Chaotic Properties of Dilute Two and Three Dimensional Random Lorentz Gases I: Equilibrium Systems

We compute the Lyapunov spectrum and the Kolmogorov-Sinai entropy for a moving particle placed in a dilute, random array of hard disk or hard sphere scatterers - i.e. the dilute Lorentz gas model. This is carried out in two ways: First we use simple kinetic theory arguments to compute the Lyapunov spectrum for both two and three dimensional systems. In order to provide a method that can easily be generalized to non-uniform systems we then use a method based upon extensions of the Lorentz-Boltzmann (LB) equation to include variables that characterize the chaotic behavior of the system. The extended LB equations depend upon the number of dimensions and on whether one is computing positive or negative Lyapunov exponents. In the latter case the extended LB equation is closely related to an "anti-Lorentz-Boltzmann equation" where the collision operator has the opposite sign from the ordinary LB equation. Finally we compare our results with computer simulations of Dellago and Posch and find very good agreement.Comment: 48 pages, 3 ps fig

Largest Lyapunov Exponent for Many Particle Systems at Low Densities

The largest Lyapunov exponent $\lambda^+$ for a dilute gas with short range interactions in equilibrium is studied by a mapping to a clock model, in which every particle carries a watch, with a discrete time that is advanced at collisions. This model has a propagating front solution with a speed that determines $\lambda^+$, for which we find a density dependence as predicted by Krylov, but with a larger prefactor. Simulations for the clock model and for hard sphere and hard disk systems confirm these results and are in excellent mutual agreement. They show a slow convergence of $\lambda^+$ with increasing particle number, in good agreement with a prediction by Brunet and Derrida.Comment: 4 pages, RevTeX, 2 Figures (encapsulated postscript). Submitted to Phys. Rev. Let

The Kolmogorov-Sinai Entropy for Dilute Gases in Equilibrium

We use the kinetic theory of gases to compute the Kolmogorov-Sinai entropy per particle for a dilute gas in equilibrium. For an equilibrium system, the KS entropy, h_KS is the sum of all of the positive Lyapunov exponents characterizing the chaotic behavior of the gas. We compute h_KS/N, where N is the number of particles in the gas. This quantity has a density expansion of the form h_KS/N = a\nu[-\ln{\tilde{n}} + b + O(\tilde{n})], where \nu is the single-particle collision frequency and \tilde{n} is the reduced number density of the gas. The theoretical values for the coefficients a and b are compared with the results of computer simulations, with excellent agreement for a, and less than satisfactory agreement for b. Possible reasons for this difference in b are discussed.Comment: 15 pages, 2 figures, submitted to Phys. Rev.

Chaotic Properties of Dilute Two and Three Dimensional Random Lorentz Gases II: Open Systems

We calculate the spectrum of Lyapunov exponents for a point particle moving in a random array of fixed hard disk or hard sphere scatterers, i.e. the disordered Lorentz gas, in a generic nonequilibrium situation. In a large system which is finite in at least some directions, and with absorbing boundary conditions, the moving particle escapes the system with probability one. However, there is a set of zero Lebesgue measure of initial phase points for the moving particle, such that escape never occurs. Typically, this set of points forms a fractal repeller, and the Lyapunov spectrum is calculated here for trajectories on this repeller. For this calculation, we need the solution of the recently introduced extended Boltzmann equation for the nonequilibrium distribution of the radius of curvature matrix and the solution of the standard Boltzmann equation. The escape-rate formalism then gives an explicit result for the Kolmogorov Sinai entropy on the repeller.Comment: submitted to Phys Rev

Novel approaches for the serodiagnosis of louse-borne relapsing fever

Louse-borne relapsing fever (LBRF) caused by B. recurrentis is a poverty-related and neglected infectious disease with an endemic focus in the Horn of Africa. Re-emergence of the disease occurred in Europe during the refugee crisis in 2015 and sporadic outbreaks were frequently reported in Eastern Africa where poor settings lack affordable diagnostics. Currently, there are no validated in vitro assays available for the serodiagnosis of LBRF. The aim of this study was to develop novel and reliable immunoassays by investigating clinically suspected and culture-confirmed serum samples from LBRF patients and a broad panel of serum samples from patients with other spirochetal, bacterial, and parasitic diseases. We identified two immunoreactive antigens (complement-inhibiting protein CihC and the glycerophosphodiester phosphodiesterase GlpQ of B. recurrentis) as the most promising target candidates leading to the evaluation of two immunoassays (line immunoblot and ELISA) for IgM and IgG. To optimize the IgM immunoassay, we conducted a bioinformatic approach to localize the relevant immunogenic regions within CihC. By utilizing a N-terminal CihC fragment, the sensitivity and specificity of both immunoassays (CihC and GlpQ) were high (IgM: sensitivity 100%, specificity of 89.9%, IgG: sensitivity 100%, specificity 99.2%). In conclusion, our findings indicate the diagnostic potential of CihC and GlpQ as valuable markers for the serodiagnosis of LBRF even at early time points of infection. Here, we provide strong evidence for the utilization of these immunoassays as reliable tools in clinical practice

Light scattering spectra of supercooled molecular liquids

The light scattering spectra of molecular liquids are derived within a generalized hydrodynamics. The wave vector and scattering angle dependences are given in the most general case and the change of the spectral features from liquid to solidlike is discussed without phenomenological model assumptions for (general) dielectric systems without long-ranged order. Exact microscopic expressions are derived for the frequency-dependent transport kernels, generalized thermodynamic derivatives and the background spectra.Comment: 12 page

