Perturbation Parameter Research Articles

Location of the collinear equilibrium points in the elliptic restricted three-body problem with various perturbation effects

Abstract This study aims to examine the elliptic restricted three-body problem (ERTBP) by modifying the classical case and applying various perturbation sources to the three-body system. In this study, the locations of the Lagrange collinear equilibrium points of ERTBP were examined. We consider that the first primary body emits radiation and has an oblate shape. In contrast, the second primary body was considered to be elongated and approximated as a finite straight-segment. In addition, the perturbations from the disk-like structure around the three-body system were also included. The equations of motion of the infinitesimal body are presented in a dimensionless pulsating coordinate system. Three collinear equilibrium points were identified. The locations of the collinear equilibrium points were calculated numerically for several cases of perturbation values and also presented versus eccentricity over its range. We observed that the position of the collinear equilibrium points (L 1, L 2, and L 3) shifted when perturbing parameters were included, as opposed to where they were in the classical ERTBP.

Value-Positivity for Matrix Games

Matrix games are the most basic model in game theory, and yet robustness with respect to small perturbations of the matrix entries is not fully understood. In this paper, we introduce value positivity and uniform value positivity, two properties that refine the notion of optimality in the context of polynomially perturbed matrix games. The first concept captures how the value depends on the perturbation parameter, and the second consists of the existence of a fixed strategy that guarantees the value of the unperturbed matrix game for every sufficiently small positive parameter. We provide polynomial-time algorithms to check whether a polynomially perturbed matrix game satisfies these properties. We further provide the functional form for a parameterized optimal strategy and the value function. Finally, we translate our results to linear programming and stochastic games, where value positivity is related to the existence of robust solutions. Funding: This research was supported by Fondation CFM pour la Recherche, the H2020 European Research Council [Grant ERC-CoG-863818 (ForM-SMArt)], the Austrian Science Fund [Grant 10.55776/COE12], ANID Chile [Grant ACT210005], and Agence Nationale de la Recherche [Grant ANR-21-CE40-0020].

A Method for Interpreting the Role of Parameterized Turbulence on Global Metrics in the Community Earth System Model

AbstractThe parameterization of subgrid‐scale processes such as boundary layer (PBL) turbulence introduces uncertainty in Earth System Model (ESM) results. This uncertainty can contribute to or exacerbate existing biases in representing key physical processes. This study analyzes the influence of tunable parameters in an experimental version of the Cloud Layers Unified by Binormals (CLUBBX) scheme. CLUBB is the operational PBL parameterization in the Community Atmosphere Model version 6 (CAM6), the atmospheric component of the Community ESM version 2 (CESM2). We perform the Morris one‐at‐a‐time (MOAT) parameter sensitivity analysis using short‐term (3‐day), initialized hindcasts of CAM6‐CLUBBX with 24 unique initial conditions. Several input parameters modulating vertical momentum flux appear most influential for various regionally‐averaged quantities, namely surface stress and shortwave cloud forcing (SWCF). These parameter sensitivities have a spatial dependence, with parameters governing momentum flux most influential in regions of high vertical wind shear (e.g., the mid‐latitude storm tracks). We next evaluate several experimental 20‐year simulations of CAM6‐CLUBBX with targeted parameter perturbations. We find that parameter perturbations produce similar physical mechanisms in both short‐term and long‐term simulations, but these physical responses can be muted due to nonlinear feedbacks manifesting over time scales longer than 3 days, thus causing differences in how output metrics respond in the long‐term simulations. Analysis of turbulent fluxes in CLUBBX indicates that the influential parameters affect vertical fluxes of heat, moisture, and momentum, providing physical pathways for the sensitivities identified in this study.

