Elastic magnetic curves of Ferromagnetic and superparamagnetic models on the surface

2020 ◽  
pp. 2150037
Author(s):  
Talat Korpinar ◽  
Ridvan Cem Demirkol ◽  
Vedat Asil
Keyword(s):  
Variational Approach ◽  
Bending Energy ◽  
Regular Surface ◽  
Energy Functionals ◽  
New Class ◽  
Darboux Vector ◽  
Critical Curves ◽  
Elastic Curves ◽  
New Energy ◽  
Approach Method

We are interested in defining new energy functionals and solving them by using the variational approach method and Darboux equations. That is, we aim to define a new class of elastic curves on the regular surface [Formula: see text]. We further improve an alternative method to find critical points of the bending energy functionals acting on a class of magnetic curves on [Formula: see text]. As a result, we classify these critical curves as elastic magnetic curves of the Darboux vector family.

Investigation of Parametric Resonance Instability in a Flexible Rod Slider Crank Mechanism

1991 ◽  
Author(s):  
David G. Beale ◽  
Shyr-Wen Lee
Keyword(s):  
Potential Energy ◽  
Parametric Resonance ◽  
Variational Approach ◽  
Equations Of Motion ◽  
Monodromy Matrix ◽  
Bending Energy ◽  
Constrained Equations ◽  
Beam Bending ◽  
Floating Frame ◽  
Crank Mechanism

Abstract A direct variational approach with a floating frame is presented to derive the ordinary differential equations of motion of a flexible rod, constant crank speed slider crank mechanism. Potential energy terms contained in the derivation include beam bending energy and energy in foreshortening of the rod tip (which were selected because of the importance of these terms in a pinned-pinned rod parametric resonance). A symbolic manipulator code is used to reduce the constrained equations of motion to unconstrained nonlinear equations. A linearized version of these equations is used to explore parametric resonance stability-instability zones at low crank speeds and small deflections by a monodromy matrix technique.

scholarly journals Hypersurface Constrained Elasticae in Lorentzian Space Forms

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Óscar J. Garay ◽  
Álvaro Pámpano ◽  
Changhwa Woo
Keyword(s):  
Space Form ◽  
Energy Functional ◽  
Bending Energy ◽  
Space Forms ◽  
Lorentzian Space ◽  
Totally Geodesic ◽  
Critical Curves ◽  
Different Types ◽  
Lorentzian Space Forms

We study geodesics in hypersurfaces of a Lorentzian space formM1n+1(c), which are critical curves of theM1n+1(c)-bending energy functional, for variations constrained to lie on the hypersurface. We characterize critical geodesics showing that they live fully immersed in a totally geodesicM13(c)and that they must be of three different types. Finally, we consider the classification of surfaces in the Minkowski 3-space foliated by critical geodesics.

scholarly journals On Existence of Multiplicity of Weak Solutions for a New Class of Nonlinear Fractional Boundary Value Systems via Variational Approach

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Fares Kamache ◽  
Salah Mahmoud Boulaaras ◽  
Rafik Guefaifia ◽  
Nguyen Thanh Chung ◽  
Bahri Belkacem Cherif ◽  
...  
Keyword(s):  
Variational Methods ◽  
Weak Solutions ◽  
Variational Approach ◽  
Fractional Derivatives ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Value Systems ◽  
Critical Point Theorem ◽  
New Class ◽  
Left And Right

This paper deals with the existence of solutions for a new class of nonlinear fractional boundary value systems involving the left and right Riemann-Liouville fractional derivatives. More precisely, we establish the existence of at least three weak solutions for the problem using variational methods combined with the critical point theorem due to Bonano and Marano. In addition, some examples in ℝ 3 and ℝ 4 are given to illustrate the theoritical results.

scholarly journals Variational quantum solver employing the PDS energy functional

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 473
Author(s):  
Bo Peng ◽  
Karol Kowalski
Keyword(s):  
Quantum Algorithms ◽  
Energy Functional ◽  
Strongly Correlated ◽  
Local Minima ◽  
New Class ◽  
Moment Expansion ◽  
Energy Gradient ◽  
Model Hamiltonian ◽  
New Energy ◽  
Quantum Approach

Recently a new class of quantum algorithms that are based on the quantum computation of the connected moment expansion has been reported to find the ground and excited state energies. In particular, the Peeters-Devreese-Soldatov (PDS) formulation is found variational and bearing the potential for further combining with the existing variational quantum infrastructure. Here we find that the PDS formulation can be considered as a new energy functional of which the PDS energy gradient can be employed in a conventional variational quantum solver. In comparison with the usual variational quantum eigensolver (VQE) and the original static PDS approach, this new variational quantum solver offers an effective approach to navigate the dynamics to be free from getting trapped in the local minima that refer to different states, and achieve high accuracy at finding the ground state and its energy through the rotation of the trial wave function of modest quality, thus improves the accuracy and efficiency of the quantum simulation. We demonstrate the performance of the proposed variational quantum solver for toy models, H2 molecule, and strongly correlated planar H4 system in some challenging situations. In all the case studies, the proposed variational quantum approach outperforms the usual VQE and static PDS calculations even at the lowest order. We also discuss the limitations of the proposed approach and its preliminary execution for model Hamiltonian on the NISQ device.

