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Symmetry, Volume 8, Issue 4 (April 2016) – 11 articles

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3091 KiB  
Letter
An Ultrasonic Lens Design Based on Prefractal Structures
by Sergio Castiñeira-Ibáñez, Daniel Tarrazó-Serrano, Constanza Rubio, Pilar Candelas and Antonio Uris
Symmetry 2016, 8(4), 28; https://doi.org/10.3390/sym8040028 - 21 Apr 2016
Cited by 8 | Viewed by 4266
Abstract
The improvement in focusing capabilities of a set of annular scatterers arranged in a fractal geometry is theoretically quantified in this work by means of the finite element method (FEM). Two different arrangements of rigid rings in water are used in the analysis. [...] Read more.
The improvement in focusing capabilities of a set of annular scatterers arranged in a fractal geometry is theoretically quantified in this work by means of the finite element method (FEM). Two different arrangements of rigid rings in water are used in the analysis. Thus, both a Fresnel ultrasonic lens and an arrangement of rigid rings based on Cantor prefractals are analyzed. Results show that the focusing capacity of the modified fractal lens is better than the Fresnel lens. This new lens is believed to have potential applications for ultrasonic imaging and medical ultrasound fields. Full article
(This article belongs to the Special Issue Symmetry and Fractals)
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303 KiB  
Article
E-Polytopes in Picard Groups of Smooth Rational Surfaces
by Jae-Hyouk Lee and YongJoo Shin
Symmetry 2016, 8(4), 27; https://doi.org/10.3390/sym8040027 - 20 Apr 2016
Cited by 2 | Viewed by 3915
Abstract
In this article, we introduce special divisors (root, line, ruling, exceptional system and rational quartic) in smooth rational surfaces and study their correspondences to subpolytopes in Gosset polytopes k 21 . We also show that the sets of rulings and exceptional systems correspond [...] Read more.
In this article, we introduce special divisors (root, line, ruling, exceptional system and rational quartic) in smooth rational surfaces and study their correspondences to subpolytopes in Gosset polytopes k 21 . We also show that the sets of rulings and exceptional systems correspond equivariantly to the vertices of 2 k 1 and 1 k 2 via E-type Weyl action. Full article
(This article belongs to the Special Issue Symmetry and Duality)
5333 KiB  
Article
Chiral Symmetry and the Nucleon-Nucleon Interaction
by Ruprecht Machleidt
Symmetry 2016, 8(4), 26; https://doi.org/10.3390/sym8040026 - 20 Apr 2016
Cited by 7 | Viewed by 5303
Abstract
We review how nuclear forces emerge from low-energy quantum chromodynamics (QCD) via chiral effective field theory (EFT). During the past two decades, this approach has evolved into a powerful tool to derive nuclear two- and many-body forces in a systematic and model-independent way. [...] Read more.
We review how nuclear forces emerge from low-energy quantum chromodynamics (QCD) via chiral effective field theory (EFT). During the past two decades, this approach has evolved into a powerful tool to derive nuclear two- and many-body forces in a systematic and model-independent way. We then focus on the nucleon-nucleon (N N) interaction and show in detail how, governed by chiral symmetry, the long- and intermediate-range of the N N potential builds up order by order. We proceed up to sixth order in small momenta, where convergence is achieved. The final result allows for a full assessment of the validity of the chiral EFT approach to the N N interaction. Full article
(This article belongs to the Special Issue Symmetry in Hadrons and Nuclei)
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420 KiB  
Article
Spontaneous Breakdown of the Time Reversal Symmetry
by Janos Polonyi
Symmetry 2016, 8(4), 25; https://doi.org/10.3390/sym8040025 - 20 Apr 2016
Cited by 12 | Viewed by 4485
Abstract
The role of the environment initial conditions in the breaking of the time reversal symmetry of effective theories and in generating the soft irreversibility is studied by the help of Closed Time Path formalism. The initial conditions break the time reversal symmetry of [...] Read more.
