arXiv subjects

E. A. Jagla

Publications and source records attributed to E. A. Jagla.

At least 55 records · Page 3Linked to original sources

arXiv2009

The mechanisms of spatial and temporal earthquake clustering

The number of earthquakes as a function of magnitude decays as a power law. This trend is usually justified using spring-block models, where slips with the appropriate global statistics have been numerically observed. However, prominent spatial and temporal clustering features of earthquakes are not reproduced by this kind of modeling. We show that when a spring-block model is complemented with a mechanism allowing for structural relaxation, realistic earthquake patterns are obtained. The proposed model does not need to include a phenomenological velocity weakening friction law, as traditional spring-block models do, since this behavior is effectively induced by the relaxational mechanism as well. In this way, the model provides also a simple microscopic basis for the widely used phenomenological rate-and-state equations of rock friction.

cond-mat.dis-nn↗

arXiv2008

The role of elastic stresses on leaf venation morphogenesis

We explore the possible role of elastic mismatch between epidermis and mesophyll as a driving force for the development of leaf venation. The current prevalent 'canalization' hypothesis for the formation of veins claims that the transport of the hormone auxin out of the leaves triggers cell differentiation to form veins. Although there is evidence that auxin plays a fundamental role in vein formation, the simple canalization mechanism may not be enough to explain some features observed in the vascular system of leaves, in particular, the abundance of vein loops. We present a model based on the existence of mechanical instabilities that leads very naturally to hierarchical patterns with a large number of closed loops. When applied to the structure of high order veins, the numerical results show the same qualitative features as actual venation patterns and, furthermore, have the same statistical properties. We argue that the agreement between actual and simulated patterns provides strong evidence for the role of mechanical effects on venation development.

physics.bio-ph↗

arXiv2008

Finite width of quasi-static shear bands

I study the average deformation rate of an amorphous material submitted to an external uniform shear strain rate, in the geometry known as the split-bottom configuration. The material is described using a stochastic model of plasticity at a mesoscopic scale. A shear band is observed to start at the split point at the bottom, and widen progressively towards the surface. In a two-dimensional geometry the average statistical properties of the shear band look similar to those of the directed polymer model. In particular, the surface width of the shear band is found to scale with the system height H as H^q with q=0.68 +/- 0.02. In more realistic three dimensional simulations the exponent changes to q=0.60 +/- 0.02 and the bulk profile of the width of the shear band is closer to a quarter of circle, as it was observed to be the case in recent simulations of granular materials.

cond-mat.soft↗

arXiv2007

Strain localization driven by structural relaxation in sheared amorphous solids

A two dimensional amorphous material is modeled as an assembly of mesoscopic elemental pieces coupled together to form an elastically coherent structure. Plasticity is introduced as the existence of different minima in the energy landscape of the elemental constituents. Upon the application of an external strain rate, the material shears through the appearance of elemental slip events with quadrupolar symmetry. When the energy landscape of the elemental constituents is kept fixed, the slip events distribute uniformly throughout the sample, producing on average a uniform deformation. However, when the energy landscape at different spatial positions can be rearranged dynamically to account for structural relaxation, the system develops inhomogeneous deformation in the form of shear bands at low shear rates, and stick-slip-like motion at the shear bands for the lowest shear rates. The origin of strain localization is traced back to a region of negative correlation between strain rate and stress, which appears only if structural relaxation is present. The model also reproduces other well known effects in the rheology of amorphous materials, as a stress peak in a strain rate controlled experiment staring from rest, and the increase of the maximum of this peak with sample age.

cond-mat.mtrl-sci↗

arXiv2007

Disorder-induced magnetic memory: Experiments and theories

Beautiful theories of magnetic hysteresis based on random microscopic disorder have been developed over the past ten years. Our goal was to directly compare these theories with precise experiments. We first developed and then applied coherent x-ray speckle metrology to a series of thin multilayer perpendicular magnetic materials. To directly observe the effects of disorder, we deliberately introduced increasing degrees of disorder into our films. We used coherent x-rays to generate highly speckled magnetic scattering patterns. The apparently random arrangement of the speckles is due to the exact configuration of the magnetic domains in the sample. In effect, each speckle pattern acts as a unique fingerprint for the magnetic domain configuration. Small changes in the domain structure change the speckles, and comparison of the different speckle patterns provides a quantitative determination of how much the domain structure has changed. How is the magnetic domain configuration at one point on the major hysteresis loop related to the configurations at the same point on the loop during subsequent cycles? The microscopic return-point memory(RPM) is partial and imperfect in the disordered samples, and completely absent when the disorder was not present. We found the complementary-point memory(CPM) is also partial and imperfect in the disordered samples and completely absent when the disorder was not present. We found that the RPM is always a little larger than the CPM. We also studied the correlations between the domains within a single ascending or descending loop. We developed new theoretical models that do fit our experiments.

