Hasil untuk "Analytic mechanics"

N. P. Landsman, C. Weert

Chaojie Gu, Michael MacDonald, Lihua Tang

Wind energy is a sustainable and plentiful form of clean energy. The vertical axis wind turbine (VAWT) is one type of cost-effective, acoustically quieter and lightweight turbines. The two mainstream types of VAWTs – Darrieus (lift type) and Savonius (drag type) – have contradictory strengths and weaknesses. Darrieus turbines possesses high efficiency but suffer from poor self-starting, while Savonius turbines start easily with poor aerodynamic performance. In this study, a novel VAWT with adaptive Darrieus–Savonius hybrid blades has been designed. Wind-tunnel experiments assessed the effectiveness of the proposed design and compared it against a conventional Darrieus-type rotor with similar dimensions. The results showed that the static torque coefficient was improved by over 65% and the self-starting wind speed was reduced from 8 to 6 ms−1. The adaptive blades can remain in the Savonius configuration at low rotation speed, facilitating self-starting, and automatically transition to the Darrieus configuration at higher rotation speed, integrating and leveraging the strengths of the two types of VAWTs.

K.R. Abdo

This research paper presents a comprehensive investigation of novel Hardy-type dynamic inequalities that incorporate two independent weight functions, denoted as u and v. A distinctive feature of this work is its focus on time scales calculus with negative parameters, a generalization that unifies and extends discrete and continuous analysis. The basic methodology involves the application of the reverse Ho¨lder’s inequality and the Minkowski integral inequality to rigorously deduce all essential results. To illustrate the adaptability of our results, we provide explicit examples of the corresponding discrete and integral analogues for various time scales: when T=N (the natural numbers, indicating discrete sequences), T= lN0 for l > 1 (a quantum time scale), and T=R (the real numbers, signifying the classical continuous case). This paper situates its findings within a wider mathematical framework by demonstrating how they contain and extend certain cases of reverse Hardy-type dynamic inequalities previously formulated by distinguished scholars including Prokhorov, Kufner, Yang, Nguyen, and Benaissa. Consequently, this work presents a cohesive framework that broadens the theoretical terrain of Hardy-type inequalities.

Nirvana Gharib, Mohammad Reza Yousefi Darestani, Kenichi Takahata

This paper presents, for the first time, a rotary actuator functionalized by an inclined disc rotor that serves as a distal optical scanner for endoscopic probes, enabling side-viewing endoscopy in luminal organs using different imaging/analytic modalities such as optical coherence tomography and Raman spectroscopy. This scanner uses a magnetic rotor designed to have a mirror surface on its backside, being electromagnetically driven to roll around the cone-shaped hollow base to create a motion just like a precessing coin. An optical probing beam directed from the probe’s optic fiber is passed through the hollow cone to be incident and bent on the back mirror of the rotating inclined rotor, circulating the probing beam around the scanner for full 360° sideway imaging. This new scanner architecture removes the need for a separate prism mirror and holding mechanics to drastically simplify the scanner design and thus, potentially enhancing device miniaturization and reliability. The first proof-of-concept is developed using 3D printing and experimentally analyzed to reveal the ability of both angular stepping at 45° and high-speed rotation up to 1500 rpm within the biologically safe temperature range, a key function for multimodal imaging. Preliminary optical testing demonstrates continuous circumferential scanning of the laser beam with no blind spot caused by power leads to the actuator. The results indicate the fundamental feasibility of the developed actuator as an endoscopic distal scanner, a significant step to further development toward advancing optical endoscope technology.

Abhirath Anand, Lina Nikolaidou, Christian Poelma et al.

