Generalized Boltzmann Equation for Lattice Gas Automata

In this paper, for the first time a theory is formulated that predicts velocity and spatial correlations between occupation numbers that occur in lattice gas automata violating semi-detailed balance. Starting from a coupled BBGKY hierarchy for the $n$-particle distribution functions, cluster expansion techniques are used to derive approximate kinetic equations. In zeroth approximation the standard nonlinear Boltzmann equation is obtained; the next approximation yields the ring kinetic equation, similar to that for hard sphere systems, describing the time evolution of pair correlations. As a quantitative test we calculate equal time correlation functions in equilibrium for two models that violate semi-detailed balance. One is a model of interacting random walkers on a line, the other one is a two-dimensional fluid type model on a triangular lattice. The numerical predictions agree very well with computer simulations.Comment: 31 pages LaTeX, 12 uuencoded tar-compressed Encapsulated PostScript figures (`psfig' macro), hardcopies available on request, 78kb + 52k

Renormalized kinetic theory of classical fluids in and out of equilibrium

We present a theory for the construction of renormalized kinetic equations to describe the dynamics of classical systems of particles in or out of equilibrium. A closed, self-consistent set of evolution equations is derived for the single-particle phase-space distribution function $f$, the correlation function $C=$, the retarded and advanced density response functions $\chi^{R,A}=\delta f/\delta\phi$ to an external potential $\phi$, and the associated memory functions $\Sigma^{R,A,C}$. The basis of the theory is an effective action functional $\Omega$ of external potentials $\phi$ that contains all information about the dynamical properties of the system. In particular, its functional derivatives generate successively the single-particle phase-space density $f$ and all the correlation and density response functions, which are coupled through an infinite hierarchy of evolution equations. Traditional renormalization techniques are then used to perform the closure of the hierarchy through memory functions. The latter satisfy functional equations that can be used to devise systematic approximations. The present formulation can be equally regarded as (i) a generalization to dynamical problems of the density functional theory of fluids in equilibrium and (ii) as the classical mechanical counterpart of the theory of non-equilibrium Green's functions in quantum field theory. It unifies and encompasses previous results for classical Hamiltonian systems with any initial conditions. For equilibrium states, the theory reduces to the equilibrium memory function approach. For non-equilibrium fluids, popular closures (e.g. Landau, Boltzmann, Lenard-Balescu) are simply recovered and we discuss the correspondence with the seminal approaches of Martin-Siggia-Rose and of Rose.and we discuss the correspondence with the seminal approaches of Martin-Siggia-Rose and of Rose.Comment: 63 pages, 10 figure

Correlations and Renormalization in Lattice Gases

A complete formulation is given of an exact kinetic theory for lattice gases. This kinetic theory makes possible the calculation of corrections to the usual Boltzmann / Chapman-Enskog analysis of lattice gases due to the buildup of correlations. It is shown that renormalized transport coefficients can be calculated perturbatively by summing terms in an infinite series. A diagrammatic notation for the terms in this series is given, in analogy with the diagrammatic expansions of continuum kinetic theory and quantum field theory. A closed-form expression for the coefficients associated with the vertices of these diagrams is given. This method is applied to several standard lattice gases, and the results are shown to correctly predict experimentally observed deviations from the Boltzmann analysis.Comment: 94 pages, pure LaTeX including all figure

Fluctuation theorem for currents and Schnakenberg network theory

A fluctuation theorem is proved for the macroscopic currents of a system in a nonequilibrium steady state, by using Schnakenberg network theory. The theorem can be applied, in particular, in reaction systems where the affinities or thermodynamic forces are defined globally in terms of the cycles of the graph associated with the stochastic process describing the time evolution.Comment: new version : 16 pages, 1 figure, to be published in Journal of Statistical Physic

Quaternionic Soliton Equations from Hamiltonian Curve Flows in HP^n

A bi-Hamiltonian hierarchy of quaternion soliton equations is derived from geometric non-stretching flows of curves in the quaternionic projective space $HP^n$. The derivation adapts the method and results in recent work by one of us on the Hamiltonian structure of non-stretching curve flows in Riemannian symmetric spaces $M=G/H$ by viewing $HP^n \simeq {\rm U}(n+1,H)/{\rm U}(1,H) \times {\rm U}(n,H)\simeq {\rm Sp}(n+1)/{\rm Sp}(1)\times {\rm Sp}(n)$ as a symmetric space in terms of compact real symplectic groups and quaternion unitary groups. As main results, scalar-vector (multi-component) versions of the sine-Gordon (SG) equation and the modified Korteveg-de Vries (mKdV) equation are obtained along with their bi-Hamiltonian integrability structure consisting of a shared hierarchy of quaternionic symmetries and conservation laws generated by a hereditary recursion operator. The corresponding geometric curve flows in $HP^n$ are shown to be described by a non-stretching wave map and a mKdV analog of a non-stretching Schrodinger map.Comment: 25 pages; typos correcte

