measures on subsets of edges of a given finite graph $G$, namely those which govern, respectively, a uniform forest, a uniform spanning tree, and a uniform connected subgraph. A conjecture concerning the negative association of two edges is reviewed for a uniform forest, and a related conjecture is posed for a uniform connected subgraph. The former conjecture is verified numerically for all graphs $G$ having eight or fewer vertices, or having nine vertices and no more than eighteen edges, using a certain computer algorithm which is summarised in this paper. Negative association is known already to be valid for a uniform spanning tree. The three cases of uniform forest, uniform spanning tree, and uniform connected subgraph are special cases of a more general conjecture arising from the random-cluster model of statistical mechanics.Comment: With minor correction

Precise time and time interval (PTTI), an overview

Present applications of precise time and frequency (T/F) technology can be grouped as follows: (1) Communications systems which require T/F for time division multiplexing and for using spread spectrum techniques. (2) Navigation systems which need T/F for position fixing using a timed signal. (3) Scientific-Metrological applications which use T/F as the most precisely reproducible standard of measurement. (4) Astronomical-Space applications which cover a variety of the most demanding applications such as pulsar research, Very Long Baseline Interferometry (VLBI) and laser/radar ranging. In particular, pulsar time-of-arrival measurements require submicrosecond precision over a period of one-half year referred to an extraterrestrial inertial system, and constitute the most stringent requirements for uniform timekeeping to date

Semiflexible polymers under external fields confined to two dimensions

The non-equilibrium structural and dynamical properties of semiflexible polymers confined to two dimensions are investigated by molecular dynamics simulations. Three different scenarios are considered: The force-extension relation of tethered polymers, the relaxation of an initially stretched semiflexible polymer, and semiflexible polymers under shear flow. We find quantitative agreement with theoretical predictions for the force-extension relation and the time dependence of the entropically contracting polymer. The semiflexible polymers under shear flow exhibit significant conformational changes at large shear rates, where less stiff polymers are extended by the flow, whereas rather stiff polymers are contracted. In addition, the polymers are aligned by the flow, thereby the two-dimensional semiflexible polymers behave similarly to flexible polymers in three dimensions. The tumbling times display a power-law dependence at high shear rate rates with an exponent comparable to the one of flexible polymers in three-dimensional systems.Comment: Accepted for publication in J. Chem. Phy

Traveling fronts in active-passive particle mixtures

The emergent dynamics in phase-separated mixtures of isometric active and passive Brownian particles is studied numerically in two dimensions. A novel steady-state of well-defined traveling fronts is observed, where the interface between the dense and the dilute phase propagates and the bulk of both phases is (nearly) at rest. Two kind of interfaces, advancing and receding, are formed by spontaneous symmetry breaking, induced by an instability of a planar interface due to the formation of localized vortices. The propagation arises due to flux imbalance at the interface, strongly resembling traveling fronts in reaction-diffusion systems. Above a threshold, the interface velocity decreases linearly with increasing fraction of active particles.Comment: 5 pages, 4 figure

External gates and transport in biased bilayer graphene

We formulate a theory of transport in graphene bilayers in the weak momentum scattering regime in such a way as to take into account contributions to the electrical conductivity to leading and next-to-leading order in the scattering potential. The response of bilayers to an electric field cannot be regarded as a sum of terms due to individual layers. Rather, interlayer tunneling and coherence between positive- and negative-energy states give the main contributions to the conductivity. At low energies, the dominant effect of scattering on transport comes from scattering within each energy band, yet a simple picture encapsulating the role of collisions in a set of scattering times is not applicable. Coherence between positive- and negative-energy states gives, as in monolayers, a term in the conductivity which depends on the order of limits. The application of an external gate, which introduces a gap between positive- and negative-energy states, does not affect transport. Nevertheless the solution to the kinetic equation in the presence of such a gate is very revealing for transport in both bilayers and monolayers.Comment: 6 pages, accepted for publication in Physical Review

