Hasil untuk "Analytic mechanics"

M. Lesieur

G.M. Aitenova, Zh.A. Sartabanov, B.Zh. Omarova et al.

The stability of differential equations with periodic and quasiperiodic coefficients is a central topic in modern stability theory, with important applications in mechanics, physics, and dynamical systems. A classical result in this area is the Lyapunov integral criterion, which provides stability conditions for linear second-order equations with periodic coefficients. In this paper, we extend this criterion to equations with quasiperiodic coefficients. Our analysis is based on the method of periodic characteristics, which has proven effective in the study of multiperiodic solutions for systems with a diagonal differentiation operator. Within this framework, the multiperiodicity condition is reduced to a functional equation, and a Floquet-type representation of the matricant of the associated system is derived. This representation shows that multiperiodicity of solutions follows from the purely imaginary nature of the characteristic multipliers and the periodicity of the helical characteristics. The obtained results confirm that the Lyapunov integral criterion remains valid for equations with quasiperiodic coefficients. More generally, they demonstrate the effectiveness of the characteristic method for analyzing stability in complex dynamical systems, thereby extending the scope of classical stability theory.

Rita Desyanti, Suparno, Niniet Indah Arvitrida

This study examines pricing decisions in closed-loop supply chains through the lens of game theory by conducting a scoping review combined with bibliometric analysis (ScoRBA). The objective is to identify research trends, influential journals, leading authors, key institutions, citation patterns, and collaborative networks in this field. A total of 1,602 articles published between 2015 and 2025 were retrieved from the Scopus database and analyzed. The review applies the PAGER framework to ensure a systematic and consistent evaluation of the literature while highlighting opportunities for future investigation. The findings show that game-theoretic models have been widely applied for addressing pricing decisions in closed-loop supply chains, with publications increasing steadily over the past decade. The bibliometric mapping clustered the research into five main themes: (1) game theory and pricing, (2) supply chain management and sustainability, (3) pricing decisions in green product and green supply chain, (4) pricing decisions in e-commerce, and (5) pricing decisions in remanufacturing. This review highlights the integration of game theory, sustainability, and digital transformation in pricing decisions across various supply chain contexts. Beyond examining the five main clusters, this study also investigates the intersections between them, including remanufacturing outsourcing, emission reduction initiatives, and renewable energy investments.

Shimul Akhanjee

The statistical mechanics of particles that populate indistinguishable energy states is explored. In particular, the mathematical treatment of the microstates differs from conventional statistical mechanics where the energy levels or states are universally treated as distinguishable, and differentiated by unique quantum numbers, or addressed by distinct spatial locations. Results from combinatorial counting problems are adapted to derive exact distribution functions for both classical and quantum particles at high degeneracy levels. Classical particles exhibit a definitive glass transition, similar to supercooled liquids where where the configurational entropy vanishes below a finite temperature $T_K$.

Filippo Azzini, Amira M’hadbi, Mohammed El Ganaoui et al.

In this study, we examine the mixing performance of thermally induced microfluidic swirlers, which are recently developed micromixers based on mixed thermal convection. In this configuration, a swirling flow motion is induced by the combination of natural convection and a pressure-driven Poiseuille flow. An experimental investigation was carried out on a microfluidic swirler composed of a glass capillary with a square cross-section of 800 $\times$ 800 $\unicode {x03BC}$ m $^2$ , measuring the three-dimensional flow fields in different operating conditions using the general defocusing particle tracking technique. Furthermore, a thorough numerical analysis was performed to characterise the mixing performance for different Reynolds numbers and microchannel dimensions. Our results show that thermally induced microfluidic swirlers have an optimal range of operation for microchannel with hydraulic diameters between 400 and 1600 $\unicode {x03BC}$ m and Reynolds numbers around 1, where they show an increase of mixing efficiency up to 60 % with respect to the case of pure diffusion. The swirl is activated already at moderate temperature differences of 20–30 K, making this approach compatible with most chemical and biomedical applications.

Jiangchao Liu, Guojian He, Kai Wang et al.

