The arctic curve of the domain-wall six-vertex model

The problem of the form of the `arctic' curve of the six-vertex model with domain wall boundary conditions in its disordered regime is addressed. It is well-known that in the scaling limit the model exhibits phase-separation, with regions of order and disorder sharply separated by a smooth curve, called the arctic curve. To find this curve, we study a multiple integral representation for the emptiness formation probability, a correlation function devised to detect spatial transition from order to disorder. We conjecture that the arctic curve, for arbitrary choice of the vertex weights, can be characterized by the condition of condensation of almost all roots of the corresponding saddle-point equations at the same, known, value. In explicit calculations we restrict to the disordered regime for which we have been able to compute the scaling limit of certain generating function entering the saddle-point equations. The arctic curve is obtained in parametric form and appears to be a non-algebraic curve in general; it turns into an algebraic one in the so-called root-of-unity cases. The arctic curve is also discussed in application to the limit shape of $q$-enumerated (with $0<q\leq 4$) large alternating sign matrices. In particular, as $q\to 0$ the limit shape tends to a nontrivial limiting curve, given by a relatively simple equation.Comment: 39 pages, 2 figures; minor correction

Geometrical Effects of Baryon Density Inhomogeneities on Primordial Nucleosynthesis

We discuss effects of fluctuation geometry on primordial nucleosynthesis. For the first time we consider condensed cylinder and cylindrical-shell fluctuation geometries in addition to condensed spheres and spherical shells. We find that a cylindrical shell geometry allows for an appreciably higher baryonic contribution to be the closure density (\Omega_b h_{50}^2 \la 0.2) than that allowed in spherical inhomogeneous or standard homogeneous big bang models. This result, which is contrary to some other recent studies, is due to both geometry and recently revised estimates of the uncertainties in the observationally inferred primordial light-element abundances. We also find that inhomogeneous primordial nucleosynthesis in the cylindrical shell geometry can lead to significant Be and B production. In particular, a primordial beryllium abundance as high as [Be] = 12 + log(Be/H) $\approx -3$ is possible while still satisfying all of the light-element abundance constraints.Comment: Latex, 20 pages + 11 figures(not included). Entire ps file with embedded figures available via anonymous ftp at ftp://genova.mtk.nao.ac.jp/pub/prepri/bbgeomet.ps.g

Plasticity in current-driven vortex lattices

We present a theoretical analysis of recent experiments on current-driven vortex dynamics in the Corbino disk geometry. This geometry introduces controlled spatial gradients in the driving force and allows the study of the onset of plasticity and tearing in clean vortex lattices. We describe plastic slip in terms of the stress-driven unbinding of dislocation pairs, which in turn contribute to the relaxation of the shear, yielding a nonlinear response. The steady state density of free dislocations induced by the applied stress is calculated as a function of the applied current and temperature. A criterion for the onset of plasticity at a radial location $r$ in the disk yields a temperature-dependent critical current that is in qualitative agreement with experiments.Comment: 11 pages, 4 figure

A model for the screen printing of Newtonian fluids

A preliminary investigation into aspects of the off-contact screen-printing process is presented. A mathematical model for the printing of a thin film of Newtonian fluid is proposed, in which the screen is modelled as a permeable membrane, and the entire region above and below the screen is flooded. By drawing upon widely used industrial circuit printing practices, the distinguished limit of greatest interest to this industry is identified. Numerical and asymptotic solutions of this distinguished limit are presented that reproduce many of the features observed in industrial screen-printing

Colored fused filament fabrication

Fused filament fabrication is the method of choice for printing 3D models at low cost and is the de-facto standard for hobbyists, makers, and schools. Unfortunately, filament printers cannot truly reproduce colored objects. The best current techniques rely on a form of dithering exploiting occlusion, that was only demonstrated for shades of two base colors and that behaves differently depending on surface slope. We explore a novel approach for 3D printing colored objects, capable of creating controlled gradients of varying sharpness. Our technique exploits off-the-shelves nozzles that are designed to mix multiple filaments in a small melting chamber, obtaining intermediate colors once the mix is stabilized. We apply this property to produce color gradients. We divide each input layer into a set of strata, each having a different constant color. By locally changing the thickness of the stratum, we change the perceived color at a given location. By optimizing the choice of colors of each stratum, we further improve quality and allow the use of different numbers of input filaments. We demonstrate our results by building a functional color printer using low cost, off-the-shelves components. Using our tool a user can paint a 3D model and directly produce its physical counterpart, using any material and color available for fused filament fabrication

Concentration fluctuations of large Stokes number particles in a one-dimensional random velocity field

We analyze the behavior of an ensemble of inertial particles in a one-dimensional smooth Gaussian velocity field, in the limit of large inertia, but considering a finite correlation time for the random field. We derive in this limit a perturbative scheme for the calculation of the concentration correlation and of the particle relative velocity distribution, providing analytical expressions for the concentration fluctuation amplitude, its correlation length, and the modification in the particle pair relative velocity variance. The amplitude of the concentration fluctuations is characterized by slow decay at large inertia and a much larger correlation length than that of the random field. The fluctuation structure in velocity space is very different from predictions from short-time correlated random velocity fields, with only few particle pairs crossing at sufficiently small relative velocity to produce correlations. Concentration fluctuations are associated with depletion of the relative velocity variance of colliding particles.Comment: 8 pages, 1 figure, revtex

Steering in computational science: mesoscale modelling and simulation

This paper outlines the benefits of computational steering for high performance computing applications. Lattice-Boltzmann mesoscale fluid simulations of binary and ternary amphiphilic fluids in two and three dimensions are used to illustrate the substantial improvements which computational steering offers in terms of resource efficiency and time to discover new physics. We discuss details of our current steering implementations and describe their future outlook with the advent of computational grids.Comment: 40 pages, 11 figures. Accepted for publication in Contemporary Physic