ON A PERIMETER-PRESERVING PLANE CURVE FLOW

The purpose of this paper is to investigate a new type of evolution problem for closed convex plane curves which will preserves the perimeter of the curve but expands the enclosed area and the final limiting curve is a circle in the Hausdorff metric in the plane.

SOME REMARKS ABOUT THE AREA-PRESERVING CONVEX CURVE FLOW IN THE PLANE

Using Picard's theorem and the Leray-Schauder fixed point theorem to reinvestigate the area-preserving convex curve flow in the plane which is considered as a coupled system and thus different from the setting handled by Gage.

Forced Inspiratory Flow Volume Curve in Patients with Obstructive Sleep Apnea-Hypopnea Syndrome

Objective: Obstructive sleep apnea-hypopnea syndrome (OSA) is a disease of obstructive apnea or hypopnea caused by a repeated partial or complete collapse of the upper airway during sleep. The inspiratory part of the flow-volume curve (F-V curve) can be used as an auxiliary means to evaluate upper airway obstruction in adults. This study is to evaluate the ability of the F-V curve to predict the OSA and explore inspiratory indicators related to airway obstruction during sleep. Methods: There were 332 patients included in this cross-sectional study, who were accompanied by snoring, daytime sleepiness and other symptoms, with suspicion of OSA. According to the nocturnal polysomnography, the subjects were distributed into mild to moderate OSA group, severe OSA group and non-OSA group. A pulmonary function test was used to collect the subjects’ spirometry and F-V curves. Results: There was no significant difference in a variety of indices derived from the F-V curve between OSA and normal subjects, including 25% inspiratory flow rate, middle inspiratory flow rate, 75% inspiratory flow rate, peak flow rate, and forced inspiratory flow rate in the first second. The pulmonary function parameters were significantly correlated with the weight, age and sex of the subjects. Conclusion: These findings suggest that the inspiratory curve of pulmonary function cannot evaluate the upper airway abnormalities in patients with obstructive apnea-hypopnea syndrome.

On a Class of Generalized Curve Flows for Planar Convex Curves

In this paper,the authors consider a class of generalized curve flow for convex curves in the plane.They show that either the maximal existence time of the flow is finite and the evolving curve collapses to a round point with the enclosed area of the evolving curve tending to zero,i.e.,limt→T A(t)=0,or the maximal time is infinite,that is,the flow is a global one.In the case that the maximal existence time of the flow is finite,they also obtain a convergence theorem for rescaled curves at the maximal time.

Rheological Behaviour for Polymer Melts and Concentrated SolutionsPart Ⅱ: Material Function with Nagai Chain Constraints and Determination of Their Parameters from Flow Curves

An integral constitutive equation and a set of material functions for describing the strain history of polymer melts were formulated in terms of the Cauchy-Green and Finger tensors. A simple memory function and the dependence of ηo and τt on M3.4 were derived from the theory of non-linear viscoelasticity with constraints of entanglements for polymer melts and substituted into the Oldroye-Walters-Fredickson constitutive equation. An integral constitutive equation for polymer melts was consequently obtained. Some material functions of the constitutive equation related to certain 'test flow' are examined as follows : (1) simple steady shear flow; (2) steady elongation flow; (3) small-amplitude oscillatory shear flow; (4) stress growth upon the inception of steady shear elongation flow; (5) stress relaxation (modulus and compllance). These theoretical relations for simple steady shear flow were compared with experimental data from our laboratory and references for various polymer melts and concentrated solutions. A good agreement between the theory and experiment was achieved.

Symmetric Development of Meso Perturbation in Zonally Curved Basic Flow

Addressed is a problem as to meso perturbation wave ensemble development in a curved basic flow in the context of a f-plane non-hydrostatic equilibrium acoustic wave filtering model in natural coordinates with the aid of the WKJB and energetic approaches. Results show that the symmetric development depends crucially on the matching of structures of the disturbance wave and background field, and for a smooth (curved) basic flow the wave ensemble evolution hinges upon the spatial imhomogeneity of nonthermal wind of the background field (under nongradient wind balance). Finally, presented is the wave ensemble evolution in relation to the thermal curvature vorticity in the background field.

