Hydrodynamic Theory Research Articles

Spinodal decomposition and phase separation in polar active matter.

We develop and study the hydrodynamic theory of flocking with autochemotaxis. This describes large collections of self-propelled entities all spontaneously moving in the same direction, each emitting a substance which attracts the others (e.g., ants). The theory combines features of the Keller-Segel model for autochemotaxis with the Toner-Tu theory of flocking. We find that sufficiently strong autochemotaxis leads to an instability of the uniformly moving state (the "flock"), in which bands of different density form moving parallel to the mean flock velocity with different speeds. This instability is, therefore, completely different from the well-known "banding instability," in which bands form perpendicular to the mean flock velocity. The bands we find, which are reminiscent of ant trails, coarsen over time to reach a phase-separated state, in which one high-density and one low-density band fill the entire system. The same instability, described by the same hydrodynamic theory, can occur in flocks phase separating due to any microscopic mechanism (e.g., sufficiently strong attractive interactions). Although in many ways analogous to equilibrium phase separation via spinodal decomposition, the two steady-state densities here are determined not by a common tangent construction, as in equilibrium, but by an uncommon tangent construction very similar to that found for motility-induced phase separation of disordered active particles. Our analytic theory agrees well with our numerical simulations of our equationsof motion.

Elastic and transport coefficients of the perfect hard-sphere crystal from the poles of the hydrodynamic spectral functions

The elastic and transport coefficients of a perfect face-centered cubic crystal of hard spheres are computed from the poles of the dynamic structure factor and of the spectral functions of transverse momentum density fluctuations. For such crystals, the relevant coefficients are the three isothermal elastic constants (C11T,C12T,C44T) , the heat conductivity κ, and the three viscosities (η11,η12,η44) (in Voigt’s notations), which are directly computed using molecular dynamics simulations. The elastic and transport coefficients are then compared to the values of the same coefficients obtained with the method of Helfand moments, showing good agreement and providing strong support for the microscopic hydrodynamic theory of perfect crystals based on the local-equilibrium approach.

Hydrodynamic correlation and spectral functions of perfect cubic crystals

We investigate the collective dynamics of the perfect cubic crystal by deriving from the hydrodynamic equations the time-dependent correlation and the spectral functions characterizing the fluctuations of mass and momentum densities. We show that the seven hydrodynamic modes of the perfect crystal can be identified from the resonances of these spectral functions. The comparison with those of a fluid is discussed. Using the numerical values of the thermodynamic, elastic, and transport coefficients computed in our previous paper (J Mabillard and P Gaspard 2024 J. Stat. Mech. 023208) for a system of hard spheres, the theoretical expressions for the correlation and spectral functions are compared to the same functions directly computed using molecular dynamics simulations. The excellent agreement between theory and simulation provides strong support for the microscopic hydrodynamic theory of perfect crystals based on the local-equilibrium approach. This work sheds light on the fundamental mechanisms governing the collective behavior of matter in the solid state.

Thermo-electric transport of dyonic Gubser-Rocha black holes

We study the thermo-electric transport coefficients of an extended version of the Gubser-Rocha model. After reviewing the two relaxation time model from holography and studying the effect of the magnetic field on thermo-electric transports from hydrodynamic theory, we present a new dilatonic dyonic asymptotically AdS black hole solution. Notice that S-duality plays an important role in finding the analytic solution with the magnetic field. Using the AdS/CMT dictionary, we analyze the electric and thermo-electric transport properties of the dual field theory. The resistivity and the Hall angle are both linear in T for fixed k/μ and B/μ2 for low temperatures. For fixed k/T and μ/T, the electric transport coefficients are strange metallic. The magnetoresistance is approximately quadratic in B for various choices of parametrizations. The Nernst signal is a bell-shaped function in terms of the magnetic field even when the momentum relaxation is strong.

Influence of Temperature on Rotational Dynamics of 3B7D2HC-2-one Molecule in Non-polar, Polar, and Polar Aprotic Solvents.

Rotational dynamics of 3-(3H-2l4-benzo[c]isothiazol-2-yl)-7-(diethylamino)-2H-chromen-2-one (3B7D2HC-2-one) is studied using steady-state fluorescence depolarization and time-resolved fluorescence techniques in non-polar, polar and polar aprotic solvents by varying temperatures. Computational calculations are performed using Gaussian 09 software. Over the general solvatochromic method, an advanced thermochromic shift method is used to estimate dipole moments. Experiment rotational diffusion of 3B7D2HC-2-one in methanol indicates slow rotation over the other two solvents. Further, experiment rotational diffusion is analyzed using hydrodynamic and Quasi-hydrodynamic theories. The observed reorientation time follows the trend as predicted by quasi-hydrodynamic models.

