Taylor's (1935) dissipation surrogate reinterpreted

New results from direct numerical simulation of decaying isotropic turbulence show that Taylor’s expression for the viscous dissipation rate ε = CεU3/L is more appropriately interpreted as a surrogate for the inertial energy flux. As a consequence, the well known dependence of the Taylor prefactor Cε on Reynolds number Cε(RL)→Cε,∞ can be understood as corresponding to the onset of an inertial range

Optical Studies of Metal- Semiconductor Transmutations Produced by Intercalation

Spectra of the alkali metal intercalation products of MoS2 and NbSc2 arc interpreted in terms of a previously published band model

Spectral analysis of structure functions and their scaling exponents in forced isotropic turbulence

The pseudospectral method, in conjunction with a new technique for obtaining scaling exponents $\zeta_n$ from the structure functions $S_n(r)$, is presented as an alternative to the extended self-similarity (ESS) method and the use of generalized structure functions. We propose plotting the ratio $|S_n(r)/S_3(r)|$ against the separation $r$ in accordance with a standard technique for analysing experimental data. This method differs from the ESS technique, which plots $S_n(r)$ against $S_3(r)$, with the assumption $S_3(r) \sim r$. Using our method for the particular case of $S_2(r)$ we obtain the new result that the exponent $\zeta_2$ decreases as the Taylor-Reynolds number increases, with $\zeta_2 \to 0.679 \pm 0.013$ as $R_{\lambda} \to \infty$. This supports the idea of finite-viscosity corrections to the K41 prediction for $S_2$, and is the opposite of the result obtained by ESS. The pseudospectral method also permits the forcing to be taken into account exactly through the calculation of the energy input in real space from the work spectrum of the stirring forces.Comment: 31 pages including appendices, 10 figure

Energy transfer and dissipation in forced isotropic turbulence

A model for the Reynolds number dependence of the dimensionless dissipation rate $C_{\varepsilon}$ was derived from the dimensionless K\'{a}rm\'{a}n-Howarth equation, resulting in $C_{\varepsilon}=C_{\varepsilon, \infty} + C/R_L + O(1/R_L^2)$, where $R_L$ is the integral scale Reynolds number. The coefficients $C$ and $C_{\varepsilon,\infty}$ arise from asymptotic expansions of the dimensionless second- and third-order structure functions. This theoretical work was supplemented by direct numerical simulations (DNSs) of forced isotropic turbulence for integral scale Reynolds numbers up to $R_L=5875$ ($R_\lambda=435$), which were used to establish that the decay of dimensionless dissipation with increasing Reynolds number took the form of a power law $R_L^n$ with exponent value $n = -1.000\pm 0.009$, and that this decay of $C_{\varepsilon}$ was actually due to the increase in the Taylor surrogate $U^3/L$. The model equation was fitted to data from the DNS which resulted in the value $C=18.9\pm 1.3$ and in an asymptotic value for $C_\varepsilon$ in the infinite Reynolds number limit of $C_{\varepsilon,\infty} = 0.468 \pm 0.006$.Comment: 26 pages including references and 6 figures. arXiv admin note: text overlap with arXiv:1307.457

Re-examination of the infra-red properties of randomly stirred hydrodynamics

Dynamic renormalization group (RG) methods were originally used by Forster, Nelson and Stephen (FNS) to study the large-scale behaviour of randomly-stirred, incompressible fluids governed by the Navier-Stokes equations. Similar calculations using a variety of methods have been performed since, but have led to a discrepancy in results. In this paper, we carefully re-examine in $d$-dimensions the approaches used to calculate the renormalized viscosity increment and, by including an additional constraint which is neglected in many procedures, conclude that the original result of FNS is correct. By explicitly using step functions to control the domain of integration, we calculate a non-zero correction caused by boundary terms which cannot be ignored. We then go on to analyze how the noise renormalization, absent in many approaches, contributes an ${\mathcal O}(k^2)$ correction to the force autocorrelation and show conditions for this to be taken as a renormalization of the noise coefficient. Following this, we discuss the applicability of this RG procedure to the calculation of the inertial range properties of fluid turbulence.Comment: 16 pages, 6 figure

Cooling of relativistic electron beams in intense laser pulses : chirps and radiation

Next-generation high-power laser facilities (such as the Extreme Light Infrastructure) will provide unprecedented field intensities, and will allow us to probe qualitatively new physical regimes for the first time. One of the important fundamental questions which will be addressed is particle dynamics when radiation reaction and quantum effects play a significant role. Classical theories of radiation reaction predict beam cooling in the interaction of a relativistic electron bunch and a high-intensity laser pulse, with final-state properties only dependent on the laser fluence. The observed quantum suppression of this cooling instead exhibits a dependence on the laser intensity directly. This offers the potential for final-state properties to be modified or even controlled by tailoring the intensity profile of the laser pulse. In addition to beam properties, quantum effects will be manifest in the emitted radiation spectra, which could be manipulated for use as radiation sources. We compare predictions made by classical, quasi-classical and stochastic theories of radiation reaction, and investigate the influence of chirped laser pulses on the observed radiation spectra

Electron beam cooling in intense focussed laser pulses

In the coming years, a new generation of high-power laser facilities (such as the Extreme Light Infrastructure) will become operational, for which it is important to understand how the interaction with intense laser pulses affects the bulk properties of relativistic electron bunches. At such high field intensities, we expect both radiation reaction and quantum effects to have a dominant role to play in determining the dynamics. The reduction in relative energy spread (beam cooling) at the expense of mean beam energy predicted by classical theories of radiation reaction has been shown to occur equally in the longitudinal and transverse directions, whereas this symmetry is broken when the theory is extended to approximate certain quantum effects. The reduction in longitudinal cooling suggests that the effects of radiation reaction could be better observed in measurements of the transverse distribution, which for real-world laser pulses motivates the investigation of the angular dependence of the interaction. Using a stochastic single-photon emission model with a (Gaussian beam) focussed pulse, we find strong angular dependence of the stochastic heating

Propagating mode-I fracture in amorphous materials using the continuous random network (CRN) model

We study propagating mode-I fracture in two dimensional amorphous materials using atomistic simulations. We used the continuous random network (CRN) model of an amorphous material, creating samples using a two dimensional analogue of the WWW (Wooten, Winer & Weaire) Monte-Carlo algorithm. For modeling fracture, molecular-dynamics simulations were run on the resulting samples. The results of our simulations reproduce the main experimental features. In addition to achieving a steady-state crack under a constant driving displacement (which had not yet been achieved by other atomistic models for amorphous materials), the runs show micro-branching, which increases with driving, transitioning to macro-branching for the largest drivings. Beside the qualitative visual similarity of the simulated cracks to experiment, the simulation also succeeds in explaining the experimentally observed oscillations of the crack velocity

Experimental analysis of lateral impact on planar brittle material

The fragmentation of alumina and glass plates due to lateral impact is studied. A few hundred plates have been fragmented at different impact velocities and the produced fragments are analyzed. The method employed in this work allows one to investigate some geometrical properties of the fragments, besides the traditional size distribution usually studied in former experiments. We found that, although both materials exhibit qualitative similar fragment size distribution function, their geometrical properties appear to be quite different. A schematic model for two-dimensional fragmentation is also presented and its predictions are compared to our experimental results. The comparison suggests that the analysis of the fragments' geometrical properties constitutes a more stringent test of the theoretical models' assumptions than the size distribution