Initial Conditions Research Articles

Convergence Analysis of Value Iteration Adaptive Dynamic Programming for Continuous-Time Nonlinear Systems.

This article is concerned with the convergence property and error bounds analysis of value iteration (VI) adaptive dynamic programming for continuous-time (CT) nonlinear systems. The size relationship between the total value function and the single integral step cost is described by assuming a contraction assumption. Then, the convergence property of VI is proved while the initial condition is an arbitrary positive semidefinite function. Moreover, the accumulated effects of approximation errors generated in each iteration are taken into consideration while using approximators to implement the algorithm. Based on the contraction assumption, the error bounds condition is proposed, which ensures the approximated iterative results converge to a neighborhood of the optimum, and the relation between the optimal solution and approximated iterative results is also derived. To make the contraction assumption more concrete, an estimation way is proposed to derive a conservative value of the assumption. Finally, three simulation cases are given to validate the theoretical results.

From tomographic imaging to numerical simulations: an open-source workflow for true morphology mesoscale FE meshes

Full-field techniques such as tomography are becoming progressively more central in the study of complex phenomena, in particular where spatiotemporal evolution is crucial, as in moisture transport or crack initiation in porous media. These techniques provide a unique insight in the local process whose quantification allows the improvement of our understanding and of the models describing them. Nevertheless, the model validation can be pushed further by attempting to explicitly represent the heterogeneities and simulate their role in the processes. Once validated, these models can be used to perform “virtual experiments”, and overcome the limitations of the experiments (e.g., sample size and number, fine control of the boundary and initial conditions). This study proposes a connection between tomography images and mesoscale models through a workflow that mainly employs open-source tools. This workflow is illustrated through the digitization of a Portland cement concrete sample, stemming from neutron tomographies and resulting in a numerical finite element mesh. The proposed workflow is flexible, allowing for the conversion of images from various sources, such as x-ray or neutron tomographies, to different numerical representations of the domain, such as finite element meshes or even a discrete domain required by discrete element methods, while preserving real morphologies with an accuracy proportionate to the specific need of the problem. Beside its generalizability, our method also offers automated labelling of the different domains and boundaries in both the volumetric and surface meshes, which is often necessary for assigning material properties and boundary conditions. Finally, the series of image, geometry and mesh processing steps described in this work are made available on a GitHub repository.

FTDO-based adaptive fuzzy fixed-time tracking control for uncertain unmanned helicopter with output constraints

During the actual flight of unmanned helicopters, there are widespread output constraints, system uncertainties and external disturbances, which bring significant threats to their safe flight. To keep the output constraints from violating predefined boundaries, the barrier Lyapunov function (BLF) is utilized in this paper. The system uncertainties are estimated by the fuzzy logic system (FLS). The compound disturbances composed of the external disturbances and the approximation errors caused by FLS are approximated by the fixed-time disturbance observers (FTDOs). According to the analysis of FTDOs and fixed-time stability theory, the observer errors and state errors converge to a region of the origin in fixed-time, and the appropriate parameters of FTDOs and controller are designed to ensure that the disturbance convergence time is faster than the one of the proposed controller, which further improves the stability of the system. Moreover, the convergence time of the FTDOs FTDOs and the proposed approach only depends on the design parameters under any initial conditions with constrained outputs. The performance of the proposed control approach is verified through the simulation results.

Study of radiative shocks using 2D interferometry and XUV spectroscopy

We report new experimental results on radiative shocks obtained in Xenon and Argon in gas cells at two different pressures below 1 bar. These shock waves are generated by the interaction of the PALS iodine laser on a CH–Au foil with a typical velocity in the range of 50–100 km/s depending on the variable laser intensity, pressure, and gas. Attention is paid to the morphology and the dynamics of the radiative precursor over large time scales up to 30 ns, using 2D sub-picosecond visible interferometry, illustrating the complex interplay of hydrodynamic and radiation absorption for different initial conditions. The comparison between 1D and 2D simulations confirms the role played by lateral radiative losses in the ionization wave and the necessity of state-of-the-art integrated opacities. This study is complemented by the first XUV analysis of the shock emission between 5 and 20 nm obtained with a grating spectrometer, with line identification, which is compatible with the ionization stages deduced from interferometry and simulations.

Modified λ-Policy Iteration Based Adaptive Dynamic Programming for Unknown Discrete-Time Linear Systems.

