Articles de revues sur le sujet « Backward Dynamical Approach »
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Attouch, Hédy, Juan Peypouquet et Patrick Redont. « A Dynamical Approach to an Inertial Forward-Backward Algorithm for Convex Minimization ». SIAM Journal on Optimization 24, no 1 (janvier 2014) : 232–56. http://dx.doi.org/10.1137/130910294.
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KLEMM, M., et P. E. BECKMANN. « THE TOPOLOGY OF BASIN BOUNDARIES IN A CLASS OF THREE-DIMENSIONAL DYNAMICAL SYSTEMS ». International Journal of Bifurcation and Chaos 06, no 01 (janvier 1996) : 161–67. http://dx.doi.org/10.1142/s0218127496001909.
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We will develop new methods to determine the topology of the basin boundary in a class of three-dimensional dynamical systems. One approach is to approximate the basin boundary by backward integration. Unfortunately, there are dynamical systems where it is hard to approximate the basin boundary by a numerical backward integration algorithm. We will introduce topological methods which will provide new information about the structure of the basin boundary. The topological invariants which we will use can be numerically computed.
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Rosatti, Giorgio, Daniel Zugliani, Marina Pirulli et Marta Martinengo. « A new method for evaluating stony debris flow rainfall thresholds : the Backward Dynamical Approach ». Heliyon 5, no 6 (juin 2019) : e01994. http://dx.doi.org/10.1016/j.heliyon.2019.e01994.
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Boţ, Radu Ioan, Sorin-Mihai Grad, Dennis Meier et Mathias Staudigl. « Inducing strong convergence of trajectories in dynamical systems associated to monotone inclusions with composite structure ». Advances in Nonlinear Analysis 10, no 1 (25 août 2020) : 450–76. http://dx.doi.org/10.1515/anona-2020-0143.
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Abstract In this work we investigate dynamical systems designed to approach the solution sets of inclusion problems involving the sum of two maximally monotone operators. Our aim is to design methods which guarantee strong convergence of trajectories towards the minimum norm solution of the underlying monotone inclusion problem. To that end, we investigate in detail the asymptotic behavior of dynamical systems perturbed by a Tikhonov regularization where either the maximally monotone operators themselves, or the vector field of the dynamical system is regularized. In both cases we prove strong convergence of the trajectories towards minimum norm solutions to an underlying monotone inclusion problem, and we illustrate numerically qualitative differences between these two complementary regularization strategies. The so-constructed dynamical systems are either of Krasnoselskiĭ-Mann, of forward-backward type or of forward-backward-forward type, and with the help of injected regularization we demonstrate seminal results on the strong convergence of Hilbert space valued evolutions designed to solve monotone inclusion and equilibrium problems.
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Martinengo, Marta, Daniel Zugliani et Giorgio Rosatti. « Uncertainty analysis of a rainfall threshold estimate for stony debris flow based on the backward dynamical approach ». Natural Hazards and Earth System Sciences 21, no 6 (3 juin 2021) : 1769–84. http://dx.doi.org/10.5194/nhess-21-1769-2021.
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Abstract. A rainfall threshold is a function of some rainfall quantities that provides the conditions beyond which the probability of debris-flow occurrence is considered significant. Many uncertainties may affect the thresholds calibration and, consequently, its robustness. This study aims to assess the uncertainty in the estimate of a rainfall threshold for stony debris flow based on the backward dynamical approach, an innovative method to compute the rainfall duration and averaged intensity strictly related to a measured debris flow. The uncertainty analysis is computed by performing two Monte Carlo cascade simulations: (i) to assess the variability in the event characteristics estimate due to the uncertainty in the backward dynamical approach parameters and data and (ii) to quantify the impact of this variability on the threshold calibration. The application of this procedure to a case study highlights that the variability in the event characteristics can be both low and high. Instead, the threshold coefficients have a low dispersion showing good robustness of the threshold estimate. Moreover, the results suggest that some event features are correlated with the variability of the rainfall event duration and intensity. The proposed method is suitable to analyse the uncertainty of other threshold calibration approaches.
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Tkach, T. B., A. S. Kvasikova et I. M. Shpinareva. « ON SOME NUMERICAL MODEL TO SOLVING DYNAMICAL EQUATIONS OF NONRELATIVISTIC AND RELATIVISTIC BACKWARD-WAVE TUBE ». Photoelectronics, no 30 (21 août 2022) : 146–51. http://dx.doi.org/10.18524/0235-2435.2021.30.262909.
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It is developed an effective computational approach to solution the master corresponding system of differential equations, which describe the nonlinear stationary and non-stationary electromagnetic processes in the nonrelativistic and relativistic backward-wave tubes (carcinotrons) with maximal accounting for the different physical factors such as the relativistic effects, effects of dissipation, the presence of a space charge, wave reflections at the ends of the slowing system, stochastic factors by means including the special elements in a whole system etc as well as the detailed investigation of characteristics (dynamical and topological invariants) of dynamics of a carcinotron in automodulation and chaotic regimes with construction the corresponding bi-furcation diagrams. Below in order to further solve the master system of dynamical equations for carcinotron it is presented in brief the realizing numerical scheme, based on the use of the conservative finite-difference schemes of the "predictor-corrector" type and the sweep algorithm.
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Boţ, Radu Ioan, et Laura Kanzler. « A forward-backward dynamical approach for nonsmooth problems with block structure coupled by a smooth function ». Applied Mathematics and Computation 394 (avril 2021) : 125822. http://dx.doi.org/10.1016/j.amc.2020.125822.
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Ioan Boţ, Radu, et Ernö Robert Csetnek. « A forward-backward dynamical approach to the minimization of the sum of a nonsmooth convex with a smooth nonconvex function ». ESAIM : Control, Optimisation and Calculus of Variations 24, no 2 (22 janvier 2018) : 463–77. http://dx.doi.org/10.1051/cocv/2017020.
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We address the minimization of the sum of a proper, convex and lower semicontinuous function with a (possibly nonconvex) smooth function from the perspective of an implicit dynamical system of forward-backward type. The latter is formulated by means of the gradient of the smooth function and of the proximal point operator of the nonsmooth one. The trajectory generated by the dynamical system is proved to asymptotically converge to a critical point of the objective, provided a regularization of the latter satisfies the Kurdyka−Łojasiewicz property. Convergence rates for the trajectory in terms of the Łojasiewicz exponent of the regularized objective function are also provided.
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Sharma, Sandeep, et Nitu Kumari. « Backward Bifurcation in a Cholera Model : A Case Study of Outbreak in Zimbabwe and Haiti ». International Journal of Bifurcation and Chaos 27, no 11 (octobre 2017) : 1750170. http://dx.doi.org/10.1142/s021812741750170x.
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In this paper, a nonlinear deterministic model is proposed with a saturated treatment function. The expression of the basic reproduction number for the proposed model was obtained. The global dynamics of the proposed model was studied using the basic reproduction number and theory of dynamical systems. It is observed that proposed model exhibits backward bifurcation as multiple endemic equilibrium points exist when [Formula: see text]. The existence of backward bifurcation implies that making [Formula: see text] is not enough for disease eradication. This, in turn, makes it difficult to control the spread of cholera in the community. We also obtain a unique endemic equilibria when [Formula: see text]. The global stability of unique endemic equilibria is performed using the geometric approach. An extensive numerical study is performed to support our analytical results. Finally, we investigate two major cholera outbreaks, Zimbabwe (2008–09) and Haiti (2010), with the help of the present study.
