Different Sets Of Initial Conditions Research Articles

On the separation of solutions to fractional differential equations of order α ∈ (1,2)

Given the Caputo-type fractional differential equation Dαy(t)=f(t,y(t)) with α∈(1,2), we consider two distinct solutions y1,y2∈C[0,T] to this equation subject to different sets of initial conditions. In this framework, we discuss nontrivial upper and lower bounds for the difference |y1(t)−y2(t)| for t∈[0,T]. The main emphasis is on describing how such bounds are related to the differences of the associated initial values.

On the impact of initial conditions in the forecast of Hurricane Leslie extratropical transition

Hurricane Leslie (2018) was a non-tropical system that lasted for a long time undergoing several transitions between tropical and extratropical states. Its trajectory was highly uncertain and difficult to predict. Here the extratropical transition of Leslie is simulated using the Model for Prediction Across Scales (MPAS) with two different sets of initial conditions (IC): the operational analysis of the Integrate Forecast System (IFS) and the Global Forecast System (GFS).Discrepancies in Leslie position are found in the IC patterns, and in the intensity and amplitude of the dorsal-trough system in which Leslie is found. Differences are identified both in the geopotential height at 300 hPa and the geopotential thickness. Potential temperature in the dynamic tropopause shows a broader, more intense trough displaced western when using the IC-IFS. The IC-IFS simulation shows lesser trajectory errors but wind speed overestimation than the IC-GFS one. The complex situation of the extratropical transition, where Leslie interacts with a trough, increases the uncertainty associated with the intensification process.The disparities observed in the simulations are attributed to inaccuracies in generating the ICs. Both ICs generate different atmospheric configurations when propagated in time. Results suggest that during an extratropical transition in a highly baroclinic atmosphere, the IFS model's data assimilation method produced a more precise analysis than GFS due to the greater number of observations assimilated by the IFS, the greater spatial resolution of the model and the continuous adjustment of the simulations with the field of observations.

Superextreme spiking oscillations and multistability in a memristor-based Hindmarsh–Rose neuron model

In this paper, we investigate the occurrence of superextreme spiking (SES) oscillations and multistability behavior in a memristor-based Hindmarsh–Rose neuron model. The presence of SES oscillations has been identified as arising due to the occurrence of an interior crisis. As the membrane current I(t), considered as the control parameter is varied, the system transits from bounded chaotic spiking (BCS) oscillations to SES oscillations. These transitions are captured numerically using geometrical representations like time series plots, phase portraits and inter-spikes interval return maps. The characterization of SES from the BCS oscillations is made using statistical tools such as phase shift analysis and probability density distribution function. The multistability nature has been observed using bifurcation analysis and confirmed by the Lyapunov exponents for two different sets of initial conditions. The numerical simulations are substantiated through real-time hardware experiments realized through a nonlinear circuit constructed using an analog model of the memristor.

Black hole-neutron star simulations with the BAM code: First tests and simulations

The first detections of black hole - neutron star mergers (GW200105 and GW200115) by the LIGO-Virgo-Kagra Collaboration mark a significant scientific breakthrough. The physical interpretation of pre- and post-merger signals requires careful cross-examination between observational and theoretical modelling results. Here we present the first set of black hole - neutron star simulations that were obtained with the numerical-relativity code BAM. Our initial data are constructed using the public LORENE spectral library which employs an excision of the black hole interior. BAM, in contrast, uses the moving-puncture gauge for the evolution. Therefore, we need to ``stuff'' the black hole interior with smooth initial data to evolve the binary system in time. This procedure introduces constraint violations such that the constraint damping properties of the evolution system are essential to increase the accuracy of the simulation and in particular to reduce spurious center-of-mass drifts. Within BAM we evolve the Z4c equations and we compare our gravitational-wave results with those of the SXS collaboration and results obtained with the SACRA code. While we find generally good agreement with the reference solutions and phase differences $\lesssim 0.5$ rad at the moment of merger, the absence of a clean convergence order in our simulations does not allow for a proper error quantification. We finally present a set of different initial conditions to explore how the merger of black hole neutron star systems depends on the involved masses, spins, and equations of state.

