A simple asynchronous replica-exchange implementation

We discuss the possibility of implementing asynchronous replica-exchange (or parallel tempering) molecular dynamics. In our scheme, the exchange attempts are driven by asynchronous messages sent by one of the computing nodes, so that different replicas are allowed to perform a different number of time-steps between subsequent attempts. The implementation is simple and based on the message-passing interface (MPI). We illustrate the advantages of our scheme with respect to the standard synchronous algorithm and we benchmark it for a model Lennard-Jones liquid on an IBM-LS21 blade center cluster.Comment: Preprint of Proceeding for CSFI 200

A 'Darboux Theorem' for shifted symplectic structures on derived Artin stacks, with applications

This is the fifth in a series arXiv:1304.4508, arXiv:1305,6302, arXiv:1211.3259, arXiv:1305.6428 on the '$k$-shifted symplectic derived algebraic geometry' of Pantev, Toen, Vaquie and Vezzosi, arXiv:1111.3209. This paper extends the previous three from (derived) schemes to (derived) Artin stacks. We prove four main results: (a) If $(X,\omega)$ is a $k$-shifted symplectic derived Artin stack for $k<0$ in the sense of arXiv:1111.3209, then near each $x\in X$ we can find a 'minimal' smooth atlas $\varphi:U\to X$ with $U$ an affine derived scheme, such that $(U,\varphi^*(\omega))$ may be written explicitly in coordinates in a standard 'Darboux form'. (b) If $(X,\omega)$ is a $-1$-shifted symplectic derived Artin stack and $X'$ the underlying classical Artin stack, then $X'$ extends naturally to a 'd-critical stack' $(X',s)$ in the sense of arXiv:1304.4508. (c) If $(X,s)$ is an oriented d-critical stack, we can define a natural perverse sheaf $P^\bullet_{X,s}$ on $X$, such that whenever $T$ is a scheme and $t:T\to X$ is smooth of relative dimension $n$, then $T$ is locally modelled on a critical locus Crit$(f:U\to{\mathbb A}^1)$ for $U$ smooth, and $t^*(P^\bullet_{X,s})[n]$ is locally modelled on the perverse sheaf of vanishing cycles $PV_{U,f}^\bullet$ of $f$. (d) If $(X,s)$ is a finite type oriented d-critical stack, we can define a natural motive $MF_{X,s}$ in a ring of motives $\bar{\mathcal M}^{st,\hat\mu}_X$ on $X$, such that whenever $T$ is a finite type scheme and $t:T\to X$ is smooth of dimension $n$, then $T$ is locally modelled on a critical locus Crit$(f:U\to{\mathbb A}^1)$ for $U$ smooth, and ${\mathbb L}^{-n/2}\odot t^*(MF_{X,s})$ is locally modelled on the motivic vanishing cycle $MF^{mot,\phi}_{U,f}$ of $f$ in $\bar{\mathcal M}^{st,\hat\mu}_T$. Our results have applications to categorified and motivic extensions of Donaldson-Thomas theory of Calabi-Yau 3-foldsComment: (v2) 61 pages. Minor corrections, foundational material on perverse sheaves shortene

A 'Darboux theorem' for derived schemes with shifted symplectic structure

We prove a 'Darboux theorem' for derived schemes with symplectic forms of degree $k<0$, in the sense of Pantev, Toen, Vaquie and Vezzosi arXiv:1111.3209. More precisely, we show that a derived scheme $X$ with symplectic form $\omega$ of degree $k$ is locally equivalent to (Spec $A,\omega'$) for Spec $A$ an affine derived scheme whose cdga $A$ has Darboux-like coordinates in which the symplectic form $\omega'$ is standard, and the differential in $A$ is given by Poisson bracket with a Hamiltonian function $H$ in $A$ of degree $k+1$. When $k=-1$, this implies that a $-1$-shifted symplectic derived scheme $(X,\omega)$ is Zariski locally equivalent to the derived critical locus Crit$(H)$ of a regular function $H:U\to{\mathbb A}^1$ on a smooth scheme $U$. We use this to show that the underlying classical scheme of $X$ has the structure of an 'algebraic d-critical locus', in the sense of Joyce arXiv:1304.4508. In the sequels arXiv:1211.3259, arXiv:1305.6428, arXiv:1312.0090, arXiv:1504.00690, 1506.04024 we will discuss applications of these results to categorified and motivic Donaldson-Thomas theory of Calabi-Yau 3-folds, and to defining new Donaldson-Thomas type invariants of Calabi-Yau 4-folds, and to defining 'Fukaya categories' of Lagrangians in algebraic symplectic manifolds using perverse sheaves, and we will extend the results of this paper and arXiv:1211.3259, arXiv:1305.6428 from (derived) schemes to (derived) Artin stacks, and to give local descriptions of Lagrangians in $k$-shifted symplectic derived schemes. Bouaziz and Grojnowski arXiv:1309.2197 independently prove a similar 'Darboux Theorem'.Comment: 54 pages. (v4) Final version to appear in Journal of the AM

