No abstract is provided for this article.
No abstract is provided for this article.
No abstract is provided for this article.
Pressure solution is an important process in sedimentary basins, and its behaviour depends mainly on the sediment rheology and temperature distribution. The compaction relation of pressure solution is typically assumed to be a viscous one and is often written as a relationship between effective stress and strain rate. A new derivation of viscous compaction relation is formulated based on more realistic boundary conditions at grain contacts. A non-linear diffusion problem with a moving boundary is solved numerically and a simple asymptotic solution is given to compare with numerical simulations. Pressure solution is significantly influenced by the temperature gradient. Porosity reduction due to pressure solution is enhanced in an environment with a higher thermal gradient, while porosity decreases much slowly in the region where the thermal gradient is small. Pressure solution tends to complete more quickly at shallower depths and earlier time in higher temperature environment than that in a low one. These features of pressure solution in porous sediments are analysed using a perturbation method to get a solution for the steady-state. Comparison with real data shows a reasonably very good agreement.
This chapter introduces the fundamentals of ordinary differential equations (ODEs). Both first-order ODEs and second-order ODEs are explained in detail, including finding their complementary functions and particular integrals. Higher-order linear ODEs can be transformed into a system of first-order ODEs, which can be solved using dynamical system approaches.
The calcium transport in biological systems is modelled as a reaction–diffusion process. Nonlinear calcium waves are then simulated using a stochastic cellular automaton whose rules are derived from the corresponding coupled partial differential equations. Numerical simulations show self-organized criticality in the complex calcium waves and patterns. Both the stochastic cellular automaton approach and the equation-based simulations can predict the characteristics of calcium waves and complex pattern formation. The implication of locality of calcium distribution with positional information in biological systems is also discussed.
Smectite‐illite reaction of sediment minerals in sedimentary basins is modelled as a one‐step dehydration reaction. The water released from the mineral reaction can affect compaction process so as to retard porosity reduction and thus may cause overpressuring, especially in the reaction region. The coupled nonlinear model equations have been solved numerically, and the asymptotic analysis has been used to get the analytical solutions of the nonlinear model equations in some regions of most practical interests. The comparison of the obtained asymptotical solutions with the numerical results and real data shows very good agreement.
The aim of this article is to demonstrate that a firm may owe its continued existence to its attempts to conceal information from its competitors about the unknown characteristics of a certain factor, not just to its savings on market transaction costs, its team-working, risk-sharing or the encouragement of ex ante specific investment. This is because the existence of a firm contract severs the relationship between the factor market and the product market, thereby making it difficult for outsiders to observe the marginal contribution of the intermediate factor and make statistical inferences about the factor’s unknown characteristics. Furthermore, an optimal contract is determined by a trade-off not only between traditional risk-sharing and incentive, but also between the incentive and information concealing. Finally, we show that this latter kind of trade-off also affects the position of the optimal boundary of the firm.
No abstract is provided for this article.
Feature selection for a given model can be transformed into an optimization task. The essential idea behind it is to find the most suitable subset of features according to some criterion. Nature-inspired optimization can mitigate this problem by producing compelling yet straightforward solutions when dealing with complicated fitness functions. Additionally, new mathematical representations, such as quaternions and octonions, are being used to handle higher-dimensional spaces. In this context, we are introducing a meta-heuristic optimization framework in a hypercomplex-based feature selection, where hypercomplex numbers are mapped to real-valued solutions and then transferred onto a boolean hypercube by a sigmoid function. The intended hypercomplex feature selection is tested for several meta-heuristic algorithms and hypercomplex representations, achieving results comparable to some state-of-the-art approaches. The good results achieved by the proposed approach make it a promising tool amongst feature selection research.
This paper proposes an elegant optimization framework consisting of a mix of linear-matrix-inequality and second-order-cone constraints. The proposed framework generalizes the semidefinite relaxation (SDR) enabled solution to the typical transmit beamforming problems presented in the form of quadratically constrained quadratic programs (QCQPs) in the literature. It is proved that the optimization problems subsumed under the framework always admit a rank-one optimal solution when they are feasible and their optimal solutions are not trivial. This finding indicates that the relaxation is tight as the optimal solution of the original beamforming QCQP can be straightforwardly obtained from that of the SDR counterpart without any loss of optimality. Four representative examples of transmit beamforming, i.e., transmit beamforming with perfect channel state information (CSI), transmit beamforming with imperfect CSI, chance-constraint approach for imperfect CSI, and reconfigurable-intelligent-surface (RIS) aided beamforming, are shown to demonstrate how the proposed optimization framework can be realized in deriving the SDR counterparts for different beamforming designs.
Nature-inspired algorithms are among the most powerful algorithms for optimization. In this study, a new nature-inspired metaheuristic optimization algorithm, called bat algorithm (BA), is introduced for solving engineering optimization tasks. The proposed BA is based on the echolocation behavior of bats. After a detailed formulation and explanation of its implementation, BA is verified using eight nonlinear engineering optimization problems reported in the specialized literature. BA has been carefully implemented and carried out optimization for eight well-known optimization tasks. Then, a comparison has been made between the proposed algorithm and other existing algorithms. The optimal solutions obtained by the proposed algorithm are better than the best solutions obtained by the existing methods. The unique search features used in BA are analyzed, and their implications for future research are also discussed in detail.
