Evolving turbulence and magnetic fields in galaxy clusters

We discuss, using simple analytical models and MHD simulations, the origin and parameters of turbulence and magnetic fields in galaxy clusters. Three physically distinct regimes can be identified in the evolution of cluster turbulence and magnetic fields. Firstly, the fluctuation dynamo will produce microgauss-strong, random magnetic fields during cluster formation and major mergers. Turbulent velocity of about 300 km/s can be maintained at scales 100-200 kpc. The magnetic field is intermittent, has a smaller scale of 20-30 kpc and average strength of 2 microgauss. Secondly, when major mergers end, turbulent speed and magnetic field undergo a power-law decay, decreasing in strength but increasing in scale by a factor of about two. Thirdly, smaller-mass subclusters and cluster galaxies produce turbulent wakes, with turbulent speeds and magnetic field strengths similar to those quoted above. The velocity scales are about 200 kpc and 10 kpc respectively, and the magnetic field scale is about 6 times smaller. Although these wakes may fill only a small fraction of the cluster volume, their area covering factor can be close to unity. So one can potentially reconcile observations that indicate the coexistence of turbulence with ordered filamentary gas structures, as in the Perseus cluster. Random Faraday rotation measure is estimated to be typically 100-200 rad/m^2, in agreement with observations. We predict detectable synchrotron polarization from cluster radio halos at wavelengths 3-6 cm, if observed at sufficiently high resolution (abridged).Comment: 20 pages, 9 figures, Replaced to match version accepted by MNRA

A Simplest Swimmer at Low Reynolds Number: Three Linked Spheres

We propose a very simple one-dimensional swimmer consisting of three spheres that are linked by rigid rods whose lengths can change between two values. With a periodic motion in a non-reciprocal fashion, which breaks the time-reversal symmetry as well as the translational symmetry, we show that the model device can swim at low Reynolds number. This model system could be used in constructing molecular-size machines

Bulletin No. 140 - The Summer Pruning of a Young Bearing Apple Orchard

The majority of horticultural writers seem to favor the summer pruning of apple trees. The practice, and the arguments made in its favor vary widely and in some instances seem almost contradictory. On the other hand some experimenters and practical workers have obtained negative results by summer pruning from the view-point of crop production and tree growth. Dickens(1) caused unproductive ten year old apple trees in Kansas to bear satisfactorily during the fourth year of summer pruning. The Gardners\u27 Chronicle(2) compiled the opinions of more than one hundrend eighty-five fruit growers who practiced summer pruning, and about 82% of these orchardists reported satisfactory results while the remainder expressed doubts as to the value of the practice. Opinions compiled from English fruit growers by the Journal of Royal Horticulture Society(3) (1908) showed that the consensus of opinion was uncertain as to the effects of summer pruning and that much depended upon soil, climate, varieties and season of practice. Drinkard(4) checked wood growth and greatly stimulated the formation of fruit buds by summer pruning but one year

On the stationarity of linearly forced turbulence in finite domains

A simple scheme of forcing turbulence away from decay was introduced by Lundgren some time ago, the `linear forcing', which amounts to a force term linear in the velocity field with a constant coefficient. The evolution of linearly forced turbulence towards a stationary final state, as indicated by direct numerical simulations (DNS), is examined from a theoretical point of view based on symmetry arguments. In order to follow closely the DNS the flow is assumed to live in a cubic domain with periodic boundary conditions. The simplicity of the linear forcing scheme allows one to re-write the problem as one of decaying turbulence with a decreasing viscosity. Scaling symmetry considerations suggest that the system evolves to a stationary state, evolution that may be understood as the gradual breaking of a larger approximate symmetry to a smaller exact symmetry. The same arguments show that the finiteness of the domain is intimately related to the evolution of the system to a stationary state at late times, as well as the consistency of this state with a high degree of isotropy imposed by the symmetries of the domain itself. The fluctuations observed in the DNS for all quantities in the stationary state can be associated with deviations from isotropy. Indeed, self-preserving isotropic turbulence models are used to study evolution from a direct dynamical point of view, emphasizing the naturalness of the Taylor microscale as a self-similarity scale in this system. In this context the stationary state emerges as a stable fixed point. Self-preservation seems to be the reason behind a noted similarity of the third order structure function between the linearly forced and freely decaying turbulence, where again the finiteness of the domain plays an significant role.Comment: 15 pages, 7 figures, changes in the discussion at the end of section VI, formula (60) correcte

