Periodic perturbations with rotational symmetry of planar systems driven by a central force

2018 ◽  
Vol 264 (12) ◽  
pp. 7055-7068 ◽  
Author(s):  
Alessandro Fonda ◽  
Anna Chiara Gallo
Keyword(s):  
Rotational Symmetry ◽  
Central Force ◽  
Periodic Perturbations ◽  
Planar Systems

scholarly journals Bifurcations of planar sliding homoclinics

2006 ◽  
Vol 2006 ◽  
pp. 1-13 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Michal Feckan ◽  
Pawel Olejnik
Keyword(s):  
Sufficient Conditions ◽  
Homoclinic Solutions ◽  
Bounded Solutions ◽  
Periodic Perturbations ◽  
Planar Systems ◽  
Perturbation Problems

We study bifurcations from sliding homoclinic solutions to bounded solutions onℝfor certain discontinuous planar systems under periodic perturbations. Sufficient conditions are derived for such perturbation problems.

scholarly journals Small periodic perturbations of autonomous self-oscillating planar systems

2004 ◽  
Vol 37 (12) ◽  
pp. 363-366
Author(s):  
Mikhail Kamenskii ◽  
Oleg Makarenkov ◽  
Paolo Nistri
Keyword(s):  
Periodic Perturbations ◽  
Planar Systems ◽  
Small Periodic

Comparison of Calculated and Recorded Electron Energy-Loss Spectra of Aluminium and Carbon

1990 ◽  
Vol 48 (2) ◽  
pp. 64-65
Author(s):  
L. Reimer ◽  
R. Oelgeklaus
Keyword(s):  
Fourier Transform ◽  
Energy Loss ◽  
Electron Energy ◽  
Rotational Symmetry ◽  
Mean Free Path ◽  
Single Scattering ◽  
Specimen Thickness ◽  
Two Dimensional ◽  
Image Position ◽  
Electron Energy Loss

Quantitative electron energy-loss spectroscopy (EELS) needs a correction for the limited collection aperture α and a deconvolution of recorded spectra for eliminating the influence of multiple inelastic scattering. Reversely, it is of interest to calculate the influence of multiple scattering on EELS. The distribution f(w,θ,z) of scattered electrons as a function of energy loss w, scattering angle θ and reduced specimen thickness z=t/Λ (Λ=total mean-free-path) can either be recorded by angular-resolved EELS or calculated by a convolution of a normalized single-scattering function ϕ(w,θ). For rotational symmetry in angle (amorphous or polycrystalline specimens) this can be realised by the following sequence of operations :(1)where the two-dimensional distribution in angle is reduced to a one-dimensional function by a projection P, T is a two-dimensional Fourier transform in angle θ and energy loss w and the exponent -1 indicates a deprojection and inverse Fourier transform, respectively.

scholarly journals Stochastic vs. deterministic magnetic coding in designed cylindrical nanowires for 3D magnetic networks

Nanoscale ◽  
2021 ◽  
Author(s):  
Cristina Bran ◽  
Elias Saugar ◽  
José Ángel Fernández-Roldán ◽  
Rafael Perez del Real ◽  
Agustina Asenjo ◽  
...  
Keyword(s):  
Information Technologies ◽  
Intrinsic Curvature ◽  
Planar Systems ◽  
3D Information

Advances in cylindrical nanowires for 3D information technologies profit from intrinsic curvature that introduces significant differences with regards to planar systems. A model is proposed to control the stochastic and...

scholarly journals On the Reconstruction of the Center of a Projection by Distances and Incidence Relations

2020 ◽  
Author(s):  
András Pongrácz ◽  
Csaba Vincze
Keyword(s):  
Algebraic Surface ◽  
Basic Problem ◽  
Rotational Symmetry ◽  
Image Plane ◽  
Equivalent Condition ◽  
Central Projection ◽  
Profile Curve ◽  
Reconstruction Process ◽  
Restricted Area ◽  
Photographic Images

AbstractUp to an orientation-preserving symmetry, photographic images are produced by a central projection of a restricted area in the space into the image plane. To obtain reliable information about physical objects and the environment through the process of recording is the basic problem of photogrammetry. We present a reconstruction process based on distances from the center of projection and incidence relations among the points to be projected. For any triplet of collinear points in the space, we construct a surface of revolution containing the center of the projection. It is a generalized conic that can be represented as an algebraic surface. The rotational symmetry allows us to restrict the investigations to the defining polynomial of the profile curve in the image plane. An equivalent condition for the boundedness is given in terms of the input parameters, and it is shown that the defining polynomial of the profile curve is irreducible.

scholarly journals Emergent chiral symmetry in a three-dimensional interacting Dirac liquid

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
András L. Szabó ◽  
Bitan Roy
Keyword(s):  
Fixed Points ◽  
Chiral Symmetry ◽  
Rotational Symmetry ◽  
Three Dimensional ◽  
Spatial Dimension ◽  
Dirac Fermions ◽  
Electronic Interactions ◽  
Emergent Phenomena ◽  
Ordered Phases ◽  
The Stability

Abstract We compute the effects of strong Hubbardlike local electronic interactions on three-dimensional four-component massless Dirac fermions, which in a noninteracting system possess a microscopic global U(1) ⊗ SU(2) chiral symmetry. A concrete lattice realization of such chiral Dirac excitations is presented, and the role of electron-electron interactions is studied by performing a field theoretic renormalization group (RG) analysis, controlled by a small parameter ϵ with ϵ = d−1, about the lower-critical one spatial dimension. Besides the noninteracting Gaussian fixed point, the system supports four quantum critical and four bicritical points at nonvanishing interaction couplings ∼ ϵ. Even though the chiral symmetry is absent in the interacting model, it gets restored (either partially or fully) at various RG fixed points as emergent phenomena. A representative cut of the global phase diagram displays a confluence of scalar and pseudoscalar excitonic and superconducting (such as the s-wave and p-wave) mass ordered phases, manifesting restoration of (a) chiral U(1) symmetry between two excitonic masses for repulsive interactions and (b) pseudospin SU(2) symmetry between scalar or pseudoscalar excitonic and superconducting masses for attractive interactions. Finally, we perturbatively study the effects of weak rotational symmetry breaking on the stability of various RG fixed points.

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