What is what?: A simple time-domain test of long-memory vs. structural breaks

This paper proposes a new time-domain test of a process being I(d), 0 < d = 1, under the null, against the alternative of being I(0) with deterministic components subject to structural breaks at known or unknown dates, with the goal of disentangling the existing identification issue between long-memory and structural breaks. Denoting by AB(t) the different types of structural breaks in the deterministic components of a time series considered by Perron (1989), the test statistic proposed here is based on the t-ratio (or the infimum of a sequence of t-ratios) of the estimated coefficient on yt-1 in an OLS regression of ?dyt on a simple transformation of the above-mentioned deterministic components and yt-1, possibly augmented by a suitable number of lags of ?dyt to account for serial correlation in the error terms. The case where d = 1 coincides with the Perron (1989) or the Zivot and Andrews (1992) approaches if the break date is known or unknown, respectively. The statistic is labelled as the SB-FDF (Structural Break-Fractional Dickey- Fuller) test, since it is based on the same principles as the well-known Dickey-Fuller unit root test. Both its asymptotic behavior and finite sample properties are analyzed, and two empirical applications are provided.

A time-domain method for the analysis of thermal impedance response preserving the convolution form

The study of the thermal behavior of complex packages as multichip modules (MCM¿s) is usually carried out by measuring the so-called thermal impedance response, that is: the transient temperature after a power step. From the analysis of this signal, the thermal frequency response can be estimated, and consequently, compact thermal models may be extracted. We present a method to obtain an estimate of the time constant distribution underlying the observed transient. The method is based on an iterative deconvolution that produces an approximation to the time constant spectrum while preserving a convenient convolution form. This method is applied to the obtained thermal response of a microstructure as analyzed by finite element method as well as to the measured thermal response of a transistor array integrated circuit (IC) in a SMD package.

Heterogeneous discounting in consumption-investment problems. Time consistent solutions

[cat] En aquest treball s'analitza un model estocàstic en temps continu en el que l'agent decisor descompta les utilitats instantànies i la funció final amb taxes de preferència temporal constants però diferents. En aquest context es poden modelitzar problemes en els quals, quan el temps s'acosta al moment final, la valoració de la funció final incrementa en comparació amb les utilitats instantànies. Aquest tipus d'asimetria no es pot descriure ni amb un descompte estàndard ni amb un variable. Per tal d'obtenir solucions consistents temporalment es deriva l'equació de programació dinàmica estocàstica, les solucions de la qual són equilibris Markovians. Per a aquest tipus de preferències temporals, s'estudia el model clàssic de consum i inversió (Merton, 1971) per a les funcions d'utilitat del tipus CRRA i CARA, comparant els equilibris Markovians amb les solucions inconsistents temporalment. Finalment es discuteix la introducció del temps final aleatori.

Intensity correlation function of dye lasers: Short-time behavior

We propose an equation to calculate the intensity correlation function of a dye-laser model with a pump parameter subject to finite-bandwidth fluctuations. The equation is valid, in the weak-noise limit, for all times. It incorporates novel non-Markovian features. Results are given for the short-time behavior of the correlation function. It exhibits a characteristic initial plateau. Our findings are supported by a numerical simulation of the model.

Escape over a potential barrier driven by colored noise: Large but finite correlation times

The recent theory of Tsironis and Grigolini for the mean first-passage time from one metastable state to another of a bistable potential for long correlation times of the noise is extended to large but finite correlation times.

