Hitting Time of Quantum Walks with Perturbation

The hitting time is the required minimum time for a Markov chain-based walk (classical or quantum) to reach a target state in the state space. We investigate the effect of the perturbation on the hitting time of a quantum walk. We obtain an upper bound for the perturbed quantum walk hitting time by applying Szegedy's work and the perturbation bounds with Weyl's perturbation theorem on classical matrix. Based on the definition of quantum hitting time given in MNRS algorithm, we further compute the delayed perturbed hitting time (DPHT) and delayed perturbed quantum hitting time (DPQHT). We show that the upper bound for DPQHT is actually greater than the difference between the square root of the upper bound for a perturbed random walk and the square root of the lower bound for a random walk.Comment: 9 page

CFD investigation of a complete floating offshore wind turbine

This chapter presents numerical computations for floating offshore wind turbines for a machine of 10-MW rated power. The rotors were computed using the Helicopter Multi-Block flow solver of the University of Glasgow that solves the Navier-Stokes equations in integral form using the arbitrary Lagrangian-Eulerian formulation for time-dependent domains with moving boundaries. Hydrodynamic loads on the support platform were computed using the Smoothed Particle Hydrodynamics method. This method is mesh-free, and represents the fluid by a set of discrete particles. The motion of the floating offshore wind turbine is computed using a Multi-Body Dynamic Model of rigid bodies and frictionless joints. Mooring cables are modelled as a set of springs and dampers. All solvers were validated separately before coupling, and the loosely coupled algorithm used is described in detail alongside the obtained results

A global method for coupling transport with chemistry in heterogeneous porous media

Modeling reactive transport in porous media, using a local chemical equilibrium assumption, leads to a system of advection-diffusion PDE's coupled with algebraic equations. When solving this coupled system, the algebraic equations have to be solved at each grid point for each chemical species and at each time step. This leads to a coupled non-linear system. In this paper a global solution approach that enables to keep the software codes for transport and chemistry distinct is proposed. The method applies the Newton-Krylov framework to the formulation for reactive transport used in operator splitting. The method is formulated in terms of total mobile and total fixed concentrations and uses the chemical solver as a black box, as it only requires that on be able to solve chemical equilibrium problems (and compute derivatives), without having to know the solution method. An additional advantage of the Newton-Krylov method is that the Jacobian is only needed as an operator in a Jacobian matrix times vector product. The proposed method is tested on the MoMaS reactive transport benchmark.Comment: Computational Geosciences (2009) http://www.springerlink.com/content/933p55085742m203/?p=db14bb8c399b49979ba8389a3cae1b0f&pi=1

The role of neuregulin-ErbB4 interactions on the proliferation and organization of cells in the subventricular zone

Coordinated regulation of neuronal progenitor differentiation in the subventricular zone (SVZ) is a fundamental feature of adult neurogenesis. However, the molecular control of this process remains mostly undeciphered. Here, we investigate the role of neuregulins (NRGs) in this process and show that a NRG receptor, ErbB4, is primarily expressed by polysialylated neural cell adhesion molecule immature neuroblasts but is also detected in a subset of GFAP+ astroglial cells, ependymal cells, and Dlx2+ precursors in the SVZ. Of the NRG ligands, both NRG1 and -2 are expressed by immature polysialylated neural cell adhesion molecule neuroblasts in the SVZ. NRG2 is also expressed by some of the GFAP+ putative stem cells lining the ventricles. Infusion of exogenous NRG1 leads to rapid aggregation of Dlx2+ cells in the SVZ and affects the initiation and maintenance of organized neuroblast migration from the SVZ toward the olfactory bulb. In contrast, the infusion of NRG2 increased the number of Sox2 and GFAP+ precursors in the SVZ. An outcome of this NRG2 effect is an increase in the number of newly generated migrating neuroblasts in the rostral migratory stream and GABAergic interneurons in the olfactory bulb. The analysis of conditional null mice that lack NRG receptor, ErbB4, in the nervous system revealed that the observed activities of NRG2 require ErbB4 activation. These results indicate that different NRG ligands affect distinct populations of differentiating neural precursors in the neurogenic regions of the mature forebrain. Furthermore, these studies identify NRG2 as a factor capable of promoting SVZ proliferation, leading to the formation of new neurons in vivo

The role of neuregulin-ErbB4 interactions on the proliferation and organization of cells in the subventricular zone

