Hydrodynamic Approximation Research Articles

Kinetic contribution to the fast spinodal decomposition controlled by diffusion

Analysis of a model for fast spinodal decomposition controlled by diffusion is proposed. Using the concept of fast phase separation, an interpretation of a purely non-equilibrium contribution to the entropy of a spinodally decomposing system is given in terms of multi-component fluids and of magnetic dipole systems with non-vanishing inertia. Conditions for violation of the standard “hydrodynamic approximation” in the description of fast spinodal decomposition are formulated.

Effect of tensor g-factor on the spectrum of eigen modes in magnetoactive plasma

The influence of the tensorial nature of the gyromagnetic coupling on a spectrum of eigen modes in magnetoactive plasma is studied. A dispersion equation for waves propagating in such a medium is obtained in the approximation of frigid hydrodynamics.

Laser absorption and third-harmonic generation in free-electron nanofilms

The collective collisionless dynamics of the electron gas in free-electron nanofilms irradiated by an obliquely incident p-polarized laser wave are considered in the classical hydrodynamic and jellium-model approximations. The two cases of cold metallic nanofilms and hot free-electron nanofilms laser ionized and laser heated by a pump-laser prepulse are investigated with proper electron statistics. Both linear and nonlinear properties of the plasma resonance excitation in the nanofilms are studied in detail for different film parameters (film thickness, thickness of the diffuse film boundary, outer-ionization degree for hot laser-ionized/heated films, etc.). The significant role of the diffuse film boundaries for both linear absorption of the laser field and third-harmonic generation is demonstrated. For this goal, we do not use the standard dielectric-permittivity approach with boundary conditions between two different media but solve continuously over all space the full set of hydrodynamic and electrodynamic equations in nonrelativistic one-dimensional approximation. It is shown that collisionless edge absorption may be dominant in thin nanofilms, while in cold metal nanofilms it results in the appearance of several linear-absorption resonances below the bulk-plasma resonance frequency. For hot nanofilms, drastic broadening of the linear-plasma-resonance profile is obtained in calculations when the film thickness is reduced. In ourmore » model, the third-harmonic generation is determined by the density gradient in the diffuse film edges. Additional resonances in third-harmonic generation as a function of laser frequency are obtained for cold metal nanofilms. They differ from the standard third-order nonlinear resonance, which is located at one third of the plasma resonance frequency. The important role of the outer-ionization degree in forming the third-order nonlinear response of the hot laser-ionized film is also analyzed and discussed.« less

Linearized hydrodynamics from probe-sources in the gauge–string duality

We study the response of an infinite, asymptotically static N = 4 plasma to a generic localized source in the probe approximation. At large distances, the energy–momentum tensor of the plasma includes a term which satisfies the constitutive relations of linearized hydrodynamics, but it can also include a non-hydrodynamical term which contributes at the same order as viscous corrections, or even at leading order in some cases. The conditions for the appearance of a laminar wake far behind the source and its relevance for phenomenological models used to explain di-hadron correlations are discussed. We also consider the energy–momentum tensor near the source, where the hydrodynamical approximation can be expected to break down. Our analysis encompasses a wide range of sources which are localized in the bulk of AdS, including trailing strings, mesonic and baryonic configurations of strings, and point particles.

Characterization of Incipient Spall Damage in Shocked Copper Multicrystals

Correlations between spall damage and local microstructure were investigated in multicrystalline copper samples via impact tests conducted with laser-driven plates at low pressures (2—6 GPa). The copper samples had a large grain size as compared to the thickness, which was either 200 or 1000 μm, to isolate the effects of microstructure on the local response. Velocity interferometry was used to measure the bulk response of the free-surface velocity of the samples to monitor traditional spall tensile failure and to examine heterogeneities on the shock response due to microstructure variability from sample to sample. The shock pressure, dynamic yield strength and spall strength were determined from the measured velocity history via standard hydrodynamic approximations, while the effect of strength was explored via 1D hydrocode calculations. Electron Backscattering Diffraction, both in-plane and through-thickness, was used to relate crystallography to the presence of porosity around microstructural features such as grain boundaries and triple points. It was found that the dynamic yield strength measured from velocity histories in different samples correlated well with the crystallographic dependence reported for the dynamic yield strength in single crystals. Transgranular damage dominated in thin specimens with 230 μm grain size, where porosity appeared close to, but not exactly at, grain boundaries. However, a transition to dominant intergranular damage was observed as the grain size was reduced to 150 μm. Thick specimens (450 μm grain size) showed both modes, with intergranular damage found mostly where grains were smaller than average and the sites for preferred damage nucleation in these samples included grain boundaries and triple points. In particular, twin boundaries, especially tips of terminated twins, showed a large mismatch in surface displacements on the diagnostic surface as compared to the surrounding grains as well as a tendency for damage localization on the through-thickness sections.

