Direct numerical method for an inverse problem of a parabolic partial differential equation

A coefficient inverse problem of the one-dimensional parabolic equation is solved by a high-order compact finite difference method in this paper. The problem of recovering a time-dependent coefficient in a parabolic partial differential equation has attracted considerable attention recently. While many theoretical results regarding the existence and uniqueness of the solution are obtained, the development of efficient and accurate numerical methods is still far from satisfactory. In this paper a fourth-order efficient numerical method is proposed to calculate the function u(x,t) and the unknown coefficient a(t) in a parabolic partial differential equation. Several numerical examples are presented to demonstrate the efficiency and accuracy of the numerical method.     

A meshless method for numerical solution of a linear hyperbolic equation with variable coefficients in two space dimensions

A meshless method is proposed for the numerical solution of the two space dimensional linear hyperbolic equation subject to appropriate initial and Dirichlet boundary conditions. The new developed scheme uses collocation points and approximates the solution employing thin plate splines radial basis functions. Numerical results are obtained for various cases involving variable, singular and constant coefficients, and are compared with analytical solutions to confirm the good accuracy of the presented scheme. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

Effective Stress in Unsaturated Soils: A Thermodynamic Approach Based on the Interfacial Energy and Hydromechanical Coupling

In recent years, the effective stress approach has received much attention in the constitutive modeling of unsaturated soils. In this approach, the effective stress parameter is very important. This parameter needs a correct definition and has to be determined properly. In this paper, a thermodynamic approach is used to develop a physically-based formula for the effective stress tensor in unsaturated soils. This approach accounts for the hydro-mechanical coupling, which is quite important when dealing with hydraulic hysteresis in unsaturated soils. The resulting formula takes into account the role of interfacial energy and the contribution of air?Cwater specific interfacial area to the effective stress tensor. Moreover, a bi-quadratic surface is proposed to represent the contribution of the so-called suction stress in the effective stress tensor. It is shown that the proposed relationship for suction stress is in agreement with available experimental data in the full hydraulic cycle (drying, scanning, and wetting).     

Numerical simulation of fluid flow of two rotating side-by-side circular cylinders by Lattice Boltzmann method

A numerical investigation of the two-dimensional laminar flow around side-by-side rotating circular cylinders using Lattice Boltzmann method is conducted. The effects of variation of rotational speed ratio β and different gap spacings g* at Reynolds number of 100 are studied. A various range of rotational speed ratio 0 ≤ β ≤ 2 for four different gap spacings of 3, 1.5, 0.7 and 0.2 are investigated. Flow conditions and its characteristics, such as lift and drag coefficients and Strouhal number, is studied. The results indicated that as β increases, the flow changes its condition from periodic to steady after a critical rotational speed. Results also indicated that variation of the gap spacing and rotational speed has significant effect on wake pattern. Wake pattern in turn has significant effect on the Strouhal number. Finally, the result is compared with experimental and other numerical data.     

Synthesis and Characterization of a Fluorescent Water-Borne Polyurethane Based on a Novel Naphthalimide Dye

A waterborne-polyurethane (WPU) dye, based on the fluorescent dye 4-diamino propane-N-allyl-1,8- naphthalimide (WPU-DAN), was synthesized by attaching 4-diamino propane-N-allyl-1,8- naphthalimide (DAN) onto both ends of the polyurethane (PU) chains according to a prepolymer?ionomer process. The synthetic process was confirmed by Fourier transform infrared spectroscopy (FTIR) and UV-visible absorption. The glass transition temperature, molecular weight and average particle sizes were measured. The glass transition temperatures of WPU and WPU-DAN were 46.6 and 49.8°C, respectively. In addition, the particle size distributions of WPU-DAN and WPU were 140 and 134 nm, respectively. The thermal behaviour of WPU-DAN showed improvement compared to WPU. The fluorescence intensity of WPU-DAN was enhanced more than DAN due to the naphthalimide groups attached to the chains, and the fluorescence intensity of WPU-DAN and DAN were increased by increasing temperature. Moreover, the fluorescence intensity of WPU-DAN emulsion was stable during 30 days and no loss of fluorescence intensity occurred for these days.     

Nonlinear integral resonant controller for vibration reduction in nonlinear systems

A new nonlinear integral resonant controller (NIRC) is introduced in this paper to suppress vibration in nonlinear oscillatory smart structures. The NIRC consists of a first-order resonant integrator that provides additional damping in a closed-loop system response to reduce high-amplitude nonlinear vibration around the fundamental reso-nance frequency. The method of multiple scales is used to obtain an approximate solution for the closed-loop system. Then closed-loop system stability is investigated using the resulting modulation equation. Finally, the effects of different control system parameters are illustrated and an approximate solution response is verified via numerical simulation results. The advantages and disadvantages of the proposed controller are presented and extensively discussed in the results. The controlled system via the NIRC shows no high-amplitude peaks in the neighboring frequencies of the resonant mode, unlike conventional second-order compensation methods. This makes the NIRC controlled system robust to excitation frequency variations.     

Advanced buckyball joints: synthesis, complex formation and computational simulations of centrohexaindane-extended tribenzotriquinacene receptors for C60 fullerene

The synthesis of a structurally optimized tribenzotriquinacene receptor 9 is described, which is extended by centrohexaindane moieties to give rise to a half-round concave ball bearing, with optimum shape complementarity towards C(60) fullerene. Spectroscopic investigations reveal that this novel host forms a 1 : 1 host-guest complex with C(60) with a complex stability constant of K(1) = 14,550 ± 867 M(-1), which is considerably higher than those reported for structurally related tribenzotriquinacene hosts reported previously. Both the suppression for binding of a second receptor (i.e. formation of a 2 : 1 host-guest complex) as well as the increase of complex stability of the 1 : 1 complex can be rationalized in terms of multiple additive van der Waals and π-π interactions between C(60) and the aromatic groups of the receptor, as revealed by DFT + D and force-field calculations. Combining results from spectroscopic and theoretical investigations leads to predictions in light of future receptor designs, which--apart from shape complementarity--will have to consider an optimized electronic match (i.e. partial charge transfer) between the receptor and the fullerene host.     

High-throughput biophysical measurement of human red blood cells

This paper reports a microfluidic system for biophysical characterization of red blood cells (RBCs) at a speed of 100-150 cells s(-1). Electrical impedance measurement is made when single RBCs flow through a constriction channel that is marginally smaller than RBCs' diameters. The multiple parameters quantified as mechanical and electrical signatures of each RBC include transit time, impedance amplitude ratio, and impedance phase increase. Histograms, compiled from 84,073 adult RBCs (from 5 adult blood samples) and 82,253 neonatal RBCs (from 5 newborn blood samples), reveal different biophysical properties across samples and between the adult and neonatal RBC populations. In comparison with previously reported microfluidic devices for single RBC biophysical measurement, this system has a higher throughput, higher signal to noise ratio, and the capability of performing multi-parameter measurements.     

A method based on meshless approach for the numerical solution of the two‐space dimensional hyperbolic telegraph equation

In the current article, we investigate the RBF solution of second‐order two‐space dimensional linear hyperbolic telegraph equation. For this purpose, we use a combination of boundary knot method (BKM) and analog equation method (AEM). The BKM is a meshfree, boundary‐only and integration‐free technique. The BKM is an alternative to the method of fundamental solution to avoid the fictitious boundary and to deal with low accuracy, singular integration and mesh generation. Also, on the basis of the AEM, the governing operator is substituted by an equivalent nonhomogeneous linear one with known fundamental solution under the same boundary conditions. Finally, several numerical results and discussions are demonstrated to show the accuracy and efficiency of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.