Differential Geometry and Topology of Curves

Aminov, Yu. A.

doi:10.1201/9781420022605

Cited by 13 publications

(9 citation statements)

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“…In what follows, the explicit expressions, in terms of x(s), for the rest of the unit vectors e a (s) are not necessary (relevant formulas can be found, for example, in [16,17]). Nonzero elements of the matrix ω in the Frenet equations (2.6) are determined by the principal curvatures…”

Section: Euler-lagrange Equations In Terms Of Principal Curvaturesmentioning

confidence: 99%

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Functionals linear in curvature and statistics of helical proteins

2005

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The effective free energy of globular protein chain is considered to be a functional defined on smooth curves in three dimensional Euclidean space. From the requirement of geometrical invariance, together with basic facts on conformation of helical proteins and dynamical characteristics of the protein chains, we are able to determine, in a unique way, the exact form of the free energy functional. Namely, the free energy density should be a linear function of the curvature * E-mail: feoli@unisannio.it; fax: +39089965275 † E-mail: nestr@thsun1.jinr.ru ‡ E-mail: scarpetta@sa.infn.it 1 of curves on which the free energy functional is defined. We briefly discuss the possibility of using the model proposed in Monte Carlo simulations of exhaustive searching the native stable state of the protein chain. The relation of the model proposed to the rigid relativistic particles and strings is also considered.

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Section: Euler-lagrange Equations In Terms Of Principal Curvaturesmentioning

confidence: 99%

“…From the differential geometry of curves [11,17] it is known that the helices in three dimensional space have a constant curvature (k 1 ) and a constant torsion (k 2 ) which determine the radius R and the step d of a helix…”

Section: Exact Integrability Of the Euler-lagrange Equations For Prinmentioning

confidence: 99%

Functionals linear in curvature and statistics of helical proteins

2005

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“…In other words, the value of the step is dependent on curvature of solution. From the course of differential geometry [8] it is known that the radius of curvature in multidimensional space is determined by relationship M = |O | P…”

Section: The Algorithm For Construction Level Sets Of Lyapunov Functionmentioning

confidence: 99%

Calculation of absolute stability regions for time-varying electromechanical systems

Berdnikov

Lohin

2017

J. Phys.: Conf. Ser.

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To cite this article: V P Berdnikov and V M Lohin 2017 J. Phys.: Conf. Ser. 803 012020 View the article online for updates and enhancements. Related contentThe transition mode of dilute binary alloys during directional solidification near to the absolute stability limit Xingguo Geng and Hengzhi Fu - IntroductionIn many real control objects, there is significant nonlinearity and nonstationarity [1]. For electromechanical systems, it can be expressed in a variable total moment of inertia on the motor shaft, in the influence of elastic ties, in external factors and etc. If the characteristics of nonlinear elements and the laws of change parameters in the form of specific formulas are known, then exact or approximate methods can be used, which are described in, for example, [2]. Often, in practice, only boundaries are known, in which nonlinearity and nonstationarity coefficients can be changed, which greatly complicates the analysis. Classical methods of the absolute stability theory, circle criteria and Popov's criteria, have already become an important step towards the study of these systems. Widespread in the scientific and engineering environment (first of all for simplicity and visibility), they almost never provide necessary and sufficient conditions of stability [3], indeed, where there is more than one nonlinear and/or time-varying element, frequency methods are much more complicated and they loose their visibility. The connection between quadratic Lyapunov functions and frequency criteria was long-established, that is why, if several nonlinear time-varying elements are in the system, it is reasonable to use a numerical algorithm for constructing quadratic Lyapunov functions [4]. The most comprehensive review of this topic is presented in [5]. In this paper, the author will describe the algorithm which is based on the research of necessary and sufficient stability conditions.

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“…This curve is the closed one with period T c = 2πm/h = πl/ω, where m, l are integers. The oriented spherical curve is characterized by the curvature k, torsion of the curve κ, apex speed V , and length of the path s [7,24]. In Fig.…”

Section: Master Equationmentioning

confidence: 99%

Quantum speed limit time in a magnetic resonance

Ivanchenko

2017

Physics Letters A

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A visualization for dynamics of a qudit spin vector in a time-dependent magnetic field is realized by means of mapping a solution for a spin vector on the three-dimensional spherical curve (vector hodograph). The obtained results obviously display the quantum interference of precessional and nutational effects on the spin vector in the magnetic resonance. For any spin the bottom bounds of the quantum speed limit time (QSL) are found. It is shown that the bottom bound goes down when using multilevel spin systems. Under certain conditions the non-nil minimal time, which is necessary to achieve the orthogonal state from the initial one, is attained at spin S=2. An estimation of the product of two and three standard deviations of the spin components are presented. We discuss the dynamics of the mutual uncertainty, conditional uncertainty and conditional variance in terms of spin standard deviations. The study can find practical applications in the magnetic resonance, 3D visualization of computational data and in designing of optimized information processing devices for quantum computation and communication.

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Differential Geometry and Topology of Curves

Cited by 13 publications

References 0 publications

Functionals linear in curvature and statistics of helical proteins

Functionals linear in curvature and statistics of helical proteins

Calculation of absolute stability regions for time-varying electromechanical systems

Quantum speed limit time in a magnetic resonance

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