Multiscale Analysis and Computation for the Three-Dimensional Incompressible Navier–Stokes Equations

In this paper, we perform a systematic multiscale analysis for the three-dimensional incompressible Navier–Stokes equations with multiscale initial data. There are two main ingredients in our multiscale method. The first one is that we reparameterize the initial data in the Fourier space into a formal two-scale structure. The second one is the use of a nested multiscale expansion together with a multiscale phase function to characterize the propagation of the small-scale solution dynamically. By using these two techniques and performing a systematic multiscale analysis, we derive a multiscale model which couples the dynamics of the small-scale subgrid problem to the large-scale solution without a closure assumption or unknown parameters. Furthermore, we propose an adaptive multiscale computational method which has a complexity comparable to a dynamic Smagorinsky model. We demonstrate the accuracy of the multiscale model by comparing with direct numerical simulations for both two- and three-dimensional problems. In the two-dimensional case we consider decaying turbulence, while in the three-dimensional case we consider forced turbulence. Our numerical results show that our multiscale model not only captures the energy spectrum very accurately, it can also reproduce some of the important statistical properties that have been observed in experimental studies for fully developed turbulent flows

Topological surface states in three-dimensional magnetic insulators

An electron moving in a magnetically ordered background feels an effective magnetic field that can be both stronger and more rapidly varying than typical externally applied fields. One consequence is that insulating magnetic materials in three dimensions can have topologically nontrivial properties of the effective band structure. For the simplest case of two bands, these "Hopf insulators" are characterized by a topological invariant as in quantum Hall states and Z_2 topological insulators, but instead of a Chern number or parity, the underlying invariant is the Hopf invariant that classifies maps from the 3-sphere to the 2-sphere. This paper gives an efficient algorithm to compute whether a given magnetic band structure has nontrivial Hopf invariant, a double-exchange-like tight-binding model that realizes the nontrivial case, and a numerical study of the surface states of this model.Comment: 4 pages, 2 figures; published versio

Multiscale analysis in Lagrangian formulation for the 2-D incompressible Euler equation

We perform a systematic multiscale analysis for the 2-D incompressible Euler equation with rapidly oscillating initial data using a Lagrangian approach. The Lagrangian formulation enables us to capture the propagation of the multiscale solution in a natural way. By making an appropriate multiscale expansion in the vorticity-stream function formulation, we derive a well-posed homogenized equation for the Euler equation. Based on the multiscale analysis in the Lagrangian formulation, we also derive the corresponding multiscale analysis in the Eulerian formulation. Moreover, our multiscale analysis reveals some interesting structure for the Reynolds stress term, which provides a theoretical base for establishing systematic multiscale modeling of 2-D incompressible flow

Complicating Decisions: The Work Ethic Heuristic and the Construction of Effortful Decisions

The notion that effort and hard work yield desired outcomes is ingrained in many cultures and affects our thinking and behavior. However, could valuing effort complicate our lives? In the present article, the authors demonstrate that individuals with a stronger tendency to link effort with positive outcomes end up complicating what should be easy decisions. People distort their preferences and the information they search and recall in a manner that intensifies the choice conflict and decisional effort they experience before finalizing their choice. Six experiments identify the effort-outcome link as the underlying mechanism for such conflict-increasing behavior. Individuals with a stronger tendency to link effort with positive outcomes (e.g., individuals who subscribe to a Protestant Work Ethic) are shown to complicate decisions by: (a) distorting evaluations of alternatives (Study 1); (b) distorting information recalled about the alternatives (Studies 2a and 2b); and (3) distorting interpretations of information about the alternatives (Study 3). Further, individuals conduct a superfluous search for information and spend more time than needed on what should have been an easy decision (Studies 4a and 4b)

Combining regenerated gratings and optical fibre Fabry-Pérot cavities for dual sensing of ultra-high temperature and strain

© 2015 Copyright SPIE. The successful regeneration of fibre Bragg gratings (FBGs) inscribed in an inline fibre etalon is demonstrated. The etalon is formed by UV-micromaching of the fibre end-face to form a cylindrical hole, the fibre is then fusion spliced to seal the cavity. Such a fibre device has excellent potential for the simultaneous measurement of ultra-high temperatures and strain

Late Quaternary history of paleoseismic activity along the Hohhot Segmentof the Daqingshan piedmont faultin Hetao depression zone, North China

The Daqingshan Piedmont Fault (DPF) is one of the major active normal faults in the Hetao depression zone in the northern part of Ordos Block, North China. It extends in NEE direction along the Daqingshan piedmont zone in the eastern part of the depression, dipping to the south, for a length of 223 km. The fault formed in the Eocene and underwent strong movement during the Cenozoic time. Its vertical displacement amplitude has exceeded 2400 m since the Quaternary. The fault can be divided into 5 active segments. Paleoseismological studies were concentrated on its western part from Baotou to Tumdzuoqi whereas the Hohhot Segment to the east was scarcely studied. To fill this gap of knowlegde, the authors carried out in-depth study on the Daqingshan piedmont fault during recent years. Excavation of trenches at Kuisu, Ulanblang, and Bakouzi sites on the Hohhot Segment of the Daqingshan piedmont fault and study of geomorphic surfaces allow us to identify and date paleoearthquakes and to evaluate the completeness of paleoseismic activity history. This was done both for the individual sites and for the entire segment since the Late Quaternary using the «method for displacement confining» along the fault and «method for correlation between multiple trenches». In this paper we present the geological loggings of two trenches at Kuisu site, provide the evidence for 6 events since 19 ka BP and the cumulative displacement amount produced by them is around 7 m. But the cumulative displacement amount obtained from difference in heights of geomorphic surfaces is 5.??.5.5 m. Results of tests using the method of displacement confining show that the event sequence revealed at this site can be considered complete. The data supplemented with information obtained in the Ulanblang and Bakouzi trenches show that 7 paleoseismic events occurred on the Hohhot Fault Segment since 19 ka BP, i.e. they occurred at 18.75 ± 0.75 ka, 16.97 ± ± 0.96 ka, 14.65 ± 0.67 ka, 11.82 ± 0.69 ka, 9.45 ± 0.26 ka, 6.83 ± 0.26 ka, and 4.50 ± 0.23 ka BP, respectively, and the average recurrence interval is 2.375 ± 0.432 ka. These results basically reflects the history of paleoseismic activity on the fault segment in this period of time

Spin Charge Separation in the Quantum Spin Hall State

The quantum spin Hall state is a topologically non-trivial insulator state protected by the time reversal symmetry. We show that such a state always leads to spin-charge separation in the presence of a $\pi$ flux. Our result is generally valid for any interacting system. We present a proposal to experimentally observe the phenomenon of spin-charge separation in the recently discovered quantum spin Hall system.Comment: acknowledgement and references revise

Evaluation of the effects of rotor harmonics in a doubly-fed induction generator with harmonic induced speed ripple

This paper is concerned with the low-frequency harmonics which originate from the rotor inverter of a doubly-fed induction generator (DFIG). By including the mechanical speed response, it expands the transformer approach previously taken to analyze the harmonic transfer in the machine. A numerical method is proposed to calculate the stator current sidebands, which can be used to predict the voltage fluctuation at the system busbar. It is shown that the pulsating torque associated with the rotor harmonics can induce speed ripple depending on the inertia, causing a significant change in the stator current spectrum. Experiment and simulation verify the analysis and the proposed calculation method