Role Of Initial Conditions Research Articles

Recovery and Growth in Transition: A Decade of Evidence

This paper reviews a range of studies that examine differences in growth performance among transition countries. There is a consensus in the literature about the core elements of transition and the policies necessary for sustainable growth, although considerable differences remain about how to implement these policies and about their proper sequencing. The empirical work identifies stabilization and structural reforms (e.g., market liberalization, private ownership) as important determinants of growth, but underlines the role of initial conditions and institutions.There is divergent evidence, however, on the importance of specific reforms. Traditional factor inputs have as yet no role in explaining growth. Copyright 2002, International Monetary Fund

Entropy and time

The emergence of a direction of time in statistical mechanics from an underlying time-reversal-invariant dynamics is explained by examining a simple model. The manner in which time-reversal symmetry is preserved and the role of initial conditions are emphasized. An extension of the model to finite temperatures also is discussed.

Transitions in a non-linear second-order system

We investigate the solutions of a second-order system of differential equations corresponding to a pair of coupled non-linear oscillators dependent on a slowly varying parameter. Turning points arise as the parameter evolves through a critical value causing these solutions to exhibit a change in behaviour. We analyse this change by employing asymptotic methods to show that the resulting bifurcation is a type of pitchfork bifurcation. The role of initial conditions in predicting the outcome of the bifurcation is analysed and numerical results are presented.

Delayed bifurcations and negative hysteresis in semiconductor lasers: the role of initial conditions

The dynamical intensity response of a semiconductor laser under the influence of injection current modulation, and the resulting hysteresis behavior, is investigated experimentally and theoretically. We report the first experimental observation, in a semiconductor laser, of the transition from a negative to a positive hysteresis as the modulation frequency of the injection current is varied. The theoretical work isolates the initial conditions on the intrinsic laser parameters as the sole determinant in influencing the kind of hysteresis one observes.

The relationship between prior performance and diversification: a study of three industries

The extensive research undertaken in studying the relationship between diversification and performance has been largely inconclusive. There have been a number of reasons for mixed results including heterogeneity of samples, pooling of data, and cross‐sectional analyses. One possible way to address these problems is to make comparisons based on homogeneity of samples, or some other well‐defined structural variable, and to study firms longitudinally. More than just the statistical analysis, this paper identifies the key role of critical antecedent conditions that affect outcomes from diversification strategies. A sample of 59 firms from three distinctly different industries (food, electronics, and petroleum) are used in this empirical study. Results indicate that statistically significant differences exist when industry homogeneity is maintained and critical antecedent variables are isolated. More importantly, the role of initial conditions and historical performance levels have an important bearing on diversification efforts and subsequent performance.

Stepping over obstacles during locomotion: insights from multiobjective optimization on set of input parameters.

In this study we investigate possible objectives that the central nervous system (CNS) may consider in planning a strategy for stepping over an obstacle. A link segment simulation model has been developed based on Lagrangian dynamics, with which muscle force inputs can be optimized to best satisfy the postulated objectives for landing stability, obstacle clearance, and efficiency of the movement. A direct optimization approach with multiobjective criteria based on the kinematic and kinetic characteristics of the swing phase of locomotion is used in the simulation. The role of initial conditions at toe-off and biarticular muscle forces during the swing phase was also investigated. The optimization was performed for both leading limb and the trailing limb during the swing phase. The simulation results demonstrate that the use of biarticular muscles is sufficient to clear a range of obstacles with the trailing limb (obstacle encountered during early swing). Stride length or landing stability objectives need not be specified suggesting a simpler control of trailing limb trajectory by the CNS (one of stride length or landing stability objectives were not necessary). In contrast while the use of biarticular muscles can be sufficient to clear obstacles with the leading limb (obstacle encountered during mid to late swing), a stable landing and smooth toe and knee trajectories are compromised without suitable initial conditions at toe-off. The results suggest that the set of postulated objectives for the lead limb is adequate, although not complete.

Introducing competition to the electricity industry in Spain: the role of initial conditions

The government of Spain has initiated a process of liberalizing the electricity market beginning in 1998. The Spanish system will be transformed from one based on a Central Purchasing Agent model to one based on retail competition. This transition raises many difficult structural questions. These include stranded cost compensation and the feasibility of genuine competition. The paper describes how these arise in Spain, with particular emphasis on the constraints associated with the prior commitments made by the government to pursue various political objectives through the electricity industry.

Precision Performances of Terminal Conditions for Short Time HorizonsForward-Looking Systems

In this paper we investigate theoretically the numerical bias due to the truncation of structurally infinite time forward-looking models, by the means of various terminal conditions. On a general multivariate optimal growth model, we first analytically confirm some well-known heuristic properties for certain extreme spectral cases. However, we show that the heuristic findings stated in the literature, relying on intermediate spectral configurations, lack theoretical basis as that they omit, among other relevant features, the crucial role of initial conditions: in this case, comparison criteria exclusively based on spectral considerations lack theoretical sense. Numerical evidence is proposed to illustrate this point and other related empirical findings are presented.

