Search Results (27)

Variational models describe deformation and stability through the first and second variations in an underlying functional, but the relationship between these responses is seldom expressed as an intrinsic equilibrium quantity of the model itself. A canonical curvature–strain representation for equilibrium ratios arising in variational field settings is developed. For a twice Fréchet differentiable functional and an admissible perturbation generator, strain is defined as normalized first-order response and curvature as normalized second-order response along the generator direction. Their quotient defines a curvature–strain ratio that measures proportional balance between deformation and curvature within the model. The main result shows that this curvature–strain ratio is a canonical representative of a response ratio already implicit in the variational data. Under canonical normalization, the curvature–strain ratio coincides with the quotient of second- and first-order response, and stationarity of the curvature–strain ratio is equivalent to proportional stationarity of that response quotient along the admissible flow. A further theorem establishes transfer of local isolation: when the second-variation operator satisfies standard hypotheses such as compact resolvent and non-degeneracy of the constrained extremum, isolated equilibrium ratios persist in the curvature–strain representation for the same operator-theoretic reasons. Quadratic scalar and Maxwell-type models illustrate the construction. The paper establishes a mathematically controlled curvature–strain representation of equilibrium ratios within ordinary variational theory, with emphasis on the analysis of variational response and equilibrium balance. Full article

To address edge contact in non-circular gears arising from installation errors, a modification strategy represented by elliptical gears and driven by an ease-off topological surface is proposed. A tooth surface model for non-circular gears was first derived from meshing theory. The modification magnitude was defined using a second-order ease-off differential surface, and the modified surface is represented through non-uniform rational B-spline (NURBS) fitting. A tooth contact analysis (TCA) model is then built to evaluate how installation errors and modification amount influence contact behavior. The results indicate that an increase in center distance error reduces the contact ratio. For equal perturbations of axial horizontal and axial vertical mounting angles, the horizontal error has the stronger impact on the size and location of the contact patch. As the longitudinal modification coefficient grows, the contact path and peak pressure position shift from the tooth edge toward the mid-width; the contact ellipse first enlarges and then shrinks, while the contact pressure shows the opposite trend. The elastic deformation of the tooth surface increases with the mounting angle. Transmission tests confirm that the proposed modification lowers the transmission error relative to the unmodified gear pair. Full article

We have theoretically examined the intermolecular interactions in the cationic states of π-stacked dimers of 4nπ antiaromatic molecules. The ground state of face-to-face π-dimer models, consisting of cyclobutadienes (CBDs), was analyzed as a function of the stacking distance (d) for their monocationic and dicationic states using multi-reference second-order perturbation theory. Multi-configurational wavefunction analysis in a diabatic representation was employed to understand the electronic structures of the dimer models in terms of the monomer electron configurations. It is found that the monocationic dimer exhibits a local minimum at about d = 2.4 Å in the ground state, where each monomer is represented by a superposition between neutral triplet and cationic doublet electron configurations. Crossing of the ground and excited states occurs through changing d, which is due to the small energy gap between the highest occupied and lowest unoccupied molecular orbitals of antiaromatic molecules. Full article

This work thoroughly investigated the compound 4-(2,5-Dimethoxyphenyl)-3,4-dihydrobenzo[g]chromene-2,5,10-trione (DMDCT) using molecular docking, quantum chemical analysis, and vibrational spectroscopy methodology. The medicinal chemistry group has been particularly interested in chromene and benzochromene derivatives due to their wide range of pharmacological actions, including anticancer, antibacterial, anti-inflammatory, antioxidant, antiviral, and neuroprotective capabilities. In this connection, DMDCT has been explored to evaluate its biological, electrical, and structural properties. DFT using the B3LYP functional and 6–31G basis was established to conduct theoretical computations with the Gaussian 09 program. The findings from these computations provide insight into the following topics: NBO interactions, optimal molecular geometry, Mulliken charge distribution, frontier molecular orbitals, and MEP. Second-order perturbation theory has been used to assess stabilization energies arising from donor–acceptor interactions. Furthermore, general features such as chemical hardness, softness, and electronegativity were studied. The results suggest that DMDCT has stable electronic configurations and biologically relevant active sites. This integrated experimental and theoretical study supports the potential of DMDCT as a practical scaffold for future therapeutic applications and contributes valuable information regarding its vibrational and electronic behavior. Full article