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Gao, Huadong. « Efficient Numerical Solution of Dynamical Ginzburg-Landau Equations under the Lorentz Gauge ». Communications in Computational Physics 22, no 1 (3 mai 2017) : 182–201. http://dx.doi.org/10.4208/cicp.oa-2016-0120.
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AbstractIn this paper, a new numerical scheme for the time dependent Ginzburg-Landau (GL) equations under the Lorentz gauge is proposed. We first rewrite the original GL equations into a new mixed formulation, which consists of three parabolic equations for the order parameter ψ, the magnetic field σ=curlA, the electric potential θ=divA and a vector ordinary differential equation for the magnetic potential A, respectively. Then, an efficient fully linearized backward Euler finite element method (FEM) is proposed for the mixed GL system, where conventional Lagrange element method is used in spatial discretization. The new approach offers many advantages on both accuracy and efficiency over existing methods for the GL equations under the Lorentz gauge. Three physical variables ψ, σ and θ can be solved accurately and directly. More importantly, the new approach is well suitable for non-convex superconductors. We present a set of numerical examples to confirm these advantages.
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Skamarock, William C. « A Linear Analysis of the NCAR CCSM Finite-Volume Dynamical Core ». Monthly Weather Review 136, no 6 (1 juin 2008) : 2112–19. http://dx.doi.org/10.1175/2007mwr2217.1.
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Abstract The NCAR Community Climate System Model (CCSM) finite-volume atmospheric core uses a C–D-grid discretization to solve the equations of motion. A linear analysis of this discretization shows that it behaves as a D grid to leading order; it possesses the poor response of the D grid for short-wavelength divergent modes, the poor response of the C and D grids for short-wavelength rotational modes, and is only first-order accurate in time and damping. The scheme combines a modified forward–backward time integration for gravity waves with forward-in-time upwind-biased advection schemes, and the solver uses a vector-invariant form of the momentum equations. Other approaches using these equations are considered that circumvent some of the problems inherent in the current approach.
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Engel, Maximilian, et Christian Kuehn. « A Random Dynamical Systems Perspective on Isochronicity for Stochastic Oscillations ». Communications in Mathematical Physics 386, no 3 (8 avril 2021) : 1603–41. http://dx.doi.org/10.1007/s00220-021-04077-z.
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AbstractFor an attracting periodic orbit (limit cycle) of a deterministic dynamical system, one defines the isochron for each point of the orbit as the cross-section with fixed return time under the flow. Equivalently, isochrons can be characterized as stable manifolds foliating neighborhoods of the limit cycle or as level sets of an isochron map. In recent years, there has been a lively discussion in the mathematical physics community on how to define isochrons for stochastic oscillations, i.e. limit cycles or heteroclinic cycles exposed to stochastic noise. The main discussion has concerned an approach finding stochastic isochrons as sections of equal expected return times versus the idea of considering eigenfunctions of the backward Kolmogorov operator. We discuss the problem in the framework of random dynamical systems and introduce a new rigorous definition of stochastic isochrons as random stable manifolds for random periodic solutions with noise-dependent period. This allows us to establish a random version of isochron maps whose level sets coincide with the random stable manifolds. Finally, we discuss links between the random dynamical systems interpretation and the equal expected return time approach via averaged quantities.
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Królikowska, Małgorzata, et Piotr A. Dybczyński. « Dynamical evolution of C/2017 K2 PANSTARRS ». Astronomy & ; Astrophysics 615 (juillet 2018) : A170. http://dx.doi.org/10.1051/0004-6361/201832917.
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Context. The comet C/2017 K2 PANSTARRS drew attention to its activity at the time of its discovery in May 2017 when it was about 16 au from the Sun. This Oort spike comet will approach its perihelion in December 2022, and the question about its dynamical past is an important issue to explore. Aims. In order to answer the question of whether C/2017 K2 is a dynamically old or new comet it is necessary to obtain its precise osculating orbit, its original orbit, and propagate its motion backwards in time to the previous perihelion. Knowledge of the previous perihelion distance is necessary to distinguish between these two groups of the Oort spike comets. We have studied the dynamical evolution of C/2017 K2 to the previous perihelion (backward calculations for about 3–4 Myr) as well as to the future (forward calculations for about 0.033 Myr) using the swarm of virtual comets (VCs) constructed from a nominal osculating orbit of this comet which we determined here using all positional measurements available at the moment. Outside the planetary system both Galactic and stellar perturbations were taken into account. Results. We derive that C/2017 K2 is a dynamically old Oort spike comet (1/aprev = (48.7 ± 7.9) × 10−6 au−1) with the previous perihelion distance below 10 au for 97% of VCs (nominal qprev = 3.77 au). According to the present data this comet will be perturbed into a more tightly bound orbit after passing the planetary zone (1/afut = (1140.4 ± 8.0) × 10−6 au−1, qfut = 1.79336 ± 0.00006 au) provided that non-gravitational effects will not change the orbit significantly. Conclusions. C/2017 K2 has already visited our planetary zone during its previous perihelion passage. Thus, it is almost certainly a dynamically old Oort spike comet. The future orbital solution of this comet is formally very precise, however, it is much less definitive since the presented analysis is based on pre-perihelion data taken at very large heliocentric distances (23.7–14.6 au from the Sun), and this comet can experience a significant non-gravitational perturbation during the upcoming perihelion passage in 2022.
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Clempner, Julio B. « A Shortest-Path Lyapunov Approach for Forward Decision Processes ». International Journal of Computer Games Technology 2009 (2009) : 1–12. http://dx.doi.org/10.1155/2009/162450.
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In previous work, attention was restricted to tracking the net using a backward method that knows the target point beforehand (Bellmans's equation), this work tracks the state-space in a forward direction, and a natural form of termination is ensured by an equilibrium point . We consider dynamical systems governed by ordinary difference equations described by Petri nets. The trajectory over the net is calculated forward using a discrete Lyapunov-like function, considered as a distance function. Because a Lyapunov-like function is a solution to a difference equation, it is constructed to respect the constraints imposed by the system (a Euclidean metric does not consider these factors). As a result, we prove natural generalizations of the standard outcomes for the deterministic shortest-path problem and shortest-path game theory.
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Lauriere, M., Z. Li, L. Mertz, J. Wylie et S. Zuo. « Free boundary value problems and hjb equations for the stochastic optimal control of elasto-plastic oscillators ». ESAIM : Proceedings and Surveys 65 (2019) : 425–44. http://dx.doi.org/10.1051/proc/201965425.
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We consider the optimal stopping and optimal control problems related to stochastic variational inequalities modeling elasto-plastic oscillators subject to random forcing. We formally derive the corresponding free boundary value problems and Hamilton-Jacobi-Bellman equations which belong to a class of nonlinear partial of differential equations with nonlocal Dirichlet boundary conditions. Then, we focus on solving numerically these equations by employing a combination of Howard’s algorithm and the numerical approach [A backward Kolmogorov equation approach to compute means, moments and correlations of non-smooth stochastic dynamical systems; Mertz, Stadler, Wylie; 2017] for this type of boundary conditions. Numerical experiments are given.
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Montoya, Oscar Danilo, Walter Gil-González et Federico Martin Serra. « Discrete-time inverse optimal control for a reaction wheel pendulum : a passivity-based control approach ». Revista UIS Ingenierías 19, no 4 (30 mai 2020) : 123–32. http://dx.doi.org/10.18273/revuin.v19n4-2020011.
