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Developing phase diagrams for inhomogeneous systems in thermodynamics is difficult, in part, due to the large phase space and the possibility of unstable and metastable solutions arising from first-order phase transitions. Pseudo-arclength continuation (PAC) is a method that allows one to trace out stable and unstable solutions of nonlinear systems. Typically, PAC utilizes the Jacobian in order to implement Newton (or quasi-Newton) steps. In this work, we present a Jacobian-free PAC method that is amenable to the usual workflows in inhomogeneous thermodynamics. We demonstrate our method in systems that have first-order phase transitions, including a novel example of polyelectrolyte complex coacervation in confinement, where multiple surface phase transitions occur and can overlap with one another. [ABSTRACT FROM AUTHOR]

The nonlinear forced vibration behavior of truncated open conical nanoshells is investigated in this paper. Nonlocal elasticity theory has been employed to modify the size-dependent effect of micro/nanostructure. Von Karman nonlinear strains are used to consider the geometric nonlinearity of the nanoshells. Using Hamilton's principle, the equations of motion and boundary conditions of truncated open conical nanoshells are derived. Galerkin method is used to solve the governing equations. Then, to determine the nonlinear forced vibration behavior of truncated open conical nanoshells, complex averaging and arc-length continuation methods are employed. Finally, the effect of nonlocal parameters, cone apex angle, the amplitude of harmonic excitation, structural damping coefficient, and geometrical parameters on the nonlinear frequency response of the truncated open conical nanoshells are discussed. [ABSTRACT FROM AUTHOR]

This paper reports the mass and energy transmission characteristics of an electrically conducting mixed convective nanofluid flow past a stretching Riga plate. An additional effect of viscous dissipation, Arrhenius activation energy and heat source is also studied. The energy and mass transmissions are evaluated by a zero-mass flux of nanoparticle and convective boundary conditions. Buongiorno's relations are proposed for the Brownian motion and thermophoretic diffusion. The similarity substitutions are employed to derive the non-dimensional set of modeled equations. The obtained set of equations is numerically processed via parametric continuation method (PCM). Several flow factors affecting the velocity, energy, and mass distributions are graphically discussed. It has been perceived that the fluid velocity field declines with the influence of velocity power index (m), while improves with the upshot of modified Hartmann number (Q). The effect of Schmidt number and chemical reaction diminishes the concentration profile φ (η). Furthermore, the energy curve enhances with the effect of thermophoresis factor, Biot and Eckert number. [ABSTRACT FROM AUTHOR]

We study a linear-convex mean-field game with input constraints for partially observed forward-backward system, where both types of mean-field terms, asynchronous style (state-averages) and synchronous style (state expectations), are considered. The observation is a controlled process, whose drift term is linear with respect to state and control variable. For the general case, by using the mean-field method and the backward separation approach, we obtain the decentralized optimal strategies through a Hamiltonian system and related Consistency Condition (CC), which are given by two types of mean-field forward-backward stochastic differential equations with filtering. In virtue of continuation method and discounting method, the well-posedness of such kind of equations is proved under two different conditions. For the linear-quadratic case under linear subspace constraints, we give the feedback representation of the decentralized optimal strategies, and the Riccati type CC system is also given. As one application, an asset-liability management problem is solved. • Partially observed mean-field game of mean-field forward-backward stochastic system. • Mean-field forward-backward stochastic differential equation with filtering. • Decentralized strategy of partially observed mean-field game with input constraints. • The method of continuation with randomized domination-monotonicity conditions. [ABSTRACT FROM AUTHOR]

The viscosity of a medium affects the amplitude attenuation and velocity dispersion of seismic waves. Therefore, it is necessary to consider these factors during migration. First, to eliminate the viscous effect of a medium, we combine the Futterman model with the integral equation of the De Wolf approximation to construct a compensation operator of the De Wolf approximation for a visco‐acoustic medium. Next, we use the visco‐acoustic screen approximation method to realize the continuation operator then establish a prestack depth migration algorithm. Finally, an error analysis, impulse response test and model test are performed. The results show that three different generalized visco‐acoustic screen methods (phase screen method, generalized screen method and extended local Born Fourier method) can satisfactorily compensate for the attenuation of deep interface amplitude. Among these methods, the visco‐acoustic extended local Born Fourier method has the highest accuracy and the best compensation effect. [ABSTRACT FROM AUTHOR]

This paper is concerned with finite element approximation for the minimal time optimal control problem $ (\mathcal{TP}) $ of the heat equation with impulse controls at some control instants. To this end, with the aid of Pontryagin's Maximum Principle, we first get the $ H^1- $regularity estimate of the optimal control by making use of the semigroup method and the unique continuation property. Then, following the high order regularity estimate of the optimal control, the error estimate of the optimal time between the original impulse control problem $ (\mathcal{TP}) $ and the semidiscrete impulse control problem $ (\mathcal{TP}_{hl}) $ is established. [ABSTRACT FROM AUTHOR]