The role of the environment initial conditions in the breaking of the time reversal symmetry of effective theories and in generating the soft irreversibility is studied by the help of Closed Time Path formalism. The initial conditions break the time reversal symmetry of the solution of the equation of motion in a trivial manner. When open systems are considered then the initial conditions of the environment must be included in the effective dynamics. This is achieved by means of a generalized ϵ-prescription where the non-uniform convergence of the limit ϵ 0 leaves behind a spontaneous breakdown of the time reversal symmetry. Full article
(This article belongs to the Special Issue Discrete Symmetries)
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359 KiB  
Commentary
Comments on Janocha et al. Lie Symmetry Analysis of the Hopf Functional-Differential Equation. Symmetry 2015, 7, 1536–1566
by Michael Frewer and George Khujadze
Symmetry 2016, 8(4), 23; https://doi.org/10.3390/sym8040023 - 18 Apr 2016
Cited by 1 | Viewed by 3590
Abstract
The recent systematic study by Janocha et al. [1] to determine all possible Lie-point symmetries for the functional Hopf–Burgers equation is re-examined. From a more consistent theoretical framework, however, some of the proposed symmetry transformations of the considered Hopf–Burgers equation [...] Read more.
The recent systematic study by Janocha et al. [1] to determine all possible Lie-point symmetries for the functional Hopf–Burgers equation is re-examined. From a more consistent theoretical framework, however, some of the proposed symmetry transformations of the considered Hopf–Burgers equation are in fact rejected. Three out of eight proposed symmetry transformations are invalidated, while two of them should be replaced by their correct intermediate formulations, but which ultimately violate internal consistency constraints of the governing equation. It is concluded that the recently proposed symmetry analysis method for functional integro-differential equations should not be adopted when aiming at a consistent and complete approach. Full article
284 KiB  
Reply
Reply to Frewer et al. Comments on Janocha et al. Lie Symmetry Analysis of the Hopf Functional-Differential Equation. Symmetry 2015, 7, 1536–1566
by Marta Wacławczyk, Daniel D. Janocha and Martin Oberlack
Symmetry 2016, 8(4), 24; https://doi.org/10.3390/sym8040024 - 16 Apr 2016
Cited by 1 | Viewed by 3557
Abstract
We reply to the comment by Frewer and Khujadze regarding our contribution “Lie Symmetry Analysis of the Hopf Functional-Differential Equation” (Symmetry 2015, 7(3), 1536). The method developed by the present authors considered the Lie group analysis of the Hopf equations with functional derivatives [...] Read more.
We reply to the comment by Frewer and Khujadze regarding our contribution “Lie Symmetry Analysis of the Hopf Functional-Differential Equation” (Symmetry 2015, 7(3), 1536). The method developed by the present authors considered the Lie group analysis of the Hopf equations with functional derivatives in the equation, not the integro-differential equations in general. It was based on previous contributions (Oberlack and Wacławczyk, Arch. Mech. 2006, 58; Wacławczyk and Oberlack, J. Math. Phys. 2013, 54). In fact, three of the symmetries calculated in (Symmetry 2015, 7(3), 1536) break due to internal consistency constrains and conditions imposed on test functions, the same concerns the corresponding symmetries derived by Frewer and Khujadze and another, spurious symmetry, which was not discussed by Frewer and Khujadze. As a result, the same set of symmetries is obtained with both approaches. Full article
238 KiB  
Article
Local Dynamics in an Infinite Harmonic Chain
by M. Howard Lee
Symmetry 2016, 8(4), 22; https://doi.org/10.3390/sym8040022 - 15 Apr 2016
Cited by 11 | Viewed by 3506
Abstract
By the method of recurrence relations, the time evolution in a local variable in a harmonic chain is obtained. In particular, the autocorrelation function is obtained analytically. Using this result, a number of important dynamical quantities are obtained, including the memory function of [...] Read more.