The effect of a constant electric field in an undisturbed plasma on the stability of the electron beam–gas discharge collisional plasma system

This work is devoted to the study of a fast non-relativistic electron beam–gas discharge plasma system within the framework of the kinetic theory of stability. The influence of a constant electric field, collinear beam velocity, on the stability of the system in an undisturbed plasma is studied. It is shown that even a relatively small electric field, which does not significantly affect the energy of the electron beam, can lead to significant changes in the parameters of harmonic disturbances propagating in the electron beam–plasma system in the region of its instability. It was found that the reason for such changes is the drift of plasma electrons, which, as a consequence, leads to a change in the frequency of disturbances in the coordinate system associated with the plasma due to the Doppler effect. The results obtained are demonstrated by calculations based on the kinetic theory of perturbation parameters in a low-voltage beam discharge in rare gases, which is used in the development of plasma electronics devices. The effect of electron-atomic collisions on the stability of the electron beam–plasma system is investigated and compared with the results of other authors' works.

Is the IROC H&N credentialing phantom an effective surrogate for different anatomical sites?: Using IROC's H&N phantom for various sites

PURPOSEThe IROC head and neck phantom is used to credential institutions for IMRT delivery for all anatomical sites where delivery of modulated therapy is a primary challenge. This study evaluated how appropriate the use of this phantom is for varied clinical anatomy by evaluating how closely the IROC head and neck phantom described clinical dose errors from beam modeling compared to various anatomical sites. METHODSThe MLC offset, transmission, PDD and seven additional beam modeling parameters for a Varian accelerator were modified in RayStation to match community data at the 2.5, 25, 50, 75 and 97.5 percentile levels. Modifications were evaluated on 25 H&N phantom cases and 25 clinical cases (H&N, prostate, lung, mesothelioma, and brain), generating 2,000 plan perturbations. Differences in mean dose delivered to clinical target volumes (CTV) and organs at risk (OAR) were compared between phantom and clinical plans to assess the relationship between dose deviations in phantom versus clinical CTVs, and as a function of 18 different complexity metrics. RESULTSPerturbations to MLC offset and transmission parameters demonstrated the greatest impact on dose accuracy for phantom and clinical plans (for all anatomic sites). The phantom demonstrated equivalent or greater sensitivity to these parameter perturbations when compared to clinical sites, largely aligning with treatment complexity. The mean MLC Gap best described the impact of errors in TPS beam modeling parameters in phantoms plan and clinical plans from various anatomical sites. CONCLUSIONWhen compared across various anatomical sites, the IROC H&N credentialing phantom exhibited similar or greater sensitivity to errors in the treatment planning system. As such, it is a suitable surrogate device for assessing institutional performance across various anatomical sites. If an institution successfully irradiates the phantom, that result confers confidence that IMRT to a wide range of anatomical sites can be successfully delivered by the institution.

Impacts of the Thermocline Feedback Uncertainty on El Niño Simulations in the Tropical Pacific

AbstractAs a key dynamic element of the Bjerknes feedback mechanism, the thermocline effect (TE) is critically important to El Niño modeling. In this study, the potential influence of TE‐related parametric uncertainties on El Niño is investigated using the conditional nonlinear optimal parametric perturbation (CNOP) method based on an intermediate coupled model (ICM). The optimal perturbation of the TE‐related parameter (OTEP), which substantially affects El Niño simulations, is estimated through the CNOP approach. Results reveal that the El Niño simulation is highly sensitive to the TE uncertainty in the eastern equatorial Pacific, with OTEP‐induced simulation errors demonstrating an El Niño‐like growth trend. On one hand, as indicated by the simulated El Niño intensity, the uncertainty in the TE in the eastern region can easily affect the strength of the Bjerknes feedback‐related thermocline effect and atmospheric circulation. On the other hand, the enhanced TE is highly favored to accelerate the growth of the SST error due to the air–sea interaction, thus severely affecting the El Niño simulations. Therefore, adequately representing the TE in the equatorial eastern Pacific is emphasized for effectively improving El Niño simulations.