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In this paper it is presented the design of a controller for a reaction wheel pendulum using a discrete-time representation via optimal control from the point of view of passivity-based control analysis. The main advantage of the proposed approach is that it allows to guarantee asymptotic stability convergence using a quadratic candidate Lyapunovfunction. Numerical simulations show that the proposed inverse optimal control design permits to reach superiornumerical performance reported by continuous approaches such as Lyapunov control functions and interconnection,and damping assignment passivity-based controllers. An additional advantageof the proposed inverse optimal controlmethod is its easy implementation since it does not employ additional states. It is only required a basic discretizationof the time-domain dynamical model based on the backward representation. All the simulations are carried out inMATLAB/OCTAVE software using a codification on the script environment.
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Oliveira, T. F., R. B. Miserda et F. R. Cunha. « Dynamical Simulation and Statistical Analysis of Velocity Fluctuations of a Turbulent Flow behind a Cube ». Mathematical Problems in Engineering 2007 (2007) : 1–28. http://dx.doi.org/10.1155/2007/24627.
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A statistical approach for the treatment of turbulence data generated by computer simulations is presented. A model for compressible flows at large Reynolds numbers and low Mach numbers is used for simulating a backward-facing step airflow. A scaling analysis has justified the commonly used assumption that the internal energy transport due to turbulent velocity fluctuations and the work done by the pressure field are the only relevant mechanisms needed to model subgrid-scale flows. From the numerical simulations, the temporal series of velocities are collected for ten different positions in the flow domain, and are statistically treated. The statistical approach is based on probability averages of the flow quantities evaluated over several realizations of the simulated flow. We look at how long of a time average is necessary to obtain well-converged statistical results. For this end, we evaluate the mean-square difference between the time average and an ensemble average as the measure of convergence. This is an interesting question since the validity of the ergodic hypothesis is implicitly assumed in every turbulent flow simulation and its analysis. The ergodicity deviations from the numerical simulations are compared with theoretical predictions given by scaling arguments. A very good agreement is observed. Results for velocity fluctuations, normalized autocorrelation functions, power spectra, probability density distributions, as well as skewness and flatness coefficients are also presented.
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Luo, Zong-Fu. « The role of the mass ratio in ballistic capture ». Monthly Notices of the Royal Astronomical Society 498, no 1 (24 août 2020) : 1515–29. http://dx.doi.org/10.1093/mnras/staa2366.
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ABSTRACT A massless particle can be naturally captured by a celestial body with the aid of a third body. In this work, the influence of the mass ratio on ballistic capture is investigated in the planar circular restricted three-body problem (CR3BP) model. Four typical dynamical environments with decreasing mass ratios, that is, the Pluto–Charon, Earth–Moon, Sun–Jupiter, and Saturn–Titan systems, are considered. A generalized method is introduced to derive ballistic capture orbits by starting from a set of initial conditions and integrating backward in time. Particular attention is paid to the backward escape orbits, following which a test particle can be temporarily trapped by a three-body gravity system, although the particle will eventually deviate away from the system. This approach is applied to the four candidate systems with a series of Jacobi constant levels to survey and compare the capture probability (quantitatively) and capture capability (qualitatively) when the mass ratio varies. Capture mechanisms inducing favourable ballistic capture are discussed. Moreover, the possibility and stability of capture by secondary celestial bodies are analysed. The obtained results may be useful in explaining the capture phenomena of minor bodies or in designing mission trajectories for interplanetary probes.
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Sulayman, Fatima, et Farah Aini Abdullah. « Dynamical Behaviour of a Modified Tuberculosis Model with Impact of Public Health Education and Hospital Treatment ». Axioms 11, no 12 (13 décembre 2022) : 723. http://dx.doi.org/10.3390/axioms11120723.
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Tuberculosis (TB), caused by Mycobacterium tuberculosis is one of the treacherous infectious diseases of global concern. In this paper, we consider a deterministic model of TB infection with the public health education and hospital treatment impact. The effective reproductive number, Rph, that measures the potential spread of TB is presented by employing the next generation matrix approach. We investigate local and global stability of the TB-free equilibrium point, endemic equilibrium point, and sensitivity analysis. The analyses of the proposed model show that the model undergoes the phenomenon of backward bifurcation when the effective reproduction number (Rph) is less than one, where two stable equilibria, namely, the DFE and an EEP coexist. Further, we compute the sensitivity of the impact of each parameter on the effective reproductive number of the model by employing a normalized sensitivity index formula. Numerical simulation of the proposed model was conducted using Maple 2016 and MatLab R2020b software and compared with the theoretical results for illustration purposes. The investigation results can be useful in providing information to policy makers and public health authorities in mitigating the spread of TB infection by public health education and hospital treatment.
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Raouf, Fareh, Saad Mohamad, Saad Maarouf et Bettayeb Maamar. « Distributed adaptive control strategy for flexible link manipulators ». Robotica 35, no 7 (1 juillet 2016) : 1562–84. http://dx.doi.org/10.1017/s0263574716000448.
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SUMMARYThis paper presents an adaptive distributed control strategy for n-serial-flexible-link manipulators. The proposed adaptive controller is used for flexible-link-manipulators: (1) to solve the tracking control problem in the joint space, and (2) to reduce vibrations of the links. The dynamical model of flexible link manipulators is reorganized to take the form of n interconnected subsystems. Each subsystem has a one-joint and one-link pair. The system parameters are deemed to be unknown. The adaptive distributed strategy controls one subsystem in each step, starting from the last one. The nth subsystem is controlled by assuming that the remaining subsystems are stable. Then, proceeding backward to the (n-1)th system, the same strategy is applied, and so on, until the first subsystem is reached. The gradient-based estimator is used to estimate the parameters of each subsystem. The control law of the ith subsystem uses its own estimated parameters and the estimated parameters of all upper level subsystems. The global stability of the error dynamics is proved using Lyapunov approach. This algorithm was implemented in real time on a two-flexible-link manipulator, and a comparison with the non-adaptive version shows the effectiveness of this approach.
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Biasetti, Jacopo, Fazle Hussain et T. Christian Gasser. « Blood flow and coherent vortices in the normal and aneurysmatic aortas : a fluid dynamical approach to intra-luminal thrombus formation ». Journal of The Royal Society Interface 8, no 63 (6 avril 2011) : 1449–61. http://dx.doi.org/10.1098/rsif.2011.0041.
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Abdominal aortic aneurysms (AAAs) are frequently characterized by the development of an intra-luminal thrombus (ILT), which is known to have multiple biochemical and biomechanical implications. Development of the ILT is not well understood, and shear–stress-triggered activation of platelets could be the first step in its evolution. Vortical structures (VSs) in the flow affect platelet dynamics, which motivated the present study of a possible correlation between VS and ILT formation in AAAs. VSs educed by the λ 2 -method using computational fluid dynamics simulations of the backward-facing step problem, normal aorta, fusiform AAA and saccular AAA were investigated. Patient-specific luminal geometries were reconstructed from computed tomography scans, and Newtonian and Carreau–Yasuda models were used to capture salient rheological features of blood flow. Particularly in complex flow domains, results depended on the constitutive model. VSs developed all along the normal aorta, showing that a clear correlation between VSs and high wall shear stress (WSS) existed, and that VSs started to break up during late systole. In contrast, in the fusiform AAA, large VSs developed at sites of tortuous geometry and high WSS, occupying the entire lumen, and lasting over the entire cardiac cycle. Downward motion of VSs in the AAA was in the range of a few centimetres per cardiac cycle, and with a VS burst at that location, the release (from VSs) of shear-stress-activated platelets and their deposition to the wall was within the lower part of the diseased artery, i.e. where the thickest ILT layer is typically observed. In the saccular AAA, only one VS was found near the healthy portion of the aorta, while in the aneurysmatic bulge, no VSs occurred. We present a fluid-dynamics-motivated mechanism for platelet activation, convection and deposition in AAAs that has the potential of improving our current understanding of the pathophysiology of fluid-driven ILT growth.
