Abstract: Modeling of a heterogeneous industrial fixed bed
reactor for selective dehydrogenation of heavy paraffin with Pt-Sn-
Al2O3 catalyst has been the subject of current study. By applying
mass balance, momentum balance for appropriate element of reactor
and using pressure drop, rate and deactivation equations, a detailed
model of the reactor has been obtained. Mass balance equations have
been written for five different components. In order to estimate
reactor production by the passage of time, the reactor model which is
a set of partial differential equations, ordinary differential equations
and algebraic equations has been solved numerically.
Paraffins, olefins, dienes, aromatics and hydrogen mole percent as
a function of time and reactor radius have been found by numerical
solution of the model. Results of model have been compared with
industrial reactor data at different operation times. The comparison
successfully confirms validity of proposed model.
Abstract: We propose a reduced-ordermodel for the instantaneous
hydrodynamic force on a cylinder. The model consists of a system of
two ordinary differential equations (ODEs), which can be integrated
in time to yield very accurate histories of the resultant force and
its direction. In contrast to several existing models, the proposed
model considers the actual (total) hydrodynamic force rather than its
perpendicular or parallel projection (the lift and drag), and captures
the complete force rather than the oscillatory part only. We study
and provide descriptions of the relationship between the model
parameters, evaluated utilizing results from numerical simulations,
and the Reynolds number so that the model can be used at any
arbitrary value within the considered range of 100 to 500 to provide
accurate representation of the force without the need to perform timeconsuming
simulations and solving the partial differential equations
(PDEs) governing the flow field.
Abstract: Reactiondiffusion systems are mathematical models that describe how the concentration of one or more substances distributed in space changes under the influence of local chemical reactions in which the substances are converted into each other, and diffusion which causes the substances to spread out in space. The classical representation of a reaction-diffusion system is given by semi-linear parabolic partial differential equations, whose general form is ÔêétX(x, t) = DΔX(x, t), where X(x, t) is the state vector, D is the matrix of the diffusion coefficients and Δ is the Laplace operator. If the solute move in an homogeneous system in thermal equilibrium, the diffusion coefficients are constants that do not depend on the local concentration of solvent and of solutes and on local temperature of the medium. In this paper a new stochastic reaction-diffusion model in which the diffusion coefficients are function of the local concentration, viscosity and frictional forces of solvent and solute is presented. Such a model provides a more realistic description of the molecular kinetics in non-homogenoeus and highly structured media as the intra- and inter-cellular spaces. The movement of a molecule A from a region i to a region j of the space is described as a first order reaction Ai k- → Aj , where the rate constant k depends on the diffusion coefficient. Representing the diffusional motion as a chemical reaction allows to assimilate a reaction-diffusion system to a pure reaction system and to simulate it with Gillespie-inspired stochastic simulation algorithms. The stochastic time evolution of the system is given by the occurrence of diffusion events and chemical reaction events. At each time step an event (reaction or diffusion) is selected from a probability distribution of waiting times determined by the specific speed of reaction and diffusion events. Redi is the software tool, developed to implement the model of reaction-diffusion kinetics and dynamics. It is a free software, that can be downloaded from http://www.cosbi.eu. To demonstrate the validity of the new reaction-diffusion model, the simulation results of the chaperone-assisted protein folding in cytoplasm obtained with Redi are reported. This case study is redrawing the attention of the scientific community due to current interests on protein aggregation as a potential cause for neurodegenerative diseases.
Abstract: A systematic way to derive the conserved quantities for the axisymmetric liquid jet, free jet and wall jet using conservation laws is presented. The flow in axisymmetric jets is governed by Prandtl-s momentum boundary layer equation and the continuity equation. The multiplier approach is used to construct a basis of conserved vectors for the system of two partial differential equations for the two velocity components. The basis consists of two conserved vectors. By integrating the corresponding conservation laws across the jet and imposing the boundary conditions, conserved quantities are derived for the axisymmetric liquid and free jet. The multiplier approach applied to the third-order partial differential equation for the stream function yields two local conserved vectors one of which is a non-local conserved vector for the system. One of the conserved vectors gives the conserved quantity for the axisymmetric free jet but the conserved quantity for the wall jet is not obtained from the second conserved vector. The conserved quantity for the axisymmetric wall jet is derived from a non-local conserved vector of the third-order partial differential equation for the stream function. This non-local conserved vector for the third-order partial differential equation for the stream function is obtained by using the stream function as multiplier.
