Modeling and Experimental Validation of DNA Motion in Uniform and Nonuniform DC Electric Fields

2010 ◽  
Vol 1 (4) ◽  
Author(s):  
Regis A. David ◽  
Brian D. Jensen ◽  
Justin L. Black ◽  
Sandra H. Burnett ◽  
Larry L. Howell
Keyword(s):  
Mathematical Model ◽  
Electric Fields ◽  
New Technique ◽  
Strongly Correlated ◽  
System A ◽  
Modeling And Experiments ◽  
Foreign Dna ◽  
A New Technique ◽  
Dna Motion ◽  
The Mathematical Model

We are developing a new technique to insert foreign DNA into a living cell using a microelectromechanical system. This new technique relies on electrical forces to move DNA in a nonuniform electric field. To better understand this phenomenon, we perform integrated modeling and experiments of DNA electrophoresis. This paper describes the protocol and presents the results for DNA motion experiments using fabricated gel electrophoresis devices. We show that DNA motion is strongly correlated with ion transport (current flow) in the system. A better understanding of electrophoretic fundamentals allows for the creation of a mathematical model to predict the motion of DNA during electrophoresis in both uniform and nonuniform electric fields. The mathematical model is validated within 4% through comparison with the experimental results.

A guaranteed deterministic approach to margining on exchange-traded derivatives market: Numerical experiment

2021 ◽  
Vol 57 (4) ◽  
pp. 76
Author(s):  
Sergey Smirnov
Keyword(s):  
Mathematical Model ◽  
Risk Management ◽  
Critical Role ◽  
Deterministic Approach ◽  
Computational Framework ◽  
Modern Approach ◽  
System A ◽  
Lipschitz Constants ◽  
Isaacs Equations ◽  
The Mathematical Model

The article discusses a modern approach to risk management of the central counterparty,primarily the issue of the sufficiency of its financial resources, including the provision of clearingmembers, the capital of the central counterparty and the mutual liability fund. The main subject is the margining system, responsible for an adequate level of collateral for clearing members, that plays critical role in risk management, being the vanguard in protecting against losses associated with default by clearing members and the most sensitive to market risk part of the central counterparty’s skin of the game. A system of margining a portfolio of options and futures in the derivatives market is described, with default management based on the methodology proposed by a number of inventors, registered in 2004. For this system, a mathematical model of margining (i.e. determining the required level of the collateral) is built, based on the ideology of a guaranteed deterministic approach to superhedging: Bellman–Isaacs equations are derived from the economic meaning of the problem. A form of these equations, convenient for calculations, is obtained. Lipschitz constants for the solutions of Bellman–Isaacs equations are estimated. A computational framework for efficient numerical solution of these equations is created. Numerical experiments are carried out on some model examples to demonstrate the efficiency of the system. These experiments also show practical implications of marginsubadditivity — a crucial property of the mathematical model.

Investigation of Rub-Impact Setup Supported on Flexible Multi-Bearing Rotor

2012 ◽  
Author(s):  
Abdulazim H. Falah ◽  
Emad A. Khorshid ◽  
Khalid A. Alhazza
Keyword(s):  
Nonlinear Dynamics ◽  
Mathematical Model ◽  
Ball Bearings ◽  
Vibration System ◽  
Test Rig ◽  
Chaotic Response ◽  
Impact Device ◽  
Modeling And Experiments ◽  
In The Beginning ◽  
The Mathematical Model

Vibration system investigation of the chaotic response of full annular rub impact rotor system supported on two ball bearings is investigated. Modeling and experiments of nonlinear dynamics on flexible multi-bearing rotor test rig is presented in this work. The test rig has two balancers that are assembled on rotor shaft, a rub impact device at the center, and ball bearings at both ends of the shaft. A 12-degree-of-freedom (DOF) linear model was developed for this test rig. The mathematical model was developed in the beginning without considering the rub impact part in order to validate the model with the experiment results. Then, then experimentally chaotic response and bifurcation diagram of the rub impact system were investigated.