The turbulent boundary layer (TBL) development over an air cavity is experimentally studied using planar particle image velocimetry. The present flow, representative of those typically encountered in ship air lubrication, resembles the geometrical characteristics of flows over solid bumps studied in the literature. However, unlike solid bumps, the cavity has a variable geometry inherent to its dynamic nature. An identification technique based on thresholding of correlation values from particle image correlations is employed to detect the cavity. The TBL does not separate at the leeward side of the cavity owing to a high boundary layer thickness to maximum cavity thickness ratio ( $\delta /t_{max}= 12$ ). As a consequence of the cavity geometry, the TBL is subjected to alternating streamwise pressure gradients: from an adverse pressure gradient (APG) to a favourable pressure gradient and back to an APG. The mean streamwise velocity and turbulence stresses over the cavity show that the streamwise pressure gradients and air injection are the dominant perturbations to the flow, with streamline curvature concluded to be marginal. Two-point correlations of the wall-normal velocity reveal an increased coherent extent over the cavity and a local anisotropy in regions under an APG, distinct from traditional APG TBLs, suggesting possible history effects.

Rishita Das, Sean D. Peterson, Maurizio Porfiri

Fish swimming together in schools interact via multiple sensory pathways, including vision, acoustics and hydrodynamics, to coordinate their movements. Disentangling the specific role of each sensory pathway is an open and important question. Here, we propose an information-theoretic approach to dissect interactions between swimming fish based on their movement and the flow velocity at selected measurement points in the environment. We test the approach in a controlled mechanical system constituted by an actively pitching airfoil and a compliant flag that simulates the behaviour of two fish swimming in line. The system consists of two distinct types of interactions – hydrodynamic and electromechanical. By using transfer entropy of the measured time series, we unveil a strong causal influence of the airfoil pitching on the flag undulation with an accurate estimate of the time delay between the two. By conditioning the computation on the flow-speed information, recorded by laser Doppler velocimetry, we discover a significant reduction in transfer entropy, correctly implying the presence of a hydrodynamic pathway of interaction. Similarly, the electromechanical pathway of interaction is identified accurately when present. The study supports the potential use of information-theoretic methods to decipher the existence of different pathways of interaction between schooling fish.

Fernando Fraternali, Julia de Castro Motta, Giovanni Germano et al.

This work studies the mechanics of novel origami solar modules with tensegrity architecture for integration in the dynamic solar façades of energy-efficient buildings. The analyzed modules are deployed by adjusting the rest lengths of cables attached to given nodes, so as to form a tensegrity origami. Their stiffness is tuned by adjusting the pretension of the actuation cables, when the deployment motion is locked. The insertion of solar thermal or photovoltaic panels into the rigid elements of the module makes it possible to form positive-energy solar systems. The work studies the kinematics and the mechanics of the investigated structures through analytic and numerical methods. Two folding motions are examined: to open and close the modules and to track sun rays. The rapid prototyping of a physical mock-up permits an experimental validation of the force–displacement response in a given configuration of the sun-tracking motion. A procedure for the computation of the fundamental vibration modes and vibration frequencies of a quadrangular solar module is also given, and the expected response of the system under wind loading is outlined.

Nikolaos Bakas

Function approximation is a fundamental process in a variety of problems in computational mechanics, structural engineering, as well as other domains that require the precise approximation of a phenomenon with an analytic function. This work demonstrates a unified approach to these techniques, utilizing partial sums of the Taylor series in a high arithmetic precision. In particular, the proposed approach is capable of interpolation, extrapolation, numerical differentiation, numerical integration, solution of ordinary and partial differential equations, and system identification. The method employs Taylor polynomials and hundreds of digits in the computations to obtain precise results. Interestingly, some well-known problems are found to arise in the calculation accuracy and not methodological inefficiencies, as would be expected. In particular, the approximation errors are precisely predictable, the Runge phenomenon is eliminated, and the extrapolation extent may a priory be anticipated. The attained polynomials offer a precise representation of the unknown system as well as its radius of convergence, which provides a rigorous estimation of the prediction ability. The approximation errors are comprehensively analyzed for a variety of calculation digits and test problems and can be reproduced by the provided computer code.

