arXiv subjects

Haitao Xu

Publications and source records attributed to Haitao Xu.

At least 55 records · Page 3Linked to original sources

arXiv2018

Observation of aerodynamic instability in the flow of a particle stream in a dilute gas

Forming macroscopic solid bodies in circumstellar discs requires local dust concentration levels significantly higher than the mean. Interactions of the dust particles with the gas must serve to augment local particle densities, and facilitate growth past barriers in the metre size range. Amongst a number of mechanisms that can amplify the local density of solids, aerodynamic streaming instability (SI) is one of the most promising. This work tests the physical assumptions of models that lead to SI in protoplanetary disks (PPDs). We conduct laboratory experiments in which we track the three-dimensional motion of spherical solid particles fluidized in a low-pressure, laminar, incompressible, gas stream. The particle sizes span the Stokes-Epstein drag regime transition and the overall dust-to-gas mass density ratio is close to unity. Lambrechts et al. (2016) established the similarity of the laboratory flow to a simplified PPD model flow. We obtain experimental results suggesting an instability due to particle-gas interaction: i) there exist variations in particle concentration in the direction of the mean drag forces; ii) the particles have a tendency to 'catch up' to one another when they are in proximity; iii) particle clumping occurs on very small scales, which implies local enhancements above the background dust-to-gas mass density ratio by factors of several tens; v) the presence of these density enhancements occurs for a mean dust-to-gas mass density ratio approaching or greater than 1; v) we find evidence for collective particle drag reduction when the local particle number density becomes high and when the background gas pressure is high so that the drag is in the continuum regime. The experiments presented here are precedent-setting for observing SI under controlled conditions and may lead to a deeper understanding of how it operates in nature.

astro-ph.EP↗

arXiv2018

Studies of Turbulence Dissipation in Taurus Molecular Cloud with Core Velocity Dispersion (CVD)

Turbulence dissipation is an important process affecting the energy balance in molecular clouds, the birth place of stars. Previously, the rate of turbulence dissipation is often estimated with semi-analytic formulae from simulation. Recently we developed a data analysis technique called core-velocity-dispersion (CVD), which, for the first time, provides direct measurements of the turbulence dissipation rate in Taurus, a star forming cloud. The thus measured dissipation rate of $(0.45\pm 0.05)\times 10^{33} {\rm erg\ s^{-1}}$ is similar to those from dimensional analysis and also consistent with the previous energy injection rate based on molecular outflows and bubbles.

astro-ph.IM↗

arXiv2017

An energy-based stability criterion for solitary traveling waves in Hamiltonian lattices

In this work, we revisit a criterion, originally proposed in [Nonlinearity {\bf 17}, 207 (2004)], for the stability of solitary traveling waves in Hamiltonian, infinite-dimensional lattice dynamical systems. We discuss the implications of this criterion from the point of view of stability theory, both at the level of the spectral analysis of the advance-delay differential equations in the co-traveling frame, as well as at that of the Floquet problem arising when considering the traveling wave as a periodic orbit modulo a shift. We establish the correspondence of these perspectives for the pertinent eigenvalue and Floquet multiplier and provide explicit expressions for their dependence on the velocity of the traveling wave in the vicinity of the critical point. Numerical results are used to corroborate the relevant predictions in two different models, where the stability may change twice. Some extensions, generalizations and future directions of this investigation are also discussed.

nlin.PS↗

arXiv2016

Anderson localization in metallic nanoparticle arrays

Anderson localization has been observed in various types of waves, such as matter waves, optical waves and acoustic waves. Here we reveal that the effect of Anderson localization can be also induced in metallic nonlinear nanoparticle arrays excited by a random electrically driving field. We find that the dipole-induced nonlinearity results in ballistic expansion of dipole intensity during evolution; while the randomness of the external driving field can suppress such an expansion. Increasing the strength of randomness above the threshold value, a localized pattern of dipole intensity can be generated in the metallic nanoparticle arrays. By means of statistics, the mean intensity distribution of the dipoles reveals the formation of Anderson localization. We further show that the generated Anderson localization is highly confined, with its size down to the scale of incident wavelength. The reported results might facilitate the manipulations of electromagnetic fields in the scale of wavelength.

