On the analysis and control of hyperbolic systems associated with vibrating networks

1994 ◽  
Vol 124 (1) ◽  
pp. 77-104 ◽  
Author(s):  
J. E. Lagnese ◽  
G. Leugering ◽  
E. J. P. G. Schmidt
Keyword(s):  
Hyperbolic Systems ◽  
Three Dimensional ◽  
Exact Controllability ◽  
General Linear Model ◽  
Regularity Of Solutions ◽  
Closed Loops ◽  
One Dimensional ◽  
First Order ◽  
And Control ◽  
First Time

In this paper a general linear model for vibrating networks of one-dimensional elements is derived. This is applied to various situations including nonplanar networks of beams modelled by a three-dimensional variant on the Timoshenko beam, described for the first time in this paper. The existence and regularity of solutions is established for all the networks under consideration. The methods of first-order hyperbolic systems are used to obtain estimates from which exact controllability follows for networks containing no closed loops.

scholarly journals The on-axis magnetic well and Mercier's criterion for arbitrary stellarator geometries

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
P. Kim ◽  
R. Jorge ◽  
W. Dorland
Keyword(s):  
Magnetic Field ◽  
Original Work ◽  
Three Dimensional ◽  
Radial Distance ◽  
Analytical Form ◽  
One Dimensional ◽  
Modern Notation ◽  
Magnetic Well ◽  
First Time ◽  
Dimensional Integral

A simplified analytical form of the on-axis magnetic well and Mercier's criterion for interchange instabilities for arbitrary three-dimensional magnetic field geometries is derived. For this purpose, a near-axis expansion based on a direct coordinate approach is used by expressing the toroidal magnetic flux in terms of powers of the radial distance to the magnetic axis. For the first time, the magnetic well and Mercier's criterion are then written as a one-dimensional integral with respect to the axis arclength. When compared with the original work of Mercier, the derivation here is presented using modern notation and in a more streamlined manner that highlights essential steps. Finally, these expressions are verified numerically using several quasisymmetric and non-quasisymmetric stellarator configurations including Wendelstein 7-X.

On the Boundary Value Problem in A Dihedral Angle for Normally Hyperbolic Systems of First Order

1998 ◽  
Vol 5 (2) ◽  
pp. 121-138
Author(s):  
O. Jokhadze
Keyword(s):  
Partial Differential Equations ◽  
Boundary Value Problem ◽  
Principal Part ◽  
Hyperbolic Systems ◽  
Boundary Value ◽  
Three Dimensional ◽  
Order System ◽  
First Order ◽  
Dimensional Boundary ◽  
Class Of Functions

Abstract Some structural properties as well as a general three-dimensional boundary value problem for normally hyperbolic systems of partial differential equations of first order are studied. A condition is given which enables one to reduce the system under consideration to a first-order system with the spliced principal part. It is shown that the initial problem is correct in a certain class of functions if some conditions are fulfilled.

scholarly journals Null controllability and finite-time stabilization in minimal time of one-dimensional first-order 2×2 linear hyperbolic systems

2021 ◽  
Author(s):  
Long Hu ◽  
Guillaume Olive
Keyword(s):  
Finite Time ◽  
Hyperbolic Systems ◽  
Null Controllability ◽  
Convolution Theorem ◽  
Backstepping Method ◽  
Technical Point ◽  
One Dimensional ◽  
First Order ◽  
Minimal Time ◽  
Finite Time Stabilization

The goal of this article is to present the minimal time needed for the null controllability and finite-time stabilization of one-dimensional first-order 2×2 linear hyperbolic systems. The main technical point is to show that we cannot obtain a better time. The proof combines the backstepping method with the Titchmarsh convolution theorem.

Francoanellit K3Al5HPO4)6(PO4)2 · 12H2O: Struktur und Synthese durch topochemische Entwässerung von Taranakit / Francoanellite K3Al5HPO4)6(PO4)2 · 12H2O: Structure and Synthesis by Topochemical Dehydration of Taranakite

1998 ◽  
Vol 53 (7) ◽  
pp. 711-719 ◽  
Author(s):  
Stefan Dick ◽  
Thomas Zeiske
Keyword(s):  
Hydrogen Bonds ◽  
Layer Structure ◽  
Intermediate Stage ◽  
Crystallographic Axis ◽  
One Dimensional ◽  
X Ray ◽  
First Order ◽  
Neutron Scattering Experiment ◽  
Rigid Layer ◽  
First Time

Abstract Single crystals of synthetic francoanellite K3Al5(HPO4)6(PO4)2-12H2O could be obtained for the first time by topochemical dehydration of taranakite crystals. An X-ray structure determination showed francoanellite to be the mineral with the second longest crystallographic axis described hitherto. Crystal data: space group R3c, a = 869.0(2), c = 8227(1)pm, Z = 6 , Rg = 0.042. Francoanellite is a layer structure mineral having six layers of composition [K3Al5(HPO4)6(PO4)2(H2O)12], connected by hydrogen bonds. The rigid layer is formed by columns of corner sharing hydrogen phosphate tetrahedra and AIO6-octahedra which are inter­ connected by additional six-coordinated Al ions. In trigonal holes of the layer orthophosphate ions are situated. The structure of francoanellite is very similar to the structure of taranakite K3H6Al5(PO4) 8 · 18H2O which has planar water interlayers between the Al-phosphate layers. A neutron scattering experiment with subsequent Rietveld refinement of the powder pattern gave the H-atom positions. Hydrogen bonds in francoanellite are formed within the rigid layers and between them.During the reaction taranakite → francoanellite crystals in an intermediate stage of dehydration could be obtained. From the c-axis of 8858 pm and one-dimensional electron density projections it can be proposed that in these crystals every second water interlayer was lost and a first order staging product of the deintercalation of water from taranakite was formed.

2,3-Dihydro-7,8-dihydroxy-3-[(4-methoxyphenyl)methylene]-4H-1-benzopyran-4-one

2006 ◽  
Vol 62 (4) ◽  
pp. o1254-o1256 ◽  
Author(s):  
Suchada Chantrapromma ◽  
Sompong Boonsri ◽  
Hoong-Kun Fun ◽  
Shazia Anjum ◽  
Akkharawit Kanjana-opas
Keyword(s):  
Hydrogen Bonds ◽  
Intermolecular Interactions ◽  
Title Compound ◽  
Three Dimensional ◽  
Molecular Network ◽  
Pyran Ring ◽  
Intramolecular Hydrogen Bonds ◽  
One Dimensional ◽  
Intramolecular Hydrogen ◽  
First Time

The title compound, also known as intricatinol, C17H14O5, is a homoisoflavanoid that was isolated for the first time from the twigs and stems of Caesalpinia digyna Rottler. The pyran ring is in an envelope form. O—H...O intramolecular hydrogen bonds are observed. Symmetry-related molecules are linked via O—H...O intermolecular interactions to form infinite one-dimensional chains. These chains are interconnected to form a three-dimensional molecular network.

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