Hasil untuk "Analytic mechanics"

Yiquan Wang, Minnuo Cai, Jialin Zhang et al.

In multi-stage production, manufacturers face a critical trade-off between the cost of proactive quality control and the risk of downstream defects. This paper challenges the default strategy of early inspection by developing a unified framework to determine when a reactive, end-of-line recovery approach is more cost-effective. Our model uniquely integrates multi-stage production dynamics, the economic trade-offs of reverse logistics, and the statistical uncertainty of sampling inspection. Through optimization with a Genetic Algorithm, we identify specific, data-driven thresholds for market failure cost and initial defect rates where the optimal policy shifts decisively from selective to comprehensive upstream inspection. Furthermore, the analysis quantifies the value of information, demonstrating that higher data accuracy from stricter sampling protocols yields lower long-term costs by stabilizing decision-making. By providing a quantitative tool that adapts to evolving risk profiles, this research offers a practical approach for aligning cost optimization with the principles of Quality 4.0 and sustainable manufacturing.

Ortwin Fromm, Felicitas Ehlen

We study Heisenberg's matrix mechanics within an algebraic pre-Hilbert framework of arbitrary finite dimension. The commutator of the position and momentum matrices naturally generates a third Hermitian operator whose unbounded character originates from boundary contributions and whose structure induces a discrete analogue of the Cauchy-Hilbert kernel. Compared with the separable Hilbert-space completion, the algebraic framework reproduces the standard spectra, canonical commutation relations, and Heisenberg uncertainty relation for finite-energy states, while the discrete kernel is absorbed into its continuous integral counterpart under completion. The comparison shows that both formulations require restrictions on admissible states for effective calculations -- analytic domain restrictions in Hilbert space and finite-energy restrictions in the pre-Hilbert framework. Finally, we discuss to what extent quantum randomness arises from the algebraic structure of the pre-Hilbert framework.

Jan Van den Berghe, Miguel A. Mendez, Yann Bartosiewicz

Ejectors are passive devices used in refrigeration, propulsion, and process industries to compress a secondary stream without moving parts. The engineering modeling of choking in these devices remains an open question, with two mechanisms-Fabri and compound choking-proposed in the literature. This work develops a unified one-dimensional framework that implements both mechanisms and compares them with axisymmetric Reynolds-Averaged Navier Stokes (RANS) data processed by cross-sectional averaging. The compound formulation incorporates wall and inter-stream friction and a local pressure-equalization procedure that enables stable integration through the sonic point, together with a normal shock reconstruction. The Fabri formulation is assessed by imposing the dividing streamline extracted from RANS, isolating the sonic condition while avoiding additional modeling assumptions. The calibrated compound model predicts on-design secondary mass flow typically within 2 % with respect to the RANS simulations, rising to 5 % for a strongly under-expanded primary jet due to the equal-pressure constraint. The Fabri analysis attains less than 1 % error in on-design entrainment but exhibits high sensitivity to the dividing streamline and closure, which limits predictive use beyond on-design. Overall, the results show that Fabri and compound mechanisms can coexist within the same device and operating map, each capturing distinct aspects of the physics and offering complementary modeling value. Nevertheless, compound choking emerges as the more general mechanism governing flow rate blockage, as evidenced by choked flows with a subsonic secondary stream.

Р.Г. Мухарлямов, Ж.К. Киргизбаев

Equations and methods of classical mechanics are used to describe the dynamics of technical systems containing elements of various physical nature, planning and management tasks of production and economic objects. The direct use of known dynamics equations with indefinite multipliers leads to an increase in deviations from the constraint equations in the numerical solution. Common methods of constraint stabilization, known from publications, are not always effective. In the general formulation, the problem of constraint stabilization was considered as an inverse problem of dynamics and it requires the determination of Lagrange multipliers or control actions, in which holonomic and differential constraints are partial integrals of the equations of the dynamics of a closed system. The conditions of stability of the integral manifold determined by the constraint equations and stabilization of the constraint in the numerical solution of the dynamic equations were formulated.

