Generalized Korn's inequality and conformal Killing vectors

Korn's inequality plays an important role in linear elasticity theory. This inequality bounds the norm of the derivatives of the displacement vector by the norm of the linearized strain tensor. The kernel of the linearized strain tensor are the infinitesimal rigid-body translations and rotations (Killing vectors). We generalize this inequality by replacing the linearized strain tensor by its trace free part. That is, we obtain a stronger inequality in which the kernel of the relevant operator are the conformal Killing vectors. The new inequality has applications in General Relativity.Comment: 8 page

Enhanced stability of layered phases in parallel hard-spherocylinders due to the addition of hard spheres

There is increasing evidence that entropy can induce microphase separation in binary fluid mixtures interacting through hard particle potentials. One such phase consists of alternating two dimensional liquid-like layers of rods and spheres. We study the transition from a uniform miscible state to this ordered state using computer simulations and compare results to experiments and theory. We conclude that (1) there is stable entropy driven microphase separation in mixtures of parallel rods and spheres, (2) adding spheres smaller then the rod length decreases the total volume fraction needed for the formation of a layered phase, therefore small spheres effectively stabilize the layered phase; the opposite is true for large spheres and (3) the degree of this stabilization increases with increasing rod length.Comment: 11 pages, 9 figures. Submitted to Phys. Rev. E. See related website http://www.elsie.brandeis.ed

Unravelling the fluorescence kinetics of light-harvesting proteins with simulated measurements

The plant light-harvesting pigment-protein complex LHCII is the major antenna sub-unit of PSII and is generally (though not universally) accepted to play a role in photoprotective energy dissipation under high light conditions, a process known Non-Photochemical Quenching (NPQ). The underlying mechanisms of energy trapping and dissipation within LHCII are still debated. Various models have been proposed for the underlying molecular detail of NPQ, but they are often based on different interpretations of very similar transient absorption measurements of isolated complexes. Here we present a simulated measurement of the fluorescence decay kinetics of quenched LHCII aggregates to determine whether this relatively simple measurement can discriminate between different potential NPQ mechanisms. We simulate not just the underlying physics (excitation, energy migration, quenching and singlet-singlet annihilation) but also the signal detection and typical experimental data analysis. Comparing this to a selection of published fluorescence decay kinetics we find that: (1) Different proposed quenching mechanisms produce noticeably different fluorescence kinetics even at low (annihilation free) excitation density, though the degree of difference is dependent on pulse width. (2) Measured decay kinetics are consistent with most LHCII trimers becoming relatively slow excitation quenchers. A small sub-population of very fast quenchers produces kinetics which do not resemble any observed measurement. (3) It is necessary to consider at least two distinct quenching mechanisms in order to accurately reproduce experimental kinetics, supporting the idea that NPQ is not a simple binary switch

Correlated fluorescence quenching and topographic mapping of Light-Harvesting Complex II within surface-assembled aggregates and lipid bilayers

Light-Harvesting Complex II (LHCII) is a chlorophyll-protein antenna complex that efficiently absorbs solar energy and transfers electronic excited states to photosystems I and II. Under excess light intensity LHCII can adopt a photoprotective state in which excitation energy is safely dissipated as heat, a process known as Non-Photochemical Quenching (NPQ). In vivo NPQ is triggered by combinatorial factors including transmembrane ΔpH, PsbS protein and LHCII-bound zeaxanthin, leading to dramatically shortened LHCII fluorescence lifetimes. In vitro, LHCII in detergent solution or in proteoliposomes can reversibly adopt an NPQ-like state, via manipulation of detergent/protein ratio, lipid/protein ratio, pH or pressure. Previous spectroscopic investigations revealed changes in exciton dynamics and protein conformation that accompany quenching, however, LHCII-LHCII interactions have not been extensively studied. Here, we correlated fluorescence lifetime imaging microscopy (FLIM) and atomic force microscopy (AFM) of trimeric LHCII adsorbed to mica substrates and manipulated the environment to cause varying degrees of quenching. AFM showed that LHCII self-assembled onto mica forming 2D-aggregates (25–150 nm width). FLIM determined that LHCII in these aggregates were in a quenched state, with much lower fluorescence lifetimes (~0.25 ns) compared to free LHCII in solution (2.2–3.9 ns). LHCII-LHCII interactions were disrupted by thylakoid lipids or phospholipids, leading to intermediate fluorescent lifetimes (0.6–0.9 ns). To our knowledge, this is the first in vitro correlation of nanoscale membrane imaging with LHCII quenching. Our findings suggest that lipids could play a key role in modulating the extent of LHCII-LHCII interactions within the thylakoid membrane and so the propensity for NPQ activation

