At scales larger than the forcing scale, some out-of-equilibrium turbulent systems (such as hydrodynamic turbulence, wave turbulence, and nonlinear optics) exhibit a state of statistical equilibrium where energy is equipartitioned among large-scale modes, in line with the Rayleigh-Jeans spectrum. Key open questions now pertain to either the emergence, decay, collapse, or other nonstationary evolutions from this state. Here, we experimentally investigate the free decay of large-scale hydroelastic turbulent waves, initially in a regime of statistical equilibrium. Using space- and time-resolved measurements, we show that the total energy of these large-scale tensional waves decays as a power law in time. We derive an energy decay law from the theoretical initial equilibrium spectrum and the linear viscous damping, as no net energy flux is carried. Our prediction then shows a good agreement with experimental data over nearly two decades in time, for various initial effective temperatures of the statistical equilibrium state. We further identify the dissipation mechanism and confirm it experimentally. Our approach could be applied to other decaying turbulence systems, with the large scales initially in statistical equilibrium.
Riccardo Piombo, Lorenzo Buffa, Dario Mazzilli
et al.
Statistical mechanics is a powerful framework for analyzing optimization yielding analytical results for matching, optimal transport, and other combinatorial problems. However, these methods typically target the zero-temperature limit, where systems collapse onto optimal configurations, a.k.a. the ground states. Real-world systems often occupy intermediate regimes where entropy and cost minimization genuinely compete, producing configurations that are structured yet sub-optimal. The Sub-Optimal Transport (SOT) model captures this competition through an ensemble of weighted bipartite graphs: a coupling parameter interpolates between entropy-dominated dense configurations and cost-dominated sparse structures. This crossover has been observed numerically but lacked analytical understanding. Here we develop a mean-field theory that characterizes this transition. We show that local fluctuations in Lagrange multipliers become sub-extensive in the thermodynamic limit, reducing the full model with strength constraints to an effective single-constraint problem admitting an exact solution in some intermediate regime. The resulting free energy is analytic in the coupling parameter, confirming a smooth crossover rather than a phase transition. We derive closed-form expressions for thermodynamic observables and weight distributions, validated against numerical simulations. These results establish the first analytical description of the SOT model, extending statistical mechanics methods beyond the zero-temperature regime.
This study investigates the effects of air pressure, glue pressure, and viscosity on atomization characteristics through experimental and simulation methods, aiming to reveal gas–liquid interaction mechanisms and optimize process parameters. The rheological parameters of aqueous polyurethane adhesives with varying viscosities were characterized. Spray characteristics, including spray angle, cured film diameter, and thickness, were quantitatively measured under different operating conditions. The internal flow field and droplet dynamics were numerically analyzed. The results indicate the following: Increasing the air pressure (from 0.3 to 0.7 MPa) enlarges the spray angle and film diameter while reducing the film thickness. In contrast, increasing the glue pressure enlarges all three parameters: spray angle, film diameter, and film thickness. Furthermore, increasing the viscosity within the test range reduces the spray angle, film diameter, and film thickness. These effects stem from enhanced gas kinetic energy and shear intensity (promoting liquid film fragmentation), an increased fluid flow rate with glue pressure, and strengthened droplet resistance to breakup with suppressed spreading at higher viscosities. This research provides useful criteria for nozzle design and the optimization of industrial atomization processes involving non-Newtonian adhesives.
Thermodynamics, Descriptive and experimental mechanics
Raghav Ram, Martín López-de-Bertodano, James A. Howard
et al.
The two-fluid model (TFM) has become a foundational tool in numerical codes used for engineering analyses of two-phase flows in energy systems. However, its completeness remains a topic of debate because improper modeling of interfacial inertial coupling can render the momentum conservation equations elliptic. This issue leads to short wavelength perturbations growing at an infinite rate. This paper demonstrates the practical feasibility of incorporating variational inertial-coupling terms into an industrial CFD TFM code to ensure it is well-posed without the need for regularization. For verification, two special cases with exact analytical solutions of the TFM equations are utilized, exhibiting convergence at a mesh resolution of 1 mm.
