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Alex Hansen

Publications and source records attributed to Alex Hansen.

At least 109 records · Page 6Linked to original sources
arXiv2006

Crossover behavior in failure avalanches

Composite materials, with statistically distributed threshold for breakdown of individual elements, are considered. During the failure process of such materials under external stress (load or voltage), avalanches consisting of simultaneous rupture of several elements occur, with a distribution $D(Δ)$ of the magnitude $Δ$ of such avalanches. The distribution is typically a power law $D(Δ)\proptoΔ^{-ξ}$. For the systems we study here, a crossover behavior is seen between two power laws, with a small exponent $ξ$ in the vicinity of complete breakdown and a larger exponent $ξ$ for failures away from the breakdown point. We demonstrate this analytically for bundles of many fibers where the load is uniformly distributed among the surviving fibers. In this case $ξ=3/2$ near the breakdown point and $ξ=5/2$ away from it. The latter is known to be the generic behavior. This crossover is a signal of imminent catastrophic failure of the material. Near the breakdown point, avalanche statistics show nontrivial finite size scaling. We observe similar crossover behavior in a network of electric fuses, and find $ξ=2$ near the catastrophic failure and $ξ=3$ away from it. For this fuse model power dissipation avalanches show a similar crossover near breakdown.

cond-mat.soft↗
arXiv2006

Cluster evolution in steady-state two-phase flow in porous media

We report numerical studies of the cluster development of two-phase flow in a steady-state environment of porous media. This is done by including biperiodic boundary conditions in a two-dimensional flow simulator. Initial transients of wetting and non-wetting phases that evolve before steady-state has occurred, undergo a cross-over where every initial patterns are broken up. For flow dominated by capillary effects with capillary numbers in order of $10^{-5}$, we find that around a critical saturation of non-wetting fluid the non-wetting clusters of size $s$ have a power-law distribution $n_s \sim s^{-τ}$ with the exponent $τ= 1.92 \pm 0.04$ for large clusters. This is a lower value than the result for ordinary percolation. We also present scaling relation and time evolution of the structure and global pressure.

cond-mat.dis-nn↗
arXiv2005

Mean Field Theory of Localization in the Fuse Model

We propose a mean field theory for the localization of damage in a quasistatic fuse model on a cylinder. Depending on the quenched disorder distribution of the fuse thresholds, we show analytically that the system can either stay in a percolation regime up to breakdown, or start at some current level to localize starting from the smallest scale (lattice spacing), or instead go to a diffuse localization regime where damage starts to concentrate in bands of width scaling as the width of the system, but remains diffuse at smaller scales. Depending on the nature of the quenched disorder on the fuse thresholds, we derive analytically the phase diagram of the system separating these regimes and the current levels for the onset of these possible localizations. We compare these predictions to numerical results.

cond-mat.stat-mech↗
arXiv2005

Networks between Professionals and Society: A Model for Protein Dependency

We propose a network model with a fixed number of nodes and links with a dynamics which favors links between nodes differing in connectivity. Parameter regimes where the degree distributions follow power-laws, P(k) ~ k^-gamma, high clustering following C(N) ~ 1/N and small-world properties, with a network diameter following D(N) ~ A+ B log N, are observed. Our model gives results comparable with real-world protein networks.

physics.soc-ph↗
arXiv2005

Fracture Roughness and Correlation Length in the Central Force Model

We measure the roughness exponent and the correlation length exponent of a stress-weighted percolation process in the central force model in 2D. The roughness exponent is found to be zeta = 0.75 \pm 0.03 and the correlation length exponent is found to be nu = 1.7 \pm 0.3. This result supports a conjecture that the fracture roughness for large scales is controlled by a stress weighted percolation process, and the fracture roughness can by calculated from the correlation length exponent by zeta = 2*nu/(1+2*nu). We also compare global and local measurements of the fracture roughness and do not find sign of anomalous scaling in the central force model.

cond-mat.stat-mech↗
arXiv2005

Stochastic Model for the Interaction of Buckling and Fracture in Thin Tension-Loaded Sheets

