Dynamics of a Semiflexible Polymer or Polymer Ring in Shear Flow

Polymers exposed to shear flow exhibit a rich tumbling dynamics. While rigid rods rotate on Jeffery orbits, flexible polymers stretch and coil up during tumbling. Theoretical results show that in both of these asymptotic regimes the tumbling frequency f_c in a linear shear flow of strength \gamma scales as a power law Wi^(2/3) in the Weissenberg number Wi=\gamma \tau, where \tau is a characteristic time of the polymer's relaxational dynamics. For flexible polymers these theoretical results are well confirmed by experimental single molecule studies. However, for the intermediate semiflexible regime the situation is less clear. Here we perform extensive Brownian dynamics simulations to explore the tumbling dynamics of semiflexible polymers over a broad range of shear strength and the polymer's persistence length l_p. We find that the Weissenberg number alone does not suffice to fully characterize the tumbling dynamics, and the classical scaling law breaks down. Instead, both the polymer's stiffness and the shear rate are relevant control parameters. Based on our Brownian dynamics simulations we postulate that in the parameter range most relevant for cytoskeletal filaments there is a distinct scaling behavior with f_c \tau*=Wi^(3/4) f_c (x) with Wi=\gamma \tau* and the scaling variable x=(l_p/L)(Wi)^(-1/3); here \tau* is the time the polymer's center of mass requires to diffuse its own contour length L. Comparing these results with experimental data on F-actin we find that the Wi^(3/4) scaling law agrees quantitatively significantly better with the data than the classical Wi^(2/3) law. Finally, we extend our results to single ring polymers in shear flow, and find similar results as for linear polymers with slightly different power laws.Comment: 17 pages, 14 figure

A renormalization group approach to time dependent transport through correlated quantum dots

We introduce a real time version of the functional renormalization group which allows to study correlation effects on nonequilibrium transport through quantum dots. Our method is equally capable to address (i) the relaxation out of a nonequilibrium initial state into a (potentially) steady state driven by a bias voltage and (ii) the dynamics governed by an explicitly time-dependent Hamiltonian. All time regimes from transient to asymptotic can be tackled; the only approximation is the consistent truncation of the flow equations at a given order. As an application we investigate the relaxation dynamics of the interacting resonant level model which describes a fermionic quantum dot dominated by charge fluctuations. Moreover, we study decoherence and relaxation phenomena within the ohmic spin-boson model by mapping the latter to the interacting resonant level model

Local Cyber-Physical Attack for Masking Line Outage and Topology Attack in Smart Grid

Malicious attacks in the power system can eventually result in a large-scale cascade failure if not attended on time. These attacks, which are traditionally classified into \emph{physical} and \emph{cyber attacks}, can be avoided by using the latest and advanced detection mechanisms. However, a new threat called \emph{cyber-physical attacks} which jointly target both the physical and cyber layers of the system to interfere the operations of the power grid is more malicious as compared with the traditional attacks. In this paper, we propose a new cyber-physical attack strategy where the transmission line is first physically disconnected, and then the line-outage event is masked, such that the control center is misled into detecting as an obvious line outage at a different position in the local area of the power system. Therefore, the topology information in the control center is interfered by our attack. We also propose a novel procedure for selecting vulnerable lines, and analyze the observability of our proposed framework. Our proposed method can effectively and continuously deceive the control center into detecting fake line-outage positions, and thereby increase the chance of cascade failure because the attention is given to the fake outage. The simulation results validate the efficiency of our proposed attack strategy.Comment: accepted by IEEE Transactions on Smart Grid. arXiv admin note: text overlap with arXiv:1708.0320

Matrix Minor Reformulation and SOCP-based Spatial Branch-and-Cut Method for the AC Optimal Power Flow Problem

Alternating current optimal power flow (AC OPF) is one of the most fundamental optimization problems in electrical power systems. It can be formulated as a semidefinite program (SDP) with rank constraints. Solving AC OPF, that is, obtaining near optimal primal solutions as well as high quality dual bounds for this non-convex program, presents a major computational challenge to today's power industry for the real-time operation of large-scale power grids. In this paper, we propose a new technique for reformulation of the rank constraints using both principal and non-principal 2-by-2 minors of the involved Hermitian matrix variable and characterize all such minors into three types. We show the equivalence of these minor constraints to the physical constraints of voltage angle differences summing to zero over three- and four-cycles in the power network. We study second-order conic programming (SOCP) relaxations of this minor reformulation and propose strong cutting planes, convex envelopes, and bound tightening techniques to strengthen the resulting SOCP relaxations. We then propose an SOCP-based spatial branch-and-cut method to obtain the global optimum of AC OPF. Extensive computational experiments show that the proposed algorithm significantly outperforms the state-of-the-art SDP-based OPF solver and on a simple personal computer is able to obtain on average a 0.71% optimality gap in no more than 720 seconds for the most challenging power system instances in the literature

Hubble-Lema\^itre fragmentation and the path to equilibrium of merger-driven cluster formation

