• 제목/요약/키워드: Mathematica

검색결과 136건 처리시간 0.028초

동결건조한 소의 치밀골에서 전해질용액의 침지시간에 따른 Strength와 Stiffness의 변화 (Changes of Strength and Stiffness of Freeze-Dried Bovine Cortical Bone according to Rehydration Time in Electrolyte Solution)

  • 김남수;장세웅;김희은;정인성;최성진;최인혁
    • 한국임상수의학회지
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    • 제20권4호
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    • pp.482-488
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    • 2003
  • Transplanted cortical bone grafts of freeze-dried bones also function as sustaining for defected bones, however, it has less strength and is fragile without rehydration. In this study, strength and stiffness of freeze-dried bone from bovine cortical bones were evaluated by three point bending test according to different time frames such as rehydration times of 0.5, 3, 6, 12 and 24 hrs in electrolyte solution and was compared with those of frozen bones. The strength and stiffness of frozen bone were $264.4\pm36.7$ MPa, $17.0\pm1.5$ GPa, respectively. The strength and stiffness of freeze-dried bone which fat was removed by treatments of chloroform-methanol solutions for 6 days, then was freeze-dried at $-80^{\circ}C$ and sterilized with ethylene oxide gas, were $224.9\pm27.6$ MPa, $19.2\pm2.8$ GPa, respectively. The strength and stiffness of feeze-dried bone were decreased 15.0% and increased 13.2% than these of frozen bone, respectively. The strength and stiffness of freeze-dried bone rehydrated for 6 hrs were restored to 96.0% strength and 99.2% stiffness of frozen bone. The rehydration time of freeze-dried bone which had the highest strength and stiffness was six hours and three hours, respectively. The results of the mathematica program for the variation of the strength and stiffness showed 3 hours and 30 minutes of rehydration time in electrolyte solution for the best condition in the strength and stiffness which was adequate to treat freeze-dried cortical bone.

Flow of MHD Powell-Eyring nanofluid: Heat absorption and Cattaneo-Christov heat flux model

  • Sharif, Humaira;Khadimallah, Mohamed A.;Naeem, Muhammad Nawaz;Hussain, Muzamal;Hussain, Sajjad;Tounsi, Abdelouahed
    • Advances in nano research
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    • 제10권3호
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    • pp.221-234
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    • 2021
  • During the previous few years, phenomenon of bioconvection along with the use of nanoparticles showed large number of applications in technological and industrial field. This paper analyzed the bioconvection phenomenon in magnetohydrodynamic boundary layer flow of a Powell-Eyring nanoliquid past a stretchable cylinder with Cattaneo-Christov heat flux. In addition, the impacts of chemical reaction and heat generation/absorption parameter are considered. By the use of appropriate transformation, the governing PDEs (nonlinear) have been transformed and formulated into nonlinear ODEs. The resulting nonlinear ODEs subjected to relevant boundary conditions are solved analytically through homotopy analysis method which is programmed in Mathematica software. Graphical and numerical results versus physical quantities like velocity, temperature, concentration and motile microorganism are investigated under the impact of physical parameters. It is noted that velocity profile enhances as the curvature parameter A and Eyring-Powell fluid parameter M increases but a decline manner for large values of buoyancy ratio parameter Nr and bio-convection Rayleigh number Rb. In the presence of Prandtl number Pr, Eyring-Powell fluid parameter M and heat absorption parameter ��, temperature profile decreases. Nano particle concentration profile increases for increasing values of magnetic parameter Ha and thermophoresis parameter Nt. The motile density profile has revealed a decrement pattern for higher values of bio-convection Lewis number Lb and bio-convection peclet number Pe. This study may find uses in bio-nano coolant systems, advance nanomechanical bio-convection energy conversion equipment's, etc.

