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Flocks of birds, schools of fish, mixtures of motors and cytoskeletal filaments, swimming bacteria and driven granular media are systems of interacting motile units that exhibit collective behaviour. These can all be described as active matter systems, since each individual unit takes energy from an internal energy depot and transduces it into work performed on the environment. We review a model for cyanobacterial phototaxis, emphasising the differences from other models for collective behaviour in active matter systems. The interactions between individual cells during phototaxis are dominated by mechanical forces mediated by their physical attachments through type IV pili (T4P) and through the production of "slime", a complex mixture of non-diffusible polysaccharides deposited by cells that acts to decrease friction locally. The slime, in particular, adds a component to the interaction that is local in space but non-local in time, perhaps most comparable to the pheromones laid down in ant trails. Our results suggest that the time-delayed component of the interactions between bacteria qualify their description as a novel active system, which we refer to as "damp" active matter., Comment: 7 pages, 4 figures

Snapshots of colloidal particles moving on disordered two-dimensional substrates can be used to extract equal-time many-body correlations in their positions. To understand the systematics of these correlations, we perform Monte Carlo simulations of a two-dimensional model fluid placed in a quenched disordered background. We use configurations generated from these simulations to compute translational and orientational two-point correlations at equal time, concentrating on correlations in local orientational order as a function of density and disorder strength. We calculate both the disorder averaged version of conventional two-point correlation functions for orientational order, as well as the disorder averaged version of a novel correlation function of time-averaged disorder-induced inhomogeneities in local orientation analogous to the Edwards-Anderson correlation function in spin systems. We demonstrate that these correlations can exhibit interesting non-monotonic behavior in proximity to the underlying fluid-solid transition and suggest that this prediction should be experimentally accessible., Comment: 9 pages, 5 figures

We present results from molecular dynamics simulations of a spherically confined neutral polymer in the presence of crowding agents, studying polymer shapes and conformations as a function of the confining potential, solvent quality and the density of crowders. The conformations of the polymer under good solvent conditions are largely independent of crowder density, even when the polymer is strongly confined. However, for poor solvents and attractive walls, the polymer shows a transition between an adsorbed extended state to a globular conformation on the surface as a function of crowder particle density. This state differs from both the desorbed globular conformation in the absence of any wall interactions and the adsorbed globular conformation at low values of the attractive wall interactions. We revisit the earlier understanding of the adsorption of confined polymers on curved, attractive surfaces in the light of these results.

Superconductivity occurs in the proximity of other competing orders in a wide variety of materials. Such competing phases may reveal themselves when superconductivity is locally suppressed by a magnetic field in the core of a vortex. We explore the competition between superconductivity and charge density wave order in the attractive Hubbard model on a square lattice. Using Bogoliubov-deGennes mean field theory, we study how vortex structures form and evolve as the magnetic flux is tuned. Each vortex seeds a CDW region whose size is determined by the energy cost of the competing phase. The vortices form a lattice whose lattice parameter shrinks with increasing flux. Eventually, their charge-ordered vortex cores overlap, leading to a field-driven coexistence phase exhibiting both macroscopic charge order and superconductivity -- a `supersolid'. Ultimately, superconductivity disappears via a first-order phase transition into a purely charge ordered state. We construct a phase diagram containing these multiple ordered states, using $t'$, the next-nearest neighbour hopping, to tune the competition between phases., Comment: 5 pages + 3 pages of supplementary materials, 9 figures

An analytic formula describing the suppression of the equilibrium melting line by quenched point pinning disorder is compared to data from ac susceptibility and magnetization measurements in the mixed phase of the layered dichalcogenide low T_c superconductor 2H-NbSe_2. This material exhibits a sharp peak effect in the critical current close to the upper critical field H_c2(T). Arguing that the disorder-suppressed melting line in this system is to be identified with the locus of peak positions of the critical current as magnetic field and temperature are varied, we demonstrate that this formula provides a remarkably accurate fit to the experimental data over three orders of magnitude in magnetic field., Comment: 14 pages, single column, 4 figures