P. D. Gujrati

We follow the Boltzmann-Clausius-Maxwell (BCM) proposal to solve a long-standing problem of identifying the underlying cause of the second law (SL) of spontaneous irreversibility, a stochastic universal principle, as the mechanical equilibrium (stable or unstable) principle (Mec-EQ-P) of analytical mechanics of an isolated nonequilibrium system of any size. The principle leads to nonnegative system intrinsic (SI) microwork and SI-average macrowork dW during any spontaneous process. In conjuction with the first law, Mec-EQ-P leads to a generalized second law (GSL) dQ=dW>0, where dQ=TdS is the purely stochastic SI-macroheat that corresponds to dS>0 for T>0 and dS<0 for T<0, where T is the temperature. The GSL supercedes the conventional SL formulation that is valid only for a macroscopic system for positive temperatures temperatures, but reformulates it to dS<0 for negative temperatures. It is quite surprising that GSL is not only a direct consequence of intertwined mechanical and stochastic macroquantities through the first law but also remains valid for any arbitrary irreversible process in a system of any size as an identity for positive and negative temperatures. It also becomes a no-go theorem for GSL-violation unless we abandon Mec-EQ-P of analytical mechanics used in the BCM proposal, which will be catastrophic for theoretical physics. In addition, Mec-EQ-P also provides new insights into the roles of spontaneity, nonspontaneity, negative temperatures, instability, and the significance of dS<0 due to nonspontaneity and inserting internal constraints.

Marek Żukowski, Marcin Markiewicz

In June 1925 Heisenberg arrived at Helgoland/Heligoland island to escape a fit of hay fever. He returned with a sketch of a strange theory of the micro-world, which we now call quantum mechanics. This essay attempts to present a look at this theory, which tries to return to the original insight of Heisenberg on what should be the essence of a theory of atomic realm: it must be a theory of the observable events, in which fundamentally unobservable quantities have no place. No ontological status is given to elements of the mathematical formulation of the theory. The theory is about our description of events in laboratories, probabilities of which are given by the Born rule. Following Bohr, these events involve macroscopic measuring apparatuses, and the accessible final events are classically describable. Information about the events is cloneable, as it is of a classical nature. The modern quantum theory of classicality is the decoherence theory. It treats "the pointer variable" of measuring apparatus as an open system interacting with an environment consisting of all other "zillions" of degrees of freedom of the device, and anything coupled to it. Because such environment is uncontrollable we have no possibility to reverse measurements. The quantum mechanical measurement theory based on decoherence theory is reproducing the predictions of Born rule. Notwithstanding, possibility of reversing measurements and of application of Born rule in situations other than these which lead to macroscopically observable events are features of a modification of quantum mechanics which is called by its adherents "unitary quantum mechanics". As its predictions, which go beyond quantum mechanics, are not testable - we claim that unitary quantum mechanics in an interpretation of quantum mechanics. As such it is metaphysics.

S. Aisagaliev, G.T. Korpebay

The paper proposes a method for solving the problem of optimal performance for linear systems of ordinary differential equations in the presence of phase and integral restrictions, when the initial and final states of the system are elements of given convex closed sets, taking into account the control value restriction. The presented work refers to the mathematical theory of optimal processes from L.S. Pontryagin and his students and the theory of controllability of dynamic systems from R.E. Kalman. We study the problem of optimal speed for linear systems with boundary conditions from given sets close to the presence of phase and integral constraints, as well as constraints on the control value. A theory of the boundary value problem has been created and a method for solving it based on the study of solvability and the construction of a general solution to the Fredholm integral equation of the first kind has been developed. The main results are the distribution of all controls’ sets, each subject of which transfers the trajectory of the system from any initial state to any final state; reducing the initial boundary point to a special initial optimal control problem; constructing a system of algorithms for the gamma-algorithm study on the derivation of problems and rational execution with restrictions on the solution of the optimal speed’ problem with restrictions.

Sadegh Pourghasemi Hanza, Hamed Ghafarirad

In this study, an inhomogeneous Cosserat rod theory is introduced and compared to the conventional homogeneous rod for modeling soft manipulators. The inhomogeneity is addressed by considering the pressure actuation as part of the rod's constitutive laws, resulting in shifting the neutral axis. This shift is investigated for a soft manipulator with three parallel fiber-reinforced actuators. Furthermore, a fiber-reinforced actuator is modeled using nonlinear continuum mechanics to extract the effect of radial pressure on axial deformation and is combined with Cosserat model. Finally, several numerical methods are employed to solve the proposed model and validated by a series of experiments.

