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Assuming that the equilibrium geometry of river channels does not depend on their initial state but solely on boundary conditions, several formulas have been derived that relate the channel depth and width to the river bankfull discharge and bed material. However, due to the existence of a threshold for sediment motion and the strong non-linearity between sediment transport and flow rate, this assumption might not be generally valid for gravel-bed rivers. This research clarifies the role of the initial conditions, more specifically the initial channel width, on the geometry of gravel-bed rivers considering a variety of boundary conditions. The approach includes laboratory experiments and two-dimensional modeling, reproducing the evolution of alluvial channels with different starting widths, discharge regimes and sediment input rates. The experiments represent the Arc River (France). Thus, the characteristics of this river were used in the numerical model to obtain a realistic virtual case complementing the experiments. Different boundary and starting conditions resulted in either braided or single-thread channels. We found that the initial width strongly influences the evolution process and leaves a footprint on the river braid-belt extension. The active width of braided systems and the width of single-thread channels do not depend on the starting condition. They depend on sediment input rather than on discharge variability. Different initial widths result in different final bed levels. This indicates that the initial channel width may affect the degree of channel incision or aggradation. The results of this study justify the use of equilibrium formulas for single-thread rivers.

Purpose: Gross Domestic Product(GDP) depends on Agriculture, Service, and industry performance. The main aim of the study is to assess the relationship between dependent variable GDP and Independent variables agriculture, industry, and service sector by using the n-variable Regression Model at initial condition. Design/Methodology/Approach: The study is an application of the n-variable Regression Model at the initial condition to analyze the situation of GDP along with reasons not becoming zero GDP even after using the initial condition. The secondary data of the GDP of Nepal from the Central Bureau of Statistics of 10 years till 2019/20 has been analyzed. By finding cofactors of correlation coefficient matrix, Mean and standard deviation of the individual data to establish the linear relationship between dependent and independent variable. Findings/Result: Under initial conditions, if all the independent variables zero, the GDP is −751028.431 billion, negative sign shows that GDP decreases highly if the entire major factor has no role in GDP. It is non-zero GDP. It means in the 11th year the stated amount will be expended from the previous year saving for forex to import which will not be possible in a sustainable economy. It will not be possible in real conditions however it may be hypothetical possible either because of the impact of informal economy or disinvestment or negative net exports. It is significant for forecasting the future GDP of a country effectively assuming different conditions for policy formulation. Originality/Value: It is the first empirical research using the n-variable Regression Model for GDP Analysis. Paper Type: Analytical Policy Research

Dynamical climate models have been extensively used over the last decade to perform seasonal sea ice predictions in the context of ensemble forecasting. To date, the sensitivity to the initial conditions has received the most attention through the evaluation of the theoretical limit of Antarctic sea ice predictability imposed by the chaotic evolution of the climate system. The respective contributions of perturbed ocean–sea ice initial conditions and perturbed atmospheric boundary conditions to this predictability remains unevaluated, though. Using the coupled ocean–sea ice model NEMO3.6–LIM3, we developed a suitable framework for evaluating both influences on seasonal Antarctic sea ice predictions. This study reveals that the uncertainty associated with the evolution of the atmospheric conditions is a major limitation to the realization of skilful sea ice extent (SIE) predictions. However, it has a limited impact on sea ice volume (SIV) predictions. The discrepancies between the SIE and SIV predictabilities have been attributed to the presence of very thin ice, which accounts for much of the SIE variability in winter. We also demonstrated that an incorrect estimate of the ocean–sea ice initial conditions has a weaker, but not negligible influence. The time evolution of different plausible ocean–sea ice initial conditions under perfect knowledge of the atmospheric conditions suggest that the initial SIE errors cannot be totally reduced by the atmospheric forcing. They even increase during the melt season. The high persistence of the SIV anomalies is found to be responsible for this behaviour. These findings imply that a correct initialization of the sea ice thickness (SIT) might be more important than previously thought for seasonal Antarctic sea ice predictions, especially if one wants to predict the SIE during the melt season.

