Spherical parametrization of genus-zero meshes by minimizing discrete harmonic energy

The problem of spherical parametrization is that of mapping a genus-zero mesh onto a spherical surface. For a given mesh, different parametrizations can be obtained by different methods. And for a certain application, some parametrization results might behave better than others. In this paper, we will propose a method to parametrize a genus-zero mesh so that a surface fitting algorithm with PHT-splines can generate good result. Here the parametrization results are obtained by minimizing discrete har- monic energy subject to spherical constraints. Then some applications are given to illustrate the advantages of our results. Based on PHT-splines, parametric surfaces can be constructed efficiently and adaptively to fit genus-zero meshes after their spherical parametrization has been obtained.

PARAMETRIZATION OF BALANCED MULTIWAVELET

This paper deals with the parametrization of balanced multiwavelets and different properties associated with them. We introduce the property balancing symmetry and orthogonal properties of multiwavelet and link these properties to the matrix of the lowpass synthesis rnultifilter. Using these new results, we present the parametrization of orthogohal multiwavelets of flip-symmetry with length two and three. This is a direct construction method, making the construction of the balanced multiwavelet as easy as the scalar wavelet.

Parametrization of Transfer Matrix:for One-Dimensional Anderson Model with Diagonal Disorder

In this paper, we developed a new parametrization method to calculate the localization length in one-dimensionalAnderson model with diagonal disorder.This method can avoid the divergence difficulty encountered in theconventional methods, and significantly save computing time as well.

Parametrization to Improve the Solution Accuracy of Problems Involving the Bi-Dimensional Dirac Delta in the Forcing Function

The representation of the Dirac delta, obtained by differentiating the parametric equation of the unit step with a riser, is used to solve two examples referring to problems of a different physical nature, each with the product of two deltas as a forcing function. Each problem was solved by an entirely different procedure. In comparison with non-parametric solutions, the present solutions are both more accurate and truer representations of the physics involved.

On the Base Point Locus of Surface Parametrizations:Formulas and Consequences

This paper shows that the multiplicity of the base point locus of a projective rational surface parametrization can be expressed as the degree of the content of a univariate resultant.As a consequence,we get a new proof of the degree formula relating the degree of the surface,the degree of the parametrization,the base point multiplicity and the degree of the rational map induced by the parametrization.In addition,we extend both formulas to the case of dominant rational maps of the projective plane and describe how the base point loci of a parametrization and its reparametrizations are related.As an application of these results,we explore how the degree of a surface reparametrization is affected by the presence of base points.

Determination and(Re)Parametrization of Rational Developable Surfaces

The developable surface is an important surface in computer aided design, geometric modeling and industrial manufactory. It is often given in the standard parametric form, but it can also be in the implicit form which is commonly used in algebraic geometry. Not all algebraic developable surfaces have rational parametrizations. In this paper, the authors focus on the rational developable surfaces. For a given algebraic surface, the authors first determine whether it is developable by geometric inspection, and then give a rational proper parametrization in the affrmative case. For a rational parametric surface, the authors also determine the developability and give a proper reparametrization for the developable surface.

Boundary-Mapping Parametrization in Isogeometric Analysis

In isogeometric analysis(IGA),parametrization is an important and difficultissue that greatly influences the numerical accuracy and efficiency of the numericalsolution.One of the problems facing the parametrization in IGA is the existence ofthe singular points in the parametrization domain.To avoid producing singular points,boundary-mapping parametrization is given by mapping the computational domainto a polygon domain which may not be a square domain and mapping each segmentof the boundary in computational domain to a corresponding boundary edge of thepolygon.Two numerical examples in finite element analysis are presented to show thenovel parametrization is efficient.

THE PROPER PARAMETRIZATION OF A SPECIAL CLASS OF RATIONAL PARAMETRIC EQUATIONS

We give a proper reparametrization theorem for a set of rational parametric equations which is proper for all but one of its parameters. We also give an algorithm to determine whether a set of rational parametric equations belongs to this class, and if it does, we reparametrize it such that the new parametric equations are proper.