INITIAL CONDITIONS TO STUDY THE TEMPORAL BEHAVIOR OF A VISCOELASTIC LIQUID JET UNDER PERTURBATION

We study the behaviour of a viscoelastic liquid jet. To that end, we carry out a temporal stability analysis. The eigenvalue problem has been already solved and is reported in Cottier et al. ILASS-Europe 2019, but does not enable a complete description on the jet's behaviour. In this paper, we propose two different sets of initial conditions to close the corresponding initial-value problem. These conditions are determined by formulating the different quantities that can be imposed over the base flow, and making a correspondence with the expression of these quantities found by solving the eigenvalue problem, evaluated at the initial time. Here the imposed quantities are considered to hold on the jet's surface position, on the axial flow velocity and on the axial normal extra stress within the flow. After giving a general formulation of the three initial conditions, two particular different initial configurations are distinguished: the pure deformation and the pure impulse configuration. A linearization of the conditions leads us to the determination of the analytical expressions of the first-order flow quantities in function of control parameters determining the choice of the initial configuration. The reduction of the initial conditions to the Newtonian case is valid and does not induce any physical change at the initial time. An application of the initial conditions is made upon a given liquid jet and the visualization of the flow quantities allows a comparison between the pure deformation and the pure impulse configuration.

Filtering Theory for a Weakly Coloured Noise Process

The problem of analyzing the Ito stochastic differential system and its filtering has received attention. The classical approach to accomplish filtering for the Ito SDE is the Kushner equation. In contrast to the classical filtering approach, this paper presents filtering for the stochastic differential system affected by weakly coloured noise, i.e., $$\dot{x}_{t} = f\left( {x_{t} } \right) + g\left( {x_{t} } \right)\xi_{t} ,$$ where the input process $$\xi_{t}$$ is a weakly coloured noise process. As a special case, the process $$\xi_{t}$$ can be regarded as the Ornstein–Uhlenbeck (OU) process, i.e., $$d\xi_{t} = - \alpha \xi_{t} dt + \beta dB_{t} ,$$ where $$\alpha > 0.$$ More precisely, the filtering model of this paper can be cast as $$\dot{x}_{t} = f\left( {x_{t} } \right) + g\left( {x_{t} } \right)\xi_{t} ,$$ $$z_{t} = \int\limits_{{t_{0} }}^{t} {h(x_{\tau } )d\tau + \eta_{t} ,}$$ where $$h(x_{t} )$$ is the measurement non-linearity and $$\eta = \{ \eta_{t} ,t_{0} \le t < \infty \}$$ is the Brownian motion process. The former expression describes the structure of a noisy dynamical system, and the latter is the observation equation. The novelties of this paper are two (1) the extension of the filtering theory for the Ito stochastic differential system to the filtering theory for the ‘weakly coloured noise-driven’ stochastic differential system (2) the theory of this paper is based on a pioneering contribution of Ruslan Stratonovich involving the perturbation-theoretic approach to noisy dynamical systems in combination with the notion of the ‘filtering density’ evolution. The stochastic evolution of condition moment is derived by utilizing the filtering density evolution equation. A scalar Duffing system driven by the OU process is employed to test the effectiveness of the filtering theory of the paper. Numerical simulations involving four different sets of initial conditions and system parameters are utilized to examine the efficacy of the filtering algorithm of this paper.

Formation reconfiguration optimization for the IRASSI space interferometer

The IRASSI mission, aimed at studying pre-biotic conditions in Earth-like planets, is composed of five free-flying telescopes operating around the Sun-Earth L2 point. To address the challenge of finding suitable relative positions in three-dimensional space which satisfy science goals over long periods of time, a reconfiguration procedure has been devised. The method assigns optimized post-maneuver positions of the individual telescopes for the next to-be-observed target. A mesh-adaptive direct search algorithm is selected for the optimization and two cost functions are analyzed: a fuel-based and a ΔV-based one, both pursuing a balanced use of these resources across the fleet. The effect of simulation variables such as initial wet mass and fuel mass balance, thruster settings and cost-function weighting parameters is evaluated with respect to overall used fuel and fuel balance, ΔV and ΔV balance and maneuver duration. Results show that for wet-mass-imbalanced cases, cost functions should be tuned differently for optimal fuel and ΔV management. This is not necessarily the case for homogeneous or fuel-mass imbalanced cases. The analysis also suggests that the ΔV-based function produces more consistent optimal ΔV-balancing potential across different sets of initial conditions and shows less variability in individual maneuvers than the fuel-based function.

