Abstract: Modeling transfer phenomena in several chemical
engineering operations leads to the resolution of partial differential
equations systems. According to the complexity of the operations
mechanisms, the equations present a nonlinear form and analytical
solution became difficult, we have then to use numerical methods
which are based on approximations in order to transform a
differential system to an algebraic one.Finite element method is one
of numerical methods which can be used to obtain an accurate
solution in many complex cases of chemical engineering.The packed
columns find a large application like contactor for liquid-liquid
systems such solvent extraction. In the literature, the modeling of this
type of equipment received less attention in comparison with the
plate columns.A mathematical bidimensionnal model with radial and
axial dispersion, simulating packed tower extraction behavior was
developed and a partial differential equation was solved using the
finite element method by adopting the Galerkine model. We
developed a Mathcad program, which can be used for a similar
equations and concentration profiles are obtained along the column.
The influence of radial dispersion was prooved and it can-t be
neglected, the results were compared with experimental concentration
at the top of the column in the extraction system:
acetone/toluene/water.
Abstract: The optimal control problem of a linear distributed
parameter system is studied via shifted Legendre polynomials (SLPs)
in this paper. The partial differential equation, representing the
linear distributed parameter system, is decomposed into an n - set
of ordinary differential equations, the optimal control problem is
transformed into a two-point boundary value problem, and the twopoint
boundary value problem is reduced to an initial value problem
by using SLPs. A recursive algorithm for evaluating optimal control
input and output trajectory is developed. The proposed algorithm is
computationally simple. An illustrative example is given to show the
simplicity of the proposed approach.
Abstract: Prior research has not effectively investigated how the
profitability of Chinese branches affect FDIs in China [1, 2], so this
study for the first time incorporates realistic earnings information
to systematically investigate effects of innovation, imitation, and
profit factors of FDI diffusions from Taiwan to China. Our nonlinear
least square (NLS) model, which incorporates earnings factors,
forms a nonlinear ordinary differential equation (ODE) in numerical
simulation programs. The model parameters are obtained through
a genetic algorithms (GA) technique and then optimized with the
collected data for the best accuracy. Particularly, Taiwanese regulatory
FDI restrictions are also considered in our modified model to meet
the realistic conditions. To validate the model-s effectiveness, this
investigation compares the prediction accuracy of modified model
with the conventional diffusion model, which does not take account
of the profitability factors.
The results clearly demonstrate the internal influence to be positive,
as early FDI adopters- consistent praises of FDI attract potential firms
to make the same move. The former erects a behavior model for the
latter to imitate their foreign investment decision. Particularly, the
results of modified diffusion models show that the earnings from
Chinese branches are positively related to the internal influence. In
general, the imitating tendency of potential consumers is substantially
hindered by the losses in the Chinese branches, and these firms would
invest less into China. The FDI inflow extension depends on earnings
of Chinese branches, and companies will adjust their FDI strategies
based on the returns. Since this research has proved that earning is
an influential factor on FDI dynamics, our revised model explicitly
performs superior in prediction ability than conventional diffusion
model.
Abstract: This paper is concerned with an epidemic model with delay. By using the comparison theorem of the differential equation and constructing a suitable Lyapunov functional, Some sufficient conditions which guarantee the permeance and existence of a unique globally attractive positive almost periodic solution of the model are obtain. Finally, an example is employed to illustrate our result.
Abstract: In this paper, using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales, the existence of periodic solutions for a two-prey one-predator system is studied. Some sufficient conditions for the existence of positive periodic solutions are obtained. The results provide unified existence theorems of periodic solution for the continuous differential equations and discrete difference equations.
Abstract: The subcellular organelles called oil bodies (OBs) are lipid-filled quasi-spherical droplets produced from the endoplasmic reticulum (ER) and then released into the cytoplasm during seed development. It is believed that an OB grows by coalescence with other OBs and that its stability depends on the composition of oleosins, major proteins inserted in the hemi membrane that covers OBs. In this study, we measured the OB-volume distribution from different genotypes of A. thaliana after 7, 8, 9, 10 and 11 days of seed development. In order to test the hypothesis of OBs dynamics, we developed a simple mathematical model using non-linear differential equations inspired from the theory of coagulation. The model describes the evolution of OB-volume distribution during the first steps of seed development by taking into consideration the production of OBs, the increase of triacylglycerol volume to be stored, and the growth by coalescence of OBs. Fitted parameters values show an increase in the OB production and coalescence rates in A. thaliana oleosin mutants compared to wild type.
