E. A. Jagla

Core-softened potentials and the anomalous properties of water

We study the phase diagram of a system of spherical particles interacting in three dimensions through a potential consisting of a strict hard core plus a linear repulsive shoulder at larger distances. The phase diagram (obtained numerically, and analytically in a limiting case) shows anomalous properties that are similar to those observed in water. Specifically, we find maxima of density and isothermal compressibility as a function of temperature, melting with volume contraction, and multiple stable crystalline structures. If in addition a long range attraction between the particles is included, the usual liquid–gas coexistence curve with its critical point is obtained. But more interestingly, a first order line in the metastable fluid branch of the phase diagram appears, ending in a new critical point, as it was suggested to occur in water. In this way the model provides a comprehensive, consistent and unified picture of most of the anomalous thermodynamical properties of water, showing that all of them ...

Phase behavior of a system of particles with core collapse

The pressure-temperature phase diagram of a one-component system, with particles interacting through a spherically symmetric pair potential in two dimensions is studied. The interaction consists of a hard core plus an additional repulsion at low energies. It is shown that at zero temperature, instead of the expected isostructural transition due to core collapse occurring when increasing pressure, the system passes through a series of ground states that are not triangular lattices. In particular, and depending on parameters, structures with squares, chains, hexagons and even quasicrystalline ground states are found. At finite temperatures the solid-fluid coexistence line presents a zone with negative slope (which implies melting with decreasing in volume) and the fluid phase has a temperature of maximum density, similar to that in water.

Low-temperature behavior of core-softened models: Water and silica behavior

A core-softened model of a glass forming fluid is numerically studied in the limit of very low temperatures. The model shows two qualitatively different behaviors depending on the strength of the attraction between particles. For no or low attraction, the changes of density as a function of pressure are smooth, although hysteretic due to mechanical metastabilities. For larger attraction, sudden changes of density upon compressing and decompressing occur. This global mechanical instability is correlated to the existence of a thermodynamic first-order amorphous-amorphous transition. The two different behaviors obtained correspond qualitatively to the different phenomenology observed in silica and water.

Liquid-liquid equilibrium for monodisperse spherical particles

A system of identical particles interacting through an isotropic potential that allows for two preferred interparticle distances is numerically studied. When the parameters of the interaction potential are adequately chosen, the system exhibits coexistence between two different liquid phases (in addition to the usual liquid-gas coexistence). It is shown that this coexistence can occur at equilibrium, namely, in the region in which the liquid is thermodynamically stable.

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.

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. To do so, 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, produced at the Advanced Light Source at Lawrence Berkeley National Laboratory, 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. Our experiments quickly answered one longstanding question: 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? This is called microscopic return-point memory RPM. We found that the RPM is partial and imperfect in the disordered samples, and completely absent when the disorder is below a threshold level. We also introduced and answered a second important question: How are the magnetic domains at one point on the major loop related to the domains at the complementary point, the inversion symmetric point on the loop, during the same and during subsequent cycles? This is called microscopic complementary-point memory CPM. We found that the CPM is also partial and imperfect in the disordered samples and completely absent when the disorder is not present. In addition, 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. This is called microscopic half-loop memory and enabled us to measure the degree of change in the domain structure due to changes in the applied field. No existing theory was capable of reproducing our experimental results. So we developed theoretical models that do fit our experiments. Our experimental and theoretical results set benchmarks for future work.

Stable propagation of an ordered array of cracks during directional drying

We study the appearance and evolution of an array of parallel cracks in a thin slab of material that is directionally dried, and show that the cracks penetrate the material uniformly if the drying front is sufficiently sharp. We also show that cracks have a tendency to become evenly spaced during the penetration. The typical distance between cracks is mainly governed by the typical distance of the pattern at the surface, and it is not modified during the penetration. Our results agree with recent experimental work, and can be extended to three dimensions to describe the properties of columnar polygonal patterns observed in some geological formations.

Minimum energy configurations of repelling particles in two dimensions

Geometrical arrangements of minimum energy of a system of identical repelling particles in two dimensions are studied for different forms of the interaction potential. Stability conditions for the triangular structure are derived, and some potentials that do not satisfy them are discussed. It is shown that in addition to the triangular lattice, other structures may appear (some of them with nontrivial unit cells, and nonequivalent positions of the particles) even for simple choices of the interaction. The same qualitative behavior is expected in three dimensions.

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.

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.