Hasil untuk "Descriptive and experimental mechanics"

Bonaventure Nana, Krystian Polczyński, Paul Woafo et al.

In the present work, we analyzed theoretically and experimentally the nonlinear dynamics of a magnetic pendulum excited through the interactions of a strong neodymium magnet and two coils placed symmetrically around the zero angular position. The forces between the magnet and coils and generated torques acting on the pendulum are derived using the magnetic charges interaction model and an experimentally fitted model. System equilibrium points are obtained, and their stability is investigated. It is found that when the currents in two coils are negative, the shape of the mechanical potential is bistable. The bistable potential might be symmetric if the currents have the same values and asymmetric when they are different. Asymmetric bistable potential is observed when coil currents have different signs. However, in the case of positive coil currents, a symmetric tristable potential is detected when the currents are the same, and an asymmetric tristable potential takes place when the positive currents have different values. Considering the sinusoidal coil current signals, analytical calculations using the harmonic balance method and numerical simulations are carried out for this electric-magneto-mechanical system. The obtained results are shown in terms of frequency-response diagrams, displacement time series, and phase portraits. The two-parameter bifurcation diagrams are plotted showing the different dynamical behaviors considering the current amplitudes and frequency as the control parameters. Amplitude jumps, hysteresis, and multistability are also observed. Some phase portraits and the coexistence of attractors are obtained numerically and confirmed experimentally. A good agreement between the numerical simulation and experimental measurement is achieved.

Jixin Hou, Kun Jiang, Arunachalam Ramanathan et al.

Understanding the mechanical behavior of brain tissue is crucial for advancing both fundamental neuroscience and clinical applications. Yet, accurately measuring these properties remains challenging due to the brain unique mechanical attributes and complex anatomical structures. This review provides a comprehensive overview of commonly used techniques for characterizing brain tissue mechanical properties, covering both invasive methods such as atomic force microscopy, indentation, axial mechanical testing, and oscillatory shear testing and noninvasive approaches like magnetic resonance elastography and ultrasound elastography. Each technique is evaluated in terms of working principles, applicability, representative studies, and experimental limitations. We further summarize existing publications that have used these techniques to measure human brain tissue mechanical properties. With a primary focus on invasive studies, we systematically compare their sample preparation, testing conditions, reported mechanical parameters, and modeling strategies. Key sensitivity factors influencing testing outcomes (e.g., sample size, anatomical location, strain rate, temperature, conditioning, and post-mortem interval) are also discussed. Additionally, selected noninvasive studies are reviewed to assess their potential for in vivo characterization. A comparative discussion between invasive and noninvasive methods, as well as in vivo versus ex vivo testing, is included. This review aims to offer practical guidance for researchers and clinicians in selecting appropriate mechanical testing approaches and contributes a curated dataset to support constitutive modeling of human brain tissue.

Emilia-Georgiana Prisăcariu, Tudor Prisecaru

Throughout many decades, the Schlieren visualization method has been mainly used as means to visualize transparent flows in a qualitative manner. The images recorded provide data regarding the existence of the flow, or illustrate predicted flow geometries and details. The colored Schlieren method has been developed in the late 1890s and has always had the intent to provide quantitative data rather than qualitative pictures of the studied phenomena. This paper centers on applying a quantitative color Schlieren method to help determine the gasodynamic parameters of an H₂–O₂ exhaust jet, developing in air. A comparison between the parameters obtained through calibrating the color filter for the Schlieren method and the results from a CFD simulation is performed to assess the range of the CS (color Schlieren) measurement. This paper’s findings address the issues of calibrated color filter Schlieren encounter during its implementation and discusses possible errors appearing when the method is applied to a 3D flow. While the qualitative Schlieren images are still impressive to observe, the quantitative Schlieren presents challenges and a low measurement accuracy (75%) when applied to 3D flows and compared to 2D cases found in the literature (97–98%).

Juan C. Assis, Ricardo D. Santos, Mateus S. Schuabb et al.