Abstract: This paper is concerned with the permanence and extinction problem of enterprises cluster constituted by m satellite enterprises and a dominant enterprise. We present the model involving impulsive effect based on ecology theory, which effectively describe the competition and cooperation of enterprises cluster in real economic environment. Applying comparison theorem of impulsive differential equation, we establish sufficient conditions which ultimately affect the fate of enterprises: permanence, extinction, and co-existence. Finally, we present numerical examples to explain the economical significance of mathematical results.
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: In this paper, position vector of a partially null unit speed curve with respect to standard frame of Minkowski space-time is studied. First, it is proven that position vector of every partially null unit speed curve satisfies a vector differential equation of fourth order. In terms of solution of the differential equation, position vector of a partially null unit speed curve is expressed.
Abstract: In this paper, we study the stability of n-dimensional linear fractional neutral differential equation with time delays. By using the Laplace transform, we introduce a characteristic equation for the above system with multiple time delays. We discover that if all roots of the characteristic equation have negative parts, then the equilibrium of the above linear system with fractional order is Lyapunov globally asymptotical stable if the equilibrium exist that is almost the same as that of classical differential equations. An example is provided to show the effectiveness of the approach presented in this paper.
Abstract: This paper investigates the solutions of two-point fuzzy boundary value problems as the form x = f(t, x(t)), x(0) = A and x(l) = B, where A and B are fuzzy numbers. There are four different solutions for the problems when the lateral type of H-derivative is employed to solve the problems. As f(t, x) is a monotone function of x, these four solutions are reduced to two different solutions. As f(t, x(t)) = λx(t) or f(t, x(t)) = -λx(t), solutions and several comparison results are presented to indicate advantages of each solution.
Abstract: Equations with differentials relating to the inverse of an unknown function rather than to the unknown function itself are solved exactly for some special cases and numerically for the general case. Invertibility combined with differentiability over connected domains forces solutions always to be monotone. Numerical function inversion is key to all solution algorithms which either are of a forward type or a fixed point type considering whole approximate solution functions in each iteration. The given considerations are restricted to ordinary differential equations with inverted functions (ODEIs) of first order. Forward type computations, if applicable, admit consistency of order one and, under an additional accuracy condition, convergence of order one.
Abstract: Kernel function, which allows the formulation of nonlinear variants of any algorithm that can be cast in terms of dot products, makes the Support Vector Machines (SVM) have been successfully applied in many fields, e.g. classification and regression. The importance of kernel has motivated many studies on its composition. It-s well-known that reproducing kernel (R.K) is a useful kernel function which possesses many properties, e.g. positive definiteness, reproducing property and composing complex R.K by simple operation. There are two popular ways to compute the R.K with explicit form. One is to construct and solve a specific differential equation with boundary value whose handicap is incapable of obtaining a unified form of R.K. The other is using a piecewise integral of the Green function associated with a differential operator L. The latter benefits the computation of a R.K with a unified explicit form and theoretical analysis, whereas there are relatively later studies and fewer practical computations. In this paper, a new algorithm for computing a R.K is presented. It can obtain the unified explicit form of R.K in general reproducing kernel Hilbert space. It avoids constructing and solving the complex differential equations manually and benefits an automatic, flexible and rigorous computation for more general RKHS. In order to validate that the R.K computed by the algorithm can be used in SVM well, some illustrative examples and a comparison between R.K and Gaussian kernel (RBF) in support vector regression are presented. The result shows that the performance of R.K is close or slightly superior to that of RBF.
Abstract: In this paper, we study the numerical method for solving second-order fuzzy differential equations using Adomian method under strongly generalized differentiability. And, we present an example with initial condition having four different solutions to illustrate the efficiency of the proposed method under strongly generalized differentiability.
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: In this paper the Laplace Decomposition method is developed to solve linear and nonlinear fractional integro- differential equations of Volterra type.The fractional derivative is described in the Caputo sense.The Laplace decomposition method is found to be fast and accurate.Illustrative examples are included to demonstrate the validity and applicability of presented technique and comparasion is made with exacting results.
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: The deviation between the target state variable and the
practical state variable should be used to form the state tending factor
of complex systems, which can reflect the process for the complex
system to tend rationalization. Relating to the system of basic
equations of complete factor synergetics consisting of twenty
nonlinear stochastic differential equations, the two new models are
considered to set, which should be called respectively the
rationalizing tendency model and the non- rationalizing tendency
model. Therefore we can extend the theory of programming with the
objective function & constraint condition suitable only for the realm
of man-s activities into the new analysis with the tendency function &
constraint condition suitable for all the field of complex system.