Publications related to Plane (mathematics)

Asymmetric phase modulation of light with parity-symmetry broken metasurfaces

The design of wavefront-shaping devices is conventionally approached using real-frequency modeling. However, since these devices interact with light through radiative channels, they are by default non-Hermitian objects having complex eigenvalues (poles and ...

Optica Publishing Group2023

Intrinsic-Strain Engineering by Dislocation Imprint in Bulk Ferroelectrics

Dragan Damjanovic, Fangping Zhuo

We report an intrinsic strain engineering, akin to thin filmlike approaches, via irreversible hightemperature plastic deformation of a tetragonal ferroelectric single-crystal BaTiO3. Dislocations wellaligned along the [001] axis and associated strain field ...

AMER PHYSICAL SOC2023

On the optimal controllability time for linear hyperbolic systems with time-dependent coefficients

Hoài-Minh Nguyên

The optimal time for the controllability of linear hyperbolic systems in one dimensional space with one-side controls has been obtained recently for time-independent coefficients in our previous works. In this paper, we consider linear hyperbolic systems w ...

2021

Efficient equilibrium-based stress recovery for isogeometric laminated curved structures

Pablo Antolin Sanchez, Alessandro Reali

This work extends the stress recovery for laminated composite solid plates, proposed in [1,2], to curved structures. Based on 3D Isogeometric Analysis (IGA) computations and equilibrium, this procedure uses a single element through the thickness in combina ...

ELSEVIER SCI LTD2021

How to weave a perfect sphere with curved strips

Mark Pauly, Pedro Miguel Nunes Pereira de Almeida Reis, Tian Chen, Yingying Ren, Samuel Jean Bernard Poincloux, Francis Julian Panetta

Triaxial weaving, a craft technique that enables the generation of surfaces with tri-directional arrays of initially straight elastic strips, has long been loved by basket makers and artists seeking a combination of practical and aesthetically-pleasing str ...

American Physical Society2020

Shapes From Echoes: Uniqueness From Point-to-Plane Distance Matrices

Martin Vetterli, Ivan Dokmanic, Miranda Krekovic

We study the problem of localizing a configuration of points and planes from the collection of point-to-plane distances. This problem models simultaneous localization and mapping from acoustic echoes as well as the & x201C;structure from sound & x201D; app ...

2020

Simple Realizability of Complete Abstract Topological Graphs Simplified

Jan Kyncl

An abstract topological graph (briefly an AT-graph) is a pair A = (G, X) where G = (V, E) is a graph and X. E2 is a set of pairs of its edges. The AT-graph A is simply realizable if G can be drawn in the plane so that each pair of edges from X crosses exac ...

SPRINGER2020

Monolithic Fabrication of Silicon Nanowires Bridging Thick Silicon Structures

Davide Sacchetto, Yusuf Leblebici, Oliver Peric, Zuhal Tasdemir

A monolithic process is developed for the fabrication of Si nanowires within thick Si substrates. A combination of anisotropic etch and sidewall passivation is utilized to protect and release Si lines during the subsequent deep etch. An etch depth of 10 mu ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2018

Omnidirectional bats, point-to-plane distances, and the price of uniqueness

Martin Vetterli, Ivan Dokmanic, Miranda Krekovic

We study simultaneous localization and mapping with a device that uses reflections to measure its distance from walls. Such a device can be realized acoustically with a synchronized collocated source and receiver; it behaves like a bat with no capacity for ...

Ieee2017

The effect of “objecthood” in the Ebbinghaus illusion

Michael Herzog, Aline Françoise Cretenoud, Einat Rashal

In the Ebbinghaus illusion, observers overestimate the size of a target when it is surrounded by large flakers and compared with a control target surrounded by small flankers. We examined whether “objecthood” – the degree to which an object is a cohesive e ...

2017

Apparatus for imaging a page of a book or other similar document

Martin Vetterli, Loïc Arnaud Baboulaz

The present invention relates to an apparatus for imaging a page of a book or other similar document comprising: - a table defining a support plane, the book being disposed on the table such that the page to image is substantially parallel to the support p ...

2017

Near-Field Integration of a SiN Nanobeam and a SiO2 Microcavity for Heisenberg-Limited Displacement Sensing

Tobias Kippenberg, Dalziel Joseph Wilson, Ryan Daniel Schilling, Vivishek Sudhir, Amir Hossein Ghadimi

Placing a nanomechanical object in the evanescent near field of a high-Q optical microcavity gives access to strong gradient forces and quantum-limited displacement readout, offering an attractive platform for both precision sensing technology and basic qu ...

American Physical Society (APS)2016

Comb Drive Designs With Minimized Levitation

Matthias Imboden

This paper presents two capacitive comb drive designs for electrostatic actuation of MEMS with the aim to eliminate the levitation effect often observed in such systems. By placing a shield over the comb drive fingers, it is possible to balance the electri ...

Institute of Electrical and Electronics Engineers2016

Free Edge Lengths in Plane Graphs

Radoslav Fulek, Filip Moric

We study the impact of metric constraints on the realizability of planar graphs. Let G be a subgraph of a planar graph H (where H is the "host" of G). The graph G is free in H if for every choice of positive lengths for the edges of G, the host H has a pla ...

Springer2015

Generalized eigenvalue problems with specified eigenvalues

Daniel Kressner

We consider the distance from a (square or rectangular) matrix pencil to the nearest matrix pencil in 2-norm that has a set of specified eigenvalues. We derive a singular value optimization characterization for this problem and illustrate its usefulness fo ...

Oxford University Press2014

A note on coloring line arrangements

János Pach, Rom Pinchasi

We show that the lines of every arrangement of n lines in the plane can be colored with O(root n/log n) colors such that no face of the arrangement is monochromatic. This improves a bound of Bose et al. by a circle minus(root/log n) factor. Any further imp ...

Electronic Journal Of Combinatorics2014

The number of distinct distances from a vertex of a convex polygon

János Pach, Gabriel Nivasch, Rom Pinchasi

Erd\H{o}s conjectured in 1946 that every n-point set P in convex position in the plane contains a point that determines at least floor(n/2) distinct distances to the other points of P. The best known lower bound due to Dumitrescu (2006) is 13n/36 - O(1). I ...

2013

Phase extraction in speckle interferometry by a circle fitting procedure in the complex plane

Pierre Jacquot, Sébastien Equis

In speckle interferometry (SI), temporal signals are amplitude- and frequency-modulated signals and exhibit a fluctuating background. Prior to phase computation, this background intensity must be eliminated. Here our approach is to build a complex signal f ...

Optical Society of America2011

Theoretical Investigation of Iterative Phase Retrieval Algorithm for Quasi-Optical Millimeter-Wave RF Beams

Stefano Alberti, Jean-Philippe Hogge

In this paper, we present a detailed analysis of the iterative phase retrieval approach (TPRA) for determining the phase profile of the output microwave beam of a gyrotron from known intensity patterns emphasizing the field propagation techniques which are ...

IEEE2009

Convexly independent subsets of the Minkowski sum of planar point sets

János Pach, Friedrich Eisenbrand, Thomas Rothvoss

Let P and Q be finite sets of points in the plane. In this note we consider the largest cardinality of a subset of the Minkowski sum S ⊆ P⊕Q which consist of convex independent points. We show that, if P and Q contain at most n points, then |S| = O(n^(4/3) ...

American Mathematical Society2008