Creating time-marching unsteady governing equations for a steady state in high-speed flows is not a trivial task. Residue convergence in time cannot be achieved when using most low- and high-order spatial discretization schemes. Recently, high-order, weighted, essentially non-oscillatory schemes have been specially designed for steady-state simulations. They have been shown to be capable of achieving machine precision residues when simulating the Euler equations under canonical coordinates. In the present work, we review these schemes and show that they can also achieve machine residues when simulating the Navier–Stokes equations under generalized coordinates. This is carried out by considering three supersonic flows of perfect fluids, namely the flow upstream a cylinder, the flow over a blunt wedge, and the flow over a compression ramp.

Dalia M. Bonilla-Correa, Oscar E. Coronado-Hernández, Alfonso Arrieta-Pastrana et al.

Water utilities are concerned about the issue of pipeline collapses, as service interruptions lead to water shortages. Pipeline collapses can occur during the maintenance phase when water columns compress entrapped air pockets, consequently increasing the pressure head. Analysing entrapped air pockets is complex due to the necessity of numerically solving a system of differential equations. Currently, water utilities need more tools to perform this analysis effectively. This research provides a numerical solution to the problem of entrapped air pockets in pipelines which can be utilised to predict filling operations. The study develops an analytical solution to examine the filling process. A practical application is shown, considering a 600 m long pipeline with an internal diameter of 400 mm. Compared with existing mathematical models, the results of the new analytical equations demonstrate their effectiveness as a new tool for computing the main hydraulic and thermodynamic variables involved in this issue.

Safia Ihsan Ali, David Patton, Kimberley A. Myers et al.

Tetralogy of Fallot (TOF) is the most prevalent cyanotic congenital heart defect (CHD) that alters normal blood flow through the heart and accounts for 10% of all CHD. Pulmonary stenosis and regurgitation are common in adults who have undergone TOF repair (rTOF) and can impact the load on the right ventricle, blood flow pressure, and pulmonary hemodynamics. Pressure mapping, obtained through 4D-flow magnetic resonance imaging (4D-flow MRI), has been applied to identify abnormal heart hemodynamics in CHD. Hence, the aim of this research was to compare pressure drop and relative pressures between patients with repaired TOF (rTOF) and healthy volunteers. An in vitro validation was performed, followed by an in vivo validation. We hypothesized that pressure drop is a more stable pressure mapping method than relative pressures to detect altered hemodynamics. A total of 36 subjects, 18 rTOF patients and 18 controls underwent cardiac MRI scans and 4D-flow MRI. Pressure drops and relative pressures in the MPA were higher in rTOF patients compared to the controls (<i>p</i> < 0.05). Following the in vitro validation, pressure drops proved to be a more stable pressure mapping method than relative pressures, as the flow loses its laminarity and becomes more turbulent. In conclusion, this study demonstrated that flow hemodynamics in rTOF can exhibit altered pressure maps. Pressure mapping can help provide further insight into rTOF patients’ hemodynamics to improve patient care and clinical decisions.

Md. Mahbubur Rahman, Djiby Bal, Keishi Kariya et al.

Due to its low global warming potential (GWP) and good environmental properties, CF₃I can be a suitable component of refrigerant mixtures in the field of refrigeration and air conditioning. In this work, the local condensation heat transfer characteristics of CF₃I were experimentally investigated in a plate heat exchanger (PHE). The condensation heat transfer experiments were carried out under conditions of vapor qualities from 1.0 to 0.0, at saturation temperatures of 25–30 °C, mass fluxes of 20–50 kg/m²s, and heat fluxes of 10.4–13.7 kW/m². Local heat transfer coefficients were found to vary in both the horizontal and vertical directions of the plate heat exchanger showing similar trends in all mass fluxes. In addition, the characteristics of local heat flux and wall temperature distribution as a function of distance from the inlet to the outlet of the refrigerant channel were explored in detail. The comparison of the experimental data of CF₃I with that of R1234yf in the same test facility showed that the heat transfer coefficients of CF₃I were comparable to R1234yf at a low vapor quality and a mass flux of 20 kg/m²s. However, R1234yf exhibited a transfer coefficient about 1.5 times higher at all vapor qualities and a mass flux of 50 kg/m²s. The newly developed correlation predicts well the experimentally obtained data for both CF₃I and R1234yf within ±30%.