Comparison on Mathematical Models for Description of Flow Curves of Stable Austenitic Steels

The flow curves were measured for the stable austenitic steels 304L and 304LN by means of tensile test at room temperature,which are described by the models σ=K1εn1 + exp(K2 + n2ε), σ=Kεn1+n2lnε and σ=σ0+Kεn (where, K1, K2, n1 andn2; K, n1 and n2; σ0, K and n are constant). The comparison of the maximum deviations and the consideration of thevariation of the work hardening rate with true strain show that the flow curves for the austenitic steels 304L and 304LN canbe described by the model σ=Kεn1+n2 lnε at higher precision.The derivatives of the models σ=K1εn1 + exp(K2 + n2ε) and σ=Kεn1+n2lnε with respect to true strain, exhibit theextreme at low true strain. This inherent character indicates that both models are unsuitable to describe the part of the workhardening rate curve at low true strain.

NUMERICAL INVESTIGATION OF THREE-DIMENSIONAL VISCOUS INCOMPRESSIBLE FLOWS IN DIVERGENT CURVED CHANNELS AND TURBULENT MODEL STUDY

In order to make the numerical calculation of viscous flows more convenient for the flows in channel with complicated profile governing equations expressed in the arbitrary curvilinear coordinates were derived by means of Favre density-weighted averaged method, and a turbulent model with effect of curvature modification was also derived. The numerical calculation of laminar and turbulent flown in divergent curved channels was carried out by means of parabolizeil computation method. The calculating results were used to analyze and investigate the aerodynamic performance of talor cascades in compressors preliminarily.

Prediction of Flow Duration Curves for Ungauged Basins with Quasi-Newton Method

Prediction of flow-duration-curves (FDC) is an important task for water resources planning, management and hydraulic energy production. Classification of the basins as carstic and non-carstic may be used to estimate parameters of the FDC with predictive tools for catchments with/without observed stream flow. There is a need for obtaining FDC for ungauged stations for efficient water resource planning. Thus, study proposes a quite new approach, called the EREFDC model, for estimating the parameters of the FDC for which the parameters of the FDC are obtained with quasi-Newton method. Estimation are made for using the bv gauged stations at first than the FDC parameters are estimated for ungauged stations based on drainage area, annual mean precipitation, mean permeability, mean slope, latitude, longitude, and elevation from the mean sea level are used. The EREFDC model consists of various type of linear- and nonlinear mathematical equations, is able to predict a wide range of the FDC parameters for gauged and ungauged basins. The method is applied to 72 unimpaired catchments studied are about for 50 years average daily measured stream flow. Results showed that the EREFDC model may be used for estimating. FDC parameters for ungauged hydrological basins in order to find FDC for ungauged stations. Results also showed that the EREFDC model performs better in carstic regions than non-carstic regions. In addition, parameters of FDC for tributaries at the basins with insufficient flow data or without flow data may be determined by using basin characteristics.

Performance improvement of air-breathing proton exchange membrane fuel cell(PEMFC) with a condensing-tower-like curved flow field

Air-breathing proton exchange membrane fuel cells(PEMFCs) are very promising portable energy with many advantages. However, its power density is low and many additional supporting parts affect its specific power. In this paper, we aim to improve the air diffusion and fuel cell performance by employing a novel condensing-tower-like curved flow field rather than an additional fan, making the fuel cell more compact and has less internal power consumption. Polarization curve test and galvanostatic discharge test are carried out and proved that curved flow field can strengthen the air diffusion into the PEMFC and improve its performance. With appropriate curved flow field, the fuel cell peak power can be 55.2%higher than that of planar flow field in our study. A four-layer stack with curved cathode flow field is fabricated and has a peak power of 2.35 W(120 W/kg).

