skip to main content


Title: Berry Curvature, Semiclassical Electron Dynamics, and Topological Materials: Lecture Notes for Introduction to Solid State Physics
Lecture notes used in a graduate-level Introduction to Solid State Physics course at Cornell University, to serve as a supplement to textbooks at the level of Ashcroft & Mermin.  more » « less
Award ID(s):
1708499
NSF-PAR ID:
10301387
Author(s) / Creator(s):
Date Published:
Journal Name:
ArXivorg
ISSN:
2331-8422
Page Range / eLocation ID:
2001.04797
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    The human visual cortex is organized in a hierarchical manner. Although previous evidence supporting this hypothesis has been accumulated, specific details regarding the spatiotemporal information flow remain open. Here we present detailed spatiotemporal correlation profiles of neural activity with low‐level and high‐level features derived from an eight‐layer neural network pretrained for object recognition. These correlation profiles indicate an early‐to‐late shift from low‐level features to high‐level features and from low‐level regions to higher‐level regions along the visual hierarchy, consistent with feedforward information flow. Additionally, we computed three sets of features from the low‐ and high‐level features provided by the neural network: object‐category‐relevant low‐level features (the common components between low‐level and high‐level features), low‐level features roughly orthogonal to high‐level features (the residual Layer 1 features), and unique high‐level features that were roughly orthogonal to low‐level features (the residual Layer 7 features). Contrasting the correlation effects of the common components and the residual Layer 1 features, we observed that the early visual cortex (EVC) exhibited a similar amount of correlation with the two feature sets early in time, but in a later time window, the EVC exhibited a higher and longer correlation effect with the common components (i.e., the low‐level object‐category‐relevant features) than with the low‐level residual features—an effect unlikely to arise from purely feedforward information flow. Overall, our results indicate that non‐feedforward processes, for example, top‐down influences from mental representations of categories, may facilitate differentiation between these two types of low‐level features within the EVC.

     
    more » « less
  2. SUMMARY

    Mass loss from polar ice sheets is becoming the dominant contributor to current sea level changes, as well as one of the largest sources of uncertainty in sea level projections. The spatial pattern of sea level change is sensitive to the geometry of ice sheet mass changes, and local sea level changes can deviate from the global mean sea level change due to gravitational, Earth rotational and deformational (GRD) effects. The pattern of GRD sea level change associated with the melting of an ice sheet is often considered to remain relatively constant in time outside the vicinity of the ice sheet. For example, in the sea level projections from the most recent IPCC sixth assessment report (AR6), the geometry of ice sheet mass loss was treated as constant during the 21st century. However, ice sheet simulations predict that the geometry of ice mass changes across a given ice sheet and the relative mass loss from each ice sheet will vary during the coming century, producing patters of global sea level changes that are spatiotemporally variable. We adopt a sea level model that includes GRD effects and shoreline migration to calculate time-varying sea level patterns associated with projections of the Greenland and Antarctic Ice Sheets during the coming century. We find that in some cases, sea level changes can be substantially amplified above the global mean early in the century, with this amplification diminishing by 2100. We explain these differences by calculating the contributions of Earth rotation as well as gravitational and deformational effects to the projected sea level changes separately. We find in one case, for example, that ice gain on the Antarctic Peninsula can cause an amplification of up to 2.9 times the global mean sea level equivalent along South American coastlines due to positive interference of GRD effects. To explore the uncertainty introduced by differences in predicted ice mass geometry, we predict the sea level changes following end-member mass loss scenarios for various regions of the Antarctic Ice Sheet from the ISMIP6 model ensemblely, and find that sea level amplification above the global mean sea level equivalent differ by up to 1.9 times between different ice mass projections along global coastlines outside of Greenland and Antarctica. This work suggests that assessments of future sea level hazard should consider not only the integrated mass changes of ice sheets, but also temporal variations in the geometry of the ice mass changes across the ice sheets. As well, this study highlights the importance of constraining the relative timing of ice mass changes between the Greenland and Antarctic Ice Sheets.