William Banks, Asma Harcharras, Dominique Lecomte

The type $τ$($α$) of an irrational number $α$ measures the extent to which rational numbers can closely approximate $α$. More precisely, $τ$($α$) is the infimum over those t$\in$R for which |$α$--h/k|<k^{--t--1} has at most finitely many solutions h,k$\in$Z, k>0. In this paper, we regard the type as a function $τ$:R\Q$\rightarrow$[1,$\infty$] and explore its descriptive properties. We show that $τ$ is invariant under the natural action of GL2(Q) on R\Q. We show that $τ$ is densely onto, and we compute the descriptive complexity of the pre-image of the singletons and of certain intervals. Finally, we show that the function $τ$ is [1,$\infty$]-upper semi-Baire class 1 complete.

María Guadalupe González-Solórzano, Rodolfo Morales Dávila, Javier Guarneros et al.

The characterization of the fluid flow of liquid steel in a slab mold, using two nozzle designs under unclogged and clogged conditions, is performed using physical and mathematical simulations. Nozzle A, with an expanding and contracting geometry, yields larger sub-meniscus experimental velocities than nozzle B, with internal flow deflectors. The numerical predictions indicate quick time-changing velocity profiles in the submeniscus region between the mold’s narrow face and the nozzles. The flow deflectors in nozzle B have two effects; the high dissipation rate of kinetic energy in the upper-half length induces lower velocities in the ports than nozzle A. The neutralization of the biased flow caused by the sliding gate allows a balanced fluid through the ports. According to the results, nozzle A yields velocity profiles in the sub-meniscus region with larger standard deviations than nozzle B, leading to an unstable bath surface. The clogged nozzles produced biased-asymmetrical flow patterns in the mold, finding approximated matchings between numerical predictions and experimental measurements. The internal protrusions of the deposits lead to covariance losses of the bath surface wave heights. The use of internal deflectors helped to decrease the amount of clog material in nozzle B.

Tran Ich Thinh

In this paper, an approach is proposed and presented to tackle the vibro-acoustic properties of finite clamped composite sandwich plates with foam core. Composite sandwich plates are treated as being orthotropic and the apparent bending stiffnesses are calculated for the two principal directions. The apparent bending stiffnesses of composite sandwich plate are estimated by finite element calculation on beam elements cut from the considered composite sandwich plates. The sound transmission loss of clamped composite sandwich plates is predicted using orthotropic Kirchhoff’s plate theory, together with the obtained bending stiffnesses in two principal directions. Several sound transmission loss measurements were conducted in the laboratory on fiberglass/polyester composite sandwich plates with polyurethane foam core. The predicted sound transmission loss is compared with measured data and the agreement is reasonable.

Pham Ngoc Thanh, Tran Ich Thinh, Ta Thi Hien

In this investigation, by an analytical approach, the influence of several key parameters, especially the temperature on the sound isolation capacity of the symmetrically finite orthotropic laminated composite plate is studied. The plate is modeled with classic thin-plate theory and is assumed to be simply supported on all four sides. The incident acoustic pressure is modeled as a harmonic plane wave impinging on the plate at an arbitrary angle. The sound transmission loss is calculated from the ratio of incident to transmitted acoustic powers