A PLATE BACKED BY A CAVITY: THE FEATURES OF DYNAMIC INSTABILITY

The response (both chaotic and non-chaotic) of a fluttering plate with a cavity behind it in a highly supersonic flow is considered. Evaluations of the dependencies among characteristics non-dimensional parameters have been obtained by numerical time integration. Among the main features of this system are the role of initial conditions and frames of Hopf bifurcations which are transformed with the length-to-depth ratio. Results for the basic one-plate system are compared with those for the analogous two-plate system, the system without a cavity, and the plate under random excitation.

Role of initial conditions in the classification of the rule space of cellular automata dynamics.

In the qualitative classification of cellular automata (CA) rules by Wolfram [Rev. Mod. Phys. 55, 601 (1983)], there exists a class of CA rules (called class 4) which exhibit complex pattern formation and long-lived dynamical activity (long transients). These properties of class 4 CA's has led to the conjecture that class 4 rules are universal Turing machines, i.e., they are bases for computational universality. We describe the embedding of a ``small'' universal turing machine, due to Minski [Computation: Finite and Infinite Machines (Prentice-Hall, Englewood Cliffs, NJ 1967)], into a cellular automaton rule table. This produces a collection of (k=18, r=1) cellular automata, all of which are computationally universal. However, we observe that these rules are distributed among the various Wolfram classes. More precisely, we show that the identification of the Wolfram class depends crucially on the set of initial conditions used to simulate the given CA. This work, among others, indicates that a description of complex systems and information dynamics may need a new framework for nonequilibrium statistical mechanics.

Three-dimensional structure of straight and curved plane wakes

The formation and evolution of the three-dimensional structure of straight and mildly curved ($b/\bar{R} < 2\%$) flat plate wakes at relatively high Reynolds numbers (Reb = 28 000) have been studied through detailed measurements of the mean and fluctuating velocities. In both cases, the role of initial conditions was examined by generating wakes from untripped (laminar) and tripped (turbulent) initial boundary layers. The curved wake was affected by the angular momentum instability such that the inside half of the wake was unstable, whereas the outside half was stable. In both the straight and curved untripped wakes, large spanwise variations, in the form of ‘pinches’ and ‘crests’, were observed in the contours of mean velocity and Reynolds stresses. Well-organized, ‘spatially stationary’ streamwise vorticity was generated in the near-field region in the form of quadrupoles, to which the spanwise variations in the velocity contours were attributed. The presence of mean streamwise vorticity had a significant effect on the wake growth and defect decay rates, mainly by providing additional entrainment. In the straight wake, the mean streamwise vorticity decayed on both sides of the wake such that it had decayed completely by the far-field region. However, in the curved case, the mean streamwise vorticity on the unstable side decayed at a rate significantly lower than that on the stable side. Despite the decay of mean streamwise vorticity, the spanwise variations persisted into the far wake in both cases. The effects of curvature were also apparent in the Reynolds stress results which showed that the levels on the unstable side were increased significantly compared to those on the stable side, with the effect much stronger in the initially laminar wake. With the initial boundary layers tripped, spatially stationary streamwise vortex structures were not observed in either the straight or curved wakes and the velocity contours appeared nominally two-dimensional. This result further confirms the strong dependency of the three-dimensional structure of plane wakes on initial conditions.

Influence of swelling on reaction efficiency in intercalated clay minerals

A lattice model is designed to determine the extent which the efficiency of reaction between a fixed target molecule and a diffusing coreactant is affected when the interlamellar space separating the atomic layers defining a smectite-type clay is expanded (or swollen). The authors consider partially ordered layer lattices of hexagonal symmetry, and for the case where the target molecule is positioned in the basal lattice at the centrosymmetric site exact numerical solution of the underlying stochastic problem shows that in the limit of large planar arrays the reaction efficiency (as calibrated by the mean walklength (n) of the diffusing coreactant) decreases by a factor of approx. 1.7 for a (stacked) two-layer hexagonal structure and by approx. 2.4 for a three-layer structure. The role of initial conditions and system size is explored, and the exponential character of the decay is quantified.