Arrhenius law for interacting diffusive systems.

Finding the mean time it takes for a particle to escape from a metastable state due to thermal fluctuations is a fundamental problem in physics, chemistry, and biology. Here, we consider the escape rate of interacting diffusive particles, from a deep potential trap within the framework of the macroscopic fluctuation theory-a nonequilibrium hydrodynamic theory. For systems without excluded volume, our investigation reveals adherence to the well-established Arrhenius law. However, in the presence of excluded volume, a universality class emerges, fundamentally altering the escape rate. Remarkably, the modified escape rate within this universality class is independent of the interactions at play. The universality class, demonstrating the importance of excluded volume effects, may bring insights to the interpretation of escape processes in the realm of chemical physics.

Navigating the Dynamics of Squeeze Film Dampers: Unraveling Stiffness and Damping Using a Dual Lens of Reynolds Equation and Neural Network Models for Sensitivity Analysis and Predictive Insights

The squeeze film damper (SFD) is proven to be highly effective in mitigating rotor vibration as it traverses the critical speed, thus making it extensively utilized in the aeroengine domain. In this paper, we investigate the stiffness and damping of SFD using the Reynolds equation and neural network models. Our specific focus includes examining the structural and operating parameters of SFDs, such as clearance, feed pressure of oil, rotor whirl, and rotational speed. Firstly, the pressure distribution analytical model of the oil film inside the SFD based on the hydrodynamic lubrication theory is established, as described by the Reynolds equation. It obtained oil film forces, pressure, stiffness, and damping values under various sets of structural, lubrication, and operating parameters, including length, clearance, boundary pressure at both sides, rotational speed, and whirling motion, by applying difference computations to the Reynolds equation. Secondly, according to the significant analyses of the obtained oil film stiffness and damping, the following three parameters of the most significance are found: clearance, rotational speed, and rotor whirl. Furthermore, neural network models, including GA-BP and decision tree models, are established based on the obtained results of difference computation. The numerical simulation and calculation of these models are then applied to show their validity with all given parameters and the three significant parameters separately as two sets of model input. Regardless of either set of model inputs, these established neural network models are capable of predicting the nonlinear stiffness and damping of the oil film inside an SFD. These sensitive parameters merely require measurement, followed by the utilization of a neural network to predict stiffness and damping instead of the Reynolds equation. This process serves structural enhancement, facilitates parameter optimization in SFDs, and provides crucial support for refining the design parameters of SFDs.

Approximate higher-form symmetries, topological defects, and dynamical phase transitions

Higher-form symmetries are a valuable tool for classifying topological phases of matter. However, emergent higher-form symmetries in interacting many-body systems are typically not exact due to the presence of topological defects. In this paper, we develop a systematic framework for building effective theories with approximate higher-form symmetries. We focus on a continuous U(1) q-form symmetry and study phases with various patterns of spontaneous and explicit symmetry breaking. We uncover a web of dualities between such phases and highlight their role in describing the presence of dynamical higher-form topological defects. In order to study the out-of-equilibrium dynamics of these phases of matter, we formulate respective hydrodynamic theories and study the spectra of excitations exhibiting higher-form charge relaxation and Goldstone relaxation effects. We show that our framework is able to describe various phase transitions due to proliferation of vortices or defects. This includes the melting transition in smectic crystals, the plasma phase transition from polarized gases to magnetohydrodynamics, the spin-ice transition, the superfluid to neutral fluid transition, and the Meissner effect in superconductors, among many others. Published by the American Physical Society 2024

Theory of nonlocal modal hydrodynamic functions for beam and plate vibrations in viscous fluids

