scholarly journals Effect of Ventricular Elasticity Due to Congenital Hydrocephalus

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2087
Author(s):  
Hemalatha Balasundaram ◽  
Senthamilselvi Sathiamoorthy ◽  
Shyam Sundar Santra ◽  
Rifaqat Ali ◽  
Vediyappan Govindan ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Cerebrospinal Fluid ◽  
Perturbation Technique ◽  
Current Model ◽  
Governing Equations ◽  
Symmetric Flow ◽  
Cerebrospinal Fluid Flow ◽  
Flow Transport ◽  
Brain Biomechanics ◽  
The Mathematical Model

Cerebrospinal fluid (CSF) is a symmetric flow transport that surrounds brain and central nervous system (CNS). Congenital hydrocephalusis is an asymmetric and unusual cerebrospinal fluid flow during fetal development. This dumping impact enhances the elasticity over the ventricle wall. Henceforth, compression change influences the force of brain tissues. This paper presents a mathematical model to establish the effects of ventricular elasticity through a porous channel. The current model is good enough for immediate use by a neurosurgeon. The mathematical model is likely to be a powerful tool for the better treatment of hydrocephalus and other brain biomechanics. The non-linear dimensionless governing equations are solved using a perturbation technique, and the outcome is portrayed graphically with the aid of MATLAB.

scholarly journals Statistical Analysis of the Mathematical Model of Entropy Generation of Magnetized Nanofluid

Inventions ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 32 ◽  
Author(s):  
Munawwar Ali Abbas ◽  
Ibrahim Hussain
Keyword(s):  
Mathematical Model ◽  
Reynolds Number ◽  
Statistical Analysis ◽  
Entropy Generation ◽  
Concentration Profile ◽  
Perturbation Technique ◽  
Governing Equations ◽  
Friction Forces ◽  
Long Wavelength ◽  
The Mathematical Model

This investigation introduces a mathematical model of entropy generation for Magnetohydrodynamic (MHD) peristaltic wave of nanofluid. The governing equations have been created by the supposition of low Reynolds number and long wavelength estimation. The scientific arrangement has been procured with the help of perturbation technique. The concentration profile, temperature profile, pressure distribution and friction forces are shown graphically for some important parameters. Further, the eventual outcomes of connection between the entropy generation and some various parameters have been plotted by means of correlation and regression. It is fundamental to find the affectability of each parameter on entropy generation.

scholarly journals Assessment of Steady and Unsteady Friction Models in the Draining Processes of Hydraulic Installations

Water ◽  
2021 ◽  
Vol 13 (14) ◽  
pp. 1888
Author(s):  
Óscar E. Coronado-Hernández ◽  
Ivan Derpich ◽  
Vicente S. Fuertes-Miquel ◽  
Jairo R. Coronado-Hernández ◽  
Gustavo Gatica
Keyword(s):  
Mathematical Model ◽  
Turbulent Flow ◽  
Water Velocity ◽  
Experimental Facility ◽  
Governing Equations ◽  
Pressure Oscillations ◽  
Air Pocket ◽  
Friction Models ◽  
The Mathematical Model

The study of draining processes without admitting air has been conducted using only steady friction formulations in the implementation of governing equations. However, this hydraulic event involves transitions from laminar to turbulent flow, and vice versa, because of the changes in water velocity. In this sense, this research improves the current mathematical model considering unsteady friction models. An experimental facility composed by a 4.36 m long methacrylate pipe was configured, and measurements of air pocket pressure oscillations were recorded. The mathematical model was performed using steady and unsteady friction models. Comparisons between measured and computed air pocket pressure patterns indicated that unsteady friction models slightly improve the results compared to steady friction models.

Effect of superfused insulin on cerebral cortical glucose utilization in awake goats

1987 ◽  
Vol 253 (4) ◽  
pp. E418-E427
Author(s):  
D. A. Pelligrino ◽  
D. J. Miletich ◽  
R. F. Albrecht
Keyword(s):  
Mathematical Model ◽  
Cerebrospinal Fluid ◽  
Metabolic Regulation ◽  
Glucose Utilization ◽  
The Other ◽  
Insulin Administration ◽  
Cortical Tissue ◽  
Control Tissue ◽  
The Mathematical Model ◽  
Test Control

