Helicoidal Surfaces and Their Relationship to Bonnet Surfaces

An important question that arises is which surfaces in three-space admit a mean curvature preserving isometry which is not an isometry of the whole space. This leads to a class of surface known as a Bonnet surface in which the number of noncongruent immersions is two or infinity. The intention here is to present a proof of a theorem using an approach which is based on differential forms and moving frames and states that helicoidal surfaces necessarily fall into the class of Bonnet surfaces. Some other results are developed in the same manner.

Far-Field Pattern Reconstruction from Positioning Errors Affected Near-Field Data Acquired via Helicoidal Scanning

In this paper, an effective technique to compensate the positioning errors in a near-field—far-field (NF-FF) transformation with helicoidal scanning for elongated antennas is presented and validated both numerically and experimentally. It relies on a nonredundant sampling representation of the voltage measured by the probe, obtained by considering the antenna as enclosed in a cylinder ended in two half-spheres. An iterative scheme is used to reconstruct the helicoidal NF data at the points fixed by the representation from the acquired irregularly spaced ones. Once the helicoidal data have been retrieved, those needed by a classical NF-FF transformation with cylindrical scanning are efficiently evaluated by using an optimal sampling interpolation algorithm. Some numerical tests, assessing the accuracy of the approach and its stability with respect to random errors affecting the data, are reported. Experimental tests performed at the Antenna Characterization Lab of the University of Salerno further confirm the validity of the proposed technique.

Transcription's bubble under the influence of long-range interactions and helicoidal coupling

The influence of power-low long-range interactions （LRI） and helicoidal coupling （HC） on the properties of localized solitons in a DNA molecule when a ribonucleic acid polymerase （RNAP） binds to it at the physiological temperature is analytically and numerically investigated in this paper. We have made an analogy with the Heisenberg model Hamiltonian of an anisotropic spin ladder with ferromagnetic legs and anti-ferromagnetic rung coupling. When we limit ourselves to the second-order terms in the Taylor expansion, the DNA dynamics is found to be governed by a completely integrable nonlinear Schr？dinger （NLS） equation. In this case, results show that increasing the value of HC force or LRI parameter enhances the bubble height and reduces the number of base pairs which form the bubble. For the fourth-order terms in a Taylor expansion, results are closely resembling those of second-order terms, and are confirmed by numerical investigation. These results match with some experimental data and thus provide a better representation of the base pairs opening in DNA which is essential for the transcription process.

HELICAL SYMMETRIC SOLUTION OF 3D NAVIER-STOKES EQUATIONS ARISING FROM GEOMETRIC SHAPE OF THE BOUNDARY

In this article, we investigate three-dimensional solution with helical symmetry in a gap between two concentric rotating cylinders, inside is a helicoidal surface（screw propeller）while outside is a cylindrical surface. Establish the partial differential equations and its variational formulation satisfied by a helical solution in a helical coordinate system using tensor analysis method, we provide a computational method for the power and propulsion of the screw. The existence and uniqueness of weak helical solutions are proved.

Helix unwinding in ferroelectric liquid crystals induced by tilted electric field

Helix unwinding in ferroelectric liquid crystals induced by an electric field is theoretically studied on the basis of the continuum theory. By applying a weak electric field tilted to the smectic layers, the contribution of the dielectric interaction energy density to the total free energy density is increased. Approximation methods are used to calculate the free energy for different tilt angles between the electric field and the smectic layers. The obtained results suggest selecting the optimal number of pitches in the film that matches to the minimum of the free energy.

Stem Cell Ophthalmology Treatment Study (SCOTS)： improvement in serpiginous choroidopathy following autologous bone marrow derived stem cell treatment

We report results in a 77-year-old male patient with visual loss from long-standing serpiginous choroidop- athy treated with bone marrow derived stem cells （BMSC） within the Stem Cell Ophthalmology Treatment Study （SCOTS）. SCOTS is an Institutional Review Board approved clinical trial and the largest ophthal- mology stem cell study registered at the National Institutes of Health to date （ClinicalTrials.gov Identifier： NCT01920867）. Eight months after treatment by a combination of retrobulbar, subtenon, intravitreal and intravenous injection of BMSC, the patient＇s best corrected Snellen acuity improved from 20/80- to 20/60.1 in the right eye and from 20/50- to 20/20 3 in the left eye. The Early Treatment of Diabetic Retinopathy Study （ETDRS） visual acuity continued to improve over the succeeding 8 months and the optical coherence tomography macular volume increased. The increases in visual acuity and macular volume are encouraging and suggest that the use of BMSC as provided in SCOTS may be a viable approach to treating serpiginous choroidopathy.

