Hasil untuk "Analytic mechanics"

Y. Lanir

Aaron Duane Sequeira, Woutijn Baars, Tomas Sinnige et al.

This study quantifies the viscous interaction between propeller tip vortices and a turbulent boundary layer developing over a semi-elliptic leading-edge plate, located downstream. The experimental wind-tunnel set-up is designed to be representative of the tractor–propeller–wing configuration. Using stereoscopic particle image velocimetry and static wall-pressure measurements, the near-wall flow topology is resolved over the plate, semi-immersed in the propeller slipstream. The results show that the interaction exhibits high spatio-temporal coherence and is dominated by a coupling between primary and secondary vortical structures. Two distinct interaction regions are identified relative to the tip-vortex core: on the inboard side, towards the slipstream interior, the boundary-layer flow experiences strong velocity gradient transitions and amplified near-wall vorticity. The flow on the outboard side, moving out of the slipstream, exhibits wall-parallel velocity deficits and vorticity lift-up consistent with unsteady vortex-induced separation mechanisms. Spanwise velocity induced by the wall-normal component of the primary vortex connects these two regions, with the secondary vortex structure identified as enhancing boundary-layer lift-up on the outboard side. Although no local flow reversal occurs under the tested conditions, localised shear amplification and vorticity roll-up indicative of separation-like behaviour were observed. These findings advance the understanding of viscous slipstream–boundary-layer interaction and its implications for tractor–propeller–wing integration.

S.A. Iskakov, A.O. Tanin

The academic community of Kazakhstan honors Nurzhan Adilkhanovich Bokayev, Doctor of Physical and Mathematical Sciences and Professor of the Department of Fundamental Mathematics at L.N. Gumilyov Eurasian National University for his distinguished contributions to the field. His 70th anniversary is a celebration not only for his colleagues and students, but also for the entire mathematical community of our country.

A. Turón, P. Camanho, J. Costa et al.

Artem Alexandrov, Alexey Glutsyuk, Alexander Gorsky

In this study, we discuss the Prufer transform that connects the dynamical system on the torus and the Hill equation, which is interpreted as either the equation of motion for the parametric oscillator or the Schrodinger equation with periodic potential. The structure of phase-locking domains in the dynamical system on torus is mapped into the band-gap structure of the Hill equation. For the parametric oscillator, we provide the relation between the non-adiabatic Hannay angle and the Poincare rotation number of the corresponding dynamical system. In terms of quantum mechanics, the integer rotation number is connected to the quantization number via the Milne quantization approach and exact WKB. Using recent results concerning the exact WKB approach in quantum mechanics, we discuss the possible non-perturbative effects in the dynamical systems on the torus and for parametric oscillator. The semiclassical WKB is interpreted in the framework of a slow-fast dynamical system. The link between the classification of the coadjoint Virasoro orbits and the Hill equation yields a classification of the phase-locking domains in the parameter space in terms of the classification of Virasoro orbits. Our picture is supported by numerical simulations for the model of the Josephson junction and Mathieu equation.

Rodrigo Vilumbrales-Garcia, Putu Brahmanda Sudarsana, Anchal Sareen

In this study, a novel smart surface-morphing technique is devised that dynamically optimises roughness parameter on a sphere with varying flow conditions to minimise drag. A comprehensive series of experiments are first performed to systematically study the effect of dimple depth ratios in the range of 0 ≤ k/d ≤ 2 × 10−2 across a Reynolds number range of 6 × 104 ≤ Re ≤ 1.3 × 105. It is observed that k/d significantly affects both the onset of the drag crisis and the minimum achievable drag. For a constant Re, drag monotonically reduces as k/d increases. However, there is a critical threshold beyond which drag starts to increase. Particle image velocimetry (PIV) reveals a delay in flow separation on the sphere’s surface with increasing k/d, causing the flow separation angle to shift downstream. This results in a smaller wake size and reduced drag. However, when k/d exceeds the critical threshold, flow separation moves upstream, causing an increase in drag. Using the experimental data, a predictive model is developed relating optimal k/d to Re for minimising drag. This control model is then implemented to demonstrate closed-loop drag control of a sphere. The results demonstrate up to a 50 % reduction in drag compared with a smooth sphere, across all Reynolds numbers tested.