We study pressurised self-avoiding ring polymers in two dimensions using Monte Carlo simulations, scaling arguments and Flory-type theories, through models which generalise the model of Leibler, Singh and Fisher [Phys. Rev. Lett. Vol. 59, 1989 (1987)]. We demonstrate the existence of a thermodynamic phase transition at a non-zero scaled pressure $\tilde{p}$, where $\tilde{p} = Np/4\pi$, with the number of monomers $N \rightarrow \infty$ and the pressure $p \rightarrow 0$, keeping $\tilde{p}$ constant, in a class of such models. This transition is driven by bond energetics and can be either continuous or discontinuous. It can be interpreted as a shape transition in which the ring polymer takes the shape, above the critical pressure, of a regular N-gon whose sides scale smoothly with pressure, while staying unfaceted below this critical pressure. In the general case, we argue that the transition is replaced by a sharp crossover. The area, however, scales with $N^2$ for all positive $p$ in all such models, consistent with earlier scaling theories., Comment: 6 pages, 4 figures, EPL format

We analyze the time-series data for the onset of A(H1N1)v influenza pandemic in India during the period June 1- September 30, 2009. Using a variety of statistical fitting procedures, we obtain a robust estimate of the exponential growth rate $\langle \lambda \rangle \simeq 0.15$. This corresponds to a basic reproductive number $R_0 \simeq 1.45$ for influenza A(H1N1)v in India, a value which lies towards the lower end of the range of values reported for different countries affected by the pandemic., Comment: 5 pages, 4 figures

A variety of complex fluids under shear exhibit complex spatio-temporal behaviour, including what is now termed rheological chaos, at moderate values of the shear rate. Such chaos associated with rheological response occurs in regimes where the Reynolds number is very small. It must thus arise as a consequence of the coupling of the flow to internal structural variables describing the local state of the fluid. We propose a coupled map lattice (CML) model for such complex spatio-temporal behaviour in a passively sheared nematic liquid crystal, using local maps constructed so as to accurately describe the spatially homogeneous case. Such local maps are coupled diffusively to nearest and next nearest neighbours to mimic the effects of spatial gradients in the underlying equations of motion. We investigate the dynamical steady states obtained as parameters in the map and the strength of the spatial coupling are varied, studying local temporal properties at a single site as well as spatio-temporal features of the extended system. Our methods reproduce the full range of spatio-temporal behaviour seen in earlier one-dimensional studies based on partial differential equations. We report results for both the one and two-dimensional cases, showing that spatial coupling favours uniform or periodically time-varying states, as intuitively expected. We demonstrate and characterize regimes of spatio-temporal intermittency out of which chaos develops. Our work suggests that such simplified lattice representations of the spatio-temporal dynamics of complex fluids under shear may provide useful insights as well as fast and numerically tractable alternatives to continuum representations., Comment: 32 pages, single column, 20 figures

We study the inflated phase of two dimensional lattice polygons, both convex and column-convex, with fixed area A and variable perimeter, when a weight \mu^t \exp[- Jb] is associated to a polygon with perimeter t and b bends. The mean perimeter is calculated as a function of the fugacity \mu and the bending rigidity J. In the limit \mu -> 0, the mean perimeter has the asymptotic behaviour \avg{t}/4 \sqrt{A} \simeq 1 - K(J)/(\ln \mu)^2 + O (\mu/ \ln \mu) . The constant K(J) is found to be the same for both types of polygons, suggesting that self-avoiding polygons should also exhibit the same asymptotic behaviour., Comment: 10 pages, 3 figures

The term active matter describes diverse systems, spanning macroscopic (e.g. shoals of fish and flocks of birds) to microscopic scales (e.g. migrating cells, motile bacteria and gels formed through the interaction of nanoscale molecular motors with cytoskeletal filaments within cells). Such systems are often idealizable in terms of collections of individual units, referred to as active particles or self-propelled particles, which take energy from an internal replenishable energy depot or ambient medium and transduce it into useful work performed on the environment, in addition to dissipating a fraction of this energy into heat. These individual units may interact both directly as well as through disturbances propagated via the medium in which they are immersed. Active particles can exhibit remarkable collective behaviour as a consequence of these interactions, including non-equilibrium phase transitions between novel dynamical phases, large fluctuations violating expectations from the central limit theorem and substantial robustness against the disordering effects of thermal fluctuations. In this chapter, following a brief summary of experimental systems which may be classified as examples of active matter, I describe some of the principles which underlie the modeling of such systems., Comment: Pedagogical review, 26 pages, chapter to appear in "Rheology of Complex Fluids"