A method is presented to obtain initial conditions for Smoothed Particle Hydrodynamic (SPH) scenarios where arbitrarily complex density distributions and low particle noise are needed. Our method, named ALARIC, tampers with the evolution of the internal variables to obtain a fast and efficient profile evolution towards the desired goal. The result has very low levels of particle noise and constitutes a perfect candidate to study the equilibrium and stability properties of SPHISPMHD systems. The method uses the iso-thermal SPH equations to calculate hydrodynamical forces under the presence of an external fictitious potential and evolves them in time with a 2nd-order symplectic integrator. The proposed method generates tailored initial conditions that perforrri better in many cases than those based on purely crystalline lattices, since it prevents the appearance of anisotropies. The authors would like to thank J.M. Reynolds, D. Price and F. Stasyszyn for the fruitful conversations which, although brief in duration, were rich in content and helped shape the contents of this paper. This research was sponsored in part by DGICYT (Dirección General de Investigaciones Científicas y Tecnológicas) of Spain under Project No. ENE2015-68265 and the Erasmus Mundus Program: International Doctoral College in Fusion Science and Engineering FUSION-DC. The authors thank the editor and referees for the constructive comments and their patience.

One-of-a-kind experimental and numerical investigation is provided in this paper about energy sheet pile walls: earth retaining structures that embed heat exchanger probes within piles for the exploitation of shallow geothermal energy. The study resorts to the results of full-scale in situ tests and coupled three-dimensional thermo-mechanical finite element analyses of an energy sheet pile wall constructed in an underground station. In this context, an investigation about the influence of thermal boundary and initial conditions on thermo-mechanical behaviour of the energy sheet pile wall is performed. The addressed thermal boundary conditions are associated with the thermal load imposed on the considered foundation by the field environment and the geothermal operation of some energy piles constituting the wall. The addressed thermal initial conditions are associated with the undisturbed ground temperature field of the considered site. Based on a comparison between the experimental and numerical results, and the development of numerical sensitivity analyses, criticalities associated with the analysis and modelling of the thermo-mechanical behaviour of energy sheet pile walls are denoted. The results highlight that: a marked non-uniformity of the temperature field can characterise real applications of energy sheet pile walls, representing a significant challenge to capture numerically at all spatial locations; a comparable influence denotes thermal loads that derive from the field environment and the geothermal operation of energy sheet pile walls, deserving attention when modelling the behaviour of such geostructures; and a critical role of the initial thermal conditions is connected to the satisfactory understanding and prediction of the thermo-mechanical behaviour of energy sheet pile walls, requiring careful consideration for analysis and design purposes.

Numerous evacuation models are now able to represent populations with different movement abilities. However, this representation is not always supported by empirical data; i.e. the functionality can occasionally overreach the empirical support for it. The goals of this work are: (1) to provide data that adds to the understanding and quantification of vulnerable population's evacuation performance, and (2) to provide sufficiently detailed and transparent data-sets for model configuration and validation. Data was collected during five evacuations from the same school, conducted between 2011 and 2014. Children from 4 to 16 years old were involved in these drills. Four of the evacuations were unannounced, while one was semi-announced (i.e. staff were aware that the drill would be conducted on a particular day). In addition to the initial scenario conditions (e.g. the building geometry, population, procedures employed, etc.), a number of different performance data-sets were collected: pre-evacuation times, travel speeds, route use and evacuation arrival curves. Through the provision of detailed architectural diagrams and other initial conditions and raw data/analysis describing evacuee performance it is hoped that this data-set will be used in the development of evacuation models and their application. The limitations in the data collection and analysis process are outlined allowing the modeler to identify where issues might arise and take corrective actions where possible. Language: en

In this paper, we study turbulent mixing between two miscible fluids that is induced gravitationally by Rayleigh–Taylor instability in a tightly confined domain. In our experimental configurations, one lateral dimension is between two and three orders of magnitude smaller than the other. Our motivation is to examine the relationship between domain width and certain key flow statistics, as the geometric restriction changes in relative significance. We match our experiments with carefully-resolved numerical simulations and in order to impose appropriate initial conditions, we extend Taylor’s linear model of instability growth to characterise the influence of geometry on early modal development and use measured experimental data to inform our initialisation. We find that our experiments exhibit initial conditions with a k − 1 spectral scaling of interfacial perturbation of volume fraction with a high degree of repeatability, where k denotes wavenumber. We discovered that our form of geometric restriction couples favourably with the spectral composition of our initial condition. We observe no early-stage transient relaxation towards self–similarity, because the instability already begins in that stable self-similar equilibrium, and this important special case has not previously been noticed despite decades of related research. We present our statistical observations from both experiment and numerical simulation as a validation resource for the community; such simulations are inexpensive to compute yet capture many dynamically significant properties.

