Thermal collapse of a granular gas under gravity

Free cooling of a gas of inelastically colliding hard spheres represents a central paradigm of kinetic theory of granular gases. At zero gravity the temperature of a freely cooling homogeneous granular gas follows a power law in time. How does gravity, which brings inhomogeneity, affect the cooling? We combine molecular dynamics simulations, a numerical solution of hydrodynamic equations and an analytic theory to show that a granular gas cooling under gravity undergoes thermal collapse: it cools down to zero temperature and condenses on the bottom of the container in a finite time.Comment: 4 pages, 12 eps figures, to appear in PR

Regeneration Of Diesel Particulate Filters With Hydrogen Rich Gas

The options for the regeneration of a Diesel Particulate Filter (DPF) using hydrogen rich gas are investigated. The advantages of using hydrogen rich gas for this purpose are described. The system requirements for such a system are also evaluated. The use of a plasmatron fuel converter for the onboard generation of hydrogen rich gas from diesel fuel is discussed. The advantages of homogeneous, non-catalytic reforming by the plasmatron fuel converter are described. Finally, the effect of homogeneous combustion of the hydrogen rich gas in the exhaust (upstream from the DPF) is investigated. I

Navier-Stokes hydrodynamics of thermal collapse in a freely cooling granular gas

We employ Navier-Stokes granular hydrodynamics to investigate the long-time behavior of clustering instability in a freely cooling dilute granular gas in two dimensions. We find that, in circular containers, the homogeneous cooling state (HCS) of the gas loses its stability via a sub-critical pitchfork bifurcation. There are no time-independent solutions for the gas density in the supercritical region, and we present analytical and numerical evidence that the gas develops thermal collapse unarrested by heat diffusion. To get more insight, we switch to a simpler geometry of a narrow-sector-shaped container. Here the HCS loses its stability via a transcritical bifurcation. For some initial conditions a time-independent inhomogeneous density profile sets in, qualitatively similar to that previously found in a narrow-channel geometry. For other initial conditions, however, the dilute gas develops thermal collapse unarrested by heat diffusion. We determine the dynamic scalings of the flow close to collapse analytically and verify them in hydrodynamic simulations. The results of this work imply that, in dimension higher than one, Navier-Stokes hydrodynamics of a dilute granular gas is prone to finite-time density blowups. This provides a natural explanation to the formation of densely packed clusters of particles in a variety of initially dilute granular flows.Comment: 18 pages, 19 figure

Layered connectors: revisiting the formal basis of architectural connection for complex distributed systems

The complex distributed systems of nowadays require the dynamic composition of multiple components, which are autonomous and so complex that they can be considered as systems in themselves. These components often use different application protocols and are implemented on top of heterogeneous middleware, which hamper their successful interaction. The explicit and rigorous description and analysis of components interaction is essential in order to enable the dynamic composition of these components. In this paper, we propose a formal approach to represent and reason about interactions between components using layered connectors. Layered connectors describe components interaction at both the application and middleware layers and make explicit the role of middleware in the realisation of this interaction. We provide formal semantics of layered connectors and present an approach for the synthesis of layered connectors in order to enable the dynamic composition of highly heterogeneous components. We validate our approach through a case study in the area of collaborative emergency management

Attempted density blowup in a freely cooling dilute granular gas: hydrodynamics versus molecular dynamics

It has been recently shown (Fouxon et al. 2007) that, in the framework of ideal granular hydrodynamics (IGHD), an initially smooth hydrodynamic flow of a granular gas can produce an infinite gas density in a finite time. Exact solutions that exhibit this property have been derived. Close to the singularity, the granular gas pressure is finite and almost constant. This work reports molecular dynamics (MD) simulations of a freely cooling gas of nearly elastically colliding hard disks, aimed at identifying the "attempted" density blowup regime. The initial conditions of the simulated flow mimic those of one particular solution of the IGHD equations that exhibits the density blowup. We measure the hydrodynamic fields in the MD simulations and compare them with predictions from the ideal theory. We find a remarkable quantitative agreement between the two over an extended time interval, proving the existence of the attempted blowup regime. As the attempted singularity is approached, the hydrodynamic fields, as observed in the MD simulations, deviate from the predictions of the ideal solution. To investigate the mechanism of breakdown of the ideal theory near the singularity, we extend the hydrodynamic theory by accounting separately for the gradient-dependent transport and for finite density corrections.Comment: 11 pages, 9 figures, accepted for publication on Physical Review

