Pacifying the Fermi-liquid: battling the devious fermion signs

The fermion sign problem is studied in the path integral formalism. The standard picture of Fermi liquids is first critically analyzed, pointing out some of its rather peculiar properties. The insightful work of Ceperley in constructing fermionic path integrals in terms of constrained world-lines is then reviewed. In this representation, the minus signs associated with Fermi-Dirac statistics are self consistently translated into a geometrical constraint structure (the {\em nodal hypersurface}) acting on an effective bosonic dynamics. As an illustrative example we use this formalism to study 1+1-dimensional systems, where statistics are irrelevant, and hence the sign problem can be circumvented. In this low-dimensional example, the structure of the nodal constraints leads to a lucid picture of the entropic interaction essential to one-dimensional physics. Working with the path integral in momentum space, we then show that the Fermi gas can be understood by analogy to a Mott insulator in a harmonic trap. Going back to real space, we discuss the topological properties of the nodal cells, and suggest a new holographic conjecture relating Fermi liquids in higher dimensions to soft-core bosons in one dimension. We also discuss some possible connections between mixed Bose/Fermi systems and supersymmetry.Comment: 28 pages, 5 figure

Developed turbulence: From full simulations to full mode reductions

Developed Navier-Stokes turbulence is simulated with varying wavevector mode reductions. The flatness and the skewness of the velocity derivative depend on the degree of mode reduction. They show a crossover towards the value of the full numerical simulation when the viscous subrange starts to be resolved. The intermittency corrections of the scaling exponents of the pth order velocity structure functions seem to depend mainly on the proper resolution of the inertial subrange. Universal scaling properties (i.e., independent of the degree of mode reduction) are found for the relative scaling exponents rho which were recently defined by Benzi et al.Comment: 4 pages, 5 eps-figures, replaces version from August 5th, 199

Application of CRISPR/Cas9 in crop quality improvement

The various crop species are major agricultural products and play an indispensable role in sustaining human life. Over a long period, breeders strove to increase crop yield and improve quality through traditional breeding strategies. Today, many breeders have achieved remarkable results using modern molecular technologies. Recently, a new gene-editing system, named the clustered regularly interspaced short palindromic repeats (CRISPR)/Cas9 technology, has also succeeded in improving crop quality. It has become the most popular tool for crop improvement due to its versatility. It has accelerated crop breeding progress by virtue of its precision in specific gene editing. This review summarizes the current application of CRISPR/Cas9 technology in crop quality improvement. It includes the modulation in appearance, palatability, nutritional components and other preferred traits of various crops. In addition, the challenge in its future application is also discussed

Finite size corrections to scaling in high Reynolds number turbulence

We study analytically and numerically the corrections to scaling in turbulence which arise due to the finite ratio of the outer scale $L$ of turbulence to the viscous scale $\eta$, i.e., they are due to finite size effects as anisotropic forcing or boundary conditions at large scales. We find that the deviations \dzm from the classical Kolmogorov scaling $\zeta_m = m/3$ of the velocity moments \langle |\u(\k)|^m\rangle \propto k^{-\zeta_m} decrease like $\delta\zeta_m (Re) =c_m Re^{-3/10}$. Our numerics employ a reduced wave vector set approximation for which the small scale structures are not fully resolved. Within this approximation we do not find $Re$ independent anomalous scaling within the inertial subrange. If anomalous scaling in the inertial subrange can be verified in the large $Re$ limit, this supports the suggestion that small scale structures should be responsible, originating from viscosity either in the bulk (vortex tubes or sheets) or from the boundary layers (plumes or swirls)

Photolithographic Approaches for Fabricating Highly Ordered Nanopatterned Arrays

In this work, we report that large area metal nanowire and polymer nanotube arrays were successfully patterned by photolithographic approach using anodic aluminum oxide (AAO) templates. Nanowires were produced by electrochemical deposition, and nanotubes by solution-wetting. The highly ordered patterns of nanowire and nanotube arrays were observed using scanning electron microscopy (SEM) and found to stand free on the substrate. The method is expected to play an important role in the application of microdevices in the future

Circulation Statistics in Three-Dimensional Turbulent Flows

We study the large $\lambda$ limit of the loop-dependent characteristic functional $Z(\lambda)=$, related to the probability density function (PDF) of the circulation around a closed contour $c$. The analysis is carried out in the framework of the Martin-Siggia-Rose field theory formulation of the turbulence problem, by means of the saddle-point technique. Axisymmetric instantons, labelled by the component $\sigma_{zz}$ of the strain field -- a partially annealed variable in our formalism -- are obtained for a circular loop in the $xy$ plane, with radius defined in the inertial range. Fluctuations of the velocity field around the saddle-point solutions are relevant, leading to the lorentzian asymptotic behavior $Z(\lambda) \sim 1/{\lambda^2}$. The ${\cal O}(1 / {\lambda^4})$ subleading correction and the asymmetry between right and left PDF tails due to parity breaking mechanisms are also investigated.Comment: Computations are discussed in a more detailed way; accepted for publication in Physical Review

Scaling properties of three-dimensional magnetohydrodynamic turbulence

The scaling properties of three-dimensional magnetohydrodynamic turbulence are obtained from direct numerical simulations of decaying turbulence using $512^3$ modes. The results indicate that the turbulence does not follow the Iroshnikov-Kraichnan phenomenology.In the case of hyperresistivity, the structure functions exhibit a clear scaling range yielding absolute values of the scaling exponents $\zeta_p$. The scaling exponents agree with a modified She-Leveque model $\zeta_p=p/9 + 1 - (1/3)^{p/3}$, corresponding to Kolmogorov scaling but sheet-like geometry of the dissipative structures

Universality in fully developed turbulence

We extend the numerical simulations of She et al. [Phys.\ Rev.\ Lett.\ 70, 3251 (1993)] of highly turbulent flow with $15 \le$ Taylor-Reynolds number $Re_\lambda\le 200$ up to $Re_\lambda \approx 45000$, employing a reduced wave vector set method (introduced earlier) to approximately solve the Navier-Stokes equation. First, also for these extremely high Reynolds numbers $Re_\lambda$, the energy spectra as well as the higher moments -- when scaled by the spectral intensity at the wave number $k_p$ of peak dissipation -- can be described by {\it one universal} function of $k/k_p$ for all $Re_\lambda$. Second, the ISR scaling exponents $\zeta_m$ of this universal function are in agreement with the 1941 Kolmogorov theory (the better, the large $Re_\lambda$ is), as is the $Re_\lambda$ dependence of $k_p$. Only around $k_p$ viscous damping leads to slight energy pileup in the spectra, as in the experimental data (bottleneck phenomenon).Comment: 14 pages, Latex, 5 figures (on request), 3 tables, submitted to Phys. Rev.

Toward the End of Time

The null-brane space-time provides a simple model of a big crunch/big bang singularity. A non-perturbative definition of M-theory on this space-time was recently provided using matrix theory. We derive the fermion couplings for this matrix model and study the leading quantum effects. These effects include particle production and a time-dependent potential. Our results suggest that as the null-brane develops a big crunch singularity, the usual notion of space-time is replaced by an interacting gluon phase. This gluon phase appears to constitute the end of our conventional picture of space and time.Comment: 31 pages, reference adde