Theoretical Framework for Microscopic Osmotic Phenomena

The basic ingredients of osmotic pressure are a solvent fluid with a soluble molecular species which is restricted to a chamber by a boundary which is permeable to the solvent fluid but impermeable to the solute molecules. For macroscopic systems at equilibrium, the osmotic pressure is given by the classical van't Hoff Law, which states that the pressure is proportional to the product of the temperature and the difference of the solute concentrations inside and outside the chamber. For microscopic systems the diameter of the chamber may be comparable to the length-scale associated with the solute-wall interactions or solute molecular interactions. In each of these cases, the assumptions underlying the classical van't Hoff Law may no longer hold. In this paper we develop a general theoretical framework which captures corrections to the classical theory for the osmotic pressure under more general relationships between the size of the chamber and the interaction length scales. We also show that notions of osmotic pressure based on the hydrostatic pressure of the fluid and the mechanical pressure on the bounding walls of the chamber must be distinguished for microscopic systems. To demonstrate how the theoretical framework can be applied, numerical results are presented for the osmotic pressure associated with a polymer of N monomers confined in a spherical chamber as the bond strength is varied

A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales

In this work it is shown how the immersed boundary method of (Peskin2002) for modeling flexible structures immersed in a fluid can be extended to include thermal fluctuations. A stochastic numerical method is proposed which deals with stiffness in the system of equations by handling systematically the statistical contributions of the fastest dynamics of the fluid and immersed structures over long time steps. An important feature of the numerical method is that time steps can be taken in which the degrees of freedom of the fluid are completely underresolved, partially resolved, or fully resolved while retaining a good level of accuracy. Error estimates in each of these regimes are given for the method. A number of theoretical and numerical checks are furthermore performed to assess its physical fidelity. For a conservative force, the method is found to simulate particles with the correct Boltzmann equilibrium statistics. It is shown in three dimensions that the diffusion of immersed particles simulated with the method has the correct scaling in the physical parameters. The method is also shown to reproduce a well-known hydrodynamic effect of a Brownian particle in which the velocity autocorrelation function exhibits an algebraic tau^(-3/2) decay for long times. A few preliminary results are presented for more complex systems which demonstrate some potential application areas of the method.Comment: 52 pages, 11 figures, published in journal of computational physic

Stochastic Eulerian-Lagrangian Methods for Fluid-Structure Interactions with Thermal Fluctuations and Shear Boundary Conditions

A computational approach is introduced for the study of the rheological properties of complex fluids and soft materials. The approach allows for a consistent treatment of microstructure elastic mechanics, hydrodynamic coupling, thermal fluctuations, and externally driven shear flows. A mixed description in terms of Eulerian and Lagrangian reference frames is used for the physical system. Microstructure configurations are represented in a Lagrangian reference frame. Conserved quantities, such as momentum of the fluid and microstructures, are represented in an Eulerian reference frame. The mathematical formalism couples these different descriptions using general operators subject to consistency conditions. Thermal fluctuations are taken into account in the formalism by stochastic driving fields introduced in accordance with the principles of statistical mechanics. To study the rheological responses of materials subject to shear, generalized periodic boundary conditions are developed where periodic images are shifted relative to the unit cell to induce shear. Stochastic numerical methods are developed for the formalism. As a demonstration of the methods, results are presented for the shear responses of a polymeric fluid, lipid vesicle fluid, and a gel-like material.Comment: 36 pages, 10 figures, stochastic computational methods for soft materials and complex fluids at microstructure leve

A Numerical Model for Brownian Particles Fluctuating in Incompressible Fluids

We present a numerical method that consistently implements thermal fluctuations and hydrodynamic interactions to the motion of Brownian particles dispersed in incompressible host fluids. In this method, the thermal fluctuations are introduced as random forces acting on the Brownian particles. The hydrodynamic interactions are introduced by directly resolving the fluid motions with the particle motion as a boundary condition to be satisfied. The validity of the method has been examined carefully by comparing the present numerical results with the fluctuation-dissipation theorem whose analytical form is known for dispersions of a single spherical particle. Simulations are then performed for more complicated systems, such as a dispersion composed of many spherical particles and a single polymeric chain in a solvent.Comment: 6 pages, 8 figure

Assessment of suitable observation conditions for a monthly operational remote sensing based crop monitoring system.

