In the prospecting and exploiting of oil, to estimate the reserves and boundaries of areservoir has a great significance. Therefore, we propose approximate formulas to estimatethe volume of oil-storing space of a rese...In the prospecting and exploiting of oil, to estimate the reserves and boundaries of areservoir has a great significance. Therefore, we propose approximate formulas to estimatethe volume of oil-storing space of a reservoir.展开更多
Micropipette aspiration(MA) is widely applied in cell mechanics, however, at small deformations a common model corresponding to the MA is the half-space model wherein the finite cell size and cell compressibility are ...Micropipette aspiration(MA) is widely applied in cell mechanics, however, at small deformations a common model corresponding to the MA is the half-space model wherein the finite cell size and cell compressibility are neglected. This study extends the half-space model by accounting for the influence of cell geometry and compressibility(sphere model). Using a finite element analysis of cell aspiration into a micropipette, an elastic approximation formula of the aspirated length was derived for the sphere model. The approximation formula includes the geometry parameter of the sphere model(ζ = R/a, R is the radius of the cell, and a is the inner radius of the micropipette) and the Poisson's ratio v of the cell. The results indicate that the parameter and Poisson's ratio v markedly affect the aspirated length, particularly for small and v. When ζ→∞ and v→0.5,the approximation formula tends to the analytical solution for the half-space model. In the incompressible case(v = 0.5), within the general experimental range(ζ varying from 2 to 4), the difference between the analytical solution and the approximate one is significant, and is up to 29% of the approximation solution when ζ= 2. Additionally, parametere was introduced to evaluate the error of elastic moduli between the half-space model and sphere model. Based on the approximation formula, the ζ thresholds, beyond which e becomes larger than 10% and 20%, were derived.展开更多
A saddlepoint approximation for a two-sample permutation test was obtained by Robinson[7].Although the approximation is very accurate, the formula is very complicated and difficult toapply. In this papert we shall rev...A saddlepoint approximation for a two-sample permutation test was obtained by Robinson[7].Although the approximation is very accurate, the formula is very complicated and difficult toapply. In this papert we shall revisit the same problem from a different angle. We shall first turnthe problem into a conditional probability and then apply a Lugannani-Rice type formula to it,which was developed by Skovagard[8] for the mean of i.i.d. samples and by Jing and Robinson[5]for smooth function of vector means. Both the Lugannani-Rice type formula and Robinson'sformula achieve the same relative error of order O(n-3/2), but the former is very compact andmuch easier to use in practice. Some numerical results will be presented to compare the twoformulas.展开更多
An alternative set of angles for determining the position of a rigid body,instead of Euler angles,is proposed.These angles were used to model the motion of a rigid body(rotor)rotating around a horizontal axis.For the ...An alternative set of angles for determining the position of a rigid body,instead of Euler angles,is proposed.These angles were used to model the motion of a rigid body(rotor)rotating around a horizontal axis.For the proposed angles,equations similar to Euler’s kinematic equations were derived.Most machines with rotating shafts are designed horizontally,and the proposed angles are convenient for studying these machines using Euler’s dynamic equations.Equations were derived that allow one to obtain Euler angles from known proposed angles and to obtain proposed angles from known Euler angles.For a freely rotating rigid body,one can observe the Dzhanibekov’s effect,which can be classified as the periodic motion of an asymmetrical top and a type of tennis racket effect.The horizontal movement of the rotor,which is accompanied by the Dzhanibekov effect,well illustrates the advantages of the proposed angles.Based on Euler’s equations and using the proposed angles,two types of systems of differential equations were obtained.These systems do not degenerate,are tested on a well-known classical example and are applicable to any motion of a rigid body.Systems of differential equations were solved numerically using the Matlab software package using the ode45 subroutine(the simplest solver).The resulting solutions are stable and repeatable.The numerical results obtained are compared with the results obtained using the well-known modified predictor-corrector method.The preference of using the proposed coordinate system for numerical solutions of a system of differential equations compared to Eulerian angles is shown.For the free movement of an asymmetrical top,an analytical solution is known,obtained in the form of elliptic functions.This solution is extended to the Dzhanibekov’s effect and the results obtained are compared with the results of the numerical simulation of the Dzhanibekov’s effect.The formulas were obtained to determine the time before the first 180degree turn and the time between the next 180-degree turns.The formula for determining the time to the first turn was adjusted for the case of non-zero initial conditions for the three angular velocities,taking into account their sign.The known formula for the period of an asymmetrical top movement process during Dzhanibekov’s effect was confirmed.展开更多
基金This project is in part supported by the National Natural Science Foundation of China
文摘In the prospecting and exploiting of oil, to estimate the reserves and boundaries of areservoir has a great significance. Therefore, we propose approximate formulas to estimatethe volume of oil-storing space of a reservoir.