Given the current enthusiasm for lunar exploration, the 2:1 resonant distant retrograde orbit (DRO) in Earth-Moon space is of interest. To gain an in-depth understanding of the complex dynamic environment in cislunar space and provide more options for parking orbits, this paper investigates the existence of quasi-periodic orbits near the 2:1 resonant DRO in the circular restricted three-body problem (CR3BP). Firstly, the numerical computation approach, continuation strategy, and stability analysis method of quasi-periodic orbits are introduced. Then, addressing the primary challenges in the continuation progress, we have developed an adaptive continuation algorithm with automatic adjustment of the step size and the number of discrete points that characterize the invariant torus. Finally, two types of 2D quasi-DROs and their linear stability properties are explored. Using Poincare sections, we investigated the boundaries of the maximum extent attainable by both 2D quasi-DRO families in the CR3BP at a specific Jacobi energy, confirming that both types of quasi-periodic families have reached their respective boundaries. The algorithm described in this paper is beneficial for facilitating the computation of quasi-periodic families and aids in discovering additional potential dynamical structures. [ABSTRACT FROM AUTHOR]

This study investigates the effective mitigation of free and forced vibrations in nonlinear functionally graded (FG) shear deformable beams through the application of a nonlinear energy sink (NES) near resonance (1:1). FG structures, characterized by varying material properties across dimensions, pose unique challenges in vibration control. We employ a comprehensive approach, combining higher-order shear deformation theories with advanced numerical methods. Our investigation begins by modeling a geometrically nonlinear beam using von Kármán theory. The equations of motion are derived through the assumed modes method and the Lagrange approach. To analyze free vibrations, we calculate both linear and nonlinear frequencies using the assumed modes method and the local concordant deformation assumption (LCDA), respectively. Our research primarily focuses on the forced vibration analysis performed using the complexification-averaging method. Steady-state frequency response curves are systematically generated using an arc-length continuation method, revealing valuable insights into the system’s behavior under various conditions. An optimization procedure employs a genetic algorithm to fine-tune NES parameters, resulting in an impressive 92.5% reduction in vibration amplitude. Notably, our study critically evaluates different shear deformation theories and investigates how varying FG material distributions influence optimal NES parameters. [ABSTRACT FROM AUTHOR]

This article presents an approach to solve the problem of end-to-end optimization of the low-thrust interplanetary trajectory. At first, the problem of optimizing low-thrust interplanetary trajectory, which passes through the collinear libration points near the planets of departure and arrival is considered. The obtained solutions from this problem can be used as an initial guess to solve the end-to-end optimization problem, i.e., to calculate interplanetary low-thrust trajectories that satisfy the necessary optimality conditions at the match points of the heliocentric and planetocentric segments of trajectory. The minimum-fuel problem is considered. An indirect method based on the maximum principle, and the continuation method is applied to optimize interplanetary spacecraft trajectories. Numerical examples of trajectories from the Earth orbit to the orbit around the destination planet (Mars and Jupiter) are given. The possibility of a significant reduction in the required characteristic velocity is shown in comparison with the estimates obtained by using the zero-radius sphere of influence model. • End-to-end optimization, low-thrust, minimum-fuel trajectory, interplanetary transfer. • Using libration points as an initial guess to figure out the optimal match points of trajectory segments. • Analysing optimality conditions at the match points of the trajectory segments. • Comparison with conventional approach using zero-radius sphere of influence model. • End-to-end trajectory optimization significantly reduces characteristic velocity. [ABSTRACT FROM AUTHOR]

This work provides a systematic recipe for computing accurate high order Fourier expansions of quasiperiodic invariant circles (and systems of such circles) in area preserving maps. The recipe requires only a finite data set sampled from the quasiperiodic circle. Our approach, being based on the parameterization method of [A. Haro and R. de la Llave, SIAM J. Appl. Dyn. Syst., 6 (2007), pp. 142--207; A. Haro and R. de la Llave, Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), pp. 1261--1300; A. Haro and R. de la Llave, J. Differential Equations, 228 (2006), pp. 530--579], uses a Newton scheme to iteratively solve a conjugacy equation describing the invariant circle (or systems of circles). A critical step in properly formulating the conjugacy equation is to determine the rotation number of the quasiperiodic subsystem. For this we exploit the weighted Birkhoff averaging method of [S. Das et al., Nonlinearity, 30 (2017), pp. 4111--4140; S. Das et al., The Foundations of Chaos Revisited, Springer, Cham, 2016, pp. 103--118; S. Das and J. A. Yorke, Nonlinearity, 31 (2018), pp. 491--501]. This approach facilities accurate computation of the rotation number given nothing but the already mentioned orbit data. The weighted Birkhoff averages also facilitate the computation of other integral observables like Fourier coefficients of the parameterization of the invariant circle. Since, the parameterization method is based on a Newton scheme, we only need to approximate a small number of Fourier coefficients with low accuracy (say, a few correct digits) to find a good enough initial approximation so that Newton converges. Moreover, the Fourier coefficients may be computed independently, so we can sample the higher modes to guess the decay rate of the Fourier coefficients. This allows us to choose, a priori, an appropriate number of modes in the truncation. We illustrate the utility of the approach for explicit example systems including the area preserving H\'enon map and the standard map (polynomial and trigonometric nonlinearity respectively). We present example computations for invariant circles and for systems of invariant circles with as many as 120 components. We also employ a numerical continuation scheme (where the rotation number is the continuation parameter) to compute large numbers of quasiperiodic circles in these systems. During the continuation we monitor the Sobolev norm of the parameterization, as explained in [R. Calleja and R. de la Llave, Nonlinearity, 23 (2010), pp. 2029--2058], to automatically detect the breakdown of the family. [ABSTRACT FROM AUTHOR]

