Terms Of Initial Conditions Research Articles

Naturalness in cosmological initial conditions

We propose a novel approach to the problem of constraining cosmological initial conditions. Within the framework of effective field theory, we classify initial conditions in terms of boundary terms added to the effective action describing the cosmological evolution below Planckian energies. These boundary terms can be thought of as spacelike branes which may support extra instantaneous degrees of freedom and extra operators. Interactions and renormalization of these boundary terms allow us to apply to the boundary terms the field-theoretical requirement of naturalness, i.e. stability under radiative corrections. We apply this requirement to slow-roll inflation with non-adiabatic initial conditions, and to cyclic cosmology. This allows us to define in a precise sense when some of these models are fine-tuned. We also describe how to parametrize in a model-independent way non-Gaussian initial conditions; we show that in some cases they are both potentially observable and pass our naturalness requirement.

Efficient Procedure to Compute the Microcanonical Volume of Initial Conditions that Lead to Escape Trajectories from a Multidimensional Potential Well

A procedure is presented for computing the phase space volume of initial conditions for trajectories that escape or "react" from a multidimensional potential well. The procedure combines a phase space transition state theory, which allows one to construct dividing surfaces that are free of local recrossing and that minimize the directional flux, and a classical spectral theorem. The procedure gives the volume of reactive initial conditions in terms of a sum over each entrance channel of the well of the product of the phase space flux across the dividing surface associated with the channel and the mean residence time in the well of trajectories which enter through the channel. This approach is illustrated for HCN isomerization in three dimensions, for which the method is several orders of magnitude more efficient than standard Monte Carlo sampling.

Trade liberalization and the skill premium in developing economies

Empirical evidence shows that while the skill premium narrowed in some developing countries following trade liberalization, it widened in others, or even exhibited non-monotonic behavior. This paper studies a simple dynamic general equilibrium trade model in which differences in initial conditions across developing countries play a key role in explaining the variety of skill premium behaviors. Differences in initial conditions in terms of skilled labor and physical capital emerge in the model due to differences in trade policies. The model can generate non-monotonic behavior for the skill premium following trade liberalization.

Variable sensitivity of plant communities in Iceland to experimental warming

AbstractFacing an increased threat of rapid climate change in cold‐climate regions, it is important to understand the sensitivity of plant communities both in terms of degree and direction of community change. We studied responses to 3–5 years of moderate experimental warming by open‐top chambers in two widespread but contrasting tundra communities in Iceland. In a species‐poor and nutrient‐deficient moss heath, dominated by Racomitrium lanuginosum, mean daily air temperatures at surface were 1–2°C higher in the warmed plots than the controls whereas soil temperatures tended to be lower in the warmed plots throughout the season. In a species‐rich dwarf shrub heath on relatively rich soils at a cooler site, dominated by Betula nana and R. lanuginosum, temperature changes were in the same direction although more moderate. In the moss heath, there were no detectable community changes while significant changes were detected in the dwarf shrub heath: the abundance of deciduous and evergreen dwarf shrubs significantly increased (>50%), bryophytes decreased (18%) and canopy height increased (100%). Contrary to some other studies of tundra communities, we detected no changes in species richness or other diversity measures in either community and the abundance of lichens did not change. It is concluded that the sensitivity of Icelandic tundra communities to climate warming varies greatly depending on initial conditions in terms of species diversity, dominant species, soil and climatic conditions as well as land‐use history.

Estimates on the growth of meromorphic solutions of linear differential equations

We give a pointwise estimate of meromorphic solutions of linear differential equations with coefficients meromorphic in a finite disk or in the open plane. Our results improve some earlier estimates of Bank and Laine. In particular we show that the growth of meromorphic solutions with ()>0 can be estimated in terms of initial conditions of the solution at or near the origin and the characteristic functions of the coefficients. Examples show that the estimates are sharp in a certain sense. Our results give an affirmative answer to a question of Milne Anderson.

Response of a Native Perennial Grass Stand to Disturbance in California's Coast Range Grassland

