Shear-induced crystallization of a dense rapid granular flow: hydrodynamics beyond the melting point?

We investigate shear-induced crystallization in a very dense flow of mono-disperse inelastic hard spheres. We consider a steady plane Couette flow under constant pressure and neglect gravity. We assume that the granular density is greater than the melting point of the equilibrium phase diagram of elastic hard spheres. We employ a Navier-Stokes hydrodynamics with constitutive relations all of which (except the shear viscosity) diverge at the crystal packing density, while the shear viscosity diverges at a smaller density. The phase diagram of the steady flow is described by three parameters: an effective Mach number, a scaled energy loss parameter, and an integer number m: the number of half-oscillations in a mechanical analogy that appears in this problem. In a steady shear flow the viscous heating is balanced by energy dissipation via inelastic collisions. This balance can have different forms, producing either a uniform shear flow or a variety of more complicated, nonlinear density, velocity and temperature profiles. In particular, the model predicts a variety of multi-layer two-phase steady shear flows with sharp interphase boundaries. Such a flow may include a few zero-shear (solid-like) layers, each of which moving as a whole, separated by fluid-like regions. As we are dealing with a hard sphere model, the granulate is fluidized within the "solid" layers: the granular temperature is non-zero there, and there is energy flow through the boundaries of the "solid" layers. A linear stability analysis of the uniform steady shear flow is performed, and a plausible bifurcation diagram of the system, for a fixed m, is suggested. The problem of selection of m remains open.Comment: 11 pages, 7 eps figures, to appear in PR

Oscillatory instability in a driven granular gas

We discovered an oscillatory instability in a system of inelastically colliding hard spheres, driven by two opposite "thermal" walls at zero gravity. The instability, predicted by a linear stability analysis of the equations of granular hydrodynamics, occurs when the inelasticity of particle collisions exceeds a critical value. Molecular dynamic simulations support the theory and show a stripe-shaped cluster moving back and forth in the middle of the box away from the driving walls. The oscillations are irregular but have a single dominating frequency that is close to the frequency at the instability onset, predicted from hydrodynamics.Comment: 7 pages, 4 figures, to appear in Europhysics Letter

Fluctuations and stability in front propagation

Propagating fronts arising from bistable reaction-diffusion equations are a purely deterministic effect. Stochastic reaction-diffusion processes also show front propagation which coincides with the deterministic effect in the limit of small fluctuations (usually, large populations). However, for larger fluctuations propagation can be affected. We give an example, based on the classic spruce-budworm model, where the direction of wave propagation, i.e., the relative stability of two phases, can be reversed by fluctuations.Comment: 5 pages, 5 figure

Resonance Hopping Effect in the Neptune-planet Nine System

The observed physical clustering of the orbits of small bodies in the distant Kuiper Belt (TNOs) has recently prompted the prediction of an additional planet in the outer solar system. Since the initial posing of the hypothesis, the effects of Planet Nine on the dynamics of the main cluster of TNOs—the objects anti-aligned with its orbit—have been well-studied. In particular, numerical simulations have revealed a fascinating phenomenon, referred to as "resonance hopping," in which these objects abruptly transition between different mean-motion commensurabilities with Planet Nine. In this work, we explore this effect in greater detail, with the goal of understanding what mechanism prompts the hopping events to occur. In the process, we elucidate the often underestimated role of Neptune scattering interactions, which leads to diffusion in the semimajor axes of these distant TNOs. In addition, we demonstrate that although some resonant interactions with Planet Nine do occur, the anti-aligned objects are able to survive without the resonances, confirming that the dynamics of the TNOs are predominantly driven by secular, rather than resonant, interactions with Planet Nine

Resonance Hopping Effect in the Neptune-planet Nine System

The observed physical clustering of the orbits of small bodies in the distant Kuiper Belt (TNOs) has recently prompted the prediction of an additional planet in the outer solar system. Since the initial posing of the hypothesis, the effects of Planet Nine on the dynamics of the main cluster of TNOs—the objects anti-aligned with its orbit—have been well-studied. In particular, numerical simulations have revealed a fascinating phenomenon, referred to as "resonance hopping," in which these objects abruptly transition between different mean-motion commensurabilities with Planet Nine. In this work, we explore this effect in greater detail, with the goal of understanding what mechanism prompts the hopping events to occur. In the process, we elucidate the often underestimated role of Neptune scattering interactions, which leads to diffusion in the semimajor axes of these distant TNOs. In addition, we demonstrate that although some resonant interactions with Planet Nine do occur, the anti-aligned objects are able to survive without the resonances, confirming that the dynamics of the TNOs are predominantly driven by secular, rather than resonant, interactions with Planet Nine

Dynamics and pattern formation in invasive tumor growth

In this work, we study the in-vitro dynamics of the most malignant form of the primary brain tumor: Glioblastoma Multiforme. Typically, the growing tumor consists of the inner dense proliferating zone and the outer less dense invasive region. Experiments with different types of cells show qualitatively different behavior. Wild-type cells invade a spherically symmetric manner, but mutant cells are organized in tenuous branches. We formulate a model for this sort of growth using two coupled reaction-diffusion equations for the cell and nutrient concentrations. When the ratio of the nutrient and cell diffusion coefficients exceeds some critical value, the plane propagating front becomes unstable with respect to transversal perturbations. The instability threshold and the full phase-plane diagram in the parameter space are determined. The results are in a good agreement with experimental findings for the two types of cells.Comment: 4 pages, 4 figure

