An iterative method for a Cauchy problem for the heat equation

An iterative method for reconstruction of the solution to a parabolic initial boundary value problem of second order from Cauchy data is presented. The data are given on a part of the boundary. At each iteration step, a series of well-posed mixed boundary value problems are solved for the parabolic operator and its adjoint. The convergence proof of this method in a weighted L2-space is included.

A new three phase method (SDP method) for the multi-objective vehicle routing problem with simultaneous delvery and pickup (VRPSDP)

Transportation service operators are witnessing a growing demand for bi-directional movement of goods. Given this, the following thesis considers an extension to the vehicle routing problem (VRP) known as the delivery and pickup transportation problem (DPP), where delivery and pickup demands may occupy the same route. The problem is formulated here as the vehicle routing problem with simultaneous delivery and pickup (VRPSDP), which requires the concurrent service of the demands at the customer location. This formulation provides the greatest opportunity for cost savings for both the service provider and recipient. The aims of this research are to propose a new theoretical design to solve the multi-objective VRPSDP, provide software support for the suggested design and validate the method through a set of experiments. A new real-life based multi-objective VRPSDP is studied here, which requires the minimisation of the often conflicting objectives: operated vehicle fleet size, total routing distance and the maximum variation between route distances (workload variation). The former two objectives are commonly encountered in the domain and the latter is introduced here because it is essential for real-life routing problems. The VRPSDP is defined as a hard combinatorial optimisation problem, therefore an approximation method, Simultaneous Delivery and Pickup method (SDPmethod) is proposed to solve it. The SDPmethod consists of three phases. The first phase constructs a set of diverse partial solutions, where one is expected to form part of the near-optimal solution. The second phase determines assignment possibilities for each sub-problem. The third phase solves the sub-problems using a parallel genetic algorithm. The suggested genetic algorithm is improved by the introduction of a set of tools: genetic operator switching mechanism via diversity thresholds, accuracy analysis tool and a new fitness evaluation mechanism. This three phase method is proposed to address the shortcoming that exists in the domain, where an initial solution is built only then to be completely dismantled and redesigned in the optimisation phase. In addition, a new routing heuristic, RouteAlg, is proposed to solve the VRPSDP sub-problem, the travelling salesman problem with simultaneous delivery and pickup (TSPSDP). The experimental studies are conducted using the well known benchmark Salhi and Nagy (1999) test problems, where the SDPmethod and RouteAlg solutions are compared with the prominent works in the VRPSDP domain. The SDPmethod has demonstrated to be an effective method for solving the multi-objective VRPSDP and the RouteAlg for the TSPSDP.

A meshless method for an inverse two-phase one-dimensional nonlinear Stefan problem

We extend a meshless method of fundamental solutions recently proposed by the authors for the one-dimensional two-phase inverse linear Stefan problem, to the nonlinear case. In this latter situation the free surface is also considered unknown which is more realistic from the practical point of view. Building on the earlier work, the solution is approximated in each phase by a linear combination of fundamental solutions to the heat equation. The implementation and analysis are more complicated in the present situation since one needs to deal with a nonlinear minimization problem to identify the free surface. Furthermore, the inverse problem is ill-posed since small errors in the input measured data can cause large deviations in the desired solution. Therefore, regularization needs to be incorporated in the objective function which is minimized in order to obtain a stable solution. Numerical results are presented and discussed. © 2014 IMACS.

Power conversion and signal transmission integration method based on dual modulation of DC-DC converters

For the development of communication systems such as Internet of Things, integrating communication with power supplies is an attractive solution to reduce supply cost. This paper presents a novel method of power/signal dual modulation (PSDM), by which signal transmission is integrated with power conversion. This method takes advantage of the intrinsic ripple initiated in switch mode power supplies as signal carriers, by which cost-effective communications can be realized. The principles of PSDM are discussed, and two basic dual modulation methods (specifically PWM/FSK and PWM/PSK) are concluded. The key points of designing a PWM/FSK system, including topology selection, carrier shape, and carrier frequency, are discussed to provide theoretical guidelines. A practical signal modulation-demodulation method is given, and a prototype system provides experimental results to verify the effectiveness of the proposed solution.

