Strong Phase Separation in a Model of Sedimenting Lattices

We study the steady state resulting from instabilities in crystals driven through a dissipative medium, for instance, a colloidal crystal which is steadily sedimenting through a viscous fluid. The problem involves two coupled fields, the density and the tilt; the latter describes the orientation of the mass tensor with respect to the driving field. We map the problem to a 1-d lattice model with two coupled species of spins evolving through conserved dynamics. In the steady state of this model each of the two species shows macroscopic phase separation. This phase separation is robust and survives at all temperatures or noise levels--- hence the term Strong Phase Separation. This sort of phase separation can be understood in terms of barriers to remixing which grow with system size and result in a logarithmically slow approach to the steady state. In a particular symmetric limit, it is shown that the condition of detailed balance holds with a Hamiltonian which has infinite-ranged interactions, even though the initial model has only local dynamics. The long-ranged character of the interactions is responsible for phase separation, and for the fact that it persists at all temperatures. Possible experimental tests of the phenomenon are discussed.Comment: To appear in Phys Rev E (1 January 2000), 16 pages, RevTex, uses epsf, three ps figure

Topology by Design in Magnetic nano-Materials: Artificial Spin Ice

Artificial Spin Ices are two dimensional arrays of magnetic, interacting nano-structures whose geometry can be chosen at will, and whose elementary degrees of freedom can be characterized directly. They were introduced at first to study frustration in a controllable setting, to mimic the behavior of spin ice rare earth pyrochlores, but at more useful temperature and field ranges and with direct characterization, and to provide practical implementation to celebrated, exactly solvable models of statistical mechanics previously devised to gain an understanding of degenerate ensembles with residual entropy. With the evolution of nano--fabrication and of experimental protocols it is now possible to characterize the material in real-time, real-space, and to realize virtually any geometry, for direct control over the collective dynamics. This has recently opened a path toward the deliberate design of novel, exotic states, not found in natural materials, and often characterized by topological properties. Without any pretense of exhaustiveness, we will provide an introduction to the material, the early works, and then, by reporting on more recent results, we will proceed to describe the new direction, which includes the design of desired topological states and their implications to kinetics.Comment: 29 pages, 13 figures, 116 references, Book Chapte

A Model for Growth of Binary Alloys with Fast Surface Equilibration

We study a simple growth model for (d+1)-dimensional films of binary alloys in which atoms are allowed to interact and equilibrate at the surface, but are frozen in the bulk. The resulting crystal is highly anisotropic: Correlations perpendicular to the growth direction are identical to a d-dimensional two-layer system in equilibrium, while parallel correlations generally reflect the (Glauber) dynamics of such a system. For stronger in-plane interactions, the correlation volumes change from oblate to highly prolate shapes near a critical demixing or ordering transition. In d=1, the critical exponent z relating the scaling of the two correlation lengths varies continuously with the chemical interactions.Comment: 7 pages RevTeX, 5 postscript figure

Reduced SL(2,R) WZNW Quantum Mechanics

The $SL(2,\R)$ WZNW $\rightarrow$ Liouville reduction leads to a nontrivial phase space on the classical level both in $0+1$ and $1+1$ dimensions. To study the consequences in the quantum theory, the quantum mechanics of the $0+1$ dimensional, point particle version of the constrained WZNW model is investigated. The spectrum and the eigenfunctions of the obtained---rather nontrivial---theory are given, and the physical connection between the pieces of the reduced configuration space is discussed in all the possible cases of the constraint parameters.Comment: LaTeX file, 33 pages. Results extended, contains all technical information not detailed in version to appear in J. Math. Phy

Project MAXWELL: Towards Rapid Realization of Superior Products

We describe a new methodology for the design and manufacture of mechanical components. The methodology is a synergism of a new, mathematically rigorous procedure for the concurrent design of shape and material composition of components, and a new manufacturing process called MD* for their realization. The concurrent design strategy yields information about the global shape of the component and its material composition. The fabrication of such designs with novel microstructural configurations require unconventional manufacturing processes. MD* is a shape deposition process for the free-form fabrication of parts from single or composite materials and is ideally suited for realizing the aforementioned designs. Project MAXWELL, therefore, promotes the use of layered manufacturing beyond prototyping tasks and offers the possibility of their integration into the mainstream product development and fabrication process..Mechanical Engineerin

Kinesin Is an Evolutionarily Fine-Tuned Molecular Ratchet-and-Pawl Device of Decisively Locked Direction

Conventional kinesin is a dimeric motor protein that transports membranous organelles toward the plus-end of microtubules (MTs). Individual kinesin dimers show steadfast directionality and hundreds of consecutive steps, yetthe detailed physical mechanism remains unclear. Here we compute free energies for the entire dimer-MT system for all possible interacting configurations by taking full account of molecular details. Employing merely first principles and several measured binding and barrier energies, the system-level analysis reveals insurmountable energy gaps between configurations, asymmetric ground state caused by mechanically lifted configurational degeneracy, and forbidden transitions ensuring coordination between both motor domains for alternating catalysis. This wealth of physical effects converts a kinesin dimer into a molecular ratchet-and-pawl device, which determinedly locks the dimer's movement into the MT plus-end and ensures consecutive steps in hand-over-hand gait.Under a certain range of extreme loads, however, the ratchet-and-pawl device becomes defective but not entirely abolished to allow consecutive back-steps. This study yielded quantitative evidence that kinesin's multiple molecular properties have been evolutionarily adapted to fine-tune the ratchet-and-pawl device so as to ensure the motor's distinguished performance.Comment: 10 printed page

Large deviations of the dynamical activity in the East model: analysing structure in biased trajectories

We consider large deviations of the dynamical activity in the East model. We bias this system to larger than average activity and investigate the structure that emerges. To best characterise this structure, we exploit the fact that there are effective interactions that would reproduce the same behaviour in an equilibrium system. We combine numerical results with linear response theory and variational estimates of these effective interactions, giving the first insights into such interactions in a many-body system, across a wide range of biases. The system exhibits a hierarchy of responses to the bias, remaining quasi-equilibrated on short length scales, but deviating far from equilibrium on large length scales. We discuss the connection between this hierarchy and the hierarchical aging behaviour of the system.Comment: Revised version, 29 pages, 9 fig

Long range order in gauge theories. Deformed QCD as a toy model

We study a number of different ingredients, related to long range order observed in lattice QCD simulations, using a simple "deformed QCD" model. This model is a weakly coupled gauge theory, which however has all the relevant crucial elements allowing us to study difficult and nontrivial problems which are known to be present in real strongly coupled QCD. In the present study, we want to understand the physics of long range order in form of coherent low dimensional vacuum configurations observed in Monte Carlo lattice simulations. We demonstrate the presence of double-layer domain wall structures in the deformed QCD, and study their interaction with localized topological monopoles. Furthermore, we show that there is in fact an attractive interaction between the two, such that the monopole favors a position within the domain wall.Comment: 10 pages, 5 figure