Biomedical subjects

Werner Krauth

Publications and source records attributed to Werner Krauth.

7 recordsLinked to original sources

PubMed2006

Dynamics below the depinning threshold in disordered elastic systems.

We study the steady-state low-temperature dynamics of an elastic line in a disordered medium below the depinning threshold. Analogously to the equilibrium dynamics, in the limit T-->0, the steady state is dominated by a single configuration which is occupied with probability 1. We develop an exact algorithm to target this dominant configuration and to analyze its geometrical properties as a function of the driving force. The roughness exponent of the line at large scales is identical to the one at depinning. No length scale diverges in the steady-state regime as the depinning threshold is approached from below. We do find a divergent length, but it is associated only with the transient relaxation between metastable states.

Journal Article↗

PubMed2005

Critical exponents of the driven elastic string in a disordered medium.

We analyze the harmonic elastic string driven through a continuous random potential above the depinning threshold. The velocity exponent beta = 0.33(2) is calculated. We observe a crossover in the roughness exponent zeta from the critical value 1.26 to the asymptotic (large force) value of 0.5. We calculate directly the velocity correlation function and the corresponding correlation length exponent nu = 1.29(5), which obeys the scaling relation nu = 1/(2 - zeta), and agrees with nu(FS), the finite-size-scaling exponent of fluctuations in the critical force. Surprisingly, the velocity correlation function is nonuniversal at short distances.

Journal Article↗

PubMed2004

Width distribution of contact lines on a disordered substrate.

We have studied the roughness of a contact line on a disordered substrate by measuring its width distribution, which characterizes the roughness completely. The measured distribution is in excellent agreement with the distribution calculated in previous works, extended here to the case of open boundary conditions. This type of analysis, which is performed here on experimental data, provides a strong confirmation that the Joanny-de Gennes model is not sufficient to describe the dynamics of the contact line at the depinning threshold.

Journal Article↗

PubMed2003

Coulomb and liquid dimer models in three dimensions.

We study classical hard-core dimer models on three-dimensional lattices using analytical approaches and Monte Carlo simulations. On the bipartite cubic lattice, a local gauge field generalization of the height representation used on the square lattice predicts that the dimers are in a critical Coulomb phase with algebraic, dipolar correlations, in excellent agreement with our large-scale Monte Carlo simulations. The nonbipartite fcc and Fisher lattices lack such a representation, and we find that these models have both confined and exponentially deconfined but no critical phases. We conjecture that extended critical phases are realized only on bipartite lattices, even in higher dimensions.

Journal Article↗

PubMed2003

Universal interface width distributions at the depinning threshold.

We compute the probability distribution of the interface width at the depinning threshold, using recent powerful algorithms. It confirms the universality classes found previously. In all cases, the distribution is surprisingly well approximated by a generalized Gaussian theory of independent modes which decay with a characteristic propagator G(q)=1/q(d+2zeta); zeta, the roughness exponent, is computed independently. A functional renormalization analysis explains this result and allows one to compute the small deviations, i.e., a universal kurtosis ratio, in agreement with numerics. We stress the importance of the Gaussian theory to interpret numerical data and experiments.

Journal Article↗

PubMed2003

Depinning of elastic manifolds.

We compute roughness exponents of elastic d-dimensional manifolds in (d+1)-dimensional embedding spaces at the depinning transition for d=1, em leader,4. Our numerical method is rigorously based on a Hamiltonian formulation; it allows us to determine the critical manifold in finite samples for an arbitrary convex elastic energy. For a harmonic elastic energy (Delta(2) model), we find values of the roughness exponent between the one-loop and two-loop functional renormalization group results, in good agreement with earlier cellular automaton simulations. We find that the Delta(2) model is unstable with respect both to slight stiffening and to weakening of the elastic potential. Anharmonic corrections to the elastic energy allow us to obtain the critical exponents of the quenched Kardar, Parisi, Zhang class.

Journal Article↗

PubMed2002

Roughness at the depinning threshold for a long-range elastic string.

In this paper, we compute to high precision the roughness exponent zeta of a long-range elastic string, at the depinning threshold, in a random medium. Our numerical method exploits the analytic structure of the problem ("no-passing" theorem), but avoids direct simulation of the evolution equations. The roughness exponent has recently been studied by simulations, functional renormalization-group calculations, and by experiments (fracture of solids, liquid meniscus in 4He). Our result zeta=0.388 +/- 0.002 is significantly larger than what was stated in previous simulations, which were consistent with a one-loop renormalization-group calculation. Furthermore, the data are incompatible with the experimental results for crack propagation in solids and for a 4He contact line on a rough substrate. This implies that the experiments cannot be described by pure harmonic long-range elasticity in the quasistatic limit.

Journal Article↗