Constraining the particle production mechanism in Au+Au collisions at sNN=7.7 , 27, and 200 GeV using a multiphase transport model

We study the production of pions, kaons, and (anti)protons in A Multi Phase Transport (AMPT) Model in Au+Au collisions at $\sqrt{s_{NN}}=$ 7.7, 27, and 200 GeV. We present the centrality and energy dependence of various bulk observables such as invariant yields as a function of transverse momentum $p_T$, particle yields $dN/dy$, average transverse momentum $\langle p_T \rangle$, and various particle ratios, and compare them with experimental data. Both default and string melting (SM) versions of the AMPT model are used with three different sets of initial conditions. We observe that neither the default nor the SM version of the model could consistently describe the centrality dependence of all observables at the above energies with any one set of initial conditions. The energy dependence behavior of the experimental observables for 0--5\% central collisions is in general better described by the default AMPT model using the modified HIJING parameters for Lund string fragmentation and 3mb parton scattering cross-section. In addition, the kaon production as well as the $K/\pi$ ratio at 7.7 GeV are under predicted by the AMPT model.

Development and Research FMEA Expert Team Model

This paper presents a description and research of the model of the team of experts in the application of the Failure Mode and Effects Analysis (FMEA). The main factors affecting the efficiency of the team of experts are highlighted. The generalized mathematical model of influence of these factors on efficiency of work of team is described. The research of this model on three different sets of initial data characterizing typical situations arising at the enterprise at application of the FMEA method is presented. An assessment was made of the simultaneous change of two types of competencies and motivation of both the participants and the team-wide single parameter. The model is studied on three typical situations with a different set of initial conditions and the corresponding parameters. The use of this technique allows for a preliminary assessment of the change in the effectiveness of the analysis by a team of specialists over time, which allows on the one hand to plan correctly not only the application of the FMEA itself within the overall schedule of work, but also to properly organize the training of the team. In addition, this technique will allow you to visually compare the various teams with each other and choose the most optimal or effective team.

Isolation: an Alternative to the “Acting White” Hypothesis in Explaining Black Under-Enrollment in Advanced Courses

In this paper we propose a model for understanding the under-enrollment of black students in advanced courses that demonstrates how group differences in educational investment decisions can arise even in the absence of any group-level differences in underlying incentives or behavioral propensities. In our model, students gain peer group acceptance by spending time with other peer group members. This can occur during both leisure time and class time, provided enough members of their relevant peer group also take the same academic courses. This produces a scenario in which taking advanced courses is a complement to peer group acceptance for some students (those who have enough peer group members taking advanced courses) and a tradeoff for other students (those who do not have enough peer group members in advanced courses). Structural and historical forces, such as racialized tracking, that contribute to an initial condition of fewer black students in advanced courses can create an environment where black students are more likely to be isolated from other members of their racial group, relative to white students. Our model is distinct from theories like the “acting white” hypothesis that assume a cultural or non-cognitive skill deficit on the part of black students. The results from this model arise not because black students respond to incentives differently, but because they face a different set of initial conditions, most likely as the result of institutional barriers.

Synchronization of Synchronous Reluctance Motors Using the Discrete Sliding Mode Control Technique

The synchronous reluctance motor (SynRM) drive system is known to exhibit chaotic behavior under specified conditions. In this paper, the discrete-time sliding mode control (DSMC) technique is used to synchronize two SynRMs starting from different sets of initial conditions. The mixed variable speed reaching law is adopted in the design of the controller scheme. The parameters of the designed control scheme are tuned using a genetic algorithm (GA). Simulation results are presented to demonstrate the effectiveness of the proposed controller. In addition, the performance of the proposed control scheme is studied through simulations when bounded disturbances and mismatches between the parameters of the systems and those of the control scheme exist. The simulation results show that the designed control scheme is robust to bounded external disturbances and to mismatches in the parameters of the systems.

Secondary seed dispersal in the Klausmeier model of vegetation for sloped semi-arid environments

The effects of secondary seed dispersal on the dynamics of banded vegetation are investigated in the framework of a generalized version of one of the easiest tools for the description of pattern formation along the hillsides of semi-arid environments: the Klausmeier model. The generalization here considered consists in augmenting the evolution equation for the vegetation biomass with an advection term mimicking the anisotropic dispersal of seeds by overland flow. Linear stability analysis is used to deduce the threshold condition for the occurrence of wave instability as well as to obtain approximated explicit expressions for some key quantities: pattern speed, locus of stationary patterns and excited wavenumber. The generalized model is also integrated numerically considering two different sets of initial conditions that yield pattern dynamics originating from degradation of uniform vegetation or colonization of bare ground. These numerical simulations are performed to corroborate the analytical predictions, to characterize more deeply the propagating character of the edges of vegetation patches and to emphasize how distinct initial conditions may lead to significantly different ecological scenarios.

