Symmetric Structures

2022 ◽  
pp. 185-186
Keyword(s):  
Symmetric Structures

scholarly journals Odd Willis coupling induced by broken time-reversal symmetry

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Li Quan ◽  
Simon Yves ◽  
Yugui Peng ◽  
Hussein Esfahlani ◽  
Andrea Alù
Keyword(s):  
Time Reversal ◽  
Time Reversal Symmetry ◽  
Acoustic Metamaterials ◽  
Asymmetric Structures ◽  
Sound Control ◽  
Wavefront Shaping ◽  
Scattering Response ◽  
Symmetric Structures ◽  
Signal Routing ◽  
Broad Interest

AbstractWhen sound interacts with geometrically asymmetric structures, it experiences coupling between pressure and particle velocity, known as Willis coupling. While in most instances this phenomenon is perturbative in nature, tailored asymmetries combined with resonances can largely enhance it, enabling exotic acoustic phenomena. In these systems, Willis coupling obeys reciprocity, imposing an even symmetry of the Willis coefficients with respect to time reversal and the impinging wave vector, which translates into stringent constraints on the overall scattering response. In this work, we introduce and experimentally observe a dual form of acoustic Willis coupling, arising in geometrically symmetric structures when time-reversal symmetry is broken, for which the pressure-velocity coupling is purely odd-symmetric. We derive the conditions to maximize this effect, we experimentally verify it in a symmetric subwavelength scatterer biased by angular momentum, and we demonstrate the opportunities for sound scattering enabled by odd Willis coupling. Our study opens directions for acoustic metamaterials, with direct implications for sound control, non-reciprocal scattering, wavefront shaping and signal routing, of broad interest also for nano-optics, photonics, elasto-dynamics, and mechanics.

scholarly journals Newtonian Fractional-dimension Gravity and Rotationally Supported Galaxies

2021 ◽  
Author(s):  
Gabriele U Varieschi
Keyword(s):  
Fractional Dimension ◽  
Newtonian Gravity ◽  
Axially Symmetric ◽  
Local Dimension ◽  
Radial Acceleration ◽  
Modified Newtonian Dynamics ◽  
Newtonian Dynamics ◽  
The Subject ◽  
Symmetric Structures ◽  
Natural Scale

Abstract We continue our analysis of Newtonian Fractional-Dimension Gravity, an extension of the standard laws of Newtonian gravity to lower dimensional spaces including those with fractional (i.e., non-integer) dimension. We apply our model to three rotationally supported galaxies: NGC 7814 (Bulge-Dominated Spiral), NGC 6503 (Disk-Dominated Spiral), and NGC 3741 (Gas-Dominated Dwarf). As was done in the general cases of spherically-symmetric and axially-symmetric structures, which were studied in previous work on the subject, we examine a possible connection between our model and Modified Newtonian Dynamics, a leading alternative gravity model which explains the observed properties of these galaxies without requiring the Dark Matter hypothesis. In our model, the MOND acceleration constant a0 ≃ 1.2 × 10−10m s−2 can be related to a natural scale length l0, namely $a_{0} \approx GM/l_{0}^{2}$ for a galaxy of mass M. Also, the empirical Radial Acceleration Relation, connecting the observed radial acceleration gobs with the baryonic one gbar, can be explained in terms of a variable local dimension D. As an example of this methodology, we provide detailed rotation curve fits for the three galaxies mentioned above.

scholarly journals Associative Superalgebras with Homogeneous Symmetric Structures

2012 ◽  
Vol 40 (4) ◽  
pp. 1234-1259 ◽  
Author(s):  
Imen Ayadi ◽  
Saïd Benayadi
Keyword(s):  
Symmetric Structures

High Resolution Sequence Stratigraphic Frameworks Research in the XII Group of the Member III of Qing Shankou Formation in the Qian'an Oilfield

