Hydrodynamic Theory Research Articles

Анализ параметров ударных волн на стенке взрывной полости при преломлении детонационных волн через воздушную и водную среду

Анализ параметров ударных волн на стенке взрывной полости при преломлении детонационных волн через воздушную и водную среду

Multiscale heat transport with inertia and thermal vortices

In this paper, we present a Hamiltonian and thermodynamic theory of heat transport on various levels of description. Transport of heat is formulated within kinetic theory of polarized phonons, kinetic theory of unpolarized phonons, hydrodynamics of polarized phonons, and hydrodynamics of unpolarized phonons. These various levels of description are linked by Poisson reductions, where no linearizations are made. Consequently, we obtain a new phonon hydrodynamics that contains convective terms dependent on vorticity of the heat flux, which are missing in the standard theories of phonon hydrodynamics. Within the zero-order Chapman-Enskog reduction, the resulting hydrodynamic equations are hyperbolic and Galilean invariant, while the first Chapman-Enskog expansion gives additional viscous-like terms. The vorticity-dependent terms violate the alignment of the heat flux with the temperature gradient even in the stationary state, which is expressed by a Fourier-Crocco equation. Those terms also cause that temperature plays in heat transport a similar role as pressure in aerodynamics, which is illustrated on numerical simulations of flow past a cylinder. In particular, we show that the vorticity-dependent terms lead to a colder spot just behind the cylinder, and for high-enough Reynolds numbers they lead to the von Kármán vortex street.

U(1) quasi-hydrodynamics: Schwinger-Keldysh effective field theory and holography

We study the quasi-hydrodynamics of a system with a softly broken U(1) global symmetry using effective field theory (EFT) and holographic methods. In the gravity side, we consider a holographic Proca model in the limit of small bulk mass, which is responsible for a controllable explicit breaking of the U(1) global symmetry in the boundary field theory. We perform a holographic Schwinger-Keldysh analysis, which allows us to derive the form of the boundary effective action in presence of dissipation. We compare our results with the previously proposed EFT and hydrodynamic theories, and we confirm their validity by computing the low-energy quasi-normal modes spectrum analytically and numerically. Additionally, we derive the broken holographic Ward identity for the U(1) current, and discuss the recently proposed novel transport coefficients for systems with explicitly broken symmetries. The setup considered is expected to serve as a toy model for more realistic situations where quasi-hydrodynamics is at work, such as axial charge relaxation in QCD, spin relaxation in relativistic systems, electric field relaxation in magneto-hydrodynamics, or momentum relaxation in condensed matter systems.

Active XY model on a substrate: Density fluctuations and phase ordering.

We explore the generic long-wavelength properties of an active XY model on a substrate, consisting of a collection of nearly phase-ordered active XY spins in contact with a diffusing, conserved species, as a representative system of active spinners with a conservation law. The spins rotate actively in response to the local density fluctuations and local phase differences, on a solid substrate. We investigate this system by Monte Carlo simulations of an agent-based model, which we set up, complemented by the hydrodynamic theory for the system. We demonstrate that this system can phase-synchronize without any hydrodynamic interactions. Our combined numerical and analytical studies show that this model, when stable, displays hitherto unstudied scaling behavior: As a consequence of the interplay between the mobility, active rotation, and number conservation, such a system can be stable over a wide range of the model parameters characterized by a novel correspondence between the phase and density fluctuations. In different regions of the phase space where the phase-ordered system is stable, it displays generalized quasi-long-range order (QLRO): It shows phase ordering which is generically either logarithmically stronger than the conventional QLRO found in its equilibrium limit, together with "miniscule number fluctuations," or logarithmically weaker than QLRO along with "giant number fluctuations," showing a novel one-to-one correspondence between phase ordering and density fluctuations in the ordered states. Intriguingly, these scaling exponents are found to depend explicitly on the model parameters. We further show that in other parameter regimes there are no stable, ordered phases. Instead, two distinct types of disordered states with short-range phase order are found, characterized by the presence or absence of stable clusters of finite sizes. In a surprising connection, the hydrodynamic theory for this model also describes the fluctuations in a Kardar-Parisi-Zhang (KPZ) surface with a conserved species on it, or an active fluid membrane with a finite tension, without momentum conservation and a conserved species living on it. This implies the existence of stable fluctuating surfaces that are only logarithmically smoother or rougher than the Edward-Wilkinson surface at two dimensions (2D) can exist, in contrast to the 2D pure KPZ-like "rough" surfaces.

