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The purpose of this paper is to demonstrate an effective and robust numerical solution for Raman fiber amplifier (RFA) equations which have no explicit solution. MATLAB BVP solvers are addressed for the solution.

The continuation method proposed for the solution of RFA equations using MATLAB BVP solvers is explained. Scripts for improving the power values at the boundaries with continuation, extending fiber length with continuation and calculation of the analytical partial derivatives using the MATLAB Symbolic toolbox are introduced. Comparisons among the different MATLAB BVP solvers have been made. Using the continuation method, signal evolutions for different kinds of RFA amplifier configurations are plotted.

The paper finds that MATLAB BVP solver with the continuation method can be used in the design of various kinds of RFAs for high powers/long gain fiber spans.

The paper will assist the fiber optic research community who suffer from two or more point boundary‐value problems. Moreover, the stiffness of the signal evolution which is faced with high pump powers and/or long fiber lengths can be solved with continuation. This superiority of the solver can be used to overcome any stiff changes of the signals for future studies.

The increased research interests and practical demands for RFAs have been calling for reasonable and efficient means for the performance evaluation of RFAs before the real amplifiers are fabricated. The solution method presented in this paper will be an efficient means for the solution of this issue.

MATLAB BVP solvers have been proven to be effective for the numerical solution of RFAs with multiple pumps and signal waves. Using the continuation method, in a distributed RFA with ten pump sources, 2,400 mW total input pump power is achieved. The improvement of the total power is about 1.4 times compared with those of the previously reported methods. Using the MATLAB BVP solvers, total power/fiber span can be improved further using the continuation process with the cost of computational time. This is a notable and promising improvement from a RFA designer's point of view.

Shows how a strongly non‐linear semiconductor equation can be solved via homotopy deformation methods combined with the arclength continuation procedures. The fundamental goal of these methods is to overcome the instabilities or the failure of the classical Newton‐Raphson’s schemes which appear when the non‐linearity is strong or near limit or bifurcation points. The system, in its artificial transient form, is discretized by the non‐linear implicit scheme with local time steps. Uses the mixed finite element (MFE) approach. Presents numerical results, in two dimension, for a realistic device: an Abrupt Heterojunction Bipolar Transistor working as an amplifier.

We present an abstract mathematical and numerical analysis for Drift‐Diffusion equation of heterojunction semiconductor devices with Fermi‐Dirac statistic. For the approximation, a mixed finite element method is considered. This can be profitably used in the investigation of the current through the device structure. A peculiar feature of this mixed formulation is that the electric displacement D and the current densities jn and jp for electrons and holes, are taken as unknowns, together with the potential φ and quas‐Fermi levels φn and φp. This enably D, jn and jp to be determined directly and accurately. For decoupled system, existence, uniqueness, regularity and stability results of the approximate solution are given. A priori and a posteriori error estimates are also presented. A nonlinear implicit scheme with local time steps is used. This algorithm appears to be efficient and gives satisfactory results. Numerical results for an heterojunction bipolar transistor, In two dimension, are presented.

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.

The author examine the sequestration of CO₂ in abandoned geological formations where leakages are permitted up to only a certain threshold to meet the international CO₂ emissions standards. Technically, the author address a Bayesian experimental design problem to optimally mitigate uncertainties and to perform risk assessment on a CO₂ sequestration model, where the parameters to be inferred are random subsurface properties while the quantity of interest is desired to be kept within safety margins.

The author start with a probabilistic formulation of learning the leak-age rate, and the author later relax it to a Bayesian experimental design of learning the formations geo-physical properties. The injection rate is the design parameter, and the learned properties are used to estimate the leakage rate by means of a nonlinear operator. The forward model governs a two-phase two-component flow in a porous medium with no solubility of CO₂ in water. The Laplace approximation is combined with Monte Carlo sampling to estimate the expectation of the Kullback–Leibler divergence that stands for the objective function.

Different scenarios, of confining CO₂ while measuring the risk of harmful leakages, are analyzed numerically. The efficiency of the inversion of the CO₂ leakage rate improves with the injection rate as great improvements, in terms of the accuracy of the estimation of the formation properties, are noticed. However, this study shows that those results do not imply in any way that the learned value of the CO₂ leakage should exhibit the same behavior. Also this study enhances the implementation of CO₂ sequestrations by extending the duration given by the reservoir capacity, controlling the injection while the emissions remain in agreement with the international standards.

Uncertainty quantification of the reservoir properties is addressed. Nonlinear goal-oriented inverse problem, for the estimation of the leakage rate, is known to be very challenging. This study presents a relaxation of the probabilistic design of learning the leakage rate to the Bayesian experimental design of learning the reservoir geophysical properties.

This is an attempt to better bridge the gap between the mathematical and the engineering/physical aspects of the topic. The authors trace the different sources of non-convexification in the context of topology optimization problems starting from domain discretization, passing through penalization for discreteness and effects of filtering methods, and end with a note on continuation methods.

Starting from the global optimum of the compliance minimization problem, the authors employ analytical tools to investigate how intermediate density penalization affects the convexity of the problem, the potential penalization-like effects of various filtering techniques, how continuation methods can be used to approach the global optimum and how the initial guess has some weight in determining the final optimum.