In this article, the λ -policy iteration ( λ -PI) method for the optimal control problem of discrete-time linear systems is reconsidered and restated from a novel aspect. First, the traditional λ -PI method is recalled, and some new properties of the traditional λ -PI are proposed. Based on these new properties, a modified λ -PI algorithm is introduced with its convergence proven. Compared with the existing results, the initial condition is further relaxed. The data-driven implementation is then constructed with a new matrix rank condition for verifying the feasibility of the proposed data-driven implementation. A simulation example verifies the effectiveness of the proposed method.

Fiboquadratic numbers and Rithmomachia

Abstract This paper shows our discovery of the fiboquadratic numbers, quadratic Fibonacci numbers in rithmomachia. This board game consists in performing mathematical operations to attack an opponent through geometric numbered pieces. We will show that the numbers on the board pieces are the first terms of six sequences that we will define through a recursive pattern of superpartients. We then prove that this extension is the solution of a recurrence relation with initial conditions, and therefore, is unique. The fiboquadratic numbers we introduce in this work are not limited to the context of this board. In general, we can generate any fiboquadratic sequence with arbitrary initial conditions.

Prediction of regional infrasound produced by supersonic sources using a ray-based Mach cone source.

The geometry of the Mach cone produced by a supersonic source is analyzed and mapped into initial conditions used in acoustic ray tracing. The resulting source model is combined with spherical geometry ray tracing methods to enable propagation simulations for infrasonic signals produced by bolides, space debris, rockets, aircraft, and other fast-than-sound sources out to typical infrasonic observation distances of hundreds or thousands of kilometers. Idealized linear and parabolic trajectories typical of bolides and rockets, respectively, are used to demonstrate the calculation of regional infrasonic signals produced by such sources and characteristics of the radiated infrasonic waves are found to vary strongly with the geometry of the trajectory and atmospheric structure. Predicted regional infrasonic signals are compared with those observed from a November 2020 bolide that passed over Scandinavia using a combination of institutionally maintained infrasound stations and "citizen scientist" data from the Raspberry Shake data repository.

Vertical water entry of a cylinder considering wind and linearly sheared flow effect: A numerical investigation

Objects entering water is a complex multiphase flow event that exhibits nonlinear and transient characteristics. This study examines the impact cavities, multiphase flow characteristics, and motion behaviors of a cylinder during vertical water entry, considering different flow and entry velocities. A three-dimensional model was carried out using OpenFOAM® framework, taking into account the effects of wind and linearly sheared flow through newly customized initial and boundary conditions. The overset mesh technique was applied to capture the water entry trajectories of the moving cylinder. Numerical results for the cavity evolution and cylinder motion behaviors were validated against published laboratory tests. The cavity closure patterns were classified into four categories based on the evolution characteristics, which were found to be more complex than those observed under calm water and uniform current conditions. Furthermore, the rapid closure of the splash dome results in a unique cavity flow phenomenon, which creates a suction air channel. The velocities of the flow and water entry have a noticeable impact on the closure modes and time of the cavity. This, accordingly, affects the motion characteristics of the cylinder, as well as the evolution of the velocity field, pressure field, and vortex structures.

Evaluation of the WRF-solar model for 72-hour ahead forecasts of global horizontal irradiance in West Africa: A case study for Ghana

Accurate global horizontal irradiance (GHI) forecasting is critical for integrating solar energy into the power grid and operating solar power plants. The Weather Research and Forecasting model with its solar radiation extension (WRF-Solar) has been used to forecast solar irradiance in different regions around the world. However, the application of the WRF-Solar model to the prediction of GHI in West Africa, particularly Ghana, has not yet been investigated. The aim of this study is to evaluate the performance of the WRF-Solar model for predicting GHI in Ghana, focusing on three automatic weather stations (Akwatia, Kumasi and Kologo) for the year 2021. We used two one-way nested domains (D1 = 15 km and D2 = 3 km) to investigate the ability of the fully coupled WRF-Solar model to forecast GHI up to 72-hour ahead under different atmospheric conditions. The initial and lateral boundary conditions were taken from the ECMWF high-resolution operational forecasts. Our findings reveal that the WRF-Solar model performs better under clear skies than cloudy skies. Under clear skies, Kologo performed best in predicting 72-hour GHI, with a first day nRMSE of 9.62 %. However, forecasting GHI under cloudy skies at all three sites had significant uncertainties. Additionally, WRF-Solar model is able to reproduce the observed GHI diurnal cycle under high AOD conditions in most of the selected days. This study enhances the understanding of the WRF-Solar model’s capabilities and limitations for GHI forecasting in West Africa, particularly in Ghana. The findings provide valuable information for stakeholders involved in solar energy generation and grid integration towards optimized management in the region.

