The Dependence of Chimera States on Initial Conditions

A chimera state consisting of both coherent and incoherent groups is a fascinating spatial pattern in non-locally coupled identical oscillators. It is thought that random initial conditions hardly evolve to chimera states. In this work, we study the dependence of chimera states on initial conditions. We show that random initial conditions may lead to chimera states and the chance of realizing chimera states becomes increasing when the model parameters axe moving away from the boundary of their stable regime.

Impacts of Initial Conditions on Cloud-Resolving Model Simulations

Impacts of initial conditions on cloud-resolving model simulations are investigated using a series of sensitivity experiments. Five experiments with perturbed initial temperature, moisture, and cloud conditions are conducted and compared to the control experiment. The model is forced by the large-scale vertical velocity and zonal wind observed and derived from NCEP/Global Data Assimilation System （GDAS）. The results indicate that model predictions of rainfall are much more sensitive to the initial conditions than those of temperature and moisture. Further analyses of the surface rainfall equation and the moisture and cloud hydrometeor budgets reveal that the calculations of vapor condensation and deposition rates in the model account for the large sensitivities in rainfall simulations.

CONTINUOUS DEPENDENCE OF THE SOLUTIONS OF IMPULSIVE DIFFERENTIAL EQUATIONS ON THE INITIAL CONDITIONS AND BARRIER CURVES

The basic objects of investigation in this article are nonlinear impulsive dif- ferential equations. The impulsive moments coincide with the moments of meeting of the integral curve and some of the so-called barrier curves. For such type of equations, suf- ficient conditions are found under which the solutions are continuously dependent on the perturbations with respect to the initial conditions and barrier curves. The results are applied to a mathematical model of population dynamics.

Uncertainty in Tropical Cyclone Intensity Predictions due to Uncertainty in Initial Conditions

Focusing on the role of initial condition uncertainty,we use WRF initial perturbation ensemble forecasts to investigate the uncertainty in intensity forecasts of Tropical Cyclone(TC)Rammasun(1409),which is the strongest TC to have made landfall in China during the past 50 years.Forecast results indicate that initial condition uncertainty leads to TC forecast uncertainty,particularly for TC intensity.This uncertainty increases with forecast time,with a more rapid and significant increase after 24 h.The predicted TC develops slowly before 24 h,and at this stage the TC in the member forecasting the strongest final TC is not the strongest among all members.However,after 24 h,the TC in this member strengthens much more than that the TC in other members.The variations in convective instability,precipitation,surface upward heat flux,and surface upward water vapor flux show similar characteristics to the variation in TC intensity,and there is a strong correlation between TC intensity and both the surface upward heat flux and the surface upward water vapor flux.The initial condition differences that result in the maximum intensity difference are smaller than the errors in the analysis system.Differences in initial humidity,and to a lesser extent initial temperature differences,at the surface and at lower heights are the key factors leading to differences in the forecasted TC intensity.These differences in initial humidity and temperature relate to both the overall values and distribution of these parameters.

Application of ERA5 Reanalysis to the Construction of Initial Conditions for WACCM Simulations

This study uses ECMWF fifth-generation reanalysis, ERA5, which extends to the mesopause, to construct the Initial Conditions(IC) for WACCM(Whole Atmosphere Community Climate Model) simulations. Because the biases between ERA5 and Sounding of the Atmosphere using Broadband Emission Radiometry(SABER) temperature data are within ±5 K below the lower mesosphere,ERA5 reanalysis is used to construct IC in the lower atmosphere. Four experiments are performed to simulate a Stratospheric Sudden Warming(SSW) event from 5 to 15 February 2016. The simulation using the WACCM default climatic IC cannot represent the sharp meteorological variation during SSW. In contrast, the 0～4 d forecast results driven by ERA5-constructed IC is consistent with ERA5 reanalysis below the middle mesosphere. Comparing with WACCM climatology ICs scheme, the ICs constructing method based on ERA5 reanalysis can obtain 67%, 40%, 22%, 4% and 6% reduction of temperature forecast RMSE at 10 hPa, 1 hPa, 0.1 hPa, 0.01 hPa and 0.001 hPa respectively. However,such improvement is not shown in the lower thermosphere.