Magnetic Susceptibility of an integrable anisotropic spin ladder system

We investigate the thermodynamics of a spin ladder model which possesses a free parameter besides the rung and leg couplings. The model is exactly solved by the Bethe Ansatz and exhibits a phase transition between a gapped and a gapless spin excitation spectrum. The magnetic susceptibility is obtained numerically and its dependence on the anisotropy parameter is determined. A connection with the compounds KCuCl3, Cu2(C5H12N2)2Cl4 and (C5H12N)2CuBr4 in the strong coupling regime is made and our results for the magnetic susceptibility fit the experimental data remarkably well.Comment: 12 pages, 12 figures included, submitted to Phys. Rev.

Bethe Ansatz study of one-dimensional Bose and Fermi gases with periodic and hard wall boundary conditions

We extend the exact periodic Bethe Ansatz solution for one-dimensional bosons and fermions with delta-interaction and arbitrary internal degrees of freedom to the case of hard wall boundary conditions. We give an analysis of the ground state properties of fermionic systems with two internal degrees of freedom, including expansions of the ground state energy in the weak and strong coupling limits in the repulsive and attractive regimes.Comment: 27 pages, 6 figures, key reference added, typos correcte

Spreading of thin films assisted by thermal fluctuations

We study the spreading of viscous drops on a solid substrate, taking into account the effects of thermal fluctuations in the fluid momentum. A nonlinear stochastic lubrication equation is derived, and studied using numerical simulations and scaling analysis. We show that asymptotically spreading drops admit self-similar shapes, whose average radii can increase at rates much faster than these predicted by Tanner's law. We discuss the physical realizability of our results for thin molecular and complex fluid films, and predict that such phenomenon can in principal be observed in various flow geometries.Comment: 5 pages, 3 figure

A Construction of Solutions to Reflection Equations for Interaction-Round-a-Face Models

We present a procedure in which known solutions to reflection equations for interaction-round-a-face lattice models are used to construct new solutions. The procedure is particularly well-suited to models which have a known fusion hierarchy and which are based on graphs containing a node of valency $1$. Among such models are the Andrews-Baxter-Forrester models, for which we construct reflection equation solutions for fixed and free boundary conditions.Comment: 9 pages, LaTe

Magnetocaloric effect in integrable spin-s chains

We study the magnetocaloric effect for the integrable antiferromagnetic high-spin chain. We present an exact computation of the Gr\"uneisen parameter, which is closely related to the magnetocaloric effect, for the quantum spin-s chain on the thermodynamical limit by means of Bethe ansatz techniques and the quantum transfer matrix approach. We have also calculated the entropy S and the isentropes in the (H,T) plane. We have been able to identify the quantum critical points H_c^{(s)}=2/(s+1/2) looking at the isentropes and/or the characteristic behaviour of the Gr\"uneisen parameter.Comment: 6 pages, 3 figure

Myosin tails and single α-helical domains

The human genome contains 39 myosin genes, divided up into 12 different classes. The structure, cellular function and biochemical properties of many of these isoforms remain poorly characterized and there is still some controversy as to whether some myosin isoforms are monomers or dimers. Myosin isoforms 6 and 10 contain a stable single α-helical (SAH) domain, situated just after the canonical lever. The SAH domain is stiff enough to be able to lengthen the lever allowing the myosin to take a larger step. In addition, atomic force microscopy and atomistic simulations show that SAH domains unfold at relatively low forces and have a high propensity to refold. These properties are likely to be important for protein function, enabling motors to carry cargo in dense actin networks, and other proteins to remain attached to binding partners in the crowded cell