     
    more » « less
  3. Abstract

    Climate variability affects sea levels as certain climate modes can accelerate or decelerate the rising sea level trend, but subseasonal variability of coastal sea levels is underexplored. This study is the first to investigate how remote tropical forcing from the MJO and ENSO impact subseasonal U.S. coastal sea level variability. Here, composite analyses using tide gauge data from six coastal regions along the U.S. East and West Coasts reveal influences on sea level anomalies from both the MJO and ENSO. Tropical MJO deep convection forces a signal that results in U.S. coastal sea level anomalies that vary based on MJO phase. Further, ENSO is shown to modulate both the MJO sea level response and background state of the teleconnections. The sea level anomalies can be significantly enhanced or weakened by the MJO-associated anomaly along the East Coast due to constructive or destructive interference with the ENSO-associated anomaly, respectively. The West Coast anomaly is found to be dominated by ENSO. We examine physical mechanisms by which MJO and ENSO teleconnections impact coastal sea levels and find consistent relationships between low-level winds and sea level pressure that are spatially varying drivers of the variability. Two case studies reveal how MJO and ENSO teleconnection interference played a role in notable coastal flooding events. Much of the focus on sea level rise concerns the long-term trend associated with anthropogenic warming, but on shorter time scales, we find subseasonal climate variability has the potential to exacerbate the regional coastal flooding impacts.

    Significance Statement

    Coastal flooding due to sea level rise is increasingly threatening communities, but natural fluctuations of coastal sea levels can exacerbate the human-caused sea level rise trend. This study assesses the role of tropical influences on coastal subseasonal (2 weeks–3 months) sea level heights. Further, we explore the mechanisms responsible, particularly for constructive interference of signals contributing to coastal flooding events. Subseasonal signals amplify or suppress the lower-frequency signals, resulting in higher or lower sea level heights than those expected from known climate modes (e.g., ENSO). Low-level onshore winds and reduced sea level pressure connected to the tropical phenomena are shown to be indicators of increased U.S. coastal sea levels, and vice versa. Two case studies reveal how MJO and ENSO teleconnection interference played a role in notable coastal flooding events. Much of the focus on sea level rise concerns the long-term trend associated with anthropogenic warming, but on shorter time scales, we find subseasonal climate variability has the potential to exacerbate the regional coastal flooding impacts.

     
    more » « less
  4. Multilevel regression discontinuity designs have been increasingly used in education research to evaluate the effectiveness of policy and programs. It is common to ignore a level of nesting in a three-level data structure (students nested in classrooms/teachers nested in schools), whether unwittingly during data analysis or due to resource constraints during the planning phase. This study investigates the consequences of ignoring intermediate or top level in blocked three-level regression discontinuity designs (BIRD3; treatment is at level 1) during data analysis and planning. Monte Carlo simulation results indicated that ignoring a level during analysis did not affect the accuracy of treatment effect estimates; however, it affected the precision (standard errors, power, and Type I error rates). Ignoring the intermediate level did not cause a significant problem. Power rates were slightly underestimated, whereas Type I error rates were stable. In contrast, ignoring a top-level resulted in overestimated power rates; however, severe inflation in Type I error deemed this strategy ineffective. As for the design phase, when the intermediate level was ignored, it is viable to use parameters from a two-level blocked regression discontinuity model (BIRD2) to plan a BIRD3 design. However, level 2 parameters from the BIRD2 model should be substituted for level 3 parameters in the BIRD3 design. When the top level was ignored, using parameters from the BIRD2 model to plan a BIRD3 design should be avoided. 
    more » « less
  5. null (Ed.)
    Abstract Background and Aims The composition and dynamics of plant communities arise from individual-level demographic outcomes, which are driven by interactions between phenotypes and the environment. Functional traits that can be measured across plants are frequently used to model plant growth and survival. Perhaps surprisingly, species average trait values are often used in these studies and, in some cases, these trait values come from other regions or averages calculated from global databases. This data aggregation potentially results in a large loss of valuable information that probably results in models of plant performance that are weak or even misleading. Methods We present individual-level trait and fine-scale growth data from >500 co-occurring individual trees from 20 species in a Chinese tropical rain forest. We construct Bayesian models of growth informed by theory and construct hierarchical Bayesian models that utilize both individual- and species-level trait data, and compare these models with models only using individual-level data. Key Results We show that trait–growth relationships measured at the individual level vary across species, are often weak using commonly measured traits and do not align with the results of analyses conducted at the species level. However, when we construct individual-level models of growth using leaf area ratio approximations and integrated phenotypes, we generated strong predictive models of tree growth. Conclusions Here, we have shown that individual-level models of tree growth that are built using integrative traits always outperform individual-level models of tree growth that use commonly measured traits. Furthermore, individual-level models, generally, do not support the findings of trait–growth relationships quantified at the species level. This indicates that aggregating trait and growth data to the species level results in poorer and probably misleading models of how traits are related to tree performance. 
    more » « less