Characterization of magneto-thermo-hydrodynamic lubrication of metal liquid film at armature/rail interface

Utilizing the magneto-thermo-hydrodynamic lubrication theory, this study investigates the armature/rail(A/R) interface under high-intensity currents and transient high-temperature conditions. A magneto-thermo-hydrodynamic lubrication model is established using the finite difference method, coupling electromagnetic field, temperature field, and hydrodynamic lubrication theory, to depict the lubrication mechanism of the A/R interface under the influence of electromagnetic and thermal interactions. The characteristics of magneto-thermal diffusion for the armature/ rail, and the dynamic lubrication properties of the metal liquid film at the interface, are analyzed, to investigate how to improve the contact state of the A/R interface and enhance the stability of the electromagnetic rail launch. The findings are of significant importance for predicting frictional and thermal losses at the A/R interface and enhancing its performance.

Mathematical Model to Study the Squeeze Film Characteristics of Diseased Human Synovial Knee Joint

Synovial fluid functions as a biological lubricant and lubricates articular cartilage to reduce friction and wear. Lubricin and hyaluronic acid are the primary components of synovial fluid responsible for its lubricating properties. The loss of properties in synovial fluid and articular cartilage due to aging and activities can restrict mobility in synovial joints, resulting in the degradation of articular cartilage and ultimately leading to pathological synovial joints, which is a major cause of disability. Thus, research on synovial joints remains crucial, and despite previous investigations on synovial joint lubrication, there are several issues related to squeeze film lubrication that require further attention. The Newtonian model of squeeze film lubrication in synovial joints needs to be extensively studied. In this study, lubrication and other related properties of synovial fluid are studied theoretically. In this paper, we have studied the flow of synovial fluid in the diseased synovial joint. Further, we have studied the effect of the viscosity of the synovial fluid, the permeability of articular cartilage, thickness of articular cartilage, and fluid film thickness on the characteristic of the squeeze film formed between the articular cartilages of the diseased human knee joint. The flow of synovial fluid is modeled by considering it as a viscous, incompressible and Newtonian fluid. We have derived the modified Reynolds equation using the principle of hydrodynamic lubrication and continuum mechanics theory and solved it by applying the suitable boundary conditions according to the physical considerations. Subsequently, we obtained the expression for pressure distribution in fluid film, load-bearing capacity, and squeeze time and have done the theoretical analysis on these properties for different parameters. Pressure increases with squeeze velocity and viscosity of the synovial fluid and decreases with permeability and fluid film thickness. Human knee joint becomes diseased due to excessive pressure, and the mobility of the knee joint decreases. The load capacity increases with viscosity and squeeze velocity and decreases with permeability resulting in the reduction of the load-carrying capacity of the knee joint in diseased conditions. Moreover, the squeeze time also increased in the diseased state of the joint.

Hydrodynamic theories for a system of weakly self-interacting classical ultrarelativistic scalar particles: Microscopic derivations and attractors

Hydrodynamic theories for a system of weakly self-interacting classical ultrarelativistic scalar particles: Microscopic derivations and attractors

Phase transitions in rotating binary Bose–Einstein condensates with Spin–orbit and Rabi couplings

We present the phase transition analysis of binary Bose–Einstein condensates (BECs) with spin–orbit (SO) and Rabi couplings in quasi-two-dimensional system under rotation. In particular, we investigate the superfluid properties induced by rotation and SO coupling within hydrodynamic theory which can explain the emergence of the domain wall. By calculating the evolution of angular momentum with respect to rotation frequency, we discover first-order phase transitions where the domain wall changes into the wall-vortex complex. On the other hand, the angular momentum changes continuously with SO coupling strength accompanying by the elongation of the domain wall along x-direction. When the Rabi coupling strength exceeds a critical value, we observe a transition from the domain wall to vortex lattice resulting from a significant change of angular momentum. A phase diagram demonstrating the boundary regime in the plane of SO and Rabi coupling strengths is obtained. Our result is not only motivated by the search for novel states of matter inaccessible to existing experiments, but also by the need to identify situations where the phase transitions can be benchmarked systematically.

