Abstract: Implicit equations play a crucial role in Engineering.
Based on this importance, several techniques have been applied to
solve this particular class of equations. When it comes to practical
applications, in general, iterative procedures are taken into account.
On the other hand, with the improvement of computers, other
numerical methods have been developed to provide a more
straightforward methodology of solution. Analytical exact approaches
seem to have been continuously neglected due to the difficulty
inherent in their application; notwithstanding, they are indispensable
to validate numerical routines. Lagrange-s Inversion Theorem is a
simple mathematical tool which has proved to be widely applicable to
engineering problems. In short, it provides the solution to implicit
equations by means of an infinite series. To show the validity of this
method, the tree-parameter infiltration equation is, for the first time,
analytically and exactly solved. After manipulating these series,
closed-form solutions are presented as H-functions.
Abstract: In this paper, we generalize some propositions in [C.Z. Wang, D.G. Chen, A short note on some properties of rough groups, Comput. Math. Appl. 59(2010)431-436.] and we give some equivalent conditions for rough subgroups. The notion of minimal upper rough subgroups is introduced and a equivalent characterization is given, which implies the rough version of Lagranges Theorem.
Abstract: This paper will discuss about an active power generator scheduling method in order to increase the limit level of steady state systems. Some power generator optimization methods such as Langrange, PLN (Indonesian electricity company) Operation, and the proposed Z-Thevenin-based method will be studied and compared in respect of their steady state aspects. A method proposed in this paper is built upon the thevenin equivalent impedance values between each load respected to each generator. The steady state stability index obtained with the REI DIMO method. This research will review the 500kV-Jawa-Bali interconnection system. The simulation results show that the proposed method has the highest limit level of steady state stability compared to other optimization techniques such as Lagrange, and PLN operation. Thus, the proposed method can be used to create the steady state stability limit of the system especially in the peak load condition.
Abstract: In this paper we improve the quasilinearization method by barycentric Lagrange interpolation because of its numerical stability and computation speed to achieve a stable semi analytical solution. Then we applied the improved method for solving the Fin problem which is a nonlinear equation that occurs in the heat transferring. In the quasilinearization approach the nonlinear differential equation is treated by approximating the nonlinear terms by a sequence of linear expressions. The modified QLM is iterative but not perturbative and gives stable semi analytical solutions to nonlinear problems without depending on the existence of a smallness parameter. Comparison with some numerical solutions shows that the present solution is applicable.
Abstract: The Wavelet-Galerkin finite element method for
solving the one-dimensional heat equation is presented in this work.
Two types of basis functions which are the Lagrange and multi-level
wavelet bases are employed to derive the full form of matrix system.
We consider both linear and quadratic bases in the Galerkin method.
Time derivative is approximated by polynomial time basis that
provides easily extend the order of approximation in time space. Our
numerical results show that the rate of convergences for the linear
Lagrange and the linear wavelet bases are the same and in order 2
while the rate of convergences for the quadratic Lagrange and the
quadratic wavelet bases are approximately in order 4. It also reveals
that the wavelet basis provides an easy treatment to improve
numerical resolutions that can be done by increasing just its desired
levels in the multilevel construction process.
Abstract: An original Direct Numerical Simulation (DNS) method to tackle the problem of particulate flows at moderate to high concentration and finite Reynolds number is presented. Our method is built on the framework established by Glowinski and his coworkers [1] in the sense that we use their Distributed Lagrange Multiplier/Fictitious Domain (DLM/FD) formulation and their operator-splitting idea but differs in the treatment of particle collisions. The novelty of our contribution relies on replacing the simple artificial repulsive force based collision model usually employed in the literature by an efficient Discrete Element Method (DEM) granular solver. The use of our DEM solver enables us to consider particles of arbitrary shape (at least convex) and to account for actual contacts, in the sense that particles actually touch each other, in contrast with the simple repulsive force based collision model. We recently upgraded our serial code, GRIFF 1 [2], to full MPI capabilities. Our new code, PeliGRIFF 2, is developed under the framework of the full MPI open source platform PELICANS [3]. The new MPI capabilities of PeliGRIFF open new perspectives in the study of particulate flows and significantly increase the number of particles that can be considered in a full DNS approach: O(100000) in 2D and O(10000) in 3D. Results on the 2D/3D sedimentation/fluidization of isometric polygonal/polyedral particles with collisions are presented.
Abstract: This paper unifies power optimization approaches in
various energy converters, such as: thermal, solar, chemical, and
electrochemical engines, in particular fuel cells. Thermodynamics
leads to converter-s efficiency and limiting power. Efficiency
equations serve to solve problems of upgrading and downgrading of
resources. While optimization of steady systems applies the
differential calculus and Lagrange multipliers, dynamic optimization
involves variational calculus and dynamic programming. In reacting
systems chemical affinity constitutes a prevailing component of an
overall efficiency, thus the power is analyzed in terms of an active
part of chemical affinity. The main novelty of the present paper in the
energy yield context consists in showing that the generalized heat
flux Q (involving the traditional heat flux q plus the product of
temperature and the sum products of partial entropies and fluxes of
species) plays in complex cases (solar, chemical and electrochemical)
the same role as the traditional heat q in pure heat engines.
