Local galaxy flows within 5 Mpc

We present Hubble Space Telescope/WFPC2 images of sixteen dwarf galaxies as part of our snapshot survey of nearby galaxy candidates. We derive their distances from the luminosity of the tip of the red giant branch stars with a typical accuracy of ~12%. The resulting distances are 4.26 Mpc (KKH 5), 4.74 Mpc (KK 16), 4.72 Mpc (KK 17), 4.66 Mpc (ESO 115-021), 4.43 Mpc (KKH 18), 3.98 Mpc (KK 27), 4.61 Mpc (KKH 34), 4.99 Mpc (KK 54), 4.23 Mpc (ESO 490-017), 4.90 Mpc (FG 202), 5.22 Mpc (UGC 3755), 5.18 Mpc (UGC 3974), 4.51 Mpc (KK 65), 5.49 Mpc (UGC 4115), 3.78 Mpc (NGC 2915), and 5.27 Mpc (NGC 6503). Based on distances and radial velocities of 156 nearby galaxies, we plot the local velocity-distance relation, which has a slope of H_0 = 73 km/(c * Mpc) and a radial velocity dispersion of 85 km/s. When members of the M81 and CenA groups are removed, and distance errors are taken into account, the radial velocity dispersion drops to sigma_v=41 km/s. The local Hubble flow within 5 Mpc exibits a significant anisotropy, with two infall peculiar velocity regions directed towards the Supergalactic poles. However, two observed regions of outflow peculiar velocity, situated on the Supergalactic equator, are far away (~50 degr.) from the Virgo/anti-Virgo direction, which disagrees with a spherically symmetric Virgo-centric flow. About 63% of galaxies within 5 Mpc belong to known compact and loose groups. Apart from them, we found six new probable groups, consisting entirely of dwarf galaxies.Comment: 22 pages, 7 figures. A&A Accepted. High resolution Figures 1 and 2 (9616k) are available at http://www.sao.ru/~sme/figs.tar.g

Galaxy Flow in the Canes Venatici I Cloud

We present an analysis of Hubble Space Telescope/WFPC2 images of eighteen galaxies in the Canes Venatici I cloud. We derive their distances from the luminosity of the tip of the red giant branch stars with a typical accuracy of ~12 %. The resulting distances are 3.9 Mpc (UGC 6541), 4.9 Mpc (NGC 3738), 3.0 Mpc (NGC 3741), 4.5 Mpc (KK 109), >6.3 Mpc (NGC 4150), 4.2 Mpc (UGC 7298), 4.5 Mpc (NGC 4244), 4.6 Mpc (NGC 4395), 4.9 Mpc (UGC 7559), 4.2 Mpc (NGC 4449), 4.4 Mpc (UGC 7605), 4.6 Mpc (IC 3687), 4.7 Mpc (KK 166), 4.7 Mpc (NGC 4736), 4.2 Mpc (UGC 8308), 4.3 Mpc (UGC 8320), 4.6 Mpc (NGC 5204), and 3.2 Mpc (UGC 8833). The CVn I cloud has a mean radial velocity of 286 +- 9 km/s, a mean distance of 4.1 +- 0.2 Mpc, a radial velocity dispersion of 50 km/s, a mean projected radius of 760 kpc, and a total blue luminosity of 2.2 * 10^{10} L_{\sun}. Assuming virial or closed orbital motions for the galaxies, we estimated their virial and their orbital mass-to-luminosity ratio to be 176 and 88 M_{\sun}/L_{\sun}, respectively. However, the CVn I cloud is characterized by a crossing time of 15 Gyr, and is thus far from a state of dynamical equilibrium. The large crossing time for the cloud, its low content of dSph galaxies ($< 6$ %), and the almost ``primordial'' shape of its luminosity function show that the CVn I complex is in a transient dynamical state, driven rather by the free Hubble expansion than by galaxy interactions.Comment: 23 pages, 6 figures, A&A in preparation. The version does not include Figure 2. High resolution figures 1 and 2 (11311k) are available at http://luna.sao.ru/~sme/figsCVn.tar.g

Constrained nonlinear optimal control: a converse HJB approach

Extending the concept of solving the Hamilton-Jacobi-Bellman (HJB) optimization equation backwards [2], the so called converse constrained optimal control problem is introduced, and used to create various classes of nonlinear systems for which the optimal controller subject to constraints is known. In this way a systematic method for the testing, validation and comparison of different control techniques with the optimal is established. Because it naturally and explicitly handles constraints, particularly control input saturation, model predictive control (MPC) is a potentially powerful approach for nonlinear control design. However, nonconvexity of the nonlinear programs (NLP) involved in the MPC optimization makes the solution problematic. In order to explore properties of MPC-based constrained control schemes, and to point out the potential issues in implementing MPC, challenging benchmark examples are generated and analyzed. Properties of MPC-based constrained techniques are then evaluated and implementation issues are explored by applying both nonlinear MPC and MPC with feedback linearization

