Correlated electrons systems on the Apollonian network

Strongly correlated electrons on an Apollonian network are studied using the Hubbard model. Ground-state and thermodynamic properties, including specific heat, magnetic susceptibility, spin-spin correlation function, double occupancy and one-electron transfer, are evaluated applying direct diagonalization and quantum Monte Carlo. The results support several types of magnetic behavior. In the strong-coupling limit, the quantum anisotropic spin 1/2 Heisenberg model is used and the phase diagram is discussed using the renormalization group method. For ferromagnetic coupling, we always observe the existence of long-range order. For antiferromagnetic coupling, we find a paramagnetic phase for all finite temperatures.Comment: 7 pages, 8 figure

An Optimal Control Approach to Bounding Transport Properties of Thermal Convection.

This dissertation explores and develops an optimal control approach to upper bounds on transport properties of fluid flows inspired by the physical phenomenon of buoyancy-driven Rayleigh-Bénard convection. This method is applied in the context of three different problems: the Lorenz equations, the Double Lorenz equations, and the Boussinesq approximation to the Navier-Stokes equations. Rather than restricting attention to flows that satisfy an equation of motion, we consider incompressible flows that satisfy suitable bulk integral constraints and boundary conditions. Bounds on transport are formulated in terms of optimal control problems where the flows are the "control" and a passive scalar tracer field is the "state". All three problems lead to non-convex optimization problems. Sharp upper bounds to the Lorenz equations are proven analytically, and it is shown that any sustained time-dependence of the control variable strictly lowers transport. For the Double Lorenz equations an upper bound is proven and saturated by steady optimizing flow fields and any time-periodic stirring protocol strictly lowers transport. In contrast to the Lorenz equations, however, the optimizing steady flow fields (solutions to the Euler-Lagrange equations for optimal transport) are not solutions to the original equations of motion. In the Boussinesq equation context the optimal control problem is rigorously formulated for steady flows, and analytic upper bounds to transport are deduced using the background method. A gradient ascent procedure for numerically solving the associated the Euler-Lagrange equations for optimal transport is developed, including optimality conditions for the domain size. The numerically computed optimizing flow fields consist of convection cells of decreasing aspect ratio as one allows for a stronger flow fields. Implications for natural convective transport in the motivating Rayleigh-Bénard problem are discussed.PhDApplied and Interdisciplinary MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133426/1/sandre_1.pd

Clustering of Dynamical Systems

In this work, we address the problem of community detection in a graph whose connectivity is given by probabilities (denoted by numbers between zero and one) rather than an adjacency matrix (only 0 or 1). The graphs themselves come from partitions of a dynamical system's state space where the probabilities denote likely transition pathways for dynamics. We propose a modification of the Leicht-Newman algorithm \cite{Leicht2008} which is able to automatically detect communities of strongly intra-connected points in state space, from which information about the residence time of the system and its principal periodicities can be extracted. Furthermore, a novel algorithm to construct the transition rate matrix of a dynamical system which encodes the time dependency of its Perron-Frobenius operator, is developed. Crucially, it overcomes the issue of time-scale separation stemming from the matrix construction based on {\it{infinitesimal}} generators and the exploration of {\it{long-term}} features of the underlying dynamical system. This method is then tested on a range of dynamical systems and datasets

A review of the stable isotope bio-geochemistry of the global silicon cycle and its associated trace elements

Silicon (Si) is the second most abundant element in the Earth's crust and is an important nutrient in the ocean. The global Si cycle plays a critical role in regulating primary productivity and carbon cycling on the continents and in the oceans. Development of the analytical tools used to study the sources, sinks, and fluxes of the global Si cycle (e.g., elemental and stable isotope ratio data for Ge, Si, Zn, etc.) have recently led to major advances in our understanding of the mechanisms and processes that constrain the cycling of Si in the modern environment and in the past. Here, we provide background on the geochemical tools that are available for studying the Si cycle and highlight our current understanding of the marine, freshwater and terrestrial systems. We place emphasis on the geochemistry (e.g., Al/Si, Ge/Si, Zn/Si, δ13C, δ15N, δ18O, δ30Si) of dissolved and biogenic Si, present case studies, such as the Silicic Acid Leakage Hypothesis, and discuss challenges associated with the development of these environmental proxies for the global Si cycle. We also discuss how each system within the global Si cycle might change over time (i.e., sources, sinks, and processes) and the potential technical and conceptual limitations that need to be considered for future studies.The work by JS was supported by the “Laboratoire d’Excellence” LabexMER (ANR-10-LABX-19) and co-funded by a grant from the French government under the program “Investissements d’Avenir,” and by a grant from the Regional Council of Brittany (SAD programme). DJC was partially supported by the Knut and Alice Wallenberg Foundation (KAW Wallenberg Scholar) and the Swedish Research Council. This review article has benefited from funding by the European Union Seventh Framework Programme under grant agreement n◦294146 (project MuSiCC, Marie Curie CIG to DC). GdS is supported by a Marie Skłodowska-Curie Research Fellowship under EU Horizon2020 (GA #708407). JuD was supported by the American Chemical Society Petroleum Research Fund (Grant # 53798-DNI2). CE acknowledges financial support by the Institute for Chemistry and Biology of the Marine Environment (Oldenburg, Germany) and the Max Planck Institute for Marine Microbiology (Bremen, Germany). KH is funded by The Royal Society (UF120084) and the European Research Council (ERC-2015-StG - 678371_ICY-LAB). PG acknowledges funding by the Collaborative Research Centre 754 “ClimateBiogeochemistry interactions in the Tropical Ocean” (www. sfb754.de), supported by the Deutsche Forschungsgemeinschaft (DFG)

