The thermohydrodynamical picture of a charged Brownian particle

We study a charged Brownian gas with a non uniform bath temperature, and present a thermohydrodynamical picture. Expansion on the collision time probes the validity of the local equilibrium approach and the relevant thermodynamical variables. For the linear regime we present several applications (some novel).

The thermohydrodynamical picture of Brownian motion via a generalized Smoluchowsky equation

Via an operator continued fraction scheme, we expand Kramers equation in the high friction limit. Then all distribution moments are expressed in terms of the first momemt (particle density). The latter satisfies a generalized Smoluchowsky equation. As an application, we present the nonequilibrium thermodynamics and hydrodynamical picture for the one-dimensional Brownian motion. (C) 2000 Elsevier B.V. B.V. All rights reserved.

Charged Brownian particles: Kramers and Smoluchowski equations and the hydrothermodynamical picture

We consider a charged Brownian gas under the influence of external and non-uniform electric, magnetic and mechanical fields, immersed in a non-uniform bath temperature. With the collision time as an expansion parameter, we study the solution to the associated Kramers equation, including a linear reactive term. To the first order we obtain the asymptotic (overdamped) regime, governed by transport equations, namely: for the particle density, a Smoluchowski- reactive like equation; for the particle's momentum density, a generalized Ohm's-like equation; and for the particle's energy density, a MaxwellCattaneo-like equation. Defining a nonequilibrium temperature as the mean kinetic energy density, and introducing Boltzmann's entropy density via the one particle distribution function, we present a complete thermohydrodynamical picture for a charged Brownian gas. We probe the validity of the local equilibrium approximation, Onsager relations, variational principles associated to the entropy production, and apply our results to: carrier transport in semiconductors, hot carriers and Brownian motors. Finally, we outline a method to incorporate non-linear reactive kinetics and a mean field approach to interacting Brownian particles. © 2011 Elsevier B.V. All rights reserved.

Hot Brownian carriers in the Langevin picture: Application to a simple model for the Gunn effect in GaAs

We consider a charged Brownian gas under the influence of external, static and uniform electric and magnetic fields, immersed in a uniform bath temperature. We obtain the solution for the associated Langevin equation, and thereafter the evolution of the nonequilibrium temperature towards a nonequilibrium (hot) steady state. We apply our results to a simple yet relevant Brownian model for carrier transport in GaAs. We obtain a negative differential conductivity regime (Gunn effect) and discuss and compare our results with the experimental results. © 2013.

Non-Markovian expansion in quantum Brownian motion

We consider the non-Markovian Langevin evolution of a dissipative dynamical system in quantum mechanics in the path integral formalism. After discussing the role of the frequency cutoff for the interaction of the system with the heat bath and the kernel and noise correlator that follow from the most common choices, we derive an analytic expansion for the exact non-Markovian dissipation kernel and the corresponding colored noise in the general case that is consistent with the fluctuation-dissipation theorem and incorporates systematically non-local corrections. We illustrate the modifications to results obtained using the traditional (Markovian) Langevin approach in the case of the exponential kernel and analyze the case of the non-Markovian Brownian motion. We present detailed results for the free and the quadratic cases, which can be compared to exact solutions to test the convergence of the method, and discuss potentials of a general nonlinear form. © 2013 Elsevier B.V. All rights reserved.

Anisotropic Brownian motion in ordered phases of DNA fragments

Using Fluorescence Recovery After Photobleaching, we investigate the Brownian motion of DNA rod-like fragments in two distinct anisotropic phases with a local nematic symmetry. The height of the measurement volume ensures the averaging of the anisotropy of the in-plane diffusive motion parallel or perpendicular to the local nematic director in aligned domains. Still, as shown in using a model specifically designed to handle such a situation and predicting a non-Gaussian shape for the bleached spot as fluorescence recovery proceeds, the two distinct diffusion coefficients of the DNA particles can be retrieved from data analysis. In the first system investigated (a ternary DNA-lipid lamellar complex), the magnitude and anisotropy of the diffusion coefficient of the DNA fragments confined by the lipid bilayers are obtained for the first time. In the second, binary DNA-solvent system, the magnitude of the diffusion coefficient is found to decrease markedly as DNA concentration is increased from isotropic to cholesteric phase. In addition, the diffusion coefficient anisotropy measured within cholesteric domains in the phase coexistence region increases with concentration, and eventually reaches a high value in the cholesteric phase.

Anomalous Velocity Distributions in Active Brownian Suspensions

Large-scale simulations and analytical theory have been combined to obtain the nonequilibrium velocity distribution, f(v), of randomly accelerated particles in suspension. The simulations are based on an event-driven algorithm, generalized to include friction. They reveal strongly anomalous but largely universal distributions, which are independent of volume fraction and collision processes, which suggests a one-particle model should capture all the essential features. We have formulated this one-particle model and solved it analytically in the limit of strong damping, where we find that f (v) decays as 1/v for multiple decades, eventually crossing over to a Gaussian decay for the largest velocities. Many particle simulations and numerical solution of the one-particle model agree for all values of the damping.

