Studies on the dynamics and rheology of dilute suspensions of Brownian particles in simple shear flow under the action of an external force

We present a novel approach to computing the orientation moments and rheological properties of a dilute suspension of spheroids in a simple shear flow at arbitrary Peclct number based on a generalised Langevin equation method. This method differs from the diffusion equation method which is commonly used to model similar systems in that the actual equations of motion for the orientations of the individual particles are used in the computations, instead of a solution of the diffusion equation of the system. It also differs from the method of 'Brownian dynamics simulations' in that the equations used for the simulations are deterministic differential equations even in the presence of noise, and not stochastic differential equations as in Brownian dynamics simulations. One advantage of the present approach over the Fokker-Planck equation formalism is that it employs a common strategy that can be applied across a wide range of shear and diffusion parameters. Also, since deterministic differential equations are easier to simulate than stochastic differential equations, the Langevin equation method presented in this work is more efficient and less computationally intensive than Brownian dynamics simulations.We derive the Langevin equations governing the orientations of the particles in the suspension and evolve a procedure for obtaining the equation of motion for any orientation moment. A computational technique is described for simulating the orientation moments dynamically from a set of time-averaged Langevin equations, which can be used to obtain the moments when the governing equations are harder to solve analytically. The results obtained using this method are in good agreement with those available in the literature.The above computational method is also used to investigate the effect of rotational Brownian motion on the rheology of the suspension under the action of an external force field. The force field is assumed to be either constant or periodic. In the case of con- I stant external fields earlier results in the literature are reproduced, while for the case of periodic forcing certain parametric regimes corresponding to weak Brownian diffusion are identified where the rheological parameters evolve chaotically and settle onto a low dimensional attractor. The response of the system to variations in the magnitude and orientation of the force field and strength of diffusion is also analyzed through numerical experiments. It is also demonstrated that the aperiodic behaviour exhibited by the system could not have been picked up by the diffusion equation approach as presently used in the literature.The main contributions of this work include the preparation of the basic framework for applying the Langevin method to standard flow problems, quantification of rotary Brownian effects by using the new method, the paired-moment scheme for computing the moments and its use in solving an otherwise intractable problem especially in the limit of small Brownian motion where the problem becomes singular, and a demonstration of how systems governed by a Fokker-Planck equation can be explored for possible chaotic behaviour.

Brownian motion with drift threshold model

In this thesis we implement estimating procedures in order to estimate threshold parameters for the continuous time threshold models driven by stochastic di®erential equations. The ¯rst procedure is based on the EM (expectation-maximization) algorithm applied to the threshold model built from the Brownian motion with drift process. The second procedure mimics one of the fundamental ideas in the estimation of the thresholds in time series context, that is, conditional least squares estimation. We implement this procedure not only for the threshold model built from the Brownian motion with drift process but also for more generic models as the ones built from the geometric Brownian motion or the Ornstein-Uhlenbeck process. Both procedures are implemented for simu- lated data and the least squares estimation procedure is also implemented for real data of daily prices from a set of international funds. The ¯rst fund is the PF-European Sus- tainable Equities-R fund from the Pictet Funds company and the second is the Parvest Europe Dynamic Growth fund from the BNP Paribas company. The data for both funds are daily prices from the year 2004. The last fund to be considered is the Converging Europe Bond fund from the Schroder company and the data are daily prices from the year 2005.

Comments on ‘‘Modeling fractional stochastic systems as non-random fractional dynamics driven Brownian motions

Applied Mathematical Modelling, Vol.33

On the relation between the fractional Brownian motion and the fractional derivatives

Physics Letters A, vol. 372; Issue 7

A fractional linear system view of the fractional brownian motion

Nonlinear Dynamics, Vol. 38

Brownian bridge and other path-dependent Gaussian processes vectorial simulation

The iterative simulation of the Brownian bridge is well known. In this article, we present a vectorial simulation alternative based on Gaussian processes for machine learning regression that is suitable for interpreted programming languages implementations. We extend the vectorial simulation of path-dependent trajectories to other Gaussian processes, namely, sequences of Brownian bridges, geometric Brownian motion, fractional Brownian motion, and Ornstein-Ulenbeck mean reversion process.

Phase behavior of shape-changing spheroids

We introduce a simple model for a biaxial nematic liquid crystal. This consists of hard spheroids that can switch shape between prolate (rodlike) and oblate (platelike) subject to an energy penalty Δε. The spheroids are approximated as hard Gaussian overlap particles and are treated at the level of Onsager's second-virial description. We use both bifurcation analysis and a numerical minimization of the free energy to show that, for additive particle shapes, (i) there is no stable biaxial phase even for Δε=0 (although there is a metastable biaxial phase in the same density range as the stable uniaxial phase) and (ii) the isotropic-to-nematic transition is into either one of two degenerate uniaxial phases, rod rich or plate rich. We confirm that even a small amount of shape nonadditivity may stabilize the biaxial nematic phase.

A novel hanging spherical drop system for the generation of cellular spheroids and high throughput combinatorial drug screening

We propose a novel hanging spherical drop system for anchoring arrays of droplets of cell suspension based on the use of biomimetic superhydrophobic flat substrates, with controlled positional adhesion and minimum contact with a solid substrate. By facing down the platform, it was possible to generate independent spheroid bodies in a high throughput manner, in order to mimic in vivo tumour models on the lab-on-chip scale. To validate this system for drug screening purposes, the toxicity of the anti-cancer drug doxorubicin in cell spheroids was tested and compared to cells in 2D culture. The advantages presented by this platform, such as feasibility of the system and the ability to control the size uniformity of the spheroid, emphasize its potential to be used as a new low cost toolbox for high-throughput drug screening and in cell or tissue engineering.

