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

Experimental analysis of lateral impact on planar brittle material: spatial properties of the cracks

The breakup of glass and alumina plates due to planar impacts on one of their lateral sides is studied. Particular attention is given to investigating the spatial location of the cracks within the plates. Analysis based on a phenomenological model suggests that bifurcations along the cracks' paths are more likely to take place closer to the impact region than far away from it, i. e., the bifurcation probability seems to lower as the perpendicular distance from the impacted lateral in- creases. It is also found that many observables are not sensitive to the plate material used in this work, as long as the fragment multiplicities corresponding to the fragmentation of the plates are similar. This gives support to the universal properties of the fragmentation process reported in for- mer experiments. However, even under the just mentioned circumstances, some spatial observables are capable of distinguishing the material of which the plates are made and, therefore, it suggests that this universality should be carefully investigated

A Mach-Zehnder interferometric switch with a 0.2 Vmm voltage length product

We have developed a 2*2 Mach Zehnder interferometric switch employing laterally contacted hetero n-i-p-i quantum wells for providing refractive index changes. We observe switching over a 4 pi range with an on/off ratio of 17:1. A differential switching voltage as low as 0.2 V.mm is observed in the push-pull configuration. It is the objective of the present paper to reduce the switching voltage-length product of a Mach-Zehnder interferometric switch by exploiting the advantages of a hetero n-i-p-i quantum well structure for providing refractive index changes in the arms of a Mach Zehnder interferometer switc

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

Nonequilibrium brittle fracture propagation: Steady state, oscillations and intermittency

A minimal model is constructed for two-dimensional fracture propagation. The heterogeneous process zone is presumed to suppress stress relaxation rate, leading to non-quasistatic behavior. Using the Yoffe solution, I construct and solve a dynamical equation for the tip stress. I discuss a generic tip velocity response to local stress and find that noise-free propagation is either at steady state or oscillatory, depending only on one material parameter. Noise gives rise to intermittency and quasi-periodicity. The theory explains the velocity oscillations and the complicated behavior seen in polymeric and amorphous brittle materials. I suggest experimental verifications and new connections between velocity measurements and material properties.Comment: To appear in Phys. Rev. Lett., 6 pages, self-contained TeX file, 3 postscript figures upon request from author at [email protected] or [email protected], http://cnls-www.lanl.gov/homepages/rafi/rafindex.htm

An accurate description of quantum size effects in InP nanocrystallites over a wide range of sizes

We obtain an effective parametrization of the bulk electronic structure of InP within the Tight Binding scheme. Using these parameters, we calculate the electronic structure of InP clusters with the size ranging upto 7.5 nm. The calculated variations in the electronic structure as a function of the cluster size is found to be in excellent agreement with experimental results over the entire range of sizes, establishing the effectiveness and transferability of the obtained parameter strengths.Comment: 9 pages, 3 figures, pdf file available at http://sscu.iisc.ernet.in/~sampan/publications.htm

Monte-Carlo simulations of the recombination dynamics in porous silicon

A simple lattice model describing the recombination dynamics in visible light emitting porous Silicon is presented. In the model, each occupied lattice site represents a Si crystal of nanometer size. The disordered structure of porous Silicon is modeled by modified random percolation networks in two and three dimensions. Both correlated (excitons) and uncorrelated electron-hole pairs have been studied. Radiative and non-radiative processes as well as hopping between nearest neighbor occupied sites are taken into account. By means of extensive Monte-Carlo simulations, we show that the recombination dynamics in porous Silicon is due to a dispersive diffusion of excitons in a disordered arrangement of interconnected Si quantum dots. The simulated luminescence decay for the excitons shows a stretched exponential lineshape while for uncorrelated electron-hole pairs a power law decay is suggested. Our results successfully account for the recombination dynamics recently observed in the experiments. The present model is a prototype for a larger class of models describing diffusion of particles in a complex disordered system.Comment: 33 pages, RevTeX, 19 figures available on request to [email protected]

Excitons in type-II quantum dots: Finite offsets

Quantum size effects for an exciton attached to a spherical quantum dot are calculated by a variational approach. The band line-ups are assumed to be type-II with finite offsets. The dependence of the exciton binding energy upon the dot radius and the offsets is studied for different sets of electron and hole effective masses

Mechanisms of viral capsid assembly around a polymer

Capsids of many viruses assemble around nucleic acids or other polymers. Understanding how the properties of the packaged polymer affect the assembly process could promote biomedical efforts to prevent viral assembly or nanomaterials applications that exploit assembly. To this end, we simulate on a lattice the dynamical assembly of closed, hollow shells composed of several hundred to 1000 subunits, around a flexible polymer. We find that assembly is most efficient at an optimum polymer length that scales with the surface area of the capsid; significantly longer than optimal polymers often lead to partial-capsids with unpackaged polymer `tails' or a competition between multiple partial-capsids attached to a single polymer. These predictions can be tested with bulk experiments in which capsid proteins assemble around homopolymeric RNA or synthetic polyelectrolytes. We also find that the polymer can increase the net rate of subunit accretion to a growing capsid both by stabilizing the addition of new subunits and by enhancing the incoming flux of subunits; the effects of these processes may be distinguishable with experiments that monitor the assembly of individual capsids.Comment: 7 figure