Vladislav M. Ovsyannikov

Professor N.E. Zhukovsky was a famous Russian mechanic and engineer. In 1876 he defended his master’s thesis at Moscow University. At a careful reading of N.E. Zhukovsky’s master’s thesis in 1997, V.A. Bubnov—a professor at the Moscow City Pedagogical University—discovered terms of the second order of smallness in the continuity equation for an incompressible fluid. Zhukovsky calculated them, but did not use the amount of substance in the balance. Ten years later, the author found high-order terms in Euler’s derivation of the 1752 continuity equation for an incompressible fluid. The physical meaning of the additional terms became clear after the derivation in 2006 of the continuity equation with terms of high order of smallness for a compressible gas. The higher order terms of the smallness of the continuity equation penetrate into the inhomogeneous part of the wave equation and lead to the generation of self-oscillations, vibrations, sound, and the initial stage of turbulent pulsations. The stochastic approach ensured success in modeling turbulent flows. The use of high-order terms of smallness of the Euler continuity equation makes it possible to transfer the description of some part of the motions from the stochastic part of the equation to the deterministic part. The article contains a review of works with the derivation of the inhomogeneous wave equation. These works use additional terms of a high order of smallness in the continuity equation.

Giulia Pomaranzi, Ombretta Bistoni, Paolo Schito et al.

Currently, the energy and environmental efficiency of buildings has led to the development of cladding systems that may help to reduce the structure’s energy demand, using techniques such as the Permeable Double Skin Façade (PDSF). Given complex aerodynamic interactions, the presence of an external porous screen in addition to an inner skin may play a crucial role in the fluid-dynamic characterization of such buildings, making the definition of wind effects very complex. A new methodology for the quantitative assessment of the impact of wind-loading conditions on this particular type of cladding is presented. It is based on a combined experimental–numerical approach, essentially based on wind-tunnel tests on a rigid scale model and computational fluid dynamic simulations. A case study is proposed as an application of this methodology. Results include the design pressure values for the inner glazed façade and the permeable facade. An estimation of the flow rate across the porous skin is quantified using the numerical model.

Stefano Savino, Carlo Nonino

Counter-flow double-layered microchannel heat sinks are very effective for thermal control of electronic components; however, they require rather complicated headers and flow maldistribution can also play a negative role. The cross-flow configuration allows a much simpler header design and the thermal performance becomes similar to that provided by the counter-flow arrangement if the velocity distribution in the microchannels is not uniform. The aim of this work is to show the possibility of achieving a favorable flow distribution in the microchannels of a cross-flow double-layered heat sink with an adequate header design and the aid of additional elements such as full or partial height baffles made of solid or porous materials. Turbulent RANS numerical simulations of the flow field in headers are carried out with the commercial code ANSYS Fluent. The flow in the microchannel layers is modeled as that in a porous material, whose properties are derived from pressure drop data obtained using an in-house FEM code. It is demonstrated that, with an appropriate baffle selection, inlet headers of cross-flow microchannel heat sinks yield velocity distributions very close to those that would allow optimal hotspot management in electronic devices.

Asmi Haldar, Arnab Das

Equilibrium statistical mechanics rests on the assumption of ergodic dynamics of a system modulo the conservation laws of local observables: extremization of entropy immediately gives Gibbs' ensemble (GE) for energy conserving systems and a generalized version of it (GGE) when the number of local conserved quantities (LCQ) is more than one. Through the last decade, statistical mechanics has been extended to describe the late-time behaviour of periodically driven (Floquet) quantum matter starting from a generic state. The structure built on the fundamental assumptions of ergodicity and identification of the relevant "conservation laws" in this inherently non-equilibrium setting. More recently, it has been shown that the statistical mechanics has a much richer structure due to the existence of {\it emergent} conservation laws: these are approximate but stable conservation laws arising {\it due to the drive}, and are not present in the undriven system. Extensive numerical and analytical results support perpetual stability of these emergent (though approximate) conservation laws, probably even in the thermodynamic limit. This banks on the recent finding of a sharp ergodicity threshold for Floquet thermalization in clean, interacting non-integrable Floquet systems. This opens up a new possibility of stable Floquet engineering in such systems. This review intends to give a theoretical overview of these developments. We conclude by briefly surveying the experimental scenario.