In this study, the method of large-eddy simulation (LES) is applied to investigate the impact of patches of coarsened riverbed sediments on near-bed hydrodynamics and flow resistance. Six simulations are performed with riverbed coverage ratios of coarser particles (Ac/At, where Ac and At are the riverbed area covered by coarsened sediments and the total riverbed area, respectively) ranging from 0 % to 100 %. By ensuring identical crest heights for all particles, the influence of heterogeneous roughness height is eliminated, allowing for an isolated investigation of heterogeneous permeability effects. Results reveal distinct high- and low-flow streaks above coarsened and uncoarsened sediments, associated with elevated and reduced Reynolds shear stress, respectively. These streaky patterns are attributed to time-averaged secondary flows spanning the entire water depth, that converge toward coarsened sediments and diverge from uncoarsened areas. Elevated Reynolds shear stress, up to 1.9 times the reach-averaged bed shear stress, is observed in the interstitial spaces between coarser particles due to intensified hyporheic exchange at the sediment–water interface. Upwelling and downwelling flows occur upstream and downstream of coarsened sediments particles, respectively, driving dominant ejection and sweep events. At Ac/At = 16 %, ejections and sweeps contribute maximally to Reynold shear stress, increasing by up to 130 % and 110 %, respectively – approximately double their contributions in the uncoarsened case. The study identifies two mechanisms driving increased flow resistance over coarsened riverbeds: water-depth-scale secondary flows and grain-scale hyporheic exchanges. Consequently, the reach-averaged friction factor increases by 29.8 % from Ac/At = 0 % to 64 %, followed by a 15.8 % reduction in the fully coarsened scenario.

Andreas G. Varias

Chemical Equilibrium Fracture Mechanics (CEFM) studies the effect of chemical reactions and phase transformations on crack-tip fields and material fracture toughness under chemical equilibrium. An important CEFM direction is hydrogen-induced embrittlement of alloys, due to several industrial applications, including those within the industrial value chain of hydrogen that is under development, which, according to European and international policies, are expected to contribute significantly to the replacement of fossil fuels by renewable energy sources. In the present study, the effect of hydrogen on the crack-tip fields of hydride- and non-hydride-forming alloys is examined. The crack-tip stress and hydrogen concentration distributions are derived under hydrogen chemical equilibrium, which is approached by considering the coupling of the operating physical mechanisms. In all cases, analytic relations are derived, thus facilitating integrity assessments, i.e., without the need to rely on complicated numerical methods, expected to lead to the development of respective tools in industrial applications. It is shown that, in the case of hydride precipitation, there are significant deviations from the K, HRR, and Prandtl fields, and, thus, the well-known approaches of Linear Elastic Fracture Mechanics (LEFM) and Elastic–Plastic Fracture Mechanics (EPFM) need to be accordingly modified/extended.

Weilun Qiu, Shenglin Huang, Celia Reina

Thermodynamics with internal variables is a common approach in continuum mechanics to model inelastic (i.e., non-equilibrium) material behavior. While this approach is computationally and theoretically attractive, it currently lacks a well-established statistical mechanics foundation. As a result, internal variables are typically chosen phenomenologically and lack a direct link to the underlying physics which hinders the predictability of the theory. To address these challenges, we propose a machine learning approach that is consistent with the principles of statistical mechanics and thermodynamics. The proposed approach leverages the following techniques (i) the information bottleneck (IB) method to ensure that the learned internal variables are functions of the microstates and are capable of capturing the salient feature of the microscopic distribution; (ii) conditional normalizing flows to represent arbitrary probability distributions of the microscopic states as functions of the state variables; and (iii) Variational Onsager Neural Networks (VONNs) to guarantee thermodynamic consistency and Markovianity of the learned evolution equations. The resulting framework, called IB-VONNs, is tested on two problems of colloidal systems, governed at the microscale by overdamped Langevin dynamics. The first one is a prototypical model for a colloidal particle in an optical trap, which can be solved analytically, and thus ideal to verify the framework. The second problem is a one-dimensional phase-transforming system, whose macroscopic description still lacks a statistical mechanics foundation under general conditions. The results in both cases indicate that the proposed machine learning strategy can indeed bridge statistical mechanics and thermodynamics with internal variables away from equilibrium.

Chaman Wijesiriwardana, Prasad Wimalaratne

This paper presents a concept of a domain-specific framework for software analytics by enabling querying, modeling, and integration of heterogeneous software repositories. The framework adheres to a multi-layered abstraction mechanism that consists of domain-specific operators. We showcased the potential of this approach by employing a case study.

F. Klauck, L. Teuber, M. Ornigotti et al.

A common wisdom in quantum mechanics is that the Hamiltonian has to be Hermitian in order to ensure a real eigenvalue spectrum. Yet, parity–time (PT)-symmetric Hamiltonians are sufficient for real eigenvalues and therefore constitute a complex extension of quantum mechanics beyond the constraints of Hermiticity. However, as only single-particle or classical wave physics has been exploited so far, an experimental demonstration of the true quantum nature of PT symmetry has been elusive. In our work, we demonstrate two-particle quantum interference in a PT-symmetric system. We employ integrated photonic waveguides to reveal that the quantum dynamics of indistinguishable photons shows strongly counterintuitive features. To substantiate our experimental data, we analytically solve the quantum master equation using Lie algebra methods. The ideas and results presented here pave the way for non-local PT-symmetric quantum mechanics as a novel building block for future quantum devices. Parity–time symmetry in second quantization is demonstrated in an integrated non-Hermitian coupled waveguide structure. A counterintuitive shift of the position of the Hong–Ou–Mandel dip is observed in integrated lossy waveguide structures.