Gellan gum (Gellan), a versatile polysaccharide applied in gel formation and prebiotic formulations, is often processed to tailor its molecular properties. Previous studies employed gamma irradiation and chemical hydrolysis, though without addressing systematic scaling behavior. This study investigates the structural and conformational modifications of Gellan in dilute aqueous salt solutions using a safer and eco-friendly approach: atmospheric low-dose electron beam (e-beam) degradation coupled with viscosity analysis. Native and E-beam-treated Gellan samples (0.05 g/cm³ in 0.1 M KCl) were examined by relative viscosity at varying temperatures, with intrinsic viscosity and molar mass determined via Solomon–Ciuta and Mark–Houwink relations. Molar mass degradation followed first-order kinetics, yielding rate constants and degradation lifetimes. Structural parameters, including radius of gyration and second virial coefficient, produced scaling coefficients of 0.62 and 0.15, consistent with perturbed coil conformations in a good solvent. The shape factor confirmed preservation of an ideal random coil structure despite irradiation. Conformational flexibility was further analyzed using theoretical models. Transition state theory (TST) revealed that e-beam radiation lowered molar mass and activation energy but raised activation entropy, implying reduced flexibility alongside enhanced solvent interactions. The freely rotating chain (FRC) model estimated end-to-end distance (R_θ) and characteristic ratio (C_∞), while the worm-like chain (WLC) model quantified persistence length (l_p). Results indicated decreased R_θ, increased l_p, and largely unchanged C_∞, suggesting diminished chain flexibility without significant deviation from ideal coil behavior. Overall, this work provides new insights into Gellan’s scaling laws and flexibility under aerobic low-dose E-beam irradiation, with relevance for bioactive polysaccharide applications. Full article

The present paper investigates a new tool for analyzing stability/convergence properties and robustness against matched perturbations of a class of nonlinear systems. We start with a scalar system, where it is shown that the state can be regulated or stabilized to a prescribed time using time-varying functions. The proof is based on Lyapunov theory. We developed a robust terminal-integral sliding mode controller that guarantees convergence of the system states to a desired equilibrium within a user-defined time, irrespective of initial conditions and under bounded disturbances. The method was extended to a class of second-order nonlinear systems, achieving both fixed-time (prescribed-time) convergence and robustness. Theoretical properties were established via Lyapunov-based analysis, and numerical simulations confirmed the effectiveness of the proposed methods in terms of robustness and convergence. Full article

This paper presents some of the most significant findings in the design of a hydraulic servomechanism for flight controls, which were primarily achieved by the first author during his activity in an aviation institute. These results are grouped into four main topics. The first one outlines a classical theory, from the 1950s–1970s, of the analysis of nonlinear automatic systems and namely the issue of absolute stability. The uninformed public may be misled by the adjective “absolute”. This is not a “maximalist” solution of stability but rather highlights in the system of equations a nonlinear function that describes, for the case of hydraulic servomechanisms, the flow-control dependence in the distributor spool. This function is odd, and it is therefore located in quadrants 1 and 3. The decision regarding stability is made within the so-called Lurie problem and is materialized by a matrix inequality, called the Lefschetz condition, which must be satisfied by the parameters of the electrohydraulic servomechanism and also by the components of the control feedback vector. Another approach starts from a classical theorem of V. M. Popov, extended in a stochastic framework by T. Morozan and I. Ursu, which ends with the description of the local and global spool valve flow-control characteristics that ensure stability in the large with respect to bounded perturbations for the mechano-hydraulic servomechanism. We add that a conjecture regarding the more pronounced flexibility of mathematical models in relation to mathematical instruments (theories) was used. Furthermore, the second topic concerns, the importance of the impedance characteristic of the mechano-hydraulic servomechanism in preventing flutter of the flight controls is emphasized. Impedance, also called dynamic stiffness, is defined as the ratio, in a dynamic regime, between the output exerted force (at the actuator rod of the servomechanism) and the displacement induced by this force under the assumption of a blocked input. It is demonstrated in the paper that there are two forms of the impedance function: one that favors the appearance of flutter and another that allows for flutter damping. It is interesting to note that these theoretical considerations were established in the institute’s reports some time before their introduction in the Aviation Regulation AvP.970. However, it was precisely the absence of the impedance criterion in the regulation at the appropriate time that ultimately led, by chance or not, to a disaster: the crash of a prototype due to tailplane flutter. A third topic shows how an important problem in the theory of automatic systems of the 1970s–1980s, namely the robust synthesis of the servomechanism, is formulated, applied and solved in the case of an electrohydraulic servomechanism. In general, the solution of a robust servomechanism problem consists of two distinct components: a servo-compensator, in fact an internal model of the exogenous dynamics, and a stabilizing compensator. These components are adapted in the case of an electrohydraulic servomechanism. In addition to the classical case mentioned above, a synthesis problem of an anti-windup (anti-saturation) compensator is formulated and solved. The fourth topic, and the last one presented in detail, is the synthesis of a fuzzy supervised neurocontrol (FSNC) for the position tracking of an electrohydraulic servomechanism, with experimental validation, in the laboratory, of this control law. The neurocontrol module is designed using a single-layered perceptron architecture. Neurocontrol is in principle optimal, but it is not free from saturation. To this end, in order to counteract saturation, a Mamdani-type fuzzy logic was developed, which takes control when neurocontrol has saturated. It returns to neurocontrol when it returns to normal, respectively, when saturation is eliminated. What distinguishes this FSNC law is its simplicity and efficiency and especially the fact that against quite a few opponents in the field, it still works very well on quite complicated physical systems. Finally, a brief section reviews some recent works by the authors, in which current approaches to hydraulic servomechanisms are presented: the backstepping control synthesis technique, input delay treated with Lyapunov–Krasovskii functionals, and critical stability treated with Lyapunov–Malkin theory. Full article