In this paper, we introduce a new nonlocal modal hydrodynamic theory for fluid–structure interactions (FSI) of light, flexible cantilever beams and plates undergoing small amplitude vibrations in Newtonian, incompressible, viscous, heavy fluids otherwise at rest. For low aspect ratio flexible structures and high mode numbers, three dimensional (3D) and nonlocal fluid effects become prominent drivers of the coupled dynamics, to the point that existing local hydrodynamic theories based on two dimensional (2D) fluid approximations become inadequate to predict the system response. On the other hand, our approach is based on a rigorous, yet efficient, 3D treatment of the hydrodynamic loading on cantilevered thin structures. The off-line solution of the FSI problem results in the so-called nonlocal modal hydrodynamic function matrix, that is, the representation of the nonlocal hydrodynamic load operator on a basis formed by the structural modes. Our theory then integrates the nonlocal hydrodynamics within a fully coupled structural modal model in the frequency domain. We compare and discuss our theory predictions in terms of frequency response functions, mode shapes, hydrodynamic loads, quality factors, added mass ratios with the predictions of the classical local approaches, for different actuation scenarios, identifying the limitations of the hypotheses underlying existing treatments. Importantly, we also validate our new model with experiments conducted on flexible square plates. While computationally efficient, our fully coupled theory is exact up to numerical truncation and can bridge knowledge gaps in the design and analysis of FSI systems based on low aspect ratio flexible beams and plates.

Electro-hydrodynamic programming reshapes liquid crystal dynamics in free-form director fields

This study unveils a groundbreaking technique leveraging the superposition of electric field vectors to manipulate liquid crystals (LCs). Demonstrated through a simple configuration of four independent electrodes at the corners of a rectangular enclosure, notably, this configuration can be further simplified or modified as needed, showcasing the versatility of the approach. Significantly, the design showcased in the paper eliminates the need for an alignment layer, highlighting the versatility of the method. Through nuanced adjustments in waveforms, amplitudes, frequencies, and phases in AC or DC from these electrodes, precise control over LC shape deformation and dynamic phase transformation is achieved in both temporal and spatial dimensions. In contrast to traditional methods, the approach presented here abolishes alignment layers and intricate electrode-array systems, opting for a streamlined configuration with varying AC frequencies and DC electric signals. This innovative methodology, founded on simplified governing equations from Q-tensor hydrodynamics theory, demonstrates true 3D control over LCs, displaying efficiency in electrode usage beyond current arrays. The study's contributions extend to temporal control emphasis, superposition techniques, and the elimination of fixed electrodes, promising unprecedented possibilities for programming LC materials and advancing the field of programmable LC devices.

Analysis of Mixing Efficiency in a Stirred Reactor Using Computational Fluid Dynamics

Lead recycling is very important for reducing environmental pollution risks and damages. Liquid lead is recovered from exhaust batteries inside stirred batch reactors; the process requires melting to be cleaned. Nevertheless, it is necessary to establish parameters for evaluating mixing to improve the efficiency of the industrial practices. Computational fluid dynamics (CFD) has become a powerful tool to analyze industrial processes for reducing operating costs, avoiding potential damages, and improving the equipment’s performance. Thus, the present work is focused on simulating the fluid hydrodynamics inside a lead-stirred reactor monitoring the distribution of an injected tracer in order to find the best injection point. Then, different injected points are placed on a control plane for evaluation; these are evaluated one by one by monitoring the tracer concentration at a group of points inside the batch. The analyzed reactor is a symmetrical, vertical batch reactor with two geometrical sections: one cylindrical body and a semi-spherical bottom. Here, one impeller with four flat blades in a shaft is used for lead stirring. The tracer concentration on the monitoring points is measured and averaged for evaluating the efficiency inside the tank reactor. Hydrodynamics theory and a comparison between the concentration profiles and distribution of tracer curves are used to demonstrate both methods’ similarities. Then, the invariability of the tracer concentration on the monitoring points is adopted as the main parameter to evaluate the mixing, and the best injection point is found as a function of the shortest mixing time. Additionally, the influence of the impeller rotation speed is analyzed as an additional control parameter to improve industrial practices.

Sustaining Quasi De-Sitter Inflation with Bulk Viscosity

The de-Sitter spacetime is a maximally symmetric Lorentzian manifold with constant positive scalar curvature that plays a fundamental role in modern cosmology. Here, we investigate bulk-viscosity-assisted quasi de-Sitter inflation, that is the period of accelerated expansion in the early universe during which −H˙≪H2, with H(t) being the Hubble expansion rate. We do so in the framework of a causal theory of relativistic hydrodynamics, which takes into account non-equilibrium effects associated with bulk viscosity, which may have been present as the early universe underwent an accelerated expansion. In this framework, the existence of a quasi de-Sitter universe emerges as a natural consequence of the presence of bulk viscosity, without requiring introducing additional scalar fields. As a result, the equation of state, determined by numerically solving the generalized momentum-conservation equation involving bulk viscosity pressure turns out to be time dependent. The transition timescale characterising its departure from an exact de-Sitter phase is intricately related to the magnitude of the bulk viscosity. We examine the properties of the new equation of state, as well as the transition timescale in the presence of bulk viscosity pressure. In addition, we construct a fluid description of inflation and demonstrate that, in the context of the causal formalism, it is equivalent to the scalar field theory of inflation. Our analysis also shows that the slow-roll conditions are realised in the bulk-viscosity-supported model of inflation. Finally, we examine the viability of our model by computing the inflationary observables, namely the spectral index and the tensor-to-scalar ratio of the curvature perturbations, and compare them with a number of different observations, finding good agreement in most cases.