The paper presents analytical expressions for solving the problem of continuation of the electromagnetic field in the frequency domain for a horizontally layered medium. The numerical solution algorithm uses layerwise recalculation of the required quantities, for which analytical expressions are presented in a form that allows calculations and layerwise recalculation without the accumulation of rounding errors. The solution to the continuation problem is obtained as a solution to the cost functional minimization problem. The strong convexity of the functional is proven, which implies the existence of a unique solution to the problem posed. [ABSTRACT FROM AUTHOR]

In this article, a multiscale nonlinear system of singularly perturbed differential equations of convection-diffusion type is considered. A numerical technique combined with the continuation method is constructed to obtain the numerical computations. The newly developed numerical method is shown to be first order convergent uniformly with respect to the perturbation parameter. [ABSTRACT FROM AUTHOR]

In this article, a nonlinear system of singularly perturbed differential equations of convectiondiffusion type with Dirichlet boundary conditions is considered on the interval [0,1]. Both components of the solution of the system exhibit boundary layers near t = 0. A new computational method involving classical finite difference operators, a piecewise-uniform Shishkin mesh and an algorithm based on the continuation method is developed to compute the numerical approximations. The computational method is proved to be first order convergent uniformly with respect to the perturbation parameters. Numerical experiments support the theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents an efficient inverse kinematics solution for redundant robotic arms. The proposed method combines the principles of continuation methods, improves the instability of the computation time by increasing the convergence of the kinematics function, and improves the efficiency of traditional numerical methods. The effectiveness and efficient performance of the method are demonstrated through comparative experiments. The computational speed of the method is twice as fast as the Newton–Raphson method under joint limit constraints and equal solution accuracy. [ABSTRACT FROM AUTHOR]

Determining the edge and horizontal position of geologic structures is one of the fundamental steps in interpreting potential field data. Several filters have been introduced that use the concept of curvature to determine the edge of potential field data. However, these filters have advantages and disadvantages in detecting causative sources. Therefore, it seems necessary to introduce more efficient approaches. In this work, the most positive and most negative curvatures of gravity field data were analyzed, and a more efficient filter was introduced and applied that uses the concept of curvature and its combination to delineate the edges of geological structures and buried sources. The proposed method, called the hybrid positive and negative curvature (PNH) approach, combines the most positive and most negative curvatures into one curvature by fitting the formula and weighted summation. The proposed strategy takes advantage of both positive and negative curvatures to improve the edge detection of gravity field data. To this end, the performance of the PNH procedure was investigated considering different density assumptions (positive, negative, and positive-negative) for the relatively imposed synthetic gravity model resulting from buried prisms. The results obtained on synthetic models with and without noise show that the PNH procedure can detect the horizontal boundaries of buried structures relatively well. Of course, due to the use of directional derivatives in the filter of the hybrid positive and negative curvature approach, it seems very necessary to use noise-reducing filters before applying edge detection methods. Moreover, conventional filters such as the second vertical derivative (SVD) and the tilt angle (TDR) were used to compare the performance of the hybrid positive and negative curvature filter on the synthetic model. However, the obtained results show that the second vertical derivative and the tilt angle do not have the required capability to determine the edge of the synthetic model. In the following, the quality of the most positive and most negative curvatures filter and the hybrid positive and negative curvature were investigated using real data from a gold mine in the Witwatersrand area (South Africa) and also gravity data from the Aji-chai salt dome, East Azerbaijan province (Iran) and then using WGM-2012 derived gravity data belonging to the Marian trench area. Due to the sensitivity of the filters to noise, the upward continuation filter was applied before determining the edge of the buried structures. The edge maps from the Witwatersrand area and the data from the Aji-chai salt dome obtained using the hybrid positive and negative curvature determination method, demonstrate acceptable accuracy of this filter in determining the edge and representing the horizontal position of various geological structures. By using the PNH filter, the lateral boundaries of the main structures and other subsurface sources are well detected. Of course, due to the noise sensitivity of this filter, which is due to the use of secondorder gravity derivatives, good quality data without noise must be used. Therefore, it is suggested that noise attenuate filters, such as upward continuation method, must be used prior to creating the maps to determine the edge. Therefore, the PNH edge detection method can be reliably used for qualitative interpretation of gravity field data. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present the potentiality of the code HOFiD_bvp based on high order finite difference, following the approach of the boundary value methods and the upwind methods. Strategies, as variable stepsize and variable order, that helps to handle with solutions of singular perturbation problems, so as the continuation strategy applied for solving nonlinear problems, will be discussed. Now, the method is suitable to solve second order scalar boundary value problems, not only singularly perturbed with one and two parameters, but also problems with discontinuous source terms. Concerning that point some numerical tests will be taken in consideration in order to show the potentiality of the code. [ABSTRACT FROM AUTHOR]

