A comparison of the responses of mature and young clonal tea to drought.

To assist commercial producers with optimising the use of irrigation water, the responses to drought of mature and young tea crops (22 and 5 years after field planting respectively) were compared using data from two adjacent long-term irrigation experiments in Southern Tanzania. Providing the maximum potential soil water deficit was below about 400-500 mm for mature, and 200-250 mm for young plants (clone 6/8), annual yields of dry tea from rainfed or partially irrigated crops were similar to those from the corresponding well-watered crops. At deficits greater than this, annual yields declined rapidly in young tea (up to 22 kg (ha mm)-1) but relatively slowly in mature tea (up to 6.5 kg (ha mm)- 1). This apparent insensitivity of the mature crop to drought was due principally to compensation that occurred during the rains for yield lost in the dry season. Differences in dry matter distribution and shoot to root ratios contributed to these contrasting responses. Thus, the total above ground dry mass of well-irrigated, mature plants was about twice that for young plants. Similarly, the total mass of structural roots (>1 mm diameter), to 3 m depth, was four times greater in the mature crop than in the young crop and, for fine roots (<1 mm diameter), eight times greater. The corresponding shoot to root ratios (dry mass) were about 1:1 and 2:1 respectively. In addition, each unit area of leaf in the canopy of a mature plant had six times more fine roots (by weight) available to extract and supply water than did a young plant. Despite the logistical benefits resulting from more even crop distribution during the year when crops are fully irrigated, producers currently prefer to save water and energy costs by allowing a substantial soil water deficit to develop prior to the start of the rains, up to 250 mm in mature tea, knowing that yield compensation will occur later

Scaling theory for vortices in the two-dimensional inverse energy cascade

B.H.B. is supported by the Natural Environment Research Council grant NE/M014983/1.We propose a new similarity theory for the two-dimensional inverse energy cascade and the coherent vortex population it contains when forced at intermediate scales. Similarity arguments taking into account enstrophy conservation and a prescribed constant energy injection rate such that E∼t yield three length scales, lω, lE and lψ, associated with the vorticity field, energy peak and streamfunction, and predictions for their temporal evolutions, t1/2, t and t3/2, respectively. We thus predict that vortex areas grow linearly in time, A∼l2ω∼t, while the spectral peak wavenumber kE ≡ 2πl−1E ∼ t−1. We construct a theoretical framework involving a three-part, time-evolving vortex number density distribution, n(A) ∼ tαiA−ri,  i ∈ 1,2,3. Just above the forcing scale (i =1) there is a forcing-equilibrated scaling range in which the number of vortices at fixed A is constant and vortex ‘self-energy’ Evcm = (2D)−1∫ωv2A2n(A) dA is conserved in A-space intervals [μA0(t), A0(t)] comoving with the growth in vortex area, A0(t) ∼ t. In this range, α1 = 0 and n(A) ∼ A−3. At intermediate scales (i = 2) sufficiently far from the forcing and the largest vortex, there is a range with a scale-invariant vortex size distribution. We predict that in this range the vortex enstrophy Zvcm = (2D)−1∫ ωv2An(A)dA is conserved and n(A) ∼ t−1A−1. The final range (i = 3), which extends over the largest vortex-containing scales, conserves σvcm = (2D)−1∫ ωv2n(A)dA. If ωv2 is constant in time, this is equivalent to conservation of vortex number Nvcm =∫ n(A)dA. This regime represents a ‘front’ of sparse vortices, which are effectively point-like; in this range we predict n(A) ∼ tr3−1A−r3. Allowing for time-varying ωv2 results in a small but significant correction to these temporal dependences. High-resolution numerical simulations verify the predicted vortex and spectral peak growth rates, as well as the theoretical picture of the three scaling ranges in the vortex population. Vortices steepen the energy spectrum E(k) past the classical k−5/3 scaling in the range k ∈ [kf , kv], where kv is the wavenumber associated with the largest vortex, while at larger scales the slope approaches −5/3. Though vortices disrupt the classical scaling, their number density distribution and evolution reveal deeper and more complex scale invariance, and suggest an effective theory of the inverse cascade in terms of vortex interactions.PostprintPeer reviewe