A New Double-Wing Chaotic System With Coexisting Attractors and Line Equilibrium: Bifurcation Analysis and Electronic Circuit Simulation

This research work reports a double-wing chaotic system with a line of equilibrium points and constructs an electronic circuit via MultiSIM for practical implementation. Explicitly, the new chaotic system has a total of six terms with two quadratic nonlinearities and absolute function nonlinearity. Using the phase plots in MATLAB, we demonstrate that the new chaotic system has double-wing chaotic attractor. We describe the Lyapunov exponents and the Kaplan-Yorke fractal dimension of the new chaotic system. A novel feature of the new chaotic system is that the system has rest points located on the z-axis as well as two rest points not on the z-axis. Thus, the new system has infinite number of rest points and hidden attractor. We also exhibit that the new double-wing chaotic system has multi-stability and we illustrate the coexistence of attractors for two different sets of initial conditions. Some interesting dynamical properties such as offset boosting are also presented. Finally, we build an electronic circuit of the new chaotic system and show that the theoretical model has practical feasibility for implementation.

Energy exchange between coupled mechanical oscillators: linear regimes

Nonlinear mechanisms are frequently invoked to explain unexpected observations during processes of energy exchange in mechanical systems. However, whether the same phenomena could be observed in a purely linear system is seldom considered. In this paper, we revisit the problem of two linearly coupled, damped, harmonic oscillators, with emphasis on the dynamics of their mutual exchange of energy. A novel criterion is established to discern between two well-differentiated regimes of energy exchange under ringdown conditions, when all external excitations are turned off and the oscillatory motion is left to decay by dissipation. The two regimes are induced by different sets of initial conditions, and correspond to extremal values of the total net energy transferred during ringdown. Although the problem is in principle fully solvable, its algebraic involvedness requires in practice to resort to approximated expressions for oscillation frequencies and decay rates. We explicitly provide such approximations in the limit of high quality factors and weak coupling. This limit is relevant to current experiments on micro- and nanomechanical oscillators, whose physical behavior is usually explained by extensive allusion to energy exchange. Our results should help to discern between observations that are genuinely due to nonlinear effects, and those that can be explained in terms of linear mechanisms only.

Population dynamics with multiple Allee effects induced by fear factors – A mathematical study on prey-predator interactions

• Mathematical models on effect of fear and strong Allee mechanism have been proposed and analysed. • We have shown how fear can significantly reduce the per-capita growth rate of prey with generalised predator. • We have shown that fear has no role in the stability of prey-predator system, with linear functional response. • Fear effect can stabilize the eco-epidemiological system and promote the coexistence of all the three populations. • Finally, fear may be a cause of the Allee effect/multiple Allee effects at low population density. In the present, ecologists generally consider the interactions, which are directly related to the density effects, that species have on each other, like predation, mutualism, refuge, etc. However, some experimental studies showed that apart from the direct killing, predation fears itself can reduce the prey growth rate by 40%. Therefore, in the present study, we have considered a trait effect, which is characterized by the reduction of prey growth rate due to fear of predator, where the prey is already suffered by the mating induced strong Allee effects, in the reproduction process. First, we developed and analyzed the single-species model and showed that how the fear effect can significantly reduce the per-capita growth rate (pgr) and may be a possible cause of the multiple Allee effects at low population density. Next, we consider a prey-predator model with linear functional response and showed that fear does not affect the equilibrium stability, but the time scale difference among two populations has a positive effect. It will help the system to converge to the stable steady states faster than before. Finally, we study an eco-epidemiological model with the same assumptions, where prey is being suffered by the disease. We showed that in eco-epidemiological systems fear can greatly affect the system stability. Fear can stabilize the system at the interior equilibrium, where all the three population coexists, or it can create the oscillatory coexistence of all the three populations. In the presence of fear, system shows bi-stability among different equilibria. We have also shown the basin stability at multiple stable parameter regions, which yields the probability of convergence of each equilibrium for a given set of different initial conditions. All these findings may have potential impacts in population management and conservation biology.