Abstract To assess the potential for enhancing an existing stand of native perennial grasses on a California Coast Range Grassland site, we experimentally manipulated the seasonal timing and presence of grazing for 3 years (1994 through 1996) and of autumn burning for 2 years (1994 and 1995) and measured species cover for 6 years (1993 through 1998). We subjected the species matrix to classification (TWINSPAN) and ordination (CCA) and tested the ordination site scores as well as diversity indices with linear mixed effects models. Four distinct plant community groups emerged from the classification. Two of these were dominated by annual grasses and two by perennial grasses. No treatment effects were observed on diversity. For composition, temporal and spatial random effects were important mixed effects model parameters, as was the fixed effect covariate, pre‐treatment CCA site score, indicating the importance of random environmental variation and initial starting conditions. Incorporation of these random effects and initial condition terms made for more powerful tests of the fixed effects, grazing season, and burning. We found no significant burning effects. Grazing removal imparted a shift in plant community from more annual‐dominated toward more perennial‐dominated vegetation. Individual perennial grass species responded differently according to genus and species. Nassella spp. increased gradually over time regardless of grazing treatment. Nassella pulchra (purple needlegrass) increase was greatest under spring grazing and N. lepida (foothill needlegrass) was greatest with grazing removal. Danthonia californica (California oatgrass) had little response over time under seasonal grazing treatments, but increased with grazing removal. Under relatively mesic weather conditions it appears that grazing removal from Coast Range Grasslands with existing native perennial grass populations can increase their cover. However if N. pulchra is the sole existing population, spring season‐restricted grazing should be equally effective at enhancing cover of the native grass species.

Energetic coefficient of restitution for planar impact in multi-rigid-body systems with friction

For two-body collisions, it has been recognized that the coefficient of restitution is not a material property but is affected by initial relative velocity at the contact point as well as orientation of the colliding bodies. This paper obtains expressions for the energetic coefficient of restitution in terms of initial conditions based on the methods of analytical mechanics for impacts of multi-rigid-body systems. We provide two examples. The first example is for two-body collision with friction to validate the rationality of the expressions given by this paper. The example used by Stronge (Mech. Struct. Mach. 29(2) (2001) 239) is served as the second example for comparison with Stronge (2001).

Laboratory evaluation of a hydrodynamic inverse modeling method based on water content data

The inverse modeling method of Lambot et al. [2002] for estimating the hydraulic properties of partially saturated soils, which was numerically validated, is further tested on laboratory‐scale transient flow experiments. The method uses the global multilevel coordinate search algorithm combined sequentially with the local Nelder‐Mead simplex algorithm to obtain the inverse of the one‐dimensional Richards equation using soil moisture time series measured at three different depths during natural infiltration. Flow experiments were conducted on a homogeneous artificial sand column and three undisturbed soil columns collected from agricultural fields. Three models describing the unsaturated soil hydraulic properties were used and compared: the model of Mualem and van Genuchten, the model of Assouline, and the decoupled van Genuchten–Brooks and Corey combination. The performances of all three models were similar, except for Assouline's model, which provided poorer results in two cases. The inversion method provided relatively good estimates for the water retention curves and also for the saturated conductivity when the moisture range explored was not too small. Water content time series were very well reproduced for the artificial soil and a sandy loam soil, but for two silt loam soils, larger errors were observed. The prediction of the water transfer behavior in the soil columns was poor when flow properties were estimated using directly determined hydraulic properties. The main limiting factor for applying the inversion method, particularly for nonsandy soils, was the characterization of the initial conditions in terms of the pressure head profile. Furthermore, the use of only soil moisture data is essential to enable the hydrogeophysical characterization of soils.

Local and Nonlocal Impacts of Soil Moisture Initialization on AGCM Seasonal Forecasts: A Model Sensitivity Study

Using a version of the Australian Bureau of Meteorology Research Centre (BMRC) atmospheric general circulation model, this study investigates the model’s sensitivity to different soil moisture initial conditions in its dynamically extended seasonal forecasts of June‐August 1998 climate anomalies, with focus on the south and northeast China regions where severe floods occurred. The authors’ primary aim is to understand the model’s responses to different soil moisture initial conditions in terms of the physical and dynamical processes involved. Due to a lack of observed global soil moisture data, the efficacy of using soil moisture anomalies derived from the NCEP‐NCAR reanalysis is assessed. Results show that by imposing soil moisture percentile anomalies derived from the reanalysis data into the BMRC model initial condition, the regional features of the model’s simulation of seasonal precipitation and temperature anomalies are modulated. Further analyses reveal that the impacts of soil moisture conditions on the model’s surface temperature forecasts are mainly from localized interactions between land surface and the overlying atmosphere. In contrast, the model’s sensitivity in its forecasts of rainfall anomalies is mainly due to the nonlocal impacts of the soil moisture conditions. Over the monsoondominated east Asian region, the contribution from local water recycling, through surface evaporation, to the model simulation of precipitation is limited. Rather, it is the horizontal moisture transport by the regional atmospheric circulation that is the dominant factor in controlling the model rainfall. The influence of different soil moisture conditions on the model forecasts of rainfall anomalies is the result of the response of regional circulation to the anomalous soil moisture condition imposed. Results from the BMRC model sensitivity study support similar findings from other model studies that have appeared in recent years and emphasize the importance of improving the land surface data assimilation and soil hydrological processes in dynamically extended GCM seasonal forecasts.