Shao Yuanzhen, Chen Zhan, Zhao Shan

Variational implicit solvation models (VISMs) have gained extensive popularity in the molecular-level solvation analysis of biological systems due to their cost-effectiveness and satisfactory accuracy. Central in the construction of VISM is an interface separating the solute and the solvent. However, traditional sharp-interface VISMs fall short in adequately representing the inherent randomness of the solute–solvent interface, a consequence of thermodynamic fluctuations within the solute–solvent system. Given that experimentally observable quantities are ensemble averaged, the computation of the ensemble average solvation energy (EASE)–the averaged solvation energy across all thermodynamic microscopic states–emerges as a key metric for reflecting thermodynamic fluctuations during solvation processes. This study introduces a novel approach to calculating the EASE. We devise two diffuse-interface VISMs: one within the classic Poisson–Boltzmann (PB) framework and another within the framework of size-modified PB theory, accounting for the finite-size effects. The construction of these models relies on a new diffuse interface definition u(x)u\left(x), which represents the probability of a point xx found in the solute phase among all microstates. Drawing upon principles of statistical mechanics and geometric measure theory, we rigorously demonstrate that the proposed models effectively capture EASE during the solvation process. Moreover, preliminary analyses indicate that the size-modified EASE functional surpasses its counterpart based on the classic PB theory across various analytic aspects. Our work is the first step toward calculating EASE through the utilization of diffuse-interface VISM.

Sankaran Ramanarayanan, Antonio L. Sánchez

Developed in this paper is a theoretical description of the fluid flow involved in contactless transport systems that operate using squeeze-film levitation. Regular perturbation methods are employed to solve the appropriate Reynolds equation that governs the viscous, compressible flow of air in the slender film separating the oscillator and the levitated object. The resulting reduced formulation allows efficient computation of the time-averaged levitation force and moment induced by fluid pressure, as well as the accompanying quasistatic thrust force that accounts additionally for shear stresses. Investigated, in particular, is the possibility of combining two distinct methods of thrust generation that have been experimentally demonstrated in previous studies – (i) inclination of the levitated body and (ii) generation of asymmetrical flexural deformations, such as travelling waves, on the oscillator surface – the latter of which is shown to allow a transition from the typically repulsive levitation force to one that is attractive. Computations reveal that systematic control of the inclination angle can provide significant performance benefits for squeeze-film transport systems. In the case of attractive levitation, the amount of improvement that can be obtained appears to correlate closely with the degree of lateral asymmetry exhibited by the flexural oscillations.

Shuichi Yokoyama

The relativistic extension of the classic stellar structure equations is investigated. It is pointed out that the Tolman-Oppenheimer-Volkov (TOV) equation with the gradient equation for local gravitational mass can be made complete as a closed set of differential equations by adding that for the Tolman temperature with one equation of state, and the set is proposed as the relativistic hydrostatic structure equations. The exact forms of the relativistic Poisson equation and the steady-state heat conduction equation in the curved spacetime are derived. The application to an ideal gas of particles with the conserved particle number current leads to a strong prediction that the heat capacity ratio almost becomes one in any Newtonian convection zone such as the solar surface. The steady-state heat conduction equation is solved exactly in the system and thermodynamic observables exhibit the power law behavior, which implies the possibility for the system to be a new model of stellar corona and a flaw in the earlier one obtained by using the non-relativistic stellar structure equations. The mixture with another ideal gas yields multilayer structure to a stellar model, in which classic stellar structure equations are reproduced and analytic multilayer structure of luminous stars including the Sun is revealed in suitable approximation.

Garrett Blum, Ryan Doris, Diego Klabjan et al.

Stress-strain curves, or more generally, stress functions, are an extremely important characterization of a material's mechanical properties. However, stress functions are often difficult to derive and are narrowly tailored to a specific material. Further, large deformations, high strain-rates, temperature sensitivity, and effect of material parameters compound modeling challenges. We propose a generalized deep neural network approach to model stress as a state function with quantile regression to capture uncertainty. We extend these models to uniaxial impact mechanics using stochastic differential equations to demonstrate a use case and provide a framework for implementing this uncertainty-aware stress function. We provide experiments benchmarking our approach against leading constitutive, machine learning, and transfer learning approaches to stress and impact mechanics modeling on publicly available and newly presented data sets. We also provide a framework to optimize material parameters given multiple competing impact scenarios.