Boundary parametrization of planar self-affine tiles with collinear digit set

We consider a class of planar self-affine tiles T = M-1 a∈D(T + a) generated by an expanding integral matrix M and a collinear digit set D as follows:M =(0-B 1-A),D = {(00),...,(|B|0-1)}.We give a parametrization S1 →T of the boundary of T with the following standard properties.It is H¨older continuous and associated with a sequence of simple closed polygonal approximations whose vertices lie on T and have algebraic preimages.We derive a new proof that T is homeomorphic to a disk if and only if 2|A| |B + 2|.

PROPER REPARAMETRIZATION FOR INHERENTLY IMPROPER UNIRATIONAL VARIETIES

In this paper, a class of lattice supports in the lattice space Zm is found to be inherently improper because any rational parametrization from Cm to Cm defined on such a support is improper. The improper index for such a lattice support is defined to be the gcd of the normalized volumes of all the simplex sub-supports. The structure of an improper support S is analyzed and shrinking transformations are constructed to transform S to a proper one. For a generic rational parametrization RP defined on an improper support S, we prove that its improper index is the improper index of S and give a proper reparametrization algorithm for RP. Finally, properties for rational parametrizations defined on an improper support and with numerical coefficients are also considered.

Differences between lower extremity joint running kinetics captured by marker-based and markerless systems were speed dependent

Background:The development of computer vision technology has enabled the use of markerless movement tracking for biomechanical analysis.Recent research has reported the feasibility of markerless systems in motion analysis but has yet to fully explore their utility for capturing faster movements,such as running.Applied studies using markerless systems in clinical and sports settings are still lacking.Thus,the present study compared running biomechanics estimated by marker-based and markerless systems.Given running speed not only affects sports performance but is also associated with clinical injury prevention,diagnosis,and rehabilitation,we aimed to investigate the effects of speed on the comparison of estimated lower extremity joint moments and powers between markerless and marker-based technologies during treadmill running as a concurrent validating study.Methods:Kinematic data from marker-based/markerless technologies were collected,along with ground reaction force data,from 16 young adults running on an instrumented treadmill at 3 speeds:2.24 m/s,2.91 m/s,and 3.58 m/s(5.0 miles/h,6.5 miles/h,and 8.0 miles/h).Sagittal plane moments and powers of the hip,knee,and ankle were calculated by inverse dynamic methods.Time series analysis and statistical parametric mapping were used to determine system differences.Results:Compared to the marker-based system,the markerless system estimated increased lower extremity joint kinetics with faster speed during the swing phase in most cases.Conclusion:Despite the promising application of markerless technology in clinical settings,systematic markerless overestimation requires focused attention.Based on segment pose estimations,the centers of mass estimated by markerless technologies were farther away from the relevant distal joint centers,which led to greater joint moments and powers estimates by markerless vs.marker-based systems.The differences were amplified by running speed.

Enhanced picosecond terahertz wave generation based on cascade effects in a terahertz parametric generator

Enhanced terahertz wave generation via a Stokes cascade process has been demonstrated using picosecond pulse pumped terahertz parametric generation at 1 kHz repetition rate.Clear cascade saturation of terahertz output was observed,and the corresponding cascade-Stokes spectra were analyzed.The maximum terahertz wave average power was 22μW under a pump power of 30 W,whereas the maximum power conversion efficiency was 8×10^(-7)under a pump power of 21 W.The THz power fluctuation was measured to be about 1%in 20 min.This THz parametric source with a relatively stable output is suitable for a variety of practical applications.

Nonlinear vibration of Timoshenko FG porous sandwich beams subjected to a harmonic axial load

In this study,the instability and bifurcation diagrams of a functionally graded(FG)porous sandwich beam on an elastic,viscous foundation which is influenced by an axial load,are investigated with an analytical attitude.To do so,the Timoshenko beam theory is utilized to take the shear deformations into account,and the nonlinear Von-Karman approach is adopted to acquire the equations of motion.Then,to turn the partial differential equations(PDEs)into ordinary differential equations(ODEs)in the case of equations of motion,the method of Galerkin is employed,followed by the multiple time scale method to solve the resulting equations.The impact of parameters affecting the response of the beam,including the porosity distribution,porosity coefficient,temperature increments,slenderness,thickness,and damping ratios,are explicitly discussed.It is found that the parameters mentioned above affect the bifurcation points and instability of the sandwich porous beams,some of which,including the effect of temperature and porosity distribution,are less noticeable.

