Symmetry

3091 KiB

Open AccessLetter

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 4149

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)

► Show Figures

Figure 1

303 KiB

Open AccessArticle

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 3835

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

Open AccessArticle

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 5173

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)

► Show Figures

Figure 1

420 KiB

Open AccessArticle

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 4399

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 \to

0 leaves behind a spontaneous breakdown of the time reversal symmetry. Full article

(This article belongs to the Special Issue Discrete Symmetries)

► Show Figures

Figure 1

359 KiB

Open AccessCommentary

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 3534

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

Open AccessReply

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 3470

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

Open AccessArticle

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 3437

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

Open AccessArticle

Anomalous Mirror Symmetry Generated by Optical Illusion

by Kokichi Sugihara

Symmetry 2016, 8(4), 21; https://doi.org/10.3390/sym8040021 - 08 Apr 2016

Cited by 10 | Viewed by 17300

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)

► Show Figures

Figure 1

3772 KiB

Open AccessArticle

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 - 05 Apr 2016

Cited by 5 | Viewed by 5063

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)

► Show Figures

Figure 1

238 KiB

Open AccessArticle

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 3810

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

Open AccessArticle

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 3632

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

(This article belongs to the Special Issue Symmetry in the Numerical Resolution of the Elliptic Monge-Ampere Equation)

Journal Menu

Journal Browser

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

Further Information

Guidelines

MDPI Initiatives

Follow MDPI