Deterministic ratchet from stationary light fields

Ratchets are dynamic systems where particle transport is induced by zero-average forces due to the interplay between nonlinearity and asymmetry. Generally, they rely on the effect of a strong external driving. We show that stationary optical lattices can be designed to generate particle flow in one direction while requiring neither noise nor driving. Such optical fields must be arranged to yield a combination of conservative (dipole) and nonconservative (radiation pressure) forces. Under strong friction all paths converge to a discrete set of limit periodic trajectories flowing in the same direction.Comment: 6 pages, 4 figure

Null Energy Condition Violation and Classical Stability in the Bianchi I Metric

The stability of isotropic cosmological solutions in the Bianchi I model is considered. We prove that the stability of isotropic solutions in the Bianchi I metric for a positive Hubble parameter follows from their stability in the Friedmann-Robertson-Walker metric. This result is applied to models inspired by string field theory, which violate the null energy condition. Examples of stable isotropic solutions are presented. We also consider the k-essence model and analyse the stability of solutions of the form $\Phi(t)=t$.Comment: 27 pages, references added, accepted for publication in Phys. Rev.

Stochastic Flux-Freezing and Magnetic Dynamo

We argue that magnetic flux-conservation in turbulent plasmas at high magnetic Reynolds numbers neither holds in the conventional sense nor is entirely broken, but instead is valid in a novel statistical sense associated to the "spontaneous stochasticity" of Lagrangian particle tra jectories. The latter phenomenon is due to the explosive separation of particles undergoing turbulent Richardson diffusion, which leads to a breakdown of Laplacian determinism for classical dynamics. We discuss empirical evidence for spontaneous stochasticity, including our own new numerical results. We then use a Lagrangian path-integral approach to establish stochastic flux-freezing for resistive hydromagnetic equations and to argue, based on the properties of Richardson diffusion, that flux-conservation must remain stochastic at infinite magnetic Reynolds number. As an important application of these results we consider the kinematic, fluctuation dynamo in non-helical, incompressible turbulence at unit magnetic Prandtl number. We present results on the Lagrangian dynamo mechanisms by a stochastic particle method which demonstrate a strong similarity between the Pr = 1 and Pr = 0 dynamos. Stochasticity of field-line motion is an essential ingredient of both. We finally consider briefly some consequences for nonlinear MHD turbulence, dynamo and reconnectionComment: 29 pages, 10 figure

Synthetic Mudscapes: Human Interventions in Deltaic Land Building

In order to defend infrastructure, economy, and settlement in Southeast Louisiana, we must construct new land to mitigate increasing risk. Links between urban environments and economic drivers have constrained the dynamic delta landscape for generations, now threatening to undermine the ecological fitness of the entire region. Static methods of measuring, controlling, and valuing land fail in an environment that is constantly in flux; change and indeterminacy are denied by traditional inhabitation. Multiple land building practices reintroduce deltaic fluctuation and strategic deposition of fertile material to form the foundations of a multi-layered defence strategy. Manufactured marshlands reduce exposure to storm surge further inland. Virtual monitoring and communication networks inform design decisions and land use becomes determined by its ecological health. Mudscapes at the threshold of land and water place new value on former wastelands. The social, economic, and ecological evolution of the region are defended by an expanded web of growing land

Evolution of Global Relativistic Jets: Collimations and Expansion with kKHI and the Weibel Instability

One of the key open questions in the study of relativistic jets is their interaction with the environment. Here, we study the initial evolution of both electron-proton and electron-positron relativistic jets, focusing on their lateral interaction with the ambient plasma. We trace the generation and evolution of the toroidal magnetic field generated by both kinetic Kelvin-Helmholtz (kKH) and Mushroom instabilities (MI). This magnetic field collimates the jet. We show that in electron-proton jet, electrons are perpendicularly accelerated with jet collimation. The magnetic polarity switches from the clockwise to anti-clockwise in the middle of jet, as the instabilities weaken. For the electron-positron jet, we find strong mixture of electron-positron with the ambient plasma, that results in the creation of a bow shock. Merger of magnetic field current filaments generate density bumps which initiate a forward shock. The strong mixing between jet and ambient particles prevents full development of the jet on the studied scale. Our results therefore provide a direct evidence for both jet collimation and particle acceleration in the created bow shock. Differences in the magnetic field structures generated by electron-proton and electron-positron jets may contribute to observable differences in the polarized properties of emission by electrons.Comment: 25 pages, 12 figures, ApJ, accepte