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Barbi, Giacomo, Valentina Giovacchini et Sandro Manservisi. « A New Anisotropic Four-Parameter Turbulence Model for Low Prandtl Number Fluids ». Fluids 7, no 1 (22 décembre 2021) : 6. http://dx.doi.org/10.3390/fluids7010006.
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Due to their interesting thermal properties, liquid metals are widely studied for heat transfer applications where large heat fluxes occur. In the framework of the Reynolds-Averaged Navier–Stokes (RANS) approach, the Simple Gradient Diffusion Hypothesis (SGDH) and the Reynolds Analogy are almost universally invoked for the closure of the turbulent heat flux. Even though these assumptions can represent a reasonable compromise in a wide range of applications, they are not reliable when considering low Prandtl number fluids and/or buoyant flows. More advanced closure models for the turbulent heat flux are required to improve the accuracy of the RANS models dealing with low Prandtl number fluids. In this work, we propose an anisotropic four-parameter turbulence model. The closure of the Reynolds stress tensor and turbulent heat flux is gained through nonlinear models. Particular attention is given to the modeling of dynamical and thermal time scales. Numerical simulations of low Prandtl number fluids have been performed over the plane channel and backward-facing step configurations.
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Raković, D., M. Dugić, M. B. Plavšić, G. Keković, Irena Ćosić et David Davidović. « Quantum Decoherence and Quantum-Holographic Information Processes : From Biomolecules to Biosystems ». Materials Science Forum 518 (juillet 2006) : 485–90. http://dx.doi.org/10.4028/www.scientific.net/msf.518.485.
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Our recently proposed quantum approach to biomolecular recognition processes is hereby additionally supported by biomolecular Resonant Recognition Model and by quantum-chemical theory of biomolecular non-radiative resonant transitions. Previously developed general quantumdecoherence framework for biopolymer conformational changes in very selective ligandproteins/ target-receptors key/lock biomolecular recognition processes (with electron-conformational coupling, giving rise to dynamical modification of many-electron energy-state hypersurface of the cellular quantum-ensemble ligand-proteins/target-receptors biomolecular macroscopic quantum system, with revealed possibility to consider cellular biomolecular recognition as a Hopfield-like quantum-holographic associative neural network) is further extended from nonlocal macroscopicquantum level of biological cell to nonlocal macroscopic-quantum level of biological organism, based on long-range coherent microwave excitations (as supported by macroscopic quantum-like microwave resonance therapy of the acupuncture system) - which might be of fundamental importance in understanding of underlying macroscopic quantum (quantum-holographic Hopfieldlike) control mechanisms of embryogenesis/ontogenesis and morphogenesis, and their backward influence on the expression of genes.
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Afshari, H. H., et E. Taheri. « Non-linear solution to the maximum height orbit transfer guidance problem ». Proceedings of the Institution of Mechanical Engineers, Part G : Journal of Aerospace Engineering 226, no 6 (juin 2012) : 620–30. http://dx.doi.org/10.1177/0954410011414991.
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An optimal control solution to the highly non-linear problem of orbit transfer mission is achieved by using a newly proposed analytical perturbation technique. The problem is classified as a two-point boundary value problem in order to optimize a performance measure in a given time. Assuming a constant thrust operating in a given length of time, it is sought to find the thrust direction history of a transfer from a given initial orbit to the largest possible orbit. The system dynamical model is stated by regarding a variable mass spacecraft moving in the variable gravitational field of the Earth, based on the two-body problem. To assess the perturbation solution fidelity, a numerical solution based on the Gauss pseudospectral method has been employed. The main novelty of this work is in applying a new analytical solution strategy that is a combination of perturbation technique and backward integration to a highly non-linear problem in the calculus of variations approach.
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Lakrisenko, Polina, Paul Stapor, Stephan Grein, Łukasz Paszkowski, Dilan Pathirana, Fabian Fröhlich, Glenn Terje Lines, Daniel Weindl et Jan Hasenauer. « Efficient computation of adjoint sensitivities at steady-state in ODE models of biochemical reaction networks ». PLOS Computational Biology 19, no 1 (3 janvier 2023) : e1010783. http://dx.doi.org/10.1371/journal.pcbi.1010783.
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Dynamical models in the form of systems of ordinary differential equations have become a standard tool in systems biology. Many parameters of such models are usually unknown and have to be inferred from experimental data. Gradient-based optimization has proven to be effective for parameter estimation. However, computing gradients becomes increasingly costly for larger models, which are required for capturing the complex interactions of multiple biochemical pathways. Adjoint sensitivity analysis has been pivotal for working with such large models, but methods tailored for steady-state data are currently not available. We propose a new adjoint method for computing gradients, which is applicable if the experimental data include steady-state measurements. The method is based on a reformulation of the backward integration problem to a system of linear algebraic equations. The evaluation of the proposed method using real-world problems shows a speedup of total simulation time by a factor of up to 4.4. Our results demonstrate that the proposed approach can achieve a substantial improvement in computation time, in particular for large-scale models, where computational efficiency is critical.
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Chen, Lin, Xiaotian Wu, Yancong Xu et Libin Rong. « Modelling the dynamics of <i>Trypanosoma rangeli</i> ; and triatomine bug with logistic growth of vector and systemic transmission ». Mathematical Biosciences and Engineering 19, no 8 (2022) : 8452–78. http://dx.doi.org/10.3934/mbe.2022393.
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<abstract><p>In this paper, an insect-parasite-host model with logistic growth of triatomine bugs is formulated to study the transmission between hosts and vectors of the Chagas disease by using dynamical system approach. We derive the basic reproduction numbers for triatomine bugs and <italic>Trypanosoma rangeli</italic> as two thresholds. The local and global stability of the vector-free equilibrium, parasite-free equilibrium and parasite-positive equilibrium is investigated through the derived two thresholds. Forward bifurcation, saddle-node bifurcation and Hopf bifurcation are proved analytically and illustrated numerically. We show that the model can lose the stability of the vector-free equilibrium and exhibit a supercritical Hopf bifurcation, indicating the occurrence of a stable limit cycle. We also find it unlikely to have backward bifurcation and Bogdanov-Takens bifurcation of the parasite-positive equilibrium. However, the sustained oscillations of infected vector population suggest that <italic>Trypanosoma rangeli</italic> will persist in all the populations, posing a significant challenge for the prevention and control of Chagas disease.</p></abstract>
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Kwon, Yuna G., Masateru Ishiguro, Jungmi Kwon, Daisuke Kuroda, Myungshin Im, Changsu Choi, Motohide Tamura, Takahiro Nagayama, Nobuyuki Kawai et Jun-Ichi Watanabe. « Near-infrared polarimetric study of near-Earth object 252P/LINEAR : an implication of scattered light from the evolved dust particles ». Astronomy & ; Astrophysics 629 (septembre 2019) : A121. http://dx.doi.org/10.1051/0004-6361/201935542.