VARIATIONAL APPROACH METHOD FOR NONLINEAR OSCILLATIONS OF THE MOTION OF A RIGID ROD ROCKING BACK AND CUBIC

2008 ◽  
Vol 4 ◽  
pp. 23-32 ◽  
Author(s):  
Seyedreza Seyedaliza Ganji ◽  
Davoodi Domiri Ganji ◽  
Hamed Babazadeh ◽  
Salim Karimpour
Keyword(s):  
Variational Approach ◽  
Nonlinear Oscillations ◽  
Approach Method ◽  
Rigid Rod

ABOUT A NEW CLASS OF INVARIANT AREAS GENERATED BY TWO-DIMENSIONAL ENDOMORPHISMS

2003 ◽  
Vol 13 (04) ◽  
pp. 905-933 ◽  
Author(s):  
J. C. CATHALA
Keyword(s):  
Mixed Type ◽  
Two Dimensional ◽  
New Class ◽  
Attracting Set ◽  
Critical Curves

Invariant areas generated by two-dimensional endomorphisms are studied using the method of critical curves. The invariant areas considered in this paper are obtained by iterating the noninvariant set constituted by the connected basin of an attracting set or the immediate basin of a nonconnected basin. This new kind of invariant area is of mixed type in the sense that its boundary is made up of critical curves arcs and arcs of saddle manifolds. The presentation is illustrated by three examples. A bifurcation changing the degree of connexity of an invariant area is described.

scholarly journals QUADRATIC CURVATURE ENERGIES IN THE 2-SPHERE

2010 ◽  
Vol 81 (3) ◽  
pp. 496-506 ◽  
Author(s):  
JOSU ARROYO ◽  
ÓSCAR J. GARAY ◽  
JOSE MENCÍA
Keyword(s):  
Variational Analysis ◽  
Lagrange Equation ◽  
Numerical Approach ◽  
Real Space ◽  
Closed Curves ◽  
Space Forms ◽  
Energy Functionals ◽  
Critical Curves ◽  
Real Space Forms ◽  
Curvature Energy

AbstractThe classical variational analysis of curvature energy functionals, acting on spaces of curves of a Riemannian manifold, is extremely complicated, and the procedure usually can not be completely developed under such a degree of generality. Sometimes this difficulty may be overcome by focusing on specific actions in real space forms. In this note, we restrict ourselves to quadratic Lagrangian energies acting on the space of closed curves of the 2-sphere. We solve the Euler–Lagrange equation and show that there exists a two-parameter family of closed critical curves. We also discuss the stability of the circular critical points. Since, even for this class of energies, the complete variational analysis is quite involved, we use instead a numerical approach to provide a useful method of visualization of relevant aspects concerning uniqueness, stability and explicit representation of the closed critical curves.

scholarly journals Direction Curves Associated with Darboux Vectors Fields and Their Characterizations

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Nidal Echabbi ◽  
Amina Ouazzani Chahdi
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Formula Unit ◽  
Regular Surface ◽  
Darboux Vector ◽  
Spherical Curve ◽  
Constant Torsion ◽  
Darboux Frame ◽  
Necessary And Sufficient ◽  
Unit Normal

In this paper, we consider the Darboux frame of a curve α lying on an arbitrary regular surface and we use its unit osculator Darboux vector D ¯ o , unit rectifying Darboux vector D ¯ r , and unit normal Darboux vector D ¯ n to define some direction curves such as D ¯ o -direction curve, D ¯ r -direction curve, and D ¯ n -direction curve, respectively. We prove some relationships between α and these associated curves. Especially, the necessary and sufficient conditions for each direction curve to be a general helix, a spherical curve, and a curve with constant torsion are found. In addition to this, we have seen the cases where the Darboux invariants δ o , δ r , and δ n are, respectively, zero. Finally, we enrich our study by giving some examples.

scholarly journals Some Special Ruled Surfaces Generated by a Direction Curve according to the Darboux Frame and their Characterizations

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Nidal Echabbi ◽  
Amina Ouazzani Chahdi
Keyword(s):  
Vector Field ◽  
Ruled Surfaces ◽  
Geodesic Curve ◽  
Regular Surface ◽  
Principal Line ◽  
Asymptotic Line ◽  
Darboux Vector ◽  
Base Curve ◽  
Darboux Frame ◽  
Made In

In this work, we consider the Darboux frame T , V , U of a curve lying on an arbitrary regular surface and we construct ruled surfaces having a base curve which is a V -direction curve. Subsequently, a detailed study of these surfaces is made in the case where the directing vector of their generatrices is a vector of the Darboux frame, a Darboux vector field. Finally, we give some examples for special curves such as the asymptotic line, geodesic curve, and principal line, with illustrations of the different cases studied.

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