Determination of Flow Curve and Plastic Anisotropy of Medium-thick Metal Plate:Experiments and Inverse Analysis

Sheet bulk metal forming is widely used for medium thick metal plate due to its convenience in the manu- facture of accurately finished 3D functional components. To obtain precise anisotropy and flow curve of metal plate is a prerequisite for correct simulation of sheet bulk metal forming processes. Inverse analysis of compression test was introduced here to evaluate the sensitivity of different flow curve models and geometric influence of compression test specimen. Besides, a methodology was proposed to compute plastic anisotropic coefficients of Hill quadratic yield cri- terion, which is based on the ratios of flow curves obtained by inverse analysis of compression tests using specimens cut in six directions on the medium-thick metal plate. The obtained flow curves and anisotropic coefficients were compared with those calculated from tensile tests. Flow curves based on inverse analysis of compression tests cover the curves of the tensile tests well, while the anisotropic coefficients are different, especially for the coefficient relat- ed to the RT45 direction. To estimate the effectiveness of the proposed method, the calculated material properties and those based on the traditional tensile tests were applied in a rim-hole process simulation. The simulation results based on the material properties from inverse analysis of compression tests accorded with the tested properties better.

Curve Shortening Flow in Arbitrary Dimensional Euclidian Space

In this paper, curve shortening flow in Euclidian space R^n（n≥3） is studied, and S. Altschuler＇s results about flow for space curves are generalized. We prove that the curve shortening flow converges to a straight line in infinite time if the initial curve is a ramp. We also prove the planar phenomenon when the curve shortening flow blows up.

Investigation of in situ Growth of SrMoO_4 Nanoplates by Microcalorimetry

SrMoO4 nanoplates were synthesized by a facile reverse microemulsion method at room temperature.Energy evolution of this in situ growth process was monitored by means of a microcalorimeter.A sharp exothermic peak for the initial reaction and two discontinuous relatively weak exothermic peaks for the subsequent crystal growth emerged on the microcalorimetric heat flow curve.Based on the in situ thermokinetic data,the rate constants of the nucleation process and crystallization process at 298.15 K were calculated to be 4.078×10-3 and 5.033×10-4 s-1,respectively.The growth mechanism and energy evolution were investigated.

Hot deformation behavior of Fe-29Ni-17Co alloy

Hot compression tests were carried out on a Fe-29Ni-17Co alloy in the temperature range of 900 ℃ to 1200 ℃ and at strain rates of 0.001-1 s-1. Dynamic recrystallization was found responsible for flow softening during hot compression. The flow behavior was successfully analyzed by the hyperbolic sine equation and the corresponding material constants A, n and αwere determined. The value of apparent activation energy was determined as 423 kJ/mol. The peak and steady state strains showed simple power-law dependence on the Zener-Hollomon parameter. The dynamic recrystallization kinetics was analyzed using Avrami equation and the corresponding exponent was determined to be about 2.7. This value, higher than 2 reported in the literatures, is associated with the mechanism of continuous dynamic recrystallization in the studied alloy. The flow curve up to the peak was modeled by the Cingara equation and the strain exponent, c, was determined about 0.85. The higher value of c compared with the value of 0.2 which has been reported for some stainless steels fortified the idea of extended dynamic recovery or continuous dynamic recrystallization in the studied alloy.

Singularities of the Curve Shortening Flow in a Riemannian Manifold

In this paper,the curve shortening flow in a general Riemannian manifold is studied,Altschuler’s results about the flow for space curves are generalized.For any n-dimensional(n ≥ 2)Riemannian manifold(M,g) with some natural assumptions,we prove the planar phenomenon when the curve shortening flow blows up.

