scholarly journals Analysis of Enhanced Diffusion in Taylor Dispersion via a Model Problem

2015 ◽  
pp. 31-71
Author(s):  
Margaret Beck ◽  
Osman Chaudhary ◽  
C. Eugene Wayne
Keyword(s):  
Model Problem ◽  
Taylor Dispersion ◽  
Enhanced Diffusion

Generalized Taylor dispersion phenomena in unbounded homogeneous shear flows

1991 ◽  
Vol 230 ◽  
pp. 147-181 ◽  
Author(s):  
I. Frankel ◽  
H. Brenner
Keyword(s):  
Degrees Of Freedom ◽  
Shear Flows ◽  
Model Problem ◽  
Physical Space ◽  
Taylor Dispersion ◽  
Positive Definite ◽  
Coarse Grained ◽  
Internal Space ◽  
Homogeneous Shear ◽  
Diffusive Model

Generalized Taylor dispersion theory is extended so as to enable the analysis of the transport in unbounded homogeneous shear flows of Brownian particles possessing internal degrees of freedom (e.g. rigid non-spherical particles possessing orientational degrees of freedom, flexible particles possessing conformational degrees of freedom, etc.). Taylor dispersion phenomena originate from the coupling between the dependence of the translational velocity of such particles in physical space upon the internal variables and the stochastic sampling of the internal space resulting from the internal diffusion process.Employing a codeformational reference frame (i.e. one deforming with the sheared fluid) and assuming that the eigenvalues of the (constant) velocity gradient are purely imaginary, we establish the existence of a coarse-grained, purely physical-space description of the more detailed physical-internal space (microscale) transport process. This macroscale description takes the form of a convective–diffusive ‘model’ problem occurring exclusively in physical space, one whose formulation and solution are independent of the internal (‘local’-space) degrees of freedom.An Einstein-type diffusion relation is obtained for the long-time limit of the temporal rate of change of the mean-square particle displacement in physical space. Despite the nonlinear (in time) asymptotic behaviour of this displacement, its Oldroyd time derivative (which is the appropriate one in the codeformational view adopted) tends to a constant, time-independent limit which is independent of the initial internal coordinates of the Brownian particle at zero time.The dyadic dispersion-like coefficient representing this asymptotic limit is, in general, not a positive-definite quantity. This apparently paradoxical behaviour arises due to the failure of the growth in particle spread to be monotonic with time as a consequence of the coupling between the Taylor dispersion mechanism and the shear field. As such, a redefinition of the solute's dispersivity dyadic (appearing as a phenomenological coefficient in the coarse-grained model constitutive equation) is proposed. This definition provides additional insight into its physical (Lagrangian) significance as well as rendering this dyadic coefficient positive-definite, thus ensuring that solutions of the convective–diffusive model problem are well behaved. No restrictions are imposed upon the magnitude of the rotary Péclet number, which represents the relative intensities of the respective shear and diffusive effects upon which the solute dispersivity and mean particle sedimentation velocity both depend.The results of the general theory are illustrated by the (relatively) elementary problem of the sedimentation in a homogeneous unbounded shear field of a size-fluctuating porous Brownian sphere (which body serves to model the behaviour of a macromolecular coil). It is demonstrated that the well-known case of the translational diffusion in a homogeneous shear flow of a rigid, non- fluctuating sphere (for which the Taylor mechanism is absent) is a particular case thereof.

Ion Beam Mixing of Ni-Ti Bilayered Thin Films

1985 ◽  
Vol 43 ◽  
pp. 290-291
Author(s):  
A. K. Rai ◽  
R. S. Bhattacharya ◽  
M. H. Rashid
Keyword(s):  
Crystal Structure ◽  
Thin Films ◽  
Amorphous Alloys ◽  
Ion Beam ◽  
Ion Bombardment ◽  
High Energy ◽  
Mixing Efficiency ◽  
Ion Beam Mixing ◽  
Enhanced Diffusion ◽  
Binary Metal