scholarly journals Melacak Dampak Perubahan Iklim Terhadap Kondisi Makroekonomi dengan Teori Permainan Dinamis

2018 ◽  
Vol 7 (2) ◽  
pp. 57-62
Author(s):  
Muhammad Wakhid Musthofa
Keyword(s):  
Climate Change ◽  
Economic Growth ◽  
Mathematical Model ◽  
Equation System ◽  
Output Function ◽  
Macroeconomic Conditions ◽  
System A ◽  
Economic Growth Model ◽  
The Impact ◽  
The Mathematical Model

Makalah ini membahas tentang model matematika dampak perubahan iklim terhadap kondisi makroekonomi suatu negara. Dengan mengacu pada model pertumbuhan ekonomi endogen pada suatu negara, dengan fungsi output berbentuk fungsi Cobb-Douglas akan diturunkan model matematika yang mendeskripsikan dampak perubahan iklim terhadap kondisi makroekonomi suatu negara. Selanjutnya, akan dikonstruksikan pula fungsi ongkos yang berhubungan dengan model matematika yang telah diturunkan. Mengingat model matematika tersebut masih dalam bentuk sistem persamaan nonlinear, maka diperlukan proses linearisasi untuk menghasilkan model matematika yang linear sehingga memudahkan untuk dianalisis maupun diaplikasikan. [This paper discusses the mathematical model of the impact of climate change on the macroeconomic conditions of a country. By referring to an endogenous economic growth model in a country, with the output function in the form of a Cobb-Douglas function, a mathematical model will be described that describes the effects of climate change on the macroeconomic conditions of a country. Furthermore, it will also construct cost functions related to mathematical models that have been derived. Considering that the mathematical model is still in the form of a nonlinear equation system, a linearisation process is needed to produce a linear mathematical model that makes it easy to analyze and apply.]

Modeling DNA Motion Under Electrostatic Repulsion Within a Living Cell

2009 ◽  
Author(s):  
Regis A. David ◽  
Brian D. Jensen
Keyword(s):  
Biological Sciences ◽  
Living Cell ◽  
Negative Charge ◽  
Electrostatic Repulsion ◽  
Dna Transfection ◽  
Transgenic Organisms ◽  
A Cell ◽  
Foreign Dna ◽  
A New Technique ◽  
Dna Motion

We are developing a new technique, called nanoinjection, to insert foreign DNA into a living cell. Such DNA transfection is commonly used to create transgenic organisms vital to the study of genetics, immunology, and many other biological sciences. In nanoinjection, DNA, which has a net negative charge, is electrostatically attracted to a micromachined lance. The lance then pierces the cell membranes, and the voltage on the lance is reversed, repelling the DNA into the cell. This paper presents a mathematical model to predict the motion (trajectory) of DNA particles within a cell in the presence of the electric field developed by the lance and the substrate. The model is used to predict the scattering of DNA through the cell due to electrostatic repulsion. We are currently preparing experiments which will be used to validate the model.

Modeling and Simulation of pH Dependent Isotachophoresis

2009 ◽  
Author(s):  
Jaesool Shim ◽  
Prashanta Dutta ◽  
Cornelius F. Ivory
Keyword(s):  
Mathematical Model ◽  
Mass Conservation ◽  
Microfluidic System ◽  
Band Broadening ◽  
System A ◽  
Band Dispersion ◽  
Electroneutrality Condition ◽  
Ph Dependent ◽  
The Mathematical Model ◽  
Ionic Components

This paper presents a mathematical model for pH gradient ITP in a microfluidic system. The mathematical model is based on mass conservation, charge conservation and electroneutrality condition in the system. A finite volume based numerical model is developed to simulate pH dependent isotachophoresis (ITP) in microfluidic devices. Numerical results of pH dependent ITP are obtained for straight and dog-leg microchannels. For both channels, five ionic components are used to simulate the model ITP system. The ITP results obtained from dog-leg microchannel capture the band broadening and band dispersion observed in T-channel junction. However, no such dispersion is noticed for ITP in the straight microchannel.

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