The effect on cortical cerebral glucose utilization (CMRglu) of intracerebral insulin administration in awake goats was studied. The insulin was superfused in a mock cerebrospinal fluid (CSF) solution employing chronically implanted cranial windows. Two windows were implanted bilaterally: one window over an equivalent portion of each parietal cortex. With one window used to deliver insulin/CSF and the other used to simultaneously deliver CSF alone (control), changes in CMRglu were assessed using a modification of a sequential 2-[3H]- then 2-[14C]deoxy-D-glucose (2DG) technique originally described by Altenau and Agranoff (Brain Res. 153: 375-381, 1978). Initial experiments employing 125I-insulin demonstrated that the superfusion procedure increased insulin levels only in the outer 1 mm of cortical tissue exposed to insulin containing perfusate. Additional preliminary evaluations, using conditions known to alter CMRglu, generally established that present methods were adequate to induce and detect CMRglu changes. However, it was also shown experimentally and using a mathematical model that 2-[3H]DG test/control tissue ratios could be influenced by subsequent changes in CMRglu and the dephosphorylation rate. Thus 3H ratios could not be used to establish preexperimental test/control CMRglu relationships as the originally devised model assumed but could be employed to indicate changes in dephosphorylation. The mathematical model allowed for improved estimates of CMRglu changes from 2-[14C]DG/2-[3H]DG test over control tissue ratios. Even with these corrections, insulin was estimated to cause no more than an 8-15% increase in cortical CMRglu. A very limited role for insulin, at least in cerebral cortical metabolic regulation, is thus indicated.

Nonlinear waves in compacting media

1986 ◽  
Vol 164 ◽  
pp. 429-448 ◽  
Author(s):  
Victor Barcilon ◽  
Frank M. Richter
Keyword(s):  
Mathematical Model ◽  
Solitary Waves ◽  
Nonlinear Waves ◽  
Nonlinear Interaction ◽  
Phase Speed ◽  
Governing Equations ◽  
One Dimensional ◽  
The Earth ◽  
Permanent Shape ◽  
The Mathematical Model

An investigation of the mathematical model of a compacting medium proposed by McKenzie (1984) for the purpose of understanding the migration and segregation of melts in the Earth is presented. The numerical observation that the governing equations admit solutions in the form of nonlinear one-dimensional waves of permanent shape is confirmed analytically. The properties of these solitary waves are presented, namely phase speed as a function of melt content, nonlinear interaction and conservation quantities. The information at hand suggests that these waves are not solitons.

scholarly journals Weak resonances of periodical nonlinear oscillations

2017 ◽  
Vol 58 ◽  
Author(s):  
Olga Lavcel-Budko ◽  
Aleksandras Krylovas
Keyword(s):  
Mathematical Model ◽  
Asymptotic Solution ◽  
Space Variable ◽  
Nonlinear Oscillations ◽  
Initial Conditions ◽  
Perturbation Technique ◽  
The Mathematical Model

The mathematical model of nonlinear oscillations of weightless string is analyzed. Coefficients of the mathematical model and initial conditions are periodical functions of the space variable. A multiscale perturbation technique and integrating along characteristics are used to construct asymptotic solution without secular members.

Inverse Dynamic Analysis of Spatial Manipulators with Elastic Legs

1988 ◽  
Vol 12 (2) ◽  
pp. 63-69
Author(s):  
K.H. Low ◽  
R.N. Dubey
Keyword(s):  
Mathematical Model ◽  
Hybrid System ◽  
Perturbation Technique ◽  
Flexible Manipulator ◽  
System Of Equations ◽  
Joint Motion ◽  
Inverse Dynamic ◽  
Inverse Dynamic Analysis ◽  
Deflection Theory ◽  
The Mathematical Model

This work presents a general formulation of flexible manipulator systems. The associated mathematical model results in a hybrid system of equations involving both ordinary and partial differential equations. The perturbation technique and model analysis have been used for the solution. In addition to the lineal deflection theory, an unperturbed joint-motion assumption has then been employed in order to further simplify the mathematical model. Finally, an inverse dynamic problem is solved using the proposed methodology.