Experimental and theoretical lifetimes and transition probabilities in Sb I

We present experimental atomic lifetimes for 12 levels in Sb I, out of which seven are reported for the first time. The levels belong to the 5p$^2$($^3$P)6s $^{2}$P, $^{4}$P and 5p$^2$($^3$P)5d $^{4}$P, $^{4}$F and $^{2}$F terms. The lifetimes were measured using time-resolved laser-induced fluorescence. In addition, we report new calculations of transition probabilities in Sb I using a Multiconfigurational Dirac-Hartree-Fock method. The physical model being tested through comparisons between theoretical and experimental lifetimes for 5d and 6s levels. The lifetimes of the 5d $^4$F$_{3/2, 5/2, 7/2}$ levels (19.5, 7.8 and 54 ns, respectively) depend strongly on the $J$-value. This is explained by different degrees of level mixing for the different levels in the $^4$F term.Comment: 10 page

A Note on the Regularity of Inviscid Shell Model of Turbulence

In this paper we continue the analytical study of the sabra shell model of energy turbulent cascade initiated in \cite{CLT05}. We prove the global existence of weak solutions of the inviscid sabra shell model, and show that these solutions are unique for some short interval of time. In addition, we prove that the solutions conserve the energy, provided that the components of the solution satisfy $|{u_n}| \le C k_n^{-1/3} (\sqrt{n} \log(n+1))^{-1}$, for some positive absolute constant $C$, which is the analogue of the Onsager's conjecture for the Euler's equations. Moreover, we give a Beal-Kato-Majda type criterion for the blow-up of solutions of the inviscid sabra shell model and show the global regularity of the solutions in the ``two-dimensional'' parameters regime

Transmission of correlated electrons through sharp domain walls in magnetic nanowires: a renormalization group approach

The transmission of correlated electrons through a domain wall in a ferromagnetic one dimensional system is studied theoretically in the limit of a domain wall width smaller or comparable to the electron Fermi wavelength. The domain wall gives rise to both potential and spin dependent scattering of the charge carriers. Using a poor man's renormalization group approach for the electron-electron interactions, we obtain the low temperature behavior of the reflection and transmission coefficients. The results show that the low-temperature conductance is governed by the electron correlations, which may suppress charge transport without suppressing spin current. The results may account for a huge magnetoresistance associated with a domain wall in ballistic nanocontacs.Comment: 13 pages, 6 figure

Relative Oscillation Theory, Weighted Zeros of the Wronskian, and the Spectral Shift Function

We develop an analog of classical oscillation theory for Sturm-Liouville operators which, rather than measuring the spectrum of one single operator, measures the difference between the spectra of two different operators. This is done by replacing zeros of solutions of one operator by weighted zeros of Wronskians of solutions of two different operators. In particular, we show that a Sturm-type comparison theorem still holds in this situation and demonstrate how this can be used to investigate the finiteness of eigenvalues in essential spectral gaps. Furthermore, the connection with Krein's spectral shift function is established.Comment: 26 page

Cosmological dynamics of R^n gravity

A detailed analysis of dynamics of cosmological models based on $R^{n}$ gravity is presented. We show that the cosmological equations can be written as a first order autonomous system and analyzed using the standard techniques of dynamical system theory. In absence of perfect fluid matter, we find exact solutions whose behavior and stability are analyzed in terms of the values of the parameter $n$. When matter is introduced, the nature of the (non-minimal) coupling between matter and higher order gravity induces restrictions on the allowed values of $n$. Selecting such intervals of values and following the same procedure used in the vacuum case, we present exact solutions and analyze their stability for a generic value of the parameter $n$. From this analysis emerges the result that for a large set of initial conditions an accelerated expansion is an attractor for the evolution of the $R^n$ cosmology. When matter is present a transient almost-Friedman phase can also be present before the transition to an accelerated expansion.Comment: revised and extended version, 35 pages, 12 tables, 14 figures which are not included and can be found at http://www.mth.uct.ac.za/~peter/R