CD36 coordinates NLRP3 inflammasome activation by facilitating the intracellular nucleation from soluble to particulate ligands in sterile inflammation

Particulate ligands including cholesterol crystals and amyloid fibrils induce NLRP3-dependent production of interleukin-1β (IL-1β) in atherosclerosis, Alzheimer's disease and diabetes. Soluble endogenous ligands including oxidized-LDL, amyloid-β and amylin peptides accumulate in these diseases. Here we identify a CD36-mediated endocytic pathway that coordinates the intracellular conversion of these soluble ligands to crystals or fibrils, resulting in lysosomal disruption and NLRP3-inflammasome activation. Consequently, macrophages lacking CD36 failed to elicit IL-1β production in response to these ligands and targeting CD36 in atherosclerotic mice reduced serum IL-1β and plaque cholesterol crystal accumulation. Collectively, these findings highlight the importance of CD36 in the accrual and nucleation of NLRP3 ligands from within the macrophage and position CD36 as a central regulator of inflammasome activation in sterile inflammation

Compartmentalization of Immune Response and Microbial Translocation in Decompensated Cirrhosis

Background: Acquired dysfunctional immunity in cirrhosis predisposes patients to frequent bacterial infections, especially spontaneous bacterial peritonitis (SBP), leading to systemic inflammation that is associated with poor outcome. But systemic inflammation can also be found in the absence of a confirmed infection. Detection of bacterial DNA has been investigated as a marker of SBP and as a predictor of prognosis. Data is, however, contradictory. Here we investigated whether levels of IL-6 and IL-8 putatively produced by myeloid cells in ascites are associated with systemic inflammation and whether inflammation depends on the presence of specific bacterial DNA.Methods and Materials: We enrolled 33 patients with decompensated liver cirrhosis from whom we collected paired samples of blood and ascites. IL-6 and IL-8 were measured in serum samples of all patients using ELISA. In a subset of 10 representative patients, bacterial DNA was extracted from ascites and whole blood, followed by 16S rRNA gene amplicon sequencing.Results: There were significantly higher levels of IL-6 in ascites fluid compared to blood samples in all patients. Interestingly, IL-6 levels in blood correlated tightly with disease severity and surrogates of systemic inflammation, while IL-6 levels in ascites did not. Moreover, patients with higher blood CRP levels showed greater SBP prevalence compared to patients with lower levels, despite similar positive culture results. Bacterial richness was also significantly higher in ascites compared to the corresponding patient blood. We identified differences in microbial composition and diversity between ascites and blood, but no tight relationship with surrogates of systemic inflammation could be observed.Discussion: In decompensated cirrhosis, markers of systemic inflammation and microbiota composition seem to be dysregulated in ascites and blood. While a relationship between systemic inflammation and microbiota composition seems to exist in blood, this is not the case for ascites in our hands. These data may suggest compartmentalization of the immune response and interaction of the latter with the microbiota especially in the blood compartment

Thermodynamic formalism for systems with Markov dynamics

The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function within the framework of discrete time Markov chains was not suitable for continuous time Markov dynamics. Here we propose another interpretation of the definition that allows us to apply the thermodynamic formalism to continuous time. We also generalize the formalism --a dynamical Gibbs ensemble construction-- to a whole family of observables and their associated large deviation functions. This allows us to make the connection between the thermodynamic formalism and the observable involved in the much-studied fluctuation theorem. We illustrate our approach on various physical systems: random walks, exclusion processes, an Ising model and the contact process. In the latter cases, we identify a signature of the occurrence of dynamical phase transitions. We show that this signature can already be unravelled using the simplest dynamical ensemble one could define, based on the number of configuration changes a system has undergone over an asymptotically large time window.Comment: 64 pages, LaTeX; version accepted for publication in Journal of Statistical Physic

Dynamical field theory for glass-forming liquids, self-consistent resummations and time-reversal symmetry

We analyse the symmetries and the self-consistent perturbative approaches of dynamical field theories for glassforming liquids. In particular, we focus on the time-reversal symmetry (TRS), which is crucial to obtain fluctuation-dissipation relations (FDRs). Previous field theoretical treatment violated this symmetry, whereas others pointed out that constructing symmetry preserving perturbation theories is a crucial and open issue. In this work we solve this problem and then apply our results to the mode-coupling theory of the glass transition (MCT). We show that in the context of dynamical field theories for glass-forming liquids TRS is expressed as a nonlinear field transformation that leaves the action invariant. Because of this nonlinearity, standard perturbation theories generically do not preserve TRS and in particular FDRs. We show how one can cure this problem and set up symmetry-preserving perturbation theories by introducing some auxiliary fields. As an outcome we obtain Schwinger-Dyson dynamical equations that automatically preserve FDRs and that serve as a basis for carrying out symmetry-preserving approximations. We apply our results to MCT, revisiting previous field theory derivations of MCT equations and showing that they generically violate FDR. We obtain symmetry-preserving mode-coupling equations and discuss their advantages and drawbacks. Furthermore, we show, contrary to previous works, that the structure of the dynamic equations is such that the ideal glass transition is not cut off at any finite order of perturbation theory, even in the presence of coupling between current and density. The opposite results found in previous field theoretical works, such as the ones based on nonlinear fluctuating hydrodynamics, were only due to an incorrect treatment of TRS.Comment: 54 pages, 21 figure