Accurate and efficient simulation of multiphase flow in a heterogeneous reservoir by using error estimate and control in the multiscale finite-volume framework

The multiscale finite-volume (MSFV) method is designed to reduce the computational cost of elliptic and parabolic problems with highly heterogeneous anisotropic coefficients. The reduction is achieved by splitting the original global problem into a set of local problems (with approximate local boundary conditions) coupled by a coarse global problem. It has been shown recently that the numerical errors in MSFV results can be reduced systematically with an iterative procedure that provides a conservative velocity field after any iteration step. The iterative MSFV (i-MSFV) method can be obtained with an improved (smoothed) multiscale solution to enhance the localization conditions, with a Krylov subspace method [e.g., the generalized-minimal-residual (GMRES) algorithm] preconditioned by the MSFV system, or with a combination of both. In a multiphase-flow system, a balance between accuracy and computational efficiency should be achieved by finding a minimum number of i-MSFV iterations (on pressure), which is necessary to achieve the desired accuracy in the saturation solution. In this work, we extend the i-MSFV method to sequential implicit simulation of time-dependent problems. To control the error of the coupled saturation/pressure system, we analyze the transport error caused by an approximate velocity field. We then propose an error-control strategy on the basis of the residual of the pressure equation. At the beginning of simulation, the pressure solution is iterated until a specified accuracy is achieved. To minimize the number of iterations in a multiphase-flow problem, the solution at the previous timestep is used to improve the localization assumption at the current timestep. Additional iterations are used only when the residual becomes larger than a specified threshold value. Numerical results show that only a few iterations on average are necessary to improve the MSFV results significantly, even for very challenging problems. Therefore, the proposed adaptive strategy yields efficient and accurate simulation of multiphase flow in heterogeneous porous media.

Continuous phase transition in a spin-glass model without time-reversal symmetry

We investigate the phase transition in a strongly disordered short-range three-spin interaction model characterized by the absence of time-reversal symmetry in the Hamiltonian. In the mean-field limit the model is well described by the Adam-Gibbs-DiMarzio scenario for the glass transition; however, in the short-range case this picture turns out to be modified. The model presents a finite temperature continuous phase transition characterized by a divergent spin-glass susceptibility and a negative specific-heat exponent. We expect the nature of the transition in this three-spin model to be the same as the transition in the Edwards-Anderson model in a magnetic field, with the advantage that the strong crossover effects present in the latter case are absent.

Heterogeneous discounting in consumption-investment problems. Time consistent solutions

[cat] En aquest treball s'analitza un model estocàstic en temps continu en el que l'agent decisor descompta les utilitats instantànies i la funció final amb taxes de preferència temporal constants però diferents. En aquest context es poden modelitzar problemes en els quals, quan el temps s'acosta al moment final, la valoració de la funció final incrementa en comparació amb les utilitats instantànies. Aquest tipus d'asimetria no es pot descriure ni amb un descompte estàndard ni amb un variable. Per tal d'obtenir solucions consistents temporalment es deriva l'equació de programació dinàmica estocàstica, les solucions de la qual són equilibris Markovians. Per a aquest tipus de preferències temporals, s'estudia el model clàssic de consum i inversió (Merton, 1971) per a les funcions d'utilitat del tipus CRRA i CARA, comparant els equilibris Markovians amb les solucions inconsistents temporalment. Finalment es discuteix la introducció del temps final aleatori.

Nonlinear Finite Element Study of Piles in Integral Abutment Bridges, HR-227, Part 2, 1982

