From lattice-gas models to nonlinear diffusion models: A derivation of macroscopic equations and fluctuations

We derive nonlinear diffusion equations and equations containing corrections due to fluctuations for a coarse-grained concentration field. To deal with diffusion coefficients with an explicit dependence on the concentration values, we generalize the Van Kampen method of expansion of the master equation to field variables. We apply these results to the derivation of equations of phase-separation dynamics and interfacial growth instabilities.

Nomenclature of the GLUT/SLC2A family of sugar/polyol transport facilitators.

The recent identification of several additional members of the family of sugar transport facilitators (gene symbol SLC2A, protein symbol GLUT) has created a heterogeneous and, in part, confusing nomenclature. Therefore, this letter provides a summary of the family members and suggests a systematic nomenclature for SLC2A and GLUT symbols.

Vesicular transport of d-serine in astrocytes

The concept of tripartite synapse suggests that astrocytes make up a functional synapse with pre- and postsynaptic neuronal elements to modulate synaptic transmission through the regulated release of neuromodulators called gliotransmitters. Release of gliotransmitters such as glutamate or D-serine has been shown to depend on Ca21-dependent exocytosis. However, the origin (cytosolic versus vesicular) of the released gliotransmitter is still a matter of debate. The existence of Ca21-regulated exocytosis in astrocytes has been questioned mostly because the nature of secretory organelles which are loaded with gliotransmitters is unknown. Here we show the existence of a population of vesicles that uptakes and stores glutamate and D-serine in astrocytes which are present in situ. Immunoisolated glial organelles expressing synaptobrevin 2 (Sb2) display morphological and biochemical features very similar to synaptic vesicles. We demonstrate that these organelles not only contain and uptake glutamate but also display a glia-specific transport activity for D-serine. Furthermore, we report that the uptake of D-serine is energized by a H1-ATPase present on the immunoisolated vesicles and that cytosolic chloride ions modulate the uptake of D-serine. Finally, we show that serine racemase (SR), the synthesizing enzyme for D-serine, is anchored to the membrane of glial organelles allowing a local and efficient concentration of the gliotransmitter to be transported. We conclude that vesicles in astrocytes do exist with the goal to store and release D-serine, glutamate and most likely other neuromodulators.

Importance of ENaC-mediated sodium transport in alveolar fluid clearance using genetically-engineered mice.

The lung possesses specific transport systems that intra- and extracellularly maintain salt and fluid balance necessary for its function. At birth, the lungs rapidly transform into a fluid (Na(+))-absorbing organ to enable efficient gas exchange. Alveolar fluid clearance, which mainly depends on sodium transport in alveolar epithelial cells, is an important mechanism by which excess water in the alveoli is reabsorbed during the resolution of pulmonary edema. In this review, we will focus and summarize on the role of ENaC in alveolar lung liquid clearance and discuss recent data from mouse models with altered activity of epithelial sodium channel function in the lung, and more specifically in alveolar fluid clearance. Recent data studying mice with hyperactivity of ENaC or mice with reduced ENaC activity clearly illustrate the impaired lung fluid clearance in these adult mice. Further understanding of the physiological role of ENaC and its regulatory proteins implicated in salt and water balance in the alveolar cells may therefore help to develop new therapeutic strategies to improve gas exchange in pulmonary edema.

Stochastic semiclassical equations for weakly inhomogeneous cosmologies

Semiclassical Einstein-Langevin equations for arbitrary small metric perturbations conformally coupled to a massless quantum scalar field in a spatially flat cosmological background are derived. Use is made of the fact that for this problem the in-in or closed time path effective action is simply related to the Feynman-Vernon influence functional which describes the effect of the ``environment,'' the quantum field which is coarse grained here, on the ``system,'' the gravitational field which is the field of interest. This leads to identify the dissipation and noise kernels in the in-in effective action, and to derive a fluctuation-dissipation relation. A tensorial Gaussian stochastic source which couples to the Weyl tensor of the spacetime metric is seen to modify the usual semiclassical equations which can be veiwed now as mean field equsations. As a simple application we derive the correlation functions of the stochastic metric fluctuations produced in a flat spacetime with small metric perturbations due to the quantum fluctuations of the matter field coupled to these perturbations.