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Context. Comets undergo resurfacing due to solar radiation, while their primordial interiors remain unchanged. Multi-epoch observations of comets enable us to characterize a change in sublimation pattern as a function of heliocentric distance, which in turn provides information on the dust environments of comets. Aims. We aim to constrain the size and porosity of ejected dust particles from comet 252P/LINEAR and their evolution near perihelion via near-infrared (NIR) multiband polarimetry. A close approach of the comet to the Earth in March 2016 (~0.036 au) provided a rare opportunity for the sampling of the comet at high spatial resolution. Methods. We made NIR JHKS-band (1.25–2.25 μm) polarimetric observations of the comet for 12 days near perihelion, interspersed between broadband optical (0.48–0.80 μm) imaging observations over four months. In addition, a dynamical simulation of the comet was performed 1000 yr backward in time. Results. We detected two discontinuous brightness enhancements of 252P/LINEAR. Before the first enhancement, the NIR polarization degrees of the comet were far lower than those of ordinary comets at a given phase angle. Soon after the activation, however, they increased by ~13% at most, showing unusual blue polarimetric color over the J and H bands (−2.55% μm−1 on average) and bluing of the dust color in both J−H and H−KS. Throughout the event, the polarization vector was marginally aligned perpendicular to the scattering plane (i.e., θr = 4.6°–10.9°). The subsequent postperihelion reactivation of the comet lasted for approximately 1.5 months, with a factor of ~30 times pre-activation dust mass-loss rates in the RC band. Conclusions. The marked increase in the polarization degree with blue NIR polarimetric color is reminiscent of the behavior of a fragmenting comet D/1999 S4 (LINEAR). The most plausible scenario for the observed polarimetric properties of 252P/LINEAR is an ejection of predominantly large (well within the geometrical optics regime) and compact dust particles from the desiccated surface layer. We conjecture that the more intense solar heating that the comet has received in the near-Earth orbit would cause the paucity of small fluffy dust particles around the nucleus of the comet.
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Capriotti, Luca, Yupeng Jiang et Andrea Macrina. « Real-time risk management : An AAD-PDE approach ». International Journal of Financial Engineering 02, no 04 (décembre 2015) : 1550039. http://dx.doi.org/10.1142/s2424786315500395.
Texte intégralRésumé :
We apply adjoint algorithmic differentiation (AAD) to the risk management of securities when their price dynamics are given by partial differential equations (PDE). We show how AAD can be applied to forward and backward PDEs in a straightforward manner. In the context of one-factor models for interest rates or default intensities, we show how price sensitivities are computed reliably and orders of magnitude faster than with a standard finite-difference (FD) approach. This significantly increased efficiency is obtained by combining (i) the adjoint forward PDE for calibrating model parameters, (ii) the adjoint backward PDE for derivatives pricing, and (iii) the implicit function theorem to avoid iterating the calibration procedure.
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Aydoğdu, Ali, Alberto Carrassi, Colin T. Guider, Chris K. R. T. Jones et Pierre Rampal. « Data assimilation using adaptive, non-conservative, moving mesh models ». Nonlinear Processes in Geophysics 26, no 3 (24 juillet 2019) : 175–93. http://dx.doi.org/10.5194/npg-26-175-2019.
Texte intégralRésumé :
Abstract. Numerical models solved on adaptive moving meshes have become increasingly prevalent in recent years. Motivating problems include the study of fluids in a Lagrangian frame and the presence of highly localized structures such as shock waves or interfaces. In the former case, Lagrangian solvers move the nodes of the mesh with the dynamical flow; in the latter, mesh resolution is increased in the proximity of the localized structure. Mesh adaptation can include remeshing, a procedure that adds or removes mesh nodes according to specific rules reflecting constraints in the numerical solver. In this case, the number of mesh nodes will change during the integration and, as a result, the dimension of the model's state vector will not be conserved. This work presents a novel approach to the formulation of ensemble data assimilation (DA) for models with this underlying computational structure. The challenge lies in the fact that remeshing entails a different state space dimension across members of the ensemble, thus impeding the usual computation of consistent ensemble-based statistics. Our methodology adds one forward and one backward mapping step before and after the ensemble Kalman filter (EnKF) analysis, respectively. This mapping takes all the ensemble members onto a fixed, uniform reference mesh where the EnKF analysis can be performed. We consider a high-resolution (HR) and a low-resolution (LR) fixed uniform reference mesh, whose resolutions are determined by the remeshing tolerances. This way the reference meshes embed the model numerical constraints and are also upper and lower uniform meshes bounding the resolutions of the individual ensemble meshes. Numerical experiments are carried out using 1-D prototypical models: Burgers and Kuramoto–Sivashinsky equations and both Eulerian and Lagrangian synthetic observations. While the HR strategy generally outperforms that of LR, their skill difference can be reduced substantially by an optimal tuning of the data assimilation parameters. The LR case is appealing in high dimensions because of its lower computational burden. Lagrangian observations are shown to be very effective in that fewer of them are able to keep the analysis error at a level comparable to the more numerous observers for the Eulerian case. This study is motivated by the development of suitable EnKF strategies for 2-D models of the sea ice that are numerically solved on a Lagrangian mesh with remeshing.
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Bolzern, P., R. M. DeSantis et A. Locatelli. « An Input-Output Linearization Approach to the Control of an n-Body Articulated Vehicle ». Journal of Dynamic Systems, Measurement, and Control 123, no 3 (3 janvier 2001) : 309–16. http://dx.doi.org/10.1115/1.1387010.
Texte intégralRésumé :
The problem of path-tracking for an autonomous vehicle composed of a tractor and n−1 trailers with off-axle hitching is considered in this paper. It is shown that an input-output feedback linearization technique can be adopted both in forward and backward maneuvers, leading to the stabilization of the path-tracking offset dynamics about circular paths. The location of the guide-point needs to be selected according to the direction of motion, and, when moving backward, the off-axle distances must be all positive.
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Casserini, Matteo, et Gechun Liang. « Fully coupled forward–backward stochastic dynamics and functional differential systems ». Stochastics and Dynamics 15, no 02 (6 avril 2015) : 1550006. http://dx.doi.org/10.1142/s0219493715500069.
Texte intégralRésumé :
This paper introduces and solves a general class of fully coupled forward–backward stochastic dynamics by investigating the associated system of functional differential equations. As a consequence, we are able to solve many different types of forward–backward stochastic differential equations (FBSDEs) that do not fit in the classical setting. In our approach, the equations are running in the same time direction rather than in a forward and backward way, and the conflicting nature of the structure of FBSDEs is therefore avoided.
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RAMANATHAN, Kuppan Chetty, Manju MOHAN et Joshuva AROCKIA DHANRAJ. « BACKWARD MOTION PLANNING AND CONTROL OF MULTIPLE MOBILE ROBOTS MOVING IN TIGHTLY COUPLED FORMATIONS ». Applied Computer Science 17, no 3 (30 septembre 2021) : 60–72. http://dx.doi.org/10.35784/acs-2021-21.
