[1]. S.S. Makhanov, K. Sonthipaumpoon and E.J. Vanderperre, "On
Generation of Curvilinear Grids", To appear in: South-East Asian Bulletin
of Mathematics, Springer-Verlag, 1999.
Abstract. We present a contribution to variational grid generation
techniques endowed with constraints imposed on spatial steps. Our approach
is based on the numerical solution of a constraint minimization problem
involving penalty functions. In order to ensure the stability/ monotonicity
of the finite difference schemes, we simultaneously adapt the grid to regions
of large numerical errors and to the specified constraints. Finally, as
an application, we demonstrate the efficiency of the algorithm for some
industrial CFD and CAD/CAM applications.
[2]. S.S.Makhanov, S.Vannakrairojn, and E.J. Vanderperre, "A
Two-Dimensional Numerical Model of Flooding in East-Bangkok", To appear
in: Journal of Hydraulic Engineering, American Soc. Civil Eng., March,
1999.
Abstract. We propose a new numerical flooding model oriented
to water systems comprising large canal networks. Our approach is based
on the diffusion wave equation related to a modified version of the so-called
"calculations with apparent cross-sectional flow areas". The mathematical
formulation is based on the analogy of a porous medium characterized by
a permeability depending on parameters and directions of the canal network.
Next, we combine the "continuous medium" approach with the non-negative
stable numerical algorithm initially developed for the one-dimensional
diffusion wave equation. A numerical solution of our resulting finite difference
equations requires a tangible generalization of the non-negative algorithm
to the case of coupled two-dimensional river-surface flows. Finally, we
simulate the flood evolution in the lower Chao-Praya river basin located
in the eastern areas of Bangkok and demonstrate the computational efficiency
of the proposed method.
[3]. D. Batanov, E.Bohez, S.S. Makhanov, K. Sonthipaumpoon and M.
Tabucanon, "Grid Generation Algorithms to Optimize a Tool-Path of a
Five-Axis Milling Machine" , To appear in: Proc. First Asian Symposium
on Industrial Automation and Robotics, Bangkok, 6-7 May 1999.
Abstract. We introduce a new area of application of variational
grid generation techniques to optimize the tool-path of an industrial milling
robot. Our approach is based on a global approximation of the required
surface by a virtual surface composed from tool trajectories. The procedure
combines inverse kinematics techniques and a variational gridding method
endowed with constraints related to the required scallop height. The proposed
technique allows to generate a tool-path for workpieces with complex geometries
comprising "islands" and/or boundaries with sharp edges requiring a combined
"spiral-zigzag" pattern. Finally, the proposed technique provides a significant
increase in the accuracy of milling.
[4]. S.S. Makhanov, "Flood Modeling in East-Bangkok", To
appear in: Proc. International Civil and Environment Conference, New Frontiers
and Challenges, Bangkok, 8-12 November, 1999.
Abstract. A new numerical model designed for large canal networks
is proposed. We prove the following notable features of the model. 1) Uniform,
easy-to-modify, two-dimensional data structures. 2) Uniform two-dimensional
numerical procedures to calculate the river-surface flows. 3) Uniform numerical
treatment of the river and surface water level within a grid cell. 4) Uniform
treatment of the "dry" and "wet" regions. 5) Stable non-negative numerical
algorithm. The techniques are extended to the case of Saint-Venant equations
comprising accelerations. However, an appropriate modification for large
Courant numbers is still an open problem.
[5]. S. S. Makhanov and E. J. Vanderperre, "A Cauchy Integral
Related to a Robot-Safety Device System", To appear in Serdica Mathematical
Journal, 1999.
Abstract. We introduce a robot-safety device system attended
by two different repairmen. The twin system is characterized by the natural
feature of cold standby and by an admissible "risky" state. In order to
analyze the random behavior of the entire system (robot, safety device,
repair facility) we employ a stochastic process endowed with probability
measures satisfying general Hokstad-type differential equations. The solution
procedure is based on the theory of sectionally holomorphic functions.
We introduce a Cauchy-type integral defined as a principal value in double
sense. An application of the Sokhotskii-Plemelj formulae determines the
long-run availability of the robot-safety device system. Finally, we consider
the particular but important case of deterministic repair.
[6]. S.S. Makahnov and S. Vannakrairojn "Correction of Curvilinear
Grids for Numerical Solution of Ground Water Problems ", To appear
in: ", Water Resources, 1999, Interperiodica Pub.
Abstract. We present a new modification of a grid generation
method for numerical solution of groundwater problems. The proposed scheme
is based on a numerical solution of the constraint optimization problem
combined with a penalty-type iterative algorithm. The method is applied
for simultaneous adaptation to large approximation errors in the regions
with complex shaped boundaries.