Ion beam mixing has recently been found to be an effective method of producing amorphous alloys in the binary metal systems where the two original constituent metals are of different crystal structure. The mechanism of ion beam mixing are not well understood yet. Several mechanisms have been proposed to account for the observed mixing phenomena. The first mechanism is enhanced diffusion due to defects created by the incoming ions. Second is the cascade mixing mechanism for which the kinematicel collisional models exist in the literature. Third mechanism is thermal spikes. In the present work we have studied the mixing efficiency and ion beam induced amorphisation of Ni-Ti system under high energy ion bombardment and the results are compared with collisional models. We have employed plan and x-sectional veiw TEM and RBS techniques in the present work.

PROGRAM TRAINING PENGEMBANGAN KEWIRAUSAHAAN UNTUK MENINGKATKAN KEMAMPUAN PENGELOLAAN BISNIS USAHA KECIL DAN MENENGAH (UKM)

SIGMA TEKNIKA ◽  
2019 ◽  
Vol 2 (1) ◽  
pp. 57
Author(s):  
Zaenal Arifin
Keyword(s):  
Model Problem ◽  
Problem Based Learning

Berdasarkan penelitian ini tentang perlunya program pelatihan kewirausahaan yang tepat Untuk UKM, terutama bagi UKM yang lagi merintis ushanya, penelitian ini bertujuan untuk memperoleh serta mengembangkan yang tepat  program pelatihan kewirausahaan untuk meningkatkan kemampuan manajemen bisnis di kalangan UKM. Model pendekatan yang digunakan dalam penelitian ini adalah; 1) model pengembangan ilmu dan teknologi pelatihan untuk Kewirausahaan, 2) model Problem Based Learning (PBL) adalah salah satu pelatihan strategi berorientasi proses pengajaran dan pembelajaran kontekstual (CTL). Konsep pelatihan CTL membantu pelatih / instruktur / guru untuk menghubungkan materi dengan situasi dunia nyata dan juga mendorong para peserta menggunakan pengetahuan mereka untuk diterapkan dalam situasi kehidupan nyata mereka para anggota masyarakat. Dari hasil implementasi model pelatihan, dapat disimpulkan bahwa: 1) Pelatihan memadukan model Problem Based Learning (PBL) dan pengembangan sains dan program pelatihan teknologi untuk Kewirausahaan dapat diterapkan secara efektif dalam suatu program pelatihan kewirausahaan untuk UKM pemula, 2) Program ini berhasil mensinergikan materi / teori pelatihan untuk situasi dunia nyata; 3) Program  ini juga berfungsi untuk membangun kerja sama tim. Akhirnya, model ini berhasil menunjukkan efektivitasnya dengan tingkat kehadiran di 90%, serta kerja tim terbentuk dalam membuat inovatif, asli dan layak untuk menjadi mengimplementasikan proposal bisnis

SOLUTION TO THE MODEL PROBLEM OF EXCITATION OF LOADED CONIC SLOT ANTENNA BY METHOD OF SINGULAR INTEGRAL EQUATIONS

2016 ◽  
Vol 75 (20) ◽  
pp. 1799-1812
Author(s):  
V. A. Doroshenko ◽  
S.N. Ievleva ◽  
N.P. Klimova ◽  
A. S. Nechiporenko ◽  
A. A. Strelnitsky
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Model Problem ◽  
Singular Integral Equations ◽  
Slot Antenna

PENERAPAN MODEL PROBLEM BASED LEARNING UNTUK MENINGKATKAN HASIL BELAJAR IPA MATERI PERUBAHAN LINGKUNGAN PADA SISWA KELAS IVSD 1 NGEMPLAK UNDAAN KUDUS SEMESTER II TAHUN PELAJARAN 2013/2014

2018 ◽  
Vol 7 (2) ◽  
pp. 136
Author(s):  
Moh Syafi'i
Keyword(s):  
Model Problem ◽  
Problem Based Learning

