Branch Curve Research Articles

The harmonic resonance and singularity analysis of bifurcation for the magnetized elastic plate with action of time-varying magnetic potential

This paper deals with the superharmonic resonance of a ferromagnetic thin rectangular plate in the air-gap magnetic field excited by armature magnetic potential. Electromagnetic forces applied on the plate by the air-gap magnetic field cause the plate to transversal vibrate, which affects the air-gap magnetic field in turn, resulting the vibration and magnetic field coupling. According to the basic electromagnetic field theory and considering the magnetoelastic coupling effect, the air-gap magnetic field intensity is obtained by solving the Laplace's equation satisfied the air-gap magnetic boundary conditions. The electromagnetic force model of soft ferromagnetic plates is determined based on theories of electromagnetic and elasticity. According to the large deflection theory of plates, basic energy relationships and variational equations of the elastic plate are given. Eventually, the nonlinear magnetoelastic vibration equation of ferromagnetic thin plates is derived using Hamilton's principle and Galerkin method. The multi-scale method is used to solve the superharmonic resonance to obtain the amplitude-frequency response equation and the stability discriminant of solutions. The topological analysis of amplitude-frequency equation is carried out using singularity theory, and the bifurcation characteristics of systems on physical parameter planes in different regions are obtained according to the transition set. The correctness of analytical solutions is verified by comparison with numerical solutions. Through numerical calculations, curves of the static deflection and equivalent magnetic force of plate with parameters are given, and the amplitude curves, dynamic phase plane trajectories and time history diagrams of system response with changes in electromagnetic and structural parameters are plotted. Results show that both the decrease of armature magnetic potential amplitude and the increases of plate thickness and initial air-gap thickness reduce the static deflection. The increase of armature magnetic potential amplitude increases the equivalent magnetic force. As the decrease of initial air-gap thickness and the increases of armature magnetic potential amplitude and excitation force amplitude, the amplitudes of the upper branch and lower branch curves representing stable solutions decrease and increase, respectively, and the single-value solution region increases.

Linear instability and nonlinear flow states in a horizontal pipe flow under bottom heating and transverse magnetic field

Linear stabilities of the liquid metal mixed convection in a horizontal pipe under bottom heating and transverse magnetic field are studied through linear global stability analyses. Three branches of the linear stability boundary curves are determined by the eigenvalue computation of the most unstable modes. One branch is located in the region of large Hartmann number and determined by the linear unstable mode which was first revealed by the numerical simulations of Zikanov, Listratov & Sviridov (J. Fluid Mech., vol. 720, 2013, pp. 486–516). This branch curve shows that the global unstable mode exists above a threshold of Hartmann number, which agrees with the experiment of Genin et al. (Temperature fluctuations in a heated horizontal tube affected by transverse magnetic field. In Proc. 8th PAMIR Conf. Fund. Appl. MHD, Borgo, Corsica, France, pp. 37–41, 2011). The other two branch curves determined by two different long-wave unstable modes intersect with each other in the region of small Hartmann number. The critical Grashof number on these two curves increases exponentially with the increase of the Hartmann number. Through energy budget analyses at the critical thresholds of these unstable modes, it is found that, for the unstable mode at large Hartmann numbers, buoyancy is the dominant destabilizing term which demonstrates the hypothetical explanation of Zikanov et al. (2013) who regard natural convection as a destabilization mechanism. It is further revealed that, with respect to the unstable modes on the critical stability curves of small Hartmann numbers, the dominant destabilization comes from the streamwise shear of the basic flow. Finally, within the linear unstable region, fully developed nonlinear flow states of the mixed convection are investigated by direct numerical simulations (DNS) with several sets of selected dimensionless parameters. The spatio-temporal structures of these nonlinear flow states are discussed in detail with comparison with the linear unstable global modes.

New dynamical features of pure k-essential cosmologies

We come back on the dynamical properties of [Formula: see text]-essential cosmological models and show how the interesting phenomenological features of those models are related to the existence of boundaries in the phase surface. We focus our attention to the branching curves where the energy density has an extremum and the effective speed of sound diverges. We discuss the behaviour of solutions of a general class of cosmological models exhibiting such curves and give two possible interpretations; the most interesting possibility regards the arrow of time that is reversed in trespassing the branching curve. This study teaches to us something new about general FLRW cosmologies where the fluids driving the cosmic evolution have equations of state that are multivalued functions of the energy density and other thermodynamical quantities.

Looking at linking numbers

This paper applies the intuitive techniques of [ 9 ] to certain 3-colored knot diagrams, generating corresponding 3-fold branched covering spaces with predictable linking numbers between branch curves.

