Localized Initial Conditions Research Articles

Multi-step variant of the parareal algorithm: convergence analysis and numerics

In this paper, we consider the problem of accelerating the numerical simulation of time dependent problems involving a multi-step time scheme by the parareal algorithm. The parareal method is based on combining predictions made by a coarse and cheap propagator, with corrections computed with two propagators: the previous coarse and a precise and expensive one used in a parallel way over the time windows. A multi-step time scheme can potentially bring higher approximation orders than plain one-step methods but the initialisation of each time window needs to be appropriately chosen. Our main contribution is the design and analysis of an algorithm adapted to this type of discretisation without being too much intrusive in the coarse or fine propagators. At convergence, the parareal algorithm provides a solution that coincides with the solution of the fine solver. In the classical version of parareal, the local initial condition of each time window is corrected at every iteration. When the fine and/or coarse propagators is a multi-step time scheme, we need to choose a consistent approximation of the solutions involved in the initialisation of the fine solver at each time windows. Otherwise, the initialisation error will prevent the parareal algorithm to converge towards the solution with fine solver’s accuracy. In this paper, we develop a variant of the algorithm that overcome this obstacle. Thanks to this, the parareal algorithm is more coherent with the underlying time scheme and we recover the properties of the original version. We show both theoretically and numerically that the accuracy and convergence of the multi-step variant of parareal algorithm are preserved when we choose carefully the initialisation of each time window.

CAPILLARY LEVELLING OF THIN LIQUID FILMS OF POWER-LAW RHEOLOGY

AbstractWe find solutions that describe the levelling of a thin fluid film, comprising a non-Newtonian power-law fluid, that coats a substrate and evolves under the influence of surface tension. We consider the evolution from periodic and localized initial conditions as separate cases. The particular (similarity) solutions in each of these two cases exhibit the generic property that the profiles are weakly singular (that is, higher-order derivatives do not exist) at points where the pressure gradient vanishes. Numerical simulations of the thin film equation, with either periodic or localized initial condition, are shown to approach the appropriate particular solution.

Soil temperature and local initial conditions drive carbon and nitrogen build-up in young proglacial soils in the Tropical Andes and European Alps

Climate warming has accelerated the retreat of mountain glaciers worldwide, exposing new areas to weathering, vegetation colonization, and soil formation. In light of probable climate changes such as warming and new extremes, understanding the factors that control soil organic carbon (SOC) and nitrogen build-up is crucial to comprehend proglacial soils and ecosystem formation. To this end, we examine the evolution of SOC, nitrogen (total N and NH4+), and phosphorus (available P) along nine 120-year chronosequences of deglacierization distributed between the European Alps and Tropical Andes. Our dataset includes geochemical analyses of 188 soil samples, in situ soil temperature data for the period 2019–2022, and hydrographic variables. Although time controls proglacial soil development at all sites, our study highlights distinct pedogenesis dynamics between proglacial landscapes depending on the micro and macro environmental context. Differences in soil development were strongly driven by growing degree days (GDD), maximum soil temperature, and parent material. Notably, we identified a positive effect of GDD on SOC and N (total N and NH4+), while our results indicate a negative effect of maximum soil temperature on SOC and NH4+, suggesting that overly high temperatures reduce microbial mineralization and organic matter input to the soil matrix. We reported the presence of higher initial SOC, total N, and NH4+ in the Andean sites than in the Alps sites, suggesting enhanced soil development at the Andean locations. This comparative study suggests the relative importance of maximum temperature and initial site conditions (e.g., parent materials, glacier biomes) during proglacial pedogenesis. Our findings highlight that soil temperature modulates pedogenesis in a complex way and suggest avoiding simply associating greater soil development with higher soil temperature in proglacial landscapes.

Pseudo-almost periodic $C^{0}$-solution for evolution inclusion with mixed nonlocal plus local initial conditions

This paper is devoted to the study of a class of evolution inclusion in Banach spaces with nonlocal plus local mixed initial conditions. Under some mild assumptions, a unique solvability result to the multivalued evolution problem is obtained via the arguments of fixed point principle and the theory of $C^0$-semigroup.