基金supported by the National Natural Science Foundation of China(Grant No.11032008)the Youth Fund of Taiyuan University of Technology
文摘Micropipette aspiration(MA) is widely applied in cell mechanics, however, at small deformations a common model corresponding to the MA is the half-space model wherein the finite cell size and cell compressibility are neglected. This study extends the half-space model by accounting for the influence of cell geometry and compressibility(sphere model). Using a finite element analysis of cell aspiration into a micropipette, an elastic approximation formula of the aspirated length was derived for the sphere model. The approximation formula includes the geometry parameter of the sphere model(ζ = R/a, R is the radius of the cell, and a is the inner radius of the micropipette) and the Poisson's ratio v of the cell. The results indicate that the parameter and Poisson's ratio v markedly affect the aspirated length, particularly for small and v. When ζ→∞ and v→0.5,the approximation formula tends to the analytical solution for the half-space model. In the incompressible case(v = 0.5), within the general experimental range(ζ varying from 2 to 4), the difference between the analytical solution and the approximate one is significant, and is up to 29% of the approximation solution when ζ= 2. Additionally, parametere was introduced to evaluate the error of elastic moduli between the half-space model and sphere model. Based on the approximation formula, the ζ thresholds, beyond which e becomes larger than 10% and 20%, were derived.
文摘A saddlepoint approximation for a two-sample permutation test was obtained by Robinson[7].Although the approximation is very accurate, the formula is very complicated and difficult toapply. In this papert we shall revisit the same problem from a different angle. We shall first turnthe problem into a conditional probability and then apply a Lugannani-Rice type formula to it,which was developed by Skovagard[8] for the mean of i.i.d. samples and by Jing and Robinson[5]for smooth function of vector means. Both the Lugannani-Rice type formula and Robinson'sformula achieve the same relative error of order O(n-3/2), but the former is very compact andmuch easier to use in practice. Some numerical results will be presented to compare the twoformulas.
文摘An alternative set of angles for determining the position of a rigid body,instead of Euler angles,is proposed.These angles were used to model the motion of a rigid body(rotor)rotating around a horizontal axis.For the proposed angles,equations similar to Euler’s kinematic equations were derived.Most machines with rotating shafts are designed horizontally,and the proposed angles are convenient for studying these machines using Euler’s dynamic equations.Equations were derived that allow one to obtain Euler angles from known proposed angles and to obtain proposed angles from known Euler angles.For a freely rotating rigid body,one can observe the Dzhanibekov’s effect,which can be classified as the periodic motion of an asymmetrical top and a type of tennis racket effect.The horizontal movement of the rotor,which is accompanied by the Dzhanibekov effect,well illustrates the advantages of the proposed angles.Based on Euler’s equations and using the proposed angles,two types of systems of differential equations were obtained.These systems do not degenerate,are tested on a well-known classical example and are applicable to any motion of a rigid body.Systems of differential equations were solved numerically using the Matlab software package using the ode45 subroutine(the simplest solver).The resulting solutions are stable and repeatable.The numerical results obtained are compared with the results obtained using the well-known modified predictor-corrector method.The preference of using the proposed coordinate system for numerical solutions of a system of differential equations compared to Eulerian angles is shown.For the free movement of an asymmetrical top,an analytical solution is known,obtained in the form of elliptic functions.This solution is extended to the Dzhanibekov’s effect and the results obtained are compared with the results of the numerical simulation of the Dzhanibekov’s effect.The formulas were obtained to determine the time before the first 180degree turn and the time between the next 180-degree turns.The formula for determining the time to the first turn was adjusted for the case of non-zero initial conditions for the three angular velocities,taking into account their sign.The known formula for the period of an asymmetrical top movement process during Dzhanibekov’s effect was confirmed.
