scholarly journals A Stress Analysis of Some Fundamental Specimens of Soft-Matter Quasicrystals with Eightfold Symmetry Based on Generalized Dynamics

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Fang Wang ◽  
Hui Cheng ◽  
Tian-You Fan ◽  
Hai-Yun Hu
Keyword(s):  
Symmetry Breaking ◽  
Stress Analysis ◽  
Soft Matter ◽  
Intermediate Phase ◽  
Equations Of Motion ◽  
Initial Boundary ◽  
Elementary Excitation ◽  
High Symmetry ◽  
Plane Field ◽  
Time Space

This paper reports a stress analysis of some fundamental samples made of soft-matter quasicrystals with 8-fold symmetry based on the generalized dynamics. The most distinction from the hydrodynamics for solid quasicrystals is that the structure of soft matter belongs to a complex liquid, which is an intermediate phase between solid and liquid and behaves natures of both solid and liquid. In addition, the soft-matter quasicrystals possess high symmetry, and the symmetry breaking is of fundamental importance. So the Landau symmetry breaking theory and elementary excitation principle are therefore the paradigm of the study of soft-matter quasicrystals. Soft-matter quasicrystals belong to the complex fluid, in which the fluid phonon elementary excitation is introduced apart from the phonon and phason elementary excitations. With this model and the equation of state, the equations of motion for possible soft-matter quasicrystals of 8-fold symmetry are derived. The initial boundary value problems for the xy plane field are solved by applying the finite difference method, in which the z-direction represents the 8-fold symmetry axis. A complete hydrodynamics analysis is given to quantitatively explore the phonon, phason, and fluid fields as well as their interactions in the physical time-space domain. The analysis shows the governing equations are exact to the prediction of the dynamics of soft-matter quasicrystals. The computational results reveal the gigantic differences of physical properties between solid and soft-matter quasicrystals.

scholarly journals Symmetry breaking in particle-forming diblock polymer/homopolymer blends

2020 ◽  
Vol 117 (29) ◽  
pp. 16764-16769 ◽  
Author(s):  
Guo Kang Cheong ◽  
Frank S. Bates ◽  
Kevin D. Dorfman
Keyword(s):  
Symmetry Breaking ◽  
Phase Behavior ◽  
Soft Matter ◽  
Diblock Copolymers ◽  
Particle Analysis ◽  
Uniform Density ◽  
High Symmetry ◽  
Block Polymer ◽  
Self Consistent Field ◽  
Self Consistent Field Theory

Compositionally asymmetric diblock copolymers provide an attractive platform for understanding the emergence of tetragonally close-packed, Frank–Kasper phases in soft matter. Block-polymer phase behavior is governed by a straightforward competition between chain stretching and interfacial tension under the constraint of filling space at uniform density. Experiments have revealed that diblock copolymers with insufficient conformational asymmetry to form Frank–Kasper phases in the neat-melt state undergo an interconversion from body-centered cubic (bcc) close-packed micelles to a succession of Frank–Kasper phases (σ to C14 to C15) upon the addition of minority-block homopolymer in the dry-brush regime, accompanied by the expected transition from bcc to hexagonally packed cylinders in the wet-brush regime. Self-consistent field theory data presented here qualitatively reproduce the salient features of the experimental phase behavior. A particle-by-particle analysis of homopolymer partitioning furnishes a basis for understanding the symmetry breaking from the high-symmetry bcc phase to the lower-symmetry Frank–Kasper phases, wherein the reconfiguration of the system into polyhedra of increasing volume asymmetry delays the onset of macroscopic phase separation.

Dynamic analysis of second kind soft-matter quasicrystals of point group 14mm

2019 ◽  
Vol 33 (13) ◽  
pp. 1950154
Author(s):  
Fang Wang ◽  
Tian You Fan ◽  
Hui Cheng ◽  
Zhu Feng Sun
Keyword(s):  
Time Domain ◽  
Soft Matter ◽  
Equations Of Motion ◽  
Point Group ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Group 14 ◽  
Elementary Excitations ◽  
The Finite Difference Method ◽  
Initial Boundary Value

The hydrodynamic model for soft-matter quasicrystals with 14-fold symmetry is investigated. The 14-fold symmetry soft-matter quasicrystals belong to the second kind of soft-matter quasicrystals. The most distinction between the first and the second kinds of the soft-matter quasicrystals lies in the four elementary excitations including two phason elementary excitations exist for the latter. The equations of motion for point group 14 mm soft-matter qusicrystals are given, and an initial-boundary value problem of the equations is solved by applying the finite difference method. The effects of the phonons, first phasons, second phasons, fluid phonon and their interactions in space-time domain are explored.

scholarly journals FORCED RESPONSE VIBRATION OF SIMPLY SUPPORTED BEAMS WITH AN ELASTIC PASTERNAK FOUNDATION UNDER A DISTRIBUTED MOVING LOAD

2020 ◽  
Vol 4 (2) ◽  
pp. 1-7
Author(s):  
Fatai Hammed ◽  
M. A. Usman ◽  
S. A. Onitilo ◽  
F. A. Alade ◽  
K. A. Omoteso
Keyword(s):  
Shear Modulus ◽  
Moving Load ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Forced Response ◽  
Dynamic Responses ◽  
Moving Force ◽  
Pasternak Elastic Foundation

