scholarly journals Invariant characterization of scalar third-order ODEs that admit the maximal point symmetry Lie algebra

2018 ◽  
Vol 41 (12) ◽  
pp. 4714-4723 ◽  
Author(s):  
Ahmad Y. Al-Dweik ◽  
M. T. Mustafa ◽  
Fazal Mahmood Mahomed
Keyword(s):  
Lie Algebra ◽  
Point Symmetry ◽  
Third Order ◽  
Maximal Point ◽  
Invariant Characterization

scholarly journals On the similarity to nonnegative and Metzler Hessenberg forms

2021 ◽  
Vol 10 (1) ◽  
pp. 1-8
Author(s):  
Christian Grussler ◽  
Anders Rantzer
Keyword(s):  
Standard Form ◽  
Complete Characterization ◽  
Nonnegative Matrices ◽  
Positive Systems ◽  
Third Order ◽  
Hessenberg Form ◽  
Hessenberg Matrices ◽  
Open Question ◽  
Order Continuous

Abstract We address the issue of establishing standard forms for nonnegative and Metzler matrices by considering their similarity to nonnegative and Metzler Hessenberg matrices. It is shown that for dimensions n 3, there always exists a subset of nonnegative matrices that are not similar to a nonnegative Hessenberg form, which in case of n = 3 also provides a complete characterization of all such matrices. For Metzler matrices, we further establish that they are similar to Metzler Hessenberg matrices if n 4. In particular, this provides the first standard form for controllable third order continuous-time positive systems via a positive controller-Hessenberg form. Finally, we present an example which illustrates why this result is not easily transferred to discrete-time positive systems. While many of our supplementary results are proven in general, it remains an open question if Metzler matrices of dimensions n 5 remain similar to Metzler Hessenberg matrices.

scholarly journals Numerical Characterization of Cohesive and Non-Cohesive ‘Sediments’ under Different Consolidation States Using 3D DEM Triaxial Experiments

Processes ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1252
Author(s):  
Hadar Elyashiv ◽  
Revital Bookman ◽  
Lennart Siemann ◽  
Uri ten Brink ◽  
Katrin Huhn
Keyword(s):  
Mechanical Response ◽  
Burial Depth ◽  
Cohesive Sediments ◽  
Third Order ◽  
First Order ◽  
Numerical Characterization ◽  
Response To Stress ◽  
Bond Strengths ◽  
Individual Bond

The Discrete Element Method has been widely used to simulate geo-materials due to time and scale limitations met in the field and laboratories. While cohesionless geo-materials were the focus of many previous studies, the deformation of cohesive geo-materials in 3D remained poorly characterized. Here, we aimed to generate a range of numerical ‘sediments’, assess their mechanical response to stress and compare their response with laboratory tests, focusing on differences between the micro- and macro-material properties. We simulated two endmembers—clay (cohesive) and sand (cohesionless). The materials were tested in a 3D triaxial numerical setup, under different simulated burial stresses and consolidation states. Variations in particle contact or individual bond strengths generate first order influence on the stress–strain response, i.e., a different deformation style of the numerical sand or clay. Increased burial depth generates a second order influence, elevating peak shear strength. Loose and dense consolidation states generate a third order influence of the endmember level. The results replicate a range of sediment compositions, empirical behaviors and conditions. We propose a procedure to characterize sediments numerically. The numerical ‘sediments’ can be applied to simulate processes in sediments exhibiting variations in strength due to post-seismic consolidation, bioturbation or variations in sedimentation rates.

Crystal growth and characterization of semi-organic 2-amino-5-nitropyridinium bromide (2A5NPBr) single crystals for third-order nonlinear optical (NLO) applications

2017 ◽  
Vol 123 (12) ◽  
Author(s):  
Sivasubramani Vediyappan ◽  
Raja Arumugam ◽  
Karuppasamy Pichan ◽  
Ramachandran Kasthuri ◽  
Senthil Pandian Muthu ◽  
...  
Keyword(s):  
Crystal Growth ◽  
Single Crystals ◽  
Nonlinear Optical ◽  
Third Order

Growth and characterization of third-order nonlinear optical lithium hydrogen maleate dihydrate single-crystal

2018 ◽  
Vol 32 (31) ◽  
pp. 1850351 ◽  
Author(s):  
S. Karuna ◽  
A. R. Balu ◽  
D. Shyamala ◽  
V. S. Nagarethinam ◽  
Z. Delci
Keyword(s):  
Nonlinear Optical ◽  
Damage Threshold ◽  
Laser Damage Threshold ◽  
Bandgap Energy ◽  
Third Order ◽  
Laser Applications ◽  
Nonlinear Characteristics ◽  
Dta Analysis ◽  
Optical Behavior

A third-order nonlinear optical crystal of lithium hydrogen maleate dihydrate (LHMD) is grown by the process of slow evaporation at room-temperature. The LHMD crystal system is orthorhombic and is a member of P space group. Using FTIR spectral investigation, the presence of main functional groups in LHMD crystal is identified. The optical behavior of the crystal is determined by UV-Visible spectroscopy. The bandgap energy of the LHMD crystal is calculated to be 3.4 eV. By Vickers microhardness measurements, the mechanical behavior has been assessed. The melting point of LHMD is determined by TG-DTA analysis. The defects present in the LHMD crystal are studied by dielectric loss and dielectric constant. SHG studies are performed for the LHMD crystal by Kurtz and Perry method. The third-order nonlinear characteristics of the LHMD crystal are analyzed by Z-scan technique. The laser damage threshold (LDT) study is carried out to verify the suitability of the crystal for laser applications.

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