[7]. S.S.Makhanov and S. Sangchan, "Numerical Methods for Problems
of Surface-Subsurface Flows with A Priori Bounded Solution", To appear
in KKU Engineering Journal, 1999.
Abstract. We propose a new modification of numerical methods
for non-linear parabolic boundary-value problems endowed with constraints
a priori imposed on the solution. The corresponding PDE's are employed
in the frame-work of Environmental Fluid Dynamics to simulate open flows
and saturated- unsaturated porous medium flows.
[8]. S.S.Makhanov, S. Vannakrairojn, and E.J. Vanderperre, "Numerical
Model of Flooding in East-Bangkok", Water Resources, 25,4, Interperiodica
Pub.,1998, pp. 458-463.
Abstract. A new numerical model of flooding based on a
diffusion wave analogy is developed. The model is designed for calculation
of flows in large canal networks. A new iterative procedure is suggested
as a generalization of the well-known non-negative algorithm. The method
is applied to the calculations of flood in the delta of Chao-Phraya
river.
[9]. E.J. Vanderperre, S. Vannakrairojn and S.S. Makhanov, "Stochastic
Behavior of a Robot-Safety Device System", Yugoslavian Journal of Operation
Research, 1998, N2, pp.2-10.
Abstract. Up-to-date robots are often connected with a (repairable)
safety device. Such a device prevents possible damage, caused by a robot
failure, in the robot's neighboring environment. However, the random behavior
of the entire system (robot, safety device, repair facility) could jeopardize
some prescribed safety requirement. In order to describe the random behavior
of the system, we introduce a stochastic process endowed with probability
kernels satisfying Kolmogorov type-equations. The solution procedure is
based on advanced methods of renewal theory. Finally, we consider the particular
but important case of fast repair.
[10]. E.J.Vanderperre S.S. Makhanov and K.Sonthipaumpoon, "A
Renewal Integral Equation Related to a Multiple Cold Standby System",
Opsearch, V35, N2, 1998, pp.154-159.
Abstract. A multiple cold standby system attended by a single
repairman is considered. The system satisfies the usual conditions (i.i.d.
random variables, perfect repair, instantaneous and perfect switch, queuing).
The operative unit has a constant failure rate but an arbitrary repair
time distribution. We analyze the total idle time of the repairman during
the survival time of the system. Finally, as an application, we consider
the case of deterministic repair.
[11]. S.S.Makhanov and A.Yu.Semenov,"New Numerical Methods for
Non-Linear Parabolic Boundary-Value Problems with A Priory Bounded Solution",
Proc. Fourth Eccomas Computational Fluid Dynamics Conference, September
7-10, 1998, Athens Greece, Ed. K.D. Papailiou, Vol. 1, Part 1, pp.78-82,
Willey & Sons.
Abstract. We present a new family of numerical methods to solve
non-linear parabolic boundary value problems with constraints a priori
imposed on the solution. The proposed procedures are based on a consistent
first-order approximation of "diffusion" and "transport" terms combined
with an unconditionally stable Gauss-Seidel-type iterative technique. We
demonstrate that the proposed algorithms provide an overall priority with
regard to conventional numerical schemes as applied to a diffusion wave
model of open flows and to a Richards-type model of saturated-unsaturated
flows. Numerical examples illustrates the computational efficiency of the
method for some particular values of underlying parameters. Finally we
present a theoretical analysis of the method and prove the convergence
theorems.
[12]. S.S.Makhanov and A.Yu.Semenov,"Numerical Methods for Non-Linear
Parabolic Boundary- Value Problems with A Priory Bounded Solution",
Proc. IV National Congress of the SIMAI-Societa' Italiana di Mathematica
Applicata e Industriale, June 1-5, 1998, Giardini Naxos, Me, Italy .
Abstract. A new family of numerical methods for solution of
1D and 2D non-linear parabolic boundary value problems with
constraints a priori imposed on the solution is proposed. We prove that
our scheme provides h³ 0, where
h is water depth, irrespective of flow conditions. For Richards model
of saturated - unsaturated flows the method conserves the bilateral inequality
0£ qmin£q
£ q max
,where q the soil moisture content and q
min, q max denote
the residual moisture content and the porosity.
[13]. S.S.Makhanov, K. Sonthipaumpoon and S. Vannakrairojn"Variational
Gridding Algorithms to Optimize a Tool-Path of a Five-Axis Milling Machine",
Proc. 1998 IEEE Asia Pacific Conf. on Circuits and Systems: Microelectronics
and Integration Systems, November 24-27, 1998, Chaingmai, Thailand, p.515-518.
