Exact Stability Research Articles

Exact soliton solutions, bifurcation, sensitivity and stability analysis of the fractional longitudinal wave equation in magneto-electro-elastic circular rod

Exact soliton solutions, bifurcation, sensitivity and stability analysis of the fractional longitudinal wave equation in magneto-electro-elastic circular rod

Optimal milling cutter helix selection for period doubling chatter suppression

In high speed milling, interrupted cutting conditions can lead to period doubling chatter vibrations. While many studies have already confirmed that the use of helical tools can effectively shrink or remove these regions of unstable cutting, none of them has provided clear guidance to select the minimum helix that completely cancels the period doubling lobes. This study addresses this gap by introducing a novel analytical formula for a critical tool helix pitch: if the helix pitch is below the critical flip depth of cut of the straight helix cutter multiplied by π, the flip lobes will totally vanish. This rule is not only valuable for chatter-free process planning purposes, but it also establishes exact limit below which the fast and simple zeroth order stability algorithm can provide exact stability boundaries for helical tools. The effectiveness of the formula is numerically corroborated over three different milling scenarios: thin wall milling, slender tool and machine tool structure chatter cases. Finally, the findings are validated through experimental cutting tests.

Exact discrete-time stability analysis of multi-DOF haptic rendering: Impact of multi-rate, time-delay, and mechanical parameters

Previous studies on the stability analysis of haptic devices have predominantly focused on single-DOF devices, thereby limiting attention to multi-DOF devices, particularly those employing multi-rate sampling schemes. In this paper, we introduce a formulation for the coupled dynamics between the haptic device and the virtual environment for a multi-DOF haptic device controlled using a dual-rate sampling scheme. Subsequently, we analyze its stability through the application of a dynamic decoupling strategy within an exact discrete-time state-space framework while the device is engaged in rendering a virtual wall along one of its operational space coordinates. Furthermore, we explore how the combined influence of the dual-rate sampling approach, time delay, and the mechanical design affects the stability boundaries of the multi-DOF haptic device at a fixed workspace location as well as within the entire usable workspace. Additionally, we utilize a model-order reduction (MOR) framework to simplify the determination of the device’s stability limits, irrespective of the specific combinations of time delay and sampling rates employed.

Isotope effects and Alfvén eigenmode stability in JET H, D, T, DT, and He plasmas

While much about Alfvén eigenmode (AE) stability has been explored in previous and current tokamaks, open questions remain for future burning plasma experiments, especially regarding exact stability threshold conditions and related isotope effects; the latter, of course, requiring good knowledge of the plasma ion composition. In the JET tokamak, eight in-vessel antennas actively excite stable AEs, from which their frequencies, toroidal mode numbers, and net damping rates are assessed. The effective ion mass can also be inferred using measurements of the plasma density and magnetic geometry. Thousands of AE stability measurements have been collected by the Alfvén Eigenmode Active Diagnostic in hundreds of JET plasmas during the recent Hydrogen, Deuterium, Tritium, DT, and Helium-4 campaigns. In this novel AE stability database, spanning all four main ion species, damping is observed to decrease with increasing Hydrogenic mass, but increase for Helium, a trend consistent with radiative damping as the dominant damping mechanism. These data are important for confident predictions of AE stability in both non-nuclear (H/He) and nuclear (D/T) operations in future devices. In particular, if radiative damping plays a significant role in overall stability, some AEs could be more easily destabilized in D/T plasmas than their H/He reference pulses, even before considering fast ion and alpha particle drive. Active MHD spectroscopy is also employed on select HD, HT, and DT plasmas to infer the effective ion mass, thereby closing the loop on isotope analysis and demonstrating a complementary method to typical diagnosis of the isotope ratio.

Exact stability criteria for linear differential equations with discrete and distributed delays

This study is devoted to the stability analysis of a scalar linear differential equation with discrete and distributed delays. We establish necessary and sufficient conditions guaranteeing the asymptotic stability of the zero solution composed of explicit delay-dependent criteria. The proofs of our results are obtained using the root analysis of the associated characteristic equation.