Lattice Boltzmann simulations of soft matter systems

This article concerns numerical simulations of the dynamics of particles immersed in a continuum solvent. As prototypical systems, we consider colloidal dispersions of spherical particles and solutions of uncharged polymers. After a brief explanation of the concept of hydrodynamic interactions, we give a general overview over the various simulation methods that have been developed to cope with the resulting computational problems. We then focus on the approach we have developed, which couples a system of particles to a lattice Boltzmann model representing the solvent degrees of freedom. The standard D3Q19 lattice Boltzmann model is derived and explained in depth, followed by a detailed discussion of complementary methods for the coupling of solvent and solute. Colloidal dispersions are best described in terms of extended particles with appropriate boundary conditions at the surfaces, while particles with internal degrees of freedom are easier to simulate as an arrangement of mass points with frictional coupling to the solvent. In both cases, particular care has been taken to simulate thermal fluctuations in a consistent way. The usefulness of this methodology is illustrated by studies from our own research, where the dynamics of colloidal and polymeric systems has been investigated in both equilibrium and nonequilibrium situations.Comment: Review article, submitted to Advances in Polymer Science. 16 figures, 76 page

Peripheral chondrosarcoma progression is associated with increased type X collagen and vascularisation

Endochondral bone formation requires a cartilage template, known as the growth plate, and vascular invasion, bringing osteoblasts and osteoclasts. Endochondral chondrocytes undergo sequences of cell division, matrix secretion, cell hypertrophy, apoptosis, and matrix calcification/mineralisation. In this study, two critical steps of endochondral bone formation, the deposition of collagen X-rich matrix and blood vessel attraction/invasion, were investigated by immunohistochemistry. Fourteen multiple osteochondromas and six secondary peripheral chondrosarcomas occurring in patients with multiple osteochondromas were studied and compared to epiphyseal growth plate samples. Mutation analysis showed all studied patients (expect one) to harbour a germ-line mutations in either EXT1 or EXT2. Here, we described that homozygous mutations in EXT1/EXT2, which are causative for osteochondroma formation, are likely to affect terminal chondrocyte differentiation and vascularisation in the osteocartilaginous interface. Contrastingly, terminal chondrocyte differentiation and vascularisation seem to be unaffected in secondary peripheral chondrosarcoma. In addition, osteochondromas with high vascular density displayed a higher proliferation rate. A similar apoptotic rate was observed in osteochondromas and secondary peripheral chondrosarcomas. Recently, it has been shown that cells with functional EXT1 and EXT2 are outnumbering EXT1/EXT2 mutated cells in secondary peripheral chondrosarcomas. This might explain the increased type X collagen production and blood vessel attraction in these malignant tumours

The Clausius-Mossotti formula and its nonlocal generalization for a dielectric suspension of spherical inclusions

Employing a recently developed cluster expansion for the effective dielectric constant of a suspension of spherical inclusions, we show which parts of the cluster integrals give rise to the Clausius-Mossotti formula. The same selection of terms is then used to obtain an approximate expression for the wave-vector-dependent effective dielectric tensor. For a system of hard spheres with only dipole polarizability this expression is evaluated in closed form. This last result is then used to derive the form of the electrostatic potential due to a point charge in the effective medium. For physically reasonable values of the polarizability, the potential has asymptotically the form corresponding to a medium with the Clausius-Mossotti dielectric constant, while at short range it oscillates about this form. For values of the polarizability beyond the physical range critical points are found at which the oscillations become long range.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45147/1/10955_2005_Article_BF01009796.pd

Suppression of circulating IgD+CD27+ memory B cells in infants living in a malaria-endemic region of Kenya

Background: Plasmodium falciparum infection leads to alterations in B cell subset distribution. During infancy, development of peripheral B cell subsets is also occurring. However, it is unknown if infants living a malaria endemic region have alterations in B cell subsets that is independent of an age effect. Methods: To evaluate the impact of exposure to P. falciparum on B cell development in infants, flow cytometry was used to analyse the distribution and phenotypic characteristic of B cell subsets in infant cohorts prospectively followed at 12, 18 and 24 months from two geographically proximate regions in western Kenya with divergent malaria exposure i.e. Kisumu (malaria-endemic, n = 24) and Nandi (unstable malaria transmission, n = 21). Results: There was significantly higher frequency and absolute cell numbers of CD19+ B cells in Kisumu relative to Nandi at 12(p = 0.0440), 18(p = 0.0210) and 24 months (p = 0.0493). No differences were observed between the infants from the two sites in frequencies of naïve B cells (IgD+CD27-) or classical memory B cells (IgD-CD27+). However, immature transitional B cells (CD19+CD10+CD34-) were higher in Kisumu relative to Nandi at all three ages. In contrast, the levels of non-class switched memory B cells (CD19+IgD+CD27+) were significantly lower overall in Kisumu relative to Nandi at significantly at 12 (p = 0.0144), 18 (p = 0.0013) and 24 months (p = 0.0129). Conclusions: These data suggest that infants living in malaria endemic regions have altered B cell subset distribution. Further studies are needed to understand the functional significance of these changes and long-term impact on ability of these infants to develop antibody responses to P. falciparum and heterologous infections