2-group global symmetries, hydrodynamics and holography

2-group global symmetries are a particular example of how higher-form and conventional global symmetries can fuse together into a larger structure. We construct a theory of hydrodynamics describing the finite-temperature realization of a 2-group global symmetry composed out of U(1)U(1) zero-form and U(1)U(1) one-form symmetries. We study aspects of the thermodynamics from a Euclidean partition function and derive constitutive relations for ideal hydrodynamics from various points of view. Novel features of the resulting theory include an analogue of the chiral magnetic effect and a chiral sound mode propagating along magnetic field lines. We also discuss a minimalist holographic description of a theory dual to 2-group global symmetry and verify predictions from hydrodynamic descriptions. Along the way we clarify some aspects of symmetry breaking in higher-form theories at finite temperature.

Thermal insulation performance and dynamic response of anti-freeze subgrade of high-speed railway in seasonally frozen regions

In order to counteract the adverse effects of seasonally frozen regions, measures need to be taken to insulate high-speed railway subgrades and implement anti-freeze structures. The present study delves into this topic by analyzing the thermal–mechanical behaviors of railway subgrade through on-site measured data. Then, using the hydrodynamic theory, a model of frozen soil with Multi-physical field coupling is built, on which the temperature field and frost heave development of six different subgrade structures are explored, and produces a vehicle-track-subgrade coupling dynamic model that is used to calculate the dynamic performance of vehicles and the dynamic response transfer between subgrade layers under the influence of different anti-freeze subgrade structures. The results show that the subgrade structure built using concrete insulation (asphalt concrete (AC) or cellular concrete (CC)) + cement stabilized crushed stone (CSCS) + polyurethane (PU) panel mitigates the impact of external air temperatures and internal cooling, helping to reduce the maximum frost heave while simultaneously achieving improved thermal insulation. Further, these anti-freeze subgrade structures also bolster the safety and stability of high-speed railway vehicle operations. Therefore, it is suggested that the “concrete insulation layer + CSCS layer + PU panel” structures be utilized as a reference during the design of subgrade structures in seasonally frozen regions.

Molecular hydrodynamic theory of the velocity autocorrelation function.

The velocity autocorrelation function (VACF) encapsulates extensive information about a fluid's molecular-structural and hydrodynamic properties. We address the following fundamental question: How well can a purely hydrodynamic description recover the molecular features of a fluid as exhibited by the VACF? To this end, we formulate a bona fide hydrodynamic theory of the tagged-particle VACF for simple fluids. Our approach is distinguished from previous efforts in two key ways: collective hydrodynamic modes and tagged-particle self-motion are modeled by linear hydrodynamic equations; the fluid's spatial velocity power spectrum is identified as a necessary initial condition for the momentum current correlation. This formulation leads to a natural physical interpretation of the VACF as a superposition of products of quasinormal hydrodynamic modes weighted commensurately with the spatial velocity power spectrum, the latter of which appears to physically bridge continuum hydrodynamical behavior and discrete-particle kinetics. The methodology yields VACF calculations quantitatively on par with existing approaches for liquid noble gases and alkali metals. Furthermore, we obtain a new, hydrodynamic form of the self-intermediate scattering function whose description has been extended to low densities where the Schmidt number is of order unity; various calculations are performed for gaseous and supercritical argon to support the general validity of the theory. Excellent quantitative agreement is obtained with recent MD calculations for a dense supercritical Lennard-Jones fluid.

NUMERICAL METHOD FOR ASSESSING EFFICIENCY OF WAVE ENERGY CONVERTOR INTEGRATED INTO COASTAL PROTECTION STRUCTURES

The use of wave energy by converting it into electricity depends on the efficiency of wave energy converters, which are negatively affected by marine factors. Many design flaws can be eliminated at the stage of design and testing of devices by using its numerical models based on the application of the hydrodynamic theory of propagation and interaction of waves with marine structures. The use of the modern computational methods of hydrodynamics to determine the influence of some design factors of wave energy converters incorporated into a submerged breakwater is considered in the paper. The results of numerical studies showed that if a submerged breakwater is located in the wave stream and with a transducer installed on its crest, there is a change in flow velocities and pressure in the transducer chamber, which affects the efficiency of energy extraction. Additional advantages arise as a result of the introduction of a complex structure with coastal protection and power supply functions. The obtained calculation results visualize the qualitative indicator of the influence of the design factors of the converter. Additional conclusions can be obtained by processing the numerical results. As a result of numerical experiments conducted with using REEF3D CFD computer system, the measures for selecting the parameters of the converters were proposed based on mathematical modeling of specific structures. The research related to the determination of the mechanisms of wave energy transformation when interacting with coastal protection elements focused on increasing the efficiency of the convertor by locating in deeper water, which includes detailed testing, investigations and improvement of various types of constructions, is carried out on the computing and laboratory base of Institute of Hydromechanics.

