Indirect forces between impurities in one-dimensional quantum liquids

We investigate the indirect interaction between two isolated impurities in a Luttinger liquid described by a microscopic lattice model. To treat the electron-electron interaction U the functional renormalization group method is used. For comparison we also study the U=0 case. We find that for a wide range of impurity parameters the impurity interaction V_{12} as a function of their separation r oscillates with decaying amplitude between being attractive and repulsive. For half-filling of the band and in a crossover regime between weak and strong impurities the interaction becomes purely attractive. For U=0 and independent of the impurity strength the amplitude of the interaction energy falls off as 1/r. For U>0 the decay for small separations and weak to intermediate impurities is governed by a U dependent exponent larger than -1, which crosses over to -1 for large r. The crossover scale depends on the impurity strength and U. We present simple pictures which explain our results in the limits of weak and strong impurities. We finally also consider attractive interactions U<0.Comment: 8 pages, 9 figures include

A comparative analysis of built environment and open terrain wind data by higher order statistics and performance evaluation of 5 kW HAWT using FAST

Small wind turbines (SWT) that are designed as per the IEC 61400-2 standard suffer structural and operational complexities when operating in the built environment, because such environments impose stochastic variations in wind speed and turbulence. The wind conditions in flat terrain of Östergarnsholm (OG) Island, Sweden and built environment of Port Kennedy (PK), Australia are compared for turbulence intensity (TI) and intermittency. The TI of the PK wind field was 24% at mean wind speed of 15 m/s, which was higher than the Normal Turbulence Model (NTM) indicated in IEC 61400-2. The TI in the open terrain was below 18% for all mean wind speeds. Similarly, for three chosen wind speed bins within a SWT's operating range, the urban wind field had higher intermittency for smaller timescales but resulted in smaller intermittency as the time lag increased. The effect of these measured wind fields on the performance and loading of a turbine was studied at the three chosen wind speed bins using an aeroelastic model of a 5 kW SWT that was developed in FAST. The predicted output statistics using measured wind fields were compared with the assumed wind fields in the IEC 61400-2 standard. The rotor thrust and blade flapwise bending moment with PK wind data were higher than that of the IEC standard due to the increased turbulence in the inflowing wind indicating the inadequacy in the current wind standard applied for such SWTs for urban installations

Dynamics of Dengue epidemics using optimal control

We present an application of optimal control theory to Dengue epidemics. This epidemiologic disease is an important theme in tropical countries due to the growing number of infected individuals. The dynamic model is described by a set of nonlinear ordinary differential equations, that depend on the dynamic of the Dengue mosquito, the number of infected individuals, and the people's motivation to combat the mosquito. The cost functional depends not only on the costs of medical treatment of the infected people but also on the costs related to educational and sanitary campaigns. Two approaches to solve the problem are considered: one using optimal control theory, another one by discretizing first the problem and then solving it with nonlinear programming. The results obtained with OC-ODE and IPOPT solvers are given and discussed. We observe that with current computational tools it is easy to obtain, in an efficient way, better solutions to Dengue problems, leading to a decrease of infected mosquitoes and individuals in less time and with lower costs.Comment: Submitted to Mathematical and Computer Modelling 25/Oct/2009; accepted for publication, after revision, 22/June/201

Combining the regularization strategy and the SQP to solve MPCC - A MATLAB implementation

Mathematical Program with Complementarity Constraints (MPCC) plays a very important role in many fields such as engineering design, economic equilibrium, multilevel game, and mathematical programming theory itself. In theory its constraints fail to satisfy a standard constraint qualification such as the linear independence constraint qualification (LICQ) or the Mangasarian-Fromovitz constraint qualification (MFCQ) at any feasible point. As a result, the developed nonlinear programming theory may not be applied to MPCC class directly. Nowadays, a natural and popular approach is try to find some suitable approximations of an MPCC so that it can be solved by solving a sequence of nonlinear programs. This work aims to solve the MPCC using nonlinear programming techniques, namely the SQP and the regularization scheme. Some algorithms with two iterative processes, the inner and the external, were developed. A set of AMPL problems from MacMPEC database [7] were tested. The algorithms performance comparative analysis was carried out

CEDIM Risk Explorer ? a map server solution in the project "Risk Map Germany"

International audienceThe project "Risk Map Germany" at the Center for Disaster Management and Risk Reduction Technology (CEDIM) aims at visualizing hazards, vulnerabilities and risks associated with natural and man made hazards. CEDIM as an interdisciplinary project unified various expertise like earthquake, storm and flood disaster research. Our aim was to visualize the manifold data exploration in thematic maps. The implemented Web-GIS solution "CEDIM Risk Explorer" represents the map visualizations of the different risk research. This Web-GIS integrates results from interdisciplinary work as maps of hazard, vulnerability and risk in one application and offers therefore new cognitions to the user by enabling visual comparisons. The present paper starts with a project introduction and a literature review of distributed GIS environments. Further the methods of map realization and visualization in the selected technical solution is worked out. Finally, the conclusions give the perspectives for future developments to the "CEDIM Risk Explorer"

Incompressible image registration using divergence-conforming B-splines

Anatomically plausible image registration often requires volumetric preservation. Previous approaches to incompressible image registration have exploited relaxed constraints, ad hoc optimisation methods or practically intractable computational schemes. Divergence-free velocity fields have been used to achieve incompressibility in the continuous domain, although, after discretisation, no guarantees have been provided. In this paper, we introduce stationary velocity fields (SVFs) parameterised by divergence-conforming B-splines in the context of image registration. We demonstrate that sparse linear constraints on the parameters of such divergence-conforming B-Splines SVFs lead to being exactly divergence-free at any point of the continuous spatial domain. In contrast to previous approaches, our framework can easily take advantage of modern solvers for constrained optimisation, symmetric registration approaches, arbitrary image similarity and additional regularisation terms. We study the numerical incompressibility error for the transformation in the case of an Euler integration, which gives theoretical insights on the improved accuracy error over previous methods. We evaluate the proposed framework using synthetically deformed multimodal brain images, and the STACOM11 myocardial tracking challenge. Accuracy measurements demonstrate that our method compares favourably with state-of-the-art methods whilst achieving volume preservation.Comment: Accepted at MICCAI 201

Optimal topological simplification of discrete functions on surfaces

We solve the problem of minimizing the number of critical points among all functions on a surface within a prescribed distance {\delta} from a given input function. The result is achieved by establishing a connection between discrete Morse theory and persistent homology. Our method completely removes homological noise with persistence less than 2{\delta}, constructively proving the tightness of a lower bound on the number of critical points given by the stability theorem of persistent homology in dimension two for any input function. We also show that an optimal solution can be computed in linear time after persistence pairs have been computed.Comment: 27 pages, 8 figure

On the Production of π+π+\pi^+\pi^+ Pairs in pp Collisions at 0.8 GeV

Data accumulated recently for the exclusive measurement of the $pp\to pp\pi^+\pi^-$ reaction at a beam energy of 0.793 GeV using the COSY-TOF spectrometer have been analyzed with respect to possible events from the $pp \to nn\pi^+\pi^+$ reaction channel. The latter is expected to be the only $\pi\pi$ production channel, which contains no major contributions from resonance excitation close to threshold and hence should be a good testing ground for chiral dynamics in the $\pi\pi$ production process. No single event has been found, which meets all conditions for being a candidate for the $pp \to nn \pi^+\pi^+$ reaction. This gives an upper limit for the cross section of 0.16 $\mu$b (90% C.L.), which is more than an order of magnitude smaller than the cross sections of the other two-pion production channels at the same incident energy