In this study, the response of two homogeneous parallel beams with two-parameter Pasternak elastic foundation subjected to a constant uniform partially distributed moving force is considered. On the basis of Euler-Bernoulli beam theory, the fourth order partial differential equations of motion describing the behavior of the beams when subjected to a moving force were formulated. In order to solve the resulting initial-boundary value problem, finite Fourier sine integral technique and differential transform scheme were employed to obtain the analytical solution. The dynamic responses of the two beams obtained was investigated under moving force conditions using MATLAB. The effects of speed of the moving force, layer parameters such as stiffness (K_0) and shear modulus (G_0 ) have been conducted for the moving force. Various values of speed of the moving load, stiffness parameters and shear modulus were considered. The results obtained indicates that response amplitudes of both the upper and lower beams increases with increase in the speed of the moving load. Increasing the stiffness parameter is observed to cause a decrease in the response amplitudes of the beams. The response amplitudes decreases with increase in the shear modulus of the linear elastic layer.

scholarly journals Spectral signatures of high-symmetry quantum dots and effects of symmetry breaking

2015 ◽  
Vol 17 (10) ◽  
pp. 103017 ◽  
Author(s):  
K F Karlsson ◽  
D Y Oberli ◽  
M A Dupertuis ◽  
V Troncale ◽  
M Byszewski ◽  
...  
Keyword(s):  
Quantum Dots ◽  
Symmetry Breaking ◽  
High Symmetry ◽  
Spectral Signatures

scholarly journals Quantum asymmetry between time and space

2016 ◽  
Vol 472 (2185) ◽  
pp. 20150670 ◽  
Author(s):  
Joan A. Vaccaro
Keyword(s):  
Conservation Laws ◽  
Time Evolution ◽  
Equations Of Motion ◽  
Time And Space ◽  
Physical Systems ◽  
Conventional View ◽  
Time Space ◽  
T Violation ◽  
The Asymmetry ◽  
Over Time

An asymmetry exists between time and space in the sense that physical systems inevitably evolve over time, whereas there is no corresponding ubiquitous translation over space. The asymmetry, which is presumed to be elemental , is represented by equations of motion and conservation laws that operate differently over time and space. If, however, the asymmetry was found to be due to deeper causes, this conventional view of time evolution would need reworking. Here we show, using a sum-over-paths formalism, that a violation of time reversal (T) symmetry might be such a cause. If T symmetry is obeyed, then the formalism treats time and space symmetrically such that states of matter are localized both in space and in time. In this case, equations of motion and conservation laws are undefined or inapplicable. However, if T symmetry is violated, then the same sum over paths formalism yields states that are localized in space and distributed without bound over time, creating an asymmetry between time and space. Moreover, the states satisfy an equation of motion (the Schrödinger equation) and conservation laws apply. This suggests that the time–space asymmetry is not elemental as currently presumed, and that T violation may have a deep connection with time evolution.

scholarly journals The Jahn–Teller and Pseudo-Jahn–Teller Effects: A Unique and Only Source of Spontaneous Symmetry Breaking in Atomic Matter

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1577
Author(s):  
Isaac B. Bersuker
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
External Perturbation ◽  
Broken Symmetry ◽  
High Symmetry ◽  
Atomic Systems ◽  
Jahn Teller ◽  
Curie Principle ◽  
Adiabatic Potential Energy Surface ◽  
Definition Of

In a mostly review paper, we show that the important problem of symmetry, broken symmetry, and spontaneous broken symmetry of polyatomic systems is directly related to the Jahn–Teller (JT) and pseudo-Jahn–Teller (PJT) effects, including the hidden-JT and hidden-PJT effects, and these JT effects (JTEs) are the only source of spontaneous symmetry breaking in matter. They are directly related to the violation of the adiabatic approximation by the vibronic and other nonadiabatic couplings (jointly termed nonadiabaticity) in the interaction between the electrons and nuclei, which becomes significant in the presence of two or more degenerate or pseudodegenerate electronic states. In a generalization of this understanding of symmetry, we suggest an improved (quantum) definition of stereo-chemical polyatomic space configuration, in which, starting with their high-symmetry configuration, we separate all atomic systems into three distinguishable groups: (1) weak nonadiabaticity, stable high-symmetry configurations; (2) moderate-to-strong nonadiabaticity, unstable high-symmetry configurations, JTEs, spontaneous symmetry breaking (SSB); (3) very strong nonadiabaticity, stable distorted configurations. The JTEs, inherent to the second group of systems, produce a rich variety of novel properties, based on their multiminimum adiabatic potential energy surface (APES), leading to a short lifetime in the distorted configuration. We show the role of the Curie principle in the possibilities to observe the SSB in atomic matter, and mention briefly the revealed recently gamma of novel properties of matter in its interaction with external perturbation that occur due to the SSB, including ferroelectricity and orientational polarization, leading to enhanced permittivity and flexoelectricity.

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