Hydrological simulation approaches for BMPs and LID practices in highly urbanized area and development of hydrological performance indicator system

Urbanization causes hydrological change and increases stormwater runoff volumes, leading to flooding, erosion, and the degradation of instream ecosystem health. Best management practices （BMPs）, like detention ponds and infiltration trenches, have been widely used to control flood runoff events for the past decade. However, low impact development （LID） options have been proposed as an alternative approach to better mimic the natural flow regime by using decentralized designs to control stormwater runoff at the source, rather than at a centralized location in the watershed. For highly urbanized areas, LID stormwater management practices such as bioretention cells and porous pavements can be used to retrofit existing infrastructure and reduce runoff volumes and peak flows. This paper describes a modeling approach to incorporate these LID practices and the two BMPs of detention ponds and infiltration trenches in an existing hydrological model to estimate the impacts of BMPs and LID practices on the surface runoff. The modeling approach has been used in a parking lot located in Lenexa, Kansas, USA, to predict hydrological performance of BMPs and LID practices. A performance indicator system including the flow duration curve, peak flow frequency exceedance curve, and runoff coefficient have been developed in an attempt to represent impacts of BMPs and LID practices on the entire spectrum of the runoff regime. Results demonstrate that use of these BMPs and LID practices leads to significant stormwater control for small rainfall events and less control for flood events.

Effect of tempering temperature on strain hardening exponent and flow stress curve of 1000MPa grade steel for construction machinery

To study the effect of tempering temperature on strain hardening exponent and flow stress curve,one kind of 1000 MPa grade low carbon bainitic steel for construction machinery was designed,and the standard uniaxial tensile tests were conducted at room temperature.A new flow stress model,which could predict the flow behavior of the tested steels at different tempering temperatures more efficiently,was established.The relationship between mobile dislocation density and strain hardening exponent was discussed based on the dislocation-stress relation.Arrhenius equation and an inverse proportional function were adopted to describe the mobile dislocation,and two mathematical models were established to describe the relationship between tempering temperature and strain hardening exponent.Nonlinear regression analysis was applied to the Arrhenius type model,hence,the activation energy was determined to be 37.6kJ/mol.Moreover,the square of correlation coefficient was 0.985,which indicated a high reliability between the fitted curve and experimental data.By comparison with the Arrhenius type curve,the general trend of the inverse proportional fitting curve was coincided with the experimental data points except of some fitting errors.Thus,the Arrhenius type model can be adopted to predict the strain hardening exponent at different tempering temperatures.

A modification of local path marginal cost on the dynamic traffic network

Path marginal cost （PMC） is the change in totaltravel cost for flow on the network that arises when timedependentpath flow changes by 1 unit. Because it is hardto obtain the marginal cost on all the links, the local PMC,considering marginal cost of partial links, is normallycalculated to approximate the global PMC. When analyzingthe marginal cost at a congested diverge intersection, ajump-point phenomenon may occur. It manifests as alikelihood that a vehicle may unsteadily lift up （down） inthe cumulative flow curve of the downstream links. Previously,the jump-point caused delay was ignored whencalculating the local PMC. This article proposes an analyticalmethod to solve this delay which can contribute toobtaining a more accurate local PMC. Next to that, we usea simple case to calculate the previously local PMC and themodified one. The test shows a large gap between them,which means that this delay should not be omitted in thelocal PMC calculation.

The Blow up Analysis of the General Curve Shortening Flow

It is shown that the curvature function satisfies a nonlinear evolution equation under the general curve shortening flow and a detailed asymptotic behavior of the closed curves is presented when they contract to a point in finite time.

Rate decline analysis of multiple fractured horizontal well in shale reservoir with triple continuum

Multiple fractured horizontal well(MFHW) is widely applied in the development of shale gas. To investigate the gas flow characteristics in shale, based on a new dual mechanism triple continuum model, an analytical solution for MFHW surrounded by stimulated reservoir volume(SRV) was presented. Pressure and pressure derivative curves were used to identify the characteristics of flow regimes in shale. Blasingame type curves were established to evaluate the effects of sensitive parameters on rate decline curves, which indicates that the whole flow regimes could be divided into transient flow, feeding flow, and pseudo steady state flow. In feeding flow regime, the production of gas well is gradually fed by adsorbed gases in sub matrix, and free gases in matrix. The proportion of different gas sources to well production is determined by such parameters as storability ratios of triple continuum, transmissibility coefficients controlled by dual flow mechanism and fracture conductivity.