Polygenic Heritability of Rose Root Rot Disease Resistance in Offspring of Rosa multiflora

Rose root rot disease caused by Pythium helicoides Drechsler has brought heavy damage to cut rose production in Japan,and it has became apparent that Rosa multiflora showed resistance to this disease.Roses have been bred by interspecies crossing with Rosa species including of R.multiflora,and many progenies of R.multiflora have been bred as determined cluster-flowered roses.However,the genetic architecture of this resistance remains.So,in this study,four kinds of R.multiflora and 21 rose cultivars that have been clarified in the cross-fertilization genealogy with R.multiflora were used as plant materials,and the inheritability of resistance to root rot disease was investigated.Four kinds of R.multiflora had all high resistance,and the resistance to root rot disease in R.multiflora was inherent characteristic of species.Five varieties not less than 50% in relatedness with R.multiflora were shown as varied ‘resistant’ and ‘moderately resistant’.Therefore,the inherent resistant characteristic in R.multiflora was not controlled by single major gene,and the resistibility in R.multiflora was not cytoplasmic but nuclear heredity.Although there was significant negative relation between relative root rot severity and relatedness with R.multiflora,the variance of relative root rot severity had tendency to expand as relatedness with R.multiflora reduced.This result,therefore,indicated that the contingency of resistance expression increased as the relatedness with R.multiflora was reduced.The varieties having low degree of relatedness with R.multiflora had similar relative root rot severity with R.multiflora.These results indicated that we would be able to select resistant roses from progenies crossed with R.multiflora.

THEORY OF HELICOID OF SPHERICAL HOB

The mechanism of spherical hob's cutting internal gear is explained and the new coneeptof generating gear of spherical hob is presented. The reason why there is theoretical error and thenew method of decreasing the error are also analysed. Some new equations about the mainparameters, the equations of helicoids, the equations of cutting edges and the flank angles of spheri-cal hob are given.

Flow hydrodynamics in embankment breach

Breaching flow occurs during the breach development of the embankment, dike, earthen dam, landslide barrier, etc. and plays an import role in the breaching erosion as the driving force. According to the previous research, the breaching process can be classified into initiation phase, breach widening phase and breach deepening phase. Based on the breaching development classifications, the breaching flow can be seen as a special compound weir flow when the breach channel is in the relatively equilibrium condition. There were five physical flow models were designed in the hypothesis of rectangular shape and trapezoidal shape for the breach channel cross sections to study the breaching flow characteristics. The distributions of water level and velocity were measured and analysed in the breaching flows in overtopping condition and emerged condition. There were two helicoidal flows above the breach channel slopes and triangular hydraulic jump in the downstream of the breach channel in the overtopping condition and emerged condition. The hydraulic energy loss was calculated according to the breaching velocity and water level distribution in the upstream and downstream of the model. It is found that the test results of the breach flow physical model can be valuable to bring insight of the breaching process of embankment and make contributions to the validations and verifications of breach numerical models.

Helical Fiber Pull-out in Biological Materials

Many biological materials, such as wood and bone, possess helicoid microstructures at microscale, which can serve as reinforcing elements to transfer stress between crack surfaces and improve the fracture toughness of their composites. Failure processes, such as fiber/matrix inter- face debonding and sliding associated with pull-out of helical fibers, are responsible mainly for the high energy dissipation needed for the fracture toughness enhancement. Here we present systemic analyses of the pull-out behavior of a helical fiber from an elastic matrix via the finite element method （FEM） simulation, with implications regarding the underlying toughening mechanism of helicoid microstructures. We find that, through their uniform curvature and torsion, helical fibers can provide high pull-out force and large interface areas, resulting in high energy dissipation that accounts, to a large extent, for the high toughness of biological materials. The helicity of fiber shape in terms of the helical angle has significant effects on the force-displacement relationships as well as the corresponding energy dissipation during fiber pull-out.