Co(II) complexes have shown promising applications as single-molecule magnets (SMMs) in quantum computing and structural biology. Deciphering the Co(II) complexes may facilitate the development of SMM materials. Structural optimizations and calculations of chemical and magnetic properties were performed for Co(II) complexes with a tripodal tetradentate phenolate-amine ligand using MP2/aug-cc-pvdz, MP2/Def2svp, and CASSCF/Def2svp methods. The Second Order Perturbation Theory Analysis of Fock Matrix in NBO Basis unravels that Co(II) ions form unusual coordinate quasi-double bonds with ligand oxygen donor atoms, and the bond strengths range from 142.01 kcal/mol to 167.36 kcal/mol but lack further spectrometric evidence. The average 151.70 kcal/mol of the Co(II-O coordinates quasi-double bonds are formed mainly by two lone pairs of electrons from the ligand phenolate donor oxygen atoms. Dispersion forces contribute 24%, 28%, 27%, and 31% to the Co(II)-ligand interaction. Theoretical results of ZFS D, transversal ZFS E, and g-factor agree well with the experimental values. Magnetic susceptibility parameters calculated based on 5 doublet roots account for 85% of results computed 40 doublet roots are specified. These insights may aid in the rational design of SMM materials and Co(II) porphyrin fullerene conjugate for CO₂ electroreduction with superior magnetic properties. Full article

The impact of photoisomerization on antioxidant properties holds significant implications for fields such as medicine, chemistry, and consumer products. This investigation employs multistate complete active space second-order perturbation theory (MS-CASPT2), complemented by density functional theory (DFT) and time-dependent DFT (TD-DFT) methods, to examine the photoisomerization behavior of sinapic acid (SA) and methyl sinapate (MS) under ultraviolet (UV) irradiation, while systematically analyzing their antioxidant properties in the S₁ state. The computational results, validated by two independent theoretical approaches, confirm that both SA and MS can undergo photoisomerization through conical intersection pathways, providing crucial insights into their non-radiative transition mechanisms. In the S₀ state, cis-SA and cis-MS exhibit higher antioxidant activity, while in the S₁ state, antioxidant performance is strongly solvent-dependent: trans-SA outperforms in ethyl acetate (Eac) and water, whereas cis-SA is more effective in methanol (MeOH). Notably, the natural population analysis (NPA) charges of all four compounds increase upon photoexcitation, suggesting that photoexcitation enhances antioxidant properties. This study addresses a critical gap in our understanding of the relationship between photoisomerization and antioxidant activity in natural phenolic compounds. Full article

Aiming at the control challenges faced by unmanned surface vessels (USVs) in complex environments, such as nonlinearities, parameter uncertainties, and environmental perturbations, we propose a non-singular terminal integral sliding mode control strategy based on an extended state observer (ESO). The strategy first employs a third-order linear extended state observer to estimate the total disturbances of the USV system, encompassing both external disturbances and internal nonlinearities. Subsequently, a backstepping sliding mode controller based on the Lyapunov theory is designed to generate the steering torque control commands for the USV. To further enhance the tracking performance of the system, we introduce a non-singular terminal integral sliding mode surface with a double power convergence law and redesign the backstepping sliding mode controller for the USV heading control. Meanwhile, to circumvent the differential explosion issue in traditional backstepping control, we simplify the controller design by utilizing a second-order sliding mode filter to accurately estimate the differential signals of the virtual control quantities. Theoretical analysis and simulation results demonstrate that the proposed control algorithm improves the convergence speed, adaptive ability, and anti-interference ability in complex environments compared to traditional linear backstepping sliding mode control, thereby enhancing its engineering practicability. This research offers a more efficient and reliable method for precise heading control and path tracking of USVs in complex and dynamic environments. Full article