In this work, we derived a new type model for spatial Hill's system considering the created perturbation by the parameter effect of the continuation fractional potential. The new model is considered a reduced system from the restricted three-body problem under the same effect for describing Hill's problem. We identified the associated Lagrangian and Hamiltonian functions of the new system, and used them to verify the existence of the new equations of motion. We also proved that the new model has different six valid solutions under different six symmetries transformations as well as the original solution, where the new model is an invariant under these transformations. The several symmetries of Hill's model can extremely simplify the calculation and analysis of preparatory studies for the dynamical behavior of the system. Finally, we confirm that these symmetries also authorize us to explore the similarities and differences among many classes of paths that otherwise differ from the obtained trajectories by restricted three-body problem. [ABSTRACT FROM AUTHOR]

Train traffic is a powerful source of seismic waves, with many applications for passive seismic imaging. Seismic signals were recorded a few metres away from the railway track. These records display harmonious waveforms below 15 Hz for trains driving at speeds of around 100 km hr−1. The sensors record an apparent wavelet emitted by the interaction of the axle on a few of the closest sleepers. From this, we build a simple modelling tool using shifted wavelets to simulate a train signal. The relationship involves the varying train speed, the distances between each axle, and the wavelet emitted by each axle. We propose a nonlinear deconvolution method to invert this relationship. We use a local minimization algorithm with gradients derived by the adjoint state method, and use a frequency continuation technique. A linearized picking-based inversion initializes the nonlinear inversion. On real data, we apply this automatic workflow to 300 train passages, with an excellent match between the best simulation and the data. We identify the trains decelerating as they enter a train station. We also identify the train type based on inverted wheel spacing with centimetric accuracy. The inverted wavelets are consistent with the assumption that trains emit seismic waves by bending the rail above sleepers, although the theory does not explain why the inverted wavelet is not zero phase. This automated kinematic inversion algorithm may allow for contactless railway monitoring, and be used for source characterization for subsurface monitoring below railway tracks. [ABSTRACT FROM AUTHOR]

This study presents a detailed numerical analysis of nonlinear aeroelastic behavior in a two degree of freedom (DOF) model, focusing on plunge and pitch motions and employing the continuation method (CM) with an adaptive step size control algorithm. The research incorporates free-play nonlinearity at the plunge hinge, a common structural nonlinearity in aeronautics that can induce detrimental limit cycle oscillations (LCOs) during flight. By examining three scenarios—linear response, unhindered plunge motion, and nonlinear stiffness behavior—the study assesses the effects of free play on flutter and LCO phenomena, including discontinuity-induced bifurcations like grazing bifurcation. Additionally, the study explores parameter variation for nonlinear flutter analysis, revealing the dynamics of grazing bifurcation and its impact on LCO behavior. The research also demonstrates the method's superior accuracy in flutter speed estimation and mode-switching identification, despite higher computational demands. The findings underscore the diminishing influence of nonlinear free-play behavior on LCO amplitude, providing insights with significant implications for aeroelastic design and aircraft safety. [ABSTRACT FROM AUTHOR]

Nonlinear science plays a vital role in modern technology. Due to the limitations over the linear theories and the chaotic nature of the problems in this technological era, the analysis of nonlinear problems has become extremely essential to investigate the dynamics of complicated and multiscale characteristics systems. In this article, a nonlinear system of singularly perturbed differential equations with Dirichlet boundary conditions is considered. Both components of the system exhibit a strong boundary layer near the boundary t = 0 of the domain, even though a perturbation parameter occurs only in one of the equations of the system. A robust and layer-resolving numerical method involving the continuation technique is constructed to obtain the numerical approximations to the system. The newly developed numerical method is shown to be first-order convergent uniformly with respect to the perturbation parameter. [ABSTRACT FROM AUTHOR]

In this work, a symbolic-numerical solution of Maxwell's equations is constructed, describing the guided modes of a two-dimensional smoothly irregular waveguide in the zeroth approximation of the model of adiabatic waveguide modes. The system of linear algebraic equations obtained in this approximation is solved symbolically. The dispersion relation is solved numerically using the parameter continuation method. [ABSTRACT FROM AUTHOR]

Proper wastewater disposal is crucial in various manufacturing and ecological systems. This study aims to prevent and regulate pollution in the water supply. It examines how the pollutant discharge concentration affects the flow of non-Newtonian nanofluids (NNNFs) over a porous Riga surface. Two different types of NNNFs, namely, Walter's B and second-grade fluids, have been examined. The fluid flow is conveyed in the form of a system of partial differential equations (PDEs), which are first reduced to a non-dimensional set of ordinary differential equations (ODEs) and then to first-order differential equations. The numerical approach parametric continuation method is employed to solve these ODEs. It has been noticed that the energy curve declines with increasing numbers of TiO2-nanoparticles (NPs). The effect of the external pollutant source variation factor enriches the concentration of pollutants in both fluid cases. Furthermore, the viscoelastic parameter K1 plays a notable role in determining the behavior of the fluids. Particularly in NNNFs, the variation of K1 enhances the fluid flow, whereas the rise of second-grade fluid factor decreases the velocity of the fluid. Our findings indicate a substantial impact of the parameters under consideration on the concentration of pollutant discharge. Significantly, it was observed that an increase in the amount of NPs and the thermal radiation parameter led to an improvement in the thermal conductivity of the nanofluid, consequently decreasing the concentration of pollutants in the discharge. The nanofluid has greater efficiency in boosting the energy transfer rate of the base fluid. In the case of the second-grade fluid, the energy propagation rate increases up to 6.25%, whereas, in the case of Walter's fluid B, it increases up to 7.85%. [ABSTRACT FROM AUTHOR]

