symmetry properties
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Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 109
Author(s):  
Roman Cherniha ◽  
Vasyl’ Davydovych ◽  
Joanna Stachowska-Pietka ◽  
Jacek Waniewski

The model for perfused tissue undergoing deformation taking into account the local exchange between tissue and blood and lymphatic systems is presented. The Lie symmetry analysis in order to identify its symmetry properties is applied. Several families of steady-state solutions in closed formulae are derived. An analysis of the impact of the parameter values and boundary conditions on the distribution of hydrostatic pressure, osmotic agent concentration and deformation of perfused tissue is provided applying the solutions obtained in examples describing real-world processes.


2022 ◽  
Author(s):  
Stephen Goldup ◽  
John Maynard ◽  
Peter Gallagher ◽  
David Lozano ◽  
Patrick Butler

Abstract The term chiral was introduced by Lord Kelvin over a century ago to describe objects that are distinct from their own mirror image. Chirality is relevant in many scientific areas, but particularly chemistry because different mirror image forms of a molecule famously have different biological properties. Chirality typically arises in molecules due to a rigidly chiral arrangement of covalently bonded atoms. Less generally appreciated is that molecular chirality can arise when molecules are threaded through one another to create a mechanical bond. For example, when two molecular rings with chemically distinct faces are joined like links in a chain the resulting structure is chiral even when the rings themselves are not. We re-examined the symmetry properties of such mechanically axially chiral catenanes and in doing so identified a straightforward route to these molecules from simple building blocks. This also led to the discovery of a previously overlooked mechanical stereogenic unit that can arise when such a ring encircles a dumbbell-shaped axle to generate a rotaxane. These insights allowed us to produce the first highly enantioenriched axially chiral catenane and the same approach gave access to a molecule containing the newly identified noncanonical axially chiral rotaxane motif. With methods to access these structures in hand, the process of exploring their properties and applications can now begin.


Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 87
Author(s):  
Júlio C. Fabris ◽  
Marcelo H. Alvarenga ◽  
Mahamadou Hamani Daouda ◽  
Hermano Velten

Unimodular gravity is characterized by an extra condition with respect to general relativity, i.e., the determinant of the metric is constant. This extra condition leads to a more restricted class of invariance by coordinate transformation: The symmetry properties of unimodular gravity are governed by the transverse diffeomorphisms. Nevertheless, if the conservation of the energy–momentum tensor is imposed in unimodular gravity, the general relativity theory is recovered with an additional integration constant which is associated to the cosmological term Λ. However, if the energy–momentum tensor is not conserved separately, a new geometric structure appears with potentially observational signatures. In this text, we consider the evolution of gravitational waves in a nonconservative unimodular gravity, showing how it differs from the usual signatures in the standard model. As our main result, we verify that gravitational waves in the nonconservative version of unimodular gravity are strongly amplified during the evolution of the universe.


Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 82
Author(s):  
Jean-Marc Girault ◽  
Sébastien Ménigot

Today, the palindromic analysis of biological sequences, based exclusively on the study of “mirror” symmetry properties, is almost unavoidable. However, other types of symmetry, such as those present in friezes, could allow us to analyze binary sequences from another point of view. New tools, such as symmetropy and symmentropy, based on new types of palindromes allow us to discriminate binarized 1/f noise sequences better than Lempel–Ziv complexity. These new palindromes with new types of symmetry also allow for better discrimination of binarized DNA sequences. A relative error of 6% of symmetropy is obtained from the HUMHBB and YEAST1 DNA sequences. A factor of 4 between the slopes obtained from the linear fits of the local symmentropies for the two DNA sequences shows the discriminative capacity of the local symmentropy. Moreover, it is highlighted that a certain number of these new palindromes of sizes greater than 30 bits are more discriminating than those of smaller sizes assimilated to those from an independent and identically distributed random variable.


Symmetry ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 49
Author(s):  
Barun Halder ◽  
Suranjana Ghosh ◽  
Pradosh Basu ◽  
Jayanta Bera ◽  
Boris Malomed ◽  
...  

We address dynamics of Bose-Einstein condensates (BECs) loaded into a one-dimensional four-color optical lattice (FOL) potential with commensurate wavelengths and tunable intensities. This configuration lends system-specific symmetry properties. The analysis identifies specific multi-parameter forms of the FOL potential which admits exact solitary-wave solutions. This newly found class of potentials includes more particular species, such as frustrated double-well superlattices, and bichromatic and three-color lattices, which are subject to respective symmetry constraints. Our exact solutions provide options for controllable positioning of density maxima of the localized patterns, and tunable Anderson-like localization in the frustrated potential. A numerical analysis is performed to establish dynamical stability and structural stability of the obtained solutions, which makes them relevant for experimental realization. The newly found solutions offer applications to the design of schemes for quantum simulations and processing quantum information.