A method of estimating initial conditions of coupled map lattices based on time-varying symbolic dynamics

A novel computationally efficient algorithm in terms of the time-varying symbolic dynamic method is proposed to estimate the unknown initial conditions of coupled map lattices （CMLs）. The presented method combines symbolic dynamics with time-varying control parameters to develop a time-varying scheme for estimating the initial condition of multi-dimensional spatiotemporal chaotic signals. The performances of the presented time-varying estimator in both noiseless and noisy environments are analysed and compared with the common time-invariant estimator. Simulations are carried out and the obtained results show that the proposed method provides an efficient estimation of the initial condition of each lattice in the coupled system. The algorithm cannot yield an asymptotically unbiased estimation due to the effect of the coupling term, but the estimation with the time-varying algorithm is closer to the Cramer-Rao lower bound （CRLB） than that with the time-invariant estimation method, especially at high signal-to-noise ratios （SNRs）.

Existence and Continuous Dependence of Mild Solutions for Some Fractional Neutral Differential Equations with Nonlocal Initial Conditions

The existence,uniqueness,and continuous dependence to the mild solutions of the nonlocal Cauchy problem were proved for a class of semilinear fractional neutral differential equations.The results are obtained by using the Krasnoselskii's fixed point theorem and the theory of resolvent operators for integral equations.

The Case of Nonzero Initial Conditions in the Evolution of the Charge Density Distribution Function for a Spherically Symmetric System

We explored the Cauchy problem for the evolution of the charge density distribution function for a spherically symmetric system with nonzero initial conditions. In our model, the evolution of the charge density distribution function is simulated for the case of a non-uniform charged sphere. The initial speed of the system is nonzero. The solution breaks down into two components: the first one describes the system’s motion as a whole and the second describes the process of the evolution of the charge density function under the influence of its own electric field in the center-of-mass system. In this paper we considered the characteristic features of the implementation of a difference scheme for numerical simulation. We also illustrate the process of “scattering” of a moving charged system under the influence of its own electric field on the basis of the solution of the Cauchy problem for vector functions of the electric field and vector velocity field of a charged medium.

Time domain system identification of unknown initial conditions

System identification is a method for using measured data to create or improve a mathematical model of the object being tested. From the measured data however, noise is noticed at the beginning of the response. One solution to avoid this noise problem is to skip the noisy data and then use the initial conditions as active parameters, to be found by using the system identification process. This paper describes the development of the equations for setting up the initial conditions as active parameters. The simulated data and response data from actual shear buildings were used to prove the accuracy of both the algorithm and the computer program, which include the initial conditions as active parameters. The numerical and experimental model analysis showed that the value of mass, stiffness and frequency were very reasonable and that the computed acceleration and measured acceleration matched very well.

Interferometry signatures of hydrodynamic sources with fluctuating initial conditions

We investigate the space-time evolution of the hydrodynamic particle-emitting sources with the fluctuating initial conditions generated by Heavy Ion Jet Interaction Generator(HIJING).In order to detect the event-by-event inhomogeneity of the sources,we examine the distribution of the error-inverse-weighted fluctuations,f,between the two-pion Bose-Einstein correlation functions of single and mixed events.We find that the distribution of f becomes wide for the fluctuating initial conditions.The large values of the distribution width and the root-mean-square frms are the signatures of the hydrodynamic particle-emitting sources with the fluctuating initial conditions.