Stability analysis of a stochastic port-Hamiltonian car-following model

Port-Hamiltonian systems are pertinent representations of many nonlinear physical systems. In this study, we formulate and analyse a general class of stochastic car-following models with a systematic port-Hamiltonian structure. The model class is a generalisation of classical car-following approaches, including the optimal velocity model of Bando et al (1995 Phys. Rev. E 51 1035), the full velocity difference model of Jiang et al (2001 Phys. Rev. E 64 017101), and recent stochastic following models based on the Ornstein–Uhlenbeck process. In contrast to traditional models where the interaction is totally asymmetric (i.e. depending only on the speed and distance to the predecessor), the port-Hamiltonian car-following model also depends on the distance to the follower. We determine the exact stability condition of the finite system with N vehicles and periodic boundaries. The stable system is ergodic with a unique Gaussian invariant measure. Other properties of the model are studied using numerical simulation. It turns out that the Hamiltonian component improves the flow stability and reduces the total energy in the system. Furthermore, it prevents the problematic formation of stop-and-go waves with oscillatory dynamics, even in the presence of stochastic perturbations.

Quick responding humidity sensor based on polyaniline/reduced graphene oxide composite

The relative humidity sensing response of the Polyaniline/ reduced Graphene Oxide (PRGO) composites has been explored in this present research work. For these observations, polyaniline (PANI), synthesised by the chemical oxidative polymerisation process, was physically blended using the different mass ratios of reduced graphene oxide (rGO). By the improved hummers method, graphene oxide (GO) is prepared, adding the minimal quantity of selenium power, and the GO was effectively and facilely reduced to rGO. By adding different weight per cent (wt%) of reduced Graphene oxide (rGO) to the polymer matrix, PRGO composites were prepared. Structural and morphological properties of rGO were confirmed by XRD, RAMAN, FTIR, SEM, EDX, and HR-TEM (elementary mapping) characterisations. XRD, FTIR SEM and EDX proficiencies were employed to characterise the PRGO composites. For the humidity sensing determination, the sensing film of the PANI, rGO, and PRGO composites is groomed by loading the sample on an IDT substrate through a drop casting technique. The PRGO-3 composite has shown an epitome response and recovery of 3 and 4 s, respectively. The PRGO-3 composite has the most minored and less real sensitivity with a lower limit of detection (LOD). Also, the prepared PRGO composites have recorded less hysteresis and good linearity and depicted exact stability over PANI and other PRGO composites. The physical parameters for PRGO composites were also calculated to determine the potentiality of a perfect sensor. The sensing mechanism also hashed out based on establishing chemisorption and physisorption layers.

New exact solution forms and stability aspects to Drinfel’d–Sokolov–Wilson model by using extended Jacobi elliptic rational function approach

New exact solution forms and stability aspects to Drinfel’d–Sokolov–Wilson model by using extended Jacobi elliptic rational function approach

Geometrically Exact Aeroelastic Stability Analysis of Composite Helicopter Rotor Blades in Hover by Updated VABS

Geometrically Exact Aeroelastic Stability Analysis of Composite Helicopter Rotor Blades in Hover by Updated VABS

On inertial iterated Tikhonov methods for solving ill-posed problems

In this manuscript we propose and analyze an implicit two-point type method (or inertial method) for obtaining stable approximate solutions to linear ill-posed operator equations. The method is based on the iterated Tikhonov (iT) scheme. We establish convergence for exact data, and stability and semi-convergence for noisy data. Regarding numerical experiments we consider: (i) a 2D inverse potential problem, (ii) an image deblurring problem; the computational efficiency of the method is compared with standard implementations of the iT method.

Investigating the anti-inflammatory potential of N-amidic acid organoselenium candidates: biological assessments, molecular docking, and molecular dynamics simulations.

