Monotonic Function Of Time Research Articles

Dynamics of entropy in evolution models

We calculate the dynamics of entropy for the Crow–Kimura evolution model on the static fitness landscape. For the standard version of the model we show that entropy is not a monotonic function of time. We solve the Smerlak’s modification of the Crow–Kimura analytically, deriving expressions for both the statics and dynamics. Contrary to the standard Crow–Kimura model, here entropy changes monotonically with time.

On the Optimal Exercise Boundaries of Swing Put Options

We use probabilistic methods to characterise time-dependent optimal stopping boundaries in a problem of multiple optimal stopping on a finite time horizon. Motivated by financial applications, we consider a payoff of immediate stopping of “put” type, and the underlying dynamics follows a geometric Brownian motion. The optimal stopping region relative to each optimal stopping time is described in terms of two boundaries, which are continuous, monotonic functions of time and uniquely solve a system of coupled integral equations of Volterra-type. Finally, we provide a formula for the value function of the problem.

On-the-Job Search and Optimal Schooling Under Uncertainty and Irreversibility

This paper develops a labour market model with on-the-job search, match-specific productivity draws and an endogenous irreversible schooling decision. The choice of schooling is modeled as an optimal stopping problem which gives rise to the equilibrium heterogeneity of workers with respect to the formal education. The optimal schooling decision is characterized by the reservation productivity of students which is a monotonic function of time. Moreover, this reservation productivity is lower in expansions when job-to-job mobility is more intensive. Therefore, the model is compatible with the empirical evidence that expansions have a positive effect on the probability of a school dropout. The schooling density is downward-sloping and the equilibrium wage distribution is right-skewed with a unique interior mode. This means that the majority of workers earn wages in the middle range of the earnings distribution. At the same time there is a small proportion of employees in the beginning of their career with wages in the left tail of the earnings distribution and a small proportion of high-skilled workers earning wages in the right tail of the distribution.

On-the-Job Search and Optimal Schooling Under Uncertainty and Irreversibility

This paper develops a labour market model with on-the-job search, match-specific productivity draws and an endogenous irreversible schooling decision. The choice of schooling is modeled as an optimal stopping problem which gives rise to the equilibrium heterogeneity of workers with respect to the formal education. The optimal schooling decision is characterized by the reservation productivity of students which is a monotonic function of time. Moreover, this reservation productivity is lower in expansions when job-to-job mobility is more intensive. Therefore, the model is compatible with the empirical evidence that expansions have a positive effect on the probability of a school dropout. The schooling density is downward-sloping and the equilibrium wage distribution is right-skewed with a unique interior mode. This means that the majority of workers earn wages in the middle range of the earnings distribution. At the same time there is a small proportion of employees in the beginning of their career with wages in the left tail of the earnings distribution and a small proportion of high-skilled workers earning wages in the right tail of the distribution.

Propagators in Lagrangian space

It has been found recently that propagators, e.g. the cross correlation spectra of the cosmic fields with the initial density field, decay exponentially at large k in an Eulerian description of the dynamics. We explore here similar quantities defined for a Lagrangian space description. We find that propagators in Lagrangian space do not exhibit the same properties: they are found not to be monotonic functions of time, and to track back the linear growth rate at late time (but with a renormalized amplitude). These results have been obtained with a novel method which we describe alongside. It allows the formal resummation of the same set of diagrams as those that led to the known results in Eulerian space. We provide a tentative explanation for the marked differences seen between the Eulerian and the Lagrangian cases, and we point out the role played by the vorticity degrees of freedom that are specific to the Lagrangian formalism. This provides us with new insights into the late-time behavior of the propagators.

