Parity and valley degeneracy in multilayer graphene

We study spatial symmetry in general ABA-stacked multilayer graphene to illustrate how electronic spectra at the two valleys are related in a magnetic field. We show that the lattice of multilayers with an even number of layers, as well as that of monolayer graphene, satisfy spatial inversion symmetry, which rigorously guarantees valley degeneracy in the absence of time-reversal symmetry. A multilayer with an odd number of layers (three or more) lacks inversion symmetry, but there is another transformation imposing an approximate valley degeneracy, which arises because the low-energy Hamiltonian consists of separate monolayerlike and bilayerlike parts. We show that an external electrostatic potential generally breaks valley degeneracy in a magnetic field, in a markedly different manner in odd and even multilayers.Comment: 6 pages, 3 figure

Interlayer screening effect in graphene multilayers with ABA and ABC stacking

We study the effect of perpendicular electric fields on the band structures of ABA and ABC graphene multilayers, and find that the electronic screening effect is significantly different between them. In ABA multilayers, the field produces a band overlap and gives a linear screening, while in ABC multilayers, in contrast, it opens an energy gap in the surface-state band at low energy, leading to a strong screening effect essentially non-linear to the field amplitude. The energy gap of a large ABC stack sharply rises when the external field exceeds a certain critical value.Comment: 8 pages, 6 figure

Effects of edge magnetism and external electric field on energy gaps in multilayer graphene nanoribbons

Using first-principles density-functional theory, we study the electronic structure of multilayer graphene nanoribbons as a function of the ribbon width and the external electric field, applied perpendicular to the ribbon layers. We consider two types of edges (armchair and zigzag), each with two edge alignments (referred to as alpha- and beta-alignments). We show that, as in monolayer and bilayer armchair nanoribbons, multilayer armchair nanoribbons exhibit three classes of energy gaps which decrease with increasing width. Nonmagnetic multilayer zigzag nanoribbons have band structures that are sensitive to the edge alignments and the number of layers, indicating different magnetic properties and resulting energy gaps. We find that energy gaps can be induced in ABC-stacked ribbons with a perpendicular external electric field while in other stacking sequences, the gaps decrease or remain closed as the external electric field increases.Comment: 7 pages, 9 figures, text revised, last version before publicatio

New formulation for flexible beams undergoing large overall plane motion

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76279/1/AIAA-21161-979.pd

A NEW FLEXIBLE BODY DYNAMIC FORMULATION FOR BEAM STRUCTURES UNDERGOING LARGE OVERALL MOTION ITHE THREE-DIMENSIONAL CASE

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77304/1/AIAA-1993-1435-369.pd

A new flexible body dynamic formulation for beam structures undergoing large overall motion

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77331/1/AIAA-1992-2261-829.pd

Electronic states and Landau levels in graphene stacks

We analyze, within a minimal model that allows analytical calculations, the electronic structure and Landau levels of graphene multi-layers with different stacking orders. We find, among other results, that electrostatic effects can induce a strongly divergent density of states in bi- and tri-layers, reminiscent of one-dimensional systems. The density of states at the surface of semi-infinite stacks, on the other hand, may vanish at low energies, or show a band of surface states, depending on the stacking order

Electronic Structure of Few-Layer Graphene: Experimental Demonstration of Strong Dependence on Stacking Sequence

The electronic structure of few-layer graphene (FLG) samples with crystalline order was investigated experimentally by infrared absorption spectroscopy for photon energies ranging from 0.2 - 1 eV. Distinct optical conductivity spectra were observed for different samples having precisely the same number of layers. The different spectra arise from the existence of two stable polytypes of FLG, namely, Bernal (AB) stacking and rhombohedral (ABC) stacking. The observed absorption features, reflecting the underlying symmetry of the two polytypes and the nature of the associated van Hone singularities, were reproduced by explicit calculations within a tight-binding model. The findings demonstrate the pronounced effect of stacking order on the electronic structure of FLG.Comment: 13 pages, 3 figure

Estimating flexibility preferences to resolve temporal scheduling conflicts in activity-based modelling

This paper presents a novel activity-based demand model that combines an optimisation framework for continuous temporal scheduling decisions (i.e. activity timings and durations) with traditional discrete choice models for non-temporal choice dimensions (i.e. activity participation, number and type of tours, and destinations). The central idea of our approach is that individuals resolve temporal scheduling conflicts that arise from overlapping activities, e.g. needing to work and desiring to shop at the same time, in order to maximise their daily utility. Flexibility parameters capture behavioural preferences that penalise deviations from desired timings. This framework has three advantages over existing activity-based modelling approaches: (i) the time conflicts between different temporal scheduling decisions including the activity sequence are treated jointly; (ii) flexibility parameters follow a utility maximisation approach; and (iii) the framework can be used to estimate and simulate a city-scale case study in reasonable time. We introduce an estimation routine that allows flexibility parameters to be estimated using real-world observations as well as a simulation routine to efficiently resolve temporal conflicts using an optimisation model. The framework is applied to the full-time workers of a synthetic population for the city of Lausanne, Switzerland. We validate the model results against reported schedules. The results demonstrate the capabilities of our approach to reproduce empirical observations in a real-world case study