The presented methodology is also applied to power limits in fuel
cells as to systems which are electrochemical flow engines propelled
by chemical reactions. The performance of fuel cells is determined by
magnitudes and directions of participating streams and mechanism of
electric current generation. Voltage lowering below the reversible
voltage is a proper measure of cells imperfection. The voltage losses,
called polarization, include the contributions of three main sources:
activation, ohmic and concentration. Examples show power maxima
in fuel cells and prove the relevance of the extension of the thermal
machine theory to chemical and electrochemical systems. The main
novelty of the present paper in the FC context consists in introducing
an effective or reduced Gibbs free energy change between products p
and reactants s which take into account the decrease of voltage and
power caused by the incomplete conversion of the overall reaction.
Abstract: The optimization problem using time scales is studied.
Time scale is a model of time. The language of time scales seems to
be an ideal tool to unify the continuous-time and the discrete-time
theories. In this work we present necessary conditions for a solution
of an optimization problem on time scales. To obtain that result we
use properties and results of the partial diamond-alpha derivatives for
continuous-multivariable functions. These results are also presented
here.
Abstract: In this paper we study the rheonomic mechanical systems from the point of view of Lagrange geometry, by means of its canonical semispray. We present an example of the constraint motion of a material point, in the rheonomic case.
Abstract: A two dimensional three segments coupled pendulum system that mathematically models human arm configuration was developed along with constructing and solving the equations of motions for this model using the energy (work) based approach of Lagrange. The equations of motion of the model were solved iteratively both as an initial value problem and as a two point boundary value problem. In the initial value problem solutions, both the initial system configuration (segment angles) and initial system velocity (segment angular velocities) were used as inputs, whereas, in the two point boundary value problem solutions initial and final configurations and time were used as inputs to solve for the trajectory of motion. The results suggest that the model solutions are sensitive to small changes in the dynamic forces applied to the system as well as to the initial and boundary conditions used. To overcome the system sensitivity a new approach is suggested.
Abstract: State Dependent Riccati Equation (SDRE) approach is
a modification of the well studied LQR method. It has the capability of being applied to control nonlinear systems. In this paper the technique
has been applied to control the single inverted pendulum (SIP) which represents a rich class of nonlinear underactuated systems. SIP
modeling is based on Euler-Lagrange equations. A procedure is developed
for judicious selection of weighting parameters and constraint handling. The controller designed by SDRE technique here gives better results than existing controllers designed by energy based techniques.
Abstract: In this paper, mesh-free element free Galerkin (EFG) method is extended to solve two-dimensional potential flow problems. Two ideal fluid flow problems (i.e. flow over a rigid cylinder and flow over a sphere) have been formulated using variational approach. Penalty and Lagrange multiplier techniques have been utilized for the enforcement of essential boundary conditions. Four point Gauss quadrature have been used for the integration on two-dimensional domain (Ω) and nodal integration scheme has been used to enforce the essential boundary conditions on the edges (┌). The results obtained by EFG method are compared with those obtained by finite element method. The effects of scaling and penalty parameters on EFG results have also been discussed in detail.
Abstract: This paper presents kinematic and dynamic analysis of a novel 8-DOF hybrid robot manipulator. The hybrid robot manipulator under consideration consists of a parallel robot which
is followed by a serial mechanism. The parallel mechanism has three translational DOF, and the serial mechanism has five DOF so that the overall degree of freedom is eight. The introduced
manipulator has a wide workspace and a high capability to reduce
the actuating energy. The inverse and forward kinematic solutions are described in closed form. The theoretical results are verified by
a numerical example. Inverse dynamic analysis of the robot is presented by utilizing the Iterative Newton-Euler and Lagrange dynamic formulation methods. Finally, for performing a multi-step
arc welding process, results have indicated that the introduced manipulator is highly capable of reducing the actuating energy.
Abstract: This paper presents the use of anti-sway angle control
approaches for a two-dimensional gantry crane with disturbances
effect in the dynamic system. Delayed feedback signal (DFS) and
proportional-derivative (PD)-type fuzzy logic controller are the
techniques used in this investigation to actively control the sway
angle of the rope of gantry crane system. A nonlinear overhead
gantry crane system is considered and the dynamic model of the
system is derived using the Euler-Lagrange formulation. A complete
analysis of simulation results for each technique is presented in time
domain and frequency domain respectively. Performances of both
controllers are examined in terms of sway angle suppression and
disturbances cancellation. Finally, a comparative assessment of the
impact of each controller on the system performance is presented and
discussed.