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Biomedical subjects

Alex Hansen

Publications and source records attributed to Alex Hansen.

18 recordsLinked to original sources
PubMed2006

Analytical approach to continuous and intermittent bottleneck flows.

We propose a many-particle-inspired theory for granular outflows from a hopper and for the escape dynamics through a bottleneck based on a continuity equation in polar coordinates. If the inflow is below the maximum outflow, we find an asymptotic stationary solution. If the inflow is above this value, we observe queue formation, which can be described by a shock wave equation. We also address the experimental observation of intermittent outflows, taking into account the lack of space in the merging zone by a minimum function and coordination problems by a stochastic variable. This results in avalanches of different sizes even if friction, force networks, inelastic collapse, or delay-induced stop-and-go waves are not assumed. Our intermittent flows result from a random alternation between particle propagation and gap propagation. Erratic flows in congested merging zones of vehicle traffic may be explained in a similar way.

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PubMed2006

Crossover behavior in failure avalanches.

Composite materials, with statistically distributed thresholds 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(Delta) of the magnitude Delta of such avalanches. The distribution is typically a power law D(Delta) proportional to Delta (-xi). For the systems we study here, a crossover behavior is seen between two power laws, with a small exponent xi in the vicinity of complete breakdown and a larger exponent xi 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 xi=3/2 near the breakdown point and xi=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 xi=2 near the catastrophic failure and xi=3 away from it. For this fuse model power dissipation avalanches show a similar crossover near breakdown.

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PubMed2006

Mean-field theory of localization in a 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 imposed current, 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.

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PubMed2006

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 nonwetting phases that evolve before steady state has occurred, undergo a crossover where every initial pattern is broken up. For flow dominated by capillary effects with capillary numbers in order of 10(-5), we find that around a critical saturation of nonwetting fluid the nonwetting clusters of size have a power-law distribution ns similar to s(-tau)with the exponent tau=1.92+/-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.

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PubMed2005

Crossover behavior in burst avalanches: signature of imminent failure.

The statistics of damage avalanches during a failure process typically follows a power law. When these avalanches are recorded only near the point at which the system fails catastrophically, one finds that the power law has an exponent which is different from that one finds if the recording of events starts away from the vicinity of catastrophic failure. We demonstrate this analytically for bundles of many fibers, with statistically distributed breakdown thresholds for the individual fibers and where the load is uniformly distributed among the surviving fibers. In this case the distribution D(Delta) of the avalanches (Delta) follows the power law Delta-xi with xi=3/2 near catastrophic failure and xi=5/2 away from it. We also study numerically square networks of electrical fuses and find xi=2.0 near catastrophic failure and xi=3.0 away from it. We propose that this crossover in xi may be used as a signal of imminent failure.

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PubMed2005

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

The 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 an equal load sharing (ELS) model and in a local load sharing (LLS) one using analytic as well as numerical methods. In the ELS model, the critical strength gets modified and, beyond a certain lower cutoff level, the whole bundle fails instantly (brittle failure) after the first fiber ruptures. Although the dynamic exponents for the order parameter, susceptibility, and relaxation time remain unchanged, the avalanche size distribution shows a gradual deviation from the mean field power law. A similar "instant failure" situation occurs in the LLS model at a lower cutoff level, which reduces to that of the equivalent ELS model at higher (high enough) dimensions. Also, the system size variation of the bundle's strength and the avalanche statistics show strong dependence on the lower cutoff level.

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PubMed2005

Crossover behavior in a mixed-mode fiber bundle model.

We introduce a mixed-mode load sharing scheme in a fiber bundle model. This model reduces exactly to equal-load-sharing (ELS) and local-load-sharing (LLS) models at the two extreme limits of a single-load-sharing parameter. We identify two distinct regimes: (a) the mean-field regime where the ELS mode dominates and (b) the short-range regime dominated by the LLS mode. The crossover behavior is explored through a numerical study of the 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, the fiber bundle model shows crossover behavior from mean-field to short-range interactions.

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PubMed2004

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=0.83+/-0.04 based on analyzing the fluctuations of the survival probability. This value is different from that of ordinary percolation, which is 0.88.

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PubMed2004

Phase diagram of optimal paths.

We show that by choosing appropriate distributions of the randomness the search for optimal paths links diverse problems of disordered media, such as directed percolation, invasion percolation, and directed and nondirected spanning polymers. We also introduce a simple and efficient algorithm, which solves the d-dimensional model numerically in O(N(1+df/d)) steps, where df 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 nondirected percolation as well as the directed random walk models at specific points and lines.

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PubMed2004

Self-affine crossover length in a layered silicate deposit.