Jakub A. Kochanowski, Bobby Carroll, Merrill E. Asp et al.

Bacteria build multicellular communities termed biofilms, which are often encased in a self-secreted extracellular matrix that gives the community mechanical strength and protection against harsh chemicals. How bacteria assemble distinct multicellular structures in response to different environmental conditions remains incompletely understood. Here, we investigated the connection between bacteria colony mechanics and the colony growth substrate by measuring the oscillatory shear and compressive rheology of bacteria colonies grown on agar substrates. We found that bacteria colonies modify their own mechanical properties in response to shear and uniaxial compression with the increasing agar concentration of their growth substrate. These findings highlight that mechanical interactions between bacteria and their microenvironment are an important element in bacteria colony development, which can aid in developing strategies to disrupt or reduce biofilm growth.

K.A. Bekmaganbetov, G.A. Chechkin, A.M. Toleubay

This article deals with two-dimensional Navier–Stokes system of equations with rapidly oscillating term in the equations and boundary conditions. Studying the problem in a perforated domain, the authors set homogeneous Dirichlet condition on the outer boundary and the Fourier (Robin) condition on the boundary of the cavities. Under such assumptions it is proved that the trajectory attractors of this system converge in some weak topology to trajectory attractors of the homogenized Navier–Stokes system of equations with an additional potential and nontrivial right hand side in the domain without pores. For this aim, the approaches from the works of A.V. Babin, V.V. Chepyzhov, J.-L. Lions, R. Temam, M.I. Vishik concerning trajectory attractors of evolution equations and homogenization methods appeared at the end of the XX-th century are used. First, we apply the asymptotic methods for formal construction of asymptotics, then, we verify the leading terms of asymptotic series by means of the methods of functional analysis and integral estimates. Defining the appropriate axillary functional spaces with weak topology, we derive the limit (homogenized) system of equations and prove the existence of trajectory attractors for this system. Lastly, we formulate the main theorem and prove it through axillary lemmas.

Tijmen Vermeij, Jorn Verstijnen, Tim Ramirez y Cantador et al.

The continuous development of new multiphase alloys with improved mechanical properties requires quantitative microstructure-resolved observation of the nanoscale deformation mechanisms at, e.g., multiphase interfaces. This calls for a combinatory approach beyond advanced testing methods such as microscale strain mapping on bulk material and micrometer sized deformation tests of single grains. We propose a nanomechanical testing framework that has been carefully designed to integrate several state-of-the-art testing and characterization methods: (i) well-defined nano-tensile testing of carefully selected and isolated multiphase specimens, (ii) front&rear-sided SEM-EBSD microstructural characterization combined with front&rear-sided in-situ SEM-DIC testing at very high resolution enabled by a recently developed InSn nano-DIC speckle pattern, (iii) optimized DIC strain mapping aided by application of SEM scanning artefact correction and DIC deconvolution for improved spatial resolution, (iv) a novel microstructure-to-strain alignment framework to deliver front&rear-sided, nanoscale, microstructure-resolved strain fields, and (v) direct comparison of microstructure, strain and SEM-BSE damage maps in the deformed configuration. Demonstration on a micrometer-sized dual-phase steel specimen, containing an incompatible ferrite-martensite interface, shows how the nanoscale deformation mechanisms can be unraveled. Discrete lath-boundary-aligned martensite strain localizations transit over the interface into diffuse ferrite plasticity, revealed by the nanoscale front&rear-sided microstructure-to-strain alignment and optimization of DIC correlations. The proposed framework yields front&rear-sided aligned microstructure and strain fields providing 3D interpretation of the deformation and opening new opportunities for unprecedented validation of advanced multiphase simulations.

