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Estimation for constant-stress accelerated life test from generalized half-normal distribution

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Journal of Systems Engineering and Electronics 2017年第4期28卷 810-816页

作者： Liang Wang Yimin Shi School of mathematics and statistics Xidian University department of Applied mathematics Northwestern Polytechnical University

In the constant-stress accelerated life test, estimation issues are discussed for a generalized half-normal distribution under a log-linear life-stress model. The maximum likelihood estimates with the corresponding fixed point type iterative algorithm for unknown parameters are presented, and the least square estimates of the parameters are also proposed. Meanwhile, confidence intervals of model parameters are constructed by using the asymptotic theory and bootstrap technique. Numerical illustration is given to investigate the performance of our methods.

关键词： accelerated life test maximum likelihood estimation least square method bootstrap technique asymptotic distribution

Centers and isochronous centers of a class of quasi-analytic switching systems

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Science China mathematics 2018年第7期61卷 1201-1218页

作者： Feng Li Pei Yu Yirong Liu Yuanyuan Liu School of mathematics and statistics Linyi University department of Applied mathematics Western University School of mathematics and statistics Central South University

In this paper, we study the integrability and linearization of a class of quadratic quasi-analytic switching systems. We improve an existing method to compute the focus values and periodic constants of quasianalytic switching systems. In particular, with our method, we demonstrate that the dynamical behaviors of quasi-analytic switching systems are more complex than those of continuous quasi-analytic systems, by showing the existence of six and seven limit cycles in the neighborhood of the origin and infinity, respectively, in a quadratic quasi-analytic switching system. Moreover, explicit conditions are obtained for classifying the centers and isochronous centers of the system.

关键词： quasi-analytic switching systems Lyapunov constant limit cycle center isochronous center

Numerical investigation of transitions in flow states and variation in aerodynamic forces for flow around square cylinders arranged inline

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Chinese Journal of Aeronautics 2018年第11期31卷 2111-2123页

作者： Waqas SARWAR ABBASI Shams UL ISLAM Lubna FAIZ Hamid RAHMAN mathematics department Air UniversityIslamabad mathematics department COMSATS Institute of Information Technology mathematics and statistics department Bacha Khan University

This study focuses on the transitions in flow states around two-, three-and four-inline square cylinders under the effect of Reynolds numbers at two different gap spacing values using the lattice Boltzmann method. For this purpose, Reynolds number is varied in the range 1–130 while two different values of spacing taken into account are gap spacing =2 and 5. Before going to actual problem, the code is tested for flow around a single square cylinder by comparing the results with experimental and numerical results of other researchers, and good agreement is *** current numerical computations yield that for both spacing values and all combinations of cylinders there exist three different sates of flow depending on Reynolds numbers: steady state, transitional state and unsteady state. It is found that the range of Reynolds numbers for these flow states is different for both spacing values. At gap spacing =2 the range of Reynolds numbers for each flow state decreases by increasing the number of cylinders while at gap spacing =5 opposite trend is observed. The results also show that at gap spacing =2 the reduction in drag force is greater than the corresponding reduction at gap spacing =5. The maximum reduction in drag force is observed at Reynolds numbers =1 at both spacing values. Similarly, at both spacing values and all Reynolds numbers, the maximum reduction in drag force is observed for the case of four-inline square cylinders.

关键词： Drag reduction Flow states Gap spacing Inline cylinders Reynolds number

Two-Way Interactions Between Equatorially-Trapped Waves and the Barotropic Flow

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Chinese Annals of mathematics,Series B 2009年第5期30卷 539-568页

作者： James FERGUSON Boualem KHOUIDER Maryam NAMAZI department of mathematics and statistics University of Victoria department of mathematics and statistics University of VictoriaPO BOX 3045 STN CSC Victoria

Lateral energy exchange between the tropics and the midlatitudes is a topic of great importance for understanding Earth＇s climate system. In this paper, the authors address this issue in an idealized set up through simple shallow water models for the interactions between equatorially trapped waves and the barotropic mode, which supports Rossby waves that propagate poleward and can excite midlatitude teleconnection patterns. It is found here that the interactions between a Kelvin wave and a fixed meridionai shear （mimicking the jet stream） generates a non-trivial meridional velocity and meridional convergence in phase with the upward motion that can attain a maximum of about 50%, which oscillates on frequencies ranging from one day to 10 days. When, on the other hand, the barotropic flow is forced by slowly propagating Kelvin waves a complex flow pattern emerges; it consists of a phase-locked barotropic response that is equatoriaily trapped and that propagates eastward with the forcing Kelvin wave and a certain number of planetary Rossby waves that propagate westward and toward the poles as seen in nature. It is suggested here that the poleward propagating waves are to some sort of multi-way resonant interaction with the phase locked response. Moreover, it is shown here that a numerical scheme with dispersion properties that depend on the direction perpendicular to the direction of propagation, namely the 2D central scheme of Nessyahu and Tadmor, can artificially alter significantly the topology of the wave fields and thus should be avoided in climate models.