F. Palombo, D. Fioretto

Brillouin spectroscopy and imaging are emerging techniques in analytical science, biophotonics, and biomedicine. They are based on Brillouin light scattering from acoustic waves or phonons in the GHz range, providing a nondestructive contactless probe of the mechanics on a microscale. Novel approaches and applications of these techniques to the field of biomedical sciences are discussed, highlighting the theoretical foundations and experimental methods that have been developed to date. Acknowledging that this is a fast moving field, a comprehensive account of the relevant literature is critically assessed here.

Kaitlin Oliver-Butler, J. Till, Caleb D. Rucker

Soft and continuum robots driven by tendons or cables have wide-ranging applications, and many mechanics-based models for their behavior have been proposed. In this paper, we address the unsolved problem of predicting robot deflection and stiffness with respect to environmental loads where the axial displacements of the tendon ends are held constant. We first solve this problem analytically for a tendon-embedded Euler–Bernoulli beam. Nondimensionalized equations and plots describe how tendon stretch and routing path affect the robot's output stiffness at any point. These analytical results enable stiffness analysis of candidate robot designs without extensive computational simulations. Insights gained through this analysis include the ability to increase robot stiffness by using converging tendon paths. Generalizing to large deflections in three dimensions (3-D), we extend a previous nonlinear Cosserat-rod-based model for tendon-driven robots to handle prescribed tendon displacements, tendon stretch, pretension, and slack. We then provide additional dimensionless plots in the actuated case for loads in 3-D. The analytical formulas and numerically computed model are experimentally validated on a prototype robot with good agreement.

M.Zh. Turgumbaev, Z.R. Suleimenova, D.I. Tungushbaeva

In this paper, we consider the questions about the weighted integrability of the sum of series with respect to multiplicative systems with monotone coefficients. Conditions are obtained for weight functions that ensure that the sum of such series belongs to the weighted Lebesgue space. The main theorems are proved without the condition that the generator sequence is bounded; in particular, it can be unbounded. In the case of boundedness of the generator sequence, the proved theorems imply an analogue of the well-known Hardy-Littlewood theorem on trigonometric series with monotone coefficients.

S. Bitimkhan, O. Mekesh

This article is devoted to the topic of absolute summation of series or Cesaro summation. The relevance of this article lies in the fact that a type of absolute summation with vector index which has not been previously studied is considered. In this article, a sufficient condition for the vector index absolute summation method was obtained in terms of the best approximation by «angle» of the functions from Lebesgue space. The theorem that gives a sufficient condition proves the conditions that are sufficient in different cases, which may depend on the parameters. From this proved theorem, a sufficient condition on the term mixed smoothness modulus of the function from Lebesgue space, which is easily obtained by a well-known inequality, is also presented.

Lodovico Scarpa, Abdulla Alhajri, Vlatko Vedral et al.

Predicting the stationary behavior of observables in isolated many-body quantum systems is a central challenge in quantum statistical mechanics. While one can often use the Gibbs ensemble, which is simple to compute, there are many scenarios where this is not possible and one must instead use another ensemble, such as the diagonal, microcanonical or generalized Gibbs ensembles. However, these all require detailed information about the energy or other conserved quantities to be constructed. Here we propose a general and computationally easy approach to determine the stationary probability distribution of observables with few outcomes. Interpreting coarse measurements at equilibrium as noisy communication channels, we provide general analytical arguments in favor of the applicability of a maximum entropy principle for this class of observables. We show that the resulting theory accurately predicts stationary probability distributions without detailed microscopic information like the energy eigenstates. Extensive numerical experiments on 7 non-weakly interacting spin-1/2 Hamiltonians demonstrate the broad applicability and robustness of this framework in both quantum integrable and chaotic models.