Kyota Kamamoto, Hajime Onuki, Yoshiyuki Tagawa

An on-demand painting system with a simple structure device that ejects highly viscous liquids as microjets is introduced. An impulsive motion of the container results in the ejection of a viscous liquid jet from the nozzle. This system enabled us to paint letters on a section of a car body using commercial car paint with a zero-shear viscosity of 100 $\textrm {Pa} \cdot \textrm {s}$. To understand the jet velocity, we conducted systematic experiments. Experimental results showed that the jet velocity increases with the ratio between the liquid depths in the container and the nozzle, up to approximately 30 times faster than the initial velocity. However, a linear relation between the jet velocity and the ratio predicted by the previous model, which considers only the pressure impulse, does not hold for the high length ratios since the actual position of the stagnation point is different from the position predicted by the previous model. By solving the Laplace equation and using the model proposed by Gordillo et al. (J. Fluid Mech., vol. 894, 2020, pp. A3–11), we reproduce the non-monotonic behaviour of the jet velocity as a function of the length ratio. For practical use, we improve the jet-velocity model by considering mass conservation as well as the pressure impulse.

Chong-Chong He

We have developed a new analytic method to calculate the galaxy two-point correlation functions (TPCFs) accurately and efficiently, applicable to surveys with finite, regular, and mask-free geometries. We have derived simple, accurate formulas of the normalized random-random pair counts $RR$ as functions of the survey area dimensions. We have also suggested algorithms to compute the normalized data-random pair counts $DR$ analytically. With all edge corrections fully accounted for analytically, our method computes $RR$ and $DR$ with perfect accuracy and zero variance in $O(1)$ and $O(N_{\rm g})$ time, respectively. We test our method on a galaxy catalogue from the EAGLE simulation. Our method calculates $RR+DR$ at a speed 3 to 6 orders of magnitude faster than the brute-force Monte Carlo method and 2.5 orders of magnitude faster than tree-based algorithms. For a galaxy catalogue with 10 million data points in a cube, this reduces the computation time to under 1 minute on a laptop. Our analytic method is favored over the traditional Monte Carlo method whenever applicable. Some applications in the study of correlation functions and power spectra in cosmological simulations and galaxy surveys are discussed. However, we recognize that its applicability is very limited for realistic surveys with masks, irregular shapes, and/or weighted patterns.

A.R. Yeshkeyev, A.K. Issaeva, N.V. Popova

The present paper concerns some properties of the so-called small models, generally speaking, not necessarily complete theories and their relationship with each other. In the well-known paper [1], R. Vaught have proved the fundamental theorem-criterion on the behavior of countable prime and atomic models for complete theories in countable language. The essence of this criterionis that in a complete theory any countable prime model is at the same time an atomic model of this theory. The result obtained in this paper is related to the classical problem of Vaught about countably prime models of complete theories but in more general formulation of the notion of countable atomicity. The main result of this paper is that it focuses on the syntactic properties on special subsets of a fragment of the semantic model the specific Jonsson theory. The concept of the so-called model-theoretic «rheostat» was also used to obtain results related to the refinement of the concept of atomicity in the framework of Jonsson theories.

M.V. Babii, V.O. Nastasenko, V.O. Protsenko et al.

In the article mathematical dependencies to determine the gripping force of the cutting plate in the socket of assembled cutoff tools with the lateral installation of multifaceted unresharpenable plates (MUP) are proposed for the first time, which makes it impossible to move the plate in any direction while the cutting forces acting on it. Moreover, the expressions are obtained to determine the minimum height of the intersection of the cutoff tool socket head, which is important at the stage of creating a methodology for designing this type of tool.

G.A. Yessenbayeva, A.T. Kasimov, B.A. Kasimov

The article is devoted to the study of bending of round plates, which are the basis for calculating many problems of mechanics. In the article the structure of this method is presented, its main components are highlighted; its types are characterized, as well as its classical approaches. In this article the research of the bending problem for round plates is carried out in particular cases. Methods of bending calculation of round plates like all analytical methods have a number of advantages, which are also noted in this article. The article is focused mainly on mechanics, engineers and technical specialists.