Solving heterogeneous-agent models by projection and perturbation

The paper proposes a numerical solution method for general equilibrium models with a continuum of heterogeneous agents, which combines elements of projection and of perturbation methods. The basic idea is to solve first for the stationary solutionof the model, without aggregate shocks but with fully specified idiosyncratic shocks. Afterwards one computes a first-order perturbation of the solution in the aggregate shocks. This approach allows to include a high-dimensional representation of the cross-sectional distribution in the state vector. The method is applied to a model of household saving with uninsurable income risk and liquidity constraints. The model includes not only productivity shocks, but also shocks to redistributive taxation, which cause substantial short-run variation in the cross-sectional distribution of wealth. If those shocks are operative, it is shown that a solution method based on very few statistics of the distribution is not suitable, while the proposed method can solve the model with high accuracy, at least for the case of small aggregate shocks. Techniques are discussed to reduce the dimension of the state space such that higher order perturbations are feasible.Matlab programs to solve the model can be downloaded.

The domain derivative in rough-surface scattering and rigorous estimates for first-order perturbation theory

We investigate Fréchet differentiability of the scattered field with respect to variation in the boundary in the case of time–harmonic acoustic scattering by an unbounded, sound–soft, one–dimensional rough surface. We rigorously prove the differentiability of the scattered field and derive a characterization of the Fréchet derivative as the solution to a Dirichlet boundary value problem. As an application of these results we give rigorous error estimates for first–order perturbation theory, justifying small perturbation methods that have a long history in the engineering literature. As an application of our rigorous estimates we show that a plane acoustic wave incident on a sound–soft rough surface can produce an unbounded scattered field.

Approximate analytical solutions for porous catalysts with nonuniform activity

Using a novel finite integral transform technique, the problem of diffusion and chemical reaction in a porous catalyst with general activity profile is investigated theoretically. Analytical expressions for the effectiveness factor are obtained for pth order and Michaelis-Menten kinetics. Perturbation methods are employed to provide useful asymptotic solutions for large or small values of Thiele modulus and Biot number.

Influence of long-term wearing of unstable shoes on compensatory control of posture: An electromyography-based analysis

Purpose: This study investigated the influence of long-term wearing of unstable shoes (WUS) on compensatory postural adjustments (CPA) to an external perturbation. Methods: Participants were divided into two groups: one wore unstable shoes while the other wore conventional shoes for 8 weeks. The ground reaction force signal was used to calculate the anterior– posterior (AP) displacement of the centre of pressure (CoP) and the electromyographic signal of gastrocnemius medialis (GM), tibialis anterior (TA), rectus femoris (RF) and biceps femoris (BF) muscles was used to assess individual muscle activity, antagonist co-activation and reciprocal activation at the joint (TA/GM and RF/(BF + GM) pairs) and muscle group levels (ventral (TA + RF)/dorsal (GM + BF) pair) within time intervals typical for CPA. The electromyographic signal was also used to assess muscle latency. The variables described were evaluated before and after the 8-week period while wearing the unstable shoes and barefoot. Results: Long-term WUS led to: an increase of BF activity in both conditions (barefoot and wearing the unstable shoes); a decrease of GM activity; an increase of antagonist co-activation and a decrease of reciprocal activation level at the TA/GM and ventral/dorsal pairs in the unstable shoe condition. Additionally, WUS led to a decrease in CoP displacement. However, no differences were observed in muscle onset and offset. Conclusion: Results suggest that the prolonged use of unstable shoes leads to increased ankle and muscle groups’ antagonist co-activation levels and higher performance by the postural control system.

Systematic study of the static electrical properties of the CO molecule: influence of the basis set size and correlation energy

The influence of the basis set size and the correlation energy in the static electrical properties of the CO molecule is assessed. In particular, we have studied both the nuclear relaxation and the vibrational contributions to the static molecular electrical properties, the vibrational Stark effect (VSE) and the vibrational intensity effect (VIE). From a mathematical point of view, when a static and uniform electric field is applied to a molecule, the energy of this system can be expressed in terms of a double power series with respect to the bond length and to the field strength. From the power series expansion of the potential energy, field-dependent expressions for the equilibrium geometry, for the potential energy and for the force constant are obtained. The nuclear relaxation and vibrational contributions to the molecular electrical properties are analyzed in terms of the derivatives of the electronic molecular properties. In general, the results presented show that accurate inclusion of the correlation energy and large basis sets are needed to calculate the molecular electrical properties and their derivatives with respect to either nuclear displacements or/and field strength. With respect to experimental data, the calculated power series coefficients are overestimated by the SCF, CISD, and QCISD methods. On the contrary, perturbation methods (MP2 and MP4) tend to underestimate them. In average and using the 6-311 + G(3df) basis set and for the CO molecule, the nuclear relaxation and the vibrational contributions to the molecular electrical properties amount to 11.7%, 3.3%, and 69.7% of the purely electronic μ, α, and β values, respectively