A general one-pot strategy for the synthesis of high-performance transparent-conducting-oxide nanocrystal inks for all-solution-processed devices

For all-solution-processed (ASP) devices, transparent conducting oxide (TCO) nanocrystal (NC) inks are anticipated as the next-generation electrodes to replace both those synthesized by sputtering techniques and those consisting of rare metals, but a universal and one-pot method to prepare these inks is still lacking. A universal one-pot strategy is now described; through simply heating a mixture of metal-organic precursors a wide range of TCO NC inks, which can be assembled into high-performance electrodes for use in ASP optoelectronics, were synthesized. This method can be used for various oxide NC inks with yields as high as 10 g. The formed NCs are of high crystallinity, uniform morphology, monodispersity, and high ink stability and feature effective doping. Therefore, the inks can be readily assembled into films with a surface roughness of 1.6 nm. Typically, a sheet resistance of 110 Ω sq-1 can be achieved with a transmittance of 88%, which is the best performance for TCO NC ink-based electrodes described to date. These electrodes can thus drive a polymer light-emitting diode (PLED) with a luminance of 2200 cdm-2 at 100 mA cm-2.

Numerical solution of parabolic Cauchy problems in planar corner domains

An iterative method for the parabolic Cauchy problem in planar domains having a finite number of corners is implemented based on boundary integral equations. At each iteration, mixed well-posed problems are solved for the same parabolic operator. The presence of corner points renders singularities of the solutions to these mixed problems, and this is handled with the use of weight functions together with, in the numerical implementation, mesh grading near the corners. The mixed problems are reformulated in terms of boundary integrals obtained via discretization of the time-derivative to obtain an elliptic system of partial differential equations. To numerically solve these integral equations a Nyström method with super-algebraic convergence order is employed. Numerical results are presented showing the feasibility of the proposed approach. © 2014 IMACS.

Nonlinear limit of alternative method to 2 × 2 MIMO for LTE RoF system

Owing to the limited cell size of eNodeB (eNB), the relay node has emerged as an attractive solution for the long-term evolution (LTE) system. The nonlinear limit of the alternative method to multipleinput and multiple-output (MIMO) based on frequency division multiplexing (FDM) for orthogonal FDM (OFDM) is analysed over varying transmission spans. In this reported work, it is shown that the degradation pattern over the linear, intermixing and nonlinear propagation regions is consistent for the 2 and the 2.6 GHz bands. The proposed bands experienced a linear increase in the error vector magnitude (EVM) for both the linear and the nonlinear regions proportional to the increasing transmission spans. In addition, an optical launch power between -2 and 2 dBm achieved a significantly lower EVM than the LTE limit of 8% for the 10-60 km spans. © The Institution of Engineering and Technology 2014.

Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations

A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.

Numerical solution of a Cauchy problem for Laplace equation in 3-dimensional domains by integral equations

A numerical method based on integral equations is proposed and investigated for the Cauchy problem for the Laplace equation in 3-dimensional smooth bounded doubly connected domains. To numerically reconstruct a harmonic function from knowledge of the function and its normal derivative on the outer of two closed boundary surfaces, the harmonic function is represented as a single-layer potential. Matching this representation against the given data, a system of boundary integral equations is obtained to be solved for two unknown densities. This system is rewritten over the unit sphere under the assumption that each of the two boundary surfaces can be mapped smoothly and one-to-one to the unit sphere. For the discretization of this system, Weinert’s method (PhD, Göttingen, 1990) is employed, which generates a Galerkin type procedure for the numerical solution, and the densities in the system of integral equations are expressed in terms of spherical harmonics. Tikhonov regularization is incorporated, and numerical results are included showing the efficiency of the proposed procedure.

Electrocatalytic regeneration of atmospherically aged MoS2 nanostructures via solution-phase sulfidation

The performance of MoS2 as a hydrogen evolution catalyst is diminished by exposure to air. We demonstrate a solution phase technique to resulfidate MoSxO2-x using Na2S2O3. The success of the method was judged by performance as a H+ reduction catalyst. Following sulfidation samples displayed a favourable decrease in both onset potential and Tafel slope, with the best decreasing from -0.23 V to -0.18 V (vs. SHE), and 282 mV dec-1 to 87 mV dec-1 respectively. Ageing studies indicate that this method may be used to recycle the MoS2 repeatedly without losing catalytic performance, although repeated sulfidation did result in homogenisation of the nanostructure.