Time-optimal orbital transfers with soft terminal conditions are studied in this work. First, a two-layer thrust continuation method is devised. The unfavorable thrust continuation path is handled by switching between different solution curves. Second, the proposed method is applied to solving time-optimal transfers under two- or three-body dynamics with Cartesian coordinates to verify its effectiveness. The near conservation of the product between the time of flight and the thrust level is observed for general orbital transfers. A linear variation of this quantity with eccentricity is also illustrated when the difference in eccentricity between the initial and terminal orbits is large enough. [ABSTRACT FROM AUTHOR]

This article develops a method for determining the areas of attraction of trajectories by stable points of dynamic equilibrium. This method is based on determining a line separating these areas. In the case of n-fold equilibrium states, there are a maximum of (n + 1)/2 regions of attraction. This is the maximum number of stable states. It may also happen that none of the states are stable and then there will not be any area of attraction. The number of all states n is odd. In the case of single stable states, we are dealing with one unlimited region of attraction. In the case of three-fold equilibrium states, two of which are stable, there are two regions of attraction, etc. In this study, the case of three-fold dynamic equilibrium states of a chemical tank reactor is considered. [ABSTRACT FROM AUTHOR]

This article analyses two furniture design exhibitions at the Belgian Saint Luke schools, organised in the 1980s within the programme of interior design. It demonstrates the pivotal role played by these exhibitions in the self-identification of interior design as a standalone discipline. Because of its relatively late emergence, the dialectic relationship with more established disciplines—most notably architecture—have heavily impacted interior design's claims to professionalism. The history of institutions with programmes in both fields offers clear insight into this phenomenon. The prominence attributed to furniture design in the 1980s student exhibits resulted from an epistemological rivalry with the architecture program. This article revisits the pedagogical practices at the heart of both exhibits, and considers them as a continuation of the teaching methods that had constituted the institutional foundations of the Saint Luke school network. As the drawing and designing of furniture served to codify specific design knowledge inherent to the discipline of interior design, the untimely recovery of this pedagogy aimed to legitimise the professional knowledge held by interior design graduates. [ABSTRACT FROM AUTHOR]

This paper wants to increase our understanding and computational know-how for time-varying matrix problems and Zhang Neural Networks. These neural networks were invented for time or single parameter-varying matrix problems around 2001 in China and almost all of their advances have been made in and most still come from its birthplace. Zhang Neural Network methods have become a backbone for solving discretized sensor driven time-varying matrix problems in real-time, in theory and in on-chip applications for robots, in control theory and other engineering applications in China. They have become the method of choice for many time-varying matrix problems that benefit from or require efficient, accurate and predictive real-time computations. A typical discretized Zhang Neural Network algorithm needs seven distinct steps in its initial set-up. The construction of discretized Zhang Neural Network algorithms starts from a model equation with its associated error equation and the stipulation that the error function decrease exponentially fast. The error function differential equation is then mated with a convergent look-ahead finite difference formula to create a distinctly new multi-step style solver that predicts the future state of the system reliably from current and earlier state and solution data. Matlab codes of discretized Zhang Neural Network algorithms for time varying matrix problems typically consist of one linear equations solve and one recursion of already available data per time step. This makes discretized Zhang Neural network based algorithms highly competitive with ordinary differential equation initial value analytic continuation methods for function given data that are designed to work adaptively. Discretized Zhang Neural Network methods have different characteristics and applicabilities than multi-step ordinary differential equations (ODEs) initial value solvers. These new time-varying matrix methods can solve matrix-given problems from sensor data with constant sampling gaps or from functional equations. To illustrate the adaptability of discretized Zhang Neural Networks and further the understanding of this method, this paper details the seven step set-up process for Zhang Neural Networks and twelve separate time-varying matrix models. It supplies new codes for seven of these. Open problems are mentioned as well as detailed references to recent work on discretized Zhang Neural Networks and time-varying matrix computations. Comparisons are given to standard non-predictive multi-step methods that use initial value problems ODE solvers and analytic continuation methods. [ABSTRACT FROM AUTHOR]

In this paper, we prove the strong unique continuation property for the following fourth order degenerate elliptic equation Δ X 2 u = V u , where Δ X = Δ x + | x | 2 α Δ y (0 < α ≤ 1), with x ∈ R m , y ∈ R n , denotes the Baouendi-Grushin type subelliptic operators, and the potential V satisfies the strongly singular growth assumption | V | ≤ c 0 ρ 4 , where ρ = (| x | 2 (α + 1) + (α + 1) 2 | y | 2) 1 2 (α + 1) is the gauge norm. The main argument is to introduce an Almgren's type frequency function for the solutions, and show its monotonicity to obtain a doubling estimate based on setting up some refined Hardy-Rellich type inequalities on the gauge balls with boundary terms. [ABSTRACT FROM AUTHOR]

The literature about the asymptotic numerical method (ANM) is reviewed in this paper as well as its application to hyperelasticity and elastoplasticity. ANM is a generic continuation method based on the computation of Taylor series for solving nonlinear partial differential equations. Modern techniques of high-order differentiation provide simple tools for computing these power series, the corresponding algorithms for finite strain elasticity and elastoplasticity being summarized here. Taylor series is not only a computation tool, but it contains also useful information about the structure of the considered solution curve. The paper ends with a short historical account about the development of this numerical method. [ABSTRACT FROM AUTHOR]

