Related papers: The energy landscape of aging systems--from a diff…
The maximum-weight matching problem and the behavior of its energy landscape is numerically investigated. We apply a perturbation method adapted from the analysis of spin glasses. This gives inside into the complexity of the energy…
High-dimensional random landscapes underlie phenomena as diverse as glassy physics and optimization in machine learning, and even their simplest toy models already display extraordinarily rich behavior. This thesis aims to deepen our…
When a liquid melt is cooled, a glass or phase transition can be obtained depending on the cooling rate. Yet, this behavior has not been clearly captured in energy landscape models. Here a model is provided in which two key ingredients are…
We develop a framework for understanding the difference between strong and fragile behavior in the dynamics of glass-forming liquids from the properties of the potential energy landscape. Our approach is based on a master equation…
According to the mean-field glass theory, the (free) energy landscape of disordered systems is hierarchical and ultrametric if they belong to the full-replica-symmetry-breaking universality class. However, examining this theoretical picture…
We present a detailed study of simple `tree' models for off equilibrium dynamics and aging in glassy systems. The simplest tree describes the landscape of a random energy model, whereas multifurcating trees occur in the solution of the…
In principle, all of the dynamical complexities of many-body systems are encapsulated in the potential energy landscapes on which the atoms move - an observation that suggests that the essentials of the dynamics ought to be determined by…
The complexity and unpredictability of postbuckling responses in even simple thin shells have raised great challenges to emerging technologies exploiting buckling transitions. Here we comprehensively survey the buckling landscapes to show…
In this paper, we review the general features of the out-of-equilibrium dynamics of spin glasses. We use this example as a guideline for a brief description of glassy dynamics in other disordered systems like structural and polymer glasses,…
For a system consisting of active soft spheres in three dimensions, we study the transition from a fluid where overlaps between particles can only occur for a short time after a collision to a state where clusters of overlapping particles…
Energetic correlations due to polymeric constraints and the locality of interactions, in conjunction with the apriori specification of the existence of a particularly low energy state, provides a method of introducing the aspect of minimal…
Methods for studying droplets in models with quenched disorder are critically examined. Low energy excitations in two dimensional models are investigated by finding minimal energy interior excitations and by computing the effect of bulk…
We offer an alternative real-space description, based purely on activated processes, for the understanding of relaxation dynamics in hierarchical landscapes. To this end, we use the cluster model, a coarse-grained lattice model of a jammed…
Canyon landscapes in high dimension can be described as manifolds of small, but extensive dimension, immersed in a higher dimensional ambient space and characterized by a zero potential energy on the manifold. Here we consider the problem…
All ground states and low-lying excitations of a +/- I Ising spin glass model on a cubic 4 x 4 x 4 lattice with periodical boundary conditions were calculated using a method of combinatorical optimization. The structure of states in the…
Properties of the free energy landscape in phase space of a dense hard sphere system characterized by a discretized free energy functional of the Ramakrishnan-Yussouff form are investigated numerically. A considerable number of glassy local…
We study energy landscape and dynamics of the three-dimensional Heisenberg Spin Glass model in the paramagnetic phase, i.e. for temperature $T$ larger than the critical temperature $T_\mathrm{c}$. The landscape is non-trivially related to…
Many problems in physics, material sciences, chemistry and biology can be abstractly formulated as a system that navigates over a complex energy landscape of high or infinite dimensions. Well-known examples include phase transitions of…
The topography of the free energy landscape in phase space of a dense hard sphere system characterized by a discretized free energy functional of the Ramakrishnan-Yussouff form is investigated numerically using a ``microcanonical'' Monte…
The effects of floppy modes in the thermodynamical properties of a system are studied. From thermodynamical arguments, we deduce that floppy modes are not at zero frequency and thus a modified Debye model is used to take into account this…