Influence of Weather and Climate on Multidecadal Trends in Atlantic Hurricane Genesis and Tracks

Abstract This study investigates the relative roles of sea surface temperature–forced climate changes and weather variability in driving the observed eastward shift of Atlantic hurricane tracks over the period from 1970 to 2021. A 10-member initial condition ensemble with a ∼25-km horizontal resolution tropical cyclone permitting atmospheric model (GFDL AM2.5-C360) with identical sea surface temperature and radiative forcing time series was analyzed in conjunction with historical hurricane track observations. While a frequency increase was recovered by all the simulations, the observed multidecadal eastward shift in tracks was not robust across the ensemble members, indicating that it included a substantial contribution from weather-scale variability. A statistical model was developed to simulate expected storm tracks based on genesis location and steering flow, and it was used to conduct experiments testing the roles of changing genesis location and changing steering flow in producing the multidecadal weather-driven shifts in storm tracks. These experiments indicated that shifts in genesis location were a substantially larger driver of these multidecadal track changes than changes in steering flow. The substantial impact of weather on tracks indicates that there may be limited predictability for multidecadal track changes like those observed, although basinwide frequency has greater potential for prediction. Additionally, understanding changes in genesis location appears essential to understanding changes in track location. Significance Statement From the 1970s to the present, there has been an increase in the frequency of North Atlantic hurricanes, but they have also shifted in location to the east, away from land. We explore whether this shift in hurricanes’ locations was caused by climatic factors or randomness to understand if and how these trends will persist. We also consider whether the shift was due to a change in where hurricanes started or how they moved over their lifespan. Analyzing data from observed and simulated hurricanes, we find that the shift was made more likely by climate factors, but ultimately occurred due to random variability in the hurricanes’ starting locations. These results suggest a higher uncertainty in the future location and impact of hurricanes and highlight the importance of studying why hurricanes originate where they do.

An exact model for enhancing/suppressing primordial fluctuations

Abstract Enhancements of primordial curvature fluctuations in single field inflation often involve departures from attractor trajectories in the phase space. We study enhancement/suppression of primordial fluctuations in one of the simplest models with exact background solutions for arbitrary initial conditions: a single field inflationary model with a piecewise exponential potential. We then present close to exact analytical solutions for primordial fluctuations in a general transition between two slow-roll attractors, valid whether the first slow parameter increases or decreases. The main features in the primordial spectrum are determined by the ratio of exponents of the potential. We also discuss the imprint of such features in the induced GW spectrum. Lastly, we apply the δN formalism to discuss non-Gaussianities and the tail of the probability distribution. We find that while non-Gaussianities are at most 𝒪(1) in the case of enhancement, they can be very large in the case of suppression. Our work can be easily generalized to multiple piecewise exponential potentials.

Satellite Attitude Control Using Faulty Double Gimbal Variable Speed Control Moment Gyroscope

A rigid satellite attitude control requires stable finite-time attitude convergence in the presence of rotation unwinding, external disturbances, and actuator faults. To achieve this, a new nonsingular fast fixed-time sliding mode controller is proposed to ensure finite-time convergence independent of the initial conditions of the system. Rotation unwinding is addressed using the body and shadow pair of the Modified Rodrigues Parameters (MRPs). Convergence behavior of the states errors in the neighborhood of the MRPs switching surface is also addressed. Attitude control is achieved using a double-gimbal variable-speed control moment gyro (DGVSCMG). For the first time, a DGVSCMG having all possible electrical and mechanical faults is considered for control design. A novel nonsingular fast fixed-time anti-unwinding fault-tolerant sliding control using a new sliding surface is proposed. This eliminates switching of the sliding surfaces and minimizes control chattering. Four new propositions are proposed and proved to establish fast fixed-time global stability of the system for tracking maneuver in fault and fault-free conditions with anti-unwinding. Simulation results are presented and compared with existing fixed-time sliding control approaches. The results show superiority of the proposed anti-unwinding fault-tolerant fast fixed-time control for the tracking maneuver in terms of convergence time, energy efficiency, and fault tolerance.

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.