We introduce a model of fracture which includes the out-of-plane degrees of freedom necessary to describe buckling in a thin-sheet material. The model is a regular square lattice of elastic beams, rigidly connected at the nodes so as to preserve rotational invariance. Fracture is initiated by displacement control, applying a uniaxial force couple at the top and bottom rows of the lattice in mode-I type loading. The approach lends itself naturally to the inclusion of disorder and enables a wide variety of fracture behaviours to be studied, ranging from systems with a simple geometrical discontinuity to more complex crack geometries and random cracking. Breakdown can be initiated from a pre-cracked sheet or from an intact sheet where the first damage appears at random, and buckling sets in when a displacement vector containing out-of-place components becomes energetically favourable over one which does not. In this paper we only consider center-cracked sheets with no disorder and include some results relevant to the force- and displacement-fields, and the buckling response ratio. Rather than carry out a comprehensive study of such systems, the emphasis presently is on the development of the model itself.

cond-mat.soft↗
arXiv2005

Effects of Buckling on Stress and Strain in Thin Randomly Disordered Tension-Loaded Sheets

We study how crack buckling affects stress and strain in a thin sheet with random disorder. The sheet is modeled as an elastic lattice of beams where each of the beams have individual thresholds for breaking. A statistical distribution with an exponential tail towards either weak or strong beams is used to generate the thresholds and the magnitude of the disorder can be varied arbitrarily between zero and infinity. Applying a uniaxial force couple along the top and bottom rows of the lattice, fracture proceeds according to where the ratio of the stress field to the local strength is most intense. Since breakdown is initiated from an intact sheet where the first crack appears at random, the onset and mode of buckling varies according to where and how the cracks grow. For a wide range of disorders the stress-strain relationships for buckling sheets are compared with those for non-buckling sheets. The ratio of the buckling to the non-buckling value of the maximum external force the system can tolerate before breaking is found to decrease with increasing disorder, as is the ratio for the corresponding displacement.

cond-mat.soft↗
arXiv2005

Scaling Laws of Stress and Strain in Brittle Fracture

A numerical realization of an elastic beam lattice is used to obtain scaling exponents relevant to the extent of damage within the controlled, catastrophic and total regimes of mode-I brittle fracture. The relative fraction of damage at the onset of catastrophic rupture approaches a fixed value in the continuum limit. This enables disorder in a real material to be quantified through its relationship with random samples generated on the computer.

cond-mat.soft↗
arXiv2005

Brittle Crack Roughness in Three-Dimensional Beam Lattices

The roughness exponent is reported in numerical simulations with a three-dimensional elastic beam lattice. Two different types of disorder have been used to generate the breaking thresholds, i.e., distributions with a tail towards either strong or weak beams. Beyond the weak disorder regime a universal exponent of 0.59(1) is obtained. This is within the range 0.4-0.6 reported experimentally for small scale quasi-static fracture, as would be expected for media with a characteristic length scale.

cond-mat.soft↗
arXiv2005

Failure properties of loaded fiber bundles having a lower cutoff in fiber threshold distribution

Presence of lower cutoff in fiber threshold distribution may affect the failure properties of a bundle of fibers subjected to external load. We investigate this possibility both in a equal load sharing (ELS) fiber bundle model and in local load sharing (LLS) one. We show analytically that in ELS model, the critical strength gets modified due to the presence of lower cutoff and it becomes bounded by an upper limit. Although the dynamic exponents for the susceptibility and relaxation time remain unchanged, the avalanche size distribution shows a permanent deviation from the mean-fiels power law. In the LLS model, we analytically estimate the upper limit of the lower cutoff above which the bundle fails at one instant. Also the system size variation of bundle's strength and the avalanche statistics show strong dependence on the lower cutoff level.

cond-mat.stat-mech↗
arXiv2005

Superdiffusive Conduction: AC Conductivity with Correlated Noise

We present evidence of the existence of a superdiffusive regime in systems with correlated disorder for which localization is suppressed. An expression for anomalous electrical conductivity at low frequencies is found by using a generalized Langevin equation whose memory function accounts for the interactions between the carriers. New mechanisms inducing a superdiffusive conductivity are discussed and experimental possibilities for observing that phenomenon in nanotubes and superlattices are presented.