Active Fault Tolerant Nonsingular Terminal Sliding Mode Control for Electromechanical System Based on Support Vector Machine

Effective fault diagnosis and fault-tolerant control method for aeronautics electromechanical actuator is concerned in this paper.By borrowing the advantages of model-driven and data-driven methods,a fault tolerant nonsingular terminal sliding mode control method based on support vector machine(SVM)is proposed.A SVM is designed to estimate the fault by off-line learning from small sample data with solving convex quadratic programming method and is introduced into a high-gain observer,so as to improve the state estimation and fault detection accuracy when the fault occurs.The state estimation value of the observer is used for state reconfiguration.A novel nonsingular terminal sliding mode surface is designed,and Lyapunov theorem is used to derive a parameter adaptation law and a control law.It is guaranteed that the proposed controller can achieve asymptotical stability which is superior to many advanced fault-tolerant controllers.In addition,the parameter estimation also can help to diagnose the system faults because the faults can be reflected by the parameters variation.Extensive comparative simulation and experimental results illustrate the effectiveness and advancement of the proposed controller compared with several other main-stream controllers.

Parametric instability in the pure-quartic nonlinear Schrödinger equation

We study the nonlinear stage of modulation instability(MI)in the non-intergrable pure-quartic nonlinear Schrödinger equation where the fourth-order dispersion is modulated periodically.Using the three-mode truncation,we reveal the complex recurrence of parametric resonance(PR)breathers,where each recurrence is associated with two oscillation periods(PR period and internal oscillation period).The nonlinear stage of parametric instability admits the maximum energy exchange between the spectrum sidebands and central mode occurring outside the MI gain band.

Parametric resonance of axially functionally graded pipes conveying pulsating fluid

Based on the generalized Hamilton's principle,the nonlinear governing equation of an axially functionally graded(AFG)pipe is established.The non-trivial equilibrium configuration is superposed by the modal functions of a simply supported beam.Via the direct multi-scale method,the response and stability boundary to the pulsating fluid velocity are solved analytically and verified by the differential quadrature element method(DQEM).The influence of Young's modulus gradient on the parametric resonance is investigated in the subcritical and supercritical regions.In general,the pipe in the supercritical region is more sensitive to the pulsating excitation.The nonlinearity changes from hard to soft,and the non-trivial equilibrium configuration introduces more frequency components to the vibration.Besides,the increasing Young's modulus gradient improves the critical pulsating flow velocity of the parametric resonance,and further enhances the stability of the system.In addition,when the temperature increases along the axial direction,reducing the gradient parameter can enhance the response asymmetry.This work further complements the theoretical analysis of pipes conveying pulsating fluid.

Overshoot phenomena:Observation and simulation

High-power O-mode radio waves can excite artificial instabilities in the F region,according to experiments conducted at the European Incoherent Scatter Science Association(EISCAT)heating facility.The main instabilities include the parametric decay instability(PDI),oscillating two-stream instability(OTSI),and thermal parametric instability(TPI).The PDI and OTSI not only compete with each other,but also compete with the TPI,leading to a two-stage overshoot phenomenon:a miniovershoot occurs on a millisecond time scale after pump-on,followed by the main overshoot.We gain insight into the miniovershoot via a generalized Zakharov model,whereas the main overshoot can be observed as an enhanced plasma line overshoot phenomenon in incoherent scatter radar spectra.We can also observe that the zero-frequency ion line exists only in the initial heating period after a cold start and that the upshifted and downshifted ion lines behave irregularly in the spectra.The simulation results show that competition between the PDI and OTSI leads to an initial peak,which we named the pre-miniovershoot.The following processes,namely ion density caviton generation,and collapse and cascade in the development of the PDI,contribute to the miniovershoot phenomenon.