Self-affine dehydrated colloidal deposits on fresh mica surfaces of the synthetic layered silicate 2:1 smectite clay laponite have been studied by means of atomic force microscopy (AFM). AFM images of these prepared assemblies of sol and gel aggregates have been analyzed both by means of standard AFM Fourier software and a wavelet method. The deposited surfaces show a persistence to antipersistent crossover with a clay concentration dependent crossover length. It is concluded that the crossover length is associated with aggregate size, and further that the persistent roughness at small length scales signals near compact clusters of fractal dimension three, whereas the antipersistent roughness at large length scales signals a sedimentation process.

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PubMed2003

Origin of the universal roughness exponent of brittle fracture surfaces:stress-weighted percolation in the damage zone.

We suggest that the observed large-scale universal roughness of brittle fracture surfaces is due to the fracture propagation being a damage coalescence process described by a stress-weighted percolation phenomenon in a self-generated quadratic damage gradient. We use the quasistatic 2D fuse model as a paradigm of a mode I fracture model. We measure for this model, which exhibits a correlated percolation process, the correlation length exponent nu approximately 1.35 and conjecture it to be equal to that of classical percolation, 4/3. We then show that the roughness exponent in the 2D fuse model is zeta=2nu/(1+2nu)=8/11. This is in accordance with the numerical value zeta=0.75. Using the value for 3D percolation, nu=0.88, we predict the roughness exponent in the 3D fuse model to be zeta=0.64, in close agreement with the previously published value of 0.62+/-0.05. We furthermore predict zeta=4/5 for 3D brittle fractures, based on a recent calculation giving nu=2. This is in full accordance with the value zeta=0.80 found experimentally.

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PubMed2003

Roughness of interfacial crack fronts: stress-weighted percolation in the damage zone.

We study numerically the roughness exponent zeta of an in-plane fracture front slowly propagating along a heterogeneous interface embedded in an elastic body, using a model based on the evolution of a process zone rather than a fracture line. We find zeta=0.60+/-0.05. For the first time, simulation results are in close agreement with experimental results. We then show that the roughness exponent is related to the correlation length exponent nu of a stress-weighted percolation problem through zeta=nu/(1+nu). A numerical study of the stress-weighted percolation problem yields nu=1.54 giving zeta=0.61 in close agreement with our numerical results and with experimental observations.

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PubMed2002

Relation between pressure and fractional flow in two-phase flow in porous media.

We study average flow properties in porous media using a two-dimensional network simulator. It models the dynamics of two-phase immiscible bulk flow where film flow can be neglected. The boundary conditions are biperiodic, which provide a means of studying steady-state flow where complex bubble dynamics dominate the flow picture. We find fractional flow curves and corresponding pressure curves for different capillary numbers. In particular, we study the case of the two phases having equal viscosity. In this case we find that the derivative of the fractional flow with respect to saturation is related to the global pressure drop. This result can also be expressed in terms of relative permeabilities or mobilities, resulting in an equation tying together the mobilities of the two phases.

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PubMed2002

Fast algorithm for generating long self-affine profiles.

We introduce a fast algorithm for generating long self-affine profiles. The algorithm, which is based on the fast wavelet transform, is faster than the conventional Fourier filtering algorithm. In addition to increased performance for large systems, the algorithm, named the wavelet filtering algorithm, a priori gives rise to profiles for which the long-range correlation extends throughout the entire system independently of the length scale.

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PubMed2002

Heterogeneous interfacial failure between two elastic blocks.

We investigate numerically the failure process when two elastic media, one hard and one soft that have been glued together thus forming a common interface, are pulled apart. We present three main results: (1) The area distribution of simultaneously failing glue (bursts) follows a power law consistent with the theoretically expected exponent 2.5, (2) the maximum load and displacement before catastrophic failure scale as L(2) and L(0), respectively, where L is the linear size of the system, and (3) the area distribution of failed glue regions (clusters) is a power law with exponent -1.6 when the system fails catastrophically.

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PubMed2002

Apolar and polar solvation thermodynamics related to the protein unfolding process.

Thermodynamics related to hydrated water upon protein unfolding is studied over a broad temperature range (5-125 degrees C). The hydration effect arising from the apolar interior is modeled as an increased number of hydrogen bonds between water molecules compared with bulk water. The corresponding contribution from the polar interior is modeled as a two-step process. First, the polar interior breaks hydrogen bonds in bulk water upon unfolding. Second, due to strong bonds between the polar surface and the nearest water molecules, we assume quantization using a simplified two-state picture. The heat capacity change upon hydration is compared with model compound data evaluated previously for 20 different proteins. We obtain good correspondence with the data for both the apolar and the polar interior. We note that the effective coupling constants for both models have small variations among the proteins we have investigated.

Biophysical Phenomena↗