Evaluation of Cloud Microphysics Simulated using a Meso-Scale Model Coupled with a Spectral Bin Microphysical Scheme through Comparison with Observation Data by Ship-Borne Doppler and Space-Borne W-Band Radars

Equivalent radar reflectivity factors (Ze) measured by W-band radars are directly compared with the corresponding values calculated from a three-dimensional non-hydrostatic meso-scale model coupled with a spectral-bin-microphysical (SBM) scheme for cloud. Three case studies are the objects of this research: one targets a part of ship-borne observation using 95 GHz Doppler radar over the Pacific Ocean near Japan in May 2001; other two are aimed at two short segments of space-borne observation by the cloud profiling radar on CloudSat in November 2006. The numerical weather prediction (NWP) simulations reproduce general features of vertical structures of Ze and Doppler velocity. A main problem in the reproducibility is an overestimation of Ze in ice cloud layers. A frequency analysis shows a strong correlation between ice water contents (IWC) and Ze in the simulation; this characteristic is similar to those shown in prior on-site studies. From comparing with the empirical correlations by the prior studies, the simulated Ze is overestimated than the corresponding values in the studies at the same IWC. Whereas the comparison of Doppler velocities suggests that large-size snowflakes are necessary for producing large velocities under the freezing level and hence rules out the possibility that an overestimation of snow size causes the overestimation of Ze. Based on the results of several sensitivity tests, we conclude that the source of the overestimation is a bias in the microphysical calculation of Ze or an overestimation of IWC. To identify the source of the problems needs further validation research with other follow-up observations

The Role of Atmospheric Aerosol Concentration on Deep Convective Precipitation: Cloud-resolving Model Simulations

Aerosols and especially their effect on clouds are one of the key components of the climate system and the hydrological cycle [Ramanathan et al., 20011. Yet, the aerosol effect on clouds remains largely unknown and the processes involved not well understood. A recent report published by the National Academy of Science states "The greatest uncertainty about the aerosol climate forcing - indeed, the largest of all the uncertainties about global climate forcing - is probably the indirect effect of aerosols on clouds NRC [2001]." The aerosol effect on clouds is often categorized into the traditional "first indirect (i.e., Twomey)" effect on the cloud droplet sizes for a constant liquid water path and the "semi-direct" effect on cloud coverage. The aerosol effect on precipitation processes, also known as the second type of aerosol indirect effect, is even more complex, especially for mixed-phase convective clouds. ln this paper, a cloud-resolving model (CRM) with detailed spectral-bin microphysics was used to examine the effect of aerosols on three different deep convective cloud systems that developed in different geographic locations: South Florida, Oklahoma and the Central Pacific. In all three cases, rain reaches the ground earlier for the low CCN (clean) case. Rain suppression is also evident in all three cases with high CCN (dirty) case. However, this suppression only occurs during the first hour of the simulations. During the mature stages of the simulations, the effects of increasing aerosol concentration range from rain suppression in the Oklahoma case, to almost no effect in the Florida case, to rain enhancement in the Pacific case. These results show the complexity of aerosol interactions with convection

The Knudsen temperature jump and the Navier-Stokes hydrodynamics of granular gases driven by thermal walls

Thermal wall is a convenient idealization of a rapidly vibrating plate used for vibrofluidization of granular materials. The objective of this work is to incorporate the Knudsen temperature jump at thermal wall in the Navier-Stokes hydrodynamic modeling of dilute granular gases of monodisperse particles that collide nearly elastically. The Knudsen temperature jump manifests itself as an additional term, proportional to the temperature gradient, in the boundary condition for the temperature. Up to a numerical pre-factor of order unity, this term is known from kinetic theory of elastic gases. We determine the previously unknown numerical pre-factor by measuring, in a series of molecular dynamics (MD) simulations, steady-state temperature profiles of a gas of elastically colliding hard disks, confined between two thermal walls kept at different temperatures, and comparing the results with the predictions of a hydrodynamic calculation employing the modified boundary condition. The modified boundary condition is then applied, without any adjustable parameters, to a hydrodynamic calculation of the temperature profile of a gas of inelastic hard disks driven by a thermal wall. We find the hydrodynamic prediction to be in very good agreement with MD simulations of the same system. The results of this work pave the way to a more accurate hydrodynamic modeling of driven granular gases.Comment: 7 pages, 3 figure

Dynamical Classification of Trans-Neptunian Objects Detected by the Dark Energy Survey

The outer solar system contains a large number of small bodies (known as trans-Neptunian objects or TNOs) that exhibit diverse types of dynamical behavior. The classification of bodies in this distant region into dynamical classes-subpopulations that experience similar orbital evolution- A ids in our understanding of the structure and formation of the solar system. In this work, we propose an updated dynamical classification scheme for the outer solar system. This approach includes the construction of a new (automated) method for identifying mean motion resonances. We apply this algorithm to the current data set of TNOs observed by the Dark Energy Survey (DES) and present a working classification for all of the DES TNOs detected to date. Our classification scheme yields 1 inner centaur, 19 outer centaurs, 21 scattering disk objects, 47 detached TNOs, 48 securely resonant objects, 7 resonant candidates, and 97 classical belt objects. Among the scattering and detached objects, we detect 8 TNOs with semimajor axes greater than 150 au. © 2020. The American Astronomical Society. All rights reserved.