Texte intégralRésumé :
This work addresses the development of a distributed switching control strategy to drive the group of mobile robots in both backward and forward motion in a tightly coupled geometric pattern, as a solution for the deadlock situation that arises while navigating the unknown environment. A generalized closed-loop tracking controller considering the leader referenced model is used for the robots to remain in the formation while navigating the environment. A tracking controller using the simple geometric approach and the Instantaneous Centre of Radius (ICR), to drive the robot in the backward motion during deadlock situation is developed and presented. State-Based Modelling is used to model the behaviors/motion states of the proposed approach in MATLAB/STATEFLOW environment. Simulation studies are carried out to test the performance and error dynamics of the proposed approach combining the formation, navigation, and backward motion of the robots in all geometric patterns of formation, and the results are discussed.
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Bond, Stephen D., et Benedict J. Leimkuhler. « Molecular dynamics and the accuracy of numerically computed averages ». Acta Numerica 16 (24 avril 2007) : 1–65. http://dx.doi.org/10.1017/s0962492906280012.
Texte intégralRésumé :
Molecular dynamics is discussed from a mathematical perspective. The recent history of method development is briefly surveyed with an emphasis on the use of geometric integration as a guiding principle. The recovery of statistical mechanical averages from molecular dynamics is then introduced, and the use of backward error analysis as a technique for analysing the accuracy of numerical averages is described. This article gives the first rigorous estimates for the error in statistical averages computed from molecular dynamics simulation based on backward error analysis. It is shown that molecular dynamics introduces an appreciable bias at stepsizes which are below the stability threshold. Simulations performed in such a regime can be corrected by use of a stepsize-dependent reweighting factor. Numerical experiments illustrate the efficacy of this approach. In the final section, several open problems in dynamics-based molecular sampling are considered.
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Insukindro, Insukindro, et Gumilang Aryo Sahadewo. « Inflation Dynamics in Indonesia : Equilibrium Correction and Forward-Looking Phillips Curve Approaches ». Gadjah Mada International Journal of Business 12, no 1 (12 janvier 2010) : 117. http://dx.doi.org/10.22146/gamaijb.5515.
Texte intégralRésumé :
A series of relatively high inflation characterize Indonesian economy, especially during the economic crisis. Economists generally agree that high inflation is one of the major economic problems, and that economic authorities need to cope with such a problem. Therefore, it is essential to understand the behavior of inflation in Indonesia. The aim of this paper is to estimate the inflation dynamics in Indonesia using equilibrium correction and forward-looking Phillips Curve approaches. Previous empirical studies show that the equilibrium correction or backward-looking approach may explain the inflation dynamics in Indonesia. The backward-looking specification does not have to be the proper model even if the fact shows that the specification holds. The major innovation of this paper is the application of a forward-looking Phillips curve model. The empirical results—estimated using the Generalized Method of Moments (GMM)—show that the forward-looking Phillips Curve approach dominates the backward-looking behavior. It indicates that after a credible monetary policy announcement, for instance, the former model predicts that economic agents will change their behavior quickly. Therefore, the policy will affect the economy more rapidly
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Endo, Akira, Quentin J. Leclerc, Gwenan M. Knight, Graham F. Medley, Katherine E. Atkins, Sebastian Funk et Adam J. Kucharski. « Implication of backward contact tracing in the presence of overdispersed transmission in COVID-19 outbreaks ». Wellcome Open Research 5 (31 mars 2021) : 239. http://dx.doi.org/10.12688/wellcomeopenres.16344.3.
Texte intégralRésumé :
Introduction: Contact tracing has the potential to control outbreaks without the need for stringent physical distancing policies, e.g. civil lockdowns. Unlike forward contact tracing, backward contact tracing identifies the source of newly detected cases. This approach is particularly valuable when there is high individual-level variation in the number of secondary transmissions (overdispersion). Methods: By using a simple branching process model, we explored the potential of combining backward contact tracing with more conventional forward contact tracing for control of COVID-19. We estimated the typical size of clusters that can be reached by backward tracing and simulated the incremental effectiveness of combining backward tracing with conventional forward tracing. Results: Across ranges of parameter values consistent with dynamics of SARS-CoV-2, backward tracing is expected to identify a primary case generating 3-10 times more infections than a randomly chosen case, typically increasing the proportion of subsequent cases averted by a factor of 2-3. The estimated number of cases averted by backward tracing became greater with a higher degree of overdispersion. Conclusion: Backward contact tracing can be an effective tool for outbreak control, especially in the presence of overdispersion as is observed with SARS-CoV-2.
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Endo, Akira, Quentin J. Leclerc, Gwenan M. Knight, Graham F. Medley, Katherine E. Atkins, Sebastian Funk et Adam J. Kucharski. « Implication of backward contact tracing in the presence of overdispersed transmission in COVID-19 outbreaks ». Wellcome Open Research 5 (18 janvier 2021) : 239. http://dx.doi.org/10.12688/wellcomeopenres.16344.2.
Texte intégralRésumé :
Introduction: Contact tracing has the potential to control outbreaks without the need for stringent physical distancing policies, e.g. civil lockdowns. Unlike forward contact tracing, backward contact tracing identifies the source of newly detected cases. This approach is particularly valuable when there is high individual-level variation in the number of secondary transmissions (overdispersion). Methods: By using a simple branching process model, we explored the potential of combining backward contact tracing with more conventional forward contact tracing for control of COVID-19. We estimated the typical size of clusters that can be reached by backward tracing and simulated the incremental effectiveness of combining backward tracing with conventional forward tracing. Results: Across ranges of parameter values consistent with dynamics of SARS-CoV-2, backward tracing is expected to identify a primary case generating 3-10 times more infections than a randomly chosen case, typically increasing the proportion of subsequent cases averted by a factor of 2-3. The estimated number of cases averted by backward tracing became greater with a higher degree of overdispersion. Conclusion: Backward contact tracing can be an effective tool for outbreak control, especially in the presence of overdispersion as is observed with SARS-CoV-2.
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Endo, Akira, Quentin J. Leclerc, Gwenan M. Knight, Graham F. Medley, Katherine E. Atkins, Sebastian Funk et Adam J. Kucharski. « Implication of backward contact tracing in the presence of overdispersed transmission in COVID-19 outbreaks ». Wellcome Open Research 5 (13 octobre 2020) : 239. http://dx.doi.org/10.12688/wellcomeopenres.16344.1.
Texte intégralRésumé :
Introduction: Contact tracing has the potential to control outbreaks without the need for stringent physical distancing policies, e.g. civil lockdowns. Unlike forward contact tracing, backward contact tracing identifies the source of newly detected cases. This approach is particularly valuable when there is high individual-level variation in the number of secondary transmissions (overdispersion). Methods: By using a simple branching process model, we explored the potential of combining backward contact tracing with more conventional forward contact tracing for control of COVID-19. We estimated the typical size of clusters that can be reached by backward tracing and simulated the incremental effectiveness of combining backward tracing with conventional forward tracing. Results: Across ranges of parameter values consistent with dynamics of SARS-CoV-2, backward tracing is expected to identify a primary case generating 3-10 times more infections than average, typically increasing the proportion of subsequent cases averted by a factor of 2-3. The estimated number of cases averted by backward tracing became greater with a higher degree of overdispersion. Conclusion: Backward contact tracing can be an effective tool for outbreak control, especially in the presence of overdispersion as was observed with SARS-CoV-2.
