Wigner crystals for a planar, equimolar binary mixture of classical, charged particles

We have investigated the ground state configurations of an equimolar, binary mixture of classical charged particles (with nominal charges $Q_1$ and $Q_2$) that condensate on a neutralizing plane. Using efficient Ewald summation techniques for the calculation of the ground state energies, we have identified the energetically most favourable ordered particle arrangements with the help of a highly reliable optimization tool based on ideas of evolutionary algorithms. Over a large range of charge ratios, $q = Q_2 / Q_1$, we identify six non-trivial ground states, some of which show a remarkable and unexpected structural complexity. For $0.59 \lesssim q < 1$ the system undergoes a phase separation where the two charge species populate in a hexagonal arrangement spatially separated areas.Comment: 14 pages, 8 figure

Inversion of the star transform

We define the star transform as a generalization of the broken ray transform introduced by us in previous work. The advantages of using the star transform include the possibility to reconstruct the absorption and the scattering coefficients of the medium separately and simultaneously (from the same data) and the possibility to utilize scattered radiation which, in the case of the conventional X-ray tomography, is discarded. In this paper, we derive the star transform from physical principles, discuss its mathematical properties and analyze numerical stability of inversion. In particular, it is shown that stable inversion of the star transform can be obtained only for configurations involving odd number of rays. Several computationally-efficient inversion algorithms are derived and tested numerically.Comment: Accepted to Inverse Problems in this for

Two-dimensional array of magnetic particles: The role of an interaction cutoff

Based on theoretical results and simulations, in two-dimensional arrangements of a dense dipolar particle system, there are two relevant local dipole arrangements: (1) a ferromagnetic state with dipoles organized in a triangular lattice, and (2) an anti-ferromagnetic state with dipoles organized in a square lattice. In order to accelerate simulation algorithms we search for the possibility of cutting off the interaction potential. Simulations on a dipolar two-line system lead to the observation that the ferromagnetic state is much more sensitive to the interaction cutoff $R$ than the corresponding anti-ferromagnetic state. For $R \gtrsim 8$ (measured in particle diameters) there is no substantial change in the energetical balance of the ferromagnetic and anti-ferromagnetic state and the ferromagnetic state slightly dominates over the anti-ferromagnetic state, while the situation is changed rapidly for lower interaction cutoff values, leading to the disappearance of the ferromagnetic ground state. We studied the effect of bending ferromagnetic and anti-ferromagnetic two-line systems and we observed that the cutoff has a major impact on the energetical balance of the ferromagnetic and anti-ferromagnetic state for $R \lesssim 4$. Based on our results we argue that $R \approx 5$ is a reasonable choice for dipole-dipole interaction cutoff in two-dimensional dipolar hard sphere systems, if one is interested in local ordering.Comment: 8 page

Computer trading and systemic risk: a nuclear perspective

Financial markets have evolved to become complex adaptive systems highly reliant on the communication speeds and processing power afforded by digital systems. Their failure could cause severe disruption to the provision of financial services and possibly the wider economy. In this study we consider whether a perspective from the nuclear industry can provide additional insights

Constructing minimum deflection fixture arrangements using frame invariant norms

This paper describes a fixture planning method that minimizes object deflection under external loads. The method takes into account the natural compliance of the contacting bodies and applies to two-dimensional and three-dimensional quasirigid bodies. The fixturing method is based on a quality measure that characterizes the deflection of a fixtured object in response to unit magnitude wrenches. The object deflection measure is defined in terms of frame-invariant rigid body velocity and wrench norms and is therefore frame invariant. The object deflection measure is applied to the planning of optimal fixture arrangements of polygonal objects. We describe minimum-deflection fixturing algorithms for these objects, and make qualitative observations on the optimal arrangements generated by the algorithms. Concrete examples illustrate the minimum deflection fixturing method. Note to Practitioners-During fixturing, a workpiece needs to not only be stable against external perturbations, but must also stay within a specified tolerance in response to machining or assembly forces. This paper describes a fixture planning approach that minimizes object deflection under applied work loads. The paper describes how to take local material deformation effects into account, using a generic quasirigid contact model. Practical algorithms that compute the optimal fixturing arrangements of polygonal workpieces are described and examples are then presented

NCeSS Project : Data mining for social scientists

We will discuss the work being undertaken on the NCeSS data mining project, a one year project at the University of Manchester which began at the start of 2007, to develop data mining tools of value to the social science community. Our primary goal is to produce a suite of data mining codes, supported by a web interface, to allow social scientists to mine their datasets in a straightforward way and hence, gain new insights into their data. In order to fully define the requirements, we are looking at a range of typical datasets to find out what forms they take and the applications and algorithms that will be required. In this paper, we will describe a number of these datasets and will discuss how easily data mining techniques can be used to extract information from the data that would either not be possible or would be too time consuming by more standard methods

Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations

One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. In the past, limited computer resources have motivated the development of efficient numerical schemes in computational fluid dynamics (CFD) utilizing structured meshes. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Unstructured grids on the other hand offer an alternative to modeling complex geometries. Unstructured meshes have irregular connectivity and usually contain combinations of triangles, quadrilaterals, tetrahedra, and hexahedra. The generation and use of unstructured grids poses new challenges in CFD. The purpose of this note is to present recent developments in the unstructured grid generation and flow solution technology

Disaggregated Bundle Methods for Distributed Market Clearing in Power Networks

A fast distributed approach is developed for the market clearing with large-scale demand response in electric power networks. In addition to conventional supply bids, demand offers from aggregators serving large numbers of residential smart appliances with different energy constraints are incorporated. Leveraging the Lagrangian relaxation based dual decomposition, the resulting optimization problem is decomposed into separate subproblems, and then solved in a distributed fashion by the market operator and each aggregator aided by the end-user smart meters. A disaggregated bundle method is adapted for solving the dual problem with a separable structure. Compared with the conventional dual update algorithms, the proposed approach exhibits faster convergence speed, which results in reduced communication overhead. Numerical results corroborate the effectiveness of the novel approach.Comment: To appear in GlobalSIP 201