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The shape of a drop on an inclined hysteretic surface has been studied both theoretically and experimentally in this paper. Surface Evolver (SE) has been used to model the shape of the drop. The triple line was initially circular. The energy minimization method from SE is coupled with a triple line dynamics model to incorporate contact angle hysteresis (CAH) into the simulations. Experiments have also been performed with sessile drops on tilting surfaces to validate the results obtained from the SE model. From this study, two critical inclination angles are identified that describe the incipient motion of the drop. The moving angle is the first critical inclination angle at which the triple line is on the verge of being deformed from a given initial shape. The sliding angle is the second critical inclination angle at which the entire drop is in a state of impending motion. It was observed that the moving angle is a strong function of the initial contact angle. It was observed to increase initially and then decrease as the initial contact angle is increased. The sliding angle decreased monotonically as the initial contact angle is increased. A quantitative correlation is developed to explain the sliding angle as a function of the initial conditions. The predictions of this correlation have been shown to compare well with the experimental data from this study as well as with the literature. � 2014 Elsevier B.V.

The effect of antecedent conditions and specific rock fragment coverage on precipitation-driven soil erosion dynamics through multiple rainfall events was investigated using a pair of 6-m × 1-m flumes with 2.2% slope. Four sequential experiments – denoted E1, E2, E3 and E4, involved 2-h precipitation (rates of 28, 74, 74 and 28 mm h-1, respectively) and 22 h without rainfall – were conducted. In each experiment, one flume was bare while the other had 40% rock fragment coverage. The soil was hand-cultivated and smoothed before the first event (E1) only, and left untouched subsequently. Sediment yields at the flume exit reached steady-state conditions over time scales that increased with sediment size. Experiments were designed such that both steady and non-steady effluent sediment yields were reached at the conclusion of E1. Results from subsequent experiments showed that short-time soil erosion was dependent on whether steady-state erosion was achieved during the preceding event, although consistent steady-state effluent sediment yields were reached for each sediment size class. Steady-state erosion rates were, however, dependent on the rainfall intensity and its duration. If steady-state sediment yields were reached for a particular size class, that class’s effluent sediment yield peaked rapidly in the next rainfall event. The early peak was followed by a gradual decline to the steady-state condition. On the other hand, for size classes in which steady state was not reached at the end of the rainfall event (i.e., E1), in the following event (E2), the sediment yields for those classes increased gradually to steady state, i.e., the sharp peak was not observed. The effect of rock fragment cover (40%) on the soil surface was also found to be significant in terms of the time to reach steady state, i.e., their presence reduced the time for steady conditions to be attained. Effluent sediment yields for the bare and rock fragment-covered flumes (E1) showed steady conditions were reached for the latter, in contrast to the former. We used the Hairsine-Rose (H-R) model to simulate the experimental data as it explicitly models soil particle size classes. Experiments E1 and E2 involved soil compaction by raindrops, and in this case the model predictions were found to be unsatisfactory. However, compaction was effectively completed by the end of experiment E2, and the model provided reasonable predictions for experiments E3 and E4.

This paper examines dynamic binary response and multi-spell duration model approaches to analyzing longitudinal discrete-time binary outcomes. Prototypical dynamic binary response models specify low-order Markovian state dependence and restrict the effects of observed and unobserved heterogeneity on the probability of transitioning into and out of a state to have the same magnitude and opposite signs. In contrast, multi-spell duration models typically allow for state-specify c duration dependence, and allow the probability of entry into and exit from a state to vary flexibly. We show that both of these approaches are special cases within a general framework. We compare specific dynamic binary response and multi-spell duration models empirically using a case study of poverty transitions. In this example, both the specification of state dependence and the restrictions on the state-specific transition probabilities imposed by the simpler dynamic binary response models are severely rejected against the more flexible multi-spell duration models. Consistent with recent literature, we conclude that the standard dynamic binary response model is unacceptably restrictive in this context.

Dynamic analysis for flexible manipulator is very important for selecting the actuator size and designing the proper control strategy. The effect of different sets of initial and boundary conditions on the joints torques is investigated in this paper. The elastic deflection for each link is computed using the assumed modes methods for four modes of vibration. A third order polynomial trajectory is designed in the joint space and the required torques are obtained through the solution of the inverse dynamics problem. The obtained results showed that the boundary conditions have a considerable effect on the elastic deflection and the corresponding actuators’ torques as well.