In this paper, we present a mathematical approach for studying the changes in pressure and temperature variables in flames. This conception extends beyond the traditional second-order Laplacian diffusion model by considering the p-Laplacian operator and a bi-stable reaction term, thereby providing a more generalized framework for flame diffusion analysis. Given the structure of our equations, we provide the boundedness and uniqueness of the solutions in a weak sense from both analytical and numerical approaches. We further reformulate the governing equations in the context of traveling wave solutions, applying singular geometric perturbation theory to derive the analytical expressions of these profiles. This theoretical development is complemented by numerical assessments, which not only validate our theoretical predictions, but also optimize the traveling wave speed to minimize the error between numerical and analytical solutions. Additionally, we explore self-similar structured solutions. The paper then concludes with a perspective on future research, with emphasis being placed on the need for experimental validation in laboratory settings. Such empirical studies could test the robustness of our model and allow for refinement based on actual measurements, thereby broadening the applicability and accuracy of our findings in practical scenarios. Full article

Exponential stability criteria for neutral second-order stochastic systems involving impulses and state-dependent delay have been addressed in this paper based on stability theory, stochastic analysis, and the inequality technique. Some sufficient conditions are given to establish the exponential stability of such systems, which is well-established in the deterministic case, but less known for the stochastic case. In our model, the noise effect can be described as a symmetric Wiener process. By formulating the impulsive integral technique, exponential stability analysis of the pth moment of the second-order system involving stochastic perturbation is established. As an application that illustrates the theoretical formulation, an example is presented. Full article

This study presents a comprehensive analysis of the second-order perturbation theory applied to the Navier–Stokes equations governing free surface flows. We focus on gravity–capillary surface waves in incompressible viscous fluids of finite depth over a flat bottom. The amplitude of these waves is regarded as the perturbation parameter. A systematic derivation of a nonlinear-surface-wave equation is presented that fully takes into account dispersion, while nonlinearity is included in the leading order. However, the presence of infinitely many over-damped modes has been neglected and only the two least-damped modes are considered. The new surface-wave equation is formulated in wave-number space rather than real space and nonlinear terms contain convolutions making the equation an integro-differential equation. Some preliminary numerical results are compared with computational-modelling data obtained via open source CFD software OpenFOAM. Full article

A comprehensive analysis of the intermolecular interaction energy and anharmonic vibrations of 41 structures of the HXeY⋯HX (X, Y = F, Cl, Br, I) family of noble-gas-compound complexes for all possible combinations of Y and X was conducted. New structures were identified, and their interaction energies were studied by means of symmetry-adapted perturbation theory, up to second-order corrections: this provided insight into the physical nature of the interaction in the complexes. The energy components were discussed, in connection to anharmonic frequency analysis. The results show that the induction and dispersion corrections were the main driving forces of the interaction, and that their relative contributions correlated with the complexation effects seen in the vibrational stretching modes of Xe–H and H–X. Reasonably clear patterns of interaction were found for different structures. Our findings corroborate previous findings with better methods, and provide new data. These results suggest that the entire group of the studied complexes can be labelled as “naturally blueshifting”, except for the complexes with HI. Full article

Pump-controlled hydraulic actuators (PHAs) contain slow mechanical and fast hydraulic dynamics, and thus singular perturbation theory can be adopted in the control strategies of PHAs. In this article, we develop a singular perturbation theory-based composite control approach for a PHA with position tracking error constraint. Disturbance observers (DOBs) are used to estimate the matched and mismatched uncertainties for online compensation. A sliding surface-like error variable is proposed to transform the second-order mechanical subsystem into a first-order error subsystem. Consequently, the position tracking error constraint of the PHA is decomposed into the output constraint of the first-order error subsystem and the stabilizing of the first-order hydraulic subsystem. Slow and fast control laws can be easily designed without using the backstepping technique, thus simplifying the control design and reducing the computational burden to a large extent. Theoretical analysis verifies that desired stability properties can be achieved by an appropriate selection of the control parameters. Simulations and experiments are performed to confirm the efficacy and practicability of the proposed control strategy. Full article