Physics of Microswimmers - Single Particle Motion and Collective Behavior

Locomotion and transport of microorganisms in fluids is an essential aspect of life. Search for food, orientation toward light, spreading of off-spring, and the formation of colonies are only possible due to locomotion. Swimming at the microscale occurs at low Reynolds numbers, where fluid friction and viscosity dominates over inertia. Here, evolution achieved propulsion mechanisms, which overcome and even exploit drag. Prominent propulsion mechanisms are rotating helical flagella, exploited by many bacteria, and snake-like or whip-like motion of eukaryotic flagella, utilized by sperm and algae. For artificial microswimmers, alternative concepts to convert chemical energy or heat into directed motion can be employed, which are potentially more efficient. The dynamics of microswimmers comprises many facets, which are all required to achieve locomotion. In this article, we review the physics of locomotion of biological and synthetic microswimmers, and the collective behavior of their assemblies. Starting from individual microswimmers, we describe the various propulsion mechanism of biological and synthetic systems and address the hydrodynamic aspects of swimming. This comprises synchronization and the concerted beating of flagella and cilia. In addition, the swimming behavior next to surfaces is examined. Finally, collective and cooperate phenomena of various types of isotropic and anisotropic swimmers with and without hydrodynamic interactions are discussed.Comment: 54 pages, 59 figures, review article, Reports of Progress in Physics (to appear

Virial pressure in systems of active Brownian particles

The pressure of suspensions of self-propelled objects is studied theoretically and by simulation of spherical active Brownian particles (ABP). We show that for certain geometries, the mechanical pressure as force/area of a confined systems can equally be expressed by bulk properties, which implies the existence of an nonequilibrium equation of state. Exploiting the virial theorem, we derive expressions for the pressure of ABPs confined by solid walls or exposed to periodic boundary conditions. In both cases, the pressure comprises three contributions: the ideal-gas pressure due to white-noise random forces, an activity-induce pressure (swim pressure), which can be expressed in terms of a product of the bare and a mean effective propulsion velocity, and the contribution by interparticle forces. We find that the pressure of spherical ABPs in confined systems explicitly depends on the presence of the confining walls and the particle-wall interactions, which has no correspondence in systems with periodic boundary conditions. Our simulations of three-dimensional APBs in systems with periodic boundary conditions reveal a pressure-concentration dependence that becomes increasingly nonmonotonic with increasing activity. Above a critical activity and ABP concentration, a phase transition occurs, which is reflected in a rapid and steep change of the pressure. We present and discuss the pressure for various activities and analyse the contributions of the individual pressure components

Steady state sedimentation of ultrasoft colloids

The structural and dynamical properties of ultra-soft colloids - star polymers - exposed to a uniform external force field are analyzed applying the multiparticle collision dynamics approach, a hybrid coarse-grain mesoscale simulation approach, which captures thermal fluctuations and long-range hydrodynamic interactions. In the weak field limit, the structure of the star polymer is nearly unchanged, however in an intermediate regime, the radius of gyration decreases, in particular transverse to the sedimentation direction. In the limit of a strong field, the radius of gyration increases with field strength. Correspondingly, the sedimentation coefficient increases with increasing field strength, passes through a maximum and decreases again at high field strengths. The maximum value depends on the functionality of the star polymer. High field strengths lead to symmetry breaking with trailing, strongly stretched polymer arms and a compact star polymer body. In the weak field linear response regime, the sedimentation coefficient follows the scaling relation of a star polymer in terms of functionality and arm length

Time on the Market: The Impact of Residential Brokerage

IThis paper examines the impact of brokers, brokerage firms and marketing strategy on time on the market (TOM) in the residential housing market. Using a duration model methodology, the study finds duration dependence to be positive, suggesting that the probability of sale increases with TOM. Pricing-related marketing strategies are found to strongly influence TOM, but individual agent and firm characteristics are not statistically significant. These results are consistent with an efficient market within a multiple listing serviceÐÐno group of agents or firms appears to possess special advantages enabling them to sell homes more quickly than their rivals.