Unified modelling of near-cathode plasma layers in high-pressure arc discharges

A model of a near-cathode region in high-pressure arc discharges is developed in the framework of the hydrodynamic (diffusion) approximation. Governing equations are solved numerically in 1D without any further simplifications, in particular, without explicitly dividing the near-cathode region into a space-charge sheath and a quasi-neutral plasma. Results of numerical simulation are reported for a very high-pressure mercury arc and an atmospheric-pressure argon arc. Physical mechanisms dominating different sections of the near-cathode region are identified. It is shown that the near-cathode space-charge sheath is of primary importance under conditions of practical interest. Physical bases of simplified models of the near-cathode region in high-pressure arc discharges are analysed. A comparison of results given by the present model with those given by a simplified model has revealed qualitative agreement; the agreement is not only qualitative but also quantitative in the case of an atmospheric-pressure argon plasma at moderate values of the near-cathode voltage drop. The modelling data are compared with results of spectroscopic measurements of the electron temperature and density in the near-cathode region.

Streamer head structure: role of ionization and photoionization

Results from experiments and numerical modelling of streamer propagation are presented. The 2D hydrodynamic numerical description of the pulsed discharge based on the local ionization and photoionization models adequately describes the streamer shape and dynamics over a wide range of pressures and voltages. This work presents a method for imaging the instantaneous emission distribution in the streamer head. A method for restoring the electrodynamic radius of the streamer head was developed on the basis of the streamer head images that were obtained with subnanosecond exposure time. The electrodynamic radius has been determined as the distance between the maxima of the electric field at the position where the streamer head transforms into the streamer channel. The dependence of the electrodynamic radius on voltage and pressure has been determined. We show that a 2D numerical model using hydrodynamic approximation predicts the streamer characteristics with an accuracy of about 15% in the 0.5–1 atmosphere pressure range and up to 40% in the 0.2–0.3 atmosphere pressure range for a voltage of U from 20 kV up to 40 kV in the 30 and 40 mm discharge gap.

Experimental analysis and modelling of positive streamer in air: towards an estimation of O and N radical production

This paper is mainly devoted to the comparison between the calculation and experimental results of primary and secondary streamer development in a point-to-plane positive corona discharge in dry air at atmospheric pressure. The qualitative agreement between experimental and calculation results based on the hydrodynamics approximation shows that the O radical is mainly produced in the secondary streamer which is in good agreement with the recent literature measurements using TALIF diagnostics. However, the O radical production yield (in terms of radicals produced per energy injected) is more efficient in the primary streamer than in the secondary one. The main positive corona discharge characteristics are revisited using fast electrical and optical ICCD and streak camera measurements. The calculation shows two streamer radii of, respectively, 10 µm (associated with the radial extension of a high electron density region) and 200 µm (corresponding to the extension of the radial space charge electric field).

Extension of the finite volume particle method to viscous flow

The finite volume particle method (FVPM) is a mesh-free method for fluid dynamics which allows simple and accurate implementation of boundary conditions and retains the conservation and consistency properties of classical finite volume methods. In this article, the FVPM is extended to viscous flows using a consistency-corrected smoothed particle hydrodynamics (SPH) approximation to evaluate velocity gradients. The accuracy of the viscous FVPM is improved by a higher-order discretisation of the inviscid flux combined with a second-order temporal discretisation. The higher-order inviscid FVPM is validated for a 1-D shock tube problem, in which it demonstrates an enhanced shock capturing ability. For two-dimensional simulations, a small arbitrary Lagrange–Euler correction to fully Lagrangian particle motion is beneficial in maintaining a favourable particle distribution over long simulation times. The viscous FVPM is validated for two-dimensional Poiseuille, Taylor–Green and lid-driven cavity flows, and good agreement is achieved with analytic or reference numerical solutions. These results establish the viability of FVPM as a tool for mesh-free simulation of viscous flows in engineering.

Non-local optical response of two-dimensional arrays of metallic nanoparticles

The optical absorption spectra of two-dimensional (2D) arrays of spatially dispersivemetallic nanoparticles is examined. The corresponding non-local dielectric functionof the spheres is provided by (a) the hydrodynamic approximation and (b) theLindhard theory. More specifically, it is shown that the adoption of either types ofnon-local dielectric functions (hydrodynamic or Lindhard-type) for dilute 2Darrays of spheres does not alter the structure of the optical absorption spectrumbut leads to a blue-shift of all its distinct features. This effect becomes moreprominent as the radius of the nanoparticles decreases. However, for a close-packedarrangement of spheres, a non-local dielectric function provides a significantlydifferent optical spectrum than the local one, due to the dominant role of near-fieldeffects, which strongly depend on the choice of the dielectric function of the metal.