Perturbing and Oblateness's Impact on the Generalized Photogravitational Restricted Three-Body Problem

In this research work, the effects of perturbing and oblateness on the generalised photogravitational restricted three body problem (RTBP) are examined when the primary are regarded as radiation sources and oblate spheroid. The perturbing forces were included in the equations of motion that we developed for the system. The triangular libration points were derived in terms of the perturbing parameters using linear approximations, and their influence was seen. Applying Murray's criteria, we determined that the triangular libration points remained unstable due to the nature of the characteristics equation matching to the variational equations of motion of the system generated.

Theoretical Analysis of Viscoelastic Friction System Characteristics of Robotic Arm Brake Based on Fractional Differential Theory

In engineering practice, the nonlinear vibration effect can easily lead to chaos in the system, which will not only reduce the performance of the system but also lead to premature fatigue of components, control failure, and increased safety risks. In view of the core position of the robotic arm in modern industry, this study relies on the robotic arm brake system to explore the theoretical basis of integrated viscoelastic materials as a vibration isolation layer. By analyzing the dynamic characteristics of the friction braking system with fractional differential terms, it aims to provide a new perspective for understanding and controlling the chaotic phenomena of a class of nonlinear friction systems. Firstly, we construct a model of a friction system and analyze its dynamic characteristics in detail. The self-excited vibration of the system under disturbance is studied. The relationship between amplitude and frequency is calculated by a nonlinear approximate analytical algorithm, and the accuracy of this relationship is verified by a numerical algorithm. Then, we compare the differences between non-fractional systems and fractional systems. It is found that with the increase in the fractional order term, the vibration amplitude of the system decreases significantly, which helps to reduce the nonlinear characteristics generated by the friction system and narrow the range of unstable solutions. Secondly, we also study the influence of parameter coefficients on the amplitude–frequency characteristics and analyze the local static bifurcation characteristics through singularity theory. Finally, we study the dynamic bifurcation behavior under different parameter perturbations and find that the change in system parameters will lead to the alternation of periodic motion and chaotic motion.

Adaptive mesh extended cubic B-spline method for singularly perturbed delay Sobolev problems

The purpose of this paper is to develop a robust numerical scheme for a class of singularly perturbed delay Sobolev (pseudo-parabolic) problems that have wide application in various branches of mathematical physics and fluid mechanics.For the small perturbation parameter, the standard numerical schemes for the solution of these problems fail to resolve the boundary layer(s) and the oscillations occur near the boundary layer. Thus, in this paper to resolve the boundary layer(s), im-plicit Euler scheme for the time derivatives on uniform mesh and extended B-spline basis functions consisting of free parameter λ are presented for spatial variable on Bakhvalov type mesh. The stability and uniform convergence analyisis of the proposed method are established. The error estimation of the developed method is shown to be firts order accurate in time and second order accurate in space. Numerical exprementation is carried out to validate the applicability of the developednumerical method. The numerical results reveals that the computational result is in agreement with the theoretical estimations

Thermodynamic relation of accelerating black holes in anti-de Sitter spacetime

We consider accelerating black holes in four-dimensional anti-de Sitter spacetime and investigate the extremality relations by examining perturbative corrections to both the entropy of black holes and their extremality bounds. It is shown that the so-called Goon and Penco (univeral) relation is also valid for accelerating black holes. Furthermore, it is found that an appropriate matching condition is necessary between the perturbation parameter of the relation with the perturbative correction to such black holes, and the parameter with information about the conical deficits on the north and south poles with the cosmic string tensions in order to satisfy the extremality relations. This result indicates that the extremality (univeral) relation of a class of accelerating black holes holds exhibit behavior similar to the Weak Gravity Conjecture.