Fractional Order Thermoelastic Waves of Cylindrical Gold Nano-Beam

2013 ◽  
Author(s):  
Hamdy M. Youssef ◽  
Khaled A. Elsibai ◽  
Alaa A. El-Bary
Keyword(s):  
Mathematical Model ◽  
Fractional Order ◽  
Thermal Load ◽  
Laplace Transforms ◽  
Thermal Waves ◽  
Governing Equations ◽  
Elastic Parameters ◽  
The Impact ◽  
The Mathematical Model ◽  
Thermoelastic Waves

In this work, a mathematical model of cylindrical nano-beam with constant elastic parameters with fractional order heat conduction will be constructed. The governing equations of the mathematical model will be taken when the beam is quiescent first. Laplace transforms techniques will be used to get the general solution for any set of boundary conditions. The solution will be obtained for a certain model when the beam is subjected to thermal load. Inversion of Laplace transforms will be obtained numerically, and the results will be presented graphically with some comparisons to study the impact of thermal load and the effect of the fractional order parameter on the speed of progress of mechanical and thermal waves through the beam.

Concentration of Samples in Microfluidic Structure Using Joule Heating Effects

2009 ◽  
Author(s):  
Zhengwei Ge ◽  
Chun Yang
Keyword(s):  
Mathematical Model ◽  
Joule Heating ◽  
Electroosmotic Flow ◽  
Scaling Analysis ◽  
Analyte Concentration ◽  
Governing Equations ◽  
Sample Concentration ◽  
Heating Effects ◽  
Concentration Enhancement ◽  
The Mathematical Model

Microfluidic concentration is achieved using temperature gradient focusing (TGF) in a microchannel with a step change in cross-section. A mathematical model is developed to describe the complex TGF processes. The proposed mathematical model includes a set of governing equations for the applied electric potential, electroosmotic flow field, Joule heating induced temperature field, and sample analyte concentration distributions as well. Scaling analysis was conducted to estimate time scales so as to simplify the mathematical model. Numerical computations were performed to obtain the temperature, velocity and sample concentration distributions. Experiments were carried out to study the effects of applied voltage, buffer concentration, and channel size on sample concentration in the TGF processes. These effects were analyzed and summarized using a dimensionless Joule number that was introduced in this study. In addition, Joule number effect in the PDMS/PDMS microdevice was compared with the PDMS/Glass microdevice. A more than 450-fold concentration enhancement was obtained within 75 seconds in the PDMS/PDMS microdevice. Overall, the numerical simulations were found in a reasonable agreement with the experimental results.

Mathematical model of steady-state countercurrent bed-shrinking reactor in dilute acid

2021 ◽  
Vol 1 (2) ◽  
pp. 001-011
Author(s):  
Saranya Jaganathan ◽  
Rajendran Lakshmanan
Keyword(s):  
Mathematical Model ◽  
Nonlinear Differential Equations ◽  
Perturbation Technique ◽  
Dilute Acid Pretreatment ◽  
Rate Equations ◽  
Dilute Acid ◽  
Acid Pretreatment ◽  
Dimensional Parameters ◽  
The Mathematical Model ◽  
Analytical Expressions

The mathematical model of bed-shrinking in a countercurrent reactor proposed by Lee (Bioresource Technology 71 (2000) 29 - 39) is explored. This model is based on system of nonlinear differential equations. Analytically, the coupled nonlinear rate equations are solved. To produce approximate analytical expressions for hemicelluloses, oligomers, and xylose concentrations for all the values of non-dimensional parameters and , the homotopy perturbation technique is applied. Our analytical results were compared to existing experimental data and found to be very similar. The dilute-acid pretreatment/hydrolysis of lignocellulosic biomass is studied using this mathematical model in the reactor.

Design and performance evaluation of a bellows-type mixture ratio stabilizer for a liquid bipropellant rocket engine

2008 ◽  
Vol 223 (3) ◽  
pp. 723-731 ◽  
Author(s):  
Taekyu Jung ◽  
Sejin Kwon
Keyword(s):  
Mathematical Model ◽  
Rocket Engine ◽  
Design Criterion ◽  
Design Parameters ◽  
Governing Equations ◽  
Mixture Ratio ◽  
And Performance ◽  
The Mathematical Model ◽  
Static Behaviour ◽  
The Ideal

A stabilizer that maintains a steady propellant mixture ratio in a liquid bipropellant rocket engine was introduced. First, a design criterion for the ideal performance of a general stabilizer was derived. A new stabilizer with bellows (bellows-type stabilizer) was proposed in the present study and relevant design parameters were identified by a mathematical model as well as a theoretical analysis. Governing equations were established to predict the static behaviour of the stabilizer. A bellows-type stabilizer was fabricated and its performance was measured. The performance predicted by the mathematical model showed satisfactory agreement with measurements and this validates the adequacy of the mathematical model proposed in the present study.

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