The notion of Darboux helix in Euclidean 3‐space was introduced and studied by Yayl? et al. 2012. They show that the class of Darboux helices coincide with the class of slant helices. In a special case, if the curvature functions satisfy the equality κ2 + τ2 = constant, then these curves are curve of the constant precession. In this paper, we study Darboux helices in Euclidean 4‐space, and we give a characterization for a curve to be a Darboux helix. We also prove that Darboux helices coincide with the general helices. In a special case, if the first and third curvatures of the curve are equal, then Darboux helix, general helix, and V4‐slant helix are the same concepts. 相似文献
The nonlinear dynamics of DNA molecular chain is studied for longitudinal and transversal motions through a new discrete helicoidal zigzag model with four degrees of freedom. We take into account the Stokes and hydrodynamical viscous forces. In the semi-discrete approximation, we show that the coupled nonlinear partial differential equations for the longitudinal and transversal out-of-phase motions can be reduced to the nonlinear Schrödinger equation with complex coefficients, allowing analytical breather soliton solution. We found analytically as well as numerically that increasing the damping constant reduces the amplitude and increases the width of the soliton. When the zigzag angle decreases, the height of the soliton increases, but its width remains constant. The linear stability analysis of the system is performed. The growth rate of the instability and the instability regions are discussed as the functions of damping constant, zigzag angle and system parameters. 相似文献
Conjugated polymers may be induced by intra‐ and/or intermolecular non‐covalent forces to fold into helical conformations. Helices formed by aromatic amide, hydrazide, and urea polymers possess a well‐organized cavity and depth, which is defined by their degree of polymerization. Driving forces may be intramolecular hydrogen bonding and/or solvophobicity, or guest induction. The resulting long helices represent a new class of unimacromolecular dynamic tubular architectures that exhibit unique properties or functions in, for example, molecular recognition, chirality transfer, and ion transporting. The recent advances are highlighted here.
A novel [36]octaphyrin analogue embedding two N‐confused pyrrole units demonstrated unique prototropy‐coupled isomerization between the Figure‐of‐eight and dumbbell conformers. Upon bis‐metal coordination, fixation of fully π‐conjugated Figure‐of‐eight structures was achieved as referred from the X‐ray crystal structure. Chirogenesis of the helical enantiomers was proved by intense circular dichroism (CD) response in the near infrared (NIR) region. 相似文献
Using the extended Huygens-Fresnel principle and the quadratic approximation of the phase structure function, and taking the Gaussian Schell-model (GSM) vortex beam as a typical example of partially coherent vortex beams, the explicit expressions for the cross-spectral density function and average intensity of GSM vortex beams with topological charge m=+1 propagating through slant atmospheric turbulence are derived, and used to study the propagation properties of GSM vortex beams in atmospheric turbulence along a slant path and evolution behavior of coherence vortices. It is shown that the spreading of GSM vortex beams along a horizontal path is larger than that along a slant path in the long atmospheric propagation. The propagation through horizontal atmospheric turbulence can be treated as a special case of the altitude-independent structure constant. The position of coherence vortices in slant atmospheric turbulence does not coincide with that in horizontal atmospheric turbulence, and the dependence of position of coherence vortices on the zenith angle, wavelength and reference point is illustrated by numerical examples. A comparison with the previous work is also made. 相似文献
The magnetic layer structure of TlCo2Se2−xSx has been thoroughly re-investigated with neutron powder diffraction. The cobalt magnetic moments are ferromagnetically arranged within the layers, but the interlayer coupling differs profoundly with varying composition (x): the spins in TlCo2Se2 form a helix along the c-axis with a turning-angle of ∼119° at 1.4 K. This kind of helical structure prevails for 0≤x≤1.5 with a gradual decrease of the angle with increasing sulphur content, down to 34°, showing an almost linear relationship with the interlayer distance of Co-Co. For x≥1.75 the interlayer coupling changes to ferromagnetic. Unexpectedly, two helices were found to coexist at x=0.5 and x=1.0. The interaction between adjacent cobalt layers is there characterized by an incommensurate angle (106°, resp., 73°) together with a commensurate angle of 90°. The magnetic structures have been refined as two magnetic phases, each having a characteristic wave vector. A tentative model where the symmetry of the structure and the interlayer distance compete is considered for explaining the simultaneous occurrence of the two kinds of diffraction profile satellites. 相似文献
A novel slotted helix slow-wave structure (SWS) is proposed to develop a high power, wide-bandwidth, and high reliability millimeter-wave traveling-wave tube (TWT). This novel structure, which has higher heat capacity than a conven- tional helix SWS, evolves from conventional helix SWS with three parallel rows of rectangular slots made in the outside of the helix tape. In this paper, the electromagnetic characteristics and the beam-wave interaction of this novel structure operating in the Ka-band are investigated. From our calculations, when the designed beam voltage and beam current are set to be 18.45 kV and 0.2 A, respectively, this novel circuit can produce over 700-W average output power in a frequency range from 27.5 GHz to 32.5 GHz, and the corresponding conversion efficiency values vary from 19% to 21.3%, and the maximum output power is 787 W at 30 GHz. 相似文献
This paper presents a three-dimensional time-dependent nonlinear theory of helix traveling wave tubes for beamwave interaction.The radio frequency electromagnetic fields are represented as the superposition of azimuthally symmetric waves in a vacuum sheath helix.Coupling impedance is introduced to the electromagnetic field equations’ stimulating sources,which makes the theory easier and more flexible to realize.The space charge fields are calculated by electron beam space-charge waves expressed as the superposition solutions of Helmholtz equations.The focusing forces due to either a solenoidal field or a periodic permanent magnetic field is also included.The dynamical equations of electrons are Lorentz equations associating with electromagnetic fields,focusing fields and space-charge fields.The numerically simulated results of a tube are presented. 相似文献
A chiral ferroelectric smectic C* liquid crystal (FLC) with the helix pitch p0?=?330nm was developed to avoid any scattering of visible light when the helix is not unwound over a certain limit. Planar cells with different FLC layer thickness (16 and 44μm) have been assembled with helix axis parallel to the glass plates and aligned along the rubbing direction. The ellipticity of the light passing through the cells vs. the electric field was investigated, and a method for evaluating the electrically controlled birefringence via ellipticity measurements has been established. We have found that the FLC cell is an optical retardation layer driven by the electric field, the effective birefringence being proportional to the square electric field. The physical origin of the electrically controlled phase shift of the light passing through the FLC layer has been analysed. 相似文献