Nutrient supply by mass flow and diffusion to maize plants in response to soil aggregate size and water potential

Nutrients are basically transported to the roots by mass flow and diffusion. The aim of this study was to quantify the contribution of these two mechanisms to the acquisition of macronutrients (N, P, K, Ca, Mg, and S) and cationic micronutrients (Fe, Mn, Zn, and Cu) by maize plants as well as xylem exudate volume and composition in response to soil aggregate size and water availability. The experiment was conducted in a greenhouse with samples of an Oxisol, from under two management systems: a region of natural savanna-like vegetation (Cerradão, CER) and continuous maize under conventional management for over 30 years (CCM). The treatments were arranged in a factorial [2 x (1 + 2) x 2] design, with two management systems (CER and CCM), (1 + 2) soil sifted through a 4 mm sieve and two aggregate classes (< 0.5 mm and 0.5 - 4.0 mm) and two soil matric potentials (-40 and -10 kPa). These were evaluated in a randomized block design with four replications. The experiment was conducted for 70 days after sowing. The influence of soil aggregate size and water potential on the nutrient transport mechanisms was highest in soil samples with higher nutrient concentrations in solution, in the CER system; diffusion became more relevant when water availability was higher and in aggregates < 0.5 mm. The volume of xylem exudate collected from maize plants increased with the decrease in aggregate size and the increased availability of soil water in the CER system. The highest Ca and Mg concentrations in the xylem exudate of plants grown on samples from the CER system were related to the high concentrations of these nutrients in the soil solution of this management system.

Kinematic reduction of reaction-diffusion fronts with multiplicative noise. Derivation of stochastic sharp-interface equations

We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the kinematic (eikonal) description in terms of a stochastic moving-boundary or sharp-interface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated with the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a non-Kardar-Parisi-Zhang universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations and kinetic roughening. We also predict and observe a noise-induced pushed-pulled transition. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise.

Modelization of surface diffusion of a molecular dimer

A simple model for a dimer molecular diffusion on a crystalline surface, as a function of temperature, is presented. The dimer is formed by two particles coupled by a quadratic potential. The dimer diffusion is modeled by an overdamped Langevin equation in the presence of a two-dimensional periodic potential. Numerical simulation¿s results exhibit some dynamical properties observed, for example, in Si2 diffusion on a silicon [100] surface. They can be used to predict the value of the effective friction parameter. Comparison between our model and experimental measurements is presented.

Heat fluctuations in Brownian transducers

The heat fluctuation probability distribution function in Brownian transducers operating between two heat reservoirs is studied. We find, both analytically and numerically, that the recently proposed fluctuation theorem for heat exchange [C. Jarzynski and D. K. Wojcik, Phys. Rev. Lett. 92, 230602 (2004)] has to be applied carefully when the coupling mechanism between both baths is considered. We also conjecture how to extend such a relation when an external work is present.

Accelerated Microstructure Imaging via Convex Optimization (AMICO) from diffusion MRI data.

Microstructure imaging from diffusion magnetic resonance (MR) data represents an invaluable tool to study non-invasively the morphology of tissues and to provide a biological insight into their microstructural organization. In recent years, a variety of biophysical models have been proposed to associate particular patterns observed in the measured signal with specific microstructural properties of the neuronal tissue, such as axon diameter and fiber density. Despite very appealing results showing that the estimated microstructure indices agree very well with histological examinations, existing techniques require computationally very expensive non-linear procedures to fit the models to the data which, in practice, demand the use of powerful computer clusters for large-scale applications. In this work, we present a general framework for Accelerated Microstructure Imaging via Convex Optimization (AMICO) and show how to re-formulate this class of techniques as convenient linear systems which, then, can be efficiently solved using very fast algorithms. We demonstrate this linearization of the fitting problem for two specific models, i.e. ActiveAx and NODDI, providing a very attractive alternative for parameter estimation in those techniques; however, the AMICO framework is general and flexible enough to work also for the wider space of microstructure imaging methods. Results demonstrate that AMICO represents an effective means to accelerate the fit of existing techniques drastically (up to four orders of magnitude faster) while preserving accuracy and precision in the estimated model parameters (correlation above 0.9). We believe that the availability of such ultrafast algorithms will help to accelerate the spread of microstructure imaging to larger cohorts of patients and to study a wider spectrum of neurological disorders.

First-passage-time statistics for diffusion processes with an external random force

We present exact equations and expressions for the first-passage-time statistics of dynamical systems that are a combination of a diffusion process and a random external force modeled as dichotomous Markov noise. We prove that the mean first passage time for this system does not show any resonantlike behavior.

Modelling diffusion of innovations in a social network

A simple model of diffusion of innovations in a social network with upgrading costs is introduced. Agents are characterized by a single real variable, their technological level. According to local information, agents decide whether to upgrade their level or not, balancing their possible benefit with the upgrading cost. A critical point where technological avalanches display a power-law behavior is also found. This critical point is characterized by a macroscopic observable that turns out to optimize technological growth in the stationary state. Analytical results supporting our findings are found for the globally coupled case.