Investigation of the crystal formation from calcium silicate in human dentinal tubules and the effect of phosphate buffer saline concentration

Background/purposeBased on hydrodynamic theory, blocking the dentinal tubules can reduce discomfort caused by dentin hypersensitivity. This study identified the crystals formed in dentinal tubules from tricalcium silicate (TCS) in phosphate-buffered saline (PBS) and evaluated the effect of PBS concentration on crystal formation. Materials and methodsSixty-nine specimens were made by isolating the cervical part of extracted premolars. TCS was applied by brushing for 10,000 strokes on dentin surface simulating sensitive dentin. Specimens were stored in PBS or solutions with concentrations 1/100, 1/10, 10, and 100 times that of PBS for 1, 30, 60, or 90 days (n = 3). Another nine specimens applied TCS, were immersed in PBS for 3 months, and divided into three subgroups: no treatment, sonication for 10 min, and 1M acetic acid treatment for 3 min. Crystal formation was examined using a scanning electron microscope, assigned five grade scores (0–4) according to maturation, and analyzed by a nonparametric two-way ANOVA (α = 0.05). Crystal components were analyzed using X-ray diffraction (XRD) and energy dispersion X-ray spectroscopy (EDS). ResultsThe maturation of intratubular crystals was dependent on time and PBS concentration (P < 0.05). In all periods, the high-concentration group showed a higher maturation grade than the low-concentration group. Intratubular crystals were similar to hydroxyapatite according to XRD and EDS, and they withstood sonication and acid application. ConclusionTCS with nanosized particles formed hydroxyapatite-like crystals in the dentinal tubules, which were dependent on time and concentration of PBS and withstood sonication and acid application.

Schwinger-Keldysh effective field theory for stable and causal relativistic hydrodynamics

We construct stable and causal effective field theories (EFTs) for describing statistical fluctuations in relativistic diffusion and relativistic hydrodynamics. These EFTs are fully non-linear, including couplings to background sources, and enable us to compute n-point time-ordered correlation functions including the effects of statistical fluctuations. The EFTs we construct are inspired by the Maxwell-Cattaneo model of relativistic diffusion and Müller-Israel-Stewart model of relativistic hydrodynamics respectively, and have been derived using both the Martin-Siggia-Rose and Schwinger-Keldysh formalisms. The EFTs non-linearly realise the dynamical Kubo-Martin-Schwinger (KMS) symmetry, which ensures that n-point correlation functions and interactions in the theory satisfy the appropriate fluctuation-dissipation theorems. Since these EFTs typically admit ultraviolet sectors that are not fixed by the low-energy infrared symmetries, we find that they simultaneously admit multiple realisations of the dynamical KMS symmetry. We also comment on certain obstructions to including statistical fluctuations in the recently-proposed stable and causal Bemfica-Disconzi-Noronha-Kovtun model of relativistic hydrodynamics.

Data Driven Model for a Fuel Cell stack development in a complex Multi-source Hybrid Renewable Energy System

Fuel cells based on polymer electrolyte membrane are considered as the most hopeful clean power technology. The operating principles of polymer electrolyte membrane fuel cells (PEMFC) system involve electrochemistry, thermodynamics and hydrodynamics theory for which it is difficult to establish a mathematical model. In this paper a nonlinear data driven model of a PEMFC stack is developed using Neural Networks (NNs). The model presented is a black-box model, based on a set of measurable exogenous inputs and is able to predict the output voltage and cathode temperature of a high power module working at the CNR- ITAE. A 5 kW PEM fuel cell stack is employed to experimentally investigate the dynamic behaviour and to reveal the most influential factors.