We construct Langevin equations describing the fluctuations of the tensor order parameter $Q_{\alpha\beta}$ in nematic liquid crystals by adding noise terms to time-dependent variational equations that follow from the Ginzburg-Landau-de Gennes free energy. The noise is required to preserve the symmetry and tracelessness of the tensor order parameter and must satisfy a fluctuation-dissipation relation at thermal equilibrium. We construct a noise with these properties in a basis of symmetric traceless matrices and show that the Langevin equations can be solved numerically in this basis using a stochastic version of the method of lines. The numerical method is validated by comparing equilibrium probability distributions, structure factors and dynamic correlations obtained from these numerical solutions with analytic predictions. We demonstrate excellent agreement between numerics and theory. This methodology can be applied to the study of phenomena where fluctuations in both the magnitude and direction of nematic order are important, as for instance in the nematic swarms which produce enhanced opalescence near the isotropic-nematic transition or the problem of nucleation of the nematic from the isotropic phase.

We study a model for the depinning and driven steady state phases of a solid tuned across a polymorphic phase transition between ground states of triangular and square symmetry. These include pinned states which may have dominantly triangular or square correlations, a plastically flowing liquid-like phase, a moving phase with hexatic correlations, flowing triangular and square states and a dynamic coexistence regime characterized by the complex interconversion of locally square and triangular regions. We locate these phases in a dynamical phase diagram. We demonstrate that the apparent power-law orientational correlations we obtain in our moving hexatic phase arise from circularly averaging an orientational correlation function with qualitatively different behaviour in the longitudinal (drive) and transverse directions. The intermediate coexistence regime exhibits several novel properties, including substantial enhancement in the current noise, an unusual power-law spectrum of current fluctuations and striking metastability effects. This noise arises from the fluctuations of the interface separating locally square and triangular ordered regions. We demonstrate the breakdown of effective ``shaking temperature'' treatments in the coexistence regime by showing that such shaking temperatures are non-monotonic functions of the drive in this regime. Finally we discuss the relevance of these simulations to the anomalous behaviour seen in the peak effect regime of vortex lines in the disordered mixed phase of type-II superconductors. We propose that this anomalous behavior is directly linked to the behavior exhibited in our simulations in the dynamical coexistence regime, thus suggesting a possible solution to the problem of the origin of peak effect anomalies., Comment: 22 pages, double column, higher quality figures available from authors

We present numerical and analytic results for uniaxial and biaxial order at the isotropic-nematic interface within Ginzburg-Landau-de Gennes theory. We study the case where an oblique anchoring condition is imposed asymptotically on the nematic side of the interface, reproducing results of previous work when this condition reduces to planar or homoeotropic anchoring. We construct physically motivated and computationally flexible variational profiles for uniaxial and biaxial order, comparing our variational results to numerical results obtained from a minimization of the Ginzburg-Landau-de Gennes free energy. While spatial variations of the scalar uniaxial and biaxial order parameters are confined to the neighbourhood of the interface, nematic elasticity requires that the director orientation interpolate linearly between either planar or homoeotropic anchoring at the location of the interface and the imposed boundary condition at infinity. The selection of planar or homoeotropic anchoring at the interface is governed by the sign of the Ginzburg-Landau-de Gennes elastic coefficient L_2. Our variational calculations are in close agreement with our numerics and agree qualitatively with results from density functional theory and molecular simulations., Comment: 26 pages, 9 figures

We revisit the classic problem of the structure of the isotropic-nematic interface within Ginzburg-Landau-de Gennes theory, refining previous analytic treatments of biaxiality at the interface. We compare our analysis with numerical results obtained through a highly accurate spectral collocation scheme for the solution of the Landau-Ginzburg-de Gennes equations. In comparison to earlier work, we obtain improved agreement with numerics for both the uniaxial and biaxial profiles, accurate asymptotic results for the decay of biaxial order on both nematic and isotropic sides of the interface and accurate fits to data from density functional approaches to this problem., Comment: 11 pages