Numerical and experimental time–frequency analysis of internal waves induced by a submerged body

Time–frequency analysis is widely applied in Kelvin ship waves. However, limited studies have been conducted on the time–frequency features of internal waves. In this study, spectrograms used to visualize the frequencies of the internal waves generated by a submerged body are studied using a short-time Fourier transform. A linear dispersion curve and numerical model are introduced considering an idealized situation. The linear dispersion curve indicates wave frequency variation with time. The effects of parameters on the dispersion curve are discussed for a linear density profile and three-layer density profile. The dispersion curve presents upper and lower branches corresponding to the divergent and transverse wave components, respectively. In contrast to surface waves, the upper-branch curve for internal waves continues to increase and finally levels to the middle Brunt–Vaisala (BV) frequency Nm of the density profile, whereas the lower branch curve continues to decrease and finally approaches a constant value. The numerical simulation provides idealized spectrograms of the linear internal waves. The linear dispersion curve provides an excellent prediction of the dominant wave signals. The high-intensity portion in the spectrograms is confined to the lower branch for a low Froude number, whereas for a larger Froude number, the high-intensity portion follows the upper branch but decays rapidly over time. The spectrograms obtained by the model test reveal that the high-color-intensity portion can be categorized into leading, reflected, nonlinear, and low-frequency regions. The experimental results also reveal that the model travel length is a critical factor affecting internal waves.

A special configuration of 12 conics and generalized Kummer surfaces

A generalized Kummer surface X obtained as the quotient of an abelian surface by a symplectic automorphism of order 3 contains a $$9\mathbf{A}_{2}$$ -configuration of $$(-2)$$ -curves. Such a configuration plays the role of the $$16\mathbf{A}_{1}$$ -configurations for usual Kummer surfaces. In this paper we construct 9 other such $$9\mathbf{A}_{2}$$ -configurations on the generalized Kummer surface associated to the double cover of the plane branched over the sextic dual curve of a cubic curve. The new $$9\mathbf{A}_{2}$$ -configurations are obtained by taking the pullback of a certain configuration of 12 conics which are in special position with respect to the branch curve, plus some singular quartic curves. We then construct some automorphisms of the K3 surface sending one configuration to another. We also give various models of X and of the generic fiber of its natural elliptic pencil.

On the Analytical Models of Confined High-Strength Steel-Fiber Concrete

Generally, confinement models of the steel-fiber concrete were very ductile because the fiber has a significant influence on the increase of the concrete deformability. Nevertheless, the existing steel fibrous confined models now have significant differences between each other, especially the peak stress value and post peak behavior. It is some of the different reviewed design parameters that affect the stress-strain equation of developed confined steel-fiber concrete. This paper investigated the existing confinement models to evaluate pre- and post-peak behavior of experimental results of confined steel fiber concrete for square sections. This paper has discussed models of existing steel fibrous concrete restraints compared to the results of experiments. In general, it can be concluded that the Hsu model is able to predict the best K value and ascending branch curve toward the experiment results. However, in the unfettered concrete ductility of the descending branch curve, the predicted values of ε'_cc and ε_50cc, it can be said that all the models reviewed are still not able to model properly. The difference is mainly due to the parameters reviewed to lower the restraints of each model are not the same. The comparison results presented in this paper recommend the need for more complete experimental research with broader parameters such as cross-sectional shape, fiber ratio, and restraint bone characteristics, in order to lower the model of restraint more generally.

On rigid germs of finite morphisms of smooth surfaces

In the article, we show that the germ of a finite morphism of smooth surfaces is rigid if and only if the germ of its branch curve has an singularity type. We establish a correspondence between the set of rigid germs of finite morphisms and the set of Belyi rational functions . Bibliography: 10 titles.

Corrosion Behavior and Characteristics of 3Cr Steel in Coexisting H2S- and CO2-Containing Solutions

The corrosion behavior and characteristics of 3Cr steel in coexisting H2S- and CO2-containing solution at temperature from 25 to 65 °C were investigated by potentiodynamic polarization sweep, electrochemical impedance spectroscopy (EIS) and scanning electron microscopy (SEM) with energy-dispersive x-ray (EDX). The EIS data fitted by ZsimpWin software were analyzed and discussed. The experimental results indicated that corrosion potential (Ecorr) became more negative and that corrosion current density (icorr) decreased as the Na2S·9H2O concentration (i.e., H2S/HS−) increased from 0 to 1.6%, with the obvious passivation characteristics occurring in anodic polarization branch curve in 1.6% Na2S·9H2O case. Warburg impedance characteristics of diffusion process in low-frequency region following a depressed capacitive semicircle in the intermediate frequency region were observed with the addition of certain Na2S·9H2O concentration or temperature, with the phase angle peaks for H2S-containing cases in the intermediate frequency region shifting to low-frequency direction and raising toward −90° significantly. Severe corrosion pits or cavities or river-liking platform could be observed after removing the corrosion products. The contents of S element in the “first deposition” black corrosion product layer were higher than those in the “second deposition” gray corrosion product crystals. All result displayed the inhibition effect with the addition of Na2S·9H2O. In addition, one four-stage corrosion model involving H2S and CO2 corrosion was proposed.