B.T. Kalimbetov, V.F. Safonov, O.D. Tuychiev

In the mathematical literature, a scalar integral equation with a degenerate kernel is well described (see below (1)), where all the written functions are scalar quantities). The authors are not aware of publications where systems of integral equations of (1) type with kernels in the form of a product of matrices would be considered in detail. It is usually said that the technique for solving such systems is easily transferred from the scalar case to the vector one (for example, in the monograph A.L. Kalashnikov "Methods for the approximate solution of integral equations of the second kind" (Nizhny Novgorod: Nizhny Novgorod State University, 2017), a brief description of systems of equations with degenerate kernels is given, where the role of degenerate kernels is played by products of scalar rather than matrix functions). However, as the simplest examples show, the generalization of the ideas of the scalar case to the case of integral systems with kernels in the form of a sum of products of matrix functions is rather unclear, although in this case the idea of reducing an integral equation to an algebraic system is also used. At the same time, the process of obtaining the conditions for the solvability of an integral system in the form of orthogonality conditions, based on the conditions for the solvability of the corresponding algebraic system, as it seems to us, has not been previously described. Bearing in mind the wide applications of the theory of integral equations in applied problems, the authors considered it necessary to give a detailed scheme for solving integral systems with degenerate kernels in the multidimensional case and to implement this scheme in the Maple program. Note that only scalar integral equations are solved in Maple using the intsolve procedure. The authors did not find a similar procedure for solving systems of integral equations, so they developed their own procedure.

A. Ashyralyev, B. Haso

Time-dependent and space-dependent source identification problems for partial differential and difference equations take an important place in applied sciences and engineering, and have been studied by several authors. Moreover, the delay appears in complicated systems with logical and computing devices, where certain time for information processing is needed. In the present paper, the time-dependent identification problem for delay hyperbolic equation is investigated. The theorems on the stability estimates for the solution of the time-dependent identification problem for the one dimensional delay hyperbolic differential equation are established. The proofs of these theorems are based on the Dalambert’s formula for the hyperbolic differential equation and integral inequality.

Oliver Knill

Analytic torsion is a functional on graphs which only needs linear algebra to be defined. In the continuum it corresponds to the Ray-Singer analytic torsion. We have formulas for analytic torsion if the graph is contractible or if it is a discrete sphere. A key insight is that analytic torsion is the super determinant of the Dirac operator of the graph.

M.I. Tleubergenov, G.K. Vassilina, G.A. Tuzelbaeva

In this paper, a force field is constructed along a given integral manifold in the presence of random perturbing forces. In this case, two types of integral manifolds are considered separately: 1) trajectories that depend on generalized coordinates and do not depend on generalized velocities, and 2) trajectories that depend on both generalized coordinates and generalized velocities. The construction of the force field is carried out in the class of second-order stochastic Ito differential equations. It is assumed that the functions in the right-hand sides of the equation must be continuous in time and satisfy the Lipschitz condition in generalized coordinates and generalized velocities. Also this functions satisfy the condition for linear growth in generalized coordinates and generalized velocities.These assumptions ensure the existence and uniqueness up to stochastic equivalence of the solution to the Cauchy problem of the constructed equations in the phase space, which is a strictly Markov process continuous with probability 1. To solve the two posed problems, stochastic differential equations of perturbed motion with respect to the integral manifold are constructed. Moreover, in the case when the trajectories depend on generalized coordinates and do not depend on generalized velocities, the second order equations of perturbed motion are constructed, and in the case when the trajectories depend on both generalized coordinates and generalized velocities, the first order equations of perturbed motion are constructed. And further, in both cases by Erugin’s method necessary and sufficient conditions for solving the posed problems are derived.

Oded Shor, Amir Glik, Amit Yaniv-Rosenfeld et al.

No diagnostic or predictive instruments to help with early diagnosis and timely therapeutic intervention are available as yet for most neuro-psychiatric disorders. A quantum potential mean and variability score (qpmvs), to identify neuropsychiatric and neurocognitive disorders with high accuracy, based on routine EEG recordings, was developed. Information processing in the brain is assumed to involve integration of neuronal activity in various areas of the brain. Thus, the presumed quantum-like structure allows quantification of connectivity as a function of space and time (locality) as well as of instantaneous quantum-like effects in information space (non-locality). EEG signals reflect the holistic (nonseparable) function of the brain, including the highly ordered hierarchy of the brain, expressed by the quantum potential according to Bohmian mechanics, combined with dendrogram representation of data and p-adic numbers. Participants consisted of 230 participants including 28 with major depression, 42 with schizophrenia, 65 with cognitive impairment, and 95 controls. Routine EEG recordings were used for the calculation of qpmvs based on ultrametric analyses, closely coupled with p-adic numbers and quantum theory. Based on area under the curve, high accuracy was obtained in separating healthy controls from those diagnosed with schizophrenia (p<0.0001), depression (p<0.0001), Alzheimer’s disease (AD; p<0.0001), and mild cognitive impairment (MCI; p<0.0001) as well as in differentiating participants with schizophrenia from those with depression (p<0.0001), AD (p<0.0001) or MCI (p<0.0001) and in differentiating people with depression from those with AD (p<0.0001) or MCI (p<0.0001). The novel EEG analytic algorithm (qpmvs) seems to be a useful and sufficiently accurate tool for diagnosis of neuropsychiatric and neurocognitive diseases and may be able to predict disease course and response to treatment.