Design of custom-shaped vascularized tissues using microtissue spheroids as minimal building units

Tissue engineering strategies are gathering clinical momentum in regenerative medicine and are expected to provide excellent opportunities for therapy for difficult-to-treat human pathologies. Being aware of the requirement to produce larger artificial tissue implants for clinical applications, we used microtissues, produced using gravity-enforced self-assembly of monodispersed primary cells, as minimal tissue units to generate scaffold-free vascularized artificial macrotissues in custom-shaped agarose molds. Mouse myoblast, pig and human articular-derived chondrocytes, and human myofibroblast (HMF)-composed microtissues (microm3 scale) were amalgamated to form coherent macrotissue patches (mm3 scale) of a desired shape. Macrotissues, assembled from the human umbilical vein endothelial cell (HUVEC)-coated HMF microtissues, developed a vascular system, which functionally connected to the chicken embryo's vasculature after implantation. The design of scaffold-free vascularized macrotissues is a first step toward the scale-up and production of artificial tissue implants for future tissue engineering initiatives.

The von Mises-Fisher distribution of the first exit point from the hypersphere of the drifted Brownian motion and the density of the first exit time

A characterization is provided for the von Mises–Fisher random variable, in terms of first exit point from the unit hypersphere of the drifted Wiener process. Laplace transform formulae for the first exit time from the unit hypersphere of the drifted Wiener process are provided. Post representations in terms of Bell polynomials are provided for the densities of the first exit times from the circle and from the sphere.

A microfluidic platform for chemoresistive testing of multicellular pleural cancer spheroids

This study reports on a microfluidic platform on which single multicellular spheroids from malignant pleural mesothelioma (MPM), an aggressive tumor with poor prognosis, can be loaded, trapped and tested for chemotherapeutic drug response. A new method to detect the spheroid viability cultured on the microfluidic chip as a function of the drug concentration is presented. This approach is based on the evaluation of the caspase activity in the supernatant sampled from the chip and tested using a microplate reader. This simple and time-saving method does only require a minimum amount of manipulations and was established for very low numbers of cells. This feature is particularly important in view of personalised medicine applications for which the number of cells obtained from the patients is low. MPM spheroids were continuously perfused for 48 hours with cisplatin, one of the standard chemotherapeutic drugs used to treat MPM. The 50% growth inhibitory concentration of cisplatin in perfused MPM spheroids was found to be twice as high as in spheroids cultured under static conditions. This chemoresistance increase might be due to the continuous support of nutrients and oxygen to the perfused spheroids.

Towards personalized medicine: Chemosensitivity assays of patient lung cancer cell spheroids in a perfused microfluidic platform

Cancer is responsible for millions of deaths worldwide and the variability in disease patterns calls for patient-specific treatment. Therefore, personalized treatment is expected to become a daily routine in prospective clinical tests. In addition to genetic mutation analysis, predictive chemosensitive assays using patient's cells will be carried out as a decision making tool. However, prior to their widespread application in clinics, several challenges linked to the establishment of such assays need to be addressed. To best predict the drug response in a patient, the cellular environment needs to resemble that of the tumor. Furthermore, the formation of homogeneous replicates from a scarce amount of patient's cells is essential to compare the responses under various conditions (compound and concentration). Here, we present a microfluidic device for homogeneous spheroid formation in eight replicates in a perfused microenvironment. Spheroid replicates from either a cell line or primary cells from adenocarcinoma patients were successfully created. To further mimic the tumor microenvironment, spheroid co-culture of primary lung cancer epithelial cells and primary pericytes were tested. A higher chemoresistance in primary co-culture spheroids compared to primary monoculture spheroids was found when both were constantly perfused with cisplatin. This result is thought to be due to the barrier created by the pericytes around the tumor spheroids. Thus, this device can be used for additional chemosensitivity assays (e.g. sequential treatment) of patient material to further approach the personalized oncology field.

A generalisation of the fractional Brownian field based on non-Euclidean norms

We explore a generalisation of the L´evy fractional Brownian field on the Euclidean space based on replacing the Euclidean norm with another norm. A characterisation result for admissible norms yields a complete description of all self-similar Gaussian random fields with stationary increments. Several integral representations of the introduced random fields are derived. In a similar vein, several non-Euclidean variants of the fractional Poisson field are introduced and it is shown that they share the covariance structure with the fractional Brownian field and converge to it. The shape parameters of the Poisson and Brownian variants are related by convex geometry transforms, namely the radial pth mean body and the polar projection transforms.