Inflammation is a complex process with many contributing factors, and it often causes pain. The pathophysiology of pain involves the release of inflammatory mediators that initiate pain sensation, as well as edema and other inflammation hallmarks. Selenium-containing compounds (OSe) are very promising for developing new medicines because they can treat many different diseases. In this study, we estimated the anti-inflammatory properties of maleanilic and succinanilic acids containing selenium (OSe). These molecules were designed by combining different strategies to enhance their anti-inflammatory properties. Hence, the anti-inflammatory impacts of compounds 8, 9, 10, and 11 were pursued using inflammatory markers COX-2, IL-1β, and IL-6. Notably, it was revealed that compounds 8, 9, 10, and 11 downregulated COX-2, IL-1β, and IL-6 by (2.01, 1.63, 2.26, and 2.05), (1.42, 1.64, 1.93, and 2.59), and (1.67, 2.54, 2.22, and 4.06)-fold changes, respectively. Moreover, molecular docking studies were conducted on compounds 8, 9, 10, and 11 to pursue their binding affinities for the COX-2 enzyme. Notably, very promising binding scores of compounds 8, 9, 10, and 11 towards the binding site of the COX-2 receptor were attained. Additionally, more accurate molecular dynamics simulations were performed for 200 ns for the docked complexes of compounds 8, 9, 10, and 11 to confirm the molecular docking findings, which ignore the protein's flexibility. Therefore, the exact stability of the N-amidic acids OSe compounds 8, 9, 10, and 11 towards the binding pocket of the COX-2 enzyme was examined and explained as well. Also, the MM-GBSA binding energy was calculated for equilibrated MD trajectory, and 200 snapshots were selected with a 50 ps interval for further analysis. Accordingly, the investigated compounds can be treated as prominent lead anti-inflammatory candidates for further optimization.

Stability of the ternary τ11-Al4Fe1.7Si intermetallic phase from experiment and Ab initio calculations

The Al-Fe-Si ternary system provides an opportunity for the design of new lightweight low cost alloys that have high melting temperature, superior strength, and excellent high-temperature corrosion and oxidation resistance. This system is exceptionally complex and exhibits up to 21 reported binary and ternary compounds. The intermetallic compound τ11-Al4Fe1.7Si is of particular interest due to its low theoretical density, promising mechanical properties, and low cost constituent elements. Knowledge of the exact composition range and thermal stability of this phase is crucial for further development. In this study, Al-Fe-Si alloys were fabricated and equilibrated at 800 and 950 °C. The composition range of τ11-Al4Fe1.7Si was analyzed using scanning electron microscopy with energy dispersive spectroscopy and X-ray diffraction to confirm the presence of the phase. Density functional theory calculations show that entropic contributions drive and stabilize the τ11-Al4Fe1.7Si phase. Based on experimental measurements, the composition range of τ11-Al4Fe1.7Si phase was determined to be Al-(24.3–25.5)Fe-(8.2–10.8)Si at% and Al-(24.6–25.2)Fe-(9.6–11.0)Si at% at 800 °C and 950 °C, respectively.

Optimal bracing system design for funicular twin arches against out-of-plane buckling

Twin arch bridges are often designed with a bracing member system that can significantly enhance the out-of-plane stability. This study presents an exact matrix stiffness method (MSM) for the out-of-plane buckling analysis of funicular twin arch bridges and investigates the optimal bracing system design. A novel 14 × 14 s-order element stiffness matrix of three-dimensional beam–columns was used in the MSM and the out-of-plane buckling analysis was performed after assembling the exact global structural stability stiffness matrix. The influences of the bracing location, number, length, and flexural rigidity of both the transverse bracing and X-bracing systems on the buckling capacity of the twin arch system were investigated. The in-plane stiffness of the bracing system (i.e., the horizontal flexural rigidity in a transverse bracing system) was found to be the critical factor in suppressing the out-of-plane buckling of the twin arch system. In addition, the twin arch system achieved the maximum out-of-plane buckling capacity with the bracing location at S/4, where S is the total arc length. For optimal bracing system design of funicular twin arches, it is recommended that one uses the more economical X-bracing system or a transverse bracing system with adequately rigid bracing members.