Impact of Initial Soil Conditions on Soil Hydrothermal and Surface Energy Fluxes in the Permafrost Region of the Tibetan Plateau

Accurate initial soil conditions play a crucial role in simulating soil hydrothermal and surface energy fluxes in land surface process modeling.This study emphasized the influence of the initial soil temperature(ST)and soil moisture(SM)conditions on a land surface energy and water simulation in the permafrost region in the Tibetan Plateau(TP)using the Community Land Model version 5.0(CLM5.0).The results indicate that the default initial schemes for ST and SM in CLM5.0 were simplistic,and inaccurately represented the soil characteristics of permafrost in the TP which led to underestimating ST during the freezing period while overestimating ST and underestimating SLW during the thawing period at the XDT site.Applying the long-term spin-up method to obtain initial soil conditions has only led to limited improvement in simulating soil hydrothermal and surface energy fluxes.The modified initial soil schemes proposed in this study comprehensively incorporate the characteristics of permafrost,which coexists with soil liquid water(SLW),and soil ice(SI)when the ST is below freezing temperature,effectively enhancing the accuracy of the simulated soil hydrothermal and surface energy fluxes.Consequently,the modified initial soil schemes greatly improved upon the results achieved through the long-term spin-up method.Three modified initial soil schemes experiments resulted in a 64%,88%,and 77%reduction in the average mean bias error(MBE)of ST,and a 13%,21%,and 19%reduction in the average root-mean-square error(RMSE)of SLW compared to the default simulation results.Also,the average MBE of net radiation was reduced by 7%,22%,and 21%.

Initial Labor Market Conditions and Individual Employability

Initial labor market conditions affect how individuals build their human capital and look for jobs and thus can have long-term effects on their income levels,work performance,and career development.Based on data from the Urban Household Survey(UHS)of urban households in China from 1986 to 2009,we perform an empirical test of how initial labor market conditions affect the employability of individuals.Our research shows that people’s future incomes suffer if they start out in an adverse job market.Each percentage point of increase in the unemployment rate at an individual’s entry into the labor market is associated with a two-percentage-point drop in his or her average annual income.Even after looking at different parts of the job market and sample groups,this conclusion still holds.In the context of global economic instability,our findings may assist government policymakers in addressing adverse labor market conditions.

A STUDY ON THE PREDICT ABILITY OF GRAPES MODEL OVER SOUTH CHINA: COMPARISONS BY TWO INITIALIZATION CONDITIONS BETWEEN ECMWF AND NCEP

This paper aims to assess the performances of different model initialization conditions(ICs)and lateral boundary conditions between two global models(GMs),i.e.,the European Centre for Medium-Range Weather Forecasts(ECMWF)and National Centers for Environmental Prediction(NCEP),on the accuracy of the Global/Regional Assimilation and Prediction System(GRAPES)forecasts for south China.A total of 3-month simulations during the rainy season were examined and a specific case of torrential rain over Guangdong Province was verified.Both ICs exhibited cold biases over south China,as well as a strong dry bias over the Pearl River Delta(PRD).In particular,the ICs from the ECMWF had a stronger cold bias over the PRD region and a more detailed structure than NCEP.In general,the NCEP provided a realistic surface temperature compared to the ECMWF over south China.Moreover,GRAPES initialized by the NCEP had better simulations of both location and intensity of precipitation than by the ECWMF.The results presented in this paper could be used as a general guideline to the operational numerical weather prediction that uses regional models driven by the GMs.

EXPERIMENTAL STUDY OF THE ROLE OF INITIAL AND BOUNDARY CONDITIONS IN MESOSCALE NUMERICAL WEATHER PREDICTION

Based on the real case of a frontal precipitation process affecting South China, 27 controlled numerical experiments was made for the effects of hydrostatic and non-hydrostatic effects, different driving models, combinations of initial/boundary conditions, updates of lateral values and initial time levels of forecast, on model predictions. Features about the impact of initial/boundary conditions on mesoscale numerical weather prediction (NWP) model are analyzed and discussed in detail. Some theoretically and practically valuable conclusions are drawn. It is found that the overall tendency of mesoscale NWP models is governed by its driving model, with the initial conditions showing remarkable impacts on mesoscale models for the first I0 hours of the predictions while leaving lateral boundary conditions to take care the period beyond; the latter affect the inner area of mesoscale predictions mainly through the propagation and movement of weather signals (waves) of different time scales; initial values of external model parameters such as soil moisture content may affect predictions of more longer time validity, while fast signals may be filtered away and only information with time scale 4 times as large as or more than the updated period of boundary values may be introduced, through lateral boundary, to mesoseale models, etc. Some results may be taken as important guidance on mesoseale model and its data a.ssimilation developments of the future.