cond-mat.mtrl-sci↗

arXiv2006

Modeling the buckling and delamination of thin films

I study numerically the problem of delamination of a thin film elastically attached to a rigid substrate. A nominally flat elastic thin film is modeled using a two-dimensional triangular mesh. Both compression and bending rigidities are included to simulate compression and bending of the film. The film can buckle (i.e., abandon its flat configuration) when enough compressive strain is applied. The possible buckled configurations of a piece of film with stripe geometry are investigated as a function of the compressive strain. It is found that the stable configuration depends strongly on the applied strain and the Poisson ratio of the film. Next, the film is considered to be attached to a rigid substrate by springs that can break when the detaching force exceeds a threshold value, producing the partial delamination of the film. Delamination is induced by a mismatch of the relaxed configurations of film and substrate. The morphology of the delaminated film can be followed and compared with available experimental results as a function of model parameters. `Telephone-cord', polygonal, and `brain-like' patterns qualitatively similar to experimentally observed configurations are obtained in different parameter regions. The main control parameters that select the different patterns are the mismatch between film and substrate and the degree of in-plane relaxation within the unbuckled regions.

cond-mat.mtrl-sci↗

arXiv2006

Some exact results for the velocity of cracks propagating in non-linear elastic models

We analyze a piece-wise linear elastic model for the propagation of a crack in a stripe geometry under mode III conditions, in the absence of dissipation. The model is continuous in the propagation direction and discrete in the perpendicular direction. The velocity of the crack is a function of the value of the applied strain. We find analytically the value of the propagation velocity close to the Griffith threshold, and close to the strain of uniform breakdown. Contrary to the case of perfectly harmonic behavior up to the fracture point, in the piece-wise linear elastic model the crack velocity is lower than the sound velocity, reaching this limiting value at the strain of uniform breakdown. We complement the analytical results with numerical simulations and find excellent agreement.

cond-mat.mtrl-sci↗

arXiv2005

Thermodynamics of volume collapse transitions in cerium and related compounds

We present a non-linear elastic model of a coherent transition with discontinuous volume change in an isotropic solid. The model reproduces the anomalous thermodynamics typical of coherent equilibrium including intrinsic hysteresis (for a pressure driven experiment) and a negative bulk modulus. The novelty of the model is that the statistical mechanics solution can be easily worked out. We find that coherency leads to an infinite-range density--density interaction, which drives classical critical behavior. The pressure width of the hysteresis loop shrinks with increasing temperature, ending at a critical point at a temperature related to the shear modulus. The bulk modulus softens with a 1/2 exponent at the transition even far from the critical point. Many well known features of the phase diagram of Ce and related systems are explained by the model.

cond-mat.mtrl-sci↗

arXiv2005

Morphologies of expansion ridges of elastic thin films onto a substrate

We consider a model of a thin film elastically attached to a rigid substrate. In the case in which the film expands relative to the substrate and assuming certain non-linear elastic behavior of the film, expansion ridges may appear, in which the material has collapsed, and the density is higher. By studying numerically this process, the possible morphologies of these collapsed regions are presented. They range from circular spots and straight stripes, to wiggle polygonal patterns and ring-shaped domains. The similarity of some of these results with patterns observed in delamination of thin films and bi-phase epitaxial growth is emphasized.

cond-mat.stat-mech↗

arXiv2005

Supersonic crack propagation in a class of lattice models of Mode III brittle fracture

We study a lattice model for mode III crack propagation in brittle materials in a stripe geometry at constant applied stretching. Stiffening of the material at large deformation produces supersonic crack propagation. For large stretching the propagation is guided by well developed soliton waves. For low stretching, the crack-tip velocity has a universal dependence on stretching that can be obtained using a simple geometrical argument.

cond-mat.mtrl-sci↗

arXiv2005

Pressure-induced amorphization, crystal-crystal transformations and the memory glass effect in interacting particles in two dimensions

We study a model of interacting particles in two dimensions to address the relation between crystal-crystal transformations and pressure-induced amorphization. On increasing pressure at very low temperature, our model undergoes a martensitic crystal-crystal transformation. The characteristics of the resulting polycrystalline structure depend on defect density, compression rate, and nucleation and growth barriers. We find two different limiting cases. In one of them the martensite crystals, once nucleated, grow easily perpendicularly to the invariant interface, and the final structure contains large crystals of the different martensite variants. Upon decompression almost every atom returns to its original position, and the original crystal is fully recovered. In the second limiting case, after nucleation the growth of martensite crystals is inhibited by energetic barriers. The final morphology in this case is that of a polycrystal with a very small crystal size. This may be taken to be amorphous if we have only access (as experimentally may be the case) to the angularly averaged structure factor. However, this `X-ray amorphous' material is anisotropic, and this shows up upon decompression, when it recovers the original crystalline structure with an orientation correlated with the one it had prior to compression. The memory effect of this X-ray amorphous material is a natural consequence of the memory effect associated to the underlying martensitic transformation. We suggest that this kind of mechanism is present in many of the experimental observations of the memory glass effect, in which a crystal with the original orientation is recovered from an apparently amorphous sample when pressure is released.