The highway departments of the states which use integral abutments in bridge design were contacted in order to study the extent of integral abutment use in skewed bridges and to survey the different guidelines used for analysis and design of integral abutments in skewed bridges. The variation in design assumptions and pile orientations among the various states in their approach to the use of integral abutments on skewed bridges is discussed. The problems associated with the treatment of the approach slab, backfill, and pile cap, and the reason for using different pile orientations are summarized in the report. An algorithm based on a state-of-the-art nonlinear finite element procedure previously developed by the authors was modified and used to study the influence of different factors on behavior of piles in integral abutment bridges. An idealized integral abutment was introduced by assuming that the pile is rigidly cast into the pile cap and that the approach slab offers no resistance to lateral thermal expansion. Passive soil and shear resistance of the cap are neglected in design. A 40-foot H pile (HP 10 X 42) in six typical Iowa soils was analyzed for fully restrained pile head and pinned pile head. According to numerical results, the maximum safe length for fully restrained pile head is one-half the maximum safe length for pinned pile head. If the pile head is partially restrained, the maximum safe length will lie between the two limits. The numerical results from an investigation of the effect of predrilled oversized holes indicate that if the length of the predrilled oversized hole is at least 4 feet below the ground, the vertical load-carrying capacity of the H pile is only reduced by 10 percent for 4 inches of lateral displacement in very stiff clay. With no predrilled oversized hole, the pile failed before the 4-inch lateral displacement was reached. Thus, the maximum safe lengths for integral abutment bridges may be increased by predrilling. Four different typical Iowa layered soils were selected and used in this investigation. In certain situations, compacted soil (> 50 blow count in standard penetration tests) is used as fill on top of natural soil. The numerical results showed that the critical conditions will depend on the length of the compacted soil. If the length of the compacted soil exceeds 4 feet, the failure mechanism for the pile is similar to one in a layer of very stiff clay. That is, the vertical load-carrying capacity of the H pile will be greatly reduced as the specified lateral displacement increases.

Reconstruction of the join time-delay Doppler-scale reflectivity density in the wide-band regime. A frame theory based approach

The inverse scattering problem concerning the determination of the joint time-delayDoppler-scale reflectivity density characterizing continuous target environments is addressed by recourse to the generalized frame theory. A reconstruction formula,involving the echoes of a frame of outgoing signals and its corresponding reciprocalframe, is developed. A ‘‘realistic’’ situation with respect to the transmission ofa finite number of signals is further considered. In such a case, our reconstruction formula is shown to yield the orthogonal projection of the reflectivity density onto a subspace generated by the transmitted signals.

Analysis of a finite volume method for a cross-diffusion model in population dynamics

The main goal of this paper is to propose a convergent finite volume method for a reactionâeuro"diffusion system with cross-diffusion. First, we sketch an existence proof for a class of cross-diffusion systems. Then the standard two-point finite volume fluxes are used in combination with a nonlinear positivity-preserving approximation of the cross-diffusion coefficients. Existence and uniqueness of the approximate solution are addressed, and it is also shown that the scheme converges to the corresponding weak solution for the studied model. Furthermore, we provide a stability analysis to study pattern-formation phenomena, and we perform two-dimensional numerical examples which exhibit formation of nonuniform spatial patterns. From the simulations it is also found that experimental rates of convergence are slightly below second order. The convergence proof uses two ingredients of interest for various applications, namely the discrete Sobolev embedding inequalities with general boundary conditions and a space-time $L^1$ compactness argument that mimics the compactness lemma due to Kruzhkov. The proofs of these results are given in the Appendix.

Real-Time Simulation of Mobile and Industrial Machines Using the Multibody Simulation Approach

This thesis introduces a real-time simulation environment based on the multibody simulation approach. The environment consists of components that are used in conventional product development, including computer aided drawing, visualization, dynamic simulation and finite element software architecture, data transfer and haptics. These components are combined to perform as a coupled system on one platform. The environment is used to simulate mobile and industrial machines at different stages of a product life time. Consequently, the demands of the simulated scenarios vary. In this thesis, a real-time simulation environment based on the multibody approach is used to study a reel mechanism of a paper machine and a gantry crane. These case systems are used to demonstrate the usability of the real-time simulation environment for fault detection purposes and in the context of a training simulator. In order to describe the dynamical performance of a mobile or industrial machine, the nonlinear equations of motion must be defined. In this thesis, the dynamical behaviour of machines is modelled using the multibody simulation approach. A multibody system may consist of rigid and flexible bodies which are joined using kinematic joint constraints while force components are used to describe the actuators. The strength of multibody dynamics relies upon its ability to describe nonlinearities arising from wearing of the components, friction, large rotations or contact forces in a systematic manner. For this reason, the interfaces between subsystems such as mechanics, hydraulics and control systems of the mechatronic machine can be defined and analyzed in a straightforward manner.