A new approach to initial value variables for the Lemaître–Tolman–Bondi dust solutions

We re-examine the Lemaître–Tolman–Bondi (LTB) dust solutions by considering as free parameters the initial value functions: Yi, ρi, (3)ℛi, obtained by restricting the curvature radius, Y ≡ , the rest mass density, ρ, and the three-dimensional Ricci scalar of the rest frames, (3)ℛ, to an arbitrary regular Cauchy hypersurface, \U0001d4afi, marked by constant cosmic time (t = ti). Assuming the existence of symmetry centres, we use Yi to fix the radial coordinate and the topology (homeomorphic class) of \U0001d4afi, while the time evolution is described in terms of an adimensional scale factor y = Y/Yi. We show that the dynamics, regularity conditions and geometric features of the models are determined by ρi, (3)ℛi and by suitably constructed volume averages and contrast functions expressible in terms of invariant scalars defined in \U0001d4afi. These quantities lead to a straightforward characterization of initial conditions in terms of the nature of the inhomogeneity of \U0001d4afi, as density and/or curvature overdensities (‘lumps’) and underdensities (‘voids’) around a symmetry centre. In general, only models with initial density and curvature lumps evolve without shell-crossing singularities, though special classes of initial conditions, associated with a simultaneous big bang, allow for a regular evolution for initial density and curvature voids. Specific restrictions are found so that a regular evolution for t ≥ ti is possible for initial voids. A brief guideline is provided for using the new variables in the construction of LTB models and for plotting all relevant quantities.

Exactly Solvable Initial Conditions in Terms of the Hypergeometric Functions for a Member of the AKNS Hierarchy

Generic forms of the initial conditions for a soliton equation in the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy which can be solved in terms of the hypergeometric function are presented. A detailed study on these conditions shows that the initial wave packets are generally consisted of only one pulse, and not symmetric around their peaks. The scattering problems associated with the initial conditions are also studied. The presented initial conditions yield a set of complete scattering data and expressions of soliton solutions explicitly.

Emergence and growth of high-tech activity in Cambridge and Grenoble

This paper compares the genesis and growth of two well-known European high-technology centres, Cambridge in the UK and Grenoble in France. This paper attempts to explain why, despite strong differences in terms of initial conditions, Cambridge and Grenoble present similarities, sometimes striking, related to the creation of their respective science parks and to the growth of high-tech activities in the wider area. In the early 1970s Cambridge was a typical British university town while Grenoble had a strong industrial past and a tradition of relationships between university and industry. Despite these differences, high-tech activities emerged at the same time in both places as a unique local dynamic milieu. The paper shows the similarities and differences in the paths of development followed in both centres. Current constraints on growth are described and new dynamics of growth are outlined.

Exact inhomogeneous cosmologies whose source is a radiation-matter mixture with consistent thermodynamics

We derive a new class of exact solutions of Einstein's equations providing a physically plausible hydrodynamical description of cosmological matter in the radiative era ($10^6 K > T > 10^3 K$), between nucleosynthesis and decoupling. The solutions are characterized by the Lema\^itre-Tolman -Bondi metric with a viscous fluid source, subjected to the following conditions: (a) the equilibrium state variables satisfy the equation of state of a mixture of an ultra-relativistic and a non-relativistic ideal gases, where the internal energy of the latter has been neglected, (b) the particle numbers of the mixture components are independently conserved, (c) the viscous stress is consistent with the transport equation and entropy balance law of Extended Irreversible Thermodynamics, with the coefficient of shear viscosity provided by Kinetic Theory for the `radiative gas' model. The fulfilment of (a), (b) and (c) restricts initial conditions in terms of an initial value function, $\Delta_i^{(s)}$, related to the average of spatial gradients of the fluctuations of photon entropy per baryon in the initial hypersurface. Constraints on the observed anisotropy of the microwave cosmic radiation and the condition that decoupling occurs at $T=T_{_D}\approx 4\times 10^3$ K yield an estimated value: $|\Delta_i^{(s)}|\approx 10^{-8}$ which can be associated with a bound on promordial entropy fluctuations. The Jeans mass at decoupling is of the same order of magnitude as that of baryon dominated perturbation models ($\approx 10^{16} M_\odot$)

A new first integral for a binary rigid body collision of arbitrarily short duration

A standard classical model of a so-called rigid two-body collision that employs the dynamic Coulomb friction law to model friction is studied. For arbitrary object geometries and initial conditions it is known that the direction of the relative sliding velocity continuously changes during the impact. A (new) exact analytical solution for the relative sliding speed utr of the two objects in terms of initial conditions and sliding direction is derived. This solution is formulated in terms of a first integral, which is used to rigorously prove that the dynamic Coulomb friction law does not allow either instantaneous sticking or stable sticking to evolve from an initially nonzero utr, except for certain very special cases. The first integral also yields a new procedure for accurately and efficiently computing the final center of mass velocity and the final angular velocity of each of the objects in the model two-body collision. Accurate solutions such as these are essential for analyzing and controlling impacts, which is important, for example, in robot manipulation. Efficient solutions are critically important for producing real-time simulations of rigid two-body collisions.

