Benchawan Wiwatanapataphee

• PhD (applied mathematics)
• Research Director at Mahidol University

Any function f from (0,∞) onto (0,∞) which is decreasing and convex has an inverse g which is positive and decreasing and convex. When f has some form of generalized convexity we determine additional convexity properties inherited by g. When f is positive, decreasing and (p,q)-convex, its inverse g is (q,p)-convex. Related properties which pertain...

In this paper, we study the risk aversion on valuing the single-name credit derivatives with the fast-scale stochastic volatility correction. Two specific utility forms, including the exponential utility and the power utility, are tested as examples in our work. We apply the asymptotic approximation to obtain the solution of the non-linear PDE, and...

We would like to thank the authors and reviewers of the papers for the excellent contributions.

We study the transient flow of a Newtonian fluid in rectangular microchannels taking into account boundary slip. An exact solution is derived by using the separation of variables in space and Fourier series expansion in time. It is found that, for different forms of driving pressure field, the effect of boundary slip on the flow behavior is qualita...

We study the pricing of American options in an incomplete market in which the dynamics of the underlying risky asset is driven by a jump diffusion process with stochastic volatility. By employing a risk-minimization criterion, we obtain the Radon-Nikodym derivative for the minimal martingale measure and consequently a linear complementarity problem...

In this work, we investigate the pulsatile blood flow in the human coronary artery system with no graft and with a bypass graft. The computational domain consists of the ascending aorta, the aortic arch, the proximal left coronary artery (LCA), the right coronary artery (RCA), and a graft. Blood is assumed to be an incompressible non-Newtonian flui...

We investigate the effect of boundary slip on the transient pulsatile fluid flow through a vessel with body acceleration. The Fahraeus-Lindqvist effect, expressing the fluid behavior near the wall by the Newtonian fluid while in the core by a non-Newtonian fluid, is also taken into account. To describe the non-Newtonian behavior, we use the modifie...

We study the following Schrodinger-Poisson system: -Delta u + V (x)u + phi u = |u|(P-1)u, -Delta phi = u(2), lim|(x)|(->+infinity)phi(x) = 0, where u,phi : R-3 -> R are positive radial functions, p epsilon (1,+infinity), x = (x(1), x(2), x(3)) epsilon R-3, and V(x) is allowed to take two different forms including V(x) = 1/(x(1)(2) + x(2)(2) + x(3)(...

Stochastic delay differential equations with jumps have a wide range of applications, particularly, in mathematical finance. Solution of the underlying initial value problems is important for the understanding and control of many phenomena and systems in the real world. In this paper, we construct a robust Taylor approximation scheme and then exami...

By establishing a maximal principle and constructing upper and lower solutions, the existence of positive solutions for the eigenvalue problem of a class of fractional differential equations is discussed. Some sufficient conditions for the existence of positive solutions are established.

We study the blood flow in a real model of the right coronary artery-bypass graft system under the real pulsatile condition. The human blood is assumed as an incompressible non-Newtonian fluid and its flow is modeled by the unsteady state Navier-Stokes equations and the continuity equation. The effect of the existence and intensity of a stenosis in...

This paper aims to investigate the effect of the silo-bottom design on the dynamic behaviour of granular flow during discharging process in a varied mass-flow silo. Three different designs of hopper bottom including a flat-bottomed silo, a cylinder-hopper silo and a silo with double-opening bottom are considered. We assume that the granular materia...

This paper aims to investigate the effect of the silo-bottom design on the dynamic behaviour of granular flow during discharging process in a varied mass-flow silo. Three different designs of hopper bottom including a flat-bottomed silo, a cylinder-hopper silo and a silo with double-opening bottom are considered. We assume that the granular materia...

This paper introduces an SEIQR epidemic model for the fuzzy transmission of a disease in a small-world network. The reproductive number of the model is derived and then the model is applied to study the disease spread on the network. In the network, each individual has a certain number of contacts which are able to pass infection with different pro...

This paper is concerned with the two-fluid flow and heat trans-fer in the continuous steel casting process under electromagnetic (EM) force. The governing equations consist of the Navier-Stokes equations, the continuity equation, and the energy equation. The influence of the EM field on the flow pattern, the meniscus shape, and temperature distribu...

In this study, we simulate the static and dynamic processes of granular flow during filling and discharging of a vertical-sided silo with conical hopper bottom. The granular material is an assembly of 7,500 soybeans. Based on the discrete element method, the governing equations for the granular flow are solved by the centred finite difference schem...