2021 ◽  
Author(s):  
Xiao-Xing Su ◽  
D zi long ◽  
Heow Pueh Lee

Abstract The stimulated Brillouin scatterings (SBSs) in the sub-wavelength rutile waveguides with slightly misaligned material and structural axes are numerically studied. The misalignment is introduced between the extraordinary material axis and longitudinal axis of the waveguide only. Four nanowire waveguides with different cross-sectional geometries are considered. They consist of a circular waveguide, two elliptical waveguides with different cross-sectional orientation angles, and a trapezoidal waveguide with a completely unsymmetrical cross-sectional shape. As reported earlier, the resonant peaks emerging rapidly in response to the introduced small misalignment angle can also be observed in the calculated Brillouin gain spectra of the considered waveguides. But these misalignment-sensitive resonant peaks further exhibit some extraordinary behaviors, which may not be intuitively understandable. For instance, despite a plausible absence of symmetry breaking, many misalignment-sensitive resonant peaks can still be observed in the forward SBS gain spectrum of the trapezoidal waveguide. Based on the symmetry properties of the considered waveguides, the physics underlying the observed extraordinary phenomena are revealed. The obtained results highlight the effectiveness of introducing symmetry breakings for activating/harnessing opto-mechanical couplings in photonic-phononic micro structures, which would enable us to gain some deeper insights into the sub-wavelength opto-mechanics in anisotropic media.


2021 ◽  
Author(s):  
John Maynard ◽  
Peter Gallagher ◽  
David Lozano ◽  
Patrick Butler ◽  
Steve Goldup

Chirality, the property of objects that are distinct from their own mirror image, is important in many scientific areas but particularly chemistry, where the appearance of molecular chirality because of rigid arrangements of atoms in space famously influences a molecule’s biological properties. Less generally appreciated is that two molecular rings with chemically distinct faces combined like links in a chain results in a chiral structure even when the rings are achiral. To date, no enantiopure examples of such mechanically axially chiral catenanes has been reported. We re-examined the symmetry properties of the mechanically axially chiral motif and identified a straightforward route to such molecules from simple building blocks. We also identify that common representations of axially chiral catenanes obscure that a previously overlooked stereogenic unit arises when a ring is threaded onto a dumbbell-shaped molecule to generate a rotaxane. These insights allowed us to demonstrate the first stereoselective syntheses of an axially chiral catenane and a noncanonical axially chiral rotaxane motif. With methods to access these structures in hand, the process of exploring their properties and applications can now begin.


2021 ◽  
Author(s):  
John Maynard ◽  
Peter Gallagher ◽  
David Lozano ◽  
Patrick Butler ◽  
Steve Goldup

Chirality, the property of objects that are distinct from their own mirror image, is important in many scientific areas but particularly chemistry, where the appearance of molecular chirality because of rigid arrangements of atoms in space famously influences a molecule’s biological properties. Less generally appreciated is that two molecular rings with chemically distinct faces combined like links in a chain results in a chiral structure even when the rings are achiral. To date, no enantiopure examples of such mechanically axially chiral catenanes has been reported. We re-examined the symmetry properties of the mechanically axially chiral motif and identified a straightforward route to such molecules from simple building blocks. We also identify that common representations of axially chiral catenanes obscure that a previously overlooked stereogenic unit arises when a ring is threaded onto a dumbbell-shaped molecule to generate a rotaxane. These insights allowed us to demonstrate the first stereoselective syntheses of an axially chiral catenane and a noncanonical axially chiral rotaxane motif. With methods to access these structures in hand, the process of exploring their properties and applications can now begin.


2021 ◽  
Author(s):  
John Maynard ◽  
Peter Gallagher ◽  
David Lozano ◽  
Patrick Butler ◽  
Steve Goldup

Chirality, the property of objects that are distinct from their own mirror image, is important in many scientific areas but particularly chemistry, where the appearance of molecular chirality because of rigid arrangements of atoms in space famously influences a molecule’s biological properties. Less generally appreciated is that two molecular rings with chemically distinct faces combined like links in a chain results in a chiral structure even when the rings are achiral. To date, no enantiopure examples of such mechanically axially chiral catenanes has been reported. We re-examined the symmetry properties of the mechanically axially chiral motif and identified a straightforward route to such molecules from simple building blocks. We also identify that common representations of axially chiral catenanes obscure that a previously overlooked stereogenic unit arises when a ring is threaded onto a dumbbell-shaped molecule to generate a rotaxane. These insights allowed us to demonstrate the first stereoselective syntheses of an axially chiral catenane and a noncanonical axially chiral rotaxane motif. With methods to access these structures in hand, the process of exploring their properties and applications can now begin.


Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2250
Author(s):  
Thidaporn Seangwattana ◽  
Kamonrat Sombut ◽  
Areerat Arunchai ◽  
Kanokwan Sitthithakerngkiet

The goal of this study was to show how a modified variational inclusion problem can be solved based on Tseng’s method. In this study, we propose a modified Tseng’s method and increase the reliability of the proposed method. This method is to modify the relaxed inertial Tseng’s method by using certain conditions and the parallel technique. We also prove a weak convergence theorem under appropriate assumptions and some symmetry properties and then provide numerical experiments to demonstrate the convergence behavior of the proposed method. Moreover, the proposed method is used for image restoration technology, which takes a corrupt/noisy image and estimates the clean, original image. Finally, we show the signal-to-noise ratio (SNR) to guarantee image quality.


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