G.B. Bakanov, S.K. Meldebekova

This paper considers a difference problem for a mixed-type equation, to which a problem of integral geometry for a family of curves satisfying certain regularity conditions is reduced. These problems are related to numerous applications, including interpretation problem of seismic data, problem of interpretation of Xray images, problems of computed tomography and technical diagnostics. The study of difference analogues of integral geometry problems has specific difficulties associated with the fact that for finite-difference analogues of partial derivatives, basic relations are performed with a certain shift in the discrete variable. In this regard, many relations obtained in a continuous formulation, when transitioned to a discrete analogue, have a more complex and cumbersome form, which requires additional studies of the resulting terms with a shift. Another important feature of the integral geometry problem is the absence of a theorem for existence of a solution in general case. Consequently, the paper uses the concept of correctness according to A.N. Tikhonov, particularly, it is assumed that there is a solution to the problem of integral geometry and its differential-difference analogue. The stability estimate of the difference analogue of the boundary value problem for a mixed-type equation obtained in this work is vital for understanding the effectiveness of numerical methods for solving problems of geotomography, medical tomography, flaw detection, etc. It also has a great practical significance in solving multidimensional inverse problems of acoustics, seismic exploration.

Mohammad Reza Setare, Meisam Koohgard

We focus on a proper candidate for the entanglement wedge in asymptotically flat bulk geometries that are described by the generalized minimal massive gravity (GMMG) in the context of the flat holography. To this end, we describe the boundary by two dimensional Galilean conformal field theory (GCFT) at the bipartite mixed state of the two disjoint intervals. We derive an analytic expression for the minimal entanglement wedge cross section (EWCS) in the GMMG/GCFT framework. Our result provides an independent derivation that precisely matches previous computations of holographic entanglement negativity, thereby offering a powerful consistency check and validating both approaches within the GMMG/GCFT framework.

M.J. Mardanov, R.S. Mammadov, S.Yu. Gasimov et al.

The article discusses the existence and uniqueness of solutions for a system of nonlinear integro-differential equations of the first order with two-point boundary conditions. The Green function is constructed, and the problem under consideration is reduced to equivalent integral equation. Existence and uniqueness of a solution to this problem is analyzed using the Banach contraction mapping principle. Schaefer’s fixed point theorem is used to prove the existence of solutions.

S.M. Davoodi, N.A. Abdul Rahman

In this paper we try to define a percentage form of LR fuzzy numbers which is a useful form of fuzzy numbers and its’ arithmetics. So, we show how the maximum variation range of optimal value of fuzzy objective function can be predicted by using this form of fuzzy numbers. Since fuzzy problems are generally solved through a complicated manner, the purpose of this study is releasing a kind of prediction for the final solution in the way that the manager can access to an outlook to optimal solution (Z∗) without solving the problem. Finally, optimal value of fuzzy objective function on fuzzy linear programming is predicted whenmaximum variation range of fuzzy variable have been predetermined.

H.M. Hasan, D.F. Ahmed, M.F. Hama et al.

In our work we have defined an operator called subspace convex-cyclic operator. The property of this newly defined operator relates eigenvalues which have eigenvectors of modulus one with kernels of the operator. We have also illustrated the effect of the subspace convex-cyclic operator when we let it function in linear dynamics and joining it with functional analysis. The work is done on infinite dimensional spaces which may make linear operators have dense orbits. Its property of measure preserving puts together probability space with measurable dynamics and widens the subject to ergodic theory. We have also applied Birkhoff’s Ergodic Theorem to give a modified version of subspace convex-cyclic operator. To work on a separable infinite Hilbert space, it is important to have Gaussian invariant measure from which we use eigenvectors of modulus one to get what we need to have. One of the important results that we have got from this paper is the study of Central Limit Theorem. We have shown that providing Gaussian measure, Central Limit Theorem holds under the certain conditions that are given to the defined operator. In general our work is theoretically new and is combining three basic concepts dynamical system, operator theory and ergodic theory under the measure and statistics theory.

S. Shaimardan, N.S. Tokmagambetov

This paper is devoted to explicit and numerical solutions to linear fractional q-difference equations and the Cauchy type problem associated with the Riemann-Liouville fractional q-derivative in q-calculus. The approaches based on the reduction to Volterra q-integral equations, on compositional relations, and on operational calculus are presented to give explicit solutions to linear q-difference equations. For simplicity, we give results involving fractional q-difference equations of real order a > 0 and given real numbers in q-calculus. Numerical treatment of fractional q-difference equations is also investigated. Finally, some examples are provided to illustrate our main results in each subsection.

Veronika Ertl, Kazuki Yamada

The purpose of this paper is to establish Hyodo--Kato theory with compact support for semistable schemes through rigid analytic methods. To this end we introduce several types of log rigid cohomology with compact support. moreover we show that additional structures on the (rigid) Hyodo--Kato cohomology and the Hyodo--Kato map introduced in our previous paper are compatible with Poincaré duality. Compared to the crystalline approach, the constructions are explicit yet versatile, and hence suitable for computations.

