The first application of theory of the rise of line thermals was to understand the rise of turbulent smoke plumes emitted from smoke stacks into a cross-wind. Initial solutions required numerical calculations. In this article analytical solutions are found, and these are used here to explore solutions for the rise of buoyant line wakes from submarine vehicles. Solutions cater for wakes in both neutral and stable environments, and for sources which have either negative or positive initial buoyancy. Account is also taken of sources with differing size and initial momentum. Practical examples of submarine thermal wake flows are given using neutral and typical stably stratified upper ocean conditions and a range of source conditions. A key result is that small-diameter submarine wakes with high temperatures produced in weakly stratified ocean waters will have a large height of rise, and may easily reach the surface. By contrast, large-source-diameter wakes, with temperatures close to ambient and emitted into strongly stratified oceans, will have very small heights of rise.
Thermodynamics, Descriptive and experimental mechanics
The flow rate through hydraulic resistance increases with the pressure drop across it, but this correlation is no longer valid under cavitation conditions. This study investigates choked flow in calibrated screw-in orifices, widely used for control and damping in fluid power components. An experimental campaign was conducted on orifices with diameters ranging from 1 to 0.4 mm at various upstream pressures using hydraulic oil. A computational fluid dynamics (CFD) model was developed and validated against experiments, then used to analyze the effects of geometric parameters such as edge chamfers, hex wrench sockets, and length-to-diameter ratio. From CFD results, an analytical correlation between flow rate and pressure drop was derived, incorporating flow saturation effects. The study revealed that under saturation conditions, flow rate is largely unaffected by geometry, except for the ideal case of a perfectly sharp-edged orifice, which is rarely encountered. Even minimal chamfers of a few hundredths of a millimeter make the restrictor non-ideal. The derived correlation can be integrated into lumped parameter models of fluid power components to account for choked flow.
Thermodynamics, Descriptive and experimental mechanics
Mouhammad El Hassan, Ali Mjalled, Philippe Miron
et al.
Fluid mechanics often involves complex systems characterized by a large number of physical parameters, which are usually described by experimental and numerical sparse data (temporal or spatial). The difficulty of obtaining complete spatio-temporal datasets is a common issue with conventional approaches, such as computational fluid dynamics (CFDs) and various experimental methods, particularly when evaluating and modeling turbulent flows. This review paper focuses on the integration of machine learning (ML), specifically physics-informed neural networks (PINNs), as a means to address this challenge. By directly incorporating governing physical equations into neural network training, PINNs present a novel method that allows for the reconstruction of flow from sparse and noisy data. This review examines various applications in fluid mechanics where sparse data is a common problem and evaluates the effectiveness of PINNs in enhancing flow prediction accuracy. An overview of diverse PINNs methods, their applications, and outcomes is discussed, demonstrating their flexibility and effectiveness in addressing challenges related to sparse data and illustrating that the future of fluid mechanics lies in the synergy between data-driven approaches and established physical theories.
Thermodynamics, Descriptive and experimental mechanics
У другій частині статті представлено механізм навчання штучної нейронної мережі (ШНМ) структура якої була розроблена у попередньому дослідженні. Значний обсяг навчальних даних (85451 навчальних пар), величина пакету навчання (2000), кількість раундів навчання (500000), а також глибина ШНМ дозволили отримати досить низьку похибку навчання (1,52·10-6) та валідації (1,99·10-6). Крім того, майже на всій тестовій вибірці ШНМ також показала досить якісне передбачення коефіцієнтів оптимального регулятора. Для цього були розраховані максимальні та середньоквадратичні похибки прогнозування.
Однак, окремі значення похибок прогнозування коефіцієнтів поставили під сумнів якість оптимального регулювання руху системи. Для того, щоб оцінити цю якість було вивчено найгірший у сенсі похибки прогнозування результат. Це дозволило встановити, що відхилення величин коефіцієнтів (максимально на 7,86%) не спричиняє значного відхилення динаміки руху системи „кран-вантаж” від того, що отримано за допомогою оптимальних коефіцієнтів лінійно-квадратичного регулятора. Для цього побудовано та проаналізовано графічні залежності фазового портрету маятникових коливань вантажу, функції керування, рушійного зусилля та швидкості руху крана.
У статті відмічена одна із переваг отриманої ШНМ – швидкодія отримання оптимального керування. Вона випливає із того, що доступ до ШНМ потребує значно менших обчислювальних ресурсів, аніж ті, що потрібні для розв’язання рівнянь Ріккаті.