Thermodynamics, Descriptive and experimental mechanics
Quantum correlations in the polarization degrees of freedom of the two-photon system have been extensively studied and form our current understanding of the quantum nature of our world. Most of the studies are concentrated on the low-energy (optical) photon pairs, for which efficient polarization measurement devices exist. However, for high-energetic (MeV) pairs of photons, e.g. produced in the decay of positronium atoms, no polarizers are available. Partial information about the polarization degree of freedom can be extracted by exploiting the measurements of photon pairs that undergo double Compton scattering. We present a Geant4-based Monte Carlo Vienna-Warsaw model capable of simulating any initial polarization state of bipartite photons. This puts us in a position to derive the behavior of the experimental observable, the angular difference $Δ\hatΦ$ formed by the two scattering planes. We validate our Vienna-Warsaw simulator with the high-statistics experimental sample -- based on a total of $3 \times 10^5 $ event candidates -- of two-photon pairs measured with the J-PET Big Barrel detector. We deduce the value of the squared visibility (interference contrast) encoding the polarization in the angle difference of the two scattering planes, $Δ\hatΦ$. The simulated spectra are in good agreement with the experimental correlation spectra and behave as predicted by theory.
July Andrea Gomez Camperos, Marlon Mauricio Hernández Cely, Aldo Pardo García
Accurately and instantly estimating the hydrodynamic characteristics in two-phase liquid–gas flow is crucial for industries like oil, gas, and other multiphase flow sectors to reduce costs and emissions, boost efficiency, and enhance operational safety. This type of flow involves constant slippage between gas and liquid phases caused by a deformable interface, resulting in changes in gas volumetric fraction and the creation of structures known as flow patterns. Empirical and numerical methods used for prediction often result in significant inaccuracies during scale-up processes. Different methodologies based on artificial intelligence (AI) are currently being applied to predict hydrodynamic characteristics in two-phase liquid–gas flow, which was corroborated with the bibliometric analysis where AI techniques were found to have been applied in flow pattern recognition, volumetric fraction determination for each fluid, and pressure gradient estimation. The results revealed that a total of 178 keywords in 70 articles, 29 of which reached the threshold (machine learning, flow pattern, two-phase flow, artificial intelligence, and neural networks as the high predominance), were published mainly in Flow Measurement and Instrumentation. This journal has the highest number of published articles related to the studied topic, with nine articles. The most relevant author is Efteknari-Zadeh, E, from the Institute of Optics and Quantum Electronics.
Thermodynamics, Descriptive and experimental mechanics
Mauricio De la Cruz-Ávila, Jorge E. De León-Ruiz, Ignacio Carvajal-Mariscal
et al.
This study investigates cavitation in a rectangular-profile Venturi tube using numerical simulations and four turbulence models. The unsteady Reynolds-averaged Navier–Stokes technique is employed to simulate vapor cloud formation and compared against experimental data. κ-ε realizable, κ-ε RNG, κ-ω SST, and κ-ω GEKO models are evaluated. The simulation results are analyzed for pressure, turbulence, and vapor cloud formation. Discrepancies in cavitation cloud formation among turbulence models are attributed to turbulence and vapor cloud interactions. RNG and SST models exhibit closer alignment with the experimental data, with RNG showing a superior performance. Key findings include significant vapor cloud shape differences across turbulence models. The RNG model best predicts velocity at the throat exit with an error of 4.145%. Static pressure predictions include an error of 4.47%. The vapor cloud length predictions show variation among models, with the RNG model having a 0.386% error for the minimum length and 4.9845% for the maximum length. The SST model exhibits 4.907% and 13.33% errors for minimum and maximum lengths, respectively. Analysis of the cavitation number reveals agreement with the experimental data and sensitivity to cavitation onset. Different turbulence models yield diverse cloud shapes and detachment points. Weber number contours illustrate the variation in the cavitation cloud behavior under different turbulence models.