Dependence of ion charge-energy emission from Nd:YAG-laser-produced plasma on laser intensity in the 0.4–40×1010 W/cm2 range

We experimentally characterize the ionic emission, including the individual charge states Snz+ (z=1, …, 8), from laser-produced tin plasma as a function of the intensity of the employed ns-pulsed laser. The plasma is generated in a vacuum from tin microdroplets (diameter ranging from 17 to 35 μm) using pulsed Nd:YAG laser light (laser wavelength λ=1.064 μm) over a range of intensities (0.4–40×1010 W/cm2). We measure charge-state-resolved and integrated ion energy distributions at seven angular positions around the plasma using seven retarding field analyzers. We highlight peak features in both types of spectra and describe the dependence of their energies on laser intensity with power-law functions. The resulting power laws match those derived from plasma radiation hydrodynamics theory. The analytical scaling laws exhibit strong isotropy, while the ion energy spectra are highly anisotropic.

Super-diffusion and crossover from diffusive to anomalous transport in a one-dimensional system

We study transport in a one-dimensional lattice system with two conserved quantities - “volume” and energy. Considering a slowly evolving local equilibrium state that is slightly deviated from an underlying global equilibrium, we estimate the correction to the local equilibrium distribution. This correction arises mainly through the space-time correlations of some local currents. In the continuum limit, we show that the local equilibrium distribution along with the correction yields drift-diffusion equation for the “volume” and super-diffusion equation for the energy in the linear response regime as macroscopic hydrodynamics as one would obtain from non-linear fluctuating hydrodynamic theory. We find explicit expression of the super-diffusion equation. Further, we find diffusive correction to the super-diffusive evolution. Such a correction allows us to study a crossover from diffusive to anomalous transport. We demonstrate this crossover numerically through the spreading of an initially localized heat pulse in equilibrium as well as through the system size scaling of the stationary current in non-equilibrium steady state.

Flow dynamics in rivers with riffle-pool morphology: a dataset from case studies and field experiments

Bars and pools, common for natural riverbeds, form sequential patterns due to interactions between river flow, alluvium and vegetation. While the morphodynamics of bar-pool units are relatively well understood, far less is known about associated riffle-pool hydrodynamics because of a lack of high-resolution data collected in rivers and problems attaining natural scaling in laboratory studies. Here we present a dataset on turbulent flow structure in riffle-pool sequences of a natural river. Two case studies and two field-based experiments were carried out in a side branch of the braided gravel-bed Tagliamento River in Italy. Our case studies deliver detailed information about the three-dimensional structure of mean and turbulent flows in natural riffle-pool/run and pool-riffle/glide transitions. Field-based experiments completed with the in-stream flume models of a riffle-pool transition and a shallow jet model provide a methodological bridge for linking simplified hydrodynamic theories of shallow jets to complex flow structure documented by our case studies. Therefore, this dataset enables examination of scaling effects and can be widely used for validation of numerical models.

Jamming and flocking in the restricted active Potts model.

We study the active Potts model with either site occupancy restriction or on-site repulsion to explore jamming and kinetic arrest in a flocking model. The incorporation of such volume exclusion features leads to a surprisingly rich variety of self-organized spatial patterns. While bands and lanes of moving particles commonly occur without or under weak volume exclusion, strong volume exclusion along with low temperature, high activity, and large particle density facilitates jams due to motility-induced phase separation. Through several phase diagrams, we identify the phase boundaries separating the jammed and free-flowing phases and study the transition between these phases which provide us with both qualitative and quantitative predictions of how jamming might be delayed or dissolved. We further formulate and analyze a hydrodynamic theory for the restricted APM which predicts various features of the microscopic model.