Abstract: This paper presents an application of level sets for the segmentation of abdominal and thoracic aortic aneurysms in CTA
datasets. An important challenge in reliably detecting aortic is the
need to overcome problems associated with intensity
inhomogeneities. Level sets are part of an important class of methods
that utilize partial differential equations (PDEs) and have been extensively applied in image segmentation. A kernel function in the
level set formulation aids the suppression of noise in the extracted
regions of interest and then guides the motion of the evolving contour
for the detection of weak boundaries. The speed of curve evolution
has been significantly improved with a resulting decrease in segmentation time compared with previous implementations of level
sets, and are shown to be more effective than other approaches in
coping with intensity inhomogeneities. We have applied the Courant
Friedrichs Levy (CFL) condition as stability criterion for our algorithm.
Abstract: This paper describes a one-dimensional numerical model for natural gas production from the dissociation of methane hydrate in hydrate-capped gas reservoir under depressurization and thermal stimulation. Some of the hydrate reservoirs discovered are overlying a free-gas layer, known as hydrate-capped gas reservoirs. These reservoirs are thought to be easiest and probably the first type of hydrate reservoirs to be produced. The mathematical equations that can be described this type of reservoir include mass balance, heat balance and kinetics of hydrate decomposition. These non-linear partial differential equations are solved using finite-difference fully implicit scheme. In the model, the effect of convection and conduction heat transfer, variation change of formation porosity, the effect of using different equations of state such as PR and ER and steam or hot water injection are considered. In addition distributions of pressure, temperature, saturation of gas, hydrate and water in the reservoir are evaluated. It is shown that the gas production rate is a sensitive function of well pressure.
Abstract: The present contribution deals with the
thermophoretic deposition of nanoparticles over a rapidly rotating
permeable disk in the presence of partial slip, magnetic field, thermal
radiation, thermal-diffusion, and diffusion-thermo effects. The
governing nonlinear partial differential equations such as continuity,
momentum, energy and concentration are transformed into nonlinear
ordinary differential equations using similarity analysis, and the
solutions are obtained through the very efficient computer algebra
software MATLAB. Graphical results for non-dimensional
concentration and temperature profiles including thermophoretic
deposition velocity and Stanton number (thermophoretic deposition
flux) in tabular forms are presented for a range of values of the
parameters characterizing the flow field. It is observed that slip
mechanism, thermal-diffusion, diffusion-thermo, magnetic field and
radiation significantly control the thermophoretic particles deposition
rate. The obtained results may be useful to many industrial and
engineering applications.
Abstract: A steady two-dimensional magnetohydrodynamics
flow and heat transfer over a stretching vertical sheet influenced by
radiation and porosity is studied. The governing boundary layer
equations of partial differential equations are reduced to a system of
ordinary differential equations using similarity transformation. The
system is solved numerically by using a finite difference scheme
known as the Keller-box method for some values of parameters,
namely the radiation parameter N, magnetic parameter M, buoyancy
parameter l , Prandtl number Pr and permeability parameter K. The
effects of the parameters on the heat transfer characteristics are
analyzed and discussed. It is found that both the skin friction
coefficient and the local Nusselt number decrease as the magnetic
parameter M and permeability parameter K increase. Heat transfer
rate at the surface decreases as the radiation parameter increases.