Symmetry Based Searching Process for Initial Conditions of Passive Running

Symmetrical passive running of a simple spring model is commonly used to predict the locomotion of real animals and develop the design strategies for legged systems. If the initial conditions for running can be found automatically, we can expand the ranges of the model parameters freely. To achieve this objective, we derive an efcient searching procedure based on analysis of the symmetries. Using this process, the desired initial states of the passive running are obtained. Existence of the results reveals that the leg symmetries can be used to generate the symmetrical running. Moreover, the leg forces are associated with the running pattern, implying that we should choose suitable motion for the given model characteristics.

Effect of Initial Stress Conditions on the Threshold Shear Strain of Nanjing's Saturated Fine Sand

By using GDS dynamic hollow cylinder torsional apparatus,a series of cyclic torsional triaxial tests under complex initial consolidation condition are performed on Nanjing saturated fine sand. The effects of the initial principal stress direction α0,the initial ratio of deviatoric stress η0,the initial average effective principal stress p0 and the initial intermediate principal stress parameter b0 on the threshold shear strain γt of Nanjing saturated fine sand are then systematically investigated. The results show that γt increases as η0,p0 and b0 increase respectively,while the other three parameters remain constant. α0 has a great influence on γt,which is reduced when α0 increases from 0° to 45° and increased when α0 increases from 45° to 90°. The effect of α0 on γt plays a leading role and the effect of η0 will weaken when α0 is approximately 45°.

Numerical Treatment of Initial-Boundary Value Problems with Mixed Boundary Conditions

In this paper, we extend the reliable modification of the Adomian Decom-position Method coupled to the Lesnic’s approach to solve boundary value problems and initial boundary value problems with mixed boundary conditions for linear and nonlinear partial differential equations. The method is applied to different forms of heat and wave equations as illustrative examples to exhibit the effectiveness of the method. The method provides the solution in a rapidly convergent series with components that can be computed iteratively. The numerical results for the illustrative examples obtained show remarkable agreement with the exact solutions. We also provide some graphical representations for clear-cut comparisons between the solutions using Maple software.

THE SECOND INITIAL-BOUNDARY VALUE PROBLEM FOR A QUASILINEAR PARABOLIC EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

With prior estimate method, the existence, uniqueness, stability and large time behavior of the solution of second initial-boundary value problem for a fast diffusion equation with nonlinear boundary conditions are investigated. The main results are : 1) there exists only one global weak solution which continuously depends on initial value; 2) when t < T-0, the solution is infinitely continuously differentiable and is a classical solution; 3) the solution converges to zero uniformly as t is large enough.

Initial and Stopping Condition in Possibility Principal Factor Rotation

Uemura [1] discovered the mapping formula for Type 1 Vague events and presented an alternative problem as an example of its application. Since it is well known that the alternative problem leads to sequential Bayesian inference, the flow of subsequent research was to make the mapping formula multidimensional, to introduce the concept of time, and to derive a Markov (decision) process. Furthermore, we formulated stochastic differential equations to derive them [2]. This paper refers to type 2 vague events based on a second-order mapping equation. This quadratic mapping formula gives a certain rotation named as possibility principal factor rotation by transforming a non-mapping function by a relation between two mapping functions. In addition, the derivation of the Type 2 Complex Markov process and the initial and stopping conditions in this rotation are mentioned. .