Global Prescribed Performance Control of Unknown Strict-Feedback Systems With Quantized References

This article is concerned with the global prescribed performance tracking control problem for strict-feedback systems with quantized references, unknown nonlinearities, and unmatched disturbances. Discontinuity appears frequently in such references, for which most nonlinear control or filtering methods are not applicable straightforward. Besides, the existing approaches of predefining tracking performance work under local initial conditions, available nonlinearity knowledge, disturbance-free cases, or have complexity issues. In this article, a novel smoothing function is first designed for the online automatic generation of smooth trajectories in place of the quantized reference. Then, the tangent barrier functions are combined with a new form of performance functions (inverse proportional functions) to form a control. The strong robustness of the resulting controller against model uncertainties and disturbances evades the need for approximation, observation, etc., yielding simplicity of the control. The new performance functions relax the specific initial condition. Their combination ensures for any initial condition, the tracking error converges to a given bound. Simulation results on vehicular platoons illustrate the theoretical findings.

A FEM‐PD coupling based on Arlequin approach to impose boundary conditions in peridynamics

AbstractThe peridynamic approach (PD) is a continuous theory that is well suited for solving damage problems. Because of the nonlocal formulation, PD can predict the response of a material and fracture patterns with high probability in high dynamic processes. In PD, some parameters differ from the continuum formulation and have some deviation in discretized PD systems, such as a horizon. A material constant becomes a parameter dependent on the mesh size. A sticking point, which has to be considered, is that an incomplete horizon at the boundaries results in an unphysical variation of the material's stiffness in these regions. Material points at the boundaries do not have an entire nonlocal neighborhood, meaning the points have fewer bonds and are softer than points within the domain. This leads to the so‐called surface effect. The difficulties in applying the classical local initial and boundary conditions happen because of the nonlocal character of the PD. To overcome this problem, several correction techniques have been developed. Nevertheless, a standard method to describe them is not available yet. An alternative approach is the application of the earlier proposed FEM‐PD coupling, which can be seen as a local‐nonlocal coupling method. The damage‐free zones are analyzed by the FEM as classical local theory, while the domain where the fracture is expected is modeled with the PD as a nonlocal theory. Consequently, the reduction of the computational effort as well as the imposing of the conventional local boundary conditions, is achieved. The coupling method is based on the Arlequin method—an energy‐based procedure where the energy of a system is found as a weighted average of both systems. The mechanical compatibility in the overlapping zone of both domains is reached by implementing constraints with the help of the penalty method. In the paper at hand, the focus is on imposing BCs. The proposed method is applied to both static and dynamic applications. The accuracy and convergence behavior is evaluated by analyzing test examples.

The International Heat Stress Genotype Experiment for modeling wheat response to heat: field experiments and AgMIP-Wheat multi-model simulations

The data set contains a portion of the International Heat Stress Genotype Experiment (IHSGE) data used in the AgMIP-Wheat project to analyze the uncertainty of 30 wheat crop models and quantify the impact of heat on global wheat yield productivity. It includes two spring wheat cultivars grown during two consecutive winter cropping cycles at hot, irrigated, and low latitude sites in Mexico (Ciudad Obregon and Tlaltizapan), Egypt (Aswan), India (Dharwar), the Sudan (Wad Medani), and Bangladesh (Dinajpur). Experiments in Mexico included normal (November-December) and late (January-March) sowing dates. Data include local daily weather data, soil characteristics and initial soil conditions, crop measurements (anthesis and maturity dates, anthesis and final total above ground biomass, final grain yields and yields components), and cultivar information. Simulations include both daily in-season and end-of-season results from 30 wheat models. All data are available via DOI 10.7910/DVN/CJJBSR.

A high-yielding traits experiment for modeling potential production of wheat: field experiments and AgMIP-Wheat multi-model simulations

Grain production must increase by 60% in the next four decades to keep up with the expected population growth and food demand. A significant part of this increase must come from the improvement of staple crop grain yield potential. Crop growth simulation models combined with field experiments and crop physiology are powerful tools to quantify the impact of traits and trait combinations on grain yield potential which helps to guide breeding towards the most effective traits and trait combinations for future wheat crosses. The dataset reported here was created to analyze the value of physiological traits identified by the International Wheat Yield Partnership (IWYP) to improve wheat potential in high-yielding environments. This dataset consists of 11 growing seasons at three high-yielding locations in Buenos Aires (Argentina), Ciudad Obregon (Mexico), and Valdivia (Chile) with the spring wheat cultivar Bacanora and a high-yielding genotype selected from a doubled haploid (DH) population developed from the cross between the Bacanora and Weebil cultivars from the International Maize and Wheat Improvement Center (CIMMYT). This dataset was used in the Agricultural Model Intercomparison and Improvement Project (AgMIP) Wheat Phase 4 to evaluate crop model performance when simulating high-yielding physiological traits and to determine the potential production of wheat using an ensemble of 29 wheat crop models. The field trials were managed for non-stress conditions with full irrigation, fertilizer application, and without biotic stress. Data include local daily weather, soil characteristics and initial soil conditions, cultivar information, and crop measurements (anthesis and maturity dates, total above-ground biomass, final grain yield, yield components, and photosynthetically active radiation interception). Simulations include both daily in-season and end-of-season results for 25 crop variables simulated by 29 wheat crop models.