Discrete charging of metallic grains: Statistics of addition spectra

We analyze the statistics of electrostatic energies (and their differences) for a quantum dot system composed of a finite number $K$ of electron islands (metallic grains) with random capacitance-inductance matrix $C$, for which the total charge is discrete, $Q=Ne$ (where $e$ is the charge of an electron and $N$ is an integer). The analysis is based on a generalized charging model, where the electrons are distributed among the grains such that the electrostatic energy E(N) is minimal. Its second difference (inverse compressibility) $\chi_{N}=E(N+1)-2 E(N)+E(N-1)$ represents the spacing between adjacent Coulomb blockade peaks appearing when the conductance of the quantum dot is plotted against gate voltage. The statistics of this quantity has been the focus of experimental and theoretical investigations during the last two decades. We provide an algorithm for calculating the distribution function corresponding to $\chi_{N}$ and show that this function is piecewise polynomial.Comment: 21 pages, no figures, mathematical nomenclature (except for Abstract and Introduction

3D culture reveals a signaling network

The behavior of a cell is significantly influenced by its context. Epithelial cells derived from glandular organs such as the breast recreate their glandular organization when grown under 3D culture conditions. While traditional monolayer cultures are powerful tools to understand how cells proliferate, grow and respond to stress, they do not recreate the 3D property observed in vivo. Multiple studies demonstrate that 3D organization can reveal novel and unexpected insights into the mechanisms by which normal and tumorderived epithelial cells function. In the present article we comment on a study that reports identification of a RasV12-induced IL-6 signaling network in mammary epithelial cells in 3D cultures

A nonlinear theory of non-stationary low Mach number channel flows of freely cooling nearly elastic granular gases

We use hydrodynamics to investigate non-stationary channel flows of freely cooling dilute granular gases. We focus on the regime where the sound travel time through the channel is much shorter than the characteristic cooling time of the gas. As a result, the gas pressure rapidly becomes almost homogeneous, while the typical Mach number of the flow drops well below unity. Eliminating the acoustic modes, we reduce the hydrodynamic equations to a single nonlinear and nonlocal equation of a reaction-diffusion type in Lagrangian coordinates. This equation describes a broad class of channel flows and, in particular, can follow the development of the clustering instability from a weakly perturbed homogeneous cooling state to strongly nonlinear states. If the heat diffusion is neglected, the reduced equation is exactly soluble, and the solution develops a finite-time density blowup. The heat diffusion, however, becomes important near the attempted singularity. It arrests the density blowup and brings about novel inhomogeneous cooling states (ICSs) of the gas, where the pressure continues to decay with time, while the density profile becomes time-independent. Both the density profile of an ICS, and the characteristic relaxation time towards it are determined by a single dimensionless parameter that describes the relative role of the inelastic energy loss and heat diffusion. At large values of this parameter, the intermediate cooling dynamics proceeds as a competition between low-density regions of the gas. This competition resembles Ostwald ripening: only one hole survives at the end.Comment: 20 pages, 15 figures, final versio

Smaller & Sooner: Exploiting High Magnetic Fields from New Superconductors for a More Attractive Fusion Energy Development Path

The current fusion energy development path, based on large volume moderate magnetic B field devices is proving to be slow and expensive. A modest development effort in exploiting new superconductor magnet technology development, and accompanying plasma physics research at high-B, could open up a viable and attractive path for fusion energy development. This path would feature smaller volume, fusion capable devices that could be built more quickly than low-to-moderate field designs based on conventional superconductors. Fusion’s worldwide development could be accelerated by using several small, flexible devices rather than relying solely on a single, very large device. These would be used to obtain the acknowledged science and technology knowledge necessary for fusion energy beyond achievement of high gain. Such a scenario would also permit the testing of multiple confinement configurations while distributing technical and scientific risk among smaller devices. Higher field and small size also allows operation away from well-known operational limits for plasma pressure, density and current. The advantages of this path have been long recognized—earlier US plans for burning plasma experiments (compact ignition tokamak, burning plasma experiment, fusion ignition research experiment) featured compact high-field designs, but these were necessarily pulsed due to the use of copper coils. Underpinning this new approach is the recent industrial maturity of high-temperature, high-field superconductor tapes that would offer a truly “game changing” opportunity for magnetic fusion when developed into large-scale coils. The superconductor tape form and higher operating temperatures also open up the possibility of demountable superconducting magnets in a fusion system, providing a modularity that vastly improves simplicity in the construction, maintenance, and upgrade of the coils and the internal nuclear engineering components required for fusion’s development. Our conclusion is that while tradeoffs exist in design choices, for example coil, cost and stress limits versus size, the potential physics and technology advantages of high-field superconductors are attractive and they should be vigorously pursued for magnetic fusion’s development