John J. Vastola, William R. Holmes

Stochastic mechanics---the study of classical stochastic systems governed by things like master equations and Fokker-Planck equations---exhibits striking mathematical parallels to quantum mechanics. In this article, we make those parallels more transparent by presenting a quantum mechanics-like formalism for deriving a path integral description of systems described by stochastic differential equations. Our formalism expediently recovers the usual path integrals (the Martin-Siggia-Rose-Janssen-De Dominicis and Onsager-Machlup forms) and is flexible enough to account for different variable domains (e.g. real line versus compact interval), stochastic interpretations, arbitrary numbers of variables, explicit time-dependence, dimensionful control parameters, and more. We discuss the implications of our formalism for stochastic biology.

Torsten V. Zache, Thomas Schweigler, Sebastian Erne et al.

Quantum field theory is a powerful tool to describe the relevant physics governing complex quantum many-body systems. Here we develop a general pathway to extract the irreducible building blocks of quantum field theoretical descriptions and its parameters purely from experimental data. This is accomplished by extracting the one-particle irreducible (1PI) vertices from which one can construct all observables. To match the capabilities of experimental techniques used in quantum simulation experiments, our approach employs a formulation of quantum field theory based on equal-time correlation functions only. We illustrate our procedure by applying it to the quantum sine-Gordon model in thermal equilibrium. The theoretical foundations are illustrated by estimating the irreducible vertices at equal times both analytically and using numerical simulations. We then demonstrate explicitly how to extract these quantities from an experiment where we quantum simulate the sine-Gordon model by two tunnel-coupled superfluids. We extract the full two-point function and the interaction vertex (four-point function) and their variation with momentum, encoding the `running' of the couplings. The measured 1PI vertices are compared to the theoretical estimates, verifying our procedure. Our work opens new ways of addressing fundamental questions in quantum field theory, which are relevant in high-energy and condensed matter physics, and in taking quantum phenomena from fundamental science to practical technology.

Juan Luis Gonzalo, Claudio Bombardelli

An approximate analytical solution for the two body problem perturbed by a radial, low acceleration is obtained, using a regularized formulation of the orbital motion and the method of multiple scales. Formulating the dynamics with the Dromo special perturbation method allows us to separate the two characteristic periods of the problem in a clear and physically significative way, namely the orbital period and a period depending on the magnitude of the perturbing acceleration. This second period becomes very large compared to the orbital one for low thrust cases, allowing us to develop an accurate approximate analytical solution through the method of multiple scales. Compared to a regular expansion, the multiple scales solution retains the qualitative contributions of both characteristic periods and has a longer validity range in time. Looking at previous solutions for this problem, our approach has the advantage of not requiring the evaluation of special functions or an initially circular orbit. Furthermore, the simple expression reached for the long period provides additional insight on the problem. Finally, the behavior of the asymptotic solution is assessed through several test cases, finding a good agreement with high-precision numerical solutions. The results presented not only advance in the study of the two body problem with constant radial thrust, but confirm the utility of the method of multiple scales for tackling problems in orbital mechanics.

Nguyen Trung Kien, Nguyen Duy Hung

A Fourier-based method is adopted to determine the permeability of periodic porous media made up of a rigid skeleton saturated by viscous fluid. The flow, induced by a prescribed macroscopic gradient of pressure, adopts the Stokes equations with incorporating a condition of adherence at the surface of the solid. The permeability is determined by solving a linear problem on a unit cell for which we determine the local velocity fields due to a prescribed gradient of pressure. The method uses the Fourier Transformation and exact expressions of the periodic Green tensor in the Fourier space. It is shown that the resolution of the problem requires an introducing of undetermined forces acting within the solid phase.

Veit Elser

These lectures were prepared for the 2014 PCMI graduate summer school and were designed to be a lightweight introduction to statistical mechanics for mathematicians. The applications feature some of the themes of the summer school: sphere packings and tilings.