Penelitian bertujuan untuk meningkatkan hasil belajar IPA materi perubahan lingkungan pada siswa kelas IV SD 1 Ngemplak Undaan Kudus Semester II Tahun Pelajaran 2013/2014. Penelitian dilaksanakan dalam dua siklus, meliputi tahap perencanaan, pelaksanaan tindakan, pengamatan, serta refleksi. Jenis data yang digunakan berupa data kuantitatif dan kualitatif. Hasil penelitian yang diperoleh berupa hasil tes dan non tes. Data hasil tes merupakan data hasil perolehan pretest, tes formatif pada tiap akhir siklus, sedangkan data hasil non tes merupakan data lembar pengamatan performansi guru, lembar pengamatan aktivitas siswa. Sumber data: guru, siswa, dan dokumentasi. Teknik pengambilan data meliputi teknik tes dan non tes. Teknik analisis data menggunakan teknik analisis statistik deskriptif. Hasil penelitian menunjukkan bahwa hasil belajar siswa pada data awal 47,62%, pada siklus I 66,67 % sedangkan pada siklus II hasil belajar siswa 80,95 % mengalami kenaikan sebesar 12,21%.

PENERAPAN MODEL PEMBELAJARAN PROBLEM BASED LEARNING UNTUK MENINGKATKAN KETERAMPILAN BERPIKIR KRITIS PADA MUATAN MATEMATIKA KELAS 4

2019 ◽  
Vol 3 (2) ◽  
pp. 378-386
Author(s):  
Selly Purwita Sari ◽  
Henny Dewi Koeswanti ◽  
Sri Giarti
Keyword(s):  
Model Problem ◽  
Problem Based Learning

Tujuan penelitian ini untuk meningkatkan keterampilan berpikir kritis matematika melalui model Problem Based Learning pada kelas IV semester II. Jenis penelitian ini adalah penelitian tindakan kelas dengan empat tahapan yaitu, perencanaan, pelaksanaan, observasi dan refleksi yang dilakukan dalam dua siklus pembelajaran. Setiap siklus terdiri dari tiga pertemuan. Data diperoleh melalui teknik tes dan non tes. Adapun subjek penelitian ini adalah siswa kelas IV SD Mulyoharjo 05 Jepara sebanyak 23 siswa. Berdasarkan hasil penelitian dapat disimpulkan bahwa meningkatkan keterampilan berpikir kritis siswa pada mata pelajaran matematika sebesar 73,8 % dengan kategori sangat kritis dan kritis pada siklus I, 100% siswa dengan kategori sangat kritis dan kritis pada siklus II. Meningkatnya keterampilan berpikir kritis siswa pada mata pelajaran matematika berdampak pada peningkatan hasil belajar matematika sebesar 78,2 siswa tuntas pada siklus I dan 95,6 % siswa tuntas pada siklus II. Dengan demikian telah terbukti bahwa model pembelajaran Problem Based Learning dapat meningkatkan keterampilan berpikir kritis dan mata pelajaran matematika

RESEARCH OF THE IMPACT DEVICE MODEL OF THE ROD TYPE BY DIFFERENCE METHOD

2020 ◽  
pp. 73-80
Author(s):  
А.М. Слиденко ◽  
В.М. Слиденко
Keyword(s):  
Boundary Value Problem ◽  
Difference Method ◽  
Model Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Cross Sectional ◽  
Impact Device ◽  
Initial Boundary Value ◽  
The Impact

