An estimate of heavy quark momentum diffusion coefficient in gluon plasma

We calculate the momentum diffusion coefficient for heavy quarks in SU(3) gluon plasma at temperatures 1-2 times the deconfinement temperature. The momentum diffusion coefficient is extracted from a Monte Carlo calculation of the correlation function of color electric fields, in the leading order of expansion in heavy quark mass. Systematics of the calculation are examined, and compared with perturbtion theory and other estimates.

Nonperturbative estimate of the heavy quark momentum diffusion coefficient

We estimate the momentum diffusion coefficient of a heavy quark within a pure SU(3) plasma at a temperature of about 1.5Tc. Large-scale Monte Carlo simulations on a series of lattices extending up to 1923×48 permit us to carry out a continuum extrapolation of the so-called color-electric imaginary-time correlator. The extrapolated correlator is analyzed with the help of theoretically motivated models for the corresponding spectral function. Evidence for a nonzero transport coefficient is found and, incorporating systematic uncertainties reflecting model assumptions, we obtain κ=(1.8–3.4)T3. This implies that the “drag coefficient,” characterizing the time scale at which heavy quarks adjust to hydrodynamic flow, is η−1D=(1.8–3.4)(Tc/T)2(M/1.5  GeV)  fm/c, where M is the heavy quark kinetic mass. The results apply to bottom and, with somewhat larger systematic uncertainties, to charm quarks.

Parton energy loss and momentum broadening at NLO in high temperature QCD plasmas

We present an overview of a perturbative-kinetic approach to jet propagation, energy loss, and momentum broadening in a high temperature quark–gluon plasma. The leading-order kinetic equations describe the interactions between energetic jet-particles and a non-abelian plasma, consisting of on-shell thermal excitations and soft gluonic fields. These interactions include ↔ scatterings, collinear bremsstrahlung, and drag and momentum diffusion. We show how the contribution from the soft gluonic fields can be factorized into a set of Wilson line correlators on the light-cone. We review recent field-theoretical developments, rooted in the causal properties of these correlators, which simplify the calculation of the appropriate Wilson lines in thermal field theory. With these simplifications lattice measurements of transverse momentum broadening have become possible, and the kinetic equations describing parton transport have been extended to next-to-leading order in the coupling g.

Shear band evolution in Zr/Hf-based bulk metallic glasses under static and dynamic indentations

Bulk metallic glasses (BMGs) exhibit superior mechanical properties as compared with other conventional materials and have been proposed for numerous engineering and technological applications. Zr/Hf-based BMGs or tungsten reinforced BMG composites are considered as a potential replacement for depleted uranium armor-piercing projectiles because of their ability to form localized shear bands during impact, which has been known to be the dominant plastic deformation mechanism in BMGs. However, in conventional tensile, compressive and bending tests, limited ductility has been observed because of fracture initiation immediately following the shear band formation. To fully investigate shear band characteristics, indentation tests that can confine the deformation in a limited region have been pursued. In this thesis, a detailed investigation of thermal stability and mechanical deformation behavior of Zr/Hf-based BMGs is conducted. First, systematic studies had been implemented to understand the influence of relative compositions of Zr and Hf on thermal stability and mechanical property evolution. Second, shear band evolution under indentations were investigated experimentally and theoretically. Three kinds of indentation studies were conducted on BMGs in the current study. (a) Nano-indentation to determine the mechanical properties as a function of Hf/Zr content. (b) Static Vickers indentation on bonded split specimens to investigate the shear band evolution characteristics beneath the indention. (c) Dynamic Vickers indentation on bonded split specimens to investigate the influence of strain rate. It was found in the present work that gradually replacing Zr by Hf remarkably increases the density and improves the mechanical properties. However, a slight decrease in glass forming ability with increasing Hf content has also been identified through thermodynamic analysis although all the materials in the current study were still found to be amorphous. Many indentation studies have revealed only a few shear bands surrounding the indent on the top surface of the specimen. This small number of shear bands cannot account for the large plastic deformation beneath the indentations. Therefore, a bonded interface technique has been used to observe the slip-steps due to shear band evolution. Vickers indentations were performed along the interface of the bonded split specimen at increasing loads. At small indentation loads, the plastic deformation was primarily accommodated by semi-circular primary shear bands surrounding the indentation. At higher loads, secondary and tertiary shear bands were formed inside this plastic zone. A modified expanding cavity model was then used to predict the plastic zone size characterized by the shear bands and to identify the stress components responsible for the evolution of the various types of shear bands. The applicability of various hardness—yield-strength ( H −σγ ) relationships currently available in the literature for bulk metallic glasses (BMGs) is also investigated. Experimental data generated on ZrHf-based BMGs in the current study and those available elsewhere on other BMG compositions were used to validate the models. A modified expanding-cavity model, employed in earlier work, was extended to propose a new H −σγ relationship. Unlike previous models, the proposed model takes into account not only the indenter geometry and the material properties, but also the pressure sensitivity index of the BMGs. The influence of various model parameters is systematically analyzed. It is shown that there is a good correlation between the model predictions and the experimental data for a wide range of BMG compositions. Under dynamic Vickers indentation, a decrease in indentation hardness at high loading rate was observed compared to static indentation hardness. It was observed that at equivalent loads, dynamic indentations produced more severe deformation features on the loading surface than static indentations. Different from static indentation, two sets of widely spaced semi-circular shear bands with two different curvatures were observed. The observed shear band pattern and the strain rate softening in indentation hardness were rationalized based on the variations in the normal stress on the slip plane, the strain rate of shear and the temperature rise associated with the indentation deformation. Finally, a coupled thermo-mechanical model is proposed that utilizes a momentum diffusion mechanism for the growth and evolution of the final spacing of shear bands. The influence of strain rate, confinement pressure and critical shear displacement on the shear band spacing, temperature rise within the shear band, and the associated variation in flow stress have been captured and analyzed. Consistent with the known pressure sensitive behavior of BMGs, the current model clearly captures the influence of the normal stress in the formation of shear bands. The normal stress not only reduces the time to reach critical shear displacement but also causes a significant temperature rise during the shear band formation. Based on this observation, the variation of shear band spacing in a typical dynamic indentation test has been rationalized. The temperature rise within a shear band can be in excess of 2000K at high strain rate and high confinement pressure conditions. The associated drop in viscosity and flow stress may explain the observed decrease in fracture strength and indentation hardness. The above investigations provide valuable insight into the deformation behavior of BMGs under static and dynamic loading conditions. The shear band patterns observed in the above indentation studies can be helpful to understand and model the deformation features under complex loading scenarios such as the interaction of a penetrator with armor. Future work encompasses (1) extending and modifying the coupled thermo-mechanical model to account for the temperature rise in quasistatic deformation; and (2) expanding this model to account for the microstructural variation-crystallization and free volume migration associated with the deformation.