关键词： Equatorially trapped waves Wave interactions Jet stream Rossby waves Phase locked Dispersion relation Central scheme Climate modeling

Decay rates of higher-order norms of solutions to the Navier-Stokes-Landau-Lifshitz system

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Applied mathematics and Mechanics(English Edition) 2018年第10期39卷 1499-1528页

作者： Ruiying WEI Yin LI Zheng'an YAO School of mathematics and statistics Shaoguan University department of mathematics Sun Yat-sen University

In this paper, we investigate a system of the incompressible Navier-Stokes equations coupled with Landau-Lifshitz equations in three spatial dimensions. Under the assumption of small initial data, we establish the global solutions with the help of an energy method. Furthermore, we obtain the time decay rates of the higher-order spatial derivatives of the solutions by applying a Fourier splitting method introduced by Schonbek(SCHONBEK, M. E. L2decay for weak solutions of the Navier-Stokes equations. Archive for Rational Mechanics and Analysis, 88, 209–222(1985)) under an additional assumption that the initial perturbation is bounded in L1(R3).

关键词： Navier-Stokes-Landau-Lifshitz system Fourier-splitting method decay rate

Fallopian tube assessment of the peristaltic-ciliary flow of a linearly viscous fluid in a finite narrow tube

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Applied mathematics and Mechanics(English Edition) 2018年第3期39卷 437-454页

作者： H.ASHRAF A.M.SIDDIQUI M.A.RANA department of mathematics and statistics Riphah International University department of mathematics York CampusPennsylvania State University

The present theoretical assessment deals with the peristaltic-ciliary trans- port of a developing embryo within a fallopian tubal fluid in the human fallopian tube. A mathematical model of peristalsis-cilia induced flow of a linearly viscous fluid within a fallopian tubal fluid in a finite two-dimensional narrow tube is developed. The lubrica- tion approximation theory is used to solve the resulting partial differential equation. The expressions for axial and radial velocities, pressure gradient, stream function, volume flow rate, and time mean volume flow rate are derived. Numerical integration is performed for the appropriate residue time over the wavelength and the pressure difference over the wavelength. Moreover, the plots of axial velocity, the appropriate residue time over wavelength, the vector, the pressure difference over wavelength, and the streamlines are displayed and discussed for emerging parameters and constants. Salient features of the pumping characteristics and the trapping phenomenon are discussed in detail. Yhrther- more, a comparison between the peristaltic flow and the peristaltic-ciliary flow is made as the special case. Relevance of the current results to the transport of a developing embryo within a fallopian tubal fluid from ampulla to the intramural in the fallopian tube is also explored. It reveals the fact that cilia along with peristalsis helps to complete the required mitotic divisions while transporting the developing embryo within a fallopian tubal fluid in the human fallopian tube.

关键词： peristaltic-ciliary flow linearly viscous fluid analytic solution human fal-lopian tube

Expansion properties for finite subdivision rules I Dedicated to the Memories of William P. Thurston and Lei Tan

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Science China mathematics 2018年第12期61卷 2237-2266页

作者： William J.Floyd Walter R.Parry Kevin M.Pilgrim department of mathematics Virginia Tech department of mathematics and statistics Eastern Michigan University department of mathematics Indiana University

Among Thurston maps (orientation-preserving, postcritically finite branched coverings of the 2-sphere to itself), those that arise as subdivision maps of a finite subdivision rule form a special family. For such maps, we investigate relationships between various notions of expansion—combinatorial, dynamical, algebraic,and coarse-geometric.

关键词： finite subdivision rule expanding map postcritically finite Thurston map

The constructive technique and its application in solving a nonlinear reaction diffusion equation

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Chinese Physics B 2009年第2期18卷 405-410页

作者：赖绍永郭云喜青音吴永宏 department of Applied mathematics Southwestern University of Finance and Economics department of mathematics and statistics Curtin University of Technology

A mathematical technique based on the consideration of a nonlinear partial differential equation together with an additional condition in the form of an ordinary differential equation is employed to study a nonlinear reaction diffusion equation which describes a real process in physics and in chemistry. Several exact solutions for the equation are acquired under certain circumstances.

关键词： additional generating condition method exact solutions nonlinear reaction-diffusion equation

Numerical Study of Mixed Convective Peristaltic Flow through Vertical Tube with Heat Generation for Moderate Reynolds and Wave Numbers

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Communications in Theoretical Physics 2018年第4期69卷 449-460页

作者： Tariq Javed B.Ahmed M.Sajid department of mathematics and statistics International Islamic University

The current study focuses on the numerical investigation of the mixed convective peristaltic mechanism through a vertical tube for non-zero Reynolds and wave number. In the set of constitutional equations, energy equation contains the term representing heat generation parameter. The problem is formulated by dropping the assumption of lubrication theory that turns the model mathematically into a system of the nonlinear partial differential equations. The results of the long wavelength in a creeping flow are deduced from the present analysis. Thus, the current study explores the neglected features of peristaltic heat flow in the mixed convective model by considering moderate values of Reynolds and wave numbers. The finite element based on Galerkin's weighted residual scheme is applied to solve the governing equations. The computed solution is presented in the form of contours of streamlines and isothermal lines, velocity and temperature profiles for variation of different involved parameters. The investigation shows that the strength of circulation for stream function increases by increasing the wave number and Reynolds number. Symmetric isotherms are reported for small values of time-mean flow. Linear behavior of pressure is noticed by vanishing inertial forces while the increase in pressure is observed by amplifying the Reynolds number.

关键词： mixed convection peristaltic flow moderate Reynolds number finite element method