The role of initial conditions in flow stability with an application to modons

Lyapunov stability arguments may be used to show that an otherwise unstable flow can be stabilized by restriction of the class of possible perturbations. It is shown that, in general, such a restriction applied only to the initial perturbation does not imply stability for dynamics on the entire phase space nor does it necessarily imply a delay of the onset of instability. As a result, proofs of linear stability based on a restriction of the initial perturbation actually are not valid. In particular, certain criteria for the stability of modons given by Pierini [Dyn. Atmos. Oceans 9, 273 (1985)] and Swaters [Phys. Fluids 29, 1419 (1986)] and synthesized by Flierl [Annu. Rev. Fluid Mech. 19, 493 (1987)] do not, in fact, ensure stability. A model is used to demonstrate that these stability criteria do not preclude instantaneous onset of linear instability. The model also demonstrates that, although conservation of energy and enstrophy implies that the transfer of energy in an instability must be to scales both larger and smaller than the modon scale, the principal direction of transfer remains undetermined.

The role of initial conditions in elementary gas-phase processes involving intermediate "complexes"

The role of initial conditions in elementary gas-phase processes involving intermediate "complexes"

Characteristics of velocity overshoot in GaAs under uniform-field conditions

The origins of velocity overshoot in homogeneous bulk GaAs under stepped forcing conditions on the electric field are analyzed by phase-portrait methods. The balance equations for particle energy and momentum taken from the uniform-field version of the semiempirical transport equation model are used to define the direction field for charge flow in an energy-velocity phase space. Certain general characteristics of the flow patterns in the nonstationary regime are examined, with emphasis on the classification of possible intrinsic behavior exhibited by the steady states for different applied fields, on the approach to the steady state, and on the role of initial conditions. It is shown that flows describable by such a model have two types of stable generalized dynamical behavior: damped oscillatory behavior under applied fields for which the steady-state energy lies near the intervalley separation energy, and damped aperiodic behavior outside this range of fields. The analysis is illustrated with results deduced from realistic input data on energy and momentum relaxation rates taken from published steady-state Monte Carlo calculations for GaAs at three representative impurity densities.

The Effect of Inertia in Lubrication Flow Including Entrance and Initial Conditions

This study is concerned with the influence of fluid inertia in thin film steady or transient laminar flows, emphasizing the role of initial conditions and inlet boundary conditions. Most existing studies implicitly omit these effects due to the method of formulation or the type of problem studied. In the present study, linearization for the convective inertia terms is used to transform the problem to a coordinate system which results in a simple diffusion equation. Closed-form solutions are obtained, considering initial or entrance conditions in the classical manner. Predictions are tested against cases for which solutions exist in the literature and against a numerical solution and excellent agreement is found. For simple squeeze films, large discrepancies from lubrication theory are found at short times following the start-up, or at moderate Reynolds numbers. In the steady flow case, fluid is assumed to enter the bearing with a slug flow profile. The inlet pressure is determined by coupling the bearing flow with the upstream inviscid flow. Large discrepancies from lubrication theory are found at Reynolds numbers where the lubrication theory was previously thought to be satisfactory. The load may increase or decrease, depending on the upstream conditions.

Role of initial conditions in the mean-field theory of spin-glass dynamics

We discuss the dynamics of the infinite-range Sherrington-Kirkpatrick spin-glass model for which relaxation times diverge when $N$, the number of spins, tends to infinity. Calculations on a large but finite system are very difficult, so we mimic a large finite system in equilibrium by working with $N=\ensuremath{\infty}$ and imposing, by hand, a canonical distribution at an initial time. For short times, where no barrier hopping has occurred, we find that the Edwards-Anderson order parameter, ${q}_{\mathrm{EA}}$, is identical to that obtained from an analysis of the mean-field equations of Thouless, Anderson, and Palmer and, with further assumptions, gives $q(x=1)$ in Parisi's theory, in agreement with earlier work. For times longer than the longest relaxation time (of the finite system), true equilibrium is reached and our theory agrees with previous statistical-mechanics calculations using the replica trick. There is no violation of the fluctuation-dissipation theorem.

Resonant Coherent Energy Transfer. Role of Initial Conditions

AbstractThe dependence of dynamics of coherent resonant energy transfer of electronic excitation between impurity ions in condensed media on the initial conditions of the donor excitation is investigated. Their crucial role in the coherence of the energy transfer process is shown. Validity criteria of different limiting cases of the energy resonant transfer are specified taking into account initial conditions of excitation. The “excitation trapping” effect at the coherent energy transfer is also shown to be present.

Role of initial conditions in spin glass dynamics and significance of Parisi's q(x)

The authors argue that standard treatments of dynamics are incorrect for non-ergodic systems such as the Sherrington-Kirkpatrick model of a spin glass. Since the system never loses the memory of its initial state it is necessary to average over initial states with a Boltzmann weight to obtain time-dependent correlation functions as conventionally defined. It is now necessary to introduce replicas. The 'dynamical' order parameter, qEA, is equal to q(x=1) in Parisi's scheme whereas the statistical mechanics order parameter, q, is given by integral 0Iq(x) dx. They also propose an interpretation of the function q(x).