scholarly journals Local symmetry theory of resonator structures for the real-space control of edge states in binary aperiodic chains

2019 ◽  
Vol 99 (21) ◽  
Author(s):  
M. Röntgen ◽  
C. V. Morfonios ◽  
R. Wang ◽  
L. Dal Negro ◽  
P. Schmelcher
Keyword(s):  
Local Symmetry ◽  
Real Space ◽  
Edge States ◽  
The Real ◽  
Symmetry Theory

scholarly journals Current Trends in Random Walks on Random Lattices

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1148
Author(s):  
Jewgeni H. Dshalalow ◽  
Ryan T. White
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Real Time ◽  
Real Space ◽  
Historical Background ◽  
Escape Time ◽  
The Real ◽  
Current Trends ◽  
One Step ◽  
Time Position

In a classical random walk model, a walker moves through a deterministic d-dimensional integer lattice in one step at a time, without drifting in any direction. In a more advanced setting, a walker randomly moves over a randomly configured (non equidistant) lattice jumping a random number of steps. In some further variants, there is a limited access walker’s moves. That is, the walker’s movements are not available in real time. Instead, the observations are limited to some random epochs resulting in a delayed information about the real-time position of the walker, its escape time, and location outside a bounded subset of the real space. In this case we target the virtual first passage (or escape) time. Thus, unlike standard random walk problems, rather than crossing the boundary, we deal with the walker’s escape location arbitrarily distant from the boundary. In this paper, we give a short historical background on random walk, discuss various directions in the development of random walk theory, and survey most of our results obtained in the last 25–30 years, including the very recent ones dated 2020–21. Among different applications of such random walks, we discuss stock markets, stochastic networks, games, and queueing.

Eulerian partial-differential-equation methods for complex-valued eikonals in attenuating media

Geophysics ◽  
2021 ◽  
pp. 1-53
Author(s):  
Jiangtao Hu ◽  
Jianliang Qian ◽  
Jian Song ◽  
Min Ouyang ◽  
Junxing Cao ◽  
...  
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Ray Tracing ◽  
Seismic Waves ◽  
Real Space ◽  
Advection Equation ◽  
Partial Differential ◽  
The Real ◽  
Eikonal Function ◽  
Complex Valued

Seismic waves in earth media usually undergo attenuation, causing energy losses and phase distortions. In the regime of high-frequency asymptotics, a complex-valued eikonal is an essential ingredient for describing wave propagation in attenuating media, where the real and imaginary parts of the eikonal function capture dispersion effects and amplitude attenuation of seismic waves, respectively. Conventionally, such a complex-valued eikonal is mainly computed either by tracing rays exactly in complex space or by tracing rays approximately in real space so that the resulting eikonal is distributed irregularly in real space. However, seismic data processing methods, such as prestack depth migration and tomography, usually require uniformly distributed complex-valued eikonals. Therefore, we propose a unified framework to Eulerianize several popular approximate real-space ray-tracing methods for complex-valued eikonals so that the real and imaginary parts of the eikonal function satisfy the classical real-space eikonal equation and a novel real-space advection equation, respectively, and we dub the resulting method the Eulerian partial-differential-equation method. We further develop highly efficient high-order methods to solve these two equations by using the factorization idea and the Lax-Friedrichs weighted essentially non-oscillatory (WENO) schemes. Numerical examples demonstrate that the proposed method yields highly accurate complex-valued eikonals, analogous to those from ray-tracing methods. The proposed methods can be useful for migration and tomography in attenuating media.

Challenging structure determination from powder diffraction data: two pharmaceutical salts and one cocrystal with Z′ = 2

2019 ◽  
Vol 234 (4) ◽  
pp. 257-268 ◽  
Author(s):  
Carina Schlesinger ◽  
Michael Bolte ◽  
Martin U. Schmidt
Keyword(s):  
Single Crystal ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Structure Determination ◽  
Real Space ◽  
Powder Diffraction Data ◽  
The Real ◽  
Pharmaceutical Salts ◽  
Structure Solution ◽  
Space Method

Abstract Structure solution of molecular crystals from powder diffraction data by real-space methods becomes challenging when the total number of degrees of freedom (DoF) for molecular position, orientation and intramolecular torsions exceeds a value of 20. Here we describe the structure determination from powder diffraction data of three pharmaceutical salts or cocrystals, each with four molecules per asymmetric unit on general position: Lamivudine camphorsulfonate (1, P 21, Z=4, Z′=2; 31 DoF), Theophylline benzamide (2, P 41, Z=8, Z′=2; 23 DoF) and Aminoglutethimide camphorsulfonate hemihydrate [3, P 21, Z=4, Z′=2; 31 DoF (if the H2O molecule is ignored)]. In the salts 1 and 3 the cations and anions have two intramolecular DoF each. The molecules in the cocrystal 2 are rigid. The structures of 1 and 2 could be solved without major problems by DASH using simulated annealing. For compound 3, indexing, space group determination and Pawley fit proceeded without problems, but the structure could not be solved by the real-space method, despite extensive trials. By chance, a single crystal of 3 was obtained and the structure was determined by single-crystal X-ray diffraction. A post-analysis revealed that the failure of the real-space method could neither be explained by common sources of error such as incorrect indexing, wrong space group, phase impurities, preferred orientation, spottiness or wrong assumptions on the molecular geometry or other user errors, nor by the real-space method itself. Finally, is turned out that the structure solution failed because of problems in the extraction of the integrated reflection intensities in the Pawley fit. With suitable extracted reflection intensities the structure of 3 could be determined in a routine way.

scholarly journals Technological displacement: The Coat Check interactive augmented reality installation in perspective