Labor market integration, local conditions and inequalities: Evidence from refugees in Switzerland

The paper examines the patterns of economic integration of refugees in Switzerland, a country with a long tradition of hosting refugees, a top-receiving host in Europe, and a prominent example of a multicultural society. It relies on a unique longitudinal dataset consisting of administrative records and social security data for the universe of refugees in Switzerland over 1998–2018. This data is used to reconstruct the individual-level trajectories of refugees and to follow them since arrival over the life-cycle. The empirical analysis exploits the government dispersal policy in place since 1998, which consists of the exogenous allocation of refugees across cantons, to identify the effects of the local initial conditions. The study finds that higher unemployment rates at arrival slow down the integration process, whereas the existence of a co-ethnic network does not consistently lead to a faster integration. It is shown that a change toward more restrictive attitudes over time in a canton (relative to attitudes in other cantons) leads to higher employment rates of the successive refugee cohorts. These effects persist over the refugees’ life-cycle. Together these results, highlight the importance of taking a longer run perspective when examining the effectiveness of policies, as the effects may vary over time and different complementary interventions may be needed in the short vs. long-run.

Coupled model biases and extended‐range prediction skill during the onset phase of the Indian summer monsoon with different initializations related to land surface and number of observations

AbstractIn this study, we have analyzed the role of the initialization in the forecast of the monsoon onset phase beyond 10 days lead time (i.e., in the extended range) to understand the impact of displacement or shift in initial conditions in the extended‐range forecast. Two displacement errors are considered: (a) the initial error arising due to a change in land surface initial conditions and (b) the initial error arising due to a change in the number of observations. For the first part (a), we have analyzed and compared the difference in prediction skills in the United Kingdom Met Office (UKMO) GloSea5 forecasts run with two different land surface initial conditions (IC) configurations. In one configuration, the IC is prepared using a monthly land surface climatology; in the other configuration, it is based on daily land surface reanalysis. In the other part (b), we used the Indian Institute of Tropical Meteorology's Climate Forecast System (IITM_CFS) model with two different ICs (NCEP and NCMRWF differing in the number of observations over the Indian land region). Both runs indicate a shift in the initial condition, which manifests as displacement error. UKMO and IITM_CFS runs have the same land surface model when the corresponding twin experiments are compared in (a) and (b). Analysis of the initial displacement errors from these runs indicates that improving the realism in the land surface initial conditions can effectively modulate or change the surface meteorological fields in the prediction model during the onset phase. The result shows that the rotational and divergence components of the surface winds differ in the two sets of runs. Results also indicate that the difference in surface initialization manifests as differences in rotational and divergent kinetic energy. This could lead to a difference in the forecast of monsoon onset rain. Further analysis also suggests that the local land surface initial condition error, in addition to an error in large‐scale teleconnections, affects the monsoon onset forecast and its prediction skill in the extended‐range time‐scale.

Hereditary Mathematical Model of the Dynamics of Radon Accumulation in the Accumulation Chamber

Mathematical modeling is used to study the hereditary mechanism of the accumulation of radioactive radon gas in a chamber with gas-discharge counters at several observation points in Kamchatka. Continuous monitoring of variations in radon volumetric activity in order to identify anomalies in its values is one of the effective methods for studying the stress–strain state of the geo-environment with the possibility of building strong earthquake forecasts. The model equation of radon transfer, taking into account its accumulation in the chamber and the presence of the hereditary effect (heredity or memory), is a nonlinear differential Riccati equation with non-constant coefficients with a fractional derivative in the sense of Gerasimov–Caputo, for which local initial conditions are set (Cauchy problem). The proposed hereditary model of radon accumulation in the chamber is a generalization of the previously known model with an integer derivative (classical model). This fact indicates the preservation of the properties of the previously obtained solution according to the classical model, as well as the presence of new properties that are applied to the study of radon volumetric activity at observation points. The paper shows that due to the order of the fractional derivative, as well as the quadratic nonlinearity in the model equation, the results of numerical simulation give a better approximation of the experimental data of radon monitoring than by classical models. This indicates that the hereditary model of radon transport is more flexible, which allows using it to describe various anomalous effects in the values of radon volume activity.