physics.optics↗

arXiv2016

Existence, Stability and Dynamics of Harmonically Trapped One-Dimensional Multi-Component Solitary Waves: The Near-Linear Limit

In the present work, we consider a variety of two-component, one-dimensional states in nonlinear Schrodinger equations in the presence of a parabolic trap, inspired by the atomic physics context of Bose-Einstein condensates. The use of Lyapunov-Schmidt reduction methods allows us to identify persistence criteria for the different families of solutions which we classify as (m,n), in accordance with the number of nodes in each component. Upon developing the existence theory, we turn to a stability analysis of the different configurations, using the Krein signature and the Hamiltonian-Krein index as topological tools identifying the number of potentially unstable eigendirections for each branch. A systematic expansion of suitably reduced eigenvalue problems when perturbing off of the linear limit permits us to obtain explicit expressions for the eigenvalues of each of the states considered. Finally, when the states are found to be unstable, typically by virtue of Hamiltonian Hopf bifurcations, their dynamics is studied in order to identify the nature of the respective instability. The dynamics is generally found to lead to a vibrational evolution over long time scales.

nlin.PS↗

arXiv2015

Existence and stability of PT-symmetric vortices in nonlinear two-dimensional square lattices

Vortices symmetric with respect to simultaneous parity and time reversing transformations are considered on the square lattice in the framework of the discrete nonlinear Schrödinger equation. The existence and stability of vortex configurations is analyzed in the limit of weak coupling between the lattice sites, when predictions on the elementary cell of a square lattice (i.e., a single square) can be extended to a large (yet finite) array of lattice cells. Our analytical predictions are found to be in good agreement with numerical computations.

nlin.PS↗

arXiv2015

Irreversibility and small-scale generation in 3D turbulent flows

In three-dimensional turbulent flows energy is supplied at large scales and cascades down to the smallest scales where viscosity dominates. The flux of energy through scales implies the generation of small scales from larger ones, which is the fundamental reason for the irreversibility of the dynamics of turbulent flows. As we showed recently, this irreversibility manifests itself by an asymmetry of the probability distribution of the instantaneous power $p$ of the forces acting on fluid elements. In particular, the third moment of $p$ was found to be negative. Yet, a physical connection between the irreversibility manifested in the distribution of $p$ and the energy flux or small-scale generation in turbulence has not been established. Here, with analytical calculations and support from numerical simulations of fully developed turbulence, we connect the asymmetry in the power distribution, {\it i.e.}, the negative value of $\langle p^3 \rangle$, to the generation of small scales, or more precisely, to the amplification (stretching) of vorticity in turbulent flows. Our result is the first step towards a quantitative understanding of the origin of the irreversibility observed at the level of individual Lagrangian trajectories in turbulent flows.

physics.flu-dyn↗

arXiv2015

Lagrangian view of time irreversibility of fluid turbulence

A turbulent flow is maintained by an external supply of kinetic energy, which is eventually dissipated into heat at steep velocity gradients. The scale at which energy is supplied greatly differs from the scale at which energy is dissipated, the more so as the turbulent intensity (the Reynolds number) is larger. The resulting energy flux over the range of scales, intermediate between energy injection and dissipation, acts as a source of time irreversibility. As it is now possible to follow accurately fluid particles in a turbulent flow field, both from laboratory experiments and from numerical simulations, a natural question arises: how do we detect time irreversibility from these Lagrangian data? Here we discuss recent results concerning this problem. For Lagrangian statistics involving more than one fluid particle, the distance between fluid particles introduces an intrinsic length scale into the problem. The evolution of quantities dependent on the relative motion between these fluid particles, including the kinetic energy in the relative motion, or the configuration of an initially isotropic structure can be related to the equal-time correlation functions of the velocity field, and is therefore sensitive to the energy flux through scales, hence to the irreversibility of the flow. In contrast, for single-particle Lagrangian statistics, the most often studied velocity structure functions cannot distinguish the "arrow of time." Recent observations from experimental and numerical simulation data, however, show that the change of kinetic energy following the particle motion, is sensitive to time-reversal. We end the survey with a brief discussion of the implication of this line of work.