Abstract. We present a new application of variational grid generation
techniques to optimize the tool-path of an industrial milling robot. Our
approach is based on a global approximation of the required surface by
a virtual surface composed from tool trajectories. The procedure combines
inverse kinematics techniques and a variational gridding method endowed
with constraints related to the required scallop height. The proposed technique
allows to generate a tool-path for workpieces with complex geometries comprising
"islands" and/or boundaries with sharp edges requiring a combined "spiral-zigzag"
pattern. Finally, our proposed technique provides a significant increase
in the accuracy of milling.
[14]. K. Sonthipaumpoon, S.S. Makhanov and E. Bohez, "Optimization
of Tool-Path Planning of a Five-Axis Milling Machine", Proc. National
Computer Science and Engineering Conf. October 29-30, 1998, Bangkok, pp.85-96
(Distinguished Paper Award).
Abstract. A new technique based on a global approximation of
the required surface composed from tool trajectories is presented. We demonstrate
capabilities of the proposed method to generate a tool-path for workpeices
with free form surface geometries requiring combined zigzag/spiral tool-path.
[15].S.S.Makhanov, A. Panitkulpong and E.J. Vanderperre, "Mathematical
Modeling of River-Groundwater Flows on Curvilinear Grids", J. Meteorology
and Hydrology, Allerton Press, N.Y., N2, pp.92-105, 1997.
Abstract. We present an adaptive grid refinement technique to
model coupled river-ground water flows. We propose a numerical procedure
based on a splitting algorithm, a domain decomposition and an algebraic
mapping technique. Our numerical experiments demonstrate an efficiency
of the proposed method.
[16] A.Yu.Semenov and S.S.Makhanov, "Non-Negative Methods for
Open Flows Modeling", Third Mississippi State Conference on Differential
Equations and Computational Simulations. May 16-17, 1997. USA. Mississippi
State Univ. pp.31-32.
Abstract. A special class of numerical methods for solution
of non-linear parabolic partial derivative equations is proposed. We present
a prove of the convergence and non-negativity theorems.
[17].E.J.Vanderperre, S.S. Makhanov and S. Suchatvejapoom, "Long-Run
Availability of a Repairable Parallel System", Microelectronics and
Reliability, Elsevier, V37, N3,pp.525-527, 1997.
Abstract. We analyze the long-run availability of a two-unit
parallel system sustained by a cold standby unit and attended by two identical
repairmen. The system satisfies the usual conditions (i.i.d. random variables,
perfect repair, instantaneous and perfect switch, queuing). We use Hokstad's
supplementary variable method to construct a system of simultaneous partial
derivative equations. A first-order numerical scheme and an iterative algorithm
for the solution of the equations is proposed and analyzed.
[18]. S.S. Makhanov and A.Yu. Semenov, "A Class of Non-Negative
Numerical Methods and its Applications to Open Flow Modeling", in Fluid
Dynamics of Natural Flows, Moscow, Nauka, FizMatLit, 1997, pp. 55-74 (in
Russian).
Abstract. The book presents a set of mathematical models and
results of numerical modeling of various natural flows in rivers, seas,
filtration and stratified flows. The modeling is based on CFD-methods and
approaches derived in the frames of shallow water equation, Navier Stokes
equations, Richards equations etc.
[19]. D. Batanov, E. Bohez, S.S.Makhanov, K. Sonthipermpoon and
M.T. Tabucanon "A Curvilinear Grid Adaptation Technique Applied to Tool-Path
Planning of a Five-Axis Milling Machine", Proc. of 4th International
Conference on Computer Integrated Manufacturing, 21-24 October, 1997, Singapore,
Springer-Verlag.
Abstract We propose a new algorithm to correct tool-paths of
a five-axis milling machine based on elliptic grid generation. Our weighting
function is represented in terms of errors related to nonlinear kinematics
of the milling machine. Numerical experiments reveal that the proposed
technique provides a significant increase in the accuracy of milling.
[20]. E.J. Vanderperre, S. Vannakrairojn and S.S. Makhanov, "Stochastic
Behavior of a Robot-Safety Device System", Proc. of 2-nd International
Workshop on Computer Cooperative Work in Design, 26-28 November, 1997,
Bangkok.
Abstract. We introduce a robot-safety device system attended
by two statistically different repairmen. In order to describe the random
behavior of the system, we introduce a stochastic process endowed with
probability kernels satisfying Kolmogorov type-equations.
[21]. S.S. Makhanov and K. Sonthipaumpoon, "A New Approach to
Tool Path Planning of a Five-Axis Milling Machine", Proc. of 2-nd International
Workshop on Computer Cooperative Work in Design, 26-28 November, 1997,
Bangkok.
Abstract A new algorithm to correct tool-paths of a five-axis
milling machine based on elliptic grid generation is proposed and analyzed..