Coordinated regulation of neuronal progenitor differentiation in the subventricular zone (SVZ) is a fundamental feature of adult neurogenesis. However, the molecular control of this process remains mostly undeciphered. Here, we investigate the role of neuregulins (NRGs) in this process and show that a NRG receptor, ErbB4, is primarily expressed by polysialylated neural cell adhesion molecule immature neuroblasts but is also detected in a subset of GFAP+ astroglial cells, ependymal cells, and Dlx2+ precursors in the SVZ. Of the NRG ligands, both NRG1 and -2 are expressed by immature polysialylated neural cell adhesion molecule neuroblasts in the SVZ. NRG2 is also expressed by some of the GFAP+ putative stem cells lining the ventricles. Infusion of exogenous NRG1 leads to rapid aggregation of Dlx2+ cells in the SVZ and affects the initiation and maintenance of organized neuroblast migration from the SVZ toward the olfactory bulb. In contrast, the infusion of NRG2 increased the number of Sox2 and GFAP+ precursors in the SVZ. An outcome of this NRG2 effect is an increase in the number of newly generated migrating neuroblasts in the rostral migratory stream and GABAergic interneurons in the olfactory bulb. The analysis of conditional null mice that lack NRG receptor, ErbB4, in the nervous system revealed that the observed activities of NRG2 require ErbB4 activation. These results indicate that different NRG ligands affect distinct populations of differentiating neural precursors in the neurogenic regions of the mature forebrain. Furthermore, these studies identify NRG2 as a factor capable of promoting SVZ proliferation, leading to the formation of new neurons in vivo

A Scalable Parallel Approach for High-Fidelity Aerostructural Analysis and Optimization

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97076/1/AIAA2012-1922.pd

Grid-Adapted FUN3D Computations for the Second High Lift Prediction Workshop

Contributions of the unstructured Reynolds-averaged Navier-Stokes code FUN3D to the 2nd AIAA CFD High Lift Prediction Workshop are described, and detailed comparisons are made with experimental data. Using workshop-supplied grids, results for the clean wing configuration are compared with results from the structured code CFL3D Using the same turbulence model, both codes compare reasonably well in terms of total forces and moments, and the maximum lift is similarly over-predicted for both codes compared to experiment. By including more representative geometry features such as slat and flap brackets and slat pressure tube bundles, FUN3D captures the general effects of the Reynolds number variation, but under-predicts maximum lift on workshop-supplied grids in comparison with the experimental data, due to excessive separation. However, when output-based, off-body grid adaptation in FUN3D is employed, results improve considerably. In particular, when the geometry includes both brackets and the pressure tube bundles, grid adaptation results in a more accurate prediction of lift near stall in comparison with the wind-tunnel data. Furthermore, a rotation-corrected turbulence model shows improved pressure predictions on the outboard span when using adapted grids

An inexact dual logarithmic barrier method for solving sparse semidefinite programs

A dual logarithmic barrier method for solving large, sparse semidefinite programs is proposed in this paper. The method avoids any explicit use of the primal variable X and therefore is well-suited to problems with a sparse dual matrix S. It relies on inexact Newton steps in dual space which are computed by the conjugate gradient method applied to the Schur complement of the reduced KKT system. The method may take advantage of low-rank representations of matrices Ai to perform implicit matrix-vector products with the Schur complement matrix and to compute only specific parts of this matrix. This allows the construction of the partial Cholesky factorization of the Schur complement matrix which serves as a good preconditioner for it and permits the method to be run in a matrix-free scheme. Convergence properties of the method are studied and a polynomial complexity result is extended to the case when inexact Newton steps are employed. A Matlab-based implementation is developed and preliminary computational results of applying the method to maximum cut and matrix completion problems are reported

Climate change litigation: a review of research on courts and litigants in climate government

Studies of climate change litigation have proliferated over the past two decades, as lawsuits across the world increasingly bring policy debates about climate change mitigation and adaptation, as well as climate change‐related loss and damage to the attention of courts. We systematically identify 130 articles on climate change litigation published in English in the law and social sciences between 2000 and 2018 to identify research trajectories. In addition to a budding interdisciplinarity in scholarly interest in climate change litigation we also document a growing understanding of the full spectrum of actors involved and implicated in climate lawsuits and the range of motivations and/or strategic imperatives underpinning their engagement with the law. Situating this within the broader academic literature on the topic we then highlight a number of cutting edge trends and opportunities for future research. Four emerging themes are explored in detail: the relationship between litigation and governance; how time and scale feature in climate litigation; the role of science; and what has been coined the “human rights turn” in climate change litigation. We highlight the limits of existing work and the need for future research—not limited to legal scholarship—to evaluate the impact of both regulatory and anti‐regulatory climate‐related lawsuits, and to explore a wider set of jurisdictions, actors and themes. Addressing these issues and questions will help to develop a deeper understanding of the conditions under which litigation will strengthen or undermine climate governance. This article is categorized under: Policy and Governance > Multilevel and Transnational Climate Change Governanc