Tzitzeica solitons versus relativistic Calogero–Moser three-body clusters

We establish a connection between the hyperbolic relativistic Calogero–Moser systems and a class of soliton solutions to the Tzitzeica equation (also called the Dodd–Bullough–Zhiber–Shabat–Mikhailov equation). In the 6N-dimensional phase space Omega of the relativistic systems with 2N particles and N antiparticles, there exists a 2N-dimensional Poincaré-invariant submanifold OmegaP corresponding to N free particles and N bound particle-antiparticle pairs in their ground state. The Tzitzeica N-soliton tau functions under consideration are real valued and obtained via the dual Lax matrix evaluated in points of OmegaP. This correspondence leads to a picture of the soliton as a cluster of two particles and one antiparticle in their lowest internal energy state

Constraints on terrestrial planet formation timescales and equilibration processes in the Grand Tack scenario from Hf-W isotopic evolution

We examine 141 N-body simulations of terrestrial planet late-stage accretion that use the Grand Tack scenario, coupling the collisional results with a hafnium-tungsten (Hf-W) isotopic evolution model. Accretion in the Grand Tack scenario results in faster planet formation than classical accretion models because of higher planetesimal surface density induced by a migrating Jupiter. Planetary embryos that grow rapidly experience radiogenic ingrowth of mantle $^{182}$W that is inconsistent with the measured terrestrial composition, unless much of the tungsten is removed by an impactor core that mixes thoroughly with the target mantle. For physically Earth-like surviving planets, we find that the fraction of equilibrating impactor core $k_\text{core} \geq 0.6$ is required to produce results agreeing with observed terrestrial tungsten anomalies (assuming equilibration with relatively large volumes of target mantle material; smaller equilibrating mantle volumes would require even larger $k_\text{core}$). This requirement of substantial core re-equilibration may be difficult to reconcile with fluid dynamical predictions and hydrocode simulations of mixing during large impacts, and hence this result does not favor the rapid planet building that results from Grand Tack accretion.Comment: 34 pages, 5 figures, published in EPS

The evening complex is central to the difference between the circadian clocks of Arabidopsis thaliana shoots and roots

The circadian clock regulates the timing of many aspects of plant physiology, and this requires entrainment of the clock to the prevailing day:night cycle. Different plant cells and tissues can oscillate with different free‐running periods, so coordination of timing across the plant is crucial. Previous work showed that a major difference between the clock in mature shoots and roots involves light inputs. The objective of this work was to define, in Arabidopsis thaliana , the operation of the root clock in more detail, and in particular how it responds to light quality. Luciferase imaging was used to study the shoot and root clocks in several null mutants of clock components and in lines with aberrant expression of phytochromes. Mutations in each of the components of the evening complex (EARLY FLOWERING 3 and 4, and LUX ARRHYTHMO) were found to have specific effects on roots, by affecting either rhythmicity or period and its response to light quality. The data suggest that the evening complex is a key part of the light input mechanism that differs between shoots and roots and show that roots sense red light via phytochrome B

How does temperature affect splicing events? Isoform switching of splicing factors regulates splicing of <i>LATE ELONGATED HYPOCOTYL</i> (<i>LHY</i>)

One of the ways in which plants can respond to temperature is via alternative splicing (AS). Previous work showed that temperature changes affected the splicing of several circadian clock gene transcripts. Here we investigated the role of RNA‐binding splicing factors (SFs) in temperature‐sensitive alternative splicing (AS) of the clock gene LATE ELONGATED HYPOCOTYL (LHY). We characterised, in wild type plants, temperature‐associated isoform switching and expression patterns for SF transcripts from a high‐resolution temperature and time series RNA‐seq experiment. In addition we employed quantitative RT‐PCR of SF mutant plants to explore the role of the SFs in cooling‐associated AS of LHY. We show that the splicing and expression of several SFs responds sufficiently rapidly and sensitively to temperature changes to contribute to the splicing of the 5’UTR of LHY. Moreover the choice of splice site in LHY was altered in some SF mutants. The splicing of the 5’UTR region of LHY has characteristics of a molecular thermostat, where the ratio of transcript isoforms is sensitive to temperature changes as modest as 2°C and is scalable over a wide dynamic range of temperature. Our work provides novel insight into SF‐mediated coupling of the perception of temperature to post‐transcriptional regulation of the clock

Vertical migration maintains phytoplankton position in a tidal channel with residual flow

A tidal channel can retain phytoplankton, despite a residual flow, if the phytoplankton migrate vertically with a daily rhythm. Tidal currents are slowed down by bed friction and so plankton experience faster flow when higher in the water column. The lateral movement of the plankton depends on the nature of the vertical migration, particularly the time spent near the surface and the phase of the tide. A model of this process accorded with observations of chlorophyll derived from in situ fluorescence at a mooring in a tidal channel. Peaks in chlorophyll at the end of the flood tide indicated the presence of a phytoplankton bloom downstream of the mooring. Peaks in chlorophyll at the ends of the morning flood tides were 3 to 4 times larger than at the ends of the evening floods, over several days. In contrast, well-mixed particulates were removed from the channel by the residual flow in just 2 d. Both the day-night asymmetry and the sustained presence of chlorophyll were explained by allowing for vertical migration of the phytoplankton and constraining the period during which they were near the surface. Tidal channels retaining phytoplankton that migrate vertically can be ecologically more diverse and yield higher commercial output of farmed bivalves. The natural timings of some phytoplankton blooms in tidal channels are controlled by the nature of the migration. Although a by-product of vertical migration, longer residence in the tidal channel affords the phytoplankton more nutrients than phytoplankton that advect offshore

Geometric discretization of the Koenigs nets

We introduce the Koenigs lattice, which is a new integrable reduction of the quadrilateral lattice (discrete conjugate net) and provides natural integrable discrete analogue of the Koenigs net. We construct the Darboux-type transformations of the Koenigs lattice and we show permutability of superpositions of such transformations, thus proving integrability of the Koenigs lattice. We also investigate the geometry of the discrete Koenigs transformation. In particular we characterize the Koenigs transformation in terms of an involution determined by a congruence conjugate to the lattice.Comment: 17 pages, 2 figures; some spelling and typing errors correcte