We report simulations of gas-liquid two-phase flows in microchannels periodically patterned with grooves and ridges. A constant effective body force is applied on both fluids to simulate a pressure-driven creeping flow, and a diffuse-interface model is used to compute the interfacial evolution and the contact line motion. Depending on the body force, capillary force and the level of liquid saturation, a number of flow regimes may appear in the corrugated microchannel: gas flow, blockage, liquid flow, bubble-slug flow, droplet flow, annular flow and annular-droplet flow. A map of flow regimes is constructed for a set of geometric and flow parameters starting from a prescribed initial configuration. Some of the regimes are new, while others have been observed before in straight tubes and pipes. The latter are compared with previous experiments in terms of the regime map and the holdup ratio. The transition among flow regimes shows significant hysteresis, largely owing to the pinning of the interface at sharp corners in the flow conduit. Hysteresis is reduced if the sharp corners are rounded. Under the same operating conditions, different flow regimes can be realized from different initial conditions. The roles of geometry and wettability of the channel walls are also elucidated. © 2011 Elsevier Ltd.

A linear differential/integral operator is associated to a rational matrix in a natural way, and the behavior is defined to be the kernel of this operator. Conditions under which two rational matrices have the same behavior are derived.

This paper deals with the construction of random power series solution of second order linear differential equations of Hermite containing uncertainty through its coefficients and initial conditions. Under appropriate hypotheses on the data, we establish that the constructed random power series solution is mean square convergent. We provide conditions in order to obtain random polynomial solutions and, as a consequence, random Hermite polynomial are introduced. Also, the main statistical functions of the approximate stochastic process solution generated by truncation of the exact power series solution are given. Finally, we apply the proposed technique to several illustrative examples comparing the numerical results with respect to those provided by other available approaches including Monte Carlo simulation. © 2011 Elsevier Inc. All rights reserved., This work has been partially supported by the Spanish M.C.Y.T. and FEDER grants MTM2009-08587, DPI2010-20891-C02-01 as well as the Universitat Politecnica de Valencia grant PAID-06-09 (Ref. 2588).

International audience; The present paper introduces a new method to generate several independent periodic attractors, based on a switching piecewise-constant controller. We demonstrate here that the state space equidistant repartition of these attractors is on an arbitrarily precise zone of a paraboloid or plane. We determine the state space domains where the attractors are generated from different initial conditions. A mathematical formula giving their maximal number in function of the controller piecewise-constant values is then deduced.

In this paper we argue that the solitary solution of the Liouville equation produced by the Exp-function method does not satisfy the original differential equation for all initial conditions. Moreover, the region where the solution is correct is located entirely on a curve in the parameter plane of initial conditions. We derive the explicit equation for this curve and argue that classical Exp-function type methods cannot identify such constraints related to initial conditions.

A new iterative method of the fourth-order for the simultaneous determination of polynomial zeros is proposed. This method is based on a suitable zero-relation derived from the fourth-order method for a single zero belonging to the Schröder basic sequence. One of the most important problems in solving polynomial equations, the construction of initial conditions that enable both guaranteed and fast convergence, is studied in detail for the proposed method. These conditions are computationally verifiable since they depend only on initial approximations, the polynomial coefficients and the polynomial degree, which is of practical importance. The construction of improved methods in ordinary complex arithmetic and complex circular arithmetic is discussed. Finally, numerical examples and the comparison with existing fourth-order methods are given.

In this paper, we consider the approximation of general multivariable non commensurate fractional systems by integer order state space models. This work contains two main contributions. First, a new state space representation using the fractional integral operator is introduced. Second, the approximate model carries explicitly the initial conditions of the system. Two examples are given to illustrate the accuracy of the approximation.

International audience; Network epidemiology has mainly focused on large-scale complex networks. It is unclear whether findings of these investigations also apply to networks of small size. This knowledge gap is of relevance for many biological applications, including meta-communities, plant-pollinator interactions and the spread of the oomycete pathogen in networks of plant nurseries. Moreover, many small-size biological networks are inherently asymmetrical and thus cannot be realistically modelled with undirected networks. We modelled disease spread and establishment in directed networks of 100 and 500 nodes at four levels of connectance in six network structures (local, small-world, random, one-way, uncorrelated and two-way scale-free networks). The model was based on the probability of infection persistence in a node and of infection transmission between connected nodes. Regardless of the size of the network, the epidemic threshold did not depend on the starting node of infection but was negatively related to the correlation coefficient between in- and out-degree for all structures, unless networks were sparsely connected. In this case clustering played a significant role. For small-size scale-free directed networks to have a lower epidemic threshold than other network structures, there needs to be a positive correlation between number of links to and from nodes. When this correlation is negative (one-way scale-free networks), the epidemic threshold for small-size networks can be higher than in non scale-free networks. Clustering does not necessarily have an influence on the epidemic threshold if connectance is kept constant. Analyses of the influence of the clustering on the epidemic threshold in directed networks can also be spurious if they do not consider simultaneously the effect of the correlation coefficient between in- and out-degree.