Abstract: Cloud cover is the main issue to consider when remote sensing images are used to identify, map and monitor croplands, especially over the summer season (October to March in Brazi). This paper aims at evaluating clear sky conditions over four Brazilian states (Sa?o Paulo, Parana?, Santa Catarina, and Rio Grande do Sul) to assess suitable observation conditions for a monthly basis operational crop monitoring system. Cloudiness was analyzed using MODIS Cloud Mask product (MOD35), which presents four labels for cloud cover status: cloudy, uncertainty, probably clear and confident clear. R software was used to compute average values of clear sky with a confidence interval of 95% for each month between July 1st, 2000 and June 30th, 2013. Results showed significant differences within and between the four tested states. Moreover, the period from November to March presented 50% less clear sky areas when compared to April to October

Cloud cover assessment for operational crop monitoring systems in tropical areas.

Abstract: The potential of optical remote sensing data to identify, map and monitor croplands is well recognized. However, clouds strongly limit the usefulness of optical imagery for these applications. This paper aims at assessing cloud cover conditions over four states in the tropical and sub-tropical Center-South region of Brazil to guide the development of an appropriate agricultural monitoring system based on Landsat-like imagery. Cloudiness was assessed during overlapping four months periods to match the typical length of crop cycles in the study area. The percentage of clear sky occurrence was computed from the 1 km resolution MODIS Cloud Mask product (MOD35) considering 14 years of data between July 2000 and June 2014. Results showed high seasonality of cloud occurrence within the crop year with strong variations across the study area. The maximum seasonality was observed for the two states in the northern part of the study area (i.e., the ones closer to the Equator line), which also presented the lowest averaged values (15%) of clear sky occurrence during the main (summer) cropping period (November to February). In these locations, optical data faces severe constraints for mapping summer crops. On the other hand, relatively favorable conditions were found in the southern part of the study region. In the South, clear sky values of around 45% were found and no signi?cant clear sky seasonality was observed. Results underpin the challenges to implement an operational crop monitoring system based solely on optical remote sensing imagery in tropical and sub-tropical regions, in particular if short-cycle crops have to be monitored during the cloudy summer months. To cope with cloudiness issues, we recommend the use of new systems with higher repetition rates such as Sentinel-2. For local studies, Unmanned Aircraft Vehicles(UAVs) might be used to augment the observing capability. Multi-sensor approaches combining optical and microwave data can be another option. In cases where wall-to-wall maps are not mandatory, statistical sampling approaches might also be a suitable alternative for obtaining useful crop area information

Quantifying Vegetation Biophysical Variables from Imaging Spectroscopy Data: A Review on Retrieval Methods

An unprecedented spectroscopic data stream will soon become available with forthcoming Earth-observing satellite missions equipped with imaging spectroradiometers. This data stream will open up a vast array of opportunities to quantify a diversity of biochemical and structural vegetation properties. The processing requirements for such large data streams require reliable retrieval techniques enabling the spatiotemporally explicit quantification of biophysical variables. With the aim of preparing for this new era of Earth observation, this review summarizes the state-of-the-art retrieval methods that have been applied in experimental imaging spectroscopy studies inferring all kinds of vegetation biophysical variables. Identified retrieval methods are categorized into: (1) parametric regression, including vegetation indices, shape indices and spectral transformations; (2) nonparametric regression, including linear and nonlinear machine learning regression algorithms; (3) physically based, including inversion of radiative transfer models (RTMs) using numerical optimization and look-up table approaches; and (4) hybrid regression methods, which combine RTM simulations with machine learning regression methods. For each of these categories, an overview of widely applied methods with application to mapping vegetation properties is given. In view of processing imaging spectroscopy data, a critical aspect involves the challenge of dealing with spectral multicollinearity. The ability to provide robust estimates, retrieval uncertainties and acceptable retrieval processing speed are other important aspects in view of operational processing. Recommendations towards new-generation spectroscopy-based processing chains for operational production of biophysical variables are given

A note on the correspondence of an immersed boundary method incorporating thermal fluctuations with Stokesian-Brownian dynamics

In this paper a direct correspondence is made between the effective stochastic dynamics of elastic structures of an Immersed Boundary Method incorporating thermal fluctuations and Stokesian-Browman Dynamics. The correspondence is made in the limit of small Reynolds number, in which the fluid relaxes rapidly on the time scale of the motion of the immersed structures, by performing an averaging procedure directly on the stochastic equations of the Immersed Boundary Method. It is found that there is agreement with Stokesian-Brownian Dynamics for the far-field hydrodynamic interactions and that a fluctuation-dissipation relation is satisfied for the stochastic fluctuations of the effective equations. (c) 2006 Elsevier B.V. All rights reserved