F. Scarpa, S. Adhikari, A. Phani

J. Dolbow, N. Moës, T. Belytschko

Abstract A new technique for the finite element modeling of crack growth with frictional contact on the crack faces is presented. The eXtended Finite Element Method (X-FEM) is used to discretize the equations, allowing for the modeling of cracks whose geometry are independent of the finite element mesh. This method greatly facilitates the simulation of a growing crack, as no remeshing of the domain is required. The conditions which describe frictional contact are formulated as a non-smooth constitutive law on the interface formed by the crack faces, and the iterative scheme implemented in the LATIN method [Nonlinear Computational Structural Mechanics, Springer, New York, 1998] is applied to resolve the nonlinear boundary value problem. The essential features of the iterative strategy and the X-FEM are reviewed, and the modifications necessary to integrate the constitutive law on the interface are presented. Several benchmark problems are solved to illustrate the robustness of the method and to examine convergence. The method is then applied to simulate crack growth when there is frictional contact on the crack faces, and the results are compared to both analytical and experimental results.

Javad Ghorbanian, Nicholas Casaprima, Audrey Olivier

In recent years, neural networks (NNs) have become increasingly popular for surrogate modeling tasks in mechanics and materials modeling applications. While traditional NNs are deterministic functions that rely solely on data to learn the input--output mapping, casting NN training within a Bayesian framework allows to quantify uncertainties, in particular epistemic uncertainties that arise from lack of training data, and to integrate a priori knowledge via the Bayesian prior. However, the high dimensionality and non-physicality of the NN parameter space, and the complex relationship between parameters (NN weights) and predicted outputs, renders both prior design and posterior inference challenging. In this work we present a novel BNN training scheme based on anchored ensembling that can integrate a priori information available in the function space, from e.g. low-fidelity models. The anchoring scheme makes use of low-rank correlations between NN parameters, learnt from pre-training to realizations of the functional prior. We also perform a study to demonstrate how correlations between NN weights, which are often neglected in existing BNN implementations, is critical to appropriately transfer knowledge between the function-space and parameter-space priors. Performance of our novel BNN algorithm is first studied on a small 1D example to illustrate the algorithm's behavior in both interpolation and extrapolation settings. Then, a thorough assessment is performed on a multi--input--output materials surrogate modeling example, where we demonstrate the algorithm's capabilities both in terms of accuracy and quality of the uncertainty estimation, for both in-distribution and out-of-distribution data.

Johanna Müller, Florian Sammüller, Matthias Schmidt

We give an introductory account of the recently identified gauge invariance of the equilibrium statistical mechanics of classical many-body systems [J. Müller et al., Phys. Rev. Lett. Phys. Rev. Lett. 133, 217101 (2024)]. The gauge transformation is a non-commutative shifting operation on phase space that keeps the differential phase space volume element and hence the Gibbs integration measure conserved. When thermally averaged any observable is an invariant, including thermodynamic and structural quantities. Shifting transformations are canonical in the sense of classical mechanics. They also form an infinite-dimensional group with generators of infinitesimal transformations that build a non-commutative Lie algebra. We lay out the connections with the underlying geometry of coordinate displacement and with Noether's theorem. Spatial localization of the shifting yields differential operators that satisfy commutator relationships, which we describe both in purely configurational and in full phase space setups. Standard operator calculus yields corresponding equilibrium hyperforce correlation sum rules for general observables and order parameters. Using Monte Carlos simulations we demonstrate explicitly the gauge invariance for finite shifting. We argue in favour of using the gauge invariance as a statistical mechanical construction principle for obtaining exact results and for formulating smart sampling algorithms.

M.T. Kassymetova, G.E. Zhumabekova

The issues of utilizing the central type to analyze the theoretical and model properties of the idea of heredity were examined in this research, taking into account both theories and the Jonsson spectrum. Finding solutions to issues related to the enriching language for the fixed Jonsson theory is associated with the problems of heredity of Jonsson theory. Another feature of Jonsson theories was described in the presented article. That is, the conclusion concerning J-non-multidimensional theories was presented in this study. The connection between J-P-stable theories and J-non-multidimensional theories was also characterired. In addition, the main result in the article was considered for the class of semantic pairs.

S. Maerivoet, B. Moor

Abstract In this paper, we give an elaborate and understandable review of traffic cellular automata (TCA) models, which are a class of computationally efficient microscopic traffic flow models. TCA models arise from the physics discipline of statistical mechanics, having the goal of reproducing the correct macroscopic behaviour based on a minimal description of microscopic interactions. After giving an overview of cellular automata (CA) models, their background and physical setup, we introduce the mathematical notations, show how to perform measurements on a TCA model's lattice of cells, as well as how to convert these quantities into real-world units and vice versa. The majority of this paper then relays an extensive account of the behavioural aspects of several TCA models encountered in literature. Already, several reviews of TCA models exist, but none of them consider all the models exclusively from the behavioural point of view. In this respect, our overview fills this void, as it focusses on the behaviour of the TCA models, by means of time–space and phase-space diagrams, and histograms showing the distributions of vehicles’ speeds, space, and time gaps. In the report, we subsequently give a concise overview of TCA models that are employed in a multi-lane setting, and some of the TCA models used to describe city traffic as a two-dimensional grid of cells, or as a road network with explicitly modelled intersections. The final part of the paper illustrates some of the more common analytical approximations to single-cell TCA models.

