On the Assouad dimension of self-similar sets with overlaps

It is known that, unlike the Hausdorff dimension, the Assouad dimension of a self-similar set can exceed the similarity dimension if there are overlaps in the construction. Our main result is the following precise dichotomy for self-similar sets in the line: either the \emph{weak separation property} is satisfied, in which case the Hausdorff and Assouad dimensions coincide; or the \emph{weak separation property} is not satisfied, in which case the Assouad dimension is maximal (equal to one). In the first case we prove that the self-similar set is Ahlfors regular, and in the second case we use the fact that if the \emph{weak separation property} is not satisfied, one can approximate the identity arbitrarily well in the group generated by the similarity mappings, and this allows us to build a \emph{weak tangent} that contains an interval. We also obtain results in higher dimensions and provide illustrative examples showing that the `equality/maximal' dichotomy does not extend to this setting.Comment: 24 pages, 2 figure

Critical current of a Josephson junction containing a conical magnet

We calculate the critical current of a superconductor/ferromagnetic/superconductor (S/FM/S) Josephson junction in which the FM layer has a conical magnetic structure composed of an in-plane rotating antiferromagnetic phase and an out-of-plane ferromagnetic component. In view of the realistic electronic properties and magnetic structures that can be formed when conical magnets such as Ho are grown with a polycrystalline structure in thin-film form by methods such as direct current sputtering and evaporation, we have modeled this situation in the dirty limit with a large magnetic coherence length ($\xi_f$). This means that the electron mean free path is much smaller than the normalized spiral length $\lambda/2\pi$ which in turn is much smaller than $\xi_f$ (with $\lambda$ as the length a complete spiral makes along the growth direction of the FM). In this physically reasonable limit we have employed the linearized Usadel equations: we find that the triplet correlations are short ranged and manifested in the critical current as a rapid oscillation on the scale of $\lambda/2\pi$. These rapid oscillations in the critical current are superimposed on a slower oscillation which is related to the singlet correlations. Both oscillations decay on the scale of $\xi_f$. We derive an analytical solution and also describe a computational method for obtaining the critical current as a function of the conical magnetic layer thickness.Comment: Extended version of the published paper. Additional information about the computational method is included in the appendi

Mitigating Cotton Revenue Risk Through Irrigation, Insurance, and Hedging

This study focuses on managing cotton production and marketing risks using combinations of irrigation levels, put options (as price insurance), and crop insurance. Stochastic cotton yields and prices are used to simulate a whole-farm financial statement for a 1,000 acre furrow irrigated cotton farm in the Texas Lower Rio Grande Valley under 16 combinations of risk management strategies. Analyses for risk-averse decision makers indicate that multiple irrigations are preferred. The benefits to purchasing put options increase with yields, as they are more beneficial when higher yields are expected from applying more irrigation applications. Crop insurance is strongly preferred at lower irrigation levels.cotton, crop insurance, irrigation, options, puts, risk, simulation, stochastic efficiency with respect to a function, Farm Management, Risk and Uncertainty, D81, Q12, Q15,

Chronic thoracic hemisection spinal cord injury in adult rats induces a progressive decline in transmission from uninjured fibers to lumbar motoneurons

Although most spinal cord injuries are anatomically incomplete, only limited functional recovery has been observed in people and rats with partial lesions. To address why surviving fibers cannot mediate more complete recovery, we evaluated the physiological and anatomical status of spared fibers after unilateral hemisection (HX) of thoracic spinal cord in adult rats. We made intracellular and extracellular recordings at L5 (below HX) in response to electrical stimulation of contralateral white matter above (T6) and below (L1) HX. Responses from T6 displayed reduced amplitude, increased latency and elevated stimulus threshold in the fibers across from HX, beginning 1-2 weeks after HX. Ultrastructural analysis revealed demyelination of intact axons contralateral to the HX, with a time course similar to the conduction changes. Behavioral studies indicated partial recovery which arrested when conduction deficits began. These findings suggest a chronic pathological state in intact fibers and necessity for prompt treatment to minimize it

Redox stratification drives enhanced growth in a commercially important deposit-feeding invertebrate: implications for bioremediation and integrated aquaculture.

Effective and affordable treatment of waste solids is a key sustainability challenge for the aquaculture industry. Here, we investigated the potential for a deposit-feeding sea cucumber, Holothuria scabra, to provide a remediation service whilst concurrently yielding a high-value secondary product in a land-based recirculating aquaculture system (RAS). The effect of sediment depth, particle size and redox regime were examined in relation to changes in the behaviour, growth and biochemical composition of juvenile sea cucumbers cultured for 81 d in manipulated sediment systems, describing either fully oxic or stratified (oxic-anoxic) redox regimes. The redox regime was the principal factor affecting growth, biochemical composition and behaviour, while substrate depth and particle size did not significantly affect growth rate or biomass production. Animals cultured under fully oxic conditions exhibited negative growth and had higher lipid and carbohydrate contents, potentially due to compensatory feeding in response to higher microphytobenthic production. In contrast, animals in the stratified treatments spent more time feeding, generated faster growth and produced significantly higher biomass yields (626.89 ± 35.44 g m-2 versus 449.22 ± 14.24 g m-2; mean ± SE). Further, unlike in oxic treatments, growth in the stratified treatments did not reach maximum biomass carrying capacity, indicating that stratified sediment is more suitable for culturing sea cucumbers. However, the stratified sediments may exhibit reduced bioremediation ability relative to the oxic sediment, signifying a trade-off between remediation efficiency and exploitable biomass yield

NICMOS Snapshot Survey of Damped Lyman Alpha Quasars

We image 19 quasars with 22 damped Lyman alpha (DLA) systems using the F160W filter and the Near-Infrared Camera and Multiobject Spectrograph aboard the Hubble Space Telescope, in both direct and coronagraphic modes. We reach 5 sigma detection limits of ~H=22 in the majority of our images. We compare our observations to the observed Lyman-break population of high-redshift galaxies, as well as Bruzual & Charlot evolutionary models of present-day galaxies redshifted to the distances of the absorption systems. We predict H magnitudes for our DLAs, assuming they are producing stars like an L* Lyman-break galaxy (LBG) at their redshift. Comparing these predictions to our sensitivity, we find that we should be able to detect a galaxy around 0.5-1.0 L* (LBG) for most of our observations. We find only one new possible candidate, that near LBQS0010-0012. This scarcity of candidates leads us to the conclusion that most DLA systems are not drawn from a normal LBG luminosity function nor a local galaxy luminosity function placed at these high redshifts.Comment: 31 pages, 8 figures, Accepted for Feb. 10 issue of Ap