Ensemble averaging in JT gravity from entanglement in Matrix Quantum Mechanics

We consider the generalization of a matrix integral with arbitrary spectral curve ρ0(E) to a 0+1D theory of matrix quantum mechanics (MQM). Using recent techniques for 1D quantum systems at large-N, we formulate a hydrodynamical effective theory for the eigenvalues. The result is a simple 2D free boson BCFT on a curved background, describing the quantum fluctuations of the eigenvalues around ρ0(E), which is now the large-N limit of the quantum expectation value of the eigenvalue density operator hat{rho}(E) .The average over the ensemble of random matrices becomes a quantum expectation value. Equal-time density correlations reproduce the results (including non-perturbative corrections) of random matrix theory. This suggests an interpretation of JT gravity as dual to a one-time-point reduction of MQM.As an application, we compute the Rényi entropy associated to a bipartition of the eigenvalues. We match a previous result by Hartnoll and Mazenc for the c = 1 matrix model dual to two-dimensional string theory and extend it to arbitrary ρ0(E). The hydrodynamical theory provides a clear picture of the emergence of spacetime in two dimensional string theory. The entropy is naturally finite and displays a large amount of short range entanglement, proportional to the microcanonical entropy. We also compute the reduced density matrix for a subset of n < N eigenvalues.

Hydrodynamic heat transfer in solids

In solids, hydrodynamics have been observed in both amorphous and crystalline materials under a wide range of conditions. However, its fundamental physics is still unclear. Recent advancements in nanotechnology, biomedicine and electronics have reinvigorated interest in research on hydrodynamic solids. Here, we established the hydrodynamic transport in solids from solid mechanics. We showed that isentropically, a solid becomes superfluid locally in space and time when subjected to periodic motions, and at resonance, the first and second sound are generated. We validated the speed of the second sound against the velocity of S waves, and the agreement is satisfactory. From the concept of the boundary of the second law, we established the boundary conditions for the governing equations of the supersolid and obtained the transient and steady-state solutions of the supersolid. The theory agrees well with the measured flash temperature of the bulk metallic glass (BMG), which elucidates the physics why thermocouples do not measure flash temperature accurately. The finding shall lead to the review of the adequacy of instrumentation where temperature measurement is critical. The validation of the steady-state solution was carried out by comparison to the interfacial thermal conductance (ITC) on solid-solid interfaces. The first dataset has metal-metal interfaces with variable pressures, and the second dataset has metal-dielectric interfaces with variable temperatures, whose ITC differs by 4 orders of magnitude. We discuss the physics of this difference. We believe that the theory of hydrodynamics in solids provides insights for a vast number of disciplines and that the methods and solutions can help practitioners.

Current fluctuations in a semi-infinite line

We present the application of a fluctuating hydrodynamic theory to study current fluctuations in diffusive systems on a semi-infinite line in contact with a reservoir with slow coupling. We show that the distribution of the time-integrated current across the boundary at large times follows a large deviation principle with a rate function that depends on the coupling strength with the reservoir. The system exhibits a long-term memory of its initial state, which was earlier reported on an infinite line and can be described using quenched and annealed averages of the initial state. We present an explicit expression for the rate function for independent particles, which we verify using an exact solution of the microscopic dynamics. For the symmetric simple exclusion process, we present expressions for the first three cumulants of both quenched and annealed averages.

Optical response of metallic nanostructures using quantum hydrodynamic theory and a hybridizable discontinuous Galerkin method

An accurate modeling of the optical interactions in metallic nanostructures with subnanometer features requires an accurate description of quantum effects at the scale of billions of atoms. At such scale, first-principle methods are not computationally viable. Quantum hydrodynamic theory (QHT) has emerged as a powerful method that includes nonlocal contributions of the kinetic energy and the spatial dependence of the electron density, and it can predict both plasmon energy and spill-out effects in large metal nanoparticles. In this paper, we introduce a hybridizable discontinuous Galerkin method for solving Maxwell's equations coupled with a QHT model in order to account for quantum effects in three-dimensional metallic nanostructures. The coupled system of Maxwell's equations and QHT model is not only nonlinear but also multi-scale due to the interaction between the micrometer electromagnetic waves and the nanometer cavities of metallic nanostructures. We present extensive numerical experiments to validate the QHT model and demonstrate the capability of the HDG method to provide accurate solutions in the presence of strong nonlinearities and multiple length scales. These results offer a possibility to enhance nonlinear optical effects or to harness quantum mechanical electron tunneling by engineering metallic nanostructures at the quantum level.