Galvanic Phase Coupling of Superconducting Flux Qubits

We investigate the galvanic coupling schemes of superconducting flux qubits. From the fundamental boundary conditions, we obtain the effective potential of the coupled system of two or three flux qubits to provide the exact Lagrangian of the system. While usually the two-qubit gate has been investigated approximately, in this study we derive the exact inductive coupling strength between two flux qubits coupled directly and coupled through a connecting central loop. We observe that the inductive coupling strength needs to be included exactly to satisfy the criteria of fault-tolerant quantum computing.

Circulator function in a Josephson junction circuit and braiding of Majorana zero modes

We propose a scheme for the circulator function in a superconducting circuit consisting of a three-Josephson junction loop and a trijunction. In this study we obtain the exact Lagrangian of the system by deriving the effective potential from the fundamental boundary conditions. We subsequently show that we can selectively choose the direction of current flowing through the branches connected at the trijunction, which performs a circulator function. Further, we use this circulator function for a non-Abelian braiding of Majorana zero modes (MZMs). In the branches of the system we introduce pairs of MZMs which interact with each other through the phases of trijunction. The circulator function determines the phases of the trijunction and thus the coupling between the MZMs to gives rise to the braiding operation. We modify the system so that MZMs might be coupled to the external ones to perform qubit operations in a scalable design.

Crossing the Pomerium: The Armed Ruler at Rome

This chapter explores the act of “crossing the pomerium” and how the distinction the pomerium created did not always correspond with lived realities. Although Republican Rome distinguished the urbs both legally and religiously from what lay beyond the pomerium, its fundamental boundary, the disintegration of this essential division was merely one of the many Republican traditions whose demise would gradually define the advent of empire. Here, the chapter provides three examples that have long been regarded as representations of the imperator, as all Roman imagery demands to be set in the context of those legal, political, and religious institutions that not merely shaped but defined it. What ensues is a sketch of the broader institutional background within which this chapter establishes what it meant to be represented in this fashion at Rome. In so doing, the chapter demonstrates what was, for the Romans of the dawning imperial age, the very real significance of “crossing the pomerium” and entering the city under arms.

Internet of Things-Based Authentication Mechanism for E-Health Applications

The sturdy advancements of internet of things are being changed into a methodology of associating smart things. E-health applications in this vision are a standout amongst IoT's most energizing applications. Indeed, security concerns were the fundamental boundary to the establishment. The encryption of various interlinked substances and the classification of the swapped information are the real concerns which should be settled for clients. This chapter proposes an e-health application using lightweight verification mechanism. The proposed model utilizes nonces as well as keyed-hash message authentication (KHAC) for checking the validity of verification trades.

Theory, history, and great transformations

In International Relations arguments abouthistoricalorigins provoketheoreticaldebates, as origins assume an emergent theoretical unit of inquiry – an international order, system, society, etc. – while at the same time defining its core properties and dynamics. By boldly casting the long 19th century as the origin of global modernity and, in turn, the modern international order, Buzan and Lawson’sThe Global Transformationchallenges the romance with Westphalia that undergirds so much of our theorizing. Yet, the contributions to this symposium push deeper than usual, challenging established ways of conceiving change, and suggesting very different models ofpropertheorizing. While all of the papers ostensibly debate large-scale systems change, three modes of change are in contention: breakpoint, evolutionary, and processual. The further one pushes towards the latter, however, the more elusive the idea of ‘system’ becomes, eroding the fundamental boundary condition that undergirds the systemic mode of theorizing that dominates the field. Similarly, a persistent theme in these contributions is Buzan and Lawson’s purported failure to theorize change. But instead of offering rival theories, contributors advance very different conceptions oftheorizing, from pre-observational conceptualization to causal explanation. This not only challenges the field to reflect more systematically on the process of theorizing, but to acknowledge forms of theorizing that it currently brackets.

The Symmetric Versions of Rouché’s Theorem via ∂--Calculus

Let (f,g) be a pair of holomorphic functions. In this expositional paper we apply the ∂--calculus to prove the symmetric version “|f+g|<|f|+|g| on ∂K” as well as the homotopic version of Rouché's theorem for arbitrary planar compacta K. Using Eilenberg's representation theorem we also give a converse to the homotopic version. Then we derive two analogs of Rouché's theorem for continuous-holomorphic pairs (a symmetric and a nonsymmetric one). One of the rarely presented properties of the non-symmetric version is that in the fundamental boundary hypothesis, |f+g|≤|g|, equality is allowed.

Boundary algebraic equations for lattice problems

Procedures for constructing boundary integral equations equivalent to linear boundary-value problems governed by partial differential equations are well established. In this paper, it is demonstrated how these procedures can be extended to linear boundary-value problems defined on lattices and governed by algebraic (‘difference’) equations. The boundary equations that arise are then themselves algebraic equations. Such ‘boundary algebraic equations’ (BAEs) are derived for fundamental boundary-value problems defined on both perfect lattices and lattices with defects. It is demonstrated that key advantages of representing a continuum boundary-value problem as an equation on the boundary, such as favourable spectral properties and minimal problem size, are preserved in the lattice environment. Certain spectral properties of BAEs are established rigorously, whereas others are supported by numerical experiments.

Six Fundamental Boundary Value Problems in the Mechanics of Periodic Composites

A new approach in the mechanics of composites is presented. We use basic solutions and regular expansions in order to represent stresses, strains and displacements in a composite. We perform homogenization and present new formulae for the effective moduli. We propose a new approach to the formulation of homogenized equations and boundary conditions.

Structural analysis of the Miniss River and related faults, western Superior Province: post-collisional displacement initiated at terrane boundaries

Mountain building in the western part of the Archean Superior Province culminated with the formation of regional strike-slip faults. This paper reports on the kinematics and timing of several major faults at the juncture between the Uchi, English River, Winnipeg River, and western Wabigoon subprovinces. Sinistral-oblique mylonitization along the northeast-striking Miniss River fault occurred at 2681 [Formula: see text] Ma. This involved ~40 km of sinistral offset and a scissor-like motion whereby vertical displacement increased southwestward toward a restraining bend near Sioux Lookout. To the north, the Miniss River fault is intersected by the east-striking, dextral strike-slip Sydney Lake – Lake St. Joseph fault; the latter merges along strike with the Pashkokogan fault. Restoration of respective displacements indicates that the faults formed sequentially, not simultaneously in response to tectonic indentation. Dextral strike-slip motion along the Sydney Lake – Lake St. Joseph (– Pashkokogan) fault was instigated at ≤2670 Ma and drove greenschist-grade, dextral reactivation of the southwest segment of the Miniss River fault. U–Pb geochronology suggests that the latter coincides with an older terrane-boundary fault that juxtaposed ca. 2735 Ma juvenile, western Wabigoon arc complexes against ca. 3.05 Ga granitoid rocks of the Winnipeg River terrane. The Sydney Lake – Lake St. Joseph (– Pashkokogan) fault similarly demarcates a fundamental boundary between Uchian volcanoplutonic rocks and the English River accretionary prism. Strike-slip faults in this region therefore initiated at terrane boundaries and in some cases evolved so as to transect and displace these boundaries to accommodate further shortening during final stages of Archean orogenesis.