This paper discusses a new method to generate self-coherent initial conditions for young substructured stellar cluster. The expansion of a uniform system allows stellar sub-structures (clumps) to grow from fragmentation modes by adiabatic cooling. We treat the system mass elements as stars, chosen according to a Salpeter mass function, and the time-evolution is performed with a collisional N-body integrator. This procedure allows to create a fully-coherent relation between the clumps' spatial distribution and the underlying velocity field. The cooling is driven by the gravitational field, as in a cosmological Hubble-Lema\^itre flow. The fragmented configuration has a `fractal'-like geometry but with a self-grown velocity field and mass profile. We compare the characteristics of the stellar population in clumps with that obtained from hydrodynamical simulations and find a remarkable correspondence between the two in terms of the stellar content and the degree of spatial mass-segregation. In the fragmented configuration, the IMF power index is ~0.3 lower in clumps in comparison to the field stellar population, in agreement with observations in the Milky Way. We follow in time the dynamical evolution of fully fragmented and sub-virial configurations, and find a soft collapse, leading rapidly to equilibrium (timescale of 1 Myr for a ~ 10^4 Msun system). The low-concentration equilibrium implies that the dynamical evolution including massive stars is less likely to induce direct collisions and the formation of exotic objects. Low-mass stars already ejected from merging clumps are depleted in the end-result stellar clusters, which harbour a top-heavy stellar mass function.Comment: 22 pages, accepted for publication in MNRA

Solution of Optimal Power Flow Problems using Moment Relaxations Augmented with Objective Function Penalization

The optimal power flow (OPF) problem minimizes the operating cost of an electric power system. Applications of convex relaxation techniques to the non-convex OPF problem have been of recent interest, including work using the Lasserre hierarchy of "moment" relaxations to globally solve many OPF problems. By preprocessing the network model to eliminate low-impedance lines, this paper demonstrates the capability of the moment relaxations to globally solve large OPF problems that minimize active power losses for portions of several European power systems. Large problems with more general objective functions have thus far been computationally intractable for current formulations of the moment relaxations. To overcome this limitation, this paper proposes the combination of an objective function penalization with the moment relaxations. This combination yields feasible points with objective function values that are close to the global optimum of several large OPF problems. Compared to an existing penalization method, the combination of penalization and the moment relaxations eliminates the need to specify one of the penalty parameters and solves a broader class of problems.Comment: 8 pages, 1 figure, to appear in IEEE 54th Annual Conference on Decision and Control (CDC), 15-18 December 201

Dynamical temperature study for classical planar spin systems

In this micro-canonical simulation the temperature and also the specific heat are determined as averages of expressions easy to implement. The XY-chain is studied for a test. The second order transition on a cubic lattice and the first order transition on an fcc lattice are analyzed in greater detail to have a more severe test about the feasibility of this micro-canonical method.Comment: 9 pages in Latex(revtex), 7 PS-figure

Convex Relaxations and Approximations of Chance-Constrained AC-OPF Problems

This paper deals with the impact of linear approximations for the unknown nonconvex confidence region of chance-constrained AC optimal power flow problems. Such approximations are required for the formulation of tractable chance constraints. In this context, we introduce the first formulation of a chance-constrained second-order cone (SOC) OPF. The proposed formulation provides convergence guarantees due to its convexity, while it demonstrates high computational efficiency. Combined with an AC feasibility recovery, it is able to identify better solutions than chance-constrained nonconvex AC-OPF formulations. To the best of our knowledge, this paper is the first to perform a rigorous analysis of the AC feasibility recovery procedures for robust SOC-OPF problems. We identify the issues that arise from the linear approximations, and by using a reformulation of the quadratic chance constraints, we introduce new parameters able to reshape the approximation of the confidence region. We demonstrate our method on the IEEE 118-bus system

Chance-Constrained AC Optimal Power Flow Integrating HVDC Lines and Controllability

The integration of large-scale renewable generation has major implications on the operation of power systems, two of which we address in this work. First, system operators have to deal with higher degrees of uncertainty due to forecast errors and variability in renewable energy production. Second, with abundant potential of renewable generation in remote locations, there is an increasing interest in the use of High Voltage Direct Current lines (HVDC) to increase transmission capacity. These HVDC transmission lines and the flexibility and controllability they offer must be incorporated effectively and safely into the system. In this work, we introduce an optimization tool that addresses both challenges by incorporating the full AC power flow equations, chance constraints to address the uncertainty of renewable infeed, modelling of point-to-point HVDC lines, and optimized corrective control policies to model the generator and HVDC response to uncertainty. The main contributions are twofold. First, we introduce a HVDC line model and the corresponding HVDC participation factors in a chance-constrained AC-OPF framework. Second, we modify an existing algorithm for solving the chance-constrained AC-OPF to allow for optimization of the generation and HVDC participation factors. Using realistic wind forecast data, for 10 and IEEE 39 bus systems with HVDC lines and wind farms, we show that our proposed OPF formulation achieves good in- and out-of-sample performance whereas not considering uncertainty leads to high constraint violation probabilities. In addition, we find that optimizing the participation factors reduces the cost of uncertainty significantly