2013 ◽  
Vol 339 ◽  
pp. 728-731 ◽  
Author(s):  
Cun Lei Li ◽  
Lei Qin ◽  
Xue Li ◽  
Xi Long Zhang
Keyword(s):  
High Resolution ◽  
Stratigraphic Correlation ◽  
Short Term ◽  
Middle Term ◽  
Sequence Stratigraphic ◽  
Base Level ◽  
Mud Logging ◽  
High Resolution Sequence Stratigraphy ◽  
Symmetric Structures

With the instruction of the high resolution sequence stratigraphy and sedimentology theory, and the comprehensive application of 11 wells core, more than 800 mud logging and log data, high resolution sequence stratigraphic characteristics research in the XII Group of the Member III of Qing Shankou Formation in the Qianan oilfield has been finished. The results show that the study area can be divided into one middle-term base level cycle and five short-term base level cycles. The only sequence structure of middle term cycle is (B type) and the short term cycle mainly consists of B types meanwhile there are small mounts of upward deepening structures (A type) and symmetric structures (C type). Based on the classification of base-level cycles, fine stratigraphic correlation is conducted by using isochronous cycle correlations. In addition, 15 high resolution sequence stratigraphic frameworks are established which unify the study area and provide the solid geological basis for the sandstone distribution, the identification of mainly oil-bearing sand bodies and potential oil reservoirs.

Tris(Pyridinium)Triazine in Crystal Synthesis of 3-Fold Symmetric Structures

2005 ◽  
Vol 5 (2) ◽  
pp. 681-693 ◽  
Author(s):  
Thomas J. Podesta ◽  
A. Guy Orpen
Keyword(s):  
Crystal Synthesis ◽  
Symmetric Structures

scholarly journals TRACKING DOWN LOCALIZED MODES IN PT-SYMMETRIC HAMILTONIANS UNDER THE INFLUENCE OF A COMPETING NONLINEARITY

2014 ◽  
Vol 54 (2) ◽  
pp. 79-84 ◽  
Author(s):  
Bijan Bagchi ◽  
Subhrajit Modak ◽  
Prasanta K. Panigrahi
Keyword(s):  
Growth Rate ◽  
Refractive Index ◽  
Stability Analysis ◽  
Linear Stability Analysis ◽  
Time Reversal ◽  
Time Parameter ◽  
Optical Systems ◽  
Localized Modes ◽  
Symmetric Structures ◽  
Schrödinger System

The relevance of parity and time reversal (PT)-symmetric structures in optical systems has been known for some time with the correspondence existing between the Schrödinger equation and the paraxial equation of diffraction, where the time parameter represents the propagating distance and the refractive index acts as the complex potential. In this paper, we systematically analyze a normalized form of the nonlinear Schrödinger system with two new families of PT-symmetric potentials in the presence of competing nonlinearities. We generate a class of localized eigenmodes and carry out a linear stability analysis on the solutions. In particular, we find an interesting feature of bifurcation characterized by the parameter of perturbative growth rate passing through zero, where a transition to imaginary eigenvalues occurs.

Forced Harmonic Response of Grouped Blade Systems: Part II—Application

1996 ◽  
Vol 118 (1) ◽  
pp. 137-145 ◽  
Author(s):  
L. F. Wagner ◽  
J. H. Griffin
Keyword(s):  
Numerical Model ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Turbine Blades ◽  
Modal Identification ◽  
Harmonic Response ◽  
Model Based ◽  
Grouped Blades ◽  
Flexible Disk ◽  
Symmetric Structures

The vibration of grouped blades on a flexible disk should, for purposes of economy and clarity of modal identification, be analyzed using procedures developed for cyclically symmetric structures. In this paper, a numerical model, based on the theory of cyclically symmetric structures, is applied to the vibration analysis, and in particular, the harmonic response, of a flexible disk supporting a number of groups, or packets, of turbine blades. Results are presented to show variations in the modal participation factors as a function of such parameters as disk flexibility, blade density, and the total number of assembled groups. It is also shown that many characteristics of the system spectra of natural frequencies are strongly dependent on the number of blade groups.

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