cond-mat.stat-mech↗
arXiv2005

Crossover Behavior in Burst Avalanches of Fiber Bundles: Signature of Imminent Failure

Bundles of many fibers, with statistically distributed thresholds for breakdown of individual fibers and where the load carried by a bursting fiber is equally distributed among the surviving members, are considered. During the breakdown process, avalanches consisting of simultaneous rupture of several fibers occur, with a distribution D(Delta) of the magnitude Delta of such avalanches. We show that there is, for certain threshold distributions, a crossover behavior of D(Delta) between two power laws D(Delta) proportional to Delta^(-xi), with xi=3/2 or xi=5/2. The latter is known to be the generic behavior, and we give the condition for which the D(Delta) proportional to Delta^(-3/2) behavior is seen. This crossover is a signal of imminent catastrophic failure in the fiber bundle. We find the same crossover behavior in the fuse model.

cond-mat.dis-nn↗
arXiv2004

Crossover behavior in a mixed mode fiber bundle model

We introduce a mixed-mode load sharing scheme in fiber bundle model. This model reduces exactly to equal load sharing (ELS) and local load sharing (LLS) models at the two extreme conditions of the load sharing rule. We identify two distinct regimes: a) Mean-field regime where ELS mode dominates and b) short range regime dominated by LLS mode. The crossover behavior is explored through the numerical study of strength variation, the avalanche statistics, susceptibility and relaxation time variations, the correlations among the broken fibers and their cluster analysis. Analyzing the moments of the cluster size distributions we locate the crossover point of these regimes. We thus conclude that even in one dimension, fiber bundle model shows crossover behavior from mean-field to short range interactions.

cond-mat.stat-mech↗
arXiv2004

Phase Diagram of Optimal Paths

We show that choosing appropriate distributions of the randomness, the search for optimal paths links diverse problems of disordered media like directed percolation, invasion percolation, directed and non-directed spanning polymers. We also introduce a simple and efficient algorithm, which solves the d-dimensional model numerically in order N^(1+d_f/d) steps where d_f is the fractal dimension of the path. Using extensive simulations in two dimensions we identify the phase boundaries of the directed polymer universality class. A new strong-disorder phase occurs where the optimum paths are self-affine with parameter-dependent scaling exponents. Furthermore, the phase diagram contains directed and non-directed percolation as well as the directed random walk models at specific points and lines.

cond-mat.stat-mech↗
arXiv2003

Correlation Length Exponent in the Three-Dimensional Fuse Network

We present numerical measurements of the critical correlation length exponent nu in the three-dimensional fuse model. Using sufficiently broad threshold distributions to ensure that the system is the strong-disorder regime, we determine nu to be nu = 0.86 +/- 0.06 based on analyzing the fluctuations of the survival probability. The value we find for nu is very close to the percolation value 0.88 and we propose that the three-dimensional fuse model is in the universality class of ordinary percolation.

cond-mat.stat-mech↗
arXiv2003

Two-phase flow in porous media: dynamical phase transition

Two-phase flow systems in porous media have complex dynamics. It is well established that a wide range of system parameters like viscosities and porosity as well as flow parameters such as pressure gradient and fluid saturation have strong impact on the dynamics. The transition from single-phase flow to two-phase flow is a dynamical phase transition. We discuss the order of the transition and investigate the phase diagram in parameter space, using a network simulator for two-phase flow. A semi-empirical theory for the location of the phase boundaries is provided.

cond-mat↗
arXiv2002

Roughness of Interfacial Crack Front: Correlated Percolation in the Damage Zone

We show that the roughness exponent zeta of an in-plane crack front slowly propagating along a heterogeneous interface embeded in a elastic body, is in full agreement with a correlated percolation problem in a linear gradient. We obtain zeta=nu/(1+nu) where nu is the correlation length critical exponent. We develop an elastic brittle model based on both the 3D Green function in an elastic half-space and a discrete interface of brittle fibers and find numerically that nu=1.5, We conjecture it to be 3/2. This yields zeta=3/5. We also obtain by direct numerical simulations zeta=0.6 in excellent agreement with our prediction. This modelling is for the first time in close agreement with experimental observations.

cond-mat↗