M. Schmidt-Kraepelin, S. Lins, S. Thiebes et al.

Organizations highly depend on enterprise systems (ES), which are unlikely to develop their full potential if end-users neglect system usage. Accordingly, organizations attempt to overcome barriers to end-user acceptance in the ES context, which can be attributed to several factors on ES, organizational, and end-user level. Trying to take advantage of the growing passion for games, Gamification is a phenomenon proposed to motivate people by applying elements common to games in other contexts that have the potential to increase end-user acceptance. While first applications of Gamification exist in areas such as finance, health, and education, utility of gamifying ES has not been explored in-depth. Aiming to understand how Gamification can be applied to ES to increase user motivation, we analyze literature concerning game elements (i.e., mechanics and dynamics) used in Gamification and related risks. Our study yields a synthesis of mechanics in clusters of system design, challenges, rewards, and user specifics as well as related dynamics. We discuss the extent to which the game elements can be used to address ES acceptance barriers. While our study reveals that Gamification has potential for motivating ES users, future research should analyze concrete implementations of Gamification in ES contexts to investigate long-term effects.

E. Hincal, M. Sayan, I.A. Baba et al.

This paper aims to study the transmission dynamics of HIV/AIDS in heterosexual, men having sex with men (MSM)/bisexuals and others in Turkey. Four equilibrium points were obtained which include disease free and endemic equilibrium points. The global stability analysis of the equilibria was carried out using the Lyapunov function which happens to depend on the basic reproduction number R0. If R0< 1 the disease free equilibrium point is globally asymptotically stable and the disease dies out, and if R0 > 1, the endemic equilibrium point is stable and epidemics will occur. We use raw data obtained from Kocaeli University, PCR Unit, Turkey to analyze and predict the trend of HIV/AIDS among heterosexuals, MSM/bisexual, and others. The basic reproduction number for heterosexuals, MSM/bisexuals, and others was found to be 1.08, 0.6719, and 0.050, respectively. This shows that the threat posed by HIV/AIDS among heterosexuals is greater than followed by MSM/bisexuals, and than the others. So, the relevant authorities should put priorities in containing the disease in order of their threat.

A.S. Erdogan, D. Kusmangazinova, I. Orazov et al.

In this paper we consider inverse problems for a fractional heat equation, where the fractional time derivative is taken into account in Riemann-Liouville sense. For the solution of this equation, we have to find an unknown right - hand side depending only on a spatial variable. The problem modeling the process of determining the temperature and density of sources in the process of fractional heat conductivity with respect to given initial and final temperatures is considered. Problems with general boundary conditions with respect to the spatial variable that are not strongly regular are investigated. The existence and uniqueness of classical solution to the problem are proved. The problem is considered independent from a corresponding spectral problem for an operator of multiple differentiation with not strongly regular boundary conditions has the basis property of root functions.

G.A. Yessenbayeva, D.N. Yesbayeva, D. Bauyrzhankyzy et al.

The problems about determination of the frequencies and forms of natural vibrations of plates and shells lead to the necessity of partial differential equations integration. The well - researched cases are those where it is possible to separate the variables. In particular, these include the vibrations of a rectangular plate hinged on opposite sides, umbrella and fan vibration of circular axisymmetric plates and vibrations of cylindrical shells, closed or hinged along generating curves. In this work, the vibration of a flat homogeneous membrane is investigated for the general case of boundary conditions.

Hayato Motohashi, Teruaki Suyama, Masahide Yamaguchi

Abstract We construct no-ghost theories of analytic mechanics involving arbitrary higher-order derivatives in Lagrangian. It has been known that for theories involving at most second-order time derivatives in the Lagrangian, eliminating linear dependence of canonical momenta in the Hamiltonian is necessary and sufficient condition to eliminate Ostrogradsky ghost. In the previous work we showed for the specific quadratic model involving third-order derivatives that the condition is necessary but not sufficient, and linear dependence of canonical coordinates corresponding to higher time-derivatives also need to be removed appropriately. In this paper, we generalize the previous analysis and establish how to eliminate all the ghost degrees of freedom for general theories involving arbitrary higher-order derivatives in the Lagrangian. We clarify a set of degeneracy conditions to eliminate all the ghost degrees of freedom, under which we also show that the Euler-Lagrange equations are reducible to a second-order system.