Enhancing e-Infrastructures with Advanced Technical Computing: Parallel MATLAB® on the Grid

MATLAB® is widely used within the engineering and scientific fields as the language and environment for technical computing, while collaborative Grid computing on e-Infrastructures is used by scientific communities to deliver a faster time to solution. MATLAB allows users to express parallelism in their applications, and then execute code on multiprocessor environments such as large-scale e-Infrastructures. This paper demonstrates the integration of MATLAB and Grid technology with a representative implementation that uses gLite middleware to run parallel programs. Experimental results highlight the increases in productivity and performance that users obtain with MATLAB parallel computing on Grids

A Continuum Description of Rarefied Gas Dynamics (I)--- Derivation From Kinetic Theory

We describe an asymptotic procedure for deriving continuum equations from the kinetic theory of a simple gas. As in the works of Hilbert, of Chapman and of Enskog, we expand in the mean flight time of the constituent particles of the gas, but we do not adopt the Chapman-Enskog device of simplifying the formulae at each order by using results from previous orders. In this way, we are able to derive a new set of fluid dynamical equations from kinetic theory, as we illustrate here for the relaxation model for monatomic gases. We obtain a stress tensor that contains a dynamical pressure term (or bulk viscosity) that is process-dependent and our heat current depends on the gradients of both temperature and density. On account of these features, the equations apply to a greater range of Knudsen number (the ratio of mean free path to macroscopic scale) than do the Navier-Stokes equations, as we see in the accompanying paper. In the limit of vanishing Knudsen number, our equations reduce to the usual Navier-Stokes equations with no bulk viscosity.Comment: 16 page

Boltzmann equation and hydrodynamic fluctuations

We apply the method of invariant manifolds to derive equations of generalized hydrodynamics from the linearized Boltzmann equation and determine exact transport coefficients, obeying Green-Kubo formulas. Numerical calculations are performed in the special case of Maxwell molecules. We investigate, through the comparison with experimental data and former approaches, the spectrum of density fluctuations and address the regime of finite Knudsen numbers and finite frequencies hydrodynamics.Comment: This is a more detailed version of a related paper: I.V. Karlin, M. Colangeli, M. Kroger, PRL 100 (2008) 214503, arXiv:0801.2932. It contains comparison between predictions and experiment, in particular. 11 pages, 6 figures, 2 table

Closedness type regularity conditions for surjectivity results involving the sum of two maximal monotone operators

In this note we provide regularity conditions of closedness type which guarantee some surjectivity results concerning the sum of two maximal monotone operators by using representative functions. The first regularity condition we give guarantees the surjectivity of the monotone operator $S(\cdot + p)+T(\cdot)$, where $p\in X$ and $S$ and $T$ are maximal monotone operators on the reflexive Banach space $X$. Then, this is used to obtain sufficient conditions for the surjectivity of $S+T$ and for the situation when $0$ belongs to the range of $S+T$. Several special cases are discussed, some of them delivering interesting byproducts.Comment: 11 pages, no figure

Enhanced chondrogenic phenotype of primary bovine articular chondrocytes in Fibrin-Hyaluronan hydrogel by multi-axial mechanical loading and FGF18