3D guidance law modeling

Proportional navigation (PN) guidance laws (GLs) have been widely used and studied in the guidance literature. But most of the guidance literature on PN has concentrated on the evaluation of empirical PNGLs or GLs obtained from very specific optimality considerations. The authors present a novel approach (called guidance laws modeling) to derive new GLs. They consider the basic requirements of capture and define a complete class of GLs that meet these requirements. It is shown that PN is a natural candidate in this class. The main consequence of this modeling process is the definition of two new GLs: one in 2D space and the other in 3D space. These new GLs can be interpreted as new generalizations of the true proportional navigation (TPN) GL. Moreover, it is shown that these generalizations allow the TPNGL to match the capturability performance of the pure proportional navigation (PPN) GL in terms of initial conditions which allow the guided object to reach its target.

Towards memories for Förster-like exciton transfer

A simple two-site model (dimer) of the exciton-phonon system leading, in the lowest order in the exciton transfer integral J, to the Förster transfer rates is examined. Dynamics is solved by the Tokuyama-Mori method. The solution in form of damped or overdamped oscillations allows to deduce standard exciton memory functions in a form summed up partially to the infinite order in J. Two surprising results are obtained: • • Up to a decaying initial condition term, an infinite class of memories can yield the same exciton dynamics. The simplest choice is even non-decaying unless additional source of dephasing is added. • • Time integrals of the memories may not reduce to the standard lowest-order Förster formula if the limitation to just the lowest order in J is performed after the integration.

Lyapunov Exponents for Finite State Nonlinear Filtering

Consider the Wonham optimal filtering problem for a finite state ergodic Markov process in both discrete and continuous time, and let $\sigma$ be the noise intensity for the observation. We examine the sensitivity of the solution with respect to the filter's initial conditions in terms of the gap between the first two Lyapunov exponents of the Zakai equation for the unnormalized conditional probability. This gap is studied in the limit as $\sigma\to 0$ by techniques involving considerations of nonlinear filtering and the stochastic Feynman--Kac formula. Conditions are given for the limit to be either negative or $-\infty$. Asymptotic bounds are derived in the latter case.

Interplay of exciton or electron transfer and relaxation

Mori theory together with canonical transformation but with quantities of interest remaining untransformed is applied to the exciton- or electron-phonon system with site-diagonal linear coupling and full exciton or electron density matrix; finite concentrations of the carriers are admitted. Partial small polaron transformation is used which allows to investigate relaxation of initially relaxed systems without initial-condition terms. The result is applied, in the lowest order in the coupling, to a particle on a symmetric dimer. Coefficients suggested in a recent generalization of the Haken-Strobl-Reineker model are identified. The theory surprisingly, is found to be, in the above order, insufficient to yield a loss of coherence of carrier propagation with increasing time, though standard Markovian treatment suggests the opposite. A new type of a so far unnoticed drawback, typical of finite-order time-convulution theories, which is connected with the infinite memory of the initial lattice relaxation becomes conspicuous.

A theory of real wage growth in LDCs

A general equilibrium framework is presented to explain a variety of developmental experiences. The demand side is modelled by assuming a system of preferences that incorporate Engel's law in a stark way. The framework explains why poverty might be impervious to industrial progress in some countries. It also explains why countries which have been able to boost the exports of manufactured goods have been more successful in raising real wages in their economies than countries which have continued to export primary goods. The framework indicates how the initial conditions in terms of the level and distribution of wealth influence the growth of real wages in an economy.

The M/G/1 processor-sharing model: transient behavior

This paper deals with the M/G/1 model with processor-sharing service discipline. LetL*(t, x) denote the number of jobs present at timet whose attained service time is not greater thanx,x⩾0, andV0(t,z) the sojourn time of a tagged job placed in the system at timet and requiringz units of service. Explicit analytical expressions are obtained for the joint distribution ofL*(t, ·) andV0(t, ·) under various initial conditions in terms of the Laplace transform with respect tot. It is shown that for initial conditions of special kind (there is one job or none) the results can be expressed in a closed form.