Model predictive controllers for reduction of mechanical fatigue in wind farms

We consider the problem of dispatching WindFarm (WF) power demand to individual Wind Turbines (WT) with the goal of minimizing mechanical stresses. We assume wind is strong enough to let each WTs to produce the required power and propose different closed-loop Model Predictive Control (MPC) dispatching algorithms. Similarly to existing approaches based on MPC, our methods do not require changes in WT hardware but only software changes in the SCADA system of the WF. However, differently from previous MPC schemes, we augment the model of a WT with an ARMA predictor of the wind turbulence, which reduces uncertainty in wind predictions over the MPC control horizon. This allows us to develop both stochastic and deterministic MPC algorithms. In order to compare different MPC schemes and demonstrate improvements with respect to classic open-loop schedulers, we performed simulations using the SimWindFarm toolbox for MatLab. We demonstrate that MPC controllers allow to achieve reduction of stresses even in the case of large installations such as the 100-WTs Thanet offshore WF

Crawling the Cosmic Network: Identifying and Quantifying Filamentary Structure

We present the Smoothed Hessian Major Axis Filament Finder (SHMAFF), an algorithm that uses the eigenvectors of the Hessian matrix of the smoothed galaxy distribution to identify individual filamentary structures. Filaments are traced along the Hessian eigenvector corresponding to the largest eigenvalue, and are stopped when the axis orientation changes more rapidly than a preset threshold. In both N-body simulations and the Sloan Digital Sky Survey (SDSS) main galaxy redshift survey data, the resulting filament length distributions are approximately exponential. In the SDSS galaxy distribution, using smoothing lengths of 10 h^{-1} Mpc and 15 h^{-1} Mpc, we find filament lengths per unit volume of 1.9x10^{-3} h^2 Mpc^{-2} and 7.6x10^{-4} h^2 Mpc^{-2}, respectively. The filament width distributions, which are much more sensitive to non-linear growth, are also consistent between the real and mock galaxy distributions using a standard cosmology. In SDSS, we find mean filament widths of 5.5 h^{-1} Mpc and 8.4 h^{-1} Mpc on 10 h^{-1} Mpc and 15 h^{-1} Mpc smoothing scales, with standard deviations of 1.1 h^{-1} Mpc and 1.4 h^{-1} Mpc, respectively. Finally, the spatial distribution of filamentary structure in simulations is very similar between z=3 and z=0 on smoothing scales as large as 15 h^{-1} Mpc, suggesting that the outline of filamentary structure is already in place at high redshift.Comment: 10 pages, 11 figures, accepted to MNRA

Learning an Approximate Model Predictive Controller with Guarantees

A supervised learning framework is proposed to approximate a model predictive controller (MPC) with reduced computational complexity and guarantees on stability and constraint satisfaction. The framework can be used for a wide class of nonlinear systems. Any standard supervised learning technique (e.g. neural networks) can be employed to approximate the MPC from samples. In order to obtain closed-loop guarantees for the learned MPC, a robust MPC design is combined with statistical learning bounds. The MPC design ensures robustness to inaccurate inputs within given bounds, and Hoeffding's Inequality is used to validate that the learned MPC satisfies these bounds with high confidence. The result is a closed-loop statistical guarantee on stability and constraint satisfaction for the learned MPC. The proposed learning-based MPC framework is illustrated on a nonlinear benchmark problem, for which we learn a neural network controller with guarantees.Comment: 6 pages, 3 figures, to appear in IEEE Control Systems Letter

Particle-Based Mesoscale Hydrodynamic Techniques

Dissipative particle dynamics (DPD) and multi-particle collision (MPC) dynamics are powerful tools to study mesoscale hydrodynamic phenomena accompanied by thermal fluctuations. To understand the advantages of these types of mesoscale simulation techniques in more detail, we propose new two methods, which are intermediate between DPD and MPC -- DPD with a multibody thermostat (DPD-MT), and MPC-Langevin dynamics (MPC-LD). The key features are applying a Langevin thermostat to the relative velocities of pairs of particles or multi-particle collisions, and whether or not to employ collision cells. The viscosity of MPC-LD is derived analytically, in very good agreement with the results of numerical simulations.Comment: 7 pages, 2 figures, 1 tabl