Simulation of the oscillation dynamics and translational motion of ultrasound contrast agents

A numerical model has been developed to simulate the oscillatory dynamics and the translational motion of both free and encapsulated bubbles in an ultrasound field. The model allows for the compressibility of the surrounding liquid and the bubble shell, which makes it possible to model the bubble dynamics at high acoustic pressures. Simulations can be carried out either by solving Rayleigh-Plesset-type equations, or in the hydrodynamic approximation taking into account the rheological properties of the liquid and the shell, or by a combined method. In the latter case, the gas pressure at the bubble surface, which is found from the gas-dynamic problem, is used as an input parameter for Rayleigh-Plesset-type equations at every time layer. The resulting radius of the bubble is then used as the boundary condition for the gas-dynamic equations. The model is a handy and flexible tool to investigate the effect of different factors on the oscillatory dynamics of the bubble, such as the thickness of the bubble shell, the rheological properties of the shell, and the translational displacement of the bubble. Using the developed model, the resonance frequency and translational displacement of contrast agents were numerically estimated.

Linear and nonlinear pulsation models with the variable Eddington factor approximation of radiative hydrodynamics

Context. Linear and also nonlinear pulsation models with the variable Eddington factor approximation of the radiative transfer are constructed. Aims. The aim of the study is to apply hydrodynamic models of radial pulsation to the observed variability in some post-AGB stars. It has been shown that the pulsation behavior could be strongly effected by the radiative field of the envelope of these stars because of high luminosity in these low mass supergiant stars. Thus, it is important to treat the radiative field with a higher approximation than the diffusion approximation which has been used successfully in classical Cepheids. Methods. The moment equations of radiative transfer are integrated into the hydrodynamic equations with a variable Eddington factor. The factor is calculated independently by solving the transfer equation of spherical geometry. The linear eigen value problem of the radial perturbation from hydrostatic equilibrium is solved, and nonlinear simulations of radial pulsation are performed with the same approximation of the radiative transfer. The method is applied to pulsation of low mass supergiant stars and, for comparison, classical Cepheids. Results. The properties of the strange modes that appear often in low mass supergiant star models e.g. post-AGB stars are seriously affected by different treatments of the radiative field in the linear analyses and nonlinear simulations.

Radiative damping of standing acoustic waves in solar coronal loops

Context. A detailed understanding of the physical processes that determine the damping timescales of magneto-acoustic waves is essential to interpret diagnostic results from the application of solar magneto-seismology. Aims. The influence of the transition region and the importance of radiative emission, arising from equilibrium and non-equilibrium ionisation balances, for the damping timescale of the fundamental mode standing acoustic wave is investigated. Methods. An extensive numerical study, in the framework of the field-aligned hydrodynamic approximation, is carried out of the damping of the fundamental mode standing wave in a solar coronal loop, for a wide range of loop lengths and apex temperatures. Results. It was found that the radiative emission arising from a non-equilibrium ionisation balance will always act to reduce the damping timescale (in comparison to the equilibrium case) and may do so by up to ∼10%. The physics of the transition region is most crucial in determining the magnitude of the reduction of the damping timescale when a non-equilibrium ionisation balance is properly accounted for. Conclusions. The methods of solar magneto-seismology, in particular the tools of coronal seismology, may be used to estimate loop lengths to a reasonable degree of accuracy, although estimates of the apex temperature are significantly less reliable, and one should use alternative (e.g. spectroscopic) diagnostics instead.

Universality of the diffusion wake in the gauge-string duality

As a particle moves through a fluid, it may generate a laminar wake behind it. In the gauge-string duality, we show that such a diffusion wake is created by a heavy quark moving through a thermal plasma and that it has a universal strength when compared to the total drag force exerted on the quark by the plasma. The universality extends over all asymptotically anti-de Sitter supergravity constructions with arbitrary scalar matter. We discuss how these results relate to the linearized hydrodynamic approximation and how they bear on our understanding of di-hadron correlators in heavy ion collisions.