This paper aims to present a mathematical model and numerical technique to study the three-dimensional fluid flow and heat transfer in the electromagnetic steel casting process. The effect of source current density on the electromagnetic force as well as on the flow and temperature fields is in-vestigated. The numerical results indicate that the so...

Recent advances in microscale experiments and molecular simulations confirm that slip of fluid on solid surface occurs at small scale, and thus the traditional no-slip boundary condition in fluid mechanics cannot be applied to flow in micrometer and nanometer scale tubes and channels. On the other hand, there is an urgent need to understand fluid f...

This article focuses on the transient behaviour of blood flow in stenotic arteries. Human blood is modelled as an incompressible non-Newtonian fluid. A numerical technique based on the finite element method is developed to simulate the blood flow taking into account of the transient periodic behaviour of the blood flow in cardiac cy-cles. The flow...

In this paper, we study two types of genuinely nonlinear K(n,n) equations and a generalized KP equation. By developing a mathematical method based on the reduction of order of nonlinear differential equations, we derive general formulas for the travelling wave solutions of the three equations. The compactons, solitary patterns, solitons and periodi...

In this paper, we study the singular boundary value problems for systems of nonlinear fourth order differential equations {(u(4) (t) = a1 (t) f1 (t, u (t), v (t), u″ (t), v″ (t)) + b1 (t) g1 (t, u (t), v (t), u″ (t), v″ (t)),; v(4) (t) = a2 (t) f2 (t, u (t), v (t), u″ (t), v″ (t)) + b2 (t) g2 (t, u (t), v (t), u″ (t), v″ (t)), 0 < t < 1,; u (0) = u...

Polymethylmethacrylate bone cements have been widely used in orthopaedic surgery for the fixation of artificial joints such as hip replacement. The fixation is achieved by mechanical interlock resulting from the flow of the cement into pores in the cancellous bone bed. In this work, a finite element technique is developed to simulate the flow of ce...

The aims of this study were (1) to demonstrate the feasibility of computational fluid dynamic (CFD) modelling of realistic blood flow in the mouse aortic arch, and (2) to determine the relation of wall shear stress and atherosclerosis in the mouse aortic arch. ApoE knockout mice were chosen for this study. The blood flow fraction in the major branc...

We present a no-tension elastic-plastic model and a numerical method for analysing the stability of underground tunnels. The gov-erning equations include equations of motion and a nonlinear consti-tutive equation. A finite element numerical scheme is developed to solve the problem taking into account the presence of tectonic stresses in rock masses...

This study focuses on the transient behavior of blood flow in stenotic arteries. Human blood is modeled as an incompressible non-Newtonian fluid. A numerical technique based on the finite element method is developed to simulate the transient periodic behavior of blood flow in cardiac cycles. The flow pattern, the distribution of pressure and the wa...

In this paper, we investigate the behavior of the pulsatile blood flow in a stenosed right coronary artery with a bypass graft. The human blood is assumed to be a non-Newtonian fluid and its viscous behavior is described by the Carreau model. The transient phenomena of blood flow though the stenosed region and the bypass grafts are simulated by sol...

In this paper, a three-dimensional mathematical model is devel-oped to simulate the flow pattern of molten steel in tundish vessels. The flow in tundish is turbulent and the k − model is used to describe the turbulence of the flow. The governing equations include the continuity equation, the Navier-Stokes equations and two transport equations for t...

We develop a three-dimensional mathematical model of unsteady blood flow in stenosed right coronary artery with bypass grafting under the pulsatile flow condition. Numerical technique based on Galerkin finite clement method is developed for the solution. To depict the characteristic pulsatile flow, the model was run over cardiac cycle. Effect of th...

Various types of discrete and continuous models have been developed to study granular flows at microscopic and macroscopic scales. In this paper, we analyse three popular types of continuum models for granular media, including viscous elastic-plastic model, double shearing model and Newtonian/non-Newtonian CFD models. The theories of these models a...

A numerical algorithm, based on the Galerkin finite element method and the enthalpy formulation, is developed for solving the coupled turbulent fluid flow and heat transfer problem in a domain with a moving phase-change boundary. The governing equations consist of the continuity equation, the Navier–Stokes equations, the energy equation and the mod...

Based on the second-order random wave theory, the joint statistical distribution of the horizontal velocity and acceleration is derived using the characteristic function expansion method. From the joint distribution and the Morison equation, the theoretical distributions of drag forces, inertia forces and total random wave forces are determined. Th...