[22]. E.J.Vanderperre, S. Vannakrairojn and S.S. Makhanov, "A
Delay Differential Equation Related to a Renewable Parallel System", Microelectronics
and Reliability, Elsevier, V37, N5,pp.937-941,1997.
Abstract. We consider Gaver's parallel system sustained by a
cold stand by unit and attended by two identical repairmen. The system
satisfies the usual conditions(random variables, perfect repair, instantaneous
and perfect switch, queuing). Each operative unit has a constant failure
rate and a deterministic repair time. We analyze the total joint idle time
of both repairmen during the survival time of the system. The analysis
requires the solution of the so-called delay differential equations. A
numerical example illustrates the structure of the solution for some particular
values of underlying parameters.
[23]. E.J. Vanderperre, T.Larsar and S.S Makhanov, "On Poisson
Summation Formula: A Probabilistic Approach", J.Sci.Soc. Thailand,
V23, pp.57-59, 1997.
Abstract. We present a summation formula embedded in the frame-work
of Probability Theory. Our result is based on a concatenation of Poisson's
summation formula and the Fourier inversion theorem. As an application
we derive a very short demonstration of the transformation formula for
the theta function.
[24]. S.Hungspreaug, S.Vannakrairojn, S.S. Makhanov, S.Sangchan,
and P. Mekpruksawong,"A New Two-Dimensional Model of Flooding in East
Bangkok", Proc. 7-th ICID International Drainage Workshop, 17-21 November
1997, Penang, Malaysia, V3, pp.T15.1-T15.6
Abstract. A new software to model water systems comprising large
drainage networks is proposed. The model is oriented to assist decision-making
in farming and agriculture.
[25]. S. Sangchan and S.S. Makhanov, "Numerical Model of Flooding
in the Eastern Areas of Bangkok", KKU Engineering Journal, V 23, N
2, pp.75-91.
Abstract. We present basic mathematical formulations and new
numerical methods to create a new computer software for simulations of
flooding in the Eastern areas of Bangkok. The first version of the Flood-Simulator,
KMITL makes it possible to calibrate the model by measurements and estimate
an efficiency of flood protection measures in order to select optimal schemes.
[26].S.S.Makhanov and A.Yu. Semenov, "Non-Negative Numerical
Method for Open Flows Modeling", Proc. Second Asian Computational Fluid
Dynamic Conference, ACFD2, December 15-18, 1996, Tokyo, V2, pp.557-562.
Abstract. A new finite-difference method for numerical modeling
of open flows by 1 and 2 D transport-diffusion equation is presented and
analyzed. The method provides a non-negativity of the flow depth including
the case of a "dry bottom interaction".
[27] S.S.Makhanov and A.Yu. Semenov, "A Two Dimensional Non-Negative
Algorithm for Calculating the Flow of a Liquid in an Open Channel",
J. Comp. Maths. Math. Phys, Elsevier N4, pp.501-507, 1996.
Abstract. A numerical start-to finish algorithm for modeling
the two-dimensional flow of liquids based on the parabolic model of diffusion
waves is described and analyzed. A feature of the algorithm is that the
flow depths are strictly non-negative for any flow regime. The work extends
the previous one-dimensional algorithm to two dimensions. The properties
of the algorithm are illustrated by results of calculations.
[28]. E.J.Vanderperre and S.S. Makhanov, "On Gaver's Parallel
System Sustained by a Cold Standby Unit and Attended by Two Repairmen",
Opsearch, Vol. 33, No 2, pp.107-114, 1996.
Abstract. We consider Gaver's parallel system sustained by a
cold standby unit and attended by two identical repairman. We analyze the
total joint idle time of both repairman during the survival time of the
system. The analysis requires the solution of the so-called delay-differential
equation. A numerical examples illustrates the structure of the solution
for some particular values of underlying parameters.
[29]. E.J. Vanderperre, S.S. Makhanov and P. Rattanathanawan,
"Reliability of a Repairable Parallel System", J.Sci.Soc. Thailand,
V22, pp.75-81, 1996.
Abstract. We analyze the reliability of Gaver's parallel system
sustained by a cold standby unit and attended by two identical repairman.
Our analysis is based on a time depended version of the supplementary variable
method. The basic PDE's are transformed into an integro-differential equation
of the Fredholm-type. A particular case motivates the proposed analysis.
[30]. S.S. Makhanov, S. Sangchan and S. Kwanpruk, "Mathematical
Modeling of Flooding in the Eastern Areas of Bangkok", Proc. RESTECS'96,
June 6-8, 1996, KMITL, Bangkok, pp.C39-C45.
Abstract. A new software to model flood development is proposed
and analyzed. The model is oriented to assist decision-making in farming
and agriculture.