On Zariski Multiplets of Branch Curves from Surfaces Isogenous to a Product

In this paper we give an asymptotic bound of the cardinality of Zariski multiples of particular irreducible plane singular curves. These curves have only nodes and cusps as singularities and are obtained as branched curves of ramified covering of the plane by surfaces isogenous to a product of curves with group ( Z / 2 Z ) k . The knowledge of the moduli space of these surfaces will enable us to produce Zariski multiplets whose number grows subexponentially in function of their degree.

2-stratifold spines of closed 3-manifolds

$2$-stratifolds are a generalization of $2$-manifolds in that there are disjoint simple closed branch curves. We obtain a list of all closed $3$-manifolds that have a $2$-stratifold as a spine.

On the almost generic covers of the projective plane

A finite morphism $f:X\to \mathbb P^2$ of a a smooth irreducible projective surface $X$ is called an almost generic cover if for each point $p\in \mathbb P^2$ the fibre $f^{-1}(p)$ is supported at least on $deg(f)-2$ distinct points and $f$ is ramified with multiplicity two at a generic point of its ramification locus $R$. In the article, the singular points of the branch curve $B\subset\mathbb P^2$ of an almost generic cover are investigated and main invariants of the covering surface $X$ are calculated in terms of invariants of the curve $B$.

On Germs of Finite Morphisms of Smooth Surfaces

Questions related to deformations of germs of finite morphisms of smooth surfaces are discussed. Four-sheeted finite cover germs F: (U, o′) → (V, o), where (U, o′) and (V, o) are two germs of smooth complex analytic surfaces, are classified up to smooth deformations. The singularity types of branch curves and the local monodromy groups of these germs are also investigated.

A plurality of (non)visualizations: Branch points and branch curves at the turn of the 19th century

A plurality of (non)visualizations: Branch points and branch curves at the turn of the 19th century

Tritangents and their space sextics

Two classical results in algebraic geometry are that the branch curve of a del Pezzo surface of degree 1 can be embedded as a space sextic curve in P3 and that every space sextic curve has exactly 120 tritangents corresponding to its odd theta characteristics. In this paper we revisit both results from the computational perspective. Specifically, we give an algorithm to construct space sextic curves that arise from blowing up P2 at eight points and provide algorithms to compute the 120 tritangents and their Steiner system of any space sextic. Furthermore, we develop efficient inverses to the aforementioned methods. We present an algorithm to either reconstruct the original eight points in P2 from a space sextic or certify that this is not possible. Moreover, we extend a construction of Lehavi [8] which recovers a space sextic from its tritangents and Steiner system. All algorithms in this paper have been implemented in magma.

A novel model of magnetorheological damper with hysteresis division

Due to the complex nonlinearity of magnetorheological (MR) behavior, the modeling of MR dampers is a challenge. A simple and effective model of MR damper remains a work in progress. A novel model of MR damper is proposed with force-velocity hysteresis division method in this study. A typical hysteresis loop of MR damper can be simply divided into two novel curves with the division idea. One is the backbone curve and the other is the branch curve. The exponential-family functions which capturing the characteristics of the two curves can simplify the model and improve the identification efficiency. To illustrate and validate the novel phenomenological model with hysteresis division idea, a dual-end MR damper is designed and tested. Based on the experimental data, the characteristics of the novel curves are investigated. To simplify the parameters identification and obtain the reversibility, the maximum force part, the non-dimensional backbone part and the non-dimensional branch part are derived from the two curves. The maximum force part and the non-dimensional part are in multiplication type add-rule. The maximum force part is dependent on the current and maximum velocity. The non-dominated sorting genetic algorithm II (NSGA II) based on the design of experiments (DOE) is employed to identify the parameters of the normalized shape functions. Comparative analysis is conducted based on the identification results. The analysis shows that the novel model with few identification parameters has higher accuracy and better predictive ability.

