Isostaticity at Frictional Jamming

Amorphous packings of frictionless, spherical particles are isostatic at jamming onset, with the number of constraints (contacts) equal to the number of degrees of freedom. Their structural and mechanical properties are controlled by the interparticle contact network. In contrast, amorphous packings of frictional particles are typically hyperstatic at jamming onset. We perform extensive numerical simulations in two dimensions of the geometrical asperity (GA) model for static friction, to further investigate the role of isostaticity. In the GA model, interparticle forces are obtained by summing up purely repulsive central forces between periodically spaced circular asperities on contacting grains. We compare the packing fraction, contact number, mobilization distribution, and vibrational density of states using the GA model to those generated using the Cundall-Strack (CS) approach. We find that static packings of frictional disks obtained from the GA model are mechanically stable and isostatic when we consider interactions between asperities on contacting particles. The crossover in the structural and mechanical properties of static packings from frictionless to frictional behavior as a function of the static friction coefficient coincides with a change in the type of interparticle contacts and the disappearance of a peak in the density of vibrational modes for the GA model. These results emphasize that mesoscale features of the model for static friction play an important role in determining the properties of granular packings.Comment: 4.5 pages, 5 figures, http://prl.aps.org/covers/110/1

Bending crystals: Emergence of fractal dislocation structures

We provide a minimal continuum model for mesoscale plasticity, explaining the cellular dislocation structures observed in deformed crystals. Our dislocation density tensor evolves from random, smooth initial conditions to form self-similar structures strikingly similar to those seen experimentally - reproducing both the fractal morphologies and some features of the scaling of cell sizes and misorientations analyzed experimentally. Our model provides a framework for understanding emergent dislocation structures on the mesoscale, a bridge across a computationally demanding mesoscale gap in the multiscale modeling program, and a new example of self-similar structure formation in non-equilibrium systems.Comment: 4 pages, 4 figures, 5 movies (They can be found at http://www.lassp.cornell.edu/sethna/Plasticity/SelfSimilarity.html .) In press at Phys. Rev. Let

Topological phases and topological entropy of two-dimensional systems with finite correlation length

We elucidate the topological features of the entanglement entropy of a region in two dimensional quantum systems in a topological phase with a finite correlation length $\xi$. Firstly, we suggest that simpler reduced quantities, related to the von Neumann entropy, could be defined to compute the topological entropy. We use our methods to compute the entanglement entropy for the ground state wave function of a quantum eight-vertex model in its topological phase, and show that a finite correlation length adds corrections of the same order as the topological entropy which come from sharp features of the boundary of the region under study. We also calculate the topological entropy for the ground state of the quantum dimer model on a triangular lattice by using a mapping to a loop model. The topological entropy of the state is determined by loop configurations with a non-trivial winding number around the region under study. Finally, we consider extensions of the Kitaev wave function, which incorporate the effects of electric and magnetic charge fluctuations, and use it to investigate the stability of the topological phase by calculating the topological entropy.Comment: 17 pages, 4 figures, published versio

Transport properties of single atoms

We present a systematic study of the ballistic electron conductance through sp and 3d transition metal atoms attached to copper and palladium crystalline electrodes. We employ the 'ab initio' screened Korringa-Kohn-Rostoker Green's function method to calculate the electronic structure of nanocontacts while the ballistic transmission and conductance eigenchannels were obtained by means of the Kubo approach as formulated by Baranger and Stone. We demonstrate that the conductance of the systems is mainly determined by the electronic properties of the atom bridging the macroscopic leads. We classify the conducting eigenchannels according to the atomic orbitals of the contact atom and the irreducible representations of the symmetry point group of the system that leads to the microscopic understanding of the conductance. We show that if impurity resonances in the density of states of the contact atom appear at the Fermi energy, additional channels of appropriate symmetry could open. On the other hand the transmission of the existing channels could be blocked by impurity scattering.Comment: RevTEX4, 9 pages, 9 figure

Energy efficiency parametric design tool in the framework of holistic ship design optimization

Recent International Maritime Organization (IMO) decisions with respect to measures to reduce the emissions from maritime greenhouse gases (GHGs) suggest that the collaboration of all major stakeholders of shipbuilding and ship operations is required to address this complex techno-economical and highly political problem efficiently. This calls eventually for the development of proper design, operational knowledge, and assessment tools for the energy-efficient design and operation of ships, as suggested by the Second IMO GHG Study (2009). This type of coordination of the efforts of many maritime stakeholders, with often conflicting professional interests but ultimately commonly aiming at optimal ship design and operation solutions, has been addressed within a methodology developed in the EU-funded Logistics-Based (LOGBASED) Design Project (2004–2007). Based on the knowledge base developed within this project, a new parametric design software tool (PDT) has been developed by the National Technical University of Athens, Ship Design Laboratory (NTUA-SDL), for implementing an energy efficiency design and management procedure. The PDT is an integral part of an earlier developed holistic ship design optimization approach by NTUA-SDL that addresses the multi-objective ship design optimization problem. It provides Pareto-optimum solutions and a complete mapping of the design space in a comprehensive way for the final assessment and decision by all the involved stakeholders. The application of the tool to the design of a large oil tanker and alternatively to container ships is elaborated in the presented paper