Impact of mixed boundary conditions and nonsmooth data on layer‐originated nonpremixed combustion problems: Higher‐order convergence analysis

AbstractThis work explores the theoretical and computational impacts of mixed‐type flux conditions and nonsmooth data on boundary/interior layer‐originated singularly perturbed semilinear reaction–diffusion problems. Such problems are prevalent in nonpremixed combustion models and catalytic reaction models. The inclusion of arbitrarily small diffusion terms results in boundary layers influenced by specific flux conditions normalized by perturbation parameters. We have demonstrated theoretically that the sharpness of the boundary layer is significantly reduced when this normalization is independent of the diffusion parameter. In addition, the presence of a nonsmooth source function gives rise to an interior layer in the current problem. We show that using upwind discretizations for mixed boundary fluxes achieves nearly second‐order accuracy if the first derivatives are not normalized concerning perturbation parameters. This outcome arises from the bounds of a prior derivative of the continuous solution. Furthermore, it is theoretically shown that nearly second‐order uniform accuracy can be attained for reaction‐dominated semilinear problems using a hybrid scheme at the discontinuity point. To ensure the uniform stability of the discrete solution, a transformation is necessary for the corresponding discrete problem. Theoretical results are supported by various experiments on nonlinear problems, illustrating the pointwise rates and highlighting both linear and higher‐order accuracy at specific points.

SBFEM with perturbation method for solving the Reynolds equation

AbstractRotordynamic simulations with nonlinear hydrodynamic bearing forces require a solution of the Reynolds equation at every time step. As a computationally efficient alternative to the standard numerical methods, a semi‐analytical solution based on the scaled boundary finite element method (SBFEM) was developed recently. Through a discretization of the hydrodynamic pressure (dependent variable) along the circumferential but not the axial coordinate, the partial differential equation is transformed into a system of ordinary differential equations. This system of differential equations is referred to as SBFEM equation and can be solved exactly if the influence of shaft tilting is neglected. In common numerical models, this influence can be taken into account without difficulties, but as far as this semi‐analytical approach is concerned, shaft tilting complicates the equations substantially. Therefore, previous studies on the SBFEM solution of the Reynolds equation were conducted without consideration of this effect. The formulation presented in the work at hand no longer requires this simplification. The terms representing the influence of shaft tilting in the SBFEM equation are handled by the perturbation method. The pressure field is expressed by a series expansion, where the solution of order correlates to the power of a perturbation parameter chosen proportional to the tilting angle. The differential equation governing the solution contains lower‐order solutions on its right‐hand side, implying a recursive computation of the series from lowest to highest order. A universal expression for the general solution is formulated, where only the coefficients and the maximum power of the axial coordinate differ for every . This allows the implementation of a general algorithm with no inherent limitation regarding the maximum order of perturbation. For verification, the pressure fields computed by the proposed method are compared to a numerical reference solution, showing that the series converges to the correct result for the investigated set of parameters.

Experimental validation and analysis of hybrid adaptive iterative learning sliding mode control for PMSM seeker coordinator

High-order nonlinearity, strong coupling, and external disturbances constrain the high-precision servo tracking control of the missile seeker coordinator, which compromises the guidance accuracy of guided weapons. The individual differences in the seekers cause model parameter perturbations, leading to uncertainty and time-varying disturbances, which reduces the tracking performance of the seeker servo system. To cope with these uncertainties various traditional Iterative learning control (ILC) strategies have been designed to suppress high-order nonlinear disturbances. However, these are very sensitive to system uncertainties, external disturbances and model parametric perturbations. In response to this challenge, this paper proposes a hybrid adaptive iterative learning sliding mode control (AILS) methodology. The iterative learning sliding mode control (ILSMC) strategy is used to reduce the impact of periodic disturbances in the system, ensuring a rapid system response. The enhanced adaptive learning law (EAL) strategy offers an estimation of the lumped disturbances of the system, encapsulating both parameter shifts and residual disturbances. Through this appropriate adaptive control, both disturbances compensation and the chattering effect due to sliding mode control are simultaneously minimized. Simulation and experimental results show that compared with the traditional open-loop iterative learning control, the learning convergence speed and convergence accuracy of the proposed hybrid AILS are highly significant. Experimental results also show that the control algorithm designed in this paper can also perform adaptively, has fast learning capability and ensures convergence while guaranteeing the tracking accuracy of the seeker coordinator servo system.

Tough Cortical Bone-Inspired Tubular Architected Cement-Based Material with Disorder.

