488 research outputs found
Largest Lyapunov Exponent for Many Particle Systems at Low Densities
The largest Lyapunov exponent 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 , 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 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
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
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
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
Molecular mode-coupling theory for supercooled liquids: Application to water
We present mode-coupling equations for the description of the slow dynamics
observed in supercooled molecular liquids close to the glass transition. The
mode-coupling theory (MCT) originally formulated to study the slow relaxation
in simple atomic liquids, and then extended to the analysis of liquids composed
by linear molecules, is here generalized to systems of arbitrarily shaped,
rigid molecules. We compare the predictions of the theory for the -vector
dependence of the molecular nonergodicity parameters, calculated by solving
numerically the molecular MCT equations in two different approximation schemes,
with ``exact'' results calculated from a molecular dynamics simulation of
supercooled water. The agreement between theory and simulation data supports
the view that MCT succeeds in describing the dynamics of supercooled molecular
liquids, even for network forming ones.Comment: 22 pages 4 figures Late
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
Analysis of microstructural effects in multi layer lithium ion battery cathodes
A possible way to increase the energy density in lithium-ion batteries, and, at the same time, reduce the production costs, is to use thicker electrodes. However, transport limitations can occur in thick electrodes, leading to a drawback in performance. A way to mitigate this problem is a more sophisticated microstructure of the electrode, using, e.g., structural gradients. This can, for instance, be achieved by multi-layer casting, i.e., casting and drying of a first layer, and then adding a second layer. An important question is how the interface between the two layers is shaped and how the corresponding microstructure influences the electrochemical performance. In the present paper, two different two-layer cathodes are analyzed and compared to single-layer cathodes of the same thickness. The analysis involved tomographic imaging, a statistical analysis of the 3D microstructure of the active material particle systems with a focus on the interface between the layers, and electrochemical characterization of the active material systems using experimental measurements as well as electrochemical simulations. The analysis showed that at the interface the connectivity of active material particles decreases, which results in higher electric resistivity. This effect is stronger if an intermediate calendering step is performed, i.e., the first layer is calendered before casting the second layer
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
Frequency dependent specific heat of viscous silica
We apply the Mori-Zwanzig projection operator formalism to obtain an
expression for the frequency dependent specific heat c(z) of a liquid. By using
an exact transformation formula due to Lebowitz et al., we derive a relation
between c(z) and K(t), the autocorrelation function of temperature fluctuations
in the microcanonical ensemble. This connection thus allows to determine c(z)
from computer simulations in equilibrium, i.e. without an external
perturbation. By considering the generalization of K(t) to finite wave-vectors,
we derive an expression to determine the thermal conductivity \lambda from such
simulations. We present the results of extensive computer simulations in which
we use the derived relations to determine c(z) over eight decades in frequency,
as well as \lambda. The system investigated is a simple but realistic model for
amorphous silica. We find that at high frequencies the real part of c(z) has
the value of an ideal gas. c'(\omega) increases quickly at those frequencies
which correspond to the vibrational excitations of the system. At low
temperatures c'(\omega) shows a second step. The frequency at which this step
is observed is comparable to the one at which the \alpha-relaxation peak is
observed in the intermediate scattering function. Also the temperature
dependence of the location of this second step is the same as the one of the
peak, thus showing that these quantities are intimately connected to
each other. From c'(\omega) we estimate the temperature dependence of the
vibrational and configurational part of the specific heat. We find that the
static value of c(z) as well as \lambda are in good agreement with experimental
data.Comment: 27 pages of Latex, 8 figure
Simple deterministic dynamical systems with fractal diffusion coefficients
We analyze a simple model of deterministic diffusion. The model consists of a
one-dimensional periodic array of scatterers in which point particles move from
cell to cell as defined by a piecewise linear map. The microscopic chaotic
scattering process of the map can be changed by a control parameter. This
induces a parameter dependence for the macroscopic diffusion coefficient. We
calculate the diffusion coefficent and the largest eigenmodes of the system by
using Markov partitions and by solving the eigenvalue problems of respective
topological transition matrices. For different boundary conditions we find that
the largest eigenmodes of the map match to the ones of the simple
phenomenological diffusion equation. Our main result is that the difffusion
coefficient exhibits a fractal structure by varying the system parameter. To
understand the origin of this fractal structure, we give qualitative and
quantitative arguments. These arguments relate the sequence of oscillations in
the strength of the parameter-dependent diffusion coefficient to the
microscopic coupling of the single scatterers which changes by varying the
control parameter.Comment: 28 pages (revtex), 12 figures (postscript), submitted to Phys. Rev.
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