Thermodynamics, Descriptive and experimental mechanics
Understanding the out-of-equilibrium dynamics of a closed quantum system driven across a quantum phase transition is an important problem with widespread implications for quantum state preparation and adiabatic algorithms. While the quantum Kibble-Zurek mechanism elucidates part of these dynamics, the subsequent and significant coarsening processes lie beyond its scope. Here, we develop a universal description of such coarsening dynamics -- and their interplay with the Kibble-Zurek mechanism -- in terms of scaling theories. Our comprehensive theoretical framework applies to a diverse set of ramp protocols and encompasses various coarsening scenarios involving both quantum and thermal fluctuations. Moreover, we highlight how such coarsening dynamics can be directly studied in today's "synthetic" quantum many-body systems, including Rydberg atom arrays, and present a detailed proposal for their experimental observation.
Maria Jabri, Younes Dehmani, Ilyasse Loulidi
et al.
This work explored the adsorption of Malachite Green (MG) dye by Acorn Pericarp (AP) in the context of biomass valorization. The Acorn Pericarp was analyzed by Fourier transform infrared spectroscopy (FTIR) and X-ray diffraction. The adsorption capacity under optimal experimental conditions was studied at different adsorbent doses, the initial concentration times of the dye and pH. The results presented in this work on the adsorption kinetics of MG showed that the pseudo-first-order model (R<sup>2</sup> = 0.9971) better described the adsorption kinetics at 10<sup>−5</sup> M. The experimental isotherms showed that Acorn Pericarp adsorption followed the Langmuir isotherm model (R<sup>2</sup> = 0.9889). The thermodynamic study showed that MG adsorption is endothermic (ΔH° > 0) and spontaneous (ΔG° < 0). For a sustainable industry, the sludge was converted into reinforcement of polystyrene using in-situ polymerization with 10% by weight of filler. A morphological and structural analysis was performed using SEM and FTIR, the results of characterization showed that the AP sludge was incorporated well into the PS matrix.
Thermodynamics, Descriptive and experimental mechanics
Jairo Eduardo Leiva Mateus, Marco Antonio Reyes Huesca, Federico Méndez Lavielle
et al.
The formation of flow-induced, oriented structures in two-phase systems, as in this study, is a phenomenon of considerable interest to the scientific and industrial sectors. The main difficulty in understanding the formation of bands of droplets is the simultaneous interplay of physicochemical, hydrodynamic, and mechanical effects. Additionally, banded structure materials frequently show multiple length scales covering several decades as a result of complex time-dependent stress fields. Here, to facilitate understanding a subset of these structures, we studied water in oil emulsions and focused on the effects of three variables specifically: the confinement factor<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mtext> </mtext><mo>(</mo><mi>C</mi><mi>o</mi><mo>=</mo><mn>2</mn><mi>R</mi><mo>/</mo><mi>H</mi><mo>)</mo></mrow></semantics></math></inline-formula>, the viscosity ratio <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>)</mo><mo>,</mo></mrow></semantics></math></inline-formula> and the applied shear rate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mover accent="true"><mrow><mi>γ</mi></mrow><mo>˙</mo></mover><mo>)</mo></mrow></semantics></math></inline-formula>. The confinement <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>C</mi><mi>o</mi><mo>)</mo></mrow></semantics></math></inline-formula> is the ratio between the drop’s diameter (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>R</mi></mrow></semantics></math></inline-formula>) and the separation of (the gap between) the circular rotating disks (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi></mrow></semantics></math></inline-formula>) containing the emulsion. We carried out (a) observations of the induced structure under different simple shear rates, as well as (b) statistical and morphological analysis of these bands. At low shear rates, the system self-assembles into bands along the direction of the flow and stacked normal to the velocity gradient direction. At higher shear rates is possible to observe bands normal to the vorticity direction. Here, we show that a detailed analysis of the dynamics of the band structures is amenable, as well as measurements of flow field anomalies simultaneously observed. The local emulsion viscosity varies in time, increasing in regions of higher droplet concentration and subsequently inducing velocity components perpendicular to the main flow direction. Thus, the emulsion morphology evolves and changes macroscopically. A relatively plausible explanation is attributed to the competitive effects of coalescence and the rupture of drops, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi></mrow></semantics></math></inline-formula> values less than one predominate coalescence.