У заключній частині статті наведено рекомендації стосовно реалізації отриманих результатів на практиці. Вони полягають у тому, що на вхід ШНМ передають вхідний вектор, що містить нормовані значення маси вантажу, довжини гнучкого підвісу та коефіцієнта ваги керування. Це дозоляє отримати прогнозні значення коефіцієнтів оптимального регулятора. У подальшому їх використовують для відшукування оптимальної стратегії керування. Остання, в свою чергу, реалізується засобами керованих електроприводних механізмів крана.
Caree A. García-Maro, Carmen S. Rochín-Wong, Laura G. Ceballos-Mendivil
et al.
The growing global population has resulted in a higher demand for energy, leading researchers to prioritize the development of alternative energy sources and the improvement of current technologies. Nanofluids (NFs) are a promising method for enhancing heat transfer and efficiently utilizing solar thermal energy. This study describes the preparation of four NFs: two mono NFs of SiC and HfC containing nanoparticle concentrations ranging from 0.10–1.0 wt.%. Moreover, two hybrid NFs were synthesized within the same concentration range (0.10–1.0 wt.%) of SiC-HfC nanocomposites in proportions of 60 wt.% SiC-40 wt.% HfC and 40 wt.% SiC-60 wt.% HfC, all dispersed in a mixture of ethylene glycol (EG) and distilled water (50EG-50H<sub>2</sub>O). The materials were synthesized by carbothermal reduction, and the NFs were prepared using the two-step method. The NFs showed stable dispersion, with HfC and 40SiC-60HfC systems exhibiting the higher zeta potential (ζ) values. Viscosity remained largely unaffected by particle addition. The thermal diffusivity of the NFs was measured by the thermal lens spectroscopy (TLS) technique using 1:20 diluted samples. The hybrid nanofluid 40SiC-60HfC improved diffusivity by 66.93%, presenting a synergistic effect in its performance, highlighting its potential in clean energy systems.
Thermodynamics, Descriptive and experimental mechanics
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.
This survey synthesizes the principal descriptive set-theoretic perspectives on deterministic Cantor sets on the real line and charts directions for future study. After recounting their historical genesis and compiling an up-to-date taxonomy, we review the Borel hierarchy and four hierarchically ordered representations-general, nested, iterated-function-system (IFS), and q-ary expansion-presented from the most general to the most specific set-theoretic description of deterministic Cantor sets. We then present explicit and recursive descriptions for two thin families of measure-zero Cantor sets and an augmented "tick" family of positive measure, respectively, showing that the classical middle-third set lies in the intersection of all three families of after-mentioned Cantor sets. The survey closes by isolating several open problems in four directions, aiming to provide mathematicians with a coherent platform for further descriptive set-theoretic investigations into Cantor-type sets on the real line.
This study aimed to determine the minimum number of repetitions for a high reliability of movement timing in fundamental physical fitness exercises using inertial sensors. Fifteen young men and fifteen women performed eight exercises (two-leg hop, forward lunge, squat, sit-up, shoulder abduction, hip abduction, back extension, and push-up) (preferred tempo, 3 trials, 20 repetitions per trial). The movement timing (cycle of movement in seconds and its phases in seconds and %tcycle) was tested for intra- and inter-trial reliability (SPSS 28.0, <i>p</i> ≤ 0.05). Just two repetitions were adequate for excellent intra- and inter-trial relative reliability (ICCs ≥ 0.75, isolated exceptions only for durations expressed as %tcycle, in only three out of the eight exercises: hip abduction, back extension, and push-up), as well as for high absolute intra- and inter-trial reliability (average SEM% at 5.9%, respectively, and 6.8% and average MDC95% at 13.7% and 15.9%, respectively, which was consistently higher than the upper boundary limit of SEM%, and a rather low CV% ranging from 1.5% to 4.9% and averaging at 3.1%). A total of four repetitions, excluding the initial and the final one, appears adequate for high overall reliability of movement timing in the eight physical fitness exercises examined.
Mechanics of engineering. Applied mechanics, Descriptive and experimental mechanics
Eden Arbel, Luco L. K. M. Buise, Charlotte C. R. M. M. van Waes
et al.