Fixed-Effects Methods for the Analysis of Nonrepeated Events

For repeated events, fixed-effects regression methods—which control for all stable covariates—can be implemented by doing Cox regression with stratification on individuals. For nonrepeated events, we consider the use of conditional logistic regression to estimate fixed-effects models with discrete-time data. Known in the epidemiological literature as the case-crossover design, this method fails when any covariate is a monotonic function of time. Hence, no control for time itself can be included, leading to potentially spurious estimates. As an alternative, we consider the case-time-control method for estimating the effect of a dichotomous predictor. This method allows for the introduction of a control for time by reversing the role of the dependent and independent variables. In contrast to earlier work, we show that the method can be applied to data that contain only uncensored cases, and that it is possible to control for additional covariates, both categorical and quantitative. Simulation studies indicate that the case-time-control method is substantially superior to the case-crossover method and to conventional logistic regression. The methods are illustrated by estimating the effect of a wife's death on the hazard of death for her husband.

Formulating and parameterizing the allocation of net primary productivity for modeling overmature stands in boreal forest ecosystems

In process-based models of forest ecosystems, carbon allocation is a key process that partitions the net primary productivity (NPP) among different biomass components and thus affects forest growth patterns at different stages of the forest's growth. Common allocation models usually express the carbon allocation as linear or monotonic functions of time. These models are acceptable for a limited growth period, but inadequate for simulating long-term development of a forest. To improve the usefulness of these models and simplify the model structure, we developed an analytical solution to partition NPP that considers the effects of litterfall and growth rate. We derived NPP allocation functions based on functions for the net growth rate (dry mass) and based on empirical growth curves estimated from normal yield tables for northern Ontario, Canada. The improved allocation reflects growth restrictions that arise in overmature stands according to different site classes across landscape. The details of the derivation and parameterization are presented and discussed. We validated the new NPP allocation functions for black spruce ( Picea mariana) in the boreal forest of northern Ontario. The improved NPP allocation simulated the NPP dynamics of forest ecosystems more accurately over the course of stand development, and the results were biologically realistic.

Stringy dark energy model with cold dark matter

Cosmological consequences of adding the cold dark matter (CDM) to the exactly solvable stringy dark energy (DE) model are investigated. The model is motivated by the consideration of our Universe as a slowly decaying D3-brane. The decay of this D-brane is described in the string field theory framework. Stability conditions of the exact solution with respect to small fluctuations of the initial value of the CDM energy density are found. Solutions with large initial value of the CDM energy density attracted by the exact solution without CDM are constructed numerically. In contrast to the ΛCDM model the Hubble parameter in the model is not a monotonic function of time. For specific initial data the DE state parameter wDE is also not monotonic function of time. For these cases there are two separate regions of time where wDE being less than −1 is close to −1.

Analysis of diurnal and seasonal cycles and trends in climatic records with arbitrary observation times

Many long‐term records of climate variables have missing data or have had changes in their times of observation. Here we present a technique to analyze such inhomogeneous records. We assume that the underlying climatic processes are nonstationary, where the observations contain a long‐term trend superimposed on periodic shorter time seasonal and diurnal cycles. The seasonal and diurnal variations are approximated using a limited number of Fourier harmonics, while the trend is represented by a monotonic function of time whose amplitude can also vary seasonally and diurnally. A least squares method is used to estimate the unknown Fourier coefficients. As an example of the technique, we present an analysis of multi‐decadal hourly observations of surface air temperature obtained from several meteorological stations within the United States.

THE MAGNETIC HELICITY BUDGET OF A CME-PROLIFIC ACTIVE REGION

Coronal mass ejections (CMEs) are thought to be the way by which the solar corona expels accumulated magnetic helicity which is injected into the corona via several methods. DeVore (2000) suggests that a significant quantity is injected by the action of differential rotation, however Demoulin et al. (2002b), based on the study of a simple bipolar active region, show that this may not be the case. This paper studies the magnetic helicity evolution in an active region (NOAA 8100) in which the main photospheric polarities rotate around each other during five Carrington rotations. As a result of this changing orientation of the bipole, the helicity injection by differential rotation is not a monotonic function of time. Instead, it experiences a maximum and even a change of sign. In this particular active region, both differential rotation and localized shearing motions are actually depleting the coronal helicity instead of building it. During this period of five solar rotations, a high number of CMEs (35 observed, 65 estimated) erupted from the active region and the helicity carried away has been calculated, assuming that each can be modeled by a twisted flux rope. It is found that the helicity injected by differential rotation (≈−7×1042 Mx2) into the active region cannot provide the amount of helicity ejected via CMEs, which is a factor 5 to 46 larger and of the opposite sign. Instead, it is proposed that the ejected helicity is provided by the twist in the sub-photospheric part of the magnetic flux tube forming the active region.