Mário j. de Oliveira

We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert space of dimension $n$ which is obtained by a peculiar canonical transformation that changes a pair of real canonical variables into a pair of complex canonical variables which are complex conjugate of each other. The probabilistic character of quantum mechanics is devised by treating the wave function as a stochastic variable. The dynamics of the underlying system is chosen so as to preserve the norm of the state vector.

A. Ashyralyev, A. Ashyralyyev, B. Abdalmohammed

In the present paper, the initial value problem for the hyperbolic type involutory in t second order linear partial differential equation is studied. The initial value problem for the fourth order partial differential equations equivalent to this problem is obtained. The stability estimates for the solution and its first and second order derivatives of this problem are established.

B. Sinsoysal, M. Rasulov, R. Iskenderova

A new numerical method is proposed for solving the generalized Buckley-Leverett problem, which describes the movement of two-phase mixtures of Bazhenov bed sediments in a class of discontinuous functions. To this end, we introduce an auxiliary problem that has advantages over the main problem, and using these advantages, an original finite difference method to solve of the auxiliary problem is developed. Using the suggested auxiliary problem, a solution which expresses exactly all physical characteristics of the problem is obtained.

O.I. Ulbrikht, N.V. Popova

The paper defines a new class of algebras, the theory of which is a special case of Jonsson theories. This class applies to both varieties and Jonsson theories. The main results of this article are the following two results. In this article, an answer is obtained to the question of the equivalence of existential closure and algebraic closure of the model of the cosemantic class of a fixed spectrum of a Robinson hereditary variety. A criterion for strong minimality is obtained in the framework of the study of central types of central classes and fragments of a fixed spectrum.

A.M. Manat, N.T. Orumbayeva

The paper investigates a non-local boundary value problem for the Benjamin-Bona-Mahony equation. This equation is a nonlinear pseudoparabolic equation of the third order with a mixed derivative. To find a solution to this problem, an algorithm for finding an approximate solution is proposed. Sufficient conditions for the feasibility and convergence of the proposed algorithm are established, as well as the existence of an isolated solution of a non-local boundary value problem for a nonlinear equation. Estimates are obtained between the exact and approximate solution of this problem.

G.A. Yessenbayeva, A.N. Yesbayev, N.K. Syzdykova et al.

The article is devoted to research on approximation theory. When approximating functions by trigonometric polynomials, the spectrum is chosen from various sets. In this paper, the spectrum consists of harmonic intervals. Devices, various processes, perception of the senses have a limited range. In the mathematical modeling of numerous practical problems and in the further study of such mathematical models, it is sufficient to find a solution in this range. It is possible to study such models to some extent with the help of harmonic intervals. To prove the main theorem, an auxiliary lemma was proved, and elements of the theory of approximations with respect to harmonic intervals were used. For the constructed families of function classes associated with the best approximations by trigonometric polynomials with a spectrum of harmonic intervals, their relationship with classical Besov spaces is shown

A. Olia, Dunja Perić

Abstract Analytical solutions for displacement, strain, and stress in a single energy pile provide rational, mechanics-based qualitative and quantitative understanding of thermomechanical load tran...

M. Lebihain, L. Ponson, D. Kondo et al.

Abstract This paper addresses the question of the homogenization of fracture properties for three-dimensional disordered brittle solids. The effective toughness, identified as the minimum elastic energy release rate required to ensure crack growth, is predicted from a semi-analytical framework inspired by both micromechanics and statistical physics, that encompasses the decisive influences of both the material disorder and the mechanisms of interaction between a crack and heterogeneities. Theoretical predictions are compared to numerical values of the effective toughness that are computed with the fracture-mechanics-based semi-analytical method of Lebihain et al. (2020). Based on a perturbative approach of Linear Elastic Fracture Mechanics, this method allows for the efficient computation of crack propagation under tensile Mode I loading in composite materials containing several millions of inclusions, where the crack interacts with them through two mechanisms : crossing, wherein the crack penetrates the inclusion, and by-pass, wherein the crack wanders out-of-plane and follows the inclusion/matrix interface. We show that our homogenization procedure provides an accurate prediction of the homogenized fracture properties for a broad range of microstructural parameters such as the inclusion toughness, density or shape. This original theoretical framework constitutes a powerful mean to connect the microstructural parameters of materials to their crack growth resistance, beyond the particular cases considered in the simulations performed. As a result, it provides new strategies for the rational design of optimized brittle composites with tailored fracture properties.