Cooperative transport is a striking phenomenon where multiple agents join forces to transit a payload too heavy for the individual. While social animals such as ants are routinely observed to coordinate transport at scale, reproducing the effect in artificial swarms remains challenging, as it requires synchronization in a noisy many-body system. Here we show that cooperative transport spontaneously emerges in swarms of stochastic self-propelled robots. Robots deprived of sensing and communication, are isotropically initialized around a passive circular payload, where directional motion is not expected without an external cue. And yet it moves. We find that a minute modification to the mechanical design of the individual agent dramatically changes its alignment response to an external force. We then show experimentally that by controlling the individual's friction and mass distribution, a swarm of active particles autonomously cooperates in the directional transport of larger objects. Surprisingly, transport increases with increasing payload size, and its persistence surpasses the persistence of the active particles by over an order of magnitude. A mechanical, coarse-grained description reveals that force-alignment is intrinsic and captured by a signed, charge-like parameter with units of curvature. Numerical simulations of swarms of active particles with a negative active charge corroborate the experimental findings. We analytically derive a geometrical criterion for cooperative transport which results from a bifurcation in a non-linear dynamical system. Our findings generalize existing models of active particles, offer new design rules for distributed robotic systems, and shed light on cooperation in natural swarms.
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.
The significant growth of artificial intelligence (AI) methods in machine learning (ML) and deep learning (DL) has opened opportunities for fluid dynamics and its applications in science, engineering and medicine. Developing AI methods for fluid dynamics encompass different challenges than applications with massive data, such as the Internet of Things. For many scientific, engineering and biomedical problems, the data are not massive, which poses limitations and algorithmic challenges. This paper reviews ML and DL research for fluid dynamics, presents algorithmic challenges and discusses potential future directions.
Thermodynamics, Descriptive and experimental mechanics
The microstructure and suspended particle behavior should be considered when studying the flow properties exhibited by particle suspension. In addition, particle migration, also known as Segré–Silberberg effects, alters the microstructure of the suspension and significantly affects the viscosity properties of the suspension. Therefore, particle behavior with respect to the changes in mechanical factors should be considered to better understand suspension. In this study, we investigated the particle behavior in asymmetric velocity profiles with respect to the channel center numerically using the lattice Boltzmann method and a two-way coupling scheme. Our findings confirmed that the final equilibrium position of particles in asymmetric velocity profiles converged differently between the outer and inner wall sides with respect to the channel center. This indicates that the mechanical equilibrium position of particles can be changed by asymmetric velocity profiles. In addition, centrifugal force acting on the particles is also important in the study of equilibrium position. These results suggest that the microstructure and viscosity characteristics of a suspension in a pipe could be handled by changes in velocity profiles.
Thermodynamics, Descriptive and experimental mechanics
Thanh Tung Nguyen, Van Thanh Hoang, Duc Binh Luu
et al.
The droplet-based microfluidic system is increasingly advancing and widely applied in various fields of analytical techniques and experiments. To optimize and advance this system, droplet dynamics is of utmost concern. The velocity of droplets is highly significant as it aids in precise droplet control and manipulation, ultimately leading to the optimization of device design and performance. This paper utilizes numerical simulations to explore the influence of flow characteristics, fluid properties, and geometric parameters of the contraction microchannel on the velocity of droplets while they are in a stable state. The findings indicate that the droplet velocity is influenced by factors such as viscosity ratio (λ), capillary number (Ca), and contraction ratio (C).
Mechanical engineering and machinery, Descriptive and experimental mechanics
Travis Leadbetter, Prashant K. Purohit, Celia Reina
Far-from-equilibrium phenomena are critical to all natural and engineered systems, and essential to biological processes responsible for life. For over a century and a half, since Carnot, Clausius, Maxwell, Boltzmann, and Gibbs, among many others, laid the foundation for our understanding of equilibrium processes, scientists and engineers have dreamed of an analogous treatment of non-equilibrium systems. But despite tremendous efforts, a universal theory of non-equilibrium behavior akin to equilibrium statistical mechanics and thermodynamics has evaded description. Several methodologies have proved their ability to accurately describe complex non-equilibrium systems at the macroscopic scale, but their accuracy and predictive capacity is predicated on either phenomenological kinetic equations fit to microscopic data, or on running concurrent simulations at the particle level. Instead, we provide a framework for deriving stand-alone macroscopic thermodynamics models directly from microscopic physics without fitting in overdamped Langevin systems. The only necessary ingredient is a functional form for a parameterized, approximate density of states, in analogy to the assumption of a uniform density of states in the equilibrium microcanonical ensemble. We highlight this framework's effectiveness by deriving analytical approximations for evolving mechanical and thermodynamic quantities in a model of coiled-coil proteins and double stranded DNA, thus producing, to the authors' knowledge, the first derivation of the governing equations for a phase propagating system under general loading conditions without appeal to phenomenology. The generality of our treatment allows for application to any system described by Langevin dynamics with arbitrary interaction energies and external driving, including colloidal macromolecules, hydrogels, and biopolymers.