Thermodynamics, Descriptive and experimental mechanics
We unify Brownian motion and quantum mechanics in a single mathematical framework. In particular, we show that non-relativistic quantum mechanics of a single spinless particle on a flat space can be described by a Wiener process that is rotated in the complex plane. We then extend this theory to relativistic stochastic theories on manifolds using the framework of second order geometry. As a byproduct, our results suggest that a consistent path integral based formulation of a quantum theory on a Lorentzian (Riemannian) manifold requires an Ito deformation of the Poincare (Galilean) symmetry, arising due to the coupling of the quadratic variation to the affine connection.
Dinmukhamed Zhangaskanov, Sagidolla Batay, Bagdaulet Kamalov
et al.
With increased interest in renewable energy, the power capacity of wind turbines is constantly increasing, which leads to increased rotor sizes. With ever larger rotor diameters, the complex and non-linear fluid-structure interaction (FSI) effects on wind turbine aerodynamic performances become significant, which can be fully studied using hi-fidelity 2-way FSI simulation. In this study, a two-way FSI model is developed and implemented in Openfoam to investigate the FSI effects on the NREL Phase VI wind turbine. The fully structured multiblock (MB) mesh method is used for the fluid and solid domains to achieve good accuracy. A coupling method based on the ALE is developed to ensure rotation and deformation can happen simultaneously and smoothly. The simulation results show that hi-fidelity CFD (Computational Fluid Dynamics) and CSD (Computational Structural Dynamics) -based 2-way FSI simulation provides high accurate results for wind turbine simulation and multi-disciplinary design optimization (MDO).
Thermodynamics, Descriptive and experimental mechanics
Chris Sungkyun Bang, Zeeshan A. Rana, László Könözsy
et al.
This research paper focuses on a novel coupling of the aerodynamic and structural behaviour of a double-element composite front wing of a Formula One (F1) vehicle, which was simulated and studied for the first time here. To achieve this goal, a modified two-way coupling method was employed in the context of high performance computing (HPC) to simulate a steady-state fluid-structure interaction (FSI) configuration using the ANSYS software package. The front wing plays a key role in generating aerodynamic forces and controlling the fresh airflow to maximise the aerodynamic performance of an F1 car. Therefore, the composite front wing becomes deflected under aerodynamic loading conditions due to its elastic behaviour which can lead to changes in the flow field and the aerodynamic performance of the wing. To reduce the uncertainty of the simulations, a grid sensitivity study and the assessment of different engineering turbulence models were carried out. The practical contribution of our investigations is the quantification of the coupled effect of the aerodynamic and structural performance of the wing and an understanding of the influence of ride heights on the ground effect. It was found that the obtained numerical surface pressure distributions, the aerodynamic forces, and the wake profiles show an accurate agreement with experimental data taken from the literature.
Thermodynamics, Descriptive and experimental mechanics
Rahul Deshpande, Dileep Chandran, Alexander J. Smits
et al.
We investigate the role of inter-scale interactions in the high-Reynolds number skin-friction drag reduction strategy reported by Marusic et al. (Nat. Commun., vol. 12, 2021). The strategy involves imposing relatively low-frequency streamwise travelling waves of spanwise velocity at the wall to actuate the drag generating outer-scales. This approach has proven to be more energy-efficient than the conventional method of directly targeting the drag producing inner-scales, which typically requires actuation at higher frequencies. Notably, it is observed that actuating the outer-scales at low frequencies leads to a substantial attenuation of the major drag producing inner-scales, suggesting that the actuations affect the non-linear inner-outer coupling inherently existing in wall-bounded flows. In the present study, we find that increased drag reduction, through imposition of spanwise wall oscillations, is always associated with an increased coupling between the inner and outer scales. This enhanced coupling emerges through manipulation of the phase relationships between these triadically linked scales, with the actuation forcing the entire range of energy-containing scales, from the inner (viscous) to the outer (inertial) scales, to be more in-phase. We also find that a similar enhancement of this non-linear coupling, via manipulation of the inter-scale phase relationships, occurs with increasing Reynolds number for canonical turbulent boundary layers. This indicates improved efficacy of the energy-efficient drag reduction strategy at very high Reynolds numbers, where the energised outer-scales are known to more strongly superimpose and modulate the inner-scales. Leveraging the inter-scale interactions, therefore, offers a plausible mechanism for achieving energy-efficient drag reduction at high Reynolds numbers.