This study presents a unique method for network reconfiguration for Searching Maximum Loading Capacity Radial Network from an interconnected meshed network using continuation power flow. The network reconfiguration outcomes are also evaluated for various graph theory approaches presented in the literature. The combined graph theory and machine learning methods are used to determine the best sectional switch position. The system's radiality is verified using graph theory. The recommended technique is tested on a 30-node mesh network with 41 sectional switches. The results demonstrate that the distribution system can manage a higher connected load using the suggested Bayesian-Ridge approach while lowering total active and reactive power losses. [ABSTRACT FROM AUTHOR]

The topology and fiber orientation of fiber-reinforced composite structures must be designed computationally to fully demonstrate their anisotropic mechanical properties. Optimization of the topology and fiber orientation is performed either sequentially or concurrently. In the sequential method, topology optimization is performed first, followed by fiber orientation optimization. This separated optimization process does not consider material anisotropy during the topology optimization process. The concurrent method has the potential to realize better results by considering the anisotropic properties during topology optimization. However, the concurrent method often obtains locally optimal solutions because of material anisotropy in the initial optimization process. A continuation approach for anisotropy, which starts with weak anisotropy and then improves the anisotropy gradually, resolves this issue. This paper proposes a new concurrent optimization that can control the growth of anisotropy. The growth of anisotropy affects the topology, which is used to determine a better structure. Optimization results were obtained serially by varying the growth of anisotropy, which allowed a highly optimal topology and fiber orientation to be explored by considering their anisotropic nature. [ABSTRACT FROM AUTHOR]

The aim of this study is to explore the space environment near the Lagrange points (L 3 – L 5) in cislunar space using 3:1/3:2 resonant orbital families that can travel in the vicinity of L 3 – L 5. First, the planar and spatial 3:1/3:2 resonant orbital families symmetrical about the x -axis are computed using the continuation method in the circular restricted Earth-Moon three-body problem. Then, the characteristics of the two resonant orbital families are analyzed, including the variation in Kepler orbital elements, apogee direction, Jacobian constant, and distances from apogees to L 3 – L 5 as well as the orbital stability analyzed by the dynamic theory. Furthermore, the correlation between shadow duration and orbit inclination including the strategy for shadow avoidance are proposed based on the Sun-Earth-Moon bicircular restricted four-body problem. The advantages of 3:1/3:2 resonant orbits used in this study are stability, shadow avoidance and L 3 – L 5 tour capability, and potential applications in the cislunar space. [ABSTRACT FROM AUTHOR]

The noticeable decline in the number of autopsies performed in recent years requires investigation into the causes of the phenomenon and attempts to prevent it. One potential cause of this trend is fear of disfiguring the body. Carrying out autopsies using a minimally invasive method may reduce the decrease in the number of autopsies performed. The first work on the development of the method and its continuation gave promising results. This allows us to start a discussion on attempts to introduce the method. The solution seems especially justified when the alternative is to completely abandon post-mortem examinations using the traditional method. Laparoscopy and thoracoscopy are tools that allow for accurate imaging and analysis of organ changes. Enriching them with additional tests using endoscopic techniques may have a positive impact on the accuracy of autopsy diagnoses. The development of a clear protocol for minimally invasive post-mortem diagnosis requires further research to determine the accuracy of the method. [ABSTRACT FROM AUTHOR]

This work concerns the application of the homotopy method to solve the mathematical model of a non-adiabatic chemical continuous stirred tank reactor (CSTR) and tubular reactor with mass recycle (TRR) (Berezowski 2000. Spatio-temporal chaos in tubular chemical reactors with the recycle of mass, Chaos, Solitons & Fractals, vol. 11, no. 8, pp. 1197–1204). This method was associated with the parametric multivariable continuation algorithm. Thanks to this, this method can automatically find all the multiple steady states of the reactor model without the need to use any iteration. The parametric continuation method is used to determine a curve whose each point is a solution of the tested model. Therefore, the starting point must be very precisely designated so that it lies on this curve. Otherwise, the result is a graph that deviates from the correct graph. However, this condition is not required when the homotopy method is also introduced into the calculations. The starting point can then be a point with any coordinates. Different curves are also obtained, but the homotopy method ensures that each of them passes through the point where the parameter p = 1. The solution we are looking for in the model is just such a point. This is undoubtedly a big advantage resulting from the combination of both above-mentioned methods. [ABSTRACT FROM AUTHOR]

We investigate the initial value problem to a class of fractional evolution equations with superlinear growth nonlinear functions in Banach spaces. When the linear operator generates an extendable compact $ C_0 $-semigroup of contractions and the nonlinearity $ f:[0,T]\times X\to Y $ is Carathéodory continuous, with $ X $ and $ Y $ two real Banach spaces such that $ X\subseteq Y $, the existence of mild solutions to such problems are established without assuming that the nonlinear term satisfies the transversality condition by combining an approximation technique with Leray-Schauder continuation principle. The obtained results allow to treat, as an application, fractional parabolic equations with continuous superlinear growth nonlinear term. [ABSTRACT FROM AUTHOR]

