67,771 research outputs found

    Arithmetic purity of strong approximation for homogeneous spaces

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    We prove that any open subset UU of a semi-simple simply connected quasi-split linear algebraic group GG with codim(G∖U,G)≥2{codim} (G\setminus U, G)\geq 2 over a number field satisfies strong approximation by establishing a fibration of GG over a toric variety. We also prove a similar result of strong approximation with Brauer-Manin obstruction for a partial equivariant smooth compactification of a homogeneous space where all invertible functions are constant and the semi-simple part of the linear algebraic group is quasi-split. Some semi-abelian varieties of any given dimension where the complements of a rational point do not satisfy strong approximation with Brauer-Manin obstruction are given

    Liquid rocket combustor computer code development

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    The Advanced Rocket Injector/Combustor Code (ARICC) that has been developed to model the complete chemical/fluid/thermal processes occurring inside rocket combustion chambers are highlighted. The code, derived from the CONCHAS-SPRAY code originally developed at Los Alamos National Laboratory incorporates powerful features such as the ability to model complex injector combustion chamber geometries, Lagrangian tracking of droplets, full chemical equilibrium and kinetic reactions for multiple species, a fractional volume of fluid (VOF) description of liquid jet injection in addition to the gaseous phase fluid dynamics, and turbulent mass, energy, and momentum transport. Atomization and droplet dynamic models from earlier generation codes are transplated into the present code. Currently, ARICC is specialized for liquid oxygen/hydrogen propellants, although other fuel/oxidizer pairs can be easily substituted

    Optical Resonator Analog of a Two-Dimensional Topological Insulator

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    A lattice of optical ring resonators can exhibit a topological insulator phase, with the role of spin played by the direction of propagation of light within each ring. Unlike the system studied by Hafezi et al., topological protection is achieved without fine-tuning the inter-resonator couplings, which are given the same periodicity as the underlying lattice. The topological insulator phase occurs for strong couplings, when the tight-binding method is inapplicable. Using the transfer matrix method, we derive the bandstructure and phase diagram, and demonstrate the existence of robust edge states. When gain and loss are introduced, the system functions as a diode for coupled resonator modes.Comment: 10 pages, 9 figure

    Mathematical problems for complex networks

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    Copyright @ 2012 Zidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This article is made available through the Brunel Open Access Publishing Fund.Complex networks do exist in our lives. The brain is a neural network. The global economy is a network of national economies. Computer viruses routinely spread through the Internet. Food-webs, ecosystems, and metabolic pathways can be represented by networks. Energy is distributed through transportation networks in living organisms, man-made infrastructures, and other physical systems. Dynamic behaviors of complex networks, such as stability, periodic oscillation, bifurcation, or even chaos, are ubiquitous in the real world and often reconfigurable. Networks have been studied in the context of dynamical systems in a range of disciplines. However, until recently there has been relatively little work that treats dynamics as a function of network structure, where the states of both the nodes and the edges can change, and the topology of the network itself often evolves in time. Some major problems have not been fully investigated, such as the behavior of stability, synchronization and chaos control for complex networks, as well as their applications in, for example, communication and bioinformatics
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