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Li, Shilun, et Hong Yin. « A Four Step Scheme Approach to the Forward-Backward Stochastic Navier-Stokes Equations ». Journal of Advances in Applied & ; Computational Mathematics 8 (1 mars 2022) : 129–43. http://dx.doi.org/10.15377/2409-5761.2021.08.10.
Texte intégralRésumé :
In this paper, the authors presented a novel fluid dynamics system, the forward-backward stochastic Navier-Stokes equations in two dimensions for incompressible fluid flows. The well-posedness of the system is obtained through a two-step process. First, certain projections of the system to the finite dimensions are employed, and the existence and uniqueness of solutions in finite dimensions are proved via the four step scheme. Then the Galerkin approximation is used to show the existence and uniqueness of a solution to the system in an infinite dimensional functional setup.
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SALEEL, C. A., A. SHAIJA et S. JAYARAJ. « COMPUTATIONAL SIMULATION OF FLUID FLOW OVER A TRIANGULAR STEP USING IMMERSED BOUNDARY METHOD ». International Journal of Computational Methods 10, no 04 (23 avril 2013) : 1350016. http://dx.doi.org/10.1142/s0219876213500163.
Texte intégralRésumé :
Handling of complex geometries with fluid–solid interaction has been one of the exigent issues in computational fluid dynamics (CFD) because most engineering problems have complex geometries with fluid–solid interaction for the purpose. Two different approaches have been developed for the same hitherto: (i) The unstructured grid method and (ii) the immersed boundary method (IBM). This paper details the IBM for the numerical investigation of two-dimensional laminar flow over a backward facing step and various geometrically configured triangular steps in hydro-dynamically developing regions (entrance region) as well in the hydro-dynamically developed regions through a channel at different Reynolds numbers. The present numerical method is rooted in a finite volume approach on a staggered grid in concert with a fractional step method. Geometrical obstructions are treated as an immersed boundary (IB), both momentum forcing and mass source terms are applied on the obstruction to satisfy the no-slip boundary condition and also to satisfy the continuity for the mesh containing the immersed boundary. Initially, numerically obtained velocity profiles and stream line plots for fluid flow over backward facing step is depicted to show its excellent agreement with the published results in various literatures. There after profiles and plots in the channel with triangular steps are also being unveiled with in depth elucidation. Results are presented for different Reynolds numbers.
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Nyegaard, Anna Kamille, Johan Raunkjær Ott et Mogens Steffensen. « An Intrinsic Value Approach to Valuation with Forward–Backward Loops in Dividend Paying Stocks ». Mathematics 9, no 13 (29 juin 2021) : 1520. http://dx.doi.org/10.3390/math9131520.
Texte intégralRésumé :
We formulate a claim valuation problem where the dynamics of the underlying asset process contain the claim value itself. The problem is motivated here by an equity valuation of a firm, with intermediary dividend payments that depend on both the underlying, that is, the assets of the company, and the equity value itself. Since the assets are reduced by the dividend payments, the entanglement of claim, claim value, and underlying is complete and numerically challenging because it forms a forward–backward stochastic system. We propose a numerical approach based on disentanglement of the forward–backward deterministic system for the intrinsic values, a parametric assumption of the claim value in its intrinsic value, and a simulation of the stochastic elements. We illustrate the method in a numerical example where the equity value is approximated efficiently, at least for the relevant ranges of the asset value.
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Mania, Michael, et Revaz Tevzadze. « Backward stochastic PDEs related to the utility maximization problem ». gmj 17, no 4 (15 novembre 2010) : 705–40. http://dx.doi.org/10.1515/gmj.2010.038.
Texte intégralRésumé :
Abstract We study utility maximization problem for general utility functions using the dynamic programming approach. An incomplete financial market model is considered, where the dynamics of asset prices is described by an -valued continuous semimartingale. Under some regularity assumptions, we derive the backward stochastic partial differential equation related directly to the primal problem and show that the strategy is optimal if and only if the corresponding wealth process satisfies a certain forward stochastic differential equation. The cases of power, exponential and logarithmic utilities are considered as examples.
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Chen, Jinghua, Shaoqiang Wang, Bin Chen, Yue Li, Muhammad Amir, Li Ma, Kai Zhu et al. « Comparative Analysis on the Estimation of Diurnal Solar-Induced Chlorophyll Fluorescence Dynamics for a Subtropical Evergreen Coniferous Forest ». Remote Sensing 13, no 16 (9 août 2021) : 3143. http://dx.doi.org/10.3390/rs13163143.
Texte intégralRésumé :
Solar-induced chlorophyll fluorescence (SIF) is considered as a prospective indicator of vegetation photosynthetic activity and the ecosystem carbon cycle. The current coarse spatial-temporal resolutions of SIF data from satellite missions and ground measurements still cannot satisfy the corroboration of its correlation with photosynthesis and carbon flux. Practical approaches are needed to be explored for the supplementation of the SIF measurements. In our study, we clarified the diurnal variations of leaf and canopy chlorophyll fluorescence for a subtropical evergreen coniferous forest and evaluated the performance of the canopy chlorophyll concentration (CCC) approach and the backward approach from gross primary production (GPP) for estimating the diurnal variations of canopy SIF by comparing with the Soil Canopy Observation Photosynthesis Energy (SCOPE) model. The results showed that the canopy SIF had similar seasonal and diurnal variations with the incident photosynthetically active radiation (PAR) above the canopy, while the leaf steady-state fluorescence remained stable during the daytime. Neither the CCC nor the raw backward approach from GPP could capture the short temporal dynamics of canopy SIF. However, after improving the backward approach with a correction factor of normalized PAR incident on leaves, the variation of the estimated canopy SIF accounted for more than half of the diurnal variations in the canopy SIF (SIF687: R2 = 0.53, p < 0.001; SIF760: R2 = 0.72, p < 0.001) for the subtropical evergreen coniferous forest without water stress. Drought interfered with the utilization of the improved backward approach because of the decoupling of SIF and GPP due to stomatal closure. This new approach offers new insight into the estimation of diurnal canopy SIF and can help understand the photosynthesis of vegetation for future climate change studies.
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Lenzo, Basilio, et Valerio Rossi. « A Simple Mono-Dimensional Approach for Lap Time Optimisation ». Applied Sciences 10, no 4 (22 février 2020) : 1498. http://dx.doi.org/10.3390/app10041498.
Texte intégralRésumé :
Lap time minimisation methods have great relevance in the analysis of race tracks, and in the design and optimisation of race vehicles. Several lap time minimisation approaches have been proposed in the literature, which are computationally demanding because they need to either solve differential equations or to implement a forward–backward integration based on an apex-finding method. This paper proposes an alternative method, based on a mono-dimensional quasi-steady-state numerical approach. The proposed approach uses a simplified vehicle model accounting for combined tyre–road interactions, aerodynamic effects, and power limitations. The method exploits the knowledge of the curvature of the trajectory, which is worked out through a rigorous approach that allows for the use trajectories defined with respect to ageneric curve parameter and not necessarily the arc length. An iterative routine is implemented that exploits the vehicle dynamics, without solving differential equations or performing forward–backward integrations from the trajectory apexes. Simulations are carried out on three different tracks and are shown to be computationally efficient. Despite being intentionally simple, the proposed method allows to grasp key aspects of the problem, such as the effect of the combined tyre–road interactions on the acceleration profiles, and the effect of aerodynamic drag and downforce on the position of the braking point on the track and on the speed profile.