We propose an efficient numerical scheme, based on the method of lines, for solving the Landau-de Gennes equations describing the relaxational dynamics of nematic liquid crystals. Our method is computationally easy to implement, balancing requirements of efficiency and accuracy. We benchmark our method through the study of the following problems: the isotropic-nematic interface, growth of nematic droplets in the isotropic phase and the kinetics of coarsening following a quench into the nematic phase. Our results, obtained through solutions of the full coarse-grained equations of motion with no approximations, provide a stringent test of the de Gennes ansatz for the isotropic - nematic interface, illustrate the anisotropic character of droplets in the nucleation regime and validate dynamical scaling in the coarsening regime.

Collections of non-Brownian particles suspended in a viscous fluid and subjected to oscillatory shear at very low Reynolds number have recently been shown to exhibit a remarkable dynamical phase transition separating reversible from irreversible behaviour as the strain amplitude or volume fraction are increased. We present a simple model for this phenomenon, based on which we argue that this transition lies in the universality class of the conserved DP models or, equivalently, the Manna model. This leads to predictions for the scaling behaviour of a large number of experimental observables. Non-Brownian suspensions under oscillatory shear may thus constitute the first experimental realization of an inactive-active phase transition which is not in the universality class of conventional directed percolation., Comment: 4 pages, 2 figures, final version

We propose and study a local map capable of describing the full variety of dynamical states, ranging from regular to chaotic, obtained when a nematic liquid crystal is subjected to a steady shear flow. The map is formulated in terms of a quaternion parametrization of rotations of the local frame described by the axes of the nematic director, subdirector and the joint normal to these, with two additional scalars describing the strength of ordering. Our model yields kayaking, wagging, tumbling, aligned and coexistence states, in agreement with previous formulations based on coupled ordinary differential equations. Such a map can serve as a building block for the construction of lattice models of the complex spatio-temporal states predicted for sheared nematics., Comment: 11 pages, higher quality figures available on request, references added

We study the inflated phase of two dimensional lattice polygons with fixed perimeter $N$ and variable area, associating a weight $\exp[pA - Jb ]$ to a polygon with area $A$ and $b$ bends. For convex and column-convex polygons, we show that $/A_{max} = 1 - K(J)/\tilde{p}^2 + \mathcal{O}(\rho^{-\tilde{p}})$, where $\tilde{p}=pN \gg 1$, and $\rho<1$. The constant $K(J)$ is found to be the same for both types of polygons. We argue that self-avoiding polygons should exhibit the same asymptotic behavior. For self-avoiding polygons, our predictions are in good agreement with exact enumeration data for J=0 and Monte Carlo simulations for $J \neq 0$. We also study polygons where self-intersections are allowed, verifying numerically that the asymptotic behavior described above continues to hold., Comment: 7 pages

We propose and study a model for the equilibrium statistical mechanics of a pressurised semiflexible polymer ring. The Hamiltonian has a term which couples to the algebraic area of the ring and a term which accounts for bending (semiflexibility). The model allows for self-intersections. Using a combination of Monte Carlo simulations, Flory-type scaling theory, mean-field approximations and lattice enumeration techniques, we obtain a phase diagram in which collapsed and inflated phases are separated by a continuous transition. The scaling properties of the averaged area as a function of the number of units of the ring are derived. For large pressures, the asymptotic behaviour of the area is calculated for both discrete and lattice versions of the model. For small pressures, the area is obtained through a mapping onto the quantum mechanical problem of an electron moving in a magnetic field. The simulation data agree well with the analytic and mean-field results., Comment: 12 pages

We investigate the driven states of a two-dimensional crystal whose ground state can be tuned through a square-triangular transition. The depinning of such a system from a quenched random background potential occurs via a complex sequence of dynamical states, which include plastic flow states, hexatics, dynamically stabilized triangle and square phases and intermediate regimes of phase coexistence. These results are relevant to transport experiments in the mixed phase of several superconductors which exhibit such structural transitions as well as to driven colloidal systems whose interactions can be tuned via surface modifications., Comment: Two-column, 4 pages, figures included