Quasiperpendicular high Mach number Shocks

Shock waves exist throughout the universe and are fundamental to understanding the nature of collisionless plasmas. Reformation is a process, driven by microphysics, which typically occurs at high Mach number supercritical shocks. While ongoing studies have investigated this process extensively both theoretically and via simulations, their observations remain few and far between. In this letter we present a study of very high Mach number shocks in a parameter space that has been poorly explored and we identify reformation using in situ magnetic field observations from the Cassini spacecraft at 10 AU. This has given us an insight into quasi-perpendicular shocks across two orders of magnitude in Alfven Mach number (MA) which could potentially bridge the gap between modest terrestrial shocks and more exotic astrophysical shocks. For the first time, we show evidence for cyclic reformation controlled by specular ion reflection occurring at the predicted timescale of ~0.3 {\tau}c, where {\tau}c is the ion gyroperiod. In addition, we experimentally reveal the relationship between reformation and MA and focus on the magnetic structure of such shocks to further show that for the same MA, a reforming shock exhibits stronger magnetic field amplification than a shock that is not reforming.Comment: Accepted and Published in Physical Review Letters (2015

Axionic D3-D7 Inflation

We study the motion of a D3 brane moving within a Type IIB string vacuum compactified to 4D on K3 x T_2/Z_2 in the presence of D7 and O7 planes. We work within the effective 4D supergravity describing how the mobile D3 interacts with the lightest bulk moduli of the compactification, including the effects of modulus-stabilizing fluxes. We seek inflationary solutions to the resulting equations, performing our search numerically in order to avoid resorting to approximate parameterizations of the low-energy potential. We consider uplifting from D-terms and from the supersymmetry-breaking effects of anti-D3 branes. We find examples of slow-roll inflation (with anti-brane uplifting) with the mobile D3 moving along the toroidal directions, falling towards a D7-O7 stack starting from the antipodal point. The inflaton turns out to be a linear combination of the brane position and the axionic partner of the K3 volume modulus, and the similarity of the potential along the inflaton direction with that of racetrack inflation leads to the prediction n_s \le 0.95 for the spectral index. The slow roll is insensitive to most of the features of the effective superpotential, and requires a one-in-10^4 tuning to ensure that the torus is close to square in shape. We also consider D-term inflation with the D3 close to the attractive D7, but find that for a broad (but not exhaustive) class of parameters the conditions for slow roll tend to destabilize the bulk moduli. In contrast to the axionic case, the best inflationary example of this kind requires the delicate adjustment of potential parameters (much more than the part-per-mille level), and gives inflation only at an inflection point of the potential (and so suffers from additional fine-tuning of initial conditions to avoid an overshoot problem).Comment: 29 pages, 5 figure

On the spacing of meandering jets in the strong-stair limit

Based on an assumption of strongly inhomogeneous potential vorticity mixing in quasi-geostrophic -plane turbulence, a relation is obtained between the mean spacing of latitudinally meandering zonal jets and the total kinetic energy of the flow. The relation applies to cases where the Rossby deformation length is much smaller than the Rhines scale, in which kinetic energy is concentrated within the jet cores. The relation can be theoretically achieved in the case of perfect mixing between regularly spaced jets with simple meanders, and of negligible kinetic energy in flow structures other than in jets. Incomplete mixing or unevenly spaced jets will result in jets being more widely separated than the estimate, while significant kinetic energy outside the jets will result in jets closer than the estimate. An additional relation, valid under the same assumptions, is obtained between the total kinetic and potential energies. In flows with large-scale dissipation, the two relations provide a means to predict the jet spacing based only on knowledge of the energy input rate of the forcing and dissipation rate, regardless of whether the latter takes the form of frictional or thermal damping. Comparison with direct numerical integrations of the forced system shows broad support for the relations, but differences between the actual and predicted jet spacings arise both from the complex structure of jet meanders and the non-negligible kinetic energy contained in the turbulent background and in coherent vortices lying between the jets.PostprintPeer reviewe