Abstract: Piezoelectric transformers are electronic devices made
from piezoelectric materials. The piezoelectric transformers as the
name implied are used for changing voltage signals from one level to another. Electrical energy carried with signals is transferred by means of mechanical vibration. Characterizing in both electrical and
mechanical properties leads to extensively use and efficiency enhancement of piezoelectric transformers in various applications. In
this paper, study and analysis of electrical and mechanical properties of multi-layer piezoelectric transformers in forms of potential and
displacement distribution throughout the volume, respectively. This
paper proposes a set of quasi-static mathematical model of electromechanical
coupling for piezoelectric transformer by using a set of
partial differential equations. Computer-based simulation utilizing the three-dimensional finite element method (3-D FEM) is exploited
as a tool for visualizing potentials and displacements distribution
within the multi-layer piezoelectric transformer. This simulation was
conducted by varying a number of layers. In this paper 3, 5 and 7 of
the circular ring type were used. The computer simulation based on
the use of the FEM has been developed in MATLAB programming environment.
Abstract: Calcium is very important for communication among
the neurons. It is vital in a number of cell processes such as secretion,
cell movement, cell differentiation. To reduce the system of reactiondiffusion
equations of [Ca2+] into a single equation, two theories
have been proposed one is excess buffer approximation (EBA) other
is rapid buffer approximation (RBA). The RBA is more realistic than
the EBA as it considers both the mobile and stationary endogenous
buffers. It is valid near the mouth of the channel. In this work we have
studied the effects of different types of buffers on calcium diffusion
under RBA. The novel thing studied is the effect of sodium ions on
calcium diffusion. The model has been made realistic by considering
factors such as variable [Ca2+], [Na+] sources, sodium-calcium
exchange protein(NCX), Sarcolemmal Calcium ATPase pump. The
proposed mathematical leads to a system of partial differential equations
which has been solved numerically to study the relationships
between different parameters such as buffer concentration, buffer
disassociation rate, calcium permeability. We have used Forward
Time Centred Space (FTCS) approach to solve the system of partial
differential equations.
Abstract: In this work, we derive two numerical schemes for
solving a class of nonlinear partial differential equations. The first
method is of second order accuracy in space and time directions, the
scheme is unconditionally stable using Von Neumann stability
analysis, the scheme produced a nonlinear block system where
Newton-s method is used to solve it. The second method is of fourth
order accuracy in space and second order in time. The method is
unconditionally stable and Newton's method is used to solve the
nonlinear block system obtained. The exact single soliton solution
and the conserved quantities are used to assess the accuracy and to
show the robustness of the schemes. The interaction of two solitary
waves for different parameters are also discussed.
Abstract: The objective of this paper is to use the Pfaffian
technique to construct different classes of exact Pfaffian solutions and
N-soliton solutions to some of the generalized integrable nonlinear
partial differential equations in (3+1) dimensions. In this paper, I will
show that the Pfaffian solutions to the nonlinear PDEs are nothing but
Pfaffian identities. Solitons are among the most beneficial solutions
for science and technology, from ocean waves to transmission of
information through optical fibers or energy transport along protein
molecules. The existence of multi-solitons, especially three-soliton
solutions, is essential for information technology: it makes possible
undisturbed simultaneous propagation of many pulses in both directions.
Abstract: Calcium is a vital second messenger used in signal transduction. Calcium controls secretion, cell movement, muscular contraction, cell differentiation, ciliary beating and so on. Two theories have been used to simplify the system of reaction-diffusion equations of calcium into a single equation. One is excess buffer approximation (EBA) which assumes that mobile buffer is present in excess and cannot be saturated. The other is rapid buffer approximation (RBA), which assumes that calcium binding to buffer is rapid compared to calcium diffusion rate. In the present work, attempt has been made to develop a model for calcium diffusion under excess buffer approximation in neuron cells. This model incorporates the effect of [Na+] influx on [Ca2+] diffusion,variable calcium and sodium sources, sodium-calcium exchange protein, Sarcolemmal Calcium ATPase pump, sodium and calcium channels. The proposed mathematical model leads to a system of partial differential equations which have been solved numerically using Forward Time Centered Space (FTCS) approach. The numerical results have been used to study the relationships among different types of parameters such as buffer concentration, association rate, calcium permeability.