Critical values for unit root and cointegration test statistics - the use of response surface equations

This note considers the value of surface response equations which can be used to calculate critical values for a range of unit root and cointegration tests popular in applied economic research.

Effects of medium thermoelasticity on high Rayleigh number steady-state heat transfer and mineralization in deformable fluid-saturated porous media heated from below

In this paper, a solution method is presented to deal with fully coupled problems between medium deformation, pore-fluid flow and heat transfer in fluid-saturated porous media having supercritical Rayleigh numbers. To validate the present solution method, analytical solutions to a benchmark problem are derived for some special cases. After the solution method is validated, a numerical study is carried out to investigate the effects of medium thermoelasticity on high Rayleigh number steady-state heat transfer and mineralization in fluid-saturated media when they are heated from below. The related numerical results have demonstrated that: (1) medium thermoelasticity has a little influence on the overall pattern of convective pore-fluid flow, but it has a considerable effect on the localization of medium deformation, pore-fluid flow, heat transfer and mineralization in a porous medium, especially when the porous medium is comprised of soft rock masses; (2) convective pore-fluid flow plays a very important role in the localization of medium deformation, heat transfer and mineralization in a porous medium. (C) 1999 Elsevier Science S.A. All rights reserved.

Simultaneous steady state and dynamic design of process systems using structural indicators

The simultaneous design of the steady-state and dynamic performance of a process has the ability to satisfy much more demanding dynamic performance criteria than the design of dynamics only by the connection of a control system. A method for designing process dynamics based on the use of a linearised systems' eigenvalues has been developed. The eigenvalues are associated with system states using the unit perturbation spectral resolution (UPSR), characterising the dynamics of each state. The design method uses a homotopy approach to determine a final design which satisfies both steady-state and dynamic performance criteria. A highly interacting single stage forced circulation evaporator system, including control loops, was designed by this method with the goal of reducing the time taken for the liquid composition to reach steady-state. Initially the system was successfully redesigned to speed up the eigenvalue associated with the liquid composition state, but this did not result in an improved startup performance. Further analysis showed that the integral action of the composition controller was the source of the limiting eigenvalue. Design changes made to speed up this eigenvalue did result in an improved startup performance. The proposed approach provides a structured way to address the design-control interface, giving significant insight into the dynamic behaviour of the system such that a systematic design or redesign of an existing system can be undertaken with confidence.

Analysis of steady-state heat transfer through mid-crustal vertical cracks with upward throughflow in hydrothermal systems

We conduct a theoretical analysis of steady-state heat transfer problems through mid-crustal vertical cracks with upward throughflow in hydrothermal systems. In particular, we derive analytical solutions for both the far field and near field of the system. In order to investigate the contribution of the forced advection to the total temperature of the system, two concepts, namely the critical Peclet number and the critical permeability of the system, have been presented and discussed in this paper. The analytical solution for the far field of the system indicates that if the pore-fluid pressure gradient in the crust is lithostatic, the critical permeability of the system can be used to determine whether or not the contribution of the forced advection to the total temperature of the system is negligible. Otherwise, the critical Peclet number should be used. For a crust of moderate thickness, the critical permeability is of the order of magnitude of 10(-20) m(2), under which heat conduction is the overwhelming mechanism to transfer heat energy, even though the pore-fluid pressure gradient in the crust is lithostatic. Furthermore, the lower bound analytical solution for the near field of the system demonstrates that the permeable vertical cracks in the middle crust can efficiently transfer heat energy from the lower crust to the upper crust of the Earth. Copyright (C) 2002 John Wiley Sons, Ltd.

A 2D numerical model for simulating the physics of fault systems

Simulations provide a powerful means to help gain the understanding of crustal fault system physics required to progress towards the goal of earthquake forecasting. Cellular Automata are efficient enough to probe system dynamics but their simplifications render interpretations questionable. In contrast, sophisticated elasto-dynamic models yield more convincing results but are too computationally demanding to explore phase space. To help bridge this gap, we develop a simple 2D elastodynamic model of parallel fault systems. The model is discretised onto a triangular lattice and faults are specified as split nodes along horizontal rows in the lattice. A simple numerical approach is presented for calculating the forces at medium and split nodes such that general nonlinear frictional constitutive relations can be modeled along faults. Single and multi-fault simulation examples are presented using a nonlinear frictional relation that is slip and slip-rate dependent in order to illustrate the model.