Efficient Algorithm Set Forming for the Computing Resources Distribution in Heterogeneous Dynamic Computational Environments Based on the Ontology Usage

Purpose of research. The purpose of this research is to develop an ontology structure as the basis of a database/knowledge base for selecting effective metaheuristic algorithms for solving the problem of load distribution in heterogeneous distributed dynamic computing environments, taking into account the overhead of data transmission over the network.Methods. The main scientific methods used in this study are domain analysis, methods for constructing subject ontologies, numerical optimization methods and computer modeling.Since the literature does not present resource allocation planning models that would take into account geographic distribution, the presence of intermediate data transmission routes, the dynamics of topologies and load, as well as system heterogeneity in terms of criteria for assessing the quality of load distribution, this article proposes a new model that takes into account these features. The complexity of solving a planning problem becomes one of the variable parameters, which has a significant impact on the planning result: with a decrease in the complexity of calculations, the result deteriorates accordingly. Therefore, a greedy strategy is proposed as a solution method: from the optimization methods to be considered, select the least labor-intensive one that would allow obtaining the best result in the allotted time. Test runs of simulated annealing algorithms demonstrate different effectiveness under different initial conditions of the problem; therefore, it is advisable for selected classes of problems to choose algorithms that are effective in terms of solution quality and labor intensity.Results. The result of the study is the structure of the ontology of effective algorithms. Also, the results are instances of simulated annealing algorithms and tasks included in the ontology, related by the “efficiency” relation.Conclusion. This article proposes the structure of an ontology of effective optimization algorithms and an approach to solving the problem of distributing the computational load, taking into account the complexity of the distribution procedure through the “greedy” selection of the most effective optimization algorithms.

A geometrical approach for consensus security

Guaranteeing security against eavesdroppers while allowing agents to reach an agreement on some shared variables is an essential feature to foster the adoption of distributed protocols. In the literature, a wide variety of methodologies have been developed in the discrete-time case, and most of them rely on encryption and undirected graphs, often exhibiting quantization or accuracy issues. In this paper, we develop a continuous-time secure consensus algorithm for agents that communicate via a broadcast-only protocol over directed and strongly connected graphs. In detail, the legitimate agents interact by exchanging an extended state, which can be converted into the hidden consensus state via a pre-deployed shared vector, thus preventing eavesdropping. In this paper, we take a geometrical perspective, and we implement our encryption via coordinate shifts. This choice guarantees, on one side, the existence of an uncountable infinity of possible vectors and, on the other side, provides a control-theoretical viewpoint on encryption that naturally blends with a dynamical system. We complement our framework by providing an additional layer of protection against honest but curious legitimate nodes, preventing them from gaining insights into the initial condition of their peers.

Uncertain data in initial boundary value problems: Impact on short and long time predictions

We investigate the influence of uncertain data on solutions to initial boundary value problems with well posed boundary conditions. Uncertainty in the forcing function, initial conditions and boundary conditions are considered and we quantify their relative influence for short and long time calculations. For short time calculations, uncertainty in the initial data dominates. As time grows, the influence of initial data vanishes exponentially fast. For longer time calculations, the uncertainty in the forcing function and boundary data dominate, as they grow in time. Errors due to the forcing function grow faster (linearly in time) than the ones due to the boundary data (grow as the square root of time). Roughly speaking, the results indicate that for short time calculations, the initial conditions are the most important, but for longer time calculations, focus should be on the forcing function and boundary conditions. The findings are especially important when similar mathematical and numerical techniques are used for both short and long times. Our qualitative results can guide more quantitative investigations where details of the uncertain data are known.

Modified Integral Transform for Solving Benney-Luke and Singular Pseudo-Hyperbolic Equations

Abstract In this article, we propose a technique based on modified double integral transforms used to solve certain equations of materials science, namely Benney–Luke (BL) and singular pseudo-hyperbolic (SP-H) equations. We have established some analytical results. This method can provide accurate one-step solutions, although the equations used may exhibit a singularity in the initial conditions. Some numerical examples have been discussed for illustration and to show the effectiveness of the technique for certain types of equations. We have developed an exact solution in just one step, whereas other approaches require several stages to succeed in a particular solution, making the proposed strategy particularly successful and straightforward to apply to various varieties of the B–L and SP-H equations.