cond-mat.mtrl-sci↗

arXiv2005

Diffuse interface approach to brittle fracture

We present a continuum model for the propagation of cracks and fractures in brittle materials. The components of the strain tensor $ε$ are the fundamental variables. The evolution equations are based on a free energy that reduces to that of linear elasticity for small $ε$, and accounts for cracks through energy saturation at large values of $ε$. We regularize the model by including terms dependent on gradients of $ε$ in the free energy. No additional fields others than the strain tensor $ε$ are introduced, and then the whole dynamics is perfectly defined. We validate the model in controlled cases, and present a couple of non trivial applications.

cond-mat.stat-mech↗

arXiv2004

Hysteresis loops of magnetic thin films with perpendicular anisotropy

We model the magnetization of quasi two-dimensional systems with easy perpendicular (z-)axis anisotropy upon change of external magnetic field along z. The model is derived from the Landau-Lifshitz-Gilbert equation for magnetization evolution, written in closed form in terms of the z component of the magnetization only. The model includes--in addition to the external field--magnetic exchange, dipolar interactions and structural disorder. The phase diagram in the disorder/interaction strength plane is presented, and the different qualitative regimes are analyzed. The results compare very well with observed experimental hysteresis loops and spatial magnetization patterns, as for instance for the case of Co-Pt multilayers.

cond-mat.mtrl-sci↗

arXiv2004

Disorder-induced microscopic magnetic memory

Using coherent x-ray speckle metrology, we have measured the influence of disorder on major loop return point memory (RPM) and complementary point memory (CPM) for a series of perpendicular anisotropy Co/Pt multilayer films. In the low disorder limit, the domain structures show no memory with field cycling--no RPM and no CPM. With increasing disorder, we observe the onset and the saturation of both the RPM and the CPM. These results provide the first direct ensemble-sensitive experimental study of the effects of varying disorder on microscopic magnetic memory and are compared against the predictions of existing theories.

cond-mat.mtrl-sci↗

arXiv2004

Numerical simulations of two dimensional magnetic domain patterns

I show that a model for the interaction of magnetic domains that includes a short range ferromagnetic and a long range dipolar anti-ferromagnetic interaction reproduces very well many characteristic features of two-dimensional magnetic domain patterns. In particular bubble and stripe phases are obtained, along with polygonal and labyrinthine morphologies. In addition, two puzzling phenomena, namely the so called `memory effect' and the `topological melting' observed experimentally are also qualitatively described. Very similar phenomenology is found in the case in which the model is changed to be represented by the Swift-Hohenberg equation driven by an external orienting field.

cond-mat.stat-mech↗

arXiv2004

The buckling transition of 2D elastic honeycombs: Numerical simulation and Landau theory

I study the buckling transition under compression of a two-dimensional, hexagonal, regular elastic honeycomb. Under isotropic compression, the system buckles to a configuration consisting of a unit cell containing four of the original hexagons. This buckling pattern preserves the sixfold rotational symmetry of the original lattice but is chiral, and can be described as a combination of three different elemental distortions in directions rotated 2pi/3 from each other. Non-isotropic compression may induce patterns consisting in a single elemental distortion or a superposition of two of them. The numerical results compare very well with the outcome of a Landau theory of second order phase transitions.

cond-mat.mtrl-sci↗

arXiv2003

On maturation of crack patterns

Superficial (two dimensional) crack patterns appear when a thin layer of material elastically attached to a substrate contracts. We study numerically the maturation process undergone by these crack patterns when they are allowed to adapt in order to reduce its energy. The process models the evolution in depth of cracks in geological formations and in starch samples (`columnar jointing'), and also the time evolution (over thousands of years) of crack patterns in frozen soils. We observe an evolution towards a polygonal pattern that consist of a fixed distribution of polygons with mainly five, six and seven sides. They compare very well with known experimental examples. The evolution of one of these `mature' patterns upon reduction of the degree of contraction is also considered. We find that the pattern adapts by closing some of the cracks and rearranging those in the immediate neighborhood. This produces a change of the mean size of the polygons, but remarkably no changes of the statistical properties of the pattern. Comparison with the same behavior recently observed in starch samples is presented.

cond-mat.stat-mech↗

arXiv2003

Mechanical versus thermodynamical melting in pressure-induced amorphization: the role of defects

We study numerically an atomistic model which is shown to exhibit a one--step crystal--to--amorphous transition upon decompression. The amorphous phase cannot be distinguished from the one obtained by quenching from the melt. For a perfectly crystalline starting sample, the transition occurs at a pressure at which a shear phonon mode destabilizes, and triggers a cascade process leading to the amorphous state. When defects are present, the nucleation barrier is greatly reduced and the transformation occurs very close to the extrapolation of the melting line to low temperatures. In this last case, the transition is not anticipated by the softening of any phonon mode. Our observations reconcile different claims in the literature about the underlying mechanism of pressure amorphization.

cond-mat.mtrl-sci↗