Creation of Small Skeletal Models in Kinetic Model Reductions

This paper outlines updates made to a method for chemical kinetic model reduction for use in computational fluid dynamics simulations. Specifically, this method uses a time-integrated flux-based algorithm to find a small skeletal model based on a detailed kinetic model, before optimization of the rate constants, using steepest descent and solution mapping methods. The new method is then applied to the reduction of a methane–air model and a dodecane–air model for two different sets of initial conditions. The results show that the optimized models are able to predict the performance of their respective detailed models over the ranges of conditions for which the optimizations are based. Results for the optimized models are also able to predict the perfectly stirred reactor response better than the optimized models generated using the older method.

The Modeling Dynamics of HIV and CD4 $$^{+}$$ + T-cells During Primary Infection in Fractional Order: Numerical Simulation

This article is devoted to introduce a numerical treatment using Adams–Bashforth–Moulton method of the fractional model of HIV-1 infection of CD4 $$^{+}$$ T-cells. We study the effect of the changing the average number of viral particles N with different sets of initial conditions on the dynamics of the presented model. The fractional derivative is described in Caputo sense. Special attention is given to present the local stability of the proposed model using fractional Routh–Hurwitz stability criterion. Qualitative results show that the model has two equilibria: the disease-free equilibrium and the endemic equilibrium points. We compare our numerical solutions with those numerical solutions using fourth-order Runge–Kutta method (RK4). The obtained numerical results of the proposed model show the simplicity and the efficiency of the proposed method.

Pre-inflationary universe in loop quantum cosmology

The evolutions of the flat FLRW universe and its linear perturbations are studied systematically in the dressed metric approach of LQC. When it is dominated by the kinetic energy of the inflaton at the quantum bounce, the evolution of the background can be divided into three different phases prior to the preheating, {\em bouncing, transition and slow-roll inflation}. During the bouncing phase, the evolution is independent of not only the initial conditions, but also the inflationary potentials. In particular, the expansion factor can be well described by the same exact solution in all the cases considered. In contrast, in the potential dominated case such a universality is lost. It is because of this universality that the linear perturbations are also independent of the inflationary models and obtained exactly. During the transition phase, the evolutions of the background and its linear perturbations are found explicitly, and then matched to the ones given in the other two phases. Hence, once the initial conditions are imposed, the linear scalar and tensor perturbations will be uniquely determined. Considering two different sets of initial conditions, one imposed during the contracting phase and the other at the bounce, we calculate the Bogoliubov coefficients and find that the two sets yield the same results and all lead to particle creations at the onset of the inflation. Due to the pre-inflationary dynamics, the scalar and tensor power spectra become scale-dependent. Comparing with the Planck 2015 data, we find constraints on the total e-folds that the universe must have expanded since the bounce, in order to be consistent with current observations.

A PREDATOR-PEST MODEL WITH ALLEE EFFECT AND PEST CULLING AND ADDITIONAL FOOD PROVISION TO THE PREDATOR — APPLICATION TO PEST CONTROL

The harmful effects of insect pests on human health and agricultural output are a major global concern. Frequent use of chemical pesticides as a means of pest control can have detrimental effects on the environment, resulting in water and soil pollution, food toxicity, resistance to pesticides, etc. As a result, there is an urgent need to develop a biological pest-control approach that would mitigate these harmful effects. The main purpose of the present study is to explore the interaction between strong Allee effects in the pest with other biological control mechanisms, such as providing additional food to the predator and pest culling as a means of proposing an efficient pest-control policy. To achieve this goal, local stability analysis around the equilibria, possible bifurcation and some basic dynamical features of the system was performed. Our work focuses on the basin of stability in multiple stable regions of the model, which yields the probability of convergence of each equilibrium for a given set of different initial conditions. The system exhibits bi-stability and tri-stability of the equilibria. Our findings indicate that providing additional food to the predator can be an efficient stand-alone pest control strategy, which can, if needed, be combined with other methods.

A matrix projection method for on line stable estimation of 1D and 3D shear building models

An estimation method is presented that combines the use of recursive least squares, a matrix parameterized model, Gershgorin circles and tridiagonal matrices properties to allow the identification of stable shear building models in the presence of low excitation or low damping. The resultant scheme yields a significant reduction on the number of calculations involved, when compared with the standard vector parameterization based schemes. As real buildings are always open loop stable, the use of an stable shear building model for vibration control purposes allows the design of more robust control laws. Extensive simulation results are presented for cases of low excitation comparing the results of using or not this matrix projection method with different sets of initial conditions. Results indicate that the use of this projection method does not have an influence in the recovery of natural frequencies, however, it significantly improves the recovery of mode shapes.