scholarly journals Seeing the entanglement wedge

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Adam Levine ◽  
Arvin Shahbazi-Moghaddam ◽  
Ronak M Soni
Keyword(s):  
Unitary Operation ◽  
First Order ◽  
Non Local ◽  
Spherical Caps ◽  
Local Coupling

Abstract We study the problem of revealing the entanglement wedge using simple operations. We ask what operation a semiclassical observer can do to bring the entanglement wedge into causal contact with the boundary, via backreaction.In a generic perturbative class of states, we propose a unitary operation in the causal wedge whose backreaction brings all of the previously causally inaccessible ‘peninsula’ into causal contact with the boundary. This class of cases includes entanglement wedges associated to boundary sub-regions that are unions of disjoint spherical caps, and the protocol works to first order in the size of the peninsula. The unitary is closely related to the so-called Connes Cocycle flow, which is a unitary that is both well-defined in QFT and localised to a sub-region. Our construction requires a generalization of the work by Ceyhan & Faulkner to regions which are unions of disconnected spherical caps. We discuss this generalization in the appendix. We argue that this cocycle should be thought of as naturally generalizing the non-local coupling introduced in the work of Gao, Jafferis & Wall.

scholarly journals Chimera states and the interplay between initial conditions and non-local coupling

2017 ◽  
Vol 27 (3) ◽  
pp. 033110 ◽  
Author(s):  
Peter Kalle ◽  
Jakub Sawicki ◽  
Anna Zakharova ◽  
Eckehard Schöll
Keyword(s):  
Initial Conditions ◽  
Chimera States ◽  
Non Local ◽  
Local Coupling

Non-Local Coupling and Partial Synchronization in Chaotic Systems

2006 ◽  
Vol 23 (4) ◽  
pp. 786-789 ◽  
Author(s):  
Ao Bin ◽  
Ma Xiao-Juan ◽  
Li Yun-Yun ◽  
Zheng Zhi-Gang
Keyword(s):  
Chaotic Systems ◽  
Partial Synchronization ◽  
Non Local ◽  
Local Coupling

scholarly journals Non-local coupling of two donor-bound electrons

2013 ◽  
Vol 15 (3) ◽  
pp. 033020 ◽  
Author(s):  
J Verduijn ◽  
R R Agundez ◽  
M Blaauboer ◽  
S Rogge
Keyword(s):  
Non Local ◽  
Local Coupling ◽  
Bound Electrons

A Non-Local Convective Flux Limiter for Upwind-Biased Finite Volume Simulations

2010 ◽  
Author(s):  
Nicole M. W. Poe ◽  
D. Keith Walters
Keyword(s):  
Finite Volume ◽  
Finite Volume Methods ◽  
Second Order ◽  
Numerical Dissipation ◽  
Ansys Fluent ◽  
First Order ◽  
Low Dissipation ◽  
Solution Convergence ◽  
Improve Accuracy ◽  
Non Local

Finite volume methods on structured and unstructured meshes often utilize second-order, upwind-biased linear reconstruction schemes to approximate the convective terms, in an attempt to improve accuracy over first-order methods. Limiters are employed to reduce the inherent variable over- and under-shoot of these schemes; however, they also can significantly increase the numerical dissipation of a solution. This paper presents a novel non-local, non-monotonic (NLNM) limiter developed by enforcing cell minima and maxima on dependent variable values projected to cell faces. The minimum and maximum values for a cell are determined primarily through the recursive reference to the minimum and maximum values of its upwind neighbors. The new limiter is implemented using the User Defined Function capability available in the commercial CFD solver Ansys FLUENT. Various simple test cases are presented which exhibit the NLNM limiter’s ability to eliminate non-physical oscillations while maintaining relatively low dissipation of the solution. Results from the new limiter are compared with those from other limited and unlimited second-order upwind (SOU) and first-order upwind (FOU) schemes. For the cases examined in the study, the NLNM limiter was found to improve accuracy without significantly increasing solution convergence rate.

scholarly journals Classification of bi-Hamiltonian pairs extended by isometries

2021 ◽  
Vol 477 (2251) ◽  
pp. 20210185
Author(s):  
Maxim V. Pavlov ◽  
Pierandrea Vergallo ◽  
Raffaele Vitolo
Keyword(s):  
Type System ◽  
Local Part ◽  
First Order ◽  
Hydrodynamic Type System ◽  
Dependent Variables ◽  
Particular Solution ◽  
Non Local ◽  
Hamiltonian Operators ◽  
Hamiltonian Pair

The aim of this article is to classify pairs of the first-order Hamiltonian operators of Dubrovin–Novikov type such that one of them has a non-local part defined by an isometry of its leading coefficient. An example of such a bi-Hamiltonian pair was recently found for the constant astigmatism equation. We obtain a classification in the case of two dependent variables, and a significant new example with three dependent variables that is an extension of a hydrodynamic-type system obtained from a particular solution of the Witten–Dijkgraaf–Verlinde–Verlinde equations.

scholarly journals A measure theoretic approach to traffic flow optimisation on networks

2018 ◽  
Vol 30 (6) ◽  
pp. 1187-1209 ◽  
Author(s):  
SIMONE CACACE ◽  
FABIO CAMILLI ◽  
RAUL DE MAIO ◽  
ANDREA TOSIN
Keyword(s):  
Traffic Flow ◽  
Gradient Descent ◽  
Optimal Control Problems ◽  
Theoretic Approach ◽  
Nonlinear Transport ◽  
Traffic Lights ◽  
First Order ◽  
Flow Problems ◽  
Non Local ◽  
Smart Traffic

We consider a class of optimal control problems for measure-valued nonlinear transport equations describing traffic flow problems on networks. The objective is to minimise/maximise macroscopic quantities, such as traffic volume or average speed, controlling few agents, e.g. smart traffic lights and automated cars. The measure theoretic approach allows to study in a same setting local and non-local drivers interactions and to consider the control variables as additional measures interacting with the drivers distribution. We also propose a gradient descent adjoint-based optimisation method, obtained by deriving first-order optimality conditions for the control problem, and we provide some numerical experiments in the case of smart traffic lights for a 2–1 junction.

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