In this work, approximate analytical solution of the sine-Gordon equation with initial conditions is obtained by the homotopy analysis method (HAM). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of the series solutions. It is shown that the solutions obtained by the variational iteration method (VIM) are only special cases of the HAM solutions. © 2008 Elsevier Inc. All rights reserved.

In this paper, nonlinear aeroelastic behavior of a two-dimensional symmetric rotor blade in the dynamic stall regime is investigated. Two different oscillation models have been considered here: pitching oscillation and flap-edgewise oscillation. Stall aeroelastic instability in such systems can potentially lead to structural damage. Hence it is an important design concern, especially for wind turbines and helicopter rotors, where such modes of oscillation are likely to take place. Most previous analyses of such dynamical systems are not exhaustive. System parameters like structural nonlinearity or initial conditions have not been studied which could play a significant role on the overall dynamics. In the present paper, a parametric study on the aeroelastic instability and the nonlinear dynamical behavior of the system has been performed. Emphasis is given on the effect of structural nonlinearity and initial conditions. The aerodynamic loads in the dynamic stall regime have been computed using the Onera model. The qualitative influence of the system parameters is different in the two systems studied. The effect of structural nonlinearity on the bifurcation pattern of the system response is significant in the case of pitching oscillation. The initial condition plays an important role on the aeroelastic stability as well as on the bifurcation pattern in both the systems. In the forced response study, interesting dynamical behavior, like period-3 response, has been observed in the pitching oscillation case. On the other hand, for the flap-edgewise oscillation case, super-harmonic and quasi-harmonic response have been found. � 2008 Elsevier Ltd. All rights reserved.

A one parameter family of iterative methods for the simultaneous approximation of simple complex zeros of a polynomial, based on a cubically convergent Hansen–Patrick's family, is studied. We show that the convergence of the basic family of the fourth order can be increased to five and six using Newton's and Halley's corrections, respectively. Since these corrections use the already calculated values, the computational efficiency of the accelerated methods is significantly increased. Further acceleration is achieved by applying the Gauss–Seidel approach (single-step mode). One of the most important problems in solving nonlinear equations, the construction of initial conditions which provide both the guaranteed and fast convergence, is considered for the proposed accelerated family. These conditions are computationally verifiable; they depend only on the polynomial coefficients, its degree and initial approximations, which is of practical importance. Some modifications of the considered family, providing the computation of multiple zeros of polynomials and simple zeros of a wide class of analytic functions, are also studied. Numerical examples demonstrate the convergence properties of the presented family of root-finding methods.

Sensitive dependence on initial conditions is widely understood as being the central idea of chaos. We first give sufficient conditions (both topological and ergodic) on an endomorphism to ensure the sensitivity property. Then, a strong sensitivity concept is introduced. Sufficient conditions on a transformation implying strong sensitivity are given. We also provide bounds for the strong sensitivity constant.

This discussion paper has led to a publication in The Refinement of Econometric Estimation and Test Procedures.An attempt is made to set rules for a fair and fruitful competition between alternative inference methods based on their performance in simulation experiments. This leads to a list of eight methodologic aspirations. Against their background we criticize aspects of many simulation studies that have been used in the past to compare competing estimators for dynamic panel data models. To illustrate particular pitfalls some further Monte Carlo results are produced, obtained from a simulation design inspired by an analysis of the (non-)invariance properties of estimators and occasionally by available higher-order asymptotic results. We focus on the very specific case of alternative implementations of one and two step generalized method of moments (GMM) estimators in homoskedastic stable zero-mean panel AR(1) models with random individual specific effects. We compare a few implementations, including GMM sytem estimators with alternative weight matrices, and illu! strate that an impartial evaluation of the outcome of a Monte Carlo based contest requires evidence - both analytical and empirical - on the completeness, orthogonality and relevance of the simulation design.