Evaluation of bond performance between deformed bars and recycled aggregate concrete after high temperatures exposure

In this paper, 84 pull-out specimens and 60 cubic specimens with different levels of recycled coarse aggregate (i.e. 0%, 30%, 50%, 70% and 100%) were fabricated to evaluate the post-fire bond at the interface between recycled aggregate concrete (RAC) and deformed rebar. Those specimens designed for thermal temperature were first heated to high temperatures of 300, 400, and 500°C for 6h, and then were submitted to the test. The testing results were compared with the results obtained from the testing for the specimens at ambient temperature (about 20°C). A semi-empirical formula was finally suggested to model the bond-slip relation between the heated RAC and the deformed rebar. The results demonstrate that an increment of the heating temperature decreases both the bond strength and the compressive strength continuously but increase the peak slip. Before and after high temperature, increasing the RAC replacement percentage gradually increases the relative bond strength. The ascending branches of bond-slip curves are uniform for all the tests. However, as an increment of the temperature and of the lateral confinement provided by stirrups, the descending branch curve of RAC becomes flatter.

Medially constrained deformable modeling for segmentation of branching medial structures: Application to aortic valve segmentation and morphometry.

Deformable modeling with medial axis representation is a useful means of segmenting and parametrically describing the shape of anatomical structures in medical images. Continuous medial representation (cm-rep) is a "skeleton-first" approach to deformable medial modeling that explicitly parameterizes an object's medial axis and derives the object's boundary algorithmically. Although cm-rep has effectively been used to segment and model a number of anatomical structures with non-branching medial topologies, the framework is challenging to apply to objects with branching medial geometries since branch curves in the medial axis are difficult to parameterize. In this work, we demonstrate the first clinical application of a new "boundary-first" deformable medial modeling paradigm, wherein an object's boundary is explicitly described and constraints are imposed on boundary geometry to preserve the branching configuration of the medial axis during model deformation. This "boundary-first" framework is leveraged to segment and morphologically analyze the aortic valve apparatus in 3D echocardiographic images. Relative to manual tracing, segmentation with deformable medial modeling achieves a mean boundary error of 0.41 ± 0.10 mm (approximately one voxel) in 22 3DE images of normal aortic valves at systole. Deformable medial modeling is additionally demonstrated on pathological cases, including aortic stenosis, Marfan syndrome, and bicuspid aortic valve disease. This study demonstrates a promising approach for quantitative 3DE analysis of aortic valve morphology.

The estimation of branching curves in the presence of subject-specific random effects.

Branching curves are a technique for modeling curves that change trajectory at a change (branching) point. Currently, the estimation framework is limited to independent data, and smoothing splines are used for estimation. This article aims to extend the branching curve framework to the longitudinal data setting where the branching point varies by subject. If the branching point is modeled as a random effect, then the longitudinal branching curve framework is a semiparametric nonlinear mixed effects model. Given existing issues with using random effects within a smoothing spline, we express the model as a B-spline based semiparametric nonlinear mixed effects model. Simple, clever smoothness constraints are enforced on the B-splines at the change point. The method is applied to Women's Health data where we model the shape of the labor curve (cervical dilation measured longitudinally) before and after treatment with oxytocin (a labor stimulant).

Automating dicentric chromosome detection from cytogenetic biodosimetry data.

We present a prototype software system with sufficient capacity and speed to estimate radiation exposures in a mass casualty event by counting dicentric chromosomes (DCs) in metaphase cells from many individuals. Top-ranked metaphase cell images are segmented by classifying and defining chromosomes with an active contour gradient vector field (GVF) and by determining centromere locations along the centreline. The centreline is extracted by discrete curve evolution (DCE) skeleton branch pruning and curve interpolation. Centromere detection minimises the global width and DAPI-staining intensity profiles along the centreline. A second centromere is identified by reapplying this procedure after masking the first. Dicentrics can be identified from features that capture width and intensity profile characteristics as well as local shape features of the object contour at candidate pixel locations. The correct location of the centromere is also refined in chromosomes with sister chromatid separation. The overall algorithm has both high sensitivity (85 %) and specificity (94 %). Results are independent of the shape and structure of chromosomes in different cells, or the laboratory preparation protocol followed. The prototype software was recoded in C++/OpenCV; image processing was accelerated by data and task parallelisation with Message Passaging Interface and Intel Threading Building Blocks and an asynchronous non-blocking I/O strategy. Relative to a serial process, metaphase ranking, GVF and DCE are, respectively, 100 and 300-fold faster on an 8-core desktop and 64-core cluster computers. The software was then ported to a 1024-core supercomputer, which processed 200 metaphase images each from 1025 specimens in 1.4 h.