Приводится анализ механических колебаний элементов ударного устройства с помощью модели стержневого типа. Ударник и инструмент связаны упругими и диссипативными элементами, которые имитируют их взаимодействие. Аналогично моделируется взаимодействие инструмента с рабочей средой. Сформулирована начально-краевая задача для системы двух волновых уравнений с учетом переменных поперечных сечений стержней. Площади поперечных сечений определяются параметрическими формулами при сохранении объемов стержней. Параметрические формулы позволяют получать различного вида зависимости площади поперечного сечения стержня от его длины. Начальные условия отражают физическую картину взаимодействия инструмента с ударником и рабочей средой. Краевые условия описывают контактные взаимодействия ударника с инструментом и последнего с рабочей средой. В качестве модельной задачи рассматривается соударение ударника и инструмента через элемент большой жесткости. Начально-краевая задача исследуется разностным методом. Проводится сравнение решений задачи, полученных с помощью двухслойной и трехслойной разностных схем. Такие схемы реализованы в общей компьютерной программе в системе Mathcad. Показано, что при вычислениях распределения нормальных напряжений по длине стержня лучшими свойствами относительно устойчивости обладает двухслойная схема The article gives the analysis of mechanical vibrations of the impact device elements using the model of the rod type. The hammer and the tool are connected by elastic and dissipative elements that simulate their interaction. The interaction of the tool with the processing medium is simulated in a similar way. An initial boundary-value problem is formulated for a system of two wave equations taking into account the variable cross sections of the rods. Cross-sectional areas are determined by parametric formulas maintaining the volume of the rods. Parametric formulas allow one to obtain various dependence types of the cross-sectional area of the rod on its length. The initial and boundary conditions reflect the physical phenomenon of the tool interaction with the processing medium, and also describe the contact interactions of the hammer with the tool. The impacting of the hammer and the tool through an element of high rigidity is considered as a model problem. To control the limiting values, the solution of the model problem by the Fourier method is used. The initial-boundary-value problem is investigated by the difference method. A comparison of solutions obtained for the two-layer and three-layer difference schemes is given. Such schemes are realized in a common computer program in the Mathcad. It is shown that the two-layer scheme has the best properties in relation to stability while calculating the distribution of normal voltage along the length of the rod

Application of Mathematical Modeling during Monitoring and Optimization of Non-Stationary Regime of Oil Well

2016 ◽  
Vol 11 (1) ◽  
pp. 53-59
Author(s):  
A.S. Topolnikov
Keyword(s):  
Mathematical Modeling ◽  
Model Problem ◽  
Cylindrical Tube ◽  
Field Measurements ◽  
Stationary Flow ◽  
Stationary Regime ◽  
Oil Well ◽  
Time Duration ◽  
Typical Time ◽  
Radial Model

The paper presents results of modeling of periodical regime of oil well for the purpose of monitoring and optimization of its operation. To describe non-stationary flow in the reservoir a planar-radial model of filtration is employed. The flow of multiphase flux in the well elements (casing, tubing, annulus) is described by 1D Navier-Stoks equations. The pump work is modelled by specification of its rate-head curve. To estimate the typical time duration of the processes in the well and in the reservoir a solution of a model problem for cylindrical tube is given. Through the examples a solution of a problem of optimization of periodical regime of oil wells is demonstrated. The comparison with field measurements is presented.

Pengaruh Jenis Masalah pada Problem Based Learning terhadap Dinamika Metakognisi Siswa SMA Kelas X pada Konsep Stoikiometri

2014 ◽  
Vol 2 (2) ◽  
Author(s):  
Issaura Sherly Pamela ◽  
Muhammad Rusdi ◽  
Asrial Asrial
Keyword(s):  
Student Achievement ◽  
Experimental Design ◽  
Learning Process ◽  
Model Problem ◽  
Learning Experience ◽  
Problem Based Learning ◽  
Meaningful Learning ◽  
Learning Model ◽  
Group Design ◽  
Experimental Group

Innovation is needed in learning to make meaningful learning, so the student constructs their ownknowledge from the learning experience of learning process. One of the innovations is to integrate Problem Based Learning model. Problem Based Learning involves students to be active in every problem. Eleven problems type in Problem Based Learning that have different solving steps, due to every student different metacognition character potential and can change by given treatment. This research is a pre-experimental design: the pretest-posttest control and experimental group design with embedded experimental design. The metacognition character data were analyzed qualitaively, whereas the average grade data were analyzed quantitatively. The analysis of metacognition character shows the different metacognition characters and on learning process there is improvement of student achievement from 14% to 84.4%.

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