The three-dimensional instability of strained vortices in a viscous fluid

The recent theory describing 3-D exact solutions of the Navier–Stokes equations is applied to the problem of stability of 2-D viscous flow with elliptical streamlines. An intrinsically inviscid instability mechanism persists in all such flows provided the length scale of the disturbance is sufficiently large. Evidence is presented that this mechanism may be responsible for 3-D instabilities in high Reynolds number flows whose vortex structures can be locally described by elliptical streamlines

Role of Democracy Assessment Tools in Democracy Consolidation: Lessons Learned From Mongolia

Executive summary 1. Democracy assessment in Mongolia was a state-led exercise conducted as part of the follow-up activities to the 5th International Conference of New or Restored Democracies and involved the active participation of the Government, Parliament, and Civil Society. 2. The process of democracy assessment itself provided a unique opportunity for critical self-reflection within Mongolia about the quality of democracy, the performance of democratic institutions, and elite and mass perceptions of democracy. 3. The follow-up activities successfully generated methods for assessing democracy in the particular context of Mongolia using comparable concepts and measures employed in the measurement and assessment of democracy in other developed and developing democracies around the world, as well as a series of ‘satellite’ indicators that captured aspects of democracy particular to the Mongolian national context. 4. Mongolia has built on the assessment process by institutionalising a democratic reform agenda through the passage of the 9th Millennium Development Goal on democracy, human rights, and zero tolerance of corruption. DOI: http://dx.doi.org/10.5564/mjia.v0i18.73 Mongolian Journal of International Affairs No.18 2013: 105-11

Fiber Orientation Estimation Guided by a Deep Network

Diffusion magnetic resonance imaging (dMRI) is currently the only tool for noninvasively imaging the brain's white matter tracts. The fiber orientation (FO) is a key feature computed from dMRI for fiber tract reconstruction. Because the number of FOs in a voxel is usually small, dictionary-based sparse reconstruction has been used to estimate FOs with a relatively small number of diffusion gradients. However, accurate FO estimation in regions with complex FO configurations in the presence of noise can still be challenging. In this work we explore the use of a deep network for FO estimation in a dictionary-based framework and propose an algorithm named Fiber Orientation Reconstruction guided by a Deep Network (FORDN). FORDN consists of two steps. First, we use a smaller dictionary encoding coarse basis FOs to represent the diffusion signals. To estimate the mixture fractions of the dictionary atoms (and thus coarse FOs), a deep network is designed specifically for solving the sparse reconstruction problem. Here, the smaller dictionary is used to reduce the computational cost of training. Second, the coarse FOs inform the final FO estimation, where a larger dictionary encoding dense basis FOs is used and a weighted l1-norm regularized least squares problem is solved to encourage FOs that are consistent with the network output. FORDN was evaluated and compared with state-of-the-art algorithms that estimate FOs using sparse reconstruction on simulated and real dMRI data, and the results demonstrate the benefit of using a deep network for FO estimation.Comment: A shorter version is accepted by MICCAI 201

Three-electron anisotropic quantum dots in variable magnetic fields: exact results for excitation spectra, spin structures, and entanglement

Exact-diagonalization calculations for N=3 electrons in anisotropic quantum dots, covering a broad range of confinement anisotropies and strength of inter-electron repulsion, are presented for zero and low magnetic fields. The excitation spectra are analyzed as a function of the strength of the magnetic field and for increasing quantum-dot anisotropy. Analysis of the intrinsic structure of the many-body wave functions through spin-resolved two-point correlations reveals that the electrons tend to localize forming Wigner molecules. For certain ranges of dot parameters (mainly at strong anisotropy), the Wigner molecules acquire a linear geometry, and the associated wave functions with a spin projection S_z=1/2 are similar to the representative class of strongly entangled states referred to as W-states. For other ranges of parameters (mainly at intermediate anisotropy), the Wigner molecules exhibit a more complex structure consisting of two mirror isosceles triangles. This latter structure can be viewed as an embryonic unit of a zig-zag Wigner crystal in quantum wires. The degree of entanglement in three-electron quantum dots can be quantified through the use of the von Neumann entropy.Comment: To appear in Physical Review B. REVTEX4. 13 pages with 16 color figures. To download a copy with higher-quality figures, go to publication #78 in http://www.prism.gatech.edu/~ph274cy

Phase-Controlled Force and Magnetization Oscillations in Superconducting Ballistic Nanowires

The emergence of superconductivity-induced phase-controlled forces in the (0.01-0.1) nN range, and of magnetization oscillations, in nanowire junctions, is discussed. A giant magnetic response to applied weak magnetic fields, is predicted in the ballistic Josephson junction formed by a superconducting tip and a surface, bridged by a normal metal nanowire where Andreev states form.Comment: 5 pages, 3 figure

Iteratively Reweighted FGMRES and FLSQR for Sparse Reconstruction

This paper presents two new algorithms to compute sparse solutions of large-scale linear discrete ill-posed problems. The proposed approach consists in constructing a sequence of quadratic problems approximating an ` 2-` 1 regularization scheme (with additional smoothing to ensure differentiability at the origin) and partially solving each problem in the sequence using flexible Krylov–Tikhonov methods. These algorithms are built upon a new solid theoretical justification that guarantees that the sequence of approximate solutions to each problem in the sequence converges to the solution of the considered modified version of the ` 2-` 1 problem. Compared to other traditional methods, the new algorithms have the advantage of building a single (flexible) approximation (Krylov) subspace that encodes regularization through variable “preconditioning” and that is expanded as soon as a new problem in the sequence is defined. Links between the new solvers and other well-established solvers based on augmenting Krylov subspaces are also established. The performance of these algorithms is shown through a variety of numerical examples modeling image deblurring and computed tomography.</p

A Magnetic-Field-Effect Transistor and Spin Transport

A magnetic-field-effect transistor is proposed that generates a spin-polarized current and exhibits a giant negative magnetoresitance. The device consists of a nonmagnetic conducting channel (wire or strip) wrapped, or sandwiched, by a grounded magnetic shell. The process underlying the operation of the device is the withdrawal of one of the spin components from the channel, and its dissipation through the grounded boundaries of the magnetic shell, resulting in a spin-polarized current in the nonmagnetic channel. The device may generate an almost fully spin-polarized current, and a giant negative magnetoresistance effect is predicted.Comment: 4 pages, 3 figure

H-CMRH: a novel inner product free hybrid Krylov method for large-scale inverse problems

This study investigates the iterative regularization properties of two Krylov methods for solving large-scale ill-posed problems: the changing minimal residual Hessenberg method (CMRH) and a novel hybrid variant called the hybrid changing minimal residual Hessenberg method (H-CMRH). Both methods share the advantages of avoiding inner products, making them efficient and highly parallelizable, and particularly suited for implementations that exploit randomization and mixed precision arithmetic. Theoretical results and extensive numerical experiments suggest that H-CMRH exhibits comparable performance to the established hybrid GMRES method in terms of stabilizing semiconvergence, but H-CMRH has does not require any inner products, and requires less work and storage per iteration