Superior Neuroprotective Efficacy of LAU-0901, a Novel Platelet-Activating Factor Antagonist, in Experimental Stroke

Platelet-activating factor (PAF) accumulates during cerebral ischemia, and inhibition of this process plays a critical role in neuronal survival. Recently, we demonstrated that LAU-0901, a novel PAF receptor antagonist, is neuroprotective in experimental stroke. We used magnetic resonance imaging in conjunction with behavior and immunohistopathology to expand our understanding of this novel therapeutic approach. Sprague–Dawley rats received 2 h middle cerebral artery occlusion (MCAo) and were treated with LAU-0901 (60 mg/kg) or vehicle 2 h from MCAo onset. Behavioral function, T2-weighted imaging (T2WI), and apparent diffusion coefficients were performed on days 1, 3, and 7 after MCAo. Infarct volume and number of GFAP, ED-1, and NeuN-positive cells were conducted on day 7. Behavioral deficit was significantly improved by LAU-0901 treatment compared to vehicle on days 1, 3, and 7. Total lesion volumes computed from T2WI were significantly reduced by LAU-0901 on days 1, 3, and 7 (by 83%, 90%, and 96%, respectively), which was consistent with decreased edema formation. Histopathology revealed that LAU-0901 treatment resulted in significant reduction of cortical and subcortical infarct volumes, attenuated microglial infiltration, and promoted astrocytic and neuronal survival. These findings suggest LAU-0901 is a promising neuroprotectant and provide the basis for future therapeutics in patients suffering ischemic stroke

Emerging Strategies for Healthy Urban Governance

Urban health promotion is not simply a matter of the right interventions, or even the necessary resources. Urban (and indeed global) health depends to an important extent on governance, the institutions and processes through which societies manage the course of events. This paper describes the concept of governance, distinguishing between reforms aimed at improving how government works and innovations that more fundamentally reinvent governance by developing new institutions and processes of local stakeholder control. The paper highlights strategies urban governors can use to maximize their influence on the national and international decisions that structure urban life. It concludes with some observations on the limitations of local governance strategies and the importance of establishing a “virtuous circuit” of governance through which urban dwellers play a greater role in the formation and implementation of policy at the national and global levels

Are men universally more dismissing than women? Gender differences in romantic attachment across 62 cultural regions

The authors thank Susan Sprecher (USA), Del Paulhus (Canada), Glenn D. Wilson (England), Qazi Rahman (England), Alois Angleitner (Germany), Angelika Hofhansl (Austria), Tamio Imagawa (Japan), Minoru Wada (Japan), Junichi Taniguchi (Japan), and Yuji Kanemasa (Japan) for helping with data collection and contributing significantly to the samples used in this study.Gender differences in the dismissing form of adult romantic attachment were investigated as part of the International Sexuality Description Project—a survey study of 17,804 people from 62 cultural regions. Contrary to research findings previously reported in Western cultures, we found that men were not significantly more dismissing than women across all cultural regions. Gender differences in dismissing romantic attachment were evident in most cultures, but were typically only small to moderate in magnitude. Looking across cultures, the degree of gender differentiation in dismissing romantic attachment was predictably associated with sociocultural indicators. Generally, these associations supported evolutionary theories of romantic attachment, with smaller gender differences evident in cultures with high–stress and high–fertility reproductive environments. Social role theories of human sexuality received less support in that more progressive sex–role ideologies and national gender equity indexes were not cross–culturally linked as expected to smaller gender differences in dismissing romantic attachment.peer-reviewe