Cortical bone is a tough biological material composed of tube-like osteons embedded in the organic matrix surrounded by weak interfaces known as cement lines. The cement lines provide a microstructurally preferable crack path, hence triggering in-plane crack deflection around osteons due to cement line-crack interaction. Inspired by this toughening mechanism and facilitated by a hybrid (3D-printing/casting) process, the study engineers architected tubular cement-based materials with the stepwise cracking toughening mechanism, that enables a non-brittle fracture. Using experimental and theoretical approaches, the study demonstrates the competition between tube size and shape on stress intensity factor from which engineering stepwise cracking can emerge. Two competing mechanisms, both positively and negatively affected by the growing tube size, arise to significantly enhance the overall fracture toughness by up to 5.6-fold compared to the monolithic brittle counterpart without sacrificing the specific strength. This is enabled by crack-tube interaction and engineering the tube size, shape, and orientation, which promotes rising resistance-curves (R-curve). "Disorder" curves and statistical mechanics parameters are proposed for the first time to quantitatively characterize the degree of disorder for describing the representation of the architected arrangement of materials in lieu of otherwise inadequate "periodicity" classification and misperceiveddisorder parameters (perturbation and Voronoi tessellation methods).

Stochastic delayed analysis of coronavirus model through efficient computational method

Stochastic delayed modeling has a significant non-pharmaceutical intervention to control transmission dynamics of infectious diseases and its results are close to the reality of nature. The covid-19 has been controlled globally but there is still a threat and appears in different variants like omicron and SARS-CoV-2 etc. globally. This article, considered pattern a mathematical model based on Susceptible, Infected, and recovered populations with highly nonlinear incidence rates. we studied the dynamics of the coronavirus model; a newly proposed version is a stochastic delayed model that is based on nonlinear stochastic delayed differential equations (SDDEs). Transition probabilities and parametric perturbation methods were used for the construction of the stochastic delayed model. The fundamental properties like positivity, boundedness, existence and uniqueness, and stability results of equilibria of the model with certain conditions of reproduction number are studied regularly. Also, the extinction and persistence of disease are studied with the help of well-known theorems. The numerical methods used to find a visualization of results due to the complexity of stochastic delayed differential equations. Furthermore, for computational analysis, we implemented existing methods in the literature and compared their results with the proposed method like nonstandard finite difference for stochastic delayed model. The proposed method restores all dynamical properties of the model with a free choice of time steps.

Adiabatic gauge potential and integrability breaking with free fermions

We revisit the problem of integrability breaking in free fermionic quantum spin chains. We investigate the so-called adiabatic gauge potential (AGP), which was recently proposed as an accurate probe of quantum chaos. We also study the so-called weak integrability breaking, which occurs if the dynamical effects of the perturbation do not appear at leading order in the perturbing parameter. A recent statement in the literature claimed that integrability breaking should generally lead to an exponential growth of the AGP norm with respect to the volume. However, afterwards it was found that weak integrability breaking is a counter-example, leading to a cross-over between polynomial and exponential growth. Here we show that in free fermionic systems the AGP norm always grows polynomially, if the perturbation is local with respect to the fermions, even if the perturbation strongly breaks integrability. As a by-product of our computations we also find, that in free fermionic spin chains there are operators which weakly break integrability, but which are not associated with known long range deformations.

A physical‒data-driven combined strategy for load identification of tire type rail transit vehicle

Tire load is one of the basic input parameters required for vehicle design and safety evaluation. Identifying the tire load with high accuracy is of great significance. However, the direct measurement of tire load is often high-cost and complex. Meanwhile, load identification solely based on physical measurement or data has great limitations of low accuracy and low robustness. This paper proposes a physical‒data-driven combined load identification strategy that includes an extended Kalman filter (EKF) and a data-driven correction model. These two models are configured in series. Derived from a physical state-space model of the vehicle dynamics, the EKF is used for the preliminary identification of the load. The data-driven model extracts the spatial and temporal characteristics of signals through the convolutional neural network and bidirectional gated recurrent unit, and then predicts the errors of the extended Kalman filter and corrects the identified results. The presented strategy is applied to an APM300 rubber wheel vehicle for load identification. The results have shown that the physical‒data-driven combined strategy can reduce the influence of parameter perturbation and improve the identification accuracy (6.4%). Thanks to organically combining the physical- and data-driven methods and integrating the rules and experience of the entire system, the strategy has strong generalization performance. Compared with traditional algorithms, the presented strategy could effectively reduce the error of load identification, improve adaptability under different operating conditions, and handle the measurement error of different noise levels, which are of practical application value in the engineering field.