Geometrically exact aeroelastic stability analysis of helicopter composite rotor blades in forward flight

In this paper, a sophisticated method for analyzing the geometrically exact aeroelastic stability of composite rotor blades in forward flight has been proposed. The unique advantage of the proposed method is to use the geometrically exact beam model with the updated Variational Asymptotic Beam Sectional analysis (VABS) for structural modeling to not only calculate the blade cross-sectional properties and blade spanwise deformations more accurately, but also take into account the effect of transverse shear deformation and blade initial twist and curvatures sophisticatedly. The Peters finite state airloads theory and the Peters-He finite state dynamic inflow model are coupled to calculate the three-dimensional unsteady airloads applied on the blade. The auto-pilot trim scheme is adopted to determine the blade pitch controls. The finite element spatial discretization method, the Newmark numerical integration method, the Newton-Raphson method and the moving-block analysis method are combined to solve the established geometrically exact aeroelastic equations and obtain the geometrically exact aeroelastic stability of composite rotor blades. The proposed method is validated by correlation with existing analytical results. The investigations show that the effect of transverse shear deformation on the aeroelastic stability of composite hingeless rotors in forward flight is non-negligible. Blade initial curvatures have significant effect on the aeroelastic stability of composite hingeless rotors in forward flight, which is not only related to the blade elastic couplings, but also to the advance ratio.

Fixed-time terminal sliding mode control for uncertain robot manipulators

This paper proposes a fixed-time tracking control for robot manipulators in the presence of parametric uncertainties and disturbances. An auxiliary function is first proposed for constructing a fixed-time sliding manifold. Benefited from this fixed-time sliding manifold, a singularity-free robust control is proposed to evade the effects of algebraic loop problem of the commonly-used sliding mode controls (SMC). The key advantages of the proposed approach are: (i) exact fixed-time stability featuring the convergence time does not relate to the initial conditions and is acquired in advance; (ii) the singularity and algebraic loop problems are eliminated completely; (iii) a simple and intuitive control structure is used for easy implementation of trajectory tracking control for uncertain robot manipulators with faster transient and higher steady-state precision. Simulations and experimental comparisons validate the improved tracking performance of the proposed approach.

Anti-breast cancer potential of a new xanthine derivative: In silico, antiproliferative, selectivity, VEGFR-2 inhibition, apoptosis induction and migration inhibition studies

BackgroundThe overexpression of VEGFR-2 receptors in breast cancer provides a valuable approach to anticancer strategies. Targeting VEGFR-2, a new semisynthetic compound (T-1-MCPAB) has been designed. MethodsComputational methods (ADMET, toxicity, DFT, Molecular Docking, Molecular Dynamics Simulations, MM-GBSA, PLIP, and PCAT) were conducted. In addition to the semi-synthesis, in vitro studies (anti-VEGFR-2, anti-proliferative, flow cytometry, and wound scratch assay) were employed. ResultsADME and toxicity profiles of T-1-MCPAB studies indicated its overall drug-likeness showing results much better than Sorafenib. Then, T-1-MCPAB’s exact 3D structure, stability, and reactivity were evoked by the DFT calculations. Molecular docking, molecular dynamics simulations, MM-GPSA, PLIP, and PCAT studies denoted the correct binding and inhibiting potential of T-1-MCPAB, towards VEGFR-2 protein. After the semisynthesis, T-1-MCPAB inhibited VEGFR-2 with an IC50 of 0.135 µM, which was comparable to sorafenib's IC50 of 0.0591 µM. T-1-MCPAB also showed a notable performance against MCF7 and T47D breast cancer cell lines with IC50 values of 30.95 µM and 63.64 µM, respectively, and had high selectivity index values of 3.7 and 1.8, respectively. Furthermore, T-1-MCPAB influenced early and late apoptosis and significantly decreased the potential of MCF7 cells to heal and migrate. ConclusionT-1-MCPAB is a promising VEGFR-2 inhibitor with potential for breast cancer treatment. Further chemical and biological studies are needed to explore its potential as a therapeutic agent.

Approaching the Transient Stability Boundary of a Power System: Theory and Applications