Towards the continuum limit in transport coefficient computations

The analytic continuation needed for the extraction of transport coefficients necessitates in principle a continuous function of the Euclidean time variable. We report on progress towards achieving the continuum limit for 2-point correlator measurements in thermal SU(3) gauge theory, with specific attention paid to scale setting. In particular, we improve upon the determination of the critical lattice coupling and the critical temperature of pure SU(3) gauge theory, estimating r0Tc ≃ 0.7470(7) after a continuum extrapolation. As an application the determination of the heavy quark momentum diffusion coefficient from a correlator of colour-electric fields attached to a Polyakov loop is discussed.

Free-Surface Aeration and Momentum Exchange at a Bottom Outlet

This study aims to provide some new understanding of the air-water flow properties in high-velocity water jets discharging past an abrupt drop. Such a setup has been little studied to date despite the relevance to bottom outlets. Downstream of the step brink, the free-jet entrains air at both upper and lower air-water interfaces, as well as along the sides. An air-water shear layer develops at the lower nappe interface. At the lower nappe, the velocity redistribution was successfully modelled and the velocity field was found to be similar to that in two-dimensional wake flow. The results highlighted further two distinct flow regions. Close to the brink (Wex < 5000), the flow was dominated by momentum transfer. Further downstream (Wex > 5000), a strong competition between air bubble diffusion and momentum exchanges took place.

Short-term spatial diffusion in sigma o+ o- optical molasses

We have measured the spatial diffusion of atoms in a three-dimensional sigma(+)-sigma(-) optical molasses over twenty milliseconds timescale, starting from the initial interaction of the atoms with the molasses. We find that the diffusion constants agree well with a linear model for these short time scales and also compare favourably to other studies of diffusion made over longer time scales. These measurements enable us to quantify the detection method known as freezing molasses. We discuss this method, for detecting and measuring the momentum distribution of cold atoms, which relies on the slow diffusion of atoms in optical molasses to produce a freeze-frame of the spatial distribution of the atoms. This method enables a longer interrogation interval, providing a greatly increased signal-to-noise ratio. (C) 1998 Elsevier Science B.V.

Non-equilibrium energy and momentum accommodation coefficients of Ar atoms scattered from Ni(001) in the thermal regime: A molecular dynamics study

Molecular dynamics simulations are used to study energy and momentum transfer of low-energy Ar atoms scattered from the Ni(001) surface. The investigation concentrates on the dependence of these processes on incident energy, angles of incidence and surface temperature. Energy transfer exhibits a strong dependence on the surface temperature, at incident energies below 500 meV, and incident angles close to specular incidence. Above 500 meV, the surface temperature dependence vanishes, and a limiting value in the amount of energy transferred to the surface is attained. Momentum exchange is investigated in terms of tangential and normal components. Both components exhibit a weak surface temperature dependence, but they have opposite behaviours at all incidence angles. In each component, momentum can be lost or gained following the interaction with the surface. (C) 1997 Elsevier Science B.V.