physics.flu-dyn↗

arXiv2015

Traveling waves for the Mass in Mass model of granular chains

In the present work, we consider the mass in mass (or mass with mass) system of granular chains, namely a granular chain involving additionally an internal resonator. For these chains, we rigorously establish that under suitable "anti-resonance" conditions connecting the mass of the resonator and the speed of the wave, bell-shaped traveling wave solutions continue to exist in the system, in a way reminiscent of the results proven for the standard granular chain of elastic Hertzian contacts. We also numerically touch upon settings where the conditions do not hold, illustrating, in line also with recent experimental work, that non-monotonic waves bearing non-vanishing tails may exist in the latter case.

nlin.PS↗

arXiv2014

Turbulence decay and cloud core relaxation in molecular clouds

The turbulent motion within molecular clouds is a key factor controlling star formation. Turbulence supports molecular cloud cores from evolving to gravitational collapse and hence sets a lower bound on the size of molecular cloud cores in which star formation can occur. On the other hand, without a continuous external energy source maintaining the turbulence, such as in molecular clouds, the turbulence decays with an energy dissipation time comparable to the dynamic timescale of clouds, which could change the size limits obtained from Jean's criterion by assuming constant turbulence intensities. Here we adopt scaling relations of physical variables in decaying turbulence to analyze its specific effects on the formation of stars. We find that the decay of turbulence provides an additional approach for Jeans' criterion to be achieved, after which gravitational infall governs the motion of the cloud core. This epoch of turbulence decay is defined as cloud core relaxation. The existence of cloud core relaxation provides a more complete understanding in the competition between turbulence and gravity on the dynamics of molecular cloud cores and star formation.

astro-ph.SR↗

arXiv2014

A Non-cooperative Differential Game Model for Frequency Reuse based Channel Allocation in Satellite Networks

In this paper, channel resource allocation problem for LEO mobile satellite systems is investigated and a new dynamic channel resource allocation scheme is proposed based on differential game. Optimal channel resource allocated to each satellite beams are formulated as Nash equilibrium. It is proved that optimal channel resource allocation can be achieved and the differential game based scheme is applicable and acceptable. Numerical results shows that system performance can be improved based on the proposed scheme.

cs.IT↗

arXiv2014

Power Fluctuations and Irreversibility in Turbulence

The breaking of detailed balance, the symmetry between forward and backward probability transition between two states, is crucial to understand irreversible systems. In hydrodynamic turbulence, a far-from equilibrium system, we observe a strong manifestation of the breaking of detailed balance by following the evolution of the kinetic energy of individual fluid elements. We found in all the flows that we have investigated that fluid elements decelerate faster than they accelerate, giving rise to negative third moment of energy increments, independently of space dimensionality. The exchange of energy between fluid elements however is fundamentally different in two and three dimensions. While pressure forces do not provide net energy change to slow or fast particles in two dimensions, they tend to transfer energy from {\it slow} to {\it fast} particles in three dimensions, possibly implying a runaway of energy.

physics.flu-dyn↗

arXiv2014

Variable Density Turbulence Tunnel Facility

The Variable Density Turbulence Tunnel (VDTT) at the Max Planck Institute for Dynamics and Self-Organization in Göttingen, Germany produces very high turbulence levels at moderate flow velocities, low power consumption and adjustable kinematic viscosity between $10^{-4} m^2/s$ and $10^{-7} m^2/s$. The Reynolds number can be varied by changing the pressure or flow rate of the gas or by using different non-flammable gases including air. The highest kinematic viscosities, and hence lowest Reynolds numbers, are reached with air or nitrogen at 0.1 bar. To reach the highest Reynolds numbers the tunnel is pressurized to 15 bar with the dense gas sulfur hexafluoride (SF$_6$). Turbulence is generated at the upstream ends of two measurement sections with grids, and the evolution of this turbulence is observed as it moves down the length of the sections. We describe the instrumentation presently in operation, which consists of the tunnel itself, classical grid turbulence generators, and state-of-the-art nano-fabricated hot-wire anemometers provided by Princeton University [Vallikivi et al. (2011) Exp. Fluids 51, 1521]. We report measurements of the characteristic scales of the flow and of turbulent spectra up to Taylor Reynolds number $R_λ\approx 1600$, higher than any other grid-turbulence experiment. We also describe instrumentation under development, which includes an active grid and a Lagrangian particle tracking system that moves down the length of the tunnel with the mean flow. In this configuration, the properties of the turbulence are adjustable and its structure is resolvable up to $R_λ\approx 8000$.