Collagen is a functional biomaterial with many applications, including wound healing. 3D collagen hydrogels mimic an in vivo cell culture experience in cell survival and growth studies. In experimentally examining human cells under contact with 3D collagen, it is possible to understand the role of collagen in human epithelial tissue repair. This study explored the growth and attachment response of human MCF-7 cells when exposed to 3D collagen by investigating if the presence of NIH/3T3 fibroblasts embedded within the collagen should produce an increased wound-healing response. 3D collagen and fibroblast presence were able to be analyzed in tandem with a "sandwich-like" configuration of the gels to determine how these variables impact or improve the tissue repair response in MCF-7 cells. Examinations in growth, attachment, viability, and migration patterns demonstrated that MCF-7 repair response may be increased when in contact with NIH/3T3 embedded 3D collagen without impairing viability. Most notably, results from the migration assay revealed that MCF-7 cells migrate the most when covered by and adhered to cellular 3D collagen. Fibroblast-embedded collagen on top of and below MCF-7 cells exceeded quantitative assessment to near confluency, whereas less than 50 counted cells per image migrated without any top collagen layering. The continuation of these methods could involve in vivo experiments that incorporate live animal models to determine if these results will continue to extend to live tissue. [ABSTRACT FROM AUTHOR]

The fluid flow across spinning discs has several applications in different fields of engineering such as flywheels, gas turbine engines, brakes, and gears. The significance of heat source, Hall current, and magnetic field on the nanofluid flow between two spinning disks is studied in the present analysis. The upper disk spins as well as rotates, which generates the 3D flow. The evaluation and modeling of the mass density, flow motion, and energy transfer are performed using a system of partial differential equations (PDEs). The computational technique parametric continuation method (PCM) is employed to solve the modeled equations. The outcomes are relatively compared to the published literature for validity purposes. It has been noticed that during the downward motion of the upper disc, the effect of the magnetic field declines, while the influence of the hall current improves the velocity field. The temperature field rises with the ascending motion of the upper disk, whereas it shrinks with the downhill oscillation. Moreover, the mass diffusion ratio develops with the impact of hall current, while lessens with the influence of chemical reaction. [ABSTRACT FROM AUTHOR]

A new diagrammatic quantum Monte Carlo approach is proposed to deal with the imaginary time propagator involving both dynamic disorder (i.e., electron–phonon interactions) and static disorder of local or nonlocal nature in a unified and numerically exact way. The establishment of the whole framework relies on a general reciprocal-space expression and a generalized Wick's theorem for the static disorder. Since the numerical cost is independent of the system size, various physical quantities, such as the thermally averaged coherence, Matsubara one-particle Green's function, and current autocorrelation function, can be efficiently evaluated in the thermodynamic limit (infinite in the system size). The validity and performance of the proposed approach are systematically examined in a broad parameter regime. This approach, combined with proper numerical analytic continuation methods and first-principles calculations, is expected to be a versatile tool toward the calculation of various transport properties, such as mobilities in realistic semiconductors involving multiple electronic energy bands, high-frequency optical and low-frequency acoustic phonons, different forms of dynamic and static disorders, and anisotropy. [ABSTRACT FROM AUTHOR]

The heuristic homogenization approach is intensively employed to characterize electromagnetic metamaterials (MMs). The effective parameters are extracted within this framework using the Nicolson–Ross–Weir (NRW) method. Special attention must be devoted to handling this procedure because of the branch ambiguity issue affecting it, i.e., the lack of uniqueness in the evaluation of the effective refractive index n e f f rooted in the use of the multivalued complex logarithm to invert the Airy–Fresnel relation. Over the years, several techniques based on the phase-unwrapping approach have been introduced, but without any theoretical justification. In this paper, we aim to clarify the theoretical connection between the phase unwrapping method and the analytic continuation theory framework. Furthermore, three-phase-unwrapping approaches, which descend directly from the theory we discussed, are compared to identify which approach is best suited to reconstruct the complex refractive index of metamaterials when the NRW method is applicable. [ABSTRACT FROM AUTHOR]

In this article, a new multi-objective topology and size optimization framework is developed for the joint concept–detailed design of stiffened panels. The normalized exponential weighted criterion (NEWC) is suggested to explore the Pareto-optimal topology point. A triple-weighting strategy (TWS) using the optimal combined weight model (OCWM) is presented to derive ideal sub-objective weights desired by NEWC. A three-stage continuation (TSC) technique with penalization power increasing by one is introduced to assist NEWC in multi-objective topology optimization considering symmetry constraints. Then, a segmented size optimization (SSO) method assisted by automation technology is used for the curved stiffened panel obtained by NEWC to fulfil the detailed design. Comparisons with the classical dual-weighting methods, average method (AM), and weighted sum method (WSM) verify the validity of TWS, OCWM and NEWC, respectively. The contrast of the multi-objective detailed design with the typical stiffened panel illustrates the improvement of SSO. [ABSTRACT FROM AUTHOR]

This paper considers a special class of quasi-periodic systems with a small parameter, whose unperturbed part has a degenerate equilibrium point. We prove the existence of response solutions for many sufficiently small parameters. The proof is based on some formal KAM techniques and the Leray-Schauder Continuation Theorem. [ABSTRACT FROM AUTHOR]