Nonlinear structure and growth rate of solitary waves for extended Zakharov-Kuznetsov equation in plasma having (r, q) distribution electrons

The Reductive Perturbation Technique (RPT) is used to investigate ion acoustic waves (IAWs) in magnetized plasmas made up of electrons obeying the generalized form of ( r,q ) distribution. The analysis makes use of the Extended Zakharov-Kuznetsov (EZK) equation and the hydrodynamic theory of plasmas. The study investigates the effects of electron flatness ( r ) at low energy and superthermal ( q ) at high energy on the characteristics of IAWs, and the solutions to the EZK equation are plotted for different values of the plasma characteristics, such as the total ion cyclotron frequency, the ion to electron temperature ratio, and the ion-specific heat. The research goes into great detail to estimate the instability threshold and growth rate of these waves by applying a small-k perturbation technique. Overall, this investigation contributes to the better understanding of ion acoustic structures in space plasmas.

Hydrodynamics and multiscale order in confluent epithelia.

We formulate a hydrodynamic theory of confluent epithelia: i.e. monolayers of epithelial cells adhering to each other without gaps. Taking advantage of recent progresses toward establishing a general hydrodynamic theory of p-atic liquid crystals, we demonstrate that collectively migrating epithelia feature both nematic (i.e. p = 2) and hexatic (i.e. p = 6) orders, with the former being dominant at large and the latter at small length scales. Such a remarkable multiscale liquid crystal order leaves a distinct signature in the system's structure factor, which exhibits two different power-law scaling regimes, reflecting both the hexagonal geometry of small cells clusters and the uniaxial structure of the global cellular flow. We support these analytical predictions with two different cell-resolved models of epithelia - i.e. the self-propelled Voronoi model and the multiphase field model - and highlight how momentum dissipation and noise influence the range of fluctuations at small length scales, thereby affecting the degree of cooperativity between cells. Our construction provides a theoretical framework to conceptualize the recent observation of multiscale order in layers of Madin-Darby canine kidney cells and pave the way for further theoretical developments.

Research of simulation and experiment on arc characteristics of gas mechanical switch

AbstractAn arc is the high‐temperature discharge plasma produced in the opening process of mechanical switches, which directly affects the breaking capability of a hybrid DC circuit breaker. According to the physical mechanism of an electric arc, the construction of an arc model for simulation analysis is an important technical means in the electrical field. In this study, based on the theory of magneto hydrodynamics (MHD), a gas mechanical switch model of a natural commutation DC circuit breaker with a compound gap is established. The arc motion process under different conditions is simulated and calculated. The influence of different initial pressures, different opening speeds, and different striking currents on the arc voltage characteristics is analysed. The results show that the larger the gas pressure, the smaller the arc volume and the higher the arc voltage. The faster the opening speed, the longer the arc and the higher the arc voltage; with the increase of the current, the arc voltage increases rapidly at a low current, while the arc voltage increases slowly at a high current.

Investigation on the Dynamic Pressure Effect of Clearance Oil Film at a Stepped Hydrostatic Thrust Bearing Working in Heavy Loading Duty

The dynamic pressure effect of the clearance oil film of stepped hydrostatic thrust bearing is studied by taking the double rectangular cavity oil cushion as an example. According to the hydrodynamics theory, the dynamic pressure of lubricating oil film in different clearance height regions is theoretically deduced and calculated. The dynamic pressure effect of the clearance oil film in the stepped hydrostatic thrust bearing is studied through the combination of theoretical calculation, simulation, and experimental verification. It is found that the experimental value of the dynamic pressure is between the theoretical value and the simulated value, which is basically not affected by the load. In the speed range of 0 r/min–200 r/min, compared with the viscosity of lubricating oil, the speed is the main factor affecting the dynamic pressure of the oil film of the stepped hydrostatic thrust bearing. The dynamic pressure value of the clearance oil film increases in a stepped fashion along the radial direction of the double rectangular cavity oil cushion. The dynamic pressure value has an obvious upward trend at the junction of the circumferential right oil cavity and the sealing edge and then decreases to 0 after reaching the peak value.

A new causal and stable theory of viscous chiral hydrodynamics

We construct the general theory of first-order relativistic hydrodynamics for a fluid exhibiting a chiral anomaly, including all possible viscous terms allowed by symmetry. Using standard techniques, we compute the necessary and sufficient conditions for this theory to be relativistically causal in the nonlinear regime and for thermal equilibria to be linearly stable. This is the first theory of first-order chiral hydrodynamics suitable for numerical simulations.