Single-hole GPR reflection imaging of solute transport in a granitic aquifer

Identifying transport pathways in fractured rock is extremely challenging as flow is often organized in a few fractures that occupy a very small portion of the rock volume. We demonstrate that saline tracer experiments combined with single-hole ground penetrating radar (GPR) reflection imaging can be used to monitor saline tracer movement within mm-aperture fractures. A dipole tracer test was performed in a granitic aquifer by injecting a saline solution in a known fracture, while repeatedly acquiring single-hole GPR sections in the pumping borehole located 6 m away. The final depth-migrated difference sections make it possible to identify consistent temporal changes over a 30 m depth interval at locations corresponding to fractures previously imaged in GPR sections acquired under natural flow and tracer-free conditions. The experiment allows determining the dominant flow paths of the injected tracer and the velocity (0.4-0.7 m/min) of the tracer front. Citation: Dorn, C., N. Linde, T. Le Borgne, O. Bour, and L. Baron (2011), Single-hole GPR reflection imaging of solute transport in a granitic aquifer, Geophys. Res. Lett., 38, L08401, doi: 10.1029/2011GL047152.

From Galilean-invariant to relativistic wave equations

Through an imaginary change of coordinates in the Galilei algebra in 4 space dimensions and making use of an original idea of Dirac and Lvy-Leblond, we are able to obtain the relativistic equations of Dirac and of Bargmann and Wigner starting with the (Galilean-invariant) Schrdinger equation.

Multisoliton solutions to Einstein's equations

We discuss a multisoliton solution to Einsteins equations in vacuum. The solution is interpreted as many gravitational solitons propagating and colliding on a homogeneous cosmological background. Following a previous letter, we characterize the solitons by their localizability and by their peculiar properties under collisions. Furthermore, we define an associated frame-dependent velocity field which illustrates the solitonic character of these gravitational solitons in the classical sense.

Semiclassical equations for weakly inhomogeneous cosmologies

The in-in effective action formalism is used to derive the semiclassical correction to Einsteins equations due to a massless scalar quantum field conformally coupled to small gravitational perturbations in spatially flat cosmological models. The vacuum expectation value of the stress tensor of the quantum field is directly derived from the renormalized in-in effective action. The usual in-out effective action is also discussed and it is used to compute the probability of particle creation. As one application, the stress tensor of a scalar field around a static cosmic string is derived and the back-reaction effect on the gravitational field of the string is discussed.

Long-tailed trapping times and Lévy flights in a self-organized critical granular system

We present a continuous time random walk model for the scale-invariant transport found in a self-organized critical rice pile [K. Christensen et al., Phys. Rev. Lett. 77, 107 (1996)]. From our analytical results it is shown that the dynamics of the experiment can be explained in terms of Lvy flights for the grains and a long-tailed distribution of trapping times. Scaling relations for the exponents of these distributions are obtained. The predicted microscopic behavior is confirmed by means of a cellular automaton model.

Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticality

A stochastic nonlinear partial differential equation is constructed for two different models exhibiting self-organized criticality: the Bak-Tang-Wiesenfeld (BTW) sandpile model [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] and the Zhang model [Phys. Rev. Lett. 63, 470 (1989)]. The dynamic renormalization group (DRG) enables one to compute the critical exponents. However, the nontrivial stable fixed point of the DRG transformation is unreachable for the original parameters of the models. We introduce an alternative regularization of the step function involved in the threshold condition, which breaks the symmetry of the BTW model. Although the symmetry properties of the two models are different, it is shown that they both belong to the same universality class. In this case the DRG procedure leads to a symmetric behavior for both models, restoring the broken symmetry, and makes accessible the nontrivial fixed point. This technique could also be applied to other problems with threshold dynamics.

Phenomenological approach to nonlinear Langevin equations

In this paper we address the problem of consistently constructing Langevin equations to describe fluctuations in nonlinear systems. Detailed balance severely restricts the choice of the random force, but we prove that this property, together with the macroscopic knowledge of the system, is not enough to determine all the properties of the random force. If the cause of the fluctuations is weakly coupled to the fluctuating variable, then the statistical properties of the random force can be completely specified. For variables odd under time reversal, microscopic reversibility and weak coupling impose symmetry relations on the variable-dependent Onsager coefficients. We then analyze the fluctuations in two cases: Brownian motion in position space and an asymmetric diode, for which the analysis based in the master equation approach is known. We find that, to the order of validity of the Langevin equation proposed here, the phenomenological theory is in agreement with the results predicted by more microscopic models