Bulk Axions, Brane Back-reaction and Fluxes

Extra-dimensional models can involve bulk pseudo-Goldstone bosons (pGBs) whose shift symmetry is explicitly broken only by physics localized on branes. Reliable calculation of their low-energy potential is often difficult because it requires details of the stabilization of the extra dimensions. In rugby ball solutions, for which two compact extra dimensions are stabilized in the presence of only positive-tension brane sources, the effects of brane back-reaction can be computed explicitly. This allows the calculation of the shape of the low-energy pGB potential and response of the extra dimensional geometry as a function of the perturbing brane properties. If the pGB-dependence is a small part of the total brane tension a very general analysis is possible, permitting an exploration of how the system responds to frustration when the two branes disagree on what the proper scalar vacuum should be. We show how the low-energy potential is given by the sum of brane tensions (in agreement with common lore) when only the brane tensions couple to the pGB. We also show how a direct brane coupling to the flux stabilizing the extra dimensions corrects this result in a way that does not simply amount to the contribution of the flux to the brane tensions. We calculate the mass of the would-be zero mode, and briefly describe several potential applications, including a brane realization of `natural inflation,' and a dynamical mechanism for suppressing the couplings of the pGB to matter localized on the branes. Since the scalar can be light enough to be relevant to precision tests of gravity (in a technically natural way) this mechanism can be relevant to evading phenomenological bounds.Comment: 36 pages, JHEP styl

Vortex scaling ranges in two-dimensional turbulence

We survey the role of coherent vortices in two-dimensional turbulence, including formation mechanisms, implications for classical similarity and inertial range theories, and characteristics of the vortex populations. We review early work on the spatial and temporal scaling properties of vortices in freely evolving turbulence and more recent developments, including a spatiotemporal scaling theory for vortices in the forced inverse energy cascade. We emphasize that Kraichnan-Batchelor similarity theories and vortex scaling theories are best viewed as complementary and together provide a more complete description of two-dimensional turbulence. In particular, similarity theory has a continued role in describing the weak filamentary sea between the vortices. Moreover, we locate both classical inertial and vortex scaling ranges within the broader framework of scaling in far-from-equilibrium systems, which generically exhibit multiple fixed point solutions with distinct scaling behaviour. We describe how stationary transport in a range of scales comoving with the dilatation of flow features, as measured by the growth in vortex area, constrains the vortex number density in both freely evolving and forced two-dimensional turbulence. The new theories for coherent vortices reveal previously hidden nontrivial scaling, point to new dynamical understanding, and provide a novel exciting window into two-dimensional turbulence.PostprintPeer reviewe

Warped Reheating in Multi-Throat Brane Inflation

We investigate in some quantitative details the viability of reheating in multi-throat brane inflationary scenarios by estimating and comparing the time scales for the various processes involved. We also calculate within perturbative string theory the decay rate of excited closed strings into KK modes and compare with that of their decay into gravitons; we find that in the inflationary throat the former is preferred. We also find that over a small but reasonable range of parameters of the background geometry, these KK modes will preferably tunnel to another throat (possibly containing the Standard Model) instead of decaying to gravitons due largely to their suppressed coupling to the bulk gravitons. Once tunneled, the same suppressed coupling to the gravitons again allows them to reheat the Standard Model efficiently. We also consider the effects of adding more throats to the system and find that for extra throats with small warping, reheating still seems viable.Comment: 29 pages, 4 figures, discussions on closed string decay expanded, references adde

Derivation of the Semi-circle Law from the Law of Corresponding States

We show that, for the transition between any two quantum Hall states, the semi-circle law and the existence of a duality symmetry follow solely from the consistency of the law of corresponding states with the two-dimensional scaling flow. This puts these two effects on a sound theoretical footing, implying that both should hold exactly at zero temperature, independently of the details of the microscopic electron dynamics. This derivation also shows how the experimental evidence favours taking the two-dimensional flow seriously for the whole transition, and not just near the critical points.Comment: 4 pages, 1 figure, typeset in LaTeX (uses revtex

Modular Groups, Visibility Diagram and Quantum Hall Effect

We consider the action of the modular group $\Gamma (2)$ on the set of positive rational fractions. From this, we derive a model for a classification of fractional (as well as integer) Hall states which can be visualized on two ``visibility" diagrams, the first one being associated with even denominator fractions whereas the second one is linked to odd denominator fractions. We use this model to predict, among some interesting physical quantities, the relative ratios of the width of the different transversal resistivity plateaus. A numerical simulation of the tranversal resistivity plot based on this last prediction fits well with the present experimental data.Comment: 17 pages, plain TeX, 4 eps figures included (macro epsf.tex), 1 figure available from reques