Impact of cancer diagnosis on life expectancy by area-level socioeconomic groups in New South Wales, Australia: a population-based study

Objective: Improvement in cancer survival over recent decades has not been accompanied by a narrowing of socioeconomic disparities. This study aimed to quantify the loss of life expectancy(LOLE) resulting from a cancer diagnosis and examine disparities in LOLE based on area-level socioeconomic status(SES).Methods: Data were collected for all people between 50 and 89 years of age who were diagnosed with cancer, registered in the NSW Cancer Registry between 2001 and 2019, and underwent mortality follow-up evaluations until December 2020. Flexible parametric survival models were fitted to estimate the LOLE by gender and area-level SES for 12 common cancers.Results: Of 422,680 people with cancer, 24% and 18% lived in the most and least disadvantaged areas, respectively. Patients from the most disadvantaged areas had a significantly greater average LOLE than patients from the least disadvantaged areas for cancers with high survival rates, including prostate [2.9 years(95% CI: 2.5±3.2 years) vs. 1.6 years(95% CI: 1.3±1.9 years)] and breast cancer [1.6 years(95% CI: 1.4±1.8 years) vs. 1.2 years(95% CI: 1.0±1.4 years)]. The highest average LOLE occurred in males residing in the most disadvantaged areas with pancreatic [16.5 years(95% CI: 16.1±16.8 years) vs. 16.2 years(95% CI: 15.7±16.7 years)] and liver cancer [15.5 years(95% CI: 15.0±16.0 years) vs. 14.7 years(95% CI: 14.0±15.5 years)]. Females residing in the least disadvantaged areas with thyroid cancer [0.9 years(95% CI: 0.4±1.4 years) vs. 0.6 years(95% CI: 0.2±1.0 years)] or melanoma [0.9 years(95% CI: 0.8±1.1 years) vs. 0.7 years(95% CI: 0.5±0.8 years)] had the lowest average LOLE.Conclusions: Patients from the most disadvantaged areas had the highest LOLE with SES-based differences greatest for patients diagnosed with cancer at an early stage or cancers with higher survival rates, suggesting the need to prioritise early detection and reduce treatment-related barriers and survivorship challenges to improve life expectancy.

Nonlinear dynamics of a circular curved cantilevered pipe conveying pulsating fluid based on the geometrically exact model

Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine,the investigations on the mechanical responses of the pipes have attracted considerable attention.The fluid-structure interaction(FSI)between the pipe with a curved shape and the time-varying internal fluid flow brings a great challenge to the revelation of the dynamical behaviors of flexible pipes,especially when the pipe is highly flexible and usually undergoes large deformations.In this work,the geometrically exact model(GEM)for a curved cantilevered pipe conveying pulsating fluid is developed based on the extended Hamilton's principle.The stability of the curved pipe with three different subtended angles is examined with the consideration of steady fluid flow.Specific attention is concentrated on the large-deformation resonance of circular pipes conveying pulsating fluid,which is often encountered in practical engineering.By constructing bifurcation diagrams,oscillating shapes,phase portraits,time traces,and Poincarémaps,the dynamic responses of the curved pipe under various system parameters are revealed.The mean flow velocity of the pulsating fluid is chosen to be either subcritical or supercritical.The numerical results show that the curved pipe conveying pulsating fluid can exhibit rich dynamical behaviors,including periodic and quasi-periodic motions.It is also found that the preferred instability type of a cantilevered curved pipe conveying steady fluid is mainly in the flutter of the second mode.For a moderate value of the mass ratio,however,a third-mode flutter may occur,which is quite different from that of a straight pipe system.

Harmonic balance simulation of the influence of component uniformity and reliability on the performance of a Josephson traveling wave parametric amplifier

A Josephson traveling wave parametric amplifier(JTWPA),which is a quantum-limited amplifier with high gain and large bandwidth,is the core device of large-scale measurement and control systems for quantum computing.A typical JTWPA consists of thousands of Josephson junctions connected in series to form a transmission line and hundreds of shunt LC resonators periodically loaded along the line for phase matching.Because the variation of these capacitors and inductors can be detrimental to their high-frequency characteristics,the fabrication of a JTWPA typically necessitates precise processing equipment.To guide the fabrication process and further improve the design for manufacturability,it is necessary to understand how each electronic component affects the amplifier.In this paper,we use the harmonic balance method to conduct a comprehensive study on the impact of nonuniformity and fabrication yield of the electronic components on the performance of a JTWPA.The results provide insightful and scientific guidance for device design and fabrication processes.