Current treatments for cartilage lesions are often associated with fibrocartilage formation and donor site morbidity. Mechanical and biochemical stimuli play an important role in hyaline cartilage formation. Biocompatible scaffolds capable of transducing mechanical loads and delivering bioactive instructive factors may better support cartilage regeneration. In this study we aimed to test the interplay between mechanical and FGF-18 mediated biochemical signals on the proliferation and differentiation of primary bovine articular chondrocytes embedded in a chondro-conductive Fibrin-Hyaluronan (FB/HA) based hydrogel. Chondrocytes seeded in a Fibrin-HA hydrogel, with or without a chondro-inductive, FGFR3 selective FGF18 variant (FGF-18v) were loaded into a joint-mimicking bioreactor applying controlled, multi-axial movements, simulating the natural movements of articular joints. Samples were evaluated for DNA content, sulphated glycosaminoglycan (sGAG) accumulation, key chondrogenic gene expression markers and histology. Under moderate loading, samples produced particularly significant amounts of sGAG/DNA compared to unloaded controls. Interestingly there was no significant effect of FGF-18v on cartilage gene expression at rest. Following moderate multi-axial loading, FGF-18v upregulated the expression of Aggrecan (ACAN), Cartilage Oligomeric Matrix Protein (COMP), type II collagen (COL2) and Lubricin (PRG4). Moreover, the combination of load and FGF-18v, significantly downregulated Matrix Metalloproteinase-9 (MMP-9) and Matrix Metaloproteinase-13 (MMP-13), two of the most important factors contributing to joint destruction in OA. Biomimetic mechanical signals and FGF-18 may work in concert to support hyaline cartilage regeneration and repair. Statement of significance: Articular cartilage has very limited repair potential and focal cartilage lesions constitute a challenge for current standard clinical procedures. The aim of the present research was to explore novel procedures and constructs, based on biomaterials and biomechanical algorithms that can better mimic joints mechanical and biochemical stimulation to promote regeneration of damaged cartilage. Using a hydrogel-based platform for chondrocyte 3D culture revealed a synergy between mechanical forces and growth factors. Exploring the mechanisms underlying this mechano-biochemical interplay may enhance our understanding of cartilage remodeling and the development of new strategies for cartilage repair and regeneration

Hydrodynamic modes, Green-Kubo relations, and velocity correlations in dilute granular gases

It is shown that the hydrodynamic modes of a dilute granular gas of inelastic hard spheres can be identified, and calculated in the long wavelength limit. Assuming they dominate at long times, formal expressions for the Navier-Stokes transport coefficients are derived. They can be expressed in a form that generalizes the Green-Kubo relations for molecular systems, and it is shown that they can also be evaluated by means of $N$-particle simulation methods. The form of the hydrodynamic modes to zeroth order in the gradients is used to detect the presence of inherent velocity correlations in the homogeneous cooling state, even in the low density limit. They manifest themselves in the fluctuations of the total energy of the system. The theoretical predictions are shown to be in agreement with molecular dynamics simulations. Relevant related questions deserving further attention are pointed out

Some thoughts about nonequilibrium temperature

The main objective of this paper is to show that, within the present framework of the kinetic theoretical approach to irreversible thermodynamics, there is no evidence that provides a basis to modify the ordinary Fourier equation relating the heat flux in a non-equilibrium steady state to the gradient of the local equilibrium temperature. This fact is supported, among other arguments, through the kinetic foundations of generalized hydrodynamics. Some attempts have been recently proposed asserting that, in the presence of non-linearities of the state variables, such a temperature should be replaced by the non-equilibrium temperature as defined in Extended Irreversible Thermodynamics. In the approximations used for such a temperature there is so far no evidence that sustains this proposal.Comment: 13 pages, TeX, no figures, to appear in Mol. Phy

Derivation of fluid dynamics from kinetic theory with the 14--moment approximation

We review the traditional derivation of the fluid-dynamical equations from kinetic theory according to Israel and Stewart. We show that their procedure to close the fluid-dynamical equations of motion is not unique. Their approach contains two approximations, the first being the so-called 14-moment approximation to truncate the single-particle distribution function. The second consists in the choice of equations of motion for the dissipative currents. Israel and Stewart used the second moment of the Boltzmann equation, but this is not the only possible choice. In fact, there are infinitely many moments of the Boltzmann equation which can serve as equations of motion for the dissipative currents. All resulting equations of motion have the same form, but the transport coefficients are different in each case.Comment: 15 pages, 3 figures, typos fixed and discussions added; EPJA: Topical issue on "Relativistic Hydro- and Thermodynamics