Counter-ion effect on surfactant-DNA gel particles as controlled DNA delivery systems

The ability to entrap drugs within vehicles and subsequently release them has led to new treatments for a number of diseases. Based on an associative phase separation and interfacial diffusion approach, we developed a way to prepare DNA gel particles without adding any kind of cross-linker or organic solvent. Among the various agents studied, cationic surfactants offered particularly efficient control for encapsulation and DNA release from these DNA gel particles. The driving force for this strong association is the electrostatic interaction between the two components, as induced by the entropic increase due to the release of the respective counter-ions. However, little is known about the influence of the respective counter-ions on this surfactant-DNA interaction. Here we examined the effect of different counter-ions on the formation and properties of the DNA gel particles by mixing DNA (either single- (ssDNA) or double-stranded (dsDNA)) with the single chain surfactant dodecyltrimethylammonium (DTA). In particular, we used as counter-ions of this surfactant the hydrogen sulfate and trifluoromethane sulfonate anions and the two halides, chloride and bromide. Effects on the morphology of the particles obtained, the encapsulation of DNA and its release, as well as the haemocompatibility of these particles, are presented, using the counter-ion structure and the DNA conformation as controlling parameters. Analysis of the data indicates that the degree of counter-ion dissociation from the surfactant micelles and the polar/hydrophobic character of the counter-ion are important parameters in the final properties of the particles. The stronger interaction with amphiphiles for ssDNA than for dsDNA suggests the important role of hydrophobic interactions in DNA.

Contrasting diffusion of Quaternary gene pools across Europe: the case of the arctic-alpine Gentiana nivalis L. (Gentianaceae).

The fate of European arctic-alpine species during Pleistocene climatic oscillations still remains debated. Did these cold-adapted species invade much of the continental steppe or did they remain restricted to warmer slopes of inner mountain massifs? To examine this question, we investigated the phylogeography of Gentiana nivalis, a typical European arctic-alpine plant species. Genome fingerprinting analyses revealed that four genetic pools are actually unevenly distributed across the continent. One cluster covers almost all mountain massifs as well as northern areas, and thus coincides with a scenario of past distribution covering a large part of the European glacial steppe. In contrast, the three other lineages are strongly restricted spatially to western, central, and eastern Alps, respectively, thus arguing towards a scenario of in situ glacial survival. The coexistence of lineages with such contrasting demographic histories in Europe challenges our classical view of refugia and corroborates several hypotheses of biogeographers from the twentieth century.

Molecular hydrogen diffusion in nanostructured amorphous silicon thin films

We study hydrogen stability and its evolution during thermal annealing in nanostructured amorphous silicon thin films. From the simultaneous measurement of heat and hydrogen desorption, we obtain the experimental evidence of molecular diffusion in these materials. In addition, we introduce a simple diffusion model which shows good agreement with the experimental data

Thermostatistical description of small systems in nonequilibrium conditions: Energy conversion and harvesting

Hysteresis cycles are very important features of energy conversion and harvesting devices, such as batteries. The efficiency of these may be strongly affected by the physical size of the system. Here, we show that in systems which are small enough, the existence of physical boundaries which produce nonhomogeneities of the interaction potential gives rise to inflections and barriers in the associated free energy. This in turn brings on irreversible processes which can be triggered under suitable external conditions imposed by a heat bath. As an example, by controlling the temperature, the state of a small system may be impelled to oscillate between two different structural configurations or aggregation states avoiding equilibrium coexistence and therefore dissipating energy. This cyclical behavior associated with a hysteresis cycle may be prototypical of energy conversion, storage, or generating nanodevices, as exemplified by Li-ion insertion batteries.

Diffusion in stationary flow from mesoscopic nonequilibrium thermodynamics

We analyze the diffusion of a Brownian particle in a fluid under stationary flow. By using the scheme of nonequilibrium thermodynamics in phase space, we obtain the Fokker-Planck equation that is compared with others derived from the kinetic theory and projector operator techniques. This equation exhibits violation of the fluctuation-dissipation theorem. By implementing the hydrodynamic regime described by the first moments of the nonequilibrium distribution, we find relaxation equations for the diffusion current and pressure tensor, allowing us to arrive at a complete description of the system in the inertial and diffusion regimes. The simplicity and generality of the method we propose makes it applicable to more complex situations, often encountered in problems of soft-condensed matter, in which not only one but more degrees of freedom are coupled to a nonequilibrium bath.

Biased diffusion in confined media: Test of the Fick-Jacobs approximation and validity criteria

We study biased, diffusive transport of Brownian particles through narrow, spatially periodic structures in which the motion is constrained in lateral directions. The problem is analyzed under the perspective of the Fick-Jacobs equation, which accounts for the effect of the lateral confinement by introducing an entropic barrier in a one-dimensional diffusion. The validity of this approximation, based on the assumption of an instantaneous equilibration of the particle distribution in the cross section of the structure, is analyzed by comparing the different time scales that characterize the problem. A validity criterion is established in terms of the shape of the structure and of the applied force. It is analytically corroborated and verified by numerical simulations that the critical value of the force up to which this description holds true scales as the square of the periodicity of the structure. The criterion can be visualized by means of a diagram representing the regions where the Fick-Jacobs description becomes inaccurate in terms of the scaled force versus the periodicity of the structure.

Entropic transport in confined media: a challenge for computational studies in biological and soft-matter systems

Transport in small-scale biological and soft-matter systems typically occurs under confinement conditions in which particles proceed through obstacles and irregularities of the boundaries that may significantly alter their trajectories. A transport model that assimilates the confinement to the presence of entropic barriers provides an efficient approach to quantify its effect on the particle current and the diffusion coefficient. We review the main peculiarities of entropic transport and treat two cases in which confinement effects play a crucial role, with the appearance of emergent properties. The presence of entropic barriers modifies the mean first-passage time distribution and therefore plays a very important role in ion transport through micro- and nano-channels. The functionality of molecular motors, modeled as Brownian ratchets, is strongly affected when the motor proceeds in a confined medium that may constitute another source of rectification. The interplay between ratchet and entropic rectification gives rise to a wide variety of dynamical behaviors, not observed when the Brownian motor proceeds in an unbounded medium. Entropic transport offers new venues of transport control and particle manipulation and new ways to engineer more efficient devices for transport at the nanoscale.