Dmitry Kachulin, Sergey Dremov, Alexander Dyachenko
This article presents a study of bound periodically oscillating coherent structures arising on the free surface of deep water. Such structures resemble the well known bi-soliton solution of the nonlinear Schrödinger equation. The research was carried out in the super-compact Dyachenko-Zakharov equation model for unidirectional deep water waves and the full system of nonlinear equations for potential flows of an ideal incompressible fluid written in conformal variables. The special numerical algorithm that includes a damping procedure of radiation and velocity adjusting was used for obtaining such bound structures. The results showed that in both nonlinear models for deep water waves after the damping is turned off, a periodically oscillating bound structure remains on the fluid surface and propagates stably over hundreds of thousands of characteristic wave periods without losing energy.
Thermodynamics, Descriptive and experimental mechanics
The linear stability theory of wind-wave generation is revisited with an emphasis on the generation of wave groups. The outcome is the fundamental requirement that the group move with a real-valued group velocity. This implies that both the wave frequency and the wavenumber should be complex-valued, and in turn this then leads to a growth rate in the reference frame moving with the group velocity which is in general different from the temporal growth rate. In the weakly nonlinear regime, the amplitude envelope of the wave group is governed by a forced nonlinear Schrödinger equation. The effect of the wind forcing term is to enhance modulation instability both in terms of the wave growth and in terms of the domain of instability in the modulation wavenumber space. Also, the soliton solution for the wave envelope grows in amplitude at twice the linear growth rate.
Thermodynamics, Descriptive and experimental mechanics
James Yang, Patrik Andreasson, Penghua Teng
et al.
Most of the hydropower dams in Sweden were built before 1980. The present dam-safety guidelines have resulted in higher design floods than their spillway discharge capacity and the need for structural upgrades. This has led to renewed laboratory model tests. For some dams, even computational fluid dynamics (CFD) simulations are performed. This provides the possibility to compare the spillway discharge data between the model tests performed a few decades apart. The paper presents the hydropower development, the needs for the ongoing dam rehabilitations and the history of physical hydraulic modeling in Sweden. More than 20 spillways, both surface and bottom types, are analyzed to evaluate their discharge modeling accuracy. The past and present model tests are compared with each other and with the CFD results if available. Discrepancies do exist in the discharges between the model tests made a few decades apart. The differences fall within the range −8.3%–+11.2%. The reasons for the discrepancies are sought from several aspects. The primary source of the errors is seemingly the model construction quality and flow measurement method. The machine milling technique and 3D printing reduce the source of construction errors and improve the model quality. Results of the CFD simulations differ, at the maximum, by 3.8% from the physical tests. They are conducted without knowledge of the physical model results in advance. Following the best practice guidelines, CFD should generate results of decent accuracy for discharge prediction.
Thermodynamics, Descriptive and experimental mechanics
This paper addresses the kinematic and dynamic modelling and analysis for a robot arm consisting of two hydraulic cylinders driving two revolute joints of the arm. The two cylinders and relevant links of the robot constitute two local closed kinematic chains added to the main robot mechanism. Therefore, the number of the generalized coordinates of the mechanical system is increased, and the mathematical modelling is more complex that requires a formulation of constraint equations with respect to the local closed chains. By using the Lagrangian formulation with Lagrangian Multipliers, the dynamic equations are first derived with respect to all extended generalized coordinates. Then a compact form of the dynamic equations is yielded by canceling the Multipliers. Since the obtained dynamic equations are expressed in terms of independent generalized coordinates which are selected according to active joint variables of the arm, the equations could be best suitable for control law design and implementation. The simulation of the forward and inverse kinematics and dynamics of the arm demonstrates the motion behavior of the robot system.
Mechanical engineering and machinery, Descriptive and experimental mechanics