physics.flu-dyn↗

arXiv2014

Time-symmetry breaking in turbulence

In three-dimensional turbulent flows, the flux of energy from large to small scales breaks time symmetry. We show here that this irreversibility can be quantified by following the relative motion of several Lagrangian tracers. We find by analytical calculation, numerical analysis and experimental observation that the existence of the energy flux implies that, at short times, two particles separate temporally slower forwards than backwards, and the difference between forward and backward dispersion grows as $t^3$. We also find the geometric deformation of material volumes, surrogated by four points spanning an initially regular tetrahedron, to show sensitivity to the time-reversal with an effect growing linearly in $t$. We associate this with the structure of the strain rate in the flow.

physics.flu-dyn↗

arXiv2013

Tetrahedron deformation and alignment of perceived vorticity and strain in a turbulent flow

We describe the structure and dynamics of turbulence by the scale-dependent perceived velocity gradient tensor as supported by following four tracers, i.e. fluid particles, that initially form a regular tetrahedron. We report results from experiments in a von Kármán swirling water flow and from numerical simulations of the incompressible Navier-Stokes equation. We analyze the statistics and the dynamics of the perceived rate of strain tensor and vorticity for initially regular tetrahedron of size $r_0$ from the dissipative to the integral scale. Just as for the true velocity gradient, at any instant, the perceived vorticity is also preferentially aligned with the intermediate eigenvector of the perceived rate of strain. However, in the perceived rate of strain eigenframe fixed at a given time $t=0$, the perceived vorticity evolves in time such as to align with the strongest eigendirection at $t=0$. This also applies to the true velocity gradient. The experimental data at the higher Reynolds number suggests the existence of a self-similar regime in the inertial range. In particular, the dynamics of alignment of the perceived vorticity and strain can be rescaled by $t_0$, the turbulence time scale of the flow when the scale $r_0$ is in the inertial range. For smaller Reynolds numbers we found the dynamics to be scale dependent.

physics.flu-dyn↗

arXiv2013

Turbulence of Dilute Polymer Solution

In fully developed three dimensional fluid turbulence the fluctuating energy is supplied at large scales, cascades through intermediate scales, and dissipates at small scales. It is the hallmark of turbulence that for intermediate scales, in the so called inertial range, the average energy flux is constant and independent of viscosity [1-3]. One very important question is how this range is altered, when an additional agent that can also transport energy is added to the fluid. Long-chain polymers dissolved at very small concentrations in the fluid are such an agent [4,5]. Based on prior work by de Gennes and Tabor [6,7] we introduce a theory that balances the energy flux through the turbulent cascade with that of the energy flux into the elastic degrees of freedom of the dilute long-chain polymer solution. We propose a refined elastic length scale, $r_\varepsilon$, which describes the effect of polymer elasticity on the turbulence energy cascade. Our experimental results agree excellently with this new energy flux balance theory.

physics.flu-dyn↗

arXiv2012

Where do small, weakly inertial particles go in a turbulent flow?

We report experimental results on the dynamics of heavy particles of the size of the Kolmogorov-scale in a fully developed turbulent flow. The mixed Eulerian structure function of two-particle velocity and acceleration difference vectors <δv\cdotδa_p> was observed to increase significantly with particle inertia for identical flow conditions. We show that this increase is related to a preferential alignment between these dynamical quantities. With increasing particle density the probability for those two vectors to be collinear was observed to grow. We show that these results are consistent with the preferential sampling of strain-dominated regions by inertial particles.

physics.flu-dyn↗

arXiv2011

Path lengths in turbulence

By tracking tracer particles at high speeds and for long times, we study the geometric statistics of Lagrangian trajectories in an intensely turbulent laboratory flow. In particular, we consider the distinction between the displacement of particles from their initial positions and the total distance they travel. The difference of these two quantities shows power-law scaling in the inertial range. By comparing them with simulations of a chaotic but non-turbulent flow and a Lagrangian Stochastic model, we suggest that our results are a signature of turbulence.

physics.data-an↗