Be-Fe coupled method for the analysis of 3D elastodynamic problems in the time domain

By coupling the Boundary Element Method (BEM) and the Finite Element Method (FEM) an algorithm that combines the advantages of both numerical processes is developed. The main aim of the work concerns the time domain analysis of general three-dimensional wave propagation problems in elastic media. In addition, mathematical and numerical aspects of the related BE-, FE- and BE/FE-formulations are discussed. The coupling algorithm allows investigations of elastodynamic problems with a BE- and a FE-subdomain. In order to observe the performance of the coupling algorithm two problems are solved and their results compared to other numerical solutions.

Real-time simulation of multibody systems with applications for working mobile vehicles

This dissertation describes an approach for developing a real-time simulation for working mobile vehicles based on multibody modeling. The use of multibody modeling allows comprehensive description of the constrained motion of the mechanical systems involved and permits real-time solving of the equations of motion. By carefully selecting the multibody formulation method to be used, it is possible to increase the accuracy of the multibody model while at the same time solving equations of motion in real-time. In this study, a multibody procedure based on semi-recursive and augmented Lagrangian methods for real-time dynamic simulation application is studied in detail. In the semirecursive approach, a velocity transformation matrix is introduced to describe the dependent coordinates into relative (joint) coordinates, which reduces the size of the generalized coordinates. The augmented Lagrangian method is based on usage of global coordinates and, in that method, constraints are accounted using an iterative process. A multibody system can be modelled as either rigid or flexible bodies. When using flexible bodies, the system can be described using a floating frame of reference formulation. In this method, the deformation mode needed can be obtained from the finite element model. As the finite element model typically involves large number of degrees of freedom, reduced number of deformation modes can be obtained by employing model order reduction method such as Guyan reduction, Craig-Bampton method and Krylov subspace as shown in this study The constrained motion of the working mobile vehicles is actuated by the force from the hydraulic actuator. In this study, the hydraulic system is modeled using lumped fluid theory, in which the hydraulic circuit is divided into volumes. In this approach, the pressure wave propagation in the hoses and pipes is neglected. The contact modeling is divided into two stages: contact detection and contact response. Contact detection determines when and where the contact occurs, and contact response provides the force acting at the collision point. The friction between tire and ground is modelled using the LuGre friction model, which describes the frictional force between two surfaces. Typically, the equations of motion are solved in the full matrices format, where the sparsity of the matrices is not considered. Increasing the number of bodies and constraint equations leads to the system matrices becoming large and sparse in structure. To increase the computational efficiency, a technique for solution of sparse matrices is proposed in this dissertation and its implementation demonstrated. To assess the computing efficiency, augmented Lagrangian and semi-recursive methods are implemented employing a sparse matrix technique. From the numerical example, the results show that the proposed approach is applicable and produced appropriate results within the real-time period.

Markovian Processes, Two-Sided Autoregressions and Finite-Sample Inference for Stationary and Nonstationary Autoregressive Processes.

In this paper, we develop finite-sample inference procedures for stationary and nonstationary autoregressive (AR) models. The method is based on special properties of Markov processes and a split-sample technique. The results on Markovian processes (intercalary independence and truncation) only require the existence of conditional densities. They are proved for possibly nonstationary and/or non-Gaussian multivariate Markov processes. In the context of a linear regression model with AR(1) errors, we show how these results can be used to simplify the distributional properties of the model by conditioning a subset of the data on the remaining observations. This transformation leads to a new model which has the form of a two-sided autoregression to which standard classical linear regression inference techniques can be applied. We show how to derive tests and confidence sets for the mean and/or autoregressive parameters of the model. We also develop a test on the order of an autoregression. We show that a combination of subsample-based inferences can improve the performance of the procedure. An application to U.S. domestic investment data illustrates the method.