Analysis of the spreading Gaussian wavepacket

Analysis of the spreading Gaussian wavepacket

Transfer of excitation energy in a three-dimensional-doped molecular crystal. V. Self-consistency of the temporal processes involved in energy transfer in photosynthetic units

Numerical experiments were carried out to determine the timewise self-consistency of different physical processes involved in the energy transfer in green plant photosynthetic units. A 6 × 6 × 6 array of chlorophyll-a with cubic lattice constants a = b = c = 20 A was chosen as a model of the thylakoid disc. Another model aggregate was obtained by substituting chlorophyll-b molecules for some of the chlorophyll-a molecules. In both models, a reaction center occupied a central site in the last xy plane. Two extreme arrangements were considered for the orientation of molecules. In one, the transition moments of all molecules were directed along the y-axis. The other had chlorophyll molecules randomly oriented. The four resulting model systems were used in our investigation on exciton generation, transport, decay by fluorescence, and trapping. All excitons were assumed to be generated by a 20 ms exposure to sunlight at high altitudes. The general trends noticed from these computations are as follows: The number of excitons generated is influenced by lattice disorders. Disorders also increase the time for the establishment of an equilibrium distribution. The decay of excitons by fluorescence is always a monotonic function of time. The energy transfer is adversely affected by a lower degree of orientation in the crystal: The trapping time increases with disorder. The number of trappings decreases with the onset of fluorescence of the host molecules and the trap. From these investigations, we also made three specific observations: (1) The efficiency of exciton utilization varies from 12% for a completely random arrangement of transition dipoles to 46% for a perfectly ordered arrangement. This agrees with the experimental efficiency, about 20%. (2) The number of excitons trapped varies from one to six. This tallies with the time scale of electron transfer along the Z-scheme that requires at least two excitons trapped in about 20 ms. Thus, the photon density and the exciton transfer rate are consistent with the rates of electron transfers. (3) The trapping rate also indicates that the thylakoid disc must resemble a considerably ordered system. © 1996 John Wiley & Sons, Inc.

On the use of series to integrate rate equations

AbstractThe coefficients in power series, in the variable time, describing coupled nonlinear chemical reactions are easily obtained from a recursion relation. Since these series have a limited radius of convergence they are not very useful as such. If the series are inverted to give time as a function of the appropriate power of a progress variable, the new series converge over the entire time course of the reaction. If, further, the long‐time asymptotic behavior, obtained from the linearized kinetic equations, is used, one can obtain a series expansion for a function that describes the correct short‐time behavior. This function can be estimated very well using truncated series. The method works well for consecutive nonlinear reactions where the progress variables are monotonic functions of time; this includes many cases where the concentrations of intermediate species go through a maximum as the reaction progresses.

Coalescence and Breakup-Induced Oscillations in the Evolution of the Raindrop Size Distribution

Models or the coalescence/breakup process yield drop number distributions that approach equilibrium but the number density often is not a monotonic function of time. In some cases, the small-raindrop portion of the distribution rapidly attains high concentration levels before settling back toward an equilibrium position. An eigenanalysis of the coalescence/breakup equation is performed to gain an understanding of the solution behavior near equilibrium. The analysis reveals that the departure of the solution from equilibrium can be expressed as a linear combination of basis functions of the form eλj where Re(λj) < 0 so that the equilibrium drop distribution is asymptotically stable. The exponential basis functions feature a wide range of decay rates, and since Im (λj) ≠ 0 in some cases, the functions provide evidence of oscillations in the drop spectrum. It is shown that one particular damped oscillation can combine with a rapidly decaying transient to describe very well the nonmonotonic behavior characteristic of model-generated drop spectra. While the physical mechanism behind the oscillation is not yet understood, the initial reversal in the small-drop peak may be explained as rapid response due to filament breakup followed by a slower response due to coalescence. A particular sequence of observed raindrop distributions is found to exhibit a reversal in the spectral peak similar to that produced by the model.