Three problems in the statistical mechanics of models for an assembly of molecular motors interacting with cytoskeletal filaments are reviewed. First, a description of the hydrodynamical behaviour of density-density correlations in fluctuating ratchet models for interacting molecular motors is outlined. Numerical evidence indicates that the scaling properties of dynamical behavior in such models belong to the KPZ universality class. Second, the generalization of such models to include boundary injection and removal of motors is provided. In common with known results for the asymmetric exclusion processes, simulations indicate that such models exhibit sharp boundary driven phase transitions in the thermodynamic limit. In the third part of this paper, recent progress towards a continuum description of pattern formation in mixtures of motors and microtubules is described, and a non-equilibrium ``phase-diagram'' for such systems discussed., Comment: Proc. Int. Workshop on "Common Trends in Traffic Systems", Kanpur, India, Feb 2006; to be published in Physica A

A liquid can exist under conditions of thermodynamic stability or metastability within boundaries defined by the liquid-gas spinodal and the glass transition line. The relationship between these boundaries has been investigated previously using computer simulations, the energy landscape formalism, and simplified model calculations. We calculate these stability boundaries semi-analytically for a model glass forming liquid, employing accurate liquid state theory and a first-principles approach to the glass transition. These boundaries intersect at a finite temperature, consistent with previous simulation-based studies., Comment: Minor text revisions. Fig.s 4, 5 updated

We obtain, using transfer matrix methods, the distribution function $P(R)$ of the end-to-end distance, the loop formation probability and force-extension relations in a model for short double-stranded DNA molecules. Accounting for the appearance of ``bubbles'', localized regions of enhanced flexibility associated with the opening of a few base pairs of double-stranded DNA in thermal equilibrium, leads to dramatic changes in $P(R)$ and unusual force-extension curves. An analytic formula for the loop formation probability in the presence of bubbles is proposed. For short {\em heterogeneous} chains, we demonstrate a strong dependence of loop formation probabilities on sequence, as seen in recent experiments., Comment: 10 pages

Several recent imaging experiments access the equilibrium density profiles of interacting particles confined to a two-dimensional substrate. When these particles are in a fluid phase, we show that such data yields precise information regarding substrate disorder as reflected in one-point functions and two-point correlations of the fluid. Using Monte Carlo simulations and replica generalizations of liquid state theories, we extract unusual two-point correlations of time-averaged density inhomogeneities induced by disorder. Distribution functions such as these have not hitherto been measured but should be experimentally accessible., Comment: 10 pages revtex 4 figures

We model the effects of confinement on the stable self-organized patterns obtained in the non-equilibrium steady states of mixtures of molecular motors and microtubules. In experiments [Nedelec et al. Nature, 389, 305 (1997); Surrey et al., Science, 292, 1167 (2001)] performed in a quasi-two-dimensional confined geometry, microtubules are oriented by complexes of motor proteins. This interaction yields a variety of patterns, including arangements of asters, vortices and disordered configurations. We model this system via a two-dimensional vector field describing the local coarse-grained microtubule orientation and two scalar density fields associated to molecular motors. These scalar fields describe motors which either attach to and move along microtubules or diffuse freely within the solvent. Transitions between single aster, spiral and vortex states are obtained as a consequence of confinement, as parameters in our model are varied. We also obtain other novel states, including ``outward asters'', distorted vortices and lattices of asters on confined systems. We calculate the steady state distribution of bound and free motors in aster and vortex configurations of microtubules and compare these to our simulation results, providing qualitative arguments for the stability of different patterns in various regimes of parameter space. We also study the role of crowding or ``saturation'' effects on the density profiles of motors in asters, discussing the role of such effects in stabilizing single asters., Comment: 34 pages, 10 figures included

We propose and study a hydrodynamic model for pattern formation in mixtures of molecular motors and microtubules. The steady state patterns we obtain in different regimes of parameter space include arrangements of vortices and asters separately as well as aster-vortex mixtures and fully disordered states. Such stable steady states are observed in experiments in vitro. The sequence of patterns obtained in the experiments can be associated with smooth trajectories in a non-equilibrium phase diagram for our model., Comment: 11 pages Latex file, 2 figures included