Deep Impactmission to Tempel 1 favours New Explosive Cosmogony of comets

The assumption that short-period (SP) comets are fragments of massive icy envelopes of Ganymede-like bodies saturated by products of ice electrolysis that underwent global explosions provides a plausible explanation of all known manifestations of comets, including the jet character of outflows, the presence of ions in the vicinity of the nucleus, the bursts and splitting of cometary nuclei, etc., with solar radiation initiating burning of the products of electrolysis in the nucleus. As shown persuasively by numerical simulation carried out in hydrodynamic approximation, the shock wave initiated by the Deep Impact (DI) impactor in the cometary ice saturated originally by the electrolysis products 2H2 + O2 is capable of activating under certain conditions exothermal reactions (of the type O2 + H2 + organics = H2O + CO + HCN + other products of incomplete burning of organics including its light and heavy pyrolyzed compounds, soot, etc.), which will slow down shock wave damping (forced detonation) and increase many times the energy release. As a result, the measured energetics of ejections and outflows from the crater have to exceed the DI energetics. Analysis of different clusters of the DI experiment data confirms these conclusions and expectations and thus it favours the planetary origin of comets.

Effect of electron–electron interaction and plasmon excitation on the density‐of‐states for a two‐dimensional electron liquid

AbstractWe calculate the Green's function for an interacting two‐dimensional electron liquid whose strength of interaction is characterized by the electron density parameter rs. The screened electron–electron interaction is expressed in terms of a frequency and wave vector‐dependent dielectric function ε (q, w). If this screening is neglected, the tunneling density of states (DOS) is strongly modified by the electron–electron interaction. This modification is seen as a dip near the Fermi energy. This dip becomes deeper and narrower as rs is increased. When screening is included, the DOS is considerably affected by the collective plasma excitations. In particular, the range of frequencies where the plasmon excitations contribute increases with rs. Also, the DOS near the Fermi energy for the screened electron liquid depends on the electron density. We treat ε (q, w) in the hydrodynamical approximation in order to investigate the way in which the tunneling DOS is modified at various electron densities. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A comparative investigation of a high-velocity impact of cosmic bodies upon water and ground

The results of numerical simulation of the dynamics of a high-velocity impact upon a water surface are described in the approximation of two-dimensional hydrodynamics in cylindrical variables for bodies with dimensions, of about 1 km and impact velocities of about 50 km/sec. In the calculations a wide-range semiempirical equation of the state of water was used, with allowance for cold compression, phase transition into vapor, and the processes of dissociation and ionization. A comparison is made between calculations of an impact upon water and impacts upon different types of ground (gabbroid anorthosite, granite), which are described by both analytical equations of state and wide-range ones with phase transitions taken into account.

Statistical Properties of Low-Grazing Range-Resolved Sea Surface Backscatter Generated Through Two-Dimensional Direct Numerical Simulations

Statistical properties of the X-band sea clutter are studied using 2-D direct numerical simulations. Surfaces are modeled as realizations of a Gaussian random process with the Pierson-Moskowitz or Elfouhaily spectrum. The Creamer transform is further applied to account for the lowest-order surface nonlinearities. Backscattered field at a given frequency is found using the first-principles boundary integral equation (BIE) technique. Calculations are repeated at a number of frequencies, which allows synthesizing the surface response to a pulse as short as 2.2 ns (the corresponding spatial resolution is 0.33 m). Large-scale Monte Carlo trials are used to evaluate the correlation properties and to obtain the probability distributions for the vertically- and horizontally-polarized clutter. This paper concentrates on the incident angle of 85deg (5deg grazing), with a few results for moderate 60deg incidence also reported for comparison. The effects of variations in wind speed (sea state) and radar resolution on the clutter statistics are investigated. An L-band example (with proportionally longer pulse) helps explore the role of a different electromagnetic (e/m) wavelength. The simulation technique also allows for the isolation and examination of the impacts of certain e/m and hydrodynamic approximations, including the replacement of rigorous solution to the BIE by a simpler analytical scattering model. The amplitude statistics of the simulated backscatter are compared to the Weibull and K distributions that are often used to describe surface clutter

Depletion in Bose-Einstein condensates using quantum field theory in curved space

Using methods developed in Quantum Field Theory in curved space we can estimate the effects of the inhomogeneities and of a non vanishing velocity on the depletion of a Bose Einstein condensate within the hydrodynamical approximation.

Quasinormal mode analysis in BEC acoustic black holes

We perform a quasinormal mode analysis of black-hole configurations in Bose-Einstein condensates (BECs). In this analysis we use the full Bogoliubov dispersion relation, not just the hydrodynamic or geometric approximation. We restrict our attention to one-dimensional flows in BECs with steplike discontinuities. For this case we show that in the hydrodynamic approximation quasinormal modes do not exist. The full dispersion relation, however, allows the existence of quasinormal modes. Remarkably, the spectrum of these modes is not discrete but continuous.