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Register a new userSuperfast amplification and superfast nonlinear saturation of perturbations as the mechanism of turbulence
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Ruelle predicted that the maximal amplification of perturbations in homogeneous isotropic turbulence is exponential $e^{sigma sqrt{Re} t}$ (where $sigma sqrt{Re}$ is the maximal Liapunov exponent). In our earlier works, we predicted that the maximal amplification of perturbations in fully developed turbulence is faster than exponential $e^{sigma sqrt{Re} sqrt{t} +sigma_1 t}$. That is, we predicted superfast initial amplification of perturbations. Built upon our earlier numerical verification of our prediction, here we conduct a large numerical verification with resolution up to $2048^3$ and Reynolds number up to $6210$. Our direct numerical simulation here confirms our analytical prediction. Our numerical simulation also demonstrates that such superfast amplification of perturbations leads to superfast nonlinear saturation. We conclude that such superfast amplification and superfast nonlinear saturation of ever existing perturbations serve as the mechanism for the generation, development and persistence of fully developed turbulence.
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Currently laser cooling schemes are fundamentally based on the weak coupling regime. This requirement sets the trap frequency as an upper bound to the cooling rate. In this work we present a numerical study that shows the feasibility of cooling in the strong coupling regime which then allows cooling rates that are faster than the trap frequency with state of the art experimental parameters. The scheme we present can work for trapped atoms or ions as well as mechanical oscillators. It can also cool medium size ions chains close to the ground state.
Recent high-precision measurements of nuclear deep inelastic scattering at high x and moderate 6 < Q$^2$ < 9GeV$^2$ give a rare opportunity to reach the quark distributions in the {it superfast} region, in which the momentum fraction of the nucleon carried by its constituent quark is larger than the total fraction of the nucleon at rest, x>1. We derive the leading-order QCD evolution equation for such quarks with the goal of relating the moderate-Q$^2$ data to the two earlier measurements of superfast quark distributions at large 60 < Q$^2$ < 200~GeV$^2$. Since the high-Q$^2$ measurements gave strongly contradictory estimates of the nuclear effects that generate superfast quarks, relating them to the high-precision, moderate-Q$^2$ data through QCD evolution allows us to clarify this longstanding issue. Our calculations indicate that the moderate-Q$^2$ data at $xlesssim 1.05$ are in better agreement with the high-Q$^2$ data measured in (anti)neutrino-nuclear reactions which require substantial high-momentum nuclear effects in the generation of superfast quarks. Our prediction for the high-Q$^2$ and x>1.1 region is somewhat in the middle of the neutrino-nuclear and muon-nuclear scattering data.
Short term unpredictability is discovered numerically for high Reynolds number fluid flows under periodic boundary conditions. Furthermore, the abundance of the short term unpredictability is also discovered. These discoveries support our theory that fully developed turbulence is constantly driven by such short term unpredictability.
We investigate universality of the Eulerian velocity structure functions using velocity fields obtained from the stereoscopic particle image velocimetry (SPIV) technique in experiments and the direct numerical simulations (DNS) of the Navier-Stokes equations. We show that the numerical and experimental velocity structure functions up to order 9 follow a log-universality; we find that they collapse on a universal curve, if we use units that include logarithmic dependence on the Reynolds number. We then investigate the meaning and consequences of such log-universality, and show that it is connected with the properties of a multifractal free energy, based on an analogy between multifractal and themodynamics. We show that in such a framework, the existence of a fluctuating dissipation scale is associated with a phase transition describing the relaminarisation of rough velocity fields with different Holder exponents. Such a phase transition has been already observed using the Lagrangian velocity structure functions, but was so far believed to be out of reach for the Eulerian data.
Simulation of fermionic many-body systems on a quantum computer requires a suitable encoding of fermionic degrees of freedom into qubits. Here we revisit the Superfast Encoding introduced by Kitaev and one of the authors. This encoding maps a target fermionic Hamiltonian with two-body interactions on a graph of degree $d$ to a qubit simulator Hamiltonian composed of Pauli operators of weight $O(d)$. A system of $m$ fermi modes gets mapped to $n=O(md)$ qubits. We propose Generalized Superfast Encodings (GSE) which require the same number of qubits as the original one but have more favorable properties. First, we describe a GSE such that the corresponding quantum code corrects any single-qubit error provided that the interaction graph has degree $dge 6$. In contrast, we prove that the original Superfast Encoding lacks the error correction property for $dle 6$. Secondly, we describe a GSE that reduces the Pauli weight of the simulator Hamiltonian from $O(d)$ to $O(log{d})$. The robustness against errors and a simplified structure of the simulator Hamiltonian offered by GSEs can make simulation of fermionic systems within the reach of near-term quantum devices. As an example, we apply the new encoding to the fermionic Hubbard model on a 2D lattice.
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