90 research outputs found

    2D and 3D reconstructions in acousto-electric tomography

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    We propose and test stable algorithms for the reconstruction of the internal conductivity of a biological object using acousto-electric measurements. Namely, the conventional impedance tomography scheme is supplemented by scanning the object with acoustic waves that slightly perturb the conductivity and cause the change in the electric potential measured on the boundary of the object. These perturbations of the potential are then used as the data for the reconstruction of the conductivity. The present method does not rely on "perfectly focused" acoustic beams. Instead, more realistic propagating spherical fronts are utilized, and then the measurements that would correspond to perfect focusing are synthesized. In other words, we use \emph{synthetic focusing}. Numerical experiments with simulated data show that our techniques produce high quality images, both in 2D and 3D, and that they remain accurate in the presence of high-level noise in the data. Local uniqueness and stability for the problem also hold

    Optimal shapes of compact strings

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    Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest packing fraction; only recently has it been proved that the answer for infinite systems is a face-centred-cubic lattice. This simply stated problem has had a profound impact in many areas, ranging from the crystallization and melting of atomic systems, to optimal packing of objects and subdivision of space. Here we study an analogous problem--that of determining the optimal shapes of closely packed compact strings. This problem is a mathematical idealization of situations commonly encountered in biology, chemistry and physics, involving the optimal structure of folded polymeric chains. We find that, in cases where boundary effects are not dominant, helices with a particular pitch-radius ratio are selected. Interestingly, the same geometry is observed in helices in naturally-occurring proteins.Comment: 8 pages, 3 composite ps figure

    Tactical Voting in Plurality Elections

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    How often will elections end in landslides? What is the probability for a head-to-head race? Analyzing ballot results from several large countries rather anomalous and yet unexplained distributions have been observed. We identify tactical voting as the driving ingredient for the anomalies and introduce a model to study its effect on plurality elections, characterized by the relative strength of the feedback from polls and the pairwise interaction between individuals in the society. With this model it becomes possible to explain the polarization of votes between two candidates, understand the small margin of victories frequently observed for different elections, and analyze the polls' impact in American, Canadian, and Brazilian ballots. Moreover, the model reproduces, quantitatively, the distribution of votes obtained in the Brazilian mayor elections with two, three, and four candidates.Comment: 7 pages, 4 figure

    Physics of the Riemann Hypothesis

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    Physicists become acquainted with special functions early in their studies. Consider our perennial model, the harmonic oscillator, for which we need Hermite functions, or the Laguerre functions in quantum mechanics. Here we choose a particular number theoretical function, the Riemann zeta function and examine its influence in the realm of physics and also how physics may be suggestive for the resolution of one of mathematics' most famous unconfirmed conjectures, the Riemann Hypothesis. Does physics hold an essential key to the solution for this more than hundred-year-old problem? In this work we examine numerous models from different branches of physics, from classical mechanics to statistical physics, where this function plays an integral role. We also see how this function is related to quantum chaos and how its pole-structure encodes when particles can undergo Bose-Einstein condensation at low temperature. Throughout these examinations we highlight how physics can perhaps shed light on the Riemann Hypothesis. Naturally, our aim could not be to be comprehensive, rather we focus on the major models and aim to give an informed starting point for the interested Reader.Comment: 27 pages, 9 figure

