Cosmic-ray acceleration at collisionless astrophysical shocks using Monte-Carlo simulations

Context. The diffusive shock acceleration mechanism has been widely accepted as the acceleration mechanism for galactic cosmic rays. While self-consistent hybrid simulations have shown how power-law spectra are produced, detailed information on the interplay of diffusive particle motion and the turbulent electromagnetic fields responsible for repeated shock crossings are still elusive. Aims. The framework of test-particle theory is applied to investigate the effect of diffusive shock acceleration by inspecting the obtained cosmic-ray energy spectra. The resulting energy spectra can be obtained this way from the particle motion and, depending on the prescribed turbulence model, the influence of stochastic acceleration through plasma waves can be studied. Methods. A numerical Monte-Carlo simulation code is extended to include collisionless shock waves. This allows one to trace the trajectories of test particle while they are being accelerated. In addition, the diffusion coefficients can be obtained directly from the particle motion, which allows for a detailed understanding of the acceleration process. Results. The classic result of an energy spectrum with $E^{-2}$ is only reproduced for parallel shocks, while, for all other cases, the energy spectral index is reduced depending on the shock obliqueness. Qualitatively, this can be explained in terms of the diffusion coefficients in the directions that are parallel and perpendicular to the shock front.Comment: 12 pages, 15 figures, accepted for publication in A&

Robust Control of Uncertain Markov Decision Processes with Temporal Logic Specifications

We present a method for designing robust controllers for dynamical systems with linear temporal logic specifications. We abstract the original system by a finite Markov Decision Process (MDP) that has transition probabilities in a specified uncertainty set. A robust control policy for the MDP is generated that maximizes the worst-case probability of satisfying the specification over all transition probabilities in the uncertainty set. To do this, we use a procedure from probabilistic model checking to combine the system model with an automaton representing the specification. This new MDP is then transformed into an equivalent form that satisfies assumptions for stochastic shortest path dynamic programming. A robust version of dynamic programming allows us to solve for a $\epsilon$-suboptimal robust control policy with time complexity $O(\log 1/\epsilon)$ times that for the non-robust case. We then implement this control policy on the original dynamical system

Sedimentation and polar order of active bottom-heavy particles

Self-propelled particles in an external gravitational field have been shown to display both an increased sedimentation length and polar order even without particle interactions. Here, we investigate self-propelled particles which additionally are bottom-heavy, that is they feel a torque aligning them to swim against the gravitational field. For bottom-heavy particles the gravitational field has the two opposite effects of i) sedimentation and ii) upward alignment of the particles' swimming direction. We perform a multipole expansion of the one-particle distribution with respect to orientation and derive expressions for sedimentation length and mean particle orientation which we check against Brownian Dynamics simulations. For large strength of gravity or small particle speeds and aligning torque, we observe sedimentation with increased sedimentation length compared with passive colloids but also active colloids without bottom-heaviness. Increasing, for example, swimming speed the sedimentation profile is inverted and the particles swim towards the top wall of the enclosing box. We find maximal orientational order at intermediate swimming speeds for both cases of particles with bottom-heaviness and those without. Ordering unsurprisingly is increased for the bottom-heavy particles, but this difference disappears at higher levels of activity and for very high activities ordering goes to zero in both cases.Comment: 6 pages, 3 figure

Thermodynamic Approach to Phase Coexistence in Ternary Phospholipi-Cholesterol Mixtures

We introduce a simple and predictive model for determining the phase stability of ternary phospholipid-cholesterol mixtures. Assuming that competition between the liquid and gel order of the phospholipids is the main driving force behind lipid segregation, we derive a Gibbs free-energy of mixing, based on the thermodynamic properties of the lipids main transition. A numerical approach was devised that enable the fast and efficient determination of the ternary diagrams associated with our Gibbs free-energy. The computed phase coexistence diagram of DOPC/DPPC/cholesterol reproduces well known features for this system at 10\circ C, as well as its evolution with temperature

An Improved Estimator for the Correlation Function of 2D Nonlinear Sigma Models

I present a new improved estimator for the correlation function of 2D nonlinear sigma models. Numerical tests for the 2D XY model and the 2D O(3)-invariant vector model were performed. For small physical volume, i.e. a lattice size small compared to the to the bulk correlation length, a reduction of the statistical error of the finite system correlation length by a factor of up to 30 compared to the cluster-improved estimator was observed. This improvement allows for a very accurate determination of the running coupling proposed by M. L"uscher et al. for 2D O(N)-invariant vector models.Comment: 20 pages, LaTeX + 2 ps figures, CERN-TH.7375/9

Cytoplasmic streaming in plant cells: the role of wall slip

We present a computer simulation study, via lattice Boltzmann simulations, of a microscopic model for cytoplasmic streaming in algal cells such as those of Chara corallina. We modelled myosin motors tracking along actin lanes as spheres undergoing directed motion along fixed lines. The sphere dimension takes into account the fact that motors drag vesicles or other organelles, and, unlike previous work, we model the boundary close to which the motors move as walls with a finite slip layer. By using realistic parameter values for actin lane and myosin density, as well as for endoplasmic and vacuole viscosity and the slip layer close to the wall, we find that this simplified view, which does not rely on any coupling between motors, cytoplasm and vacuole other than that provided by viscous Stokes flow, is enough to account for the observed magnitude of streaming velocities in intracellular fluid in living plant cells.Comment: 18 pages (incl. appendix), 10 figures, accepted in J R Soc Interfac

Surface properties of ocean fronts

Background information on oceanic fronts is presented and the results of several models which were developed to study the dynamics of oceanic fronts and their effects on various surface properties are described. The details of the four numerical models used in these studies are given in separate appendices which contain all of the physical equations, program documentation and running instructions for the models

From Uncertainty Data to Robust Policies for Temporal Logic Planning

We consider the problem of synthesizing robust disturbance feedback policies for systems performing complex tasks. We formulate the tasks as linear temporal logic specifications and encode them into an optimization framework via mixed-integer constraints. Both the system dynamics and the specifications are known but affected by uncertainty. The distribution of the uncertainty is unknown, however realizations can be obtained. We introduce a data-driven approach where the constraints are fulfilled for a set of realizations and provide probabilistic generalization guarantees as a function of the number of considered realizations. We use separate chance constraints for the satisfaction of the specification and operational constraints. This allows us to quantify their violation probabilities independently. We compute disturbance feedback policies as solutions of mixed-integer linear or quadratic optimization problems. By using feedback we can exploit information of past realizations and provide feasibility for a wider range of situations compared to static input sequences. We demonstrate the proposed method on two robust motion-planning case studies for autonomous driving

Constructing a gazebo: supporting teamwork in a tightly coupled, distributed task in virtual reality

Many tasks require teamwork. Team members may work concurrently, but there must be some occasions of coming together. Collaborative virtual environments (CVEs) allow distributed teams to come together across distance to share a task. Studies of CVE systems have tended to focus on the sense of presence or copresence with other people. They have avoided studying close interaction between us-ers, such as the shared manipulation of objects, because CVEs suffer from inherent network delays and often have cumbersome user interfaces. Little is known about the ef-fectiveness of collaboration in tasks requiring various forms of object sharing and, in particular, the concurrent manipu-lation of objects. This paper investigates the effectiveness of supporting teamwork among a geographically distributed group in a task that requires the shared manipulation of objects. To complete the task, users must share objects through con-current manipulation of both the same and distinct at-tributes. The effectiveness of teamwork is measured in terms of time taken to achieve each step, as well as the impression of users. The effect of interface is examined by comparing various combinations of walk-in cubic immersive projection technology (IPT) displays and desktop devices