Implementing the iCORAL (version 1.0) coral reef CaCO3 production module in the iLOVECLIM climate model

Abstract. Coral reef development is intricately linked to both climate and the concentration of atmospheric CO2, specifically through temperature and carbonate chemistry in the upper ocean. In turn, the calcification of corals modifies the concentration of dissolved inorganic carbon (DIC) and total alkalinity in the ocean, impacting air–sea gas exchange, atmospheric CO2 concentration, and ultimately the climate. This feedback between atmospheric conditions and coral biogeochemistry can only be accounted for with a coupled coral–carbon–climate model. Here we present the implementation of a coral reef calcification module into an Earth system model. Simulated coral reef production of the calcium carbonate mineral aragonite depends on photosynthetically active radiation, nutrient concentrations, salinity, temperature, and the aragonite saturation state. An ensemble of 210 parameter perturbation simulations was performed to identify carbonate production parameter values that optimize the simulated distribution of coral reefs and associated carbonate production. The tuned model simulates the presence of coral reefs and regional-to-global carbonate production values in good agreement with data-based estimates, despite some limitations due to the imperfect simulation of climatic and biogeochemical fields driving the simulation of coral reef development. When used in association with methods accounting for bathymetry changes resulting from different sea levels, the model enables assessment of past and future coral–climate coupling on seasonal to millennial timescales, highlighting how climatic trends and variability may affect reef development and the resulting climate–carbon feedback.

Rheological analysis of pressure-driven Jeffrey fluid flow between corrugated porous curved walls with slip constraints

Pressure-driven movement is a fundamental concept with numerous applications in various industries, scientific disciplines, and fields of engineering. Its proper execution is vital for promoting revolutionary innovations and providing solutions in numerous sectors. Therefore, this article scrutinizes the pressure-driven flow of a magnetized Jeffrey fluid between two curved corrugated walls. The geometry of the channel is represented mathematically in an orthogonal curvilinear coordinate system. The corrugation grooves are described by sinusoidal functions with phase differences between the corrugated curved walls. The boundary perturbation method is used to find the analytical solution for the velocity and temperature taking the corrugation amplitude as the perturbation parameter. Furthermore, the volumetric flow rate, skin friction coefficient, and local Nusselt numbers are precisely calculated numerically for a variety of parameters, with the results presented comprehensively in tabular form. The impact of dissimilar parameters, such as the curvature parameter, wave number, magnetic parameter, Darcy number, thermal radiation, heat source/sink parameter, Jeffery fluid parameter, and amplitude parameter, on the flow fields is analyzed through graphical and tabular forms and discussed in detail. The results show that the velocity profile increases due to the curvature parameter and the Jeffrey fluid parameter. However, it decreases due to the magnetic parameter. The temperature distribution rises with the thermal slip and heat source/sink parameters. Meanwhile, it declined for the radiation parameter and the curvature parameter. The model can be used to simulate blood flow in arteries with varying geometries and magnetic fields, aiding in the study of cardiovascular diseases and the design of medical devices such as stents.

Perturbations of exponential maps: Non-recurrent dynamics

AbstractWe study perturbations of non-recurrent parameters in the exponential family. It is shown that the set of such parameters has Lebesgue measure zero. This particularly implies that the set of escaping parameters has Lebesgue measure zero, which complements a result of Qiu from 1994. Moreover, we show that non-recurrent parameters can be approximated by hyperbolic ones.