직각 쐐기와 응착접촉 하는 반무한 평판 내 전위: 제2부 - 보정 함수의 근사 및 응용 (Dislocation in Semi-infinite Half Plane Subject to Adhesive Complete Contact with Square Wedge: Part II - Approximation and Application of Corrective Functions)

  • 김형규
    • Tribology and Lubricants
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    • 제38권3호
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    • pp.84-92
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    • 2022
  • In Part I, developed was a method to obtain the stress field due to an edge dislocation that locates in an elastic half plane beneath the contact edge of an elastically similar square wedge. Essential result was the corrective functions which incorporate a traction free condition of the free surfaces. In the sequel to Part I, features of the corrective functions, Fkij,(k = x, y;i,j = x,y) are investigated in this Part II at first. It is found that Fxxx(ŷ) = Fxyx(ŷ) where ŷ = y/η and η being the location of an edge dislocation on the y axis. When compared with the corrective functions derived for the case of an edge dislocation at x = ξ, analogy is found when the indices of y and x are exchanged with each other as can be readily expected. The corrective functions are curve fitted by using the scatter data generated using a numerical technique. The algebraic form for the curve fitting is designed as Fkij(ŷ) = $\frac{1}{\hat{y}^{1-{\lambda}}I+yp}$$\sum_{q=0}^{m}{\left}$$\left[A_q\left(\frac{\hat{y}}{1+\hat{y}} \right)^q \right]$ where λI=0.5445, the eigenvalue of the adhesive complete contact problem introduced in Part I. To investigate the exponent of Fkij, i.e.(1 - λI) and p, Log|Fkij|(ŷ)-Log|(ŷ)| is plotted and investigated. All the coefficients and powers in the algebraic form of the corrective functions are obtained using Mathematica. Method of analyzing a surface perpendicular crack emanated from the complete contact edge is explained as an application of the curve-fitted corrective functions.

라그랑지 방법을 이용할 철봉 몸굽혀 휘돌기 동작의 시뮬레이션 (Simulation of Scooped Swing in High Bar Using Lagrange's Method : A Case Study)

  • 하종규
    • 한국콘텐츠학회논문지
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    • 제7권4호
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    • pp.234-240
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    • 2007
  • 이 연구는 철봉 몸굽혀 휘돌기 동작의 최적 모델을 구축하는 것이다. 연구 대상자는 국가대표 남자체조선수(나이 18세, 신장 153cm, 질량 48kg) 1명을 선정하였고, K대학교 체조장에 기 설치된 Spieth사의 철봉을 이용하여 실험하였다. 먼저 대상자에게 연구의 목적과 주의 사항을 주지시키고 사전 서면동의를 받은 후 실험을 실시하였다. 인체를 2분절로 모형화한 몸 굽혀 휘돌기 동작의 영상분석을 위하여 Qualisys사의 카메라(MCU-240) 6대와 소프트웨어인 QTM(Qualisys Track Mannager)을 사용하였다. 이 동작을 이중진자(HAT/total leg)로 모형화하고 라그랑지 운동방정식의 파라메터에 실험에서 획득한 수치를 입력하여 시뮬레이션하였다. 데이터 처리와 모델(미분 연립 방정식)의 해는 Mathematicas5.0으로 프로그래밍하여 구하였다. 분석변인에 대한 모델치와 실험치의 비교 결과는 첫째, 철봉의 최대변위는 모델치(약 0.18 m)가 실험치(약 0.16 m)보다 약 0.02m 더 크게 나타났다. 둘째, 분절1(HAT)의 각변위 패턴은 모두 증가곡선을 보였으나 변곡점의 차이가 나타났다. 셋째, 분절2(total leg)의 각변위 패턴은 전반적으로 유사하게 나타났으나 최대 각은 약 $4^{\circ}$ 차이를 보였다. 결론적으로 실험치와 일치하는 최적모델을 도출하지는 못하였지만 라그랑지 모델을 통한 시뮬레이션의 가능성을 제시하였다. 향후 제한된 2분절 모형을 3, 4분절 모델로 확장하고 생체물성(근골격계)을 정확하게 표현하는 물리적 도구를 개발하는 연구와 인체시스템을 근골격계와 근신경계을 통합한 모델구축이 이루어져야 하겠다.