In this paper, we prove the strong unique continuation property at the origin for solutions of the following scaling critical parabolic differential inequality | div (A (x , t) ∇ u) − u t | ≤ M | x | 2 | u | , where the coefficient matrix A is Lipschitz continuous in x and t. Our main result sharpens a previous one of Vessella concerned with the subcritical case as well as extends an earlier result of one of us with Garofalo and Manna for the heat operator. [ABSTRACT FROM AUTHOR]

Voltage stability detection is currently still becoming the main issue in the modern integrated renewable energy power systems. To assess the voltage stability, the classical methods based on continuation power flow (CPF) technique were used to show nose curve. However, the classical methods require complete model of power system and long computation time. Data driven analysis and synchronized real time measurement technologies currently are developing in power systems monitoring, including the stability detection. The detection method is built based on the historical event model and uses the real time measurement as an input. For that reason, the algorithm to detect the voltage instability and critical bus is proposed using the artificial neural network (ANN) technique to represent the historical event model using the PMU measurement data. The ANN model architecture for this application is developed by creating seven hidden layers consisting of one normalization, four rectifier linear unit, one softmax and one sigmoid layer. To warrant the accuracy, the k-fold cross-validation is used. The algorithm is simulated on modified IEEE 14 test system which consider different loading scenario, line contingency, number of PMU and Photovoltaic (PV) integration. To mimic the actual historical data, the synthetic data is generated and labelled. The result shows that the proposed method can represent the complete power system model by giving high accuracy which for voltage stability detection is > 97% and critical buses detection is > 96% for all scenarios. Moreover, the required computation time is between 16 and 18 s per detection which makes the scalability to the real time detection is reasonable. [ABSTRACT FROM AUTHOR]

In the current research, we delve into the intricate realm of bifurcation analysis for Föppl–von Kármán plates, employing a precise numerical tool. This innovative numerical approach melds the power of spectral discretization with the prowess of a high-order continuation method-based Taylor series development (HODC). It is worth noting that combining the high-order continuation method with such discretization techniques offers an efficient path-following approach, complete with adaptive step lengths, capable of tackling a wide array of nonlinear problems. Despite the extensive applications of nonlinear elasticity, the spectral method remains relatively uncharted territory within this context. However, our deep-rooted understanding and expertise in the field drive us to embrace this method alongside high-order development continuation for bifurcation analysis of Föppl–von Kármán plates. The governing equations governing thin elastic plates experiencing significant elastic deflections manifest as a pair of coupled nonlinear differential equations, famously known as the von Kármán (vK) equations, presented in a strong form with two principal unknowns: deflection (w) and the Airy stress function (F). Leveraging Chebyshev decomposition matrices, we approximate these fourth-order elliptic nonlinear partial differential equations. Subsequently, we harness high-order development continuation techniques to morph these nonlinear systems into linear ones. Our rigorous evaluation and validation of this numerical approach's precision and performance come to fruition through a comprehensive buckling analysis encompassing multiple illustrative examples. [ABSTRACT FROM AUTHOR]

The present work's main objective is to investigate the natural vibrations of the thin (Kirchhoff–Love) plate resting on time-fractional viscoelastic supports in terms of the Stochastic Finite Element Method (SFEM). The behavior of the supports is described by the fractional order derivatives of the Riemann–Liouville type. The subspace iteration method, in conjunction with the continuation method, is used as a tool to solve the non-linear eigenproblem. A deterministic core for solving structural eigenvibrations is the Finite Element Method. The probabilistic analysis includes the Monte-Carlo simulation and the semi-analytical approach, as well as the iterative generalized stochastic perturbation method. Probabilistic structural response in the form of up to the second-order characteristics is investigated numerically in addition to the input uncertainty level. Finally, the probabilistic relative entropy and the safety measure are estimated. The presented investigations can be applied to the dynamics of foundation plates resting on viscoelastic soil. [ABSTRACT FROM AUTHOR]

In the work presented in this paper, a study for a class of space-time fractional Langevin diffusion equations with two different time-fractional derivatives and a spatial fractional Laplacian was conducted. Firstly, we investigate the well-posedness and regularity of the mild solutions for a nonlocal problem by using several distinctly different approaches in the following three cases with the source term f: if f is a linear source term, then some properties of the Mittag-Leffler functions, the techniques of Laplace transform and eigenfunctions expansion will be utilized to obtain our main results in this case; if f is a globally Lipschitz and uniformly bounded nonlinear source term, then the method in this case is based on the Picard approximation; if f is a locally Lipschitz and uniformly bounded nonlinear function, then the Banach fixed point theorem will be the main tool for dealing with this case. Next, for the corresponding Cauchy problem, the issues on the continuation, global existence or finite-time blowup of mild solutions are also discussed. [ABSTRACT FROM AUTHOR]

This work deals with well‐posedness and blow‐up in the setting of Lebesgue and Besov spaces to the time‐fractional Keller–Segel model for chemotaxis under homogeneous Neumann boundary conditions in a smooth domain of RN$\mathbb {R}^N$. The KS model consists in a coupled system of partial differential equations. In particular, we also treat the unique continuation of the solution and the persistence of continuous dependence on the initial data for the continued solution. [ABSTRACT FROM AUTHOR]