On motivic vanishing cycles of critical loci

Let $U$ be a smooth scheme over an algebraically closed field $\mathbb K$ of characteristic zero and $f:U\to{\mathbb A}^1$ a regular function, and write $X=$Crit$(f)$, as a closed subscheme of $U$. The motivic vanishing cycle $MF_{U,f}^\phi$ is an element of the $\hat\mu$-equivariant motivic Grothendieck ring ${\mathcal M}^{\hat\mu}_X$ defined by Denef and Loeser math.AG/0006050 and Looijenga math.AG/0006220, and used in Kontsevich and Soibelman's theory of motivic Donaldson-Thomas invariants, arXiv:0811.2435. We prove three main results: (a) $MF_{U,f}^\phi$ depends only on the third-order thickenings $U^{(3)},f^{(3)}$ of $U,f$. (b) If $V$ is another smooth scheme, $g:V\to{\mathbb A}^1$ is regular, $Y=$Crit$(g)$, and $\Phi:U\to V$ is an embedding with $f=g\circ\Phi$ and $\Phi\vert_X:X\to Y$ an isomorphism, then $\Phi\vert_X^*(MF_{V,g}^\phi)$ equals $MF_{U,f}^\phi$ "twisted" by a motive associated to a principal ${\mathbb Z}_2$-bundle defined using $\Phi$, where now we work in a quotient ring $\bar{\mathcal M}^{\hat\mu}_X$ of ${\mathcal M}^{\hat\mu}_X$. (c) If $(X,s)$ is an "oriented algebraic d-critical locus" in the sense of Joyce arXiv:1304.4508, there is a natural motive $MF_{X,s} \in\bar{\mathcal M}^{\hat\mu}_X$, such that if $(X,s)$ is locally modelled on Crit$(f:U\to{\mathbb A}^1)$, then $MF_{X,s}$ is locally modelled on $MF_{U,f}^\phi$. Using results from arXiv:1305.6302, these imply the existence of natural motives on moduli schemes of coherent sheaves on a Calabi-Yau 3-fold equipped with "orientation data", as required in Kontsevich and Soibelman's motivic Donaldson-Thomas theory arXiv:0811.2435, and on intersections of oriented Lagrangians in an algebraic symplectic manifold. This paper is an analogue for motives of results on perverse sheaves of vanishing cycles proved in arXiv:1211.3259. We extend this paper to Artin stacks in arXiv:1312.0090.Comment: 32 pages. (v3) Final version, to appear in the Journal of Algebraic Geometry. arXiv admin note: text overlap with arXiv:1211.325

Effect of permanent ground cover on agronomic properties and soil fertility in an organic peach orchard

In conventional orchards, weeds on the raw are mainly controlled with chemical herbicides because of their efficiency, their low cost and ease of use. The most common method in organic orchard to eliminate weeds on the raw consists of tillage operations. However, some drawbacks of these mechanical methods have been demonstrated: (1) the energetic cost (non-renewable energy) is high, (2) this method is time-consuming, (3) tillage interferes with the development of superficial roots and can hurt the trunk, (4) the physical, chemical and biological properties of the soil can be disturb and (5) erosion and runoff potentially increase. Cover crops are interesting alternatives to manage ground cover but the effect on the agronomic properties and the soil fertility of these methods should be assessed. This study is included in the national program “Casdar SolAB” supported by the French Ministry of Agriculture. The effect of a White Clover crop versus tillage practice on the tree raw was assessed in an irrigated organic Peach orchard. White Clover was sowed in 2004. Soil parameters (water and nutrients availability, soil porosity, root density, earthworms density, soil profile) and agronomic parameters (yield, fruit quality, pests and diseases damages) were recorded since 2004. A 50% decrease of the organic fertilizer supply in the White Clover treatment has not affected yield and fruit quality from 2005 to 2009. It suggests this cover crop is well adapted to our pedoclimatic conditions without exerting a significant competitive effect. Root density is higher in the superficial layers of the soil in the White Clover treatment. Simplified Beerkan test used to assess soil porosity has also shown that soil porosity is higher in this treatment. No vole damage was observed in the plot

Effect of White clover (Trifolium repens cv. Huia) cover crop on agronomic properties and soil biology in an organic peach orchard

In orchards, cover crops are interesting alternative strategies to tillage or chemical herbicides for managing weeds in the tree row. However, little is known about the effect of cover crops on agronomic properties and soil biology in organic orchards. To fill this gap, the effects of two weed managements, a White clover cover crop (CC) versus classical tillage practice (T) on the tree row, were assessed in an irrigated organic Peach orchard. White clover was sown in 2004, 2006 and 2009 in the tree row and ploughed in 2006 and 2008. Root density, earthworm density, water infiltration rate, nitrogen content and water availability were measured in the soil, in the tree row. In 2009, peach root density observed in the superficial layers was higher in CC treatment. Sampling dates and treatment have a significant effect on total earthworm density with higher abundance observed in CC. However, no difference was observed between CC and T anecic earthworm groups known to make large and vertical burrows. Infiltration rate measured with the simplified Beerkan method was higher in CC treatment. This could be explained by the thick superficial root mat which was associated to a significant higher epigeic earthworm density in CC. Whereas nitrogen supplies were twice lower in CC treatment since 2005, soil nitrogen availability was equivalent in both treatments. These results demonstrate the agronomic interest of nitrogen-fixing plants used as a cover crop in organic peach orchards

Reactive Force Field for Proton Diffusion in BaZrO3 using an empirical valence bond approach

A new reactive force field to describe proton diffusion within the solid-oxide fuel cell material BaZrO3 has been derived. Using a quantum mechanical potential energy surface, the parameters of an interatomic potential model to describe hydroxyl groups within both pure and yttrium-doped BaZrO3 have been determined. Reactivity is then incorporated through the use of the empirical valence bond model. Molecular dynamics simulations (EVB-MD) have been performed to explore the diffusion of hydrogen using a stochastic thermostat and barostat whose equations are extended to the isostress-isothermal ensemble. In the low concentration limit, the presence of yttrium is found not to significantly influence the diffusivity of hydrogen, despite the proton having a longer residence time at oxygen adjacent to the dopant. This lack of influence is due to the fact that trapping occurs infrequently, even when the proton diffuses through octahedra adjacent to the dopant. The activation energy for diffusion is found to be 0.42 eV, in good agreement with experimental values, though the prefactor is slightly underestimated.Comment: Corrected titl