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KAWAI, REIICHIRO. « SENSITIVITY ANALYSIS AND DENSITY ESTIMATION FOR THE HOBSON-ROGERS STOCHASTIC VOLATILITY MODEL ». International Journal of Theoretical and Applied Finance 12, no 03 (mai 2009) : 283–95. http://dx.doi.org/10.1142/s0219024909005294.
Texte intégralRésumé :
Monte Carlo estimators of sensitivity indices and the marginal density of the price dynamics are derived for the Hobson-Rogers stochastic volatility model. Our approach is based mainly upon the Kolmogorov backward equation by making full use of the Markovian property of the dynamics given the past information. Some numerical examples are presented with a GARCH-like volatility function and its extension to illustrate the effectiveness of our formulae together with a clear exhibition of the skewness and the heavy tails of the price dynamics.
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Wrzaczek, Stefan, Michael Kuhn et Ivan Frankovic. « Using Age Structure for a Multi-stage Optimal Control Model with Random Switching Time ». Journal of Optimization Theory and Applications 184, no 3 (7 décembre 2019) : 1065–82. http://dx.doi.org/10.1007/s10957-019-01598-5.
Texte intégralRésumé :
AbstractThe paper presents a transformation of a multi-stage optimal control model with random switching time to an age-structured optimal control model. Following the mathematical transformation, the advantages of the present approach, as compared to a standard backward approach, are discussed. They relate in particular to a compact and unified representation of the two stages of the model: the applicability of well-known numerical solution methods and the illustration of state and control dynamics. The paper closes with a simple example on a macroeconomic shock, illustrating the workings and advantages of the approach.
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Huillet, Thierry E. « A Duality Approach to the Genealogies of Discrete Nonneutral Wright-Fisher Models ». Journal of Probability and Statistics 2009 (2009) : 1–22. http://dx.doi.org/10.1155/2009/714701.
Texte intégralRésumé :
Discrete ancestral problems arising in population genetics are investigated. In the neutral case, the duality concept has been proved of particular interest in the understanding of backward in time ancestral process from the forward in time branching population dynamics. We show that duality formulae still are of great use when considering discrete nonneutral Wright-Fisher models. This concerns a large class of nonneutral models with completely monotone (CM) bias probabilities. We show that most classical bias probabilities used in the genetics literature fall within this CM class or are amenable to it through some “reciprocal mechanism” which we define. Next, using elementary algebra on CM functions, some suggested novel evolutionary mechanisms of potential interest are introduced and discussed.
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Merrison-Hort, Robert. « Fireflies : New Software for Interactively Exploring Dynamical Systems Using GPU Computing ». International Journal of Bifurcation and Chaos 25, no 13 (15 décembre 2015) : 1550181. http://dx.doi.org/10.1142/s0218127415501813.
Texte intégralRésumé :
In nonlinear systems, where explicit analytic solutions usually cannot be found, visualization is a powerful approach which can give insights into the dynamical behavior of models; it is also crucial for teaching this area of mathematics. In this paper, we present new software, Fireflies, which exploits the power of graphical processing unit (GPU) computing to produce spectacular interactive visualizations of arbitrary systems of ordinary differential equations. In contrast to typical phase portraits, Fireflies draws the current position of trajectories (projected onto 2D or 3D space) as single points of light, which move as the system is simulated. Due to the massively parallel nature of GPU hardware, Fireflies is able to simulate millions of trajectories in parallel (even on standard desktop computer hardware), producing “swarms” of particles that move around the screen in real-time according to the equations of the system. Particles that move forwards in time reveal stable attractors (e.g. fixed points and limit cycles), while the option of integrating another group of trajectories backwards in time can reveal unstable objects (repellers). Fireflies allows the user to change the parameters of the system as it is running, in order to see the effect that they have on the dynamics and to observe bifurcations. We demonstrate the capabilities of the software with three examples: a 2D “mean field” model of neuronal activity, the classical Lorenz system, and a 15D model of three interacting biologically realistic neurons.
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Wangari, Isaac Mwangi, et Lewi Stone. « Analysis of a Heroin Epidemic Model with Saturated Treatment Function ». Journal of Applied Mathematics 2017 (2017) : 1–21. http://dx.doi.org/10.1155/2017/1953036.
Texte intégralRésumé :
A mathematical model is developed that examines how heroin addiction spreads in society. The model is formulated to take into account the treatment of heroin users by incorporating a realistic functional form that “saturates” representing the limited availability of treatment. Bifurcation analysis reveals that the model has an intrinsic backward bifurcation whenever the saturation parameter is larger than a fixed threshold. We are particularly interested in studying the model’s global stability. In the absence of backward bifurcations, Lyapunov functions can often be found and used to prove global stability. However, in the presence of backward bifurcations, such Lyapunov functions may not exist or may be difficult to construct. We make use of the geometric approach to global stability to derive a condition that ensures that the system is globally asymptotically stable. Numerical simulations are also presented to give a more complete representation of the model dynamics. Sensitivity analysis performed by Latin hypercube sampling (LHS) suggests that the effective contact rate in the population, the relapse rate of heroin users undergoing treatment, and the extent of saturation of heroin users are mechanisms fuelling heroin epidemic proliferation.
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Veprikova, E. B., et A. A. Kislenok. « Estimation of territorial backwardness in the regional development policy-making (on the example of the Far-Eastern regions) ». POWER AND ADMINISTRATION IN THE EAST OF RUSSIA 94, no 1 (2021) : 33–44. http://dx.doi.org/10.22394/1818-4049-2021-94-1-33-44.
Texte intégralRésumé :
The problems of interregional differentiation and territorial backwardness hamper economic growth, lead to imbalances in the spatial development of the Russian Federation and increase risks of forming backward territories. The presence of backward parts within a territorial system brings down the overall state policy's effectiveness because positive development dynamics in several parts of the territory cancels by the adverse processes in other parts of the territory. Therefore, the investigation of the conditions of territorial development as a spatial system and the identification of indicators of the increasing backwardness within this system is a fundamental problem of state regional policy-making. It is worthwhile identifying risks of forming territorial backwardness earlier when accurate management's decisions can be undertaken with the higher effectiveness and smaller recourses. To this end, monitoring of the social and economic developments based upon an informative system of indicators revealing not only the present status of performance of the region but also its dynamics in terms of the determinant of the territorial backwardness. The article presents the author's approach to the assessment of territorial backwardness featured with taking into account the conditions of maintaining and reproducing high-quality human capital as a critical driver of regional development. Given the national policy's priorities towards the advanced social and economic development of the Far East of Russia, the proposed approach has been tested on the Far-Eastern regions.
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Aberqi, A., M. Elmassoudi et M. Hammoumi. « Discrete solution for the nonlinear parabolic equations with diffusion terms in Museilak-spaces ». Mathematical Modeling and Computing 8, no 4 (2021) : 584–600. http://dx.doi.org/10.23939/mmc2021.04.584.
Texte intégralRésumé :
In this paper, a class of nonlinear evolution equations with damping arising in fluid dynamics and rheology is studied. The nonlinear term is monotone and possesses a convex potential but exhibits non-standard growth. The appropriate functional framework for such equations is the modularly Museilak–spaces. The existence and uniqueness of a weak solution are proved using an approximation approach by combining an internal approximation with the backward Euler scheme, also a priori error estimate for the temporal semi-discretization is given.