A statistical, path-dependent framework to describe time-dependent macroscopic theories using the Principle of Maximum Caliber is presented. By means of this procedure, it is possible to infer predictive non-equilibrium statistical mechanical models from a variational principle, provided that the adequate time-dependent constraints and the state of the system at some specific times are given. The approach is exemplified by obtaining the description of a time-dependent Brownian particle from kinetic restrictions. We relate the predictive nature of a model to the structure of the prior distribution that represents the state of knowledge about the system before the dynamical constraints are considered. Non-predictive models are shown to be possible in the presented framework and as an example, retrodictive dynamics are obtained from the same kinetic constraints.
This paper examines the monetary policies the Federal Reserve implemented in response to the Global Financial Crisis. More specifically, it analyzes the Federal Reserve's quantitative easing (QE) programs, liquidity facilities, and forward guidance operations conducted from 2007 to 2018. The essay's detailed examination of these policies culminates in an interrupted time-series (ITS) analysis of the long-term causal effects of the QE programs on U.S. inflation and real GDP. The results of this formal design-based natural experimental approach show that the QE operations positively affected U.S. real GDP but did not significantly impact U.S. inflation. Specifically, it is found that, for the 2011Q2-2018Q4 post-QE period, real GDP per capita in the U.S. increased by an average of 231 dollars per quarter relative to how it would have changed had the QE programs not been conducted. Moreover, the results show that, in 2018Q4, ten years after the beginning of the QE programs, real GDP per capita in the U.S. was 14% higher relative to what it would have been during that quarter had there not been the QE programs. These findings contradict Williamson's (2017) informal natural experimental evidence and confirm the conclusions of VARs and new Keynesian DSGE models that the Federal Reserve's QE policies positively affected U.S. real GDP. The results suggest that the current U.S. and worldwide high inflation rates are likely not because of the QE programs implemented in response to the financial crisis that accompanied the COVID-19 pandemic. They are likely due to the unprecedentedly large fiscal stimulus packages used, the peculiar nature of the financial downturn itself, the negative supply shocks from the war in Ukraine, or a combination of these factors. This paper is the first study to measure the macroeconomic effects of QE using a design-based natural experimental approach.
Jérôme Buzzi, Nishant Chandgotia, Matthew Foreman
et al.
This file is composed of questions that emerged or were of interest during the workshop "Interactions between Descriptive Set Theory and Smooth Dynamics" that took place in Banff, Canada on 2022.
Abstract Soft heat pipes are vital in many applications. Inspired by the structure of a squid, we proposed a squid‐like soft heat pipe with multiple heat transport branches that has excellent flexibility and outstanding thermal performance. Each branch could transport heat to different locations for multiple heating or cooling applications. The proposed soft heat pipe worked as a pulsating heat pipe with a unidirectional flow of liquid slugs and vapor bubbles. Its thermal performance was investigated at different heating temperatures, bending angles, and inclination angles. The result showed that the highest equivalent thermal conductivity of the squid‐like soft heat pipe could be up to 6750 W/(m · K), almost 17 times that of copper. Besides, the bending angle had little effect on its thermal performance, with the equivalent thermal conductivity reducing 10%–13% when the heat pipe was bent from 0° to 90°. The thermal performance of the soft heat pipe was affected by the inclination angle, with the equivalent thermal conductivity reducing 20%–25% as the inclination angle was reduced from 90° to 30°. The proposed soft heat pipe is scalable by increasing the tube length and branches. It has many promising applications like waste heat recovery, electronic device cooling, personal thermal management, and renewable energy harvesting.
The use of curvilinear coordinates is sometimes indicated by the inherent geometry of a fluid dynamics problem, but this introduces fictitious forces into the momentum equations that spoil the strict conservative form. If one is willing to work in three dimensions, these fictitious forces can be eliminated by solving for rectangular (Cartesian) momentum components on a curvilinear mesh. A thoroughly geometric approach to fluid dynamics on spacetime demonstrates this transparently, while also giving insight into a greater unity of the relativistic and nonrelativistic cases than is usually appreciated.
Thermodynamics, Descriptive and experimental mechanics