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DC Transport Critical Currents
Published in David A. Cardwell, David C. Larbalestier, Aleksander I. Braginski, Handbook of Superconductivity, 2022
The noise spectrum of a Type II superconductor carrying a current exceeding Ic provides an elegant way of measuring the number of flux lines in a flux-line bundle. Van Ooijen and Van Gurp explained such noise in vanadium strips of different width (Figure G2.3.24) by assuming that flux bundles cross these strips from one side to the other in discreet events and that the voltage along these samples was therefore the superposition of many discreet pulses (Van Ooijen and Van Gurp, 1965; Van Gurp, 1968). Deducing the pulse shape from the frequency dependence of the noise, they concluded that at modest fields and currents the bundles could contain as many as 105 flux lines. This number went down drastically when the current increased or when the field approached Hc2.
Fault tolerance and ultimate physical limits of nanocomputation
Published in David Crawley, Konstantin Nikolić, Michael Forshaw, 3D Nanoelectronic Computer Architecture and Implementation, 2020
A S Sadek, K Nikolić, M Forshaw
Figure 12.8 depicts the phase portrait of equations (12.26a)–(12.26d) over the phase space of Δ and ϵ. The shaded region represents the phase space of the line-bundle activation fraction Δ and gate noise ϵ where the line-bundle bit characterizations are maintained after an infinite number of iterations. Thus, for each value of ϵ up to the threshold ϵt ≃ 0.01077, there is a maximum value for Δ defined by the full curve. This curve is, hence, a repeller in phase space: values of ϵ and Δ outside this curve cause the bit characterization to explode to ‘1’ regardless of what the correct value should be. Within the repeller curve, as n → ∞, the value for the line bundle activation fraction moves towards those defined by the attractor in phase space, depicted by the broken curve. As can be seen, the maximum tolerable noise is ϵt ≃ 0.01077 and the value of Δ at this threshold is ≃ 0.073.
Operators in the Cowen-Douglas Class and Related Topics
Published in Kehe Zhu, Handbook of Analytic Operator Theory, 2019
One of the striking results of Cowen and Douglas says that there is a one to one correspondence between the unitary equivalence class of the operators T and the (local) equivalence classes of the holomorphic Hermitian vector bundles ET determined by them. As a result of this correspondence set up by the Cowen-Douglas theorem, the invariants of the vector bundle ET like the curvature, the second fundamental form, etc. now serve as unitary invariants for the operator T, although finding a complete set of tractable invariants, not surprisingly, is much more challenging. Examples were given in [51, Example 2.1] to show that the class of the curvature alone does not determine the class of the vector bundle except in the case of a line bundle. Before we consider this case in some detail, let us recall the interesting notion of a spanning section. A holomorphic function s : Ω → ℋ is called a spanning section for an operator T in the Cowen-Douglas class if ker(T − w)s(w) = 0 and the closed linear span of {s(w) : w ∈ Ω} is ℋ. Kehe Zhu in [62] proved the existence of a spanning section for an operator T in Bn(Ω) and showed that it can be used to characterize Cowen-Douglas operators of rank n up to unitary equivalence and similarity. Unfortunately, the existential nature of the spanning section makes it difficult to apply this result in concrete examples.
Designing price-service menus in a product-service system
Published in International Journal of Systems Science: Operations & Logistics, 2023
To make things clearer, assume , and where c,f,g are constants. Then the client's utility U is linear in cost of waiting c with a negative slope , and intercepts and . For example, if U vs. c graph is as shown in Figure 2(b), then the client's optimal choice is to choose bundle with if (denoted by orange line), bundle if (denoted by blue line), bundle if (denoted by green line) and not buy anything if .
Trip-pair based clustering model for urban mobility of bus passengers in Macao
Published in Transportmetrica A: Transport Science, 2023
W.K. Ku, K.P. Kou, S.H. Lam, K.I. Wong
Other applications, such as understanding urban mobility patterns, improving operational performance, and increasing the accuracy of prediction and estimation, have also received considerable attention in recent studies. Ma et al. (2017) mined transit commuting patterns in a smartcard dataset over continuous long-term observation in Beijing. They classified passengers into groups of commuters and non-commuters according to their spatial and temporal characteristics through comparisons of their departure times, travel distances, number of travelling days, and home/workplace distributions. Yap et al. (2019) used smartcard data to address the time-table synchronisation problem (TSP) employing a data-drive and passenger-oriented model. The model determined the transfer hubs by identifying the spatial boundaries using the DBSCAN algorithm and then characterized the transfer patterns within different hubs through line bundle identification. Zhong et al. (2016) examined variability in the regularity of temporal mobility patterns using smartcard data across three metropolises: London, Singapore, and Beijing. To achieve a relatively accurate prediction of travel behaviour, they suggested a minimum time bin for analysing the regularity as 15 min. Alsger et al. (2016) improved the trip-chaining OD estimation algorithm by adjusting the estimation of the last destinations of the day and the search logic of alighting stops. In addition, they used a unique smartcard dataset with known boarding and alighting information to validate the accuracy of the trip-chaining OD estimation algorithm, and subsequently proposed an improved method.
The K-property for subadditive equilibrium states
Published in Dynamical Systems, 2021
Case 2: has multiple equilibrium states. From Proposition 4.7, over must be reducible and must have two distinct ergodic equilibrium states . In fact, denoting the -invariant and -invariant line bundle by , consider another -invariant and -invariant line bundle defined by . Since is irreducible, and are distinct bundles. In fact, differs from for all . This follows because if were to agree with for some , then and would agree on the cylinder from the -invariance, which then would imply that and agree everywhere on by the assumption of topological mixing of and -invariance of the .