Estimating the stability boundary is a fundamental and challenging problem in transient stability studies. It is known that a proper level set of a Lyapunov function or an energy function can provide an inner approximation of the stability boundary, and the estimation can be expanded by trajectory reversing methods. In this paper, we streamline the theoretical foundation of the expansion methodology, and generalize it by relaxing the request that the initial guess should be a subset of the stability region. We investigate topological characteristics of the expanded boundary, showing how an initial guess can approach the exact stability boundary locally or globally. We apply the theory to power system transient stability assessment, and propose expansion algorithms to improve the well-known Potential Energy Boundary Surface (PEBS) and Boundary of stability region based Controlling Unstable equilibrium point (BCU) methods. Case studies on the IEEE 39-bus system well verify our results and demonstrate that estimations of the stability boundary and the critical clearing time can be significantly improved with modest computational cost. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper was motivated by the problem of determining whether a power system can retain transient stability subject to large disturbances such as short-circuit fault and generator tripping. The most well-known approaches to such a problem are the direct methods that can avoid time-costly simulations and “directly” determine the transient stability by estimating the stability boundary. Nevertheless, such estimations are generally too conservative. This paper proposes a new expansion method to improve the direct methods, which allows the initial estimation to lie partially outside the real boundary and hence enables applications to both global and local direct methods. Our method can expand the initial estimation towards the real stability boundary, thus reducing the conservativeness and providing a more accurate stability assessment such as the critical clearing time (CCT) of a fault. In this paper, we first mathematically establish the expansion theory and then propose numerical algorithms for power system applications. Simulations on the IEEE 39-bus benchmark verify our approach and show that the conservativeness can be significantly reduced with modest computational cost. Our approach can be further extended to scenarios where a valid Lyapunov (energy) function is unavailable.

A general framework for the exact stability analysis of love dynamics with four independent time delays

We investigate the asymptotic stability of a linear love model with four independent time delays to mimic the complicated human emotions more precisely compared with the classic Strogatz model. These four delays stem from the perception of their own past emotions and their partner's past emotions for both individuals. The central idea is to exactly ascertain the stability switching boundaries where the emotions of these two individuals change in the domain of delays. For this, we propose a general stability analysis framework synthesizing the Dixon resultant theory, the frequency sweeping technique, and the cluster treatment of characteristic roots (CTCR) paradigm. We then present a detailed procedure of this framework to particularly study how one partner reacts to the other. Finally, we demonstrate the effectiveness of this framework through a case study and then provide some suggestions for the couple to achieve a sweet love relationship.

An unstructured finite-volume level set / front tracking method for two-phase flows with large density-ratios

We extend the unstructured LEvel set / froNT tracking (LENT) method [1,2] for handling two-phase flows with strongly different densities (high-density ratios) by providing the theoretical basis for the numerical consistency between the mass and momentum conservation in the collocated Finite Volume discretization of the single-field two-phase Navier-Stokes equations. Our analysis provides the theoretical basis for the mass conservation equation introduced by Ghods and Herrmann [3] and used in [4–8]. We use a mass flux that is consistent with mass conservation in the implicit Finite Volume discretization of the two-phase momentum convection term, and solve the single-field Navier-Stokes equations with our SAAMPLE segregated solution algorithm [2]. The proposed ρLENT method recovers exact numerical stability for the two-phase momentum advection of a spherical droplet with density ratios ρ−/ρ+∈[1,104]. Numerical stability is demonstrated for in terms of the relative L∞ velocity error norm, for density-ratios in the range of [1,104], dynamic viscosity-ratios in the range of [1,104] and very strong surface tension forces, for challenging mercury/air and water/air fluid pairings. In addition, the solver performs well in cases characterized by strong interaction between two phases, i.e., oscillating droplets and rising bubbles. The proposed ρLENT method1 is applicable to any other two-phase flow simulation method that discretizes the single-field two-phase Navier-Stokes Equations using the collocated unstructured Finite Volume Method but does not solve an advection equation for the phase indicator using a flux-based approach, by adding the proposed geometrical approximation of the mass flux and the auxiliary mass conservation equation to the solution algorithm.

Stability of thin-shell-wormhole in Robertson-Walker closed universe I: static universe

We construct a generic thin-shell wormhole (TSW) in the Robertson -Walker (RW) cosmological model of the Universe. The general formalism is presented and here in this paper—the first part of the research- we investigate the stability of the TSW constructed in the static RW universe. To do so, we perform two different stability analyses namely a mechanical linear radial perturbation and a small speed exact (not linearized) perturbation. It is shown that the corresponding TSW is stable against a linear radial perturbation provided that the variable equation of state of the surface energy-momentum tensor is finely tuned. On the other hand, the exact stability analysis in the context of small-speed perturbation reveals that the throat of the TSW for the closed static universe oscillates between the center of the Universe and the outer boundary.