1,721,013 research outputs found
Hydrodynamic limit for an anharmonic chain under boundary tension
Full text linkWe study the hydrodynamic limit for the isothermal dynamics of an anharmonic chain under hyperbolic space-time scaling under varying tension. The temperature is kept constant by a contact with a heat bath, realised via a stochastic momentum-preserving noise added to the dynamics. The noise is designed to be large at the microscopic level, but vanishing in the macroscopic scale. Boundary conditions are also considered: one end of the chain is kept fixed, while a time-varying tension is applied to the other end. We show that the volume stretch and momentum converge (in an appropriate sense) to a weak solution of a system of hyperbolic conservation laws (isothermal Euler equations in Lagrangian coordinates) with boundary conditions. This result includes the shock regime of the system. This is proven by adapting the theory of compensated compactness to a stochastic setting, as developed by Fritz (2011 Arch. Ration. Mech. Anal. 201 209-49) for the same model without boundary conditions. Finally, changing the external tension allows us to define thermodynamic isothermal transformations between equilibrium states. We use this to deduce the first and the second principle of thermodynamics for our model
Homogenization of a bond diffusion in a locally ergodic random environment
No full textWe consider a nearest neighbors random walk on Z. The jump rate from site x to site x+1 is
equal to the jump rate from x +1 to x and is a bounded, strictly positive random variable eta(x).
We assume that {eta(x)} with x∈Z is distributed by a locally ergodic probability measure. We prove
that, under diffusive scaling of space and time, the random walk converges in distribution to the
diffusion process on R with infinitesimal generator d/dX(a(X)d/dX), for a certain homogenized
diffusion function a(X), independent of eta . The main tools of the proof are a local ergodic result
and the explicit solution of the corresponding Poisson equation
Quasi-static hydrodynamic limit
No full textWe consider hydrodynamic limits of interacting particles systems with open boundaries, where the exterior parameters change in a time scale slower than the typical relaxation time scale. The limit deterministic profiles evolve quasi-statically.
These limits define rigorously the thermodynamic quasi static
transformations also for transition between non-equilibrium stationary
states. We study first the case of the symmetric simple exclusion,
where duality can be used, and then we use relative entropy methods to
extend to other models like zero range systems. Finally we consider a chain of anharmonic oscillators in contact with a thermal Langevin bath with a temperature gradient and a slowly varying tension applied
to one end
Quasi-static large deviations
Full text linkWe consider the symmetric simple exclusion with open boundaries that are in contact with particle reservoirs at different densities. The reservoir densities changes at a slower time scale with respect to the natural time scale the system reaches the stationary state. This gives rise to the quasi static hydrodynamic limit proven in (Journal of Statistical Physics 161 (5) (2015) 1037-1058). We study here the large deviations with respect to this limit for the particle density field and the total current. We identify explicitely the large deviation functional and prove that it satisfies a fluctuation relation
Quasi-static limit for a hyperbolic conservation law
Full text linkWe study the quasi-static limit for the L∞ entropy weak solution of scalar one-dimensional hyperbolic equations with strictly concave or convex flux and time dependent boundary conditions. The quasi-stationary profile evolves with the quasi-static equation, whose entropy solution is determined by the stationary profile corresponding to the boundary data at a given time
Green-Kubo Formula for Weakly Coupled Systems with Noise
No full textWe study the Green-Kubo (GK) formula κ(ε, ς) for
the heat conductivity of an infinite chain of d-dimensional finite
systems (cells) coupled by a smooth nearest neighbor potential εV .
The uncoupled systems evolve according to Hamiltonian dynamics
perturbed stochastically by an energy conserving noise of strength
ς. Noting that κ(ε, ς) exists and is finite whenever ς > 0, we are
interested in what happens when the strength of the noise ς → 0.
For this, we start in this work by formally expanding κ(ε, ς) in a
power series in ε, κ(ε, ς) = ε
2 P
n≥2
ε
n−2κn(ς) and investigating
the (formal) equations satisfied by κn(ς). We show in particular
that κ2(ς) is well defined when no pinning potential is present,
and coincides formally with the heat conductivity obtained in the
weak coupling (van Hove) limit, where time is rescaled as ε
−2
t,
for the cases where the latter has been established [24, 12]. For
one-dimensional systems, we investigate κ2(ς) as ς → 0 in three
cases: the disordered harmonic chain, the rotor chain and a chain
of strongly anharmonic oscillators. Moreover, we formally identify
κ2(ς) with the conductivity obtained by having the chain between
two reservoirs at
Pharmacophore modeling: a continuously evolving tool for computational drug design
No full textIn the latest two or three years progressive
applications of pharmacophore modeling continue to
appear in literature. Pharmacophore based parallel
screening, for instance, has been introduced in 2006.
Moreover, in 2008, a survey discussing the prospective
impact of virtual screening techniques in the
discovery of bioactive natural products has been
published. Finally, virtual screening techniques
from the drug discovery field are beginning to
be used for profiling the bioactivity of chemicals (especially those of potential environmental concern) with the aim of
prioritizing compounds for further testing using more complex systems and
reducing and ultimately replacing the use of animals in regulatory testing.
Pharmacophore modeling might be extremely helpful to allow full
achievement of all the above mentioned goals. In this contribution we report
a couple of case studies where pharmacophore generation and handling
played a pivotal role. In particular, in the first example, the development of a
novel computational pre-screening approach to be used as an in silico
filtering tool for natural products is described, applied to the estrogen
receptor-α subtype. In the second study, differently, the validation of a
preexisting pharmacophore by the prediction of the antifungal activities of
new azole compounds is discussed. In this case, it comes to light the
importance and utility of adding excluded volumes to a pharmacophore, to
increase its predictivity
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