A Symbolic Method for Solving a Class of Convolution-Type Volterra–Fredholm–Hammerstein Integro-Differential Equations under Nonlocal Boundary Conditions

Integro-differential equations involving Volterra and Fredholm operators (VFIDEs) are used to model many phenomena in science and engineering. Nonlocal boundary conditions are more effective, and in some cases necessary, because they are more accurate measurements of the true state than classical (local) initial and boundary conditions. Closed-form solutions are always desirable, not only because they are more efficient, but also because they can be valuable benchmarks for validating approximate and numerical procedures. This paper presents a direct operator method for solving, in closed form, a class of Volterra–Fredholm–Hammerstein-type integro-differential equations under nonlocal boundary conditions when the inverse operator of the associated Volterra integro-differential operator exists and can be found explicitly. A technique for constructing inverse operators of convolution-type Volterra integro-differential operators (VIDEs) under multipoint and integral conditions is provided. The proposed methods are suitable for integration into any computer algebra system. Several linear and nonlinear examples are solved to demonstrate the effectiveness of the method.

Wider economic benefits of transport corridors: Evidence from international development organizations

This paper collects data on transport corridor projects financed by the Asian Development Bank, Japan International Cooperation Agency, and World Bank and links them to a wider economic benefit—local economic activity. The paper uses the difference-in-differences methodology to link the variation in country and local initial conditions, and project characteristics to local economic activity. Construction of a new (greenfield) corridor is associated with higher growth in economic activity around the corridor than the rehabilitation or expansion of an existing corridor. Private sector involvement in the operation and management of infrastructure is associated with lower growth in economic activity along the corridors. In the short to medium term, corridor investments with a larger geographic scope are associated with increased growth in economic activity along them, while in the long term, there is no significant difference relative to smaller-scope corridor investments. The initial conditions do not seem to influence how corridor investments affect the growth in economic activity.

A critique of the EIA Report selected from the East African region, taking into consideration what is required in an ideal of EIA Report

At present, every country strives to realize development for its people. Therefore, to achieve this requires the construction of various projects for the realization of a country's socio-economic and political development. However, the development of the projects is associated with various ecological challenges that can have an impact on society as a whole and the environment. Therefore, there is a need to conduct an environmental impact assessment (EIA), a tool that can be used to determine the environmental, social and economic impacts of a project before making a decision. The EIA process is linked to the detailed report containing all possible environmental, social and health impacts after, during and after the project. Therefore, this paper aims to deliver the critique of one of the EIA reports in the East African region. To achieve this, EIA legislation and guidelines for preparing and verifying EIA reports in the East African region will be examined. The critique contains the issues that include the advisory team (environmental and social impact assessment team), an executive or non-technical summary, a description of the proposed project, a description of the development, the local environment and initial conditions, the political, legal and administrative framework, and public participation/stakeholder analysis in the EIA process.

Generalized exponential function and initial value problem for conformable dynamic equations

<abstract><p>In this article, we define the generalized exponential function on arbitrary time scales in the conformable setting and develop its fundamental characteristics. We address the fundamental theory of a conformable fractional dynamic equation on time scales, subject to the local and non-local initial conditions. We generalized the Grönwall type inequalities in a conformable environment. The generalized exponential function and the Grönwall's inequalities are indispensable for the study of the qualitative aspects of the local initial value problem. We developed some criteria related to global existence, extension and boundedness, as well as stability of solutions.</p></abstract>