The non-convexification effects of the penalization of intermediate density elements simply overshadows any other type of non-convexification introduced into the problem, mainly due to its severity and locality. Continuation methods are strongly recommended to overcome the problem of local minima, albeit its step and convergence criteria are left to the user depending on the type of application.

In this article, the authors present a comprehensive treatment of the sources of non-convexity in density-based topology optimization problems, with a focus on linear elastic compliance minimization. The authors put special emphasis on the potential penalization-like effects of various filtering techniques through a detailed mathematical treatment.

Presents an implementation of continuation methods in the context of a code for flexible multibody systems analysis. These systems are characterized by the simultaneous presence of elastic deformation terms and rigid constraints. In our formulation, the latter terms are introduced by an augmented Lagrangian technique, resulting in the presence of Lagrange multipliers in the set of unknowns, together with displacement and rotation associated terms. Essential aspects for a successful implementation are discussed: e.g. the selection of an appropriate metric for computing the path following constraint, a flexible description of control parameters which accounts for conservative and nonconservative loads, imposed displacements and imposed temperatures (dilatation effects), and the inclusion of second order derivatives of rigid constraints in the Jacobian. A large set of examples is presented, with the objective of evaluating the numerical effectiveness of the implemented schemes.

This paper is concerned with rank analysis of rectangular matrix of a homogeneous set of incremental equations regarded as an element of continuation method. The rank analysis is based on a known feature that every rectangular matrix can be transformed into the matrix of echelon form. By inspection of the rank, correct control parameters are chosen and this allows not only for rounding limit and turning points but also for branch‐switching near bifurcation points.

The aim of the paper is to demonstrate a fast numerical solution for Raman fiber amplifier equations using proposed guess functions and MATLAB intrinsic properties. MATLAB BVP solvers are addressed for the solution.

The guess functions proposed for the solution of RFA equations using MATLAB BVP solvers are derived from Taylor expansion of pump and signal wave near the boundary to specifically obtain convergence for the initial mesh point. The guess functions increase simulation speed significantly. In order to improve the simulation speed further, vectorization and analytical Jacobians are introduced. Comparisons among bvp4c and bvp5c have been made with respect to total pump power, number of signals, vectorization with/without analytical Jacobians, fiber length, relative tolerance and continuation method. The simulations are performed to determine the effect of the run time on the choice of the number of equally spaced mesh points (N) in the initial guess, and thus optimal N values are found.

MATLAB BVP solvers have been proven to be effective for the numerical solution of RFAs with the proposed guess functions. In particular, with vectorizing, run time reduction is between 2.1 and 5.4 times for bvp4c and between 1.6 and 2.1 times for bvp5c and in addition to vectorizing, with the introduction of the analytical Jacobians, the reduction is between 2.4 and 6.2 times for bvp4c and 1.7 and 2.2 times for bvp5c, respectively, depending on the total pump power between 1,000 mW and 2,000 mW and the number of signals. Also, simulation results show that the efficiency of the solution with proposed guess functions is improved more than six times compared with those of previously reported continuation methods. Results show that the proposed guess functions with the vectorization and analytical Jacobians can be used for the performance evaluation of RFAs for the high power systems/long gain fiber span.

The robust improvement of the solution proposed in this paper lies in the fact that the derived guess functions for the RFAs are highly effective in the sense that they assist the solver to converge to the solution for any total pump power value in a wide range from 1 to 3,000 mW and for any fiber lengths ranging 1 to 200 km which are used in practical applications. Hence, it is practicable for the performance evaluation of the existing RFA networks.

The novelty of this method is that, starting with the co‐propagating single pump and signal RFA schema, the authors derived the guess function specifically for the initial mesh points rather than using its analytical approximations. Moreover, the solution is generalized for co‐/counter propagating pumps/signals with the curve fitted coefficient(s).

Assuming that supplier knowledge can either strengthen the partnership by nurturing the commitment and trust between partners or allow the buyer to be more calculative, this study aims to propose two types of knowledge sharing in supplier relationship – a type benefiting the partnership and another privately benefiting only one partner.

Using structural equation modeling and a surveyed dataset from 352 buyer–supplier partnerships, this study tested the research model of dual mechanism, where two types of knowledge sharing co-exist and have opposite effects on partnership longevity.

This study found that the two types of knowledge sharing create divergent effects on partnership continuation. For a buyer firm developing supplier knowledge, its supplier firm reciprocates by sharing knowledge with the buyer. While relation-specific knowledge promotes partnership longevity through developing trust, institutionalized knowledge hampers partnership longevity.

Findings overall indicate that knowledge plays a more instrumental role in sharing knowledge in a buyer–supplier relationship, and alternative forces simultaneously work in the partnership. Although this study explicates two mediating mechanisms for the effect of supplier knowledge, there remain many unknown aspects of the effect.

From the buyer’s perspective, it is possible its institutionalized knowledge can facilitate its relationship with a current supply chain partner so that it can gain more benefits from the relationship. From the supplier’s perspective, caution should be exercised in selecting the type of knowledge to share.

This study may have a broad impact on public policy by theorizing and testing why some partnerships last longer/shorter than others in association with the dynamics of the relationship initiated by one’s relational knowledge and the other’s knowledge sharing.

What this study contributes to involves the theorizing and testing the effects of the dual mechanism of knowledge sharing on partnership longevity. This study provides an example of a private investment in knowledge that is reciprocated with each type of knowledge – benefiting the partner and also benefiting the focal buyer firm.