The rise of data-driven weather forecasting: A first statistical assessment of machine learning-based weather forecasts in an operational-like context

Abstract Data-driven modeling based on machine learning (ML) is showing enormous potential for weather forecasting. Rapid progress has been made with impressive results for some applications. The uptake of ML methods could be a game-changer for the incremental progress in traditional numerical weather prediction (NWP) known as the “quiet revolution” of weather forecasting. The computational cost of running a forecast with standard NWP systems greatly hinders the improvements that can be made from increasing model resolution and ensemble sizes. An emerging new generation of ML models, developed using high-quality reanalysis datasets like ERA5 for training, allow forecasts that require much lower computational costs and that are highly-competitive in terms of accuracy. Here, we compare for the first time ML-generated forecasts with standard NWP-based forecasts in an operational-like context, initialized from the same initial conditions. Focusing on deterministic forecasts, we apply common forecast verification tools to assess to what extent a data-driven forecast produced with one of the recently developed ML models (PanguWeather) matches the quality and attributes of a forecast from one of the leading global NWP systems (the ECMWF IFS). The results are very promising, with comparable accuracy for both global metrics and extreme events, when verified against both the operational IFS analysis and synoptic observations. Overly smooth forecasts, increasing bias with forecast lead time, and poor performance in predicting tropical cyclone intensity are identified as current drawbacks of ML-based forecasts. A new NWP paradigm is emerging relying on inference from ML models and state-of-the-art analysis and reanalysis datasets for forecast initialization and model training.

Dental Care for Cancer Patients in the Prevention of Complications of Chemotherapy and Head and Neck Radiation Therapy

Oncological diseases occupy one of the first places in the structure of disability and mortality of the population. The main methods of treating patients with malignant tumors in the maxillofacial area are surgical method, radiation therapy and chemotherapy. Treatment with only one of the listed methods It is rarely performed, mainly at the stage of cancer in situ or stage I of the disease. The treatment depends on the clinical and morphological characteristics of the tumor and requires the use of all methods simultaneously or in a certain sequence. Radiation and chemotherapy treatments not only have systemic side effects, but also side effects in the treatment area. Against the background of antitumor treatment, there is an exacerbation of concomitant chronic diseases, including odontogenic ones. Pathological changes appear on the mucous membrane oral cavity, on the skin, in the subcutaneous tissue, in the salivary glands and in the bone marrow of the jaw bones. The degree of damage to these structures during tumor treatment depends on their initial condition. At the same time, the initial condition of the oral cavity affects the quality of antitumor treatment. Poor oral hygiene and chronic odontogenic lesions can cause the development of episodic fevers and other general complications. All this requires stopping or changes in the tactics of antitumor treatment, which reduces its radicalism. It becomes obvious that sanitation of the oral cavity, carried out before treatment by an oncologist, will avoid or reduce the frequency complications in the maxillofacial area, improve the quality of life of an oncology patient. Dental care for such a patient has features and requires an individual approach. The purpose of this study was to review the literature on the main oral tissue complications arising from chemotherapy and radiation therapy in the head and neck region. In Google Scholar, Medline, Scopus, Web of Sciences, PubMed a systematic review was conducted. Search keywords terms included head and neck cancer, dental care, prevention of complications of cancer, oral tissue lesions manifestationin, chemotherapy, head and neck radiation therapy. Conducted a preliminary search and reviewed 132 titles and abstracts in this literary review included 48 article. This article analyzes the main complications of oral tissues resulting from chemotherapy and radiation therapy in the head and neck area and provides practical recommendations for the management and prevention of complications in this category of patients.

Transient Dynamics of a Fractional Fisher Equation

We investigate the transient dynamics of the Fisher equation under nonlinear diffusion and fractional operators. Firstly, we investigate the effects of the nonlinear diffusivity parameter in the integer-order Fisher equation, by considering a Gaussian distribution as the initial condition. Measuring the spread of the Gaussian distribution by u(0,t)−2, our results show that the solution reaches a steady state governed by the parameters present in the logistic function in Fisher’s equation. The initial transient is an anomalous diffusion process, but a power law cannot describe the whole transient. In this sense, the main novelty of this work is to show that a q-exponential function gives a better description of the transient dynamics. In addition to this result, we extend the Fisher equation via non-integer operators. As a fractional definition, we employ the Caputo fractional derivative and use a discretized system for the numerical approach according to finite difference schemes. We consider the numerical solutions in three scenarios: fractional differential operators acting in time, space, and in both variables. Our results show that the time to reach the steady solution strongly depends on the fractional order of the differential operator, with more influence by the time operator. Our main finding shows that a generalized q-exponential, present in the Tsallis formalism, describes the transient dynamics. The adjustment parameters of the q-exponential depend on the fractional order, connecting the generalized thermostatistics with the anomalous relaxation promoted by the fractional operators in time and space.