Multiple scales analysis of nonlinear oscillations of a portal frame foundation for several machines

An analytical study of the nonlinear vibrations of a multiple machines portal frame foundation is presented. Two unbalanced rotating machines are considered, none of them resonant with the lower natural frequencies of the supporting structure. Their combined frequencies is set in such a way as to excite, due to nonlinear behavior of the frame, either the first anti-symmetrical mode (sway) or the first symmetrical mode. The physical and geometrical characteristics of the frame are chosen to tune the natural frequencies of these two modes into a 1:2 internal resonance. The problem is reduced to a two degrees of freedom model and its nonlinear equations of motions are derived via a Lagrangian approach. Asymptotic perturbation solutions of these equations are obtained via the Multiple Scales Method.

Quantum Monte Carlo study of electrostatic polarizabilities of H and He atoms /

The infinitesimal differential quantum Monte Carlo (QMC) technique is used to estimate electrostatic polarizabilities of the H and He atoms up to the sixth order in the electric field perturbation. All 542 different QMC estimators of the nonzero atomic polarizabilities are derived and used in order to decrease the statistical error and to obtain the maximum efficiency of the simulations. We are confident that the estimates are "exact" (free of systematic error): the two atoms are nodeless systems, hence no fixed-node error is introduced. Furthermore, we develope and use techniques which eliminate systematic error inherent when extrapolating our results to zero time-step and large stack-size. The QMC results are consistent with published accurate values obtained using perturbation methods. The precision is found to be related to the number of perturbations, varying from 2 to 4 significant digits.

Estimating Nonlinear DSGE Models by the Simulated Method of Moments

This paper studies the application of the simulated method of moments (SMM) for the estimation of nonlinear dynamic stochastic general equilibrium (DSGE) models. Monte Carlo analysis is employed to examine the small-sample properties of SMM in specifications with different curvature. Results show that SMM is computationally efficient and delivers accurate estimates, even when the simulated series are relatively short. However, asymptotic standard errors tend to overstate the actual variability of the estimates and, consequently, statistical inference is conservative. A simple strategy to incorporate priors in a method of moments context is proposed. An empirical application to the macroeconomic effects of rare events indicates that negatively skewed productivity shocks induce agents to accumulate additional capital and can endogenously generate asymmetric business cycles.

Speech Analysis using Modern Techniques of Nonlinear Dynamics

Medical fields requires fast, simple and noninvasive methods of diagnostic techniques. Several methods are available and possible because of the growth of technology that provides the necessary means of collecting and processing signals. The present thesis details the work done in the field of voice signals. New methods of analysis have been developed to understand the complexity of voice signals, such as nonlinear dynamics aiming at the exploration of voice signals dynamic nature. The purpose of this thesis is to characterize complexities of pathological voice from healthy signals and to differentiate stuttering signals from healthy signals. Efficiency of various acoustic as well as non linear time series methods are analysed. Three groups of samples are used, one from healthy individuals, subjects with vocal pathologies and stuttering subjects. Individual vowels/ and a continuous speech data for the utterance of the sentence "iruvarum changatimaranu" the meaning in English is "Both are good friends" from Malayalam language are recorded using a microphone . The recorded audio are converted to digital signals and are subjected to analysis.Acoustic perturbation methods like fundamental frequency (FO), jitter, shimmer, Zero Crossing Rate(ZCR) were carried out and non linear measures like maximum lyapunov exponent(Lamda max), correlation dimension (D2), Kolmogorov exponent(K2), and a new measure of entropy viz., Permutation entropy (PE) are evaluated for all three groups of the subjects. Permutation Entropy is a nonlinear complexity measure which can efficiently distinguish regular and complex nature of any signal and extract information about the change in dynamics of the process by indicating sudden change in its value. The results shows that nonlinear dynamical methods seem to be a suitable technique for voice signal analysis, due to the chaotic component of the human voice. Permutation entropy is well suited due to its sensitivity to uncertainties, since the pathologies are characterized by an increase in the signal complexity and unpredictability. Pathological groups have higher entropy values compared to the normal group. The stuttering signals have lower entropy values compared to the normal signals.PE is effective in charaterising the level of improvement after two weeks of speech therapy in the case of stuttering subjects. PE is also effective in characterizing the dynamical difference between healthy and pathological subjects. This suggests that PE can improve and complement the recent voice analysis methods available for clinicians. The work establishes the application of the simple, inexpensive and fast algorithm of PE for diagnosis in vocal disorders and stuttering subjects.