Fast, scalable master equation solution algorithms. IV. Lanczos iteration with diffusion approximation preconditioned iterative inversion

In this paper we propose a second linearly scalable method for solving large master equations arising in the context of gas-phase reactive systems. The new method is based on the well-known shift-invert Lanczos iteration using the GMRES iteration preconditioned using the diffusion approximation to the master equation to provide the inverse of the master equation matrix. In this way we avoid the cubic scaling of traditional master equation solution methods while maintaining the speed of a partial spectral decomposition. The method is tested using a master equation modeling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long-lived isomerizing intermediates. (C) 2003 American Institute of Physics.

Fast, scalable master equation solution algorithms. III. Direct time propagation accelerated by a diffusion approximation preconditioned iterative solver

In this paper we propose a novel fast and linearly scalable method for solving master equations arising in the context of gas-phase reactive systems, based on an existent stiff ordinary differential equation integrator. The required solution of a linear system involving the Jacobian matrix is achieved using the GMRES iteration preconditioned using the diffusion approximation to the master equation. In this way we avoid the cubic scaling of traditional master equation solution methods and maintain the low temperature robustness of numerical integration. The method is tested using a master equation modelling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long lived isomerizing intermediates. (C) 2003 American Institute of Physics.

Hydrodynamic origin of diffusion in nanopores

We study the transport of a subcritical Lennard-Jones fluid in a cylindrical nanopore, using a combination of equilibrium and nonequilibrium as well as dual control volume grand canonical molecular dynamics methods. We show that all three techniques yield the same value of the transport coefficient for diffusely reflecting pore walls, even in the presence of viscous transport. We also demonstrate that the classical Knudsen mechanism is not manifested, and that a combination of viscous flow and momentum exchange at the pore wall governs the transport over a wide range of densities.

High-Momentum Response of Liquid 3He

A final-state-effects formalism suitable to analyze the high-momentum response of Fermi liquids is presented and used to study the dynamic structure function of liquid 3He. The theory, developed as a natural extension of the Gersch-Rodriguez formalism, incorporates the Fermi statistics explicitly through a new additive term which depends on the semidiagonal two-body density matrix. The use of a realistic momentum distribution, calculated using the diffusion Monte Carlo method, and the inclusion of this additive correction allows for good agreement with available deep-inelastic neutron scattering data.

Influence of mass diffusion in sea ice dynamical models

The mixing of floes of different thickness caused by repeated deformation of the ice cover is modeled as diffusion, and the mass balance equation for sea ice accounting for mass diffusion is developed. The effect of deformational diffusion on the ice thickness balance is shown to reach 1% of the divergence effect, which describes ridging and lead formation. This means that with the same accuracy the mass balance equation can be written in terms of mean velocity rather than mean mass-weighted velocity, which one should correctly use for a multicomponent fluid such as sea ice with components identified by floe thickness. Mixing (diffusion) of sea ice also occurs because of turbulent variations in wind and ocean drags that are unresolved in models. Estimates of the importance of turbulent mass diffusion on the dynamic redistribution of ice thickness are determined using empirical data for the turbulent diffusivity. For long-time-scale prediction (≫5 days), where unresolved atmospheric motion may have a length scale on the order of the Arctic basin and the time scale is larger than the synoptic time scale of atmospheric events, turbulent mass diffusion can exceed 10% of the divergence effect. However, for short-time-scale prediction, for example, 5 days, the unresolved scales are on the order of 100 km, and turbulent diffusion is about 0.1% of the divergence effect. Because inertial effects are small in the dynamics of the sea ice pack, diffusive momentum transfer can be disregarded.

The diffusion of grassroots innovations for sustainability in Italy and Great Britain: an exploratory spatial data analysis

Little research so far has been devoted to understanding the diffusion of grassroots innovation for sustainability across space. This paper explores and compares the spatial diffusion of two networks of grassroots innovations, the Transition Towns Network (TTN) and Gruppi di Acquisto Solidale (Solidarity Purchasing Groups – GAS), in Great Britain and Italy. Spatio-temporal diffusion data were mined from available datasets, and patterns of diffusion were uncovered through an exploratory data analysis. The analysis shows that GAS and TTN diffusion in Italy and Great Britain is spatially structured, and that the spatial structure has changed over time. TTN has diffused differently in Great Britain and Italy, while GAS and TTN have diffused similarly in central Italy. The uneven diffusion of these grassroots networks on the one hand challenges current narratives on the momentum of grassroots innovations, but on the other highlights important issues in the geography of grassroots innovations for sustainability, such as cross-movement transfers and collaborations, institutional thickness, and interplay of different proximities in grassroots innovation diffusion.