By the method of recurrence relations, the time evolution in a local variable in a harmonic chain is obtained. In particular, the autocorrelation function is obtained analytically. Using this result, a number of important dynamical quantities are obtained, including the memory function of the generalized Langevin equation. Also studied are the ergodicity and chaos in a local dynamical variable. Full article
(This article belongs to the Special Issue Harmonic Oscillators In Modern Physics)
14765 KiB  
Article
Anomalous Mirror Symmetry Generated by Optical Illusion
by Kokichi Sugihara
Symmetry 2016, 8(4), 21; https://doi.org/10.3390/sym8040021 - 8 Apr 2016
Cited by 10 | Viewed by 17520
Abstract
This paper introduces a new concept of mirror symmetry, called “anomalous mirror symmetry”, which is physically impossible but can be perceived by human vision systems because of optical illusion. This symmetry is characterized geometrically and a method for creating cylindrical surfaces that create [...] Read more.
This paper introduces a new concept of mirror symmetry, called “anomalous mirror symmetry”, which is physically impossible but can be perceived by human vision systems because of optical illusion. This symmetry is characterized geometrically and a method for creating cylindrical surfaces that create this symmetry is constructed. Examples of solid objects constructed by a 3D printer are also shown. Full article
(This article belongs to the Special Issue Symmetry in Vision)
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3772 KiB  
Article
Resource Symmetric Dispatch Model for Internet of Things on Advanced Logistics
by Guofeng Qin, Lisheng Wang and Qiyan Li
Symmetry 2016, 8(4), 20; https://doi.org/10.3390/sym8040020 - 5 Apr 2016
Cited by 6 | Viewed by 5142
Abstract
Business applications in advanced logistics service are highly concurrent. In this paper, we propose a resource symmetric dispatch model for the concurrent and cooperative tasks of the Internet of Things. In the model, the terminals receive and deliver commands, data, and information with [...] Read more.
Business applications in advanced logistics service are highly concurrent. In this paper, we propose a resource symmetric dispatch model for the concurrent and cooperative tasks of the Internet of Things. In the model, the terminals receive and deliver commands, data, and information with mobile networks, wireless networks, and sensor networks. The data and information are classified and processed by the clustering servers in the cloud service platform. The cluster service, resource dispatch, and load balance are cooperative for management and monitoring of every application case during the logistics service lifecycle. In order to support the high performance of cloud service, resource symmetric dispatch algorithm among clustering servers and load balancing method among multi-cores in one server, including NIO (Non-blocking Input/Output) and RMI (Remote Method Invocation) are utilized to dispatch the cooperation of computation and service resources. Full article
(This article belongs to the Special Issue Symmetry in Cooperative Applications)
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238 KiB  
Article
Casorati Inequalities for Submanifolds in a Riemannian Manifold of Quasi-Constant Curvature with a Semi-Symmetric Metric Connection
by Pan Zhang and Liang Zhang
Symmetry 2016, 8(4), 19; https://doi.org/10.3390/sym8040019 - 31 Mar 2016
Cited by 18 | Viewed by 3915
Abstract
By using new algebraic techniques, two Casorati inequalities are established for submanifolds in a Riemannian manifold of quasi-constant curvature with a semi-symmetric metric connection, which generalize inequalities obtained by Lee et al. J. Inequal. Appl. 2014, 2014, 327. Full article
355 KiB  
Article
Convergence Rate of a Stable, Monotone and Consistent Scheme for the Monge-Ampère Equation
by Gerard Awanou
Symmetry 2016, 8(4), 18; https://doi.org/10.3390/sym8040018 - 24 Mar 2016
Cited by 3 | Viewed by 3722
Abstract
We prove a rate of convergence for smooth solutions of the Monge-Ampère equation of a stable, monotone and consistent discretization. We consider the Monge-Ampère equation with a small low order perturbation. With such a perturbation, we can prove uniqueness of a solution to [...] Read more.
We prove a rate of convergence for smooth solutions of the Monge-Ampère equation of a stable, monotone and consistent discretization. We consider the Monge-Ampère equation with a small low order perturbation. With such a perturbation, we can prove uniqueness of a solution to the discrete problem and stability of the discrete solution. The discretization considered is then known to converge to the viscosity solution but no rate of convergence was known. Full article
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