Systematic study of the static electrical properties of the CO molecule: influence of the basis set size and correlation energy

The influence of the basis set size and the correlation energy in the static electrical properties of the CO molecule is assessed. In particular, we have studied both the nuclear relaxation and the vibrational contributions to the static molecular electrical properties, the vibrational Stark effect (VSE) and the vibrational intensity effect (VIE). From a mathematical point of view, when a static and uniform electric field is applied to a molecule, the energy of this system can be expressed in terms of a double power series with respect to the bond length and to the field strength. From the power series expansion of the potential energy, field-dependent expressions for the equilibrium geometry, for the potential energy and for the force constant are obtained. The nuclear relaxation and vibrational contributions to the molecular electrical properties are analyzed in terms of the derivatives of the electronic molecular properties. In general, the results presented show that accurate inclusion of the correlation energy and large basis sets are needed to calculate the molecular electrical properties and their derivatives with respect to either nuclear displacements or/and field strength. With respect to experimental data, the calculated power series coefficients are overestimated by the SCF, CISD, and QCISD methods. On the contrary, perturbation methods (MP2 and MP4) tend to underestimate them. In average and using the 6-311 + G(3df) basis set and for the CO molecule, the nuclear relaxation and the vibrational contributions to the molecular electrical properties amount to 11.7%, 3.3%, and 69.7% of the purely electronic μ, α, and β values, respectively

Iniciação ao estudo da dinâmica de rotação de um satélite em variáves de Andoyer

The dynamics of the rotation of a satellite is an old and classical problem, specially in the Euler formalism. However, with these variables, even in torque free motion problem, the integrability of the system is far from trivial, mainly when the three moments of the inertia are not equal. Another disadvantage occurs when the inclinations between some plans are null or close to zero, so the nodes become undetermined. In this work, we propose the use of modern Andoyer's variables. These are a set of canonical variables and therefore some significant advantages can be obtained when dealing with perturbation methods. On other the hand, the integrability of the torque free motion becomes very clear, as the system is reduced to a problem of one degree of freedom. The elimination of the singularities mentioned above, can be solved very easily, with Pincaré-type variables. In this work we give the background concepts of the Andoyer's variables and the disturbing potential is obtained for the rotational dynamics of a satellite perturbed by a planet. In the case when A = B (moments of inertia) and due to the current variables, the averaged system is trivially obtained through very simple integrations

Mathematical Analysis of the Effect of Rotor Geometry on Cup Anemometer Response

The calibration coefficients of two commercial anemometers equipped with different rotors were studied. The rotor cups had the same conical shape, while the size and distance to the rotation axis varied.The analysis was based on the 2-cup positions analytical model, derived using perturbation methods to include second-order effects such as pressure distribution along the rotating cups and friction.Thecomparison with the experimental data indicates a nonuniformdistribution of aerodynamic forces on the rotating cups, with higher forces closer to the rotating axis. The 2-cup analytical model is proven to be accurate enough to study the effect of complex forces on cup anemometer performance.

DROMO formulation for planar motions: Solution to the Tsien Problem

The two-body problem subject to a constant radial thrust is analyzed as a planar motion. The description of the problem is performed in terms of three perturbation methods: DROMO and two others due to Deprit. All of them rely on Hansen?s ideal frame concept. An explicit, analytic, closed-form solution is obtained for this problem when the initial orbit is circular (Tsien problem), based on the DROMO special perturbation method, and expressed in terms of elliptic integral functions. The analytical solution to the Tsien problem is later used as a reference to test the numerical performance of various orbit propagation methods, including DROMO and Deprit methods, as well as Cowell and Kustaanheimo?Stiefel methods.

A new regularization method for fast and accurate propagation of roto-translationally coupled asteroids

There is a well-distinguished group of asteroids for which the roto-translational cou-pling is known to have a non-negligible e�ect in the long-term. The study of such asteroids suggests the use of specialized propagation techniques, where perturbation methods make their best. The techniques from which the special regularization method DROMO is derived, have now been extended to the attitude dynamics, with equally remarkable results in terms of speed and accuracy, thus making the combination of these algorithms specially. well-suited to deal with the propagation of bodies with strong attitude coupling.