16,382 research outputs found
Instrumented activity and semiotic mediation: two frames to describe the conjecture construction process as curricular organizer
We document part of the process through which conjectures produced by students, with the aid of the dynamic geometry software Cabri, when they solve proposed geometric problems, become a curriculum organizer in the classroom. We first focus on characterizing students’ instrumented activity recurring to utilization schema (Rabardel, 1995, in Bartolini Bussi and Mariotti, 2008), and then describe the teacher’s content management through which the ideas produced by the students become key elements of knowledge construction
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 Lagrangian Neighbourhood Theorem for shifted symplectic derived schemes
Pantev, Toen, Vaqui\'e and Vezzosi arXiv:1111.3209 defined -shifted
symplectic derived schemes and stacks for , and
Lagrangians in them. They have important
applications to Calabi-Yau geometry and quantization. Bussi, Brav and Joyce
arXiv:1305.6302 proved a 'Darboux Theorem' giving explicit Zariski or \'etale
local models for -shifted symplectic derived schemes for
presenting them as twisted shifted cotangent bundles.
We prove a 'Lagrangian Neighbourhood Theorem' giving explicit Zariski or
etale local models for Lagrangians in -shifted
symplectic derived schemes for , relative to the
Bussi-Brav-Joyce 'Darboux form' local models for . That is, locally
such Lagrangians can be presented as twisted shifted conormal bundles. We also
give a partial result when .
We expect our results will have future applications to -shifted Poisson
geometry (see arXiv:1506.03699), to defining 'Fukaya categories' of complex or
algebraic symplectic manifolds, and to categorifying Donaldson-Thomas theory of
Calabi-Yau 3-folds and 'Cohomological Hall algebras'.Comment: 68 page
Metadynamics with Discriminants: a Tool for Understanding Chemistry
We introduce an extension of a recently published method\cite{Mendels2018} to
obtain low-dimensional collective variables for studying multiple states free
energy processes in chemical reactions. The only information needed is a
collection of simple statistics of the equilibrium properties of the reactants
and product states. No information on the reaction mechanism has to be given.
The method allows studying a large variety of chemical reactivity problems
including multiple reaction pathways, isomerization, stereo- and
regiospecificity. We applied the method to two fundamental organic chemical
reactions. First we study the \ce{S_N2} nucleophilic substitution reaction of a
\ce{Cl} in \ce{CH_2 Cl_2} leading to an understanding of the kinetic origin of
the chirality inversion in such processes. Subsequently, we tackle the problem
of regioselectivity in the hydrobromination of propene revealing that the
nature of empirical observations such as the Markovinikov's rules lies in the
chemical kinetics rather than the thermodynamic stability of the products
On the effect of the thermostat in non-equilibrium molecular dynamics simulations
The numerical investigation of the statics and dynamics of systems in
nonequilibrium in general, and under shear flow in particular, has become more
and more common. However, not all the numerical methods developed to simulate
equilibrium systems can be successfully adapted to out-of-equilibrium cases.
This is especially true for thermostats. Indeed, even though thermostats
developed to work under equilibrium conditions sometimes display good agreement
with rheology experiments, their performance rapidly degrades beyond weak
dissipation and small shear rates. Here we focus on gauging the relative
performances of three thermostats, Langevin, dissipative particle dynamics, and
Bussi-Donadio-Parrinello under varying parameters and external conditions. We
compare their effectiveness by looking at different observables and clearly
demonstrate that choosing the right thermostat (and its parameters) requires a
careful evaluation of, at least, temperature, density and velocity profiles. We
also show that small modifications of the Langevin and DPD thermostats greatly
enhance their performance in a wide range of parameters.Comment: 13 pages, 9 figure
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 '-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 is a -shifted symplectic derived Artin stack for
in the sense of arXiv:1111.3209, then near each we can find a
'minimal' smooth atlas with an affine derived scheme, such
that may be written explicitly in coordinates in a
standard 'Darboux form'.
(b) If is a -shifted symplectic derived Artin stack and
the underlying classical Artin stack, then extends naturally to a
'd-critical stack' in the sense of arXiv:1304.4508.
(c) If is an oriented d-critical stack, we can define a natural
perverse sheaf on , such that whenever is a scheme and
is smooth of relative dimension , then is locally modelled on
a critical locus Crit for smooth, and
is locally modelled on the perverse sheaf of
vanishing cycles of .
(d) If is a finite type oriented d-critical stack, we can define a
natural motive in a ring of motives on , such that whenever is a finite type scheme and
is smooth of dimension , then is locally modelled on a
critical locus Crit for smooth, and is locally modelled on the motivic vanishing
cycle of in .
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
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