Controlling chaos in a Lorenz-like system using feedback

We demonstrate that the dynamics of an autonomous chaotic laser can be controlled to a periodic or steady state under self-synchronization. In general, past the chaos threshold the dependence of the laser output on feedback applied to the pump is submerged in the Lorenz-like chaotic pulsation. However there exist specific feedback delays that stabilize the chaos to periodic behavior or even steady state. The range of control depends critically on the feedback delay time and amplitude. Our experimental results are compared with the complex Lorenz equations which show good agreement.

Asymptotically almost periodic solutions for abstract neutral integro-differential equations

We study the existence of asymptotically almost periodic classical solutions for a class of abstract neutral integro-differential equation with unbounded delay. A concrete application to partial neutral integro-differential equations which arise in the study of heat conduction in fading memory material is considered. (C) 2011 Elsevier Inc. All rights reserved.

EXISTENCE OF S-ASYMPTOTICALLY omega-PERIODIC SOLUTIONS FOR ABSTRACT NEUTRAL EQUATIONS

A bounded continuous function it u : [0, infinity) -> X is said to be S-asymptotically omega-periodic if lim(t ->infinity)[u(t + omega) - u(t)] = 0. This paper is devoted to study the existence and qualitative properties of S-asymptotically omega-periodic mild solutions for some classes of abstract neutral functional differential equations with infinite delay, Furthermore, applications to partial differential equations are given.

On recent developments in the theory of abstract differential equations with fractional derivatives

This note is motivated from some recent papers treating the problem of the existence of a solution for abstract differential equations with fractional derivatives. We show that the existence results in [Agarwal et al. (2009) [1], Belmekki and Benchohra (2010) [2], Darwish et al. (2009) [3], Hu et al. (2009) [4], Mophou and N`Guerekata (2009) [6,7], Mophou (2010) [8,9], Muslim (2009) [10], Pandey et al. (2009) [11], Rashid and El-Qaderi (2009) [12] and Tai and Wang (2009) [13]] are incorrect since the considered variation of constant formulas is not appropriate. In this note, we also consider a different approach to treat a general class of abstract fractional differential equations. (C) 2010 Elsevier Ltd. All rights reserved.

EXISTENCE RESULTS FOR ABSTRACT DEGENERATE NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper we discuss the existence of solutions for a class of abstract degenerate neutral functional differential equations. Some applications to partial differential equations are considered.

Global solutions for abstract neutral differential equations

We study the existence of global solutions for a class of abstract neutral differential equation defined on the whole real axis. Some concrete applications related to ordinary and partial differential equations are considered. (C) 2009 Elsevier Ltd. All rights reserved.

Global solutions for abstract impulsive differential equations

In this paper, we study the existence of solutions on the whole of R for a class of impulsive abstract differential equations. An application to partial differential equations is presented. (C) 2009 Elsevier Ltd. All rights reserved.

The existence of solutions for impulsive neutral functional differential equations

This work deals with the existence of mild solutions for a class of impulsive functional differential equations of the neutral type associated with the family of linear closed (not necessarily bounded) operators {A(t) : t is an element of 1}. (C) 2009 Elsevier Ltd. All rights reserved.

Existence of asymptotically almost automorphic solutions to some abstract partial neutral integro-differential equations

The paper establishes the existence and uniqueness of asymptotically almost automorphic mild solution to an abstract partial neutral integro-differential equation with unbounded delay. An example is given to illustrate our results. (C) 2008 Elsevier Ltd. All rights reserved.

Existence results for abstract impulsive second-order neutral functional differential equations

We establish the existence of mild solutions for a class of impulsive second-order partial neutral functional differential equations with infinite delay in a Banach space. (C) 2009 Published by Elsevier Ltd