    Self-similarity of Mean Flow in Pipe Turbulence

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    Based on our previous modified log-wake law in turbulent pipe ‡flows, we invent two compound similarity numbers (Y;U), where Y is a combination of the inner variable y+ and outer variable , and U is the pure exect of the wall. The two similarity numbers can well collapse mean velocity profile data with different moderate and large Reynolds numbers into a single universal profile. We then propose an arctangent law for the buffer layer and a general log law for the outer region in terms of (Y;U). From Milikan’s maximum velocity law and the Princeton superpipe data, we derive the von Kármán constant = 0:43 and the additive constant B=6. Using an asymptotic matching method, we obtain a self-similarity law that describes the mean velocity profile from the wall to axis; and embeds the linear law in the viscous sublayer, the quartic law in the bursting sublayer, the classic log law in the overlap, the sine-square wake law in the wake layer, and the parabolic law near the pipe axis. The proposed arctangent law, the general log law and the self-similarity law have been compared with the high-quality data sets, with diffrent Reynolds numbers, including those from the Princeton superpipe, Loulou et al., Durst et al., Perry et al., and den Toonder and Nieuwstadt. Finally, as an application of the proposed laws, we improve the McKeon et al. method for Pitot probe displacement correction, which can be used to correct the widely used Zagarola and Smits data set

    Quantum Simulation of Spin Models on an Arbitrary Lattice with Trapped Ions

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    A collection of trapped atomic ions represents one of the most attractive platforms for the quantum simulation of interacting spin networks and quantum magnetism. Spin-dependent optical dipole forces applied to an ion crystal create long-range effective spin-spin interactions and allow the simulation of spin Hamiltonians that possess nontrivial phases and dynamics. Here we show how appropriate design of laser fields can provide for arbitrary multidimensional spin-spin interaction graphs even for the case of a linear spatial array of ions. This scheme uses currently existing trap technology and is scalable to levels where classical methods of simulation are intractable.Comment: 5 pages, 4 figure

    Computer Simulation of Cellular Patterning Within the Drosophila Pupal Eye

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    We present a computer simulation and associated experimental validation of assembly of glial-like support cells into the interweaving hexagonal lattice that spans the Drosophila pupal eye. This process of cell movements organizes the ommatidial array into a functional pattern. Unlike earlier simulations that focused on the arrangements of cells within individual ommatidia, here we examine the local movements that lead to large-scale organization of the emerging eye field. Simulations based on our experimental observations of cell adhesion, cell death, and cell movement successfully patterned a tracing of an emerging wild-type pupal eye. Surprisingly, altering cell adhesion had only a mild effect on patterning, contradicting our previous hypothesis that the patterning was primarily the result of preferential adhesion between IRM-class surface proteins. Instead, our simulations highlighted the importance of programmed cell death (PCD) as well as a previously unappreciated variable: the expansion of cells' apical surface areas, which promoted rearrangement of neighboring cells. We tested this prediction experimentally by preventing expansion in the apical area of individual cells: patterning was disrupted in a manner predicted by our simulations. Our work demonstrates the value of combining computer simulation with in vivo experiments to uncover novel mechanisms that are perpetuated throughout the eye field. It also demonstrates the utility of the Glazier–Graner–Hogeweg model (GGH) for modeling the links between local cellular interactions and emergent properties of developing epithelia as well as predicting unanticipated results in vivo

    A Fast Panel Code for Complex Actuator Disk Flows

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    A fast, linear scaling vortex method is presented to study inviscid incompressible flow problems involving one or more actuator disks. Building upon previous efforts that were limited to axi-symmetric flow cases, the proposed methodology is able to handle arbitrary configurations with no symmetry constraints. Applications include the conceptual study of wake interaction mechanisms in wind farms, and the correction of wind tunnel blockage effects in test sections of arbitrary shape. Actuator disks represent wind turbines through the shedding of a deformable vortex wake, discretized with a plaid of triangular distributed dipole singularities. An iterative method is adopted to align the wake with the local flow field, which is reconstructed from the vorticity field with a Green function approach. Interactions are computed with a Fast Multipole Method (FMM), effectively overcoming the quadratic scaling of computational time associated with traditional panel methods. When compared to direct computation, the use of an FMM algorithm reduced solution time by a factor 30 when studying the wake of a single actuator disk with 60000 panels. In the same case, the mass flux of the actuator streamtube was conserved to 0:002%. Finally, the presence of round and square impermeable walls around the actuator is considered to demonstrate the code applicability to wind tunnel wall interference correction problems
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