2021 ◽  
Author(s):  
Aysegul Koc
Keyword(s):  
Augmented Reality ◽  
Data Storage ◽  
Motion Tracking ◽  
Physical Space ◽  
Digital Technologies ◽  
Real Space ◽  
Embodied Experience ◽  
Global Networks ◽  
The Real ◽  
Technological Displacement

Technological Displacement: The Coat Check Interactive AR Installation in Perspective is a two-part dissertation that involves the research/creation of an augmented reality installation and a textual critique of displacement both as a socio-cultural phenomenon and a technology-driven status quo. Digital technologies involve a series of displacements from data storage and transfer to creating global networks. Going hand in hand with human mobilities technological displacement affects our lives and interactions deeply. Multimedia and digital overlaying of information and interconnectedness (mobile devices, tracking technologies, the internet...) make up our quotidian in various degrees, impelling us to be 'present' in time and places we actually are not. Technological displacement may be viewed as an extension of physical displacement of individuals and communities in that the need to reconcile, re-invent and innovatively market proximity becomes more and more an underlying theme of contemporary lives. Nowhere the reorientations of presence is more accentuated than 'augmented space', as described by Lev Manovich, "a physical space overlaid with dynamically changing information, multimedia in form and localized for each user." (219) It may be argued that our sense of reality is already 'augmented' by digital stimuli in many ways. Here I make the case that in an augmented or digitally enhanced environment we are displaced multiple times, or "multiplaced". Augmentation is superimposing multimedia to real space, blurring the boundary between the real and the virtual, creating a heterogeneous space defined neither by the standards of the virtual nor the real but the coexistence and cooperation of both. Augmented reality functions on the principle of multiple displacements in that real space is not a backdrop to multimedia: it is indispensable to the overall embodied experience. I created the Coat Check in 2011 using motion tracking technologies (Intersense IS900), specialized cameras (Point Grey 360 degree Spherical Vision Camera), screens (Fog Screen), software (Max/MSP), tools and applications (Snapdragon AR). The conceptualization of The Coat Check is based on an analogy between digital technologies and coat checks that are both storage, retrieval and displacement systems. The Coat Check also raises questions on identity and history as it refers to belonging, temporality, and mobility.

scholarly journals Technological displacement: The Coat Check interactive augmented reality installation in perspective

2021 ◽  
Author(s):  
Aysegul Koc
Keyword(s):  
Augmented Reality ◽  
Data Storage ◽  
Motion Tracking ◽  
Physical Space ◽  
Digital Technologies ◽  
Real Space ◽  
Embodied Experience ◽  
Global Networks ◽  
The Real ◽  
Technological Displacement

Technological Displacement: The Coat Check Interactive AR Installation in Perspective is a two-part dissertation that involves the research/creation of an augmented reality installation and a textual critique of displacement both as a socio-cultural phenomenon and a technology-driven status quo. Digital technologies involve a series of displacements from data storage and transfer to creating global networks. Going hand in hand with human mobilities technological displacement affects our lives and interactions deeply. Multimedia and digital overlaying of information and interconnectedness (mobile devices, tracking technologies, the internet...) make up our quotidian in various degrees, impelling us to be 'present' in time and places we actually are not. Technological displacement may be viewed as an extension of physical displacement of individuals and communities in that the need to reconcile, re-invent and innovatively market proximity becomes more and more an underlying theme of contemporary lives. Nowhere the reorientations of presence is more accentuated than 'augmented space', as described by Lev Manovich, "a physical space overlaid with dynamically changing information, multimedia in form and localized for each user." (219) It may be argued that our sense of reality is already 'augmented' by digital stimuli in many ways. Here I make the case that in an augmented or digitally enhanced environment we are displaced multiple times, or "multiplaced". Augmentation is superimposing multimedia to real space, blurring the boundary between the real and the virtual, creating a heterogeneous space defined neither by the standards of the virtual nor the real but the coexistence and cooperation of both. Augmented reality functions on the principle of multiple displacements in that real space is not a backdrop to multimedia: it is indispensable to the overall embodied experience. I created the Coat Check in 2011 using motion tracking technologies (Intersense IS900), specialized cameras (Point Grey 360 degree Spherical Vision Camera), screens (Fog Screen), software (Max/MSP), tools and applications (Snapdragon AR). The conceptualization of The Coat Check is based on an analogy between digital technologies and coat checks that are both storage, retrieval and displacement systems. The Coat Check also raises questions on identity and history as it refers to belonging, temporality, and mobility.

scholarly journals Revealing topology with transformation optics

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Lizhen Lu ◽  
Kun Ding ◽  
Emanuele Galiffi ◽  
Xikui Ma ◽  
Tianyu Dong ◽  
...  
Keyword(s):  
Physical Space ◽  
Real Space ◽  
Virtual Space ◽  
Transformation Optics ◽  
Coordinate Space ◽  
Dimensional System ◽  
Edge States ◽  
And Topology ◽  
Higher Dimensional ◽  
Insight Into

AbstractSymmetry deepens our insight into a physical system and its interplay with topology enables the discovery of topological phases. Symmetry analysis is conventionally performed either in the physical space of interest, or in the corresponding reciprocal space. Here we borrow the concept of virtual space from transformation optics to demonstrate how a certain class of symmetries can be visualised in a transformed, spectrally related coordinate space, illuminating the underlying topological transitions. By projecting a plasmonic system in a higher-dimensional virtual space onto a lower-dimensional system in real space, we show how transformation optics allows us to construct a topologically non-trivial system by inspecting its modes in the virtual space. Interestingly, we find that the topological invariant can be controlled via the singularities in the conformal mapping, enabling the intuitive engineering of edge states. The confluence of transformation optics and topology here can be generalized to other wave realms beyond photonics.

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