A completely self-contained cryogen-free dilution refrigerator, the TritonDR™

Oxford Instruments have developed a new dilution refrigerator for ultralow temperatures down to below 35 mK. The TritonDRTM system is a continuous cryogenic cycle dilution refrigerator. The refrigerator is driven by a closed cycle cryocooler and hence requires no liquid cryogens. The system has a dedicated electronic control unit and software that provides full control of operation

Average Lattice Symmetry and Nanoscale Structural Correlations in Magnetoresistive Manganites

We report x-ray scattering studies of nanoscale structural correlations in the paramagnetic phases of the perovskite manganites La$_{0.75}$(Ca$_{0.45}$Sr$_{0.55}$)$_{0.25}$MnO$_3$, La$_{0.625}$Sr$_{0.375}$MnO$_3$, and Nd$_{0.45}$Sr$_{0.55}$MnO$_3$. We find that these correlations are present in the orthorhombic $O$ phase in La$_{0.75}$(Ca$_{0.45}$Sr$_{0.55}$)$_{0.25}$MnO$_3$, but they disappear abruptly at the orthorhombic-to-rhombohedral transition in this compound. The orthorhombic phase exhibits increased electrical resistivity and reduced ferromagnetic coupling, in agreement with the association of the nanoscale correlations with insulating regions. In contrast, the correlations were not detected in the two other compounds, which exhibit rhombohedral and tetragonal phases. Based on these results, as well as on previously published work, we propose that the local structure of the paramagnetic phase correlates strongly with the average lattice symmetry, and that the nanoscale correlations are an important factor distinguishing the insulating and the metallic phases in these compounds.Comment: a note on recent experimental work, and a new reference adde

Growing Environmental Activists: Developing Environmental Agency and Engagement Through Children’s Fiction.

We explore how story has the potential to encourage environmental engagement and a sense of agency provided that critical discussion takes place. We illuminate this with reference to the philosophies of John Macmurray on personal agency and social relations; of John Dewey on the primacy of experience for philosophy; and of Paul Ricoeur on hermeneutics, dialogue, dialectics and narrative. We view the use of fiction for environmental understanding as hermeneutic, a form of conceptualising place which interprets experience and perception. The four writers for young people discussed are Ernest Thompson Seton, Kenneth Grahame, Michelle Paver and Philip Pullman. We develop the concept of critical dialogue, and link this to Crick's demand for active democratic citizenship. We illustrate the educational potential for environmental discussions based on literature leading to deeper understanding of place and environment, encouraging the belief in young people that they can be and become agents for change. We develop from Zimbardo the key concept of heroic resister to encourage young people to overcome peer pressure. We conclude with a call to develop a greater awareness of the potential of fiction for learning, and for writers to produce more focused stories engaging with environmental responsibility and activism

Nonlinear weakly curved rod by Γ-Convergence

We present a nonlinear model of weakly curved rod, namely the type of curved rod where the curvature is of the order of the diameter of the cross-section. We use an approach analogous to the one for rods and curved rods and start from the strain energy functional of three dimensional nonlinear elasticity. We do not impose any constitutional behavior of the material and work in a general framework. To derive the model, by means of Γ-convergence, we need to set the order of strain energy (i.e., its relation to the thickness of the body h). We analyze the situation when the strain energy (divided by the order of volume) is of the order h 4. This is the same approach as the one used in Föppl-von Kármán model for plates and the analogous model for rods. The obtained model is analogous to Marguerre-von Kármán for shallow shells and its linearization is the linear shallow arch model which can be found in the literature

Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor

In this paper we provide a sufficient condition, in terms of only one of the nine entries of the gradient tensor, i.e., the Jacobian matrix of the velocity vector field, for the global regularity of strong solutions to the three-dimensional Navier-Stokes equations in the whole space, as well as for the case of periodic boundary conditions

The Structure of Nanoscale Polaron Correlations in La1.2Sr1.8Mn2O7

A system of strongly-interacting electron-lattice polarons can exhibit charge and orbital order at sufficiently high polaron concentrations. In this study, the structure of short-range polaron correlations in the layered colossal magnetoresistive perovskite manganite, La1.2Sr1.8Mn2O7, has been determined by a crystallographic analysis of broad satellite maxima observed in diffuse X-ray and neutron scattering data. The resulting q=(0.3,0,1) modulation is a longitudinal octahedral-stretch mode, consistent with an incommensurate Jahn-Teller-coupled charge-density-wave fluctuations, that implies an unusual orbital-stripe pattern parallel to the directions.Comment: Reformatted with RevTe