Mutations in the colony stimulating factor 1 receptor (CSF1R) gene cause hereditary diffuse leukoencephalopathy with spheroids.

Hereditary diffuse leukoencephalopathy with spheroids (HDLS) is an autosomal-dominant central nervous system white-matter disease with variable clinical presentations, including personality and behavioral changes, dementia, depression, parkinsonism, seizures and other phenotypes. We combined genome-wide linkage analysis with exome sequencing and identified 14 different mutations affecting the tyrosine kinase domain of the colony stimulating factor 1 receptor (encoded by CSF1R) in 14 families with HDLS. In one kindred, we confirmed the de novo occurrence of the mutation. Follow-up sequencing identified an additional CSF1R mutation in an individual diagnosed with corticobasal syndrome. In vitro, CSF-1 stimulation resulted in rapid autophosphorylation of selected tyrosine residues in the kinase domain of wild-type but not mutant CSF1R, suggesting that HDLS may result from partial loss of CSF1R function. As CSF1R is a crucial mediator of microglial proliferation and differentiation in the brain, our findings suggest an important role for microglial dysfunction in HDLS pathogenesis.

HSU-Robbins and Spitzer's theorems for the variations of fractional Brownian motion

Using recent results on the behavior of multiple Wiener-Itô integrals based on Stein's method, we prove Hsu-Robbins and Spitzer's theorems for sequences of correlated random variables related to the increments of the fractional Brownian motion.

Penetration and binding of radiolabeled anti-carcinoembryonic antigen monoclonal antibodies and their antigen binding fragments in human colon multicellular tumor spheroids.

The binding and penetration of two 125I-labeled anti-carcinoembryonic antigen (CEA) monoclonal antibodies (MAb) and their F(ab')2 and Fab fragments were measured in multicellular spheroids of poorly (HT29) and moderately well differentiated (Co112) human colon adenocarcinomas which express different amounts of CEA. Spheroids cultured in vitro model tumor microenvironments where poor vascular supply may modulate antigen expression and accessibility. The two MAb studied, 202 and 35, were shown previously to react with different CEA epitopes and to have high affinities of 1.2 and 5.8 X 10(9) M-1, respectively. MAb 202 has also been shown to cross-react with antigens present on human granulocytes and normal epithelial cells from human lung and pancreas. Specific binding of intact MAb and fragments of both antibodies was demonstrated for both types of human colon carcinoma spheroids compared to mouse colon carcinoma (CL26) and mammary tumor (EMT6/Ro) spheroids. Total binding of MAb and fragments was greater (1.5- to 2.5-fold) after 4 h compared to 1 h of exposure; the amount of binding compared to control IgG1 was 5- to 30-fold greater after 1-h incubation and 15 to 200 times greater after 4 h. This binding was stable as demonstrated by short and long wash experiments at 37 degrees and 4 degrees C. The binding of F(ab')2 and Fab fragments of the anti-CEA MAb 35 to spheroids of human colon Co112 was almost 2-fold greater than that of the intact MAb. However, for MAb 202, the binding of intact MAb and F(ab')2 was greater than that of Fab fragments. In addition the binding of both intact and F(ab')2 fragments of MAb 202 was greater than that obtained with MAb 35. Specific binding of both antibodies to HT29 spheroids, which express less CEA, was decreased for MAb and fragments of both 202 and 35. Autoradiography and immunoperoxidase experiments were performed to determine the penetration of MAb and fragments after incubation with intact spheroids. Comparisons were made with labeled MAb directly applied to frozen sections of spheroids. F(ab')2 and Fab fragments of both antibodies were bound at the surface of intact spheroids and penetrated to eight to ten cells, but the intact MAb were localized mainly at the spheroid surface and the outer one to three cell layers. There was much less binding at the surfaces of HT29 compared to Co112 spheroids. An enzyme immunoassay using MAb 35 and 202 demonstrated that Co112 spheroids produced about 8-fold more CEA/mg of cell protein than did monolayer cultures.(ABSTRACT TRUNCATED AT 400 WORDS)

Brownian dynamics simulation of DNA condensation.

DNA condensation observed in vitro with the addition of polyvalent counterions is due to intermolecular attractive forces. We introduce a quantitative model of these forces in a Brownian dynamics simulation in addition to a standard mean-field Poisson-Boltzmann repulsion. The comparison of a theoretical value of the effective diameter calculated from the second virial coefficient in cylindrical geometry with some experimental results allows a quantitative evaluation of the one-parameter attractive potential. We show afterward that with a sufficient concentration of divalent salt (typically approximately 20 mM MgCl(2)), supercoiled DNA adopts a collapsed form where opposing segments of interwound regions present zones of lateral contact. However, under the same conditions the same plasmid without torsional stress does not collapse. The condensed molecules present coexisting open and collapsed plectonemic regions. Furthermore, simulations show that circular DNA in 50% methanol solutions with 20 mM MgCl(2) aggregates without the requirement of torsional energy. This confirms known experimental results. Finally, a simulated DNA molecule confined in a box of variable size also presents some local collapsed zones in 20 mM MgCl(2) above a critical concentration of the DNA. Conformational entropy reduction obtained either by supercoiling or by confinement seems thus to play a crucial role in all forms of condensation of DNA.

Differential equations driven by fractional Brownian motion

A global existence and uniqueness result of the solution for multidimensional, time dependent, stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H> is proved. It is shown, also, that the solution has finite moments. The result is based on a deterministic existence and uniqueness theorem whose proof uses a contraction principle and a priori estimates.