Bjorken flow attractors with transverse dynamics

In the context of the longitudinally boost-invariant Bjorken flow with transverse expansion, we use three different numerical methods to analyze the emergence of attractor solutions in an ideal gas of massless particles exhibiting constant shear viscosity to entropy density ratio $\eta / s$. The fluid energy density is initialized using a Gaussian profile in the transverse plane, while the ratio $\chi = \mathcal{P}_L / \mathcal{P}_T$ between the longitudinal and transverse pressures is set at initial time $\tau_0$ to a constant value $\chi_0$ throughout the system employing the Romatschke-Strickland distribution. We introduce the hydrodynamization time $\delta \tau_H = (\tau_H - \tau_0)/ \tau_0$ based on the time $\tau_H$ when the standard deviation $\sigma(\chi)$ of a family of solutions with different $\chi_0$ reaches a minimum value at the point of maximum convergence of the solutions. In the $0+1{\rm D}$ setup, $\delta \tau_H$ exhibits scale invariance, being a function only of $(\eta / s) / (\tau_0 T_0)$. With transverse expansion, we find a similar $\delta \tau_H$ computed with respect to the local initial temperature, $T_0(r)$. We highlight the transition between the regimes where the longitudinal and transverse expansions dominate. We find that the hydrodynamization time required for the attractor solution to be reached increases with the distance from the origin, as expected based on the properties of the $0+1{\rm D}$ system defined by the local initial conditions. We argue that hydrodynamization is predominantly the effect of the longitudinal expansion, being significantly influenced by the transverse dynamics only for small systems or for large values of $\eta / s$.

Stability of Nonlocal Stochastic Volterra Equations

In this paper, we study Ulam-Hyers-Rassias stability of solutions for nonlocal stochastic Volterra equations. Sufficient conditions for the existence and stability of solutions are derived using the Gronwall lemma. The advantage of our model equation is that it allows for additional measurements leading to better results compared to models with local initial conditions. Examples are solved to illustrate the applications of the results.

Nonlinear Volterra delay evolution inclusions subjected to nonlocal initial conditions

This paper deals with a nonlinear Volterra delay evolution inclusion subjected to a nonlocal implicit initial condition. The evolution inclusion involves an $m$-dissipative operator (possibly multivalued and/or nonlinear) and a noncompact interval. We first consider the evolution inclusion subjected to a local initial condition and prove an existence result for bounded $C^0$-solutions. Then, using a fixed point theorem for upper semicontinuous multifunctions with contractible values, we obtain a global solvability result for the original problem. Finally, we present an example to illustrate the abstract result.

The fractional nonlinear {mathcal{PT}} dimer

We examine a fractional discrete nonlinear Schrodinger dimer, where the usual first-order derivative in the time evolution is replaced by a non integer-order derivative. The dimer is nonlinear (Kerr) and {mathcal{{PT}}}-symmetric, and for localized initial conditions we examine the exchange dynamics between both sites. By means of the Laplace transformation technique, the linear {{mathcal{{PT}}}} dimer is solved in closed form in terms of Mittag–Leffler functions, while for the nonlinear regime, we resort to numerical computations using the direct explicit Grunwald algorithm. In general, we see that the main effect of the fractional derivative is to produce a monotonically decreasing time envelope for the amplitude of the oscillatory exchange. In the presence of {mathcal{{PT}}} symmetry, the oscillations experience some amplification for gain/loss values below some threshold, while beyond threshold, the amplitudes of both sites grow unbounded. The presence of nonlinearity can arrest the unbounded growth and lead to a selftrapped state. The trapped fraction decreases as the nonlinearity is increased past a critical value, in marked contrast with the standard (non-fractional) case.

Design of multi-wing 3D chaotic systems with only stable equilibria or no equilibrium point using rotation symmetry

Some dissipative dynamical systems only have stable equilibria or have no equilibrium point but are able to generate chaos of non-Sil’nikov type. This category of chaotic attractors belong to hidden attractor, which is difficult to be located in the phase space. In this work, we aim at designing multi-wing 3D chaotic systems with hidden attractors. We first proposes a quadratic system with only two stable node-foci, which can generate double-wing chaotic hidden attractor. Using rotation symmetry, we construct multi-fold cover of the quadratic system and obtain multiple symmetric stable equilibria. Two examples of 2-fold and 3-fold covers of the chaotic system are presented. Furthermore, the rotation symmetry is applied to no-equilibrium system to generate multi-wing chaotic hidden attractors. By means of bifurcation diagram, finite-time Lyapunov exponents, phase portraits, and attraction basins, it is shown that the multi-wing chaotic attractors always coexist with stable point attractors. The local initial condition areas and complex boundaries for different coexisting attractors are addressed. Finally, the designed systems are implemented by analog circuit and microcontroller to verify the multi-wing hidden attractors.