Entropy Production in Simple Chemical Reactions

It is shown that entropy production appears to be a completely monotonic function of time for several chemical reactions or reaction sequences taking place in closed systems at constant temperature; however this monotonicity principle does not extend to autocatalytic or oscillatory processes. Where it occurs, the complete monotonicity of entropy production stems essentially from the completely monotonic behavior of the species number densities as functions of time in the evolution of the reaction.

Entropy Production in Chemically Reacting Systems

Numerical integration of the gasdynamic equations describing the coupling between vibrational relaxation and dissociation for a hydrogen–helium mixture in a plane shock wave shows that the total entropy is a completely monotonic function of time; this is found to be the case whether the system is considered to be isolated, or whether there is loss of energy or mass from the flow.

The Geomorphic Evolution of the Lunar Surface

Fundamental parameters of the geomorphology of a lunar surface are (i) the number and size distribution of craters, (ii) the degree of erosion of the craters and (iii) thickness and other characteristics of the regolith. These parameters are not independent of one another; as one changes through time, the other two will also change in a statistically predictable way.In the continuous degradation sequence, the relationship between the number of craters per unit area and the degree of erosion of the craters is continuous and monotonic. This sequence occurs in areas subjected to intermediate to small impacts, and eroded mainly by the impacts themselves plus other small-scale erosional processes. In areas subjected to large impacts and mare flooding the discontinuous degradation sequence is predominant.The relationship of the first two parameters, the number of craters and the degree of erosion, with the third parameter, the regolith, is not simple and is not yet understood. It appears, however, that the geomorphological stage is more important than the mare-versus-highland dichotomy of the lunar surface.The solution of the function relating craters of the continuous degradation sequence with degree of erosion was defined as the geomorphic index of the area. Studies of the geomorphic index of stratigraphic surfaces show that areas covered by considerable ballistic sediments have a geomorphic index which is not a monotonic function of time. On the other hand, areas covered almost exclusively by mare flooding show an index which is a monotonic function of the age of the flooding. As each mare surface shows a considerable range in indices, it is concluded that maria are covered by surfaces formed through a considerable length of time. By using Apollo 11 and 12 radiometric ages it is suggested that the time of mare flooding lasted on the order of one billion (109) years.The geomorphic index of highland surfaces shows a remarkable degree of order; i.e., the farther an area is inland from the mare shores, the higher will be the index. No explanation is given to this phenomenon, but is suggested that lunar erosion is not just a localized phenomenon centered on the locus of an impact, but has lateral trends of regional dimensions. Electrostatic transportation as suggested by Gold is a possible mechanism.

Physical Factors Involved in Ultrasonically Induced Changes in Living Systems: II. Amplitude Duration Relations and the Effect of Hydrostatic Pressure for Nerve Tissue

The results of experiments with frogs under a hydrostatic pressure demonstrate that cavitation is not an important factor in the mechanism of production of paralysis of the hind legs of frog by ultrasonic (frequency one megacycle) irradiation over the lumbar enlargement region of the spinal cord. Experimental results indicate that a linear relation exists between the reciprocal of the minimum exposure time for paralysis and the acoustic amplitude. This result is readily described in terms of a one factor rate process. On the basis of this experimentally determined relation, it is shown that time rate of change of temperature cannot be correlated with the observations. It is concluded on the basis of a theoretical calculation that absorption of ultrasound at interfaces in the spinal cord does not result in minute hot regions. Further work on summation of subparalytic doses, spaced apart at various time intervals, indicates that the recovery process following exposure to a subparalytic dose of ultrasonic radiation may not be a monotonic function of time.