복합진자 모형의 뉴튼.오일러 알고리즘 비교 (Comparison of Newton's and Euler's Algorithm in a Compound Pendulum)

  • 하종규
    • 한국운동역학회지
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    • 제16권3호
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    • pp.1-7
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    • 2006
  • The Primary type of swinging motion in human movement is that which is characteristic of a pendulum. The two types of pendulums are identified as simple and compound. A simple pendulum consist of a small body suspended by a relatively long cord. Its total mass is contained within the bob. The cord is not considered to have mass. A compound pendulum, on the other hand, is any pendulum such as the human body swinging by hands from a horizontal bar. Therefore a compound pendulum depicts important motions that are harmonic, periodic, and oscillatory. In this paper one discusses and compares two algorithms of Newton's method(F = m a) and Euler's method (M = $I{\times}{\alpha}$) in compound pendulum. Through exercise model such as human body with weight(m = 50 kg), body length(L = 1.5m), and center of gravity ($L_c$ = 0.4119L) from proximal end swinging by hands from a horizontal bar, one finds kinematic variables(angle displacement / velocity / acceleration), and simulates kinematic variables by changing body lengths and body mass. BSP by Clauser et al.(1969) & Chandler et al.(1975) is used to find moment of inertia of the compound pendulum. The radius of gyration about center of gravity (CoG) is $k_c\;=\;K_c{\times}L$ (단, k= radius of gyration, K= radius of gyration /segment length), and then moment of inertia about center of gravity(CoG) becomes $I_c\;=\;m\;k_c^2$. Finally, moment of inertia about Z-axis by parallel theorem becomes $I_o\;=\;I_c\;+\;m\;k^2$. The two-order ordinary differential equations of models are solved by ND function of numeric analysis method in Mathematica5.1. The results are as follows; First, The complexity of Newton's method is much more complex than that of Euler's method Second, one could be find kinematic variables according to changing body lengths(L = 1.3 / 1.7 m) and periods are increased by body length increment(L = 1.3 / 1.5 / 1.7 m). Third, one could be find that periods are not changing by means of changing mass(m = 50 / 55 / 60 kg). Conclusively, one is intended to meditate the possibility of applying a compound pendulum to sports(balling, golf, gymnastics and so on) necessary swinging motions. Further improvements to the study could be to apply Euler's method to real motions and one would be able to develop the simulator.

Comparative analysis on darcy-forchheimer flow of 3-D MHD hybrid nanofluid (MoS2-Fe3O4/H2O) incorporating melting heat and mass transfer over a rotating disk with dufour and soret effects

  • A.M. Abd-Alla;Esraa N. Thabet;S.M.M.El-Kabeir;H. A. Hosham;Shimaa E. Waheed
    • Advances in nano research
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    • 제16권4호
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    • pp.325-340
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    • 2024
  • There are several novel uses for dispersing many nanoparticles into a conventional fluid, including dynamic sealing, damping, heat dissipation, microfluidics, and more. Therefore, melting heat and mass transfer characteristics of a 3-D MHD Hybrid Nanofluid flow over a rotating disc with presenting dufour and soret effects are assessed numerically in this study. In this instance, we investigated both ferric sulfate and molybdenum disulfide as nanoparticles suspended within base fluid water. The governing partial differential equations are transformed into linked higher-order non-linear ordinary differential equations by the local similarity transformation. The collection of these deduced equations is then resolved using a Chebyshev spectral collocation-based algorithm built into the Mathematica software. To demonstrate how different instances of hybrid/ nanofluid are impacted by changes in temperature, velocity, and the distribution of nanoparticle concentration, examples of graphical and numerical data are given. For many values of the material parameters, the computational findings are shown. Simulations conducted for different physical parameters in the model show that adding hybrid nanoparticle to the fluid mixture increases heat transfer in comparison to simple nanofluids. It has been identified that hybrid nanoparticles, as opposed to single-type nanoparticles, need to be taken into consideration to create an effective thermal system. Furthermore, porosity lowers the velocities of simple and hybrid nanofluids in both cases. Additionally, results show that the drag force from skin friction causes the nanoparticle fluid to travel more slowly than the hybrid nanoparticle fluid. The findings also demonstrate that suction factors like magnetic and porosity parameters, as well as nanoparticles, raise the skin friction coefficient. Furthermore, It indicates that the outcomes from different flow scenarios correlate and are in strong agreement with the findings from the published literature. Bar chart depictions are altered by changes in flow rates. Moreover, the results confirm doctors' views to prescribe hybrid nanoparticle and particle nanoparticle contents for achalasia patients and also those who suffer from esophageal stricture and tumors. The results of this study can also be applied to the energy generated by the melting disc surface, which has a variety of industrial uses. These include, but are not limited to, the preparation of semiconductor materials, the solidification of magma, the melting of permafrost, and the refreezing of frozen land.