We study persistence in coupled circle map lattices at the onset of spatiotemporal intermittency, an onset which marks a continuous transition, in the universality class of directed percolation, to a unique absorbing state. We obtain a local persistence exponent of theta_l = 1.49 +- 0.02 at this transition, a value which closely matches values for theta_l obtained in stochastic models of directed percolation. This result constitutes suggestive evidence for the universality of persistence exponents at the directed percolation transition. Given that many experimental systems are modelled accurately by coupled map lattices, experimental measurements of this persistence exponent may be feasible., Comment: 7 pages, Latex, 6 Postscript figures, Europhysics Letters (to appear)

A ratchet model for coupled Brownian motors, inspired by the motion of individual two-headed molecular motors on cytoskeletal filaments, is proposed. Such motors are modeled as two elastically coupled Brownian particles, each of which moves in a flashing ratchet potential. The ratchet potentials felt by the individual particles are anti-correlated, modeling the successive binding and unbinding of the two motor heads to the filament. We obtain, via Langevin simulations, steady-state currents as functions of noise strength, the equilibrium separation of the particles and the rate of switching between potential states. We observe an enhanced current due to coupling, noise induced stability and phase-locked behaviour in the deterministic regime. A qualitative understanding of these features is provided., Comment: To be published as Proceedings of StatPhys - Kolkata IV in Physics A

We study the linearized hydrodynamics of a two-component fluid membrane near a repulsive wall, via a model which incorporates curvature- concentration coupling as well as hydrodynamic interactions. This model is a simplified version of a recently proposed one [J.-B. Manneville et al. Phys. Rev. E, 64, 021908 (2001)] for non-equilibrium force-centres embedded in fluid membranes, such as light-activated bacteriorhodopsin pumps incorporated in phospholipid (EPC) bilayers. The pump/membrane system is modeled as an impermeable, two-component bilayer fluid membrane in the presence of an ambient solvent, in which one component, representing active pumps, is described in terms of force dipoles displaced with respect to the bilayer midpoint. We first discuss the case in which such pumps are rendered inactive, computing the mode structure in the bulk as well as the modification of hydrodynamic properties by the presence of a nearby wall. We then discuss the fluctuations and mode structure in steady state of active two-component membranes near a repulsive wall. We find that proximity to the wall smoothens membrane height fluctuations in the stable regime, resulting in a logarithmic scaling of the roughness even for initially tensionless membranes. This explicitly non-equilibrium result, a consequence of the incorporation of curvature-concentration coupling in our treatment, also indicates that earlier scaling arguments which obtained an increase in the roughness of active membranes near repulsive walls may need to be reevaluated., Comment: 39 page Latex file, 3 encapsulated Postscript figures

We obtain \theta_p(q) = 2\theta_s(q) for one-dimensional q-state ferromagnetic Potts models evolving under parallel dynamics at zero temperature from an initially disordered state, where \theta_p(q) is the persistence exponent for parallel dynamics and \theta_s(q) = -{1/8}+ \frac{2}{\pi^2}[cos^{-1}{(2-q)/q\sqrt{2}}]^2 [PRL, {\bf 75}, 751, (1995)], the persistence exponent under serial dynamics. This result is a consequence of an exact, albeit non-trivial, mapping of the evolution of configurations of Potts spins under parallel dynamics to the dynamics of two decoupled reaction diffusion systems., Comment: 13 pages Latex file, 5 postscript figures

A general phenomenology for phase behaviour in the mixed phase of type-II superconductors with weak point pinning disorder is outlined. We propose that the ``Bragg glass'' phase generically transforms via two separate thermodynamic phase transitions into a disordered liquid on increasing the temperature. The first transition is into a glassy phase, topologically disordered at the largest length scales; current evidence suggests that it lacks the long-ranged phase correlations expected of a ``vortex glass''. This phase has a significant degree of short-ranged translational order, unlike the disordered liquid, but no quasi-long range order, in contrast to the Bragg glass. This glassy phase, which we call a ``multi-domain glass'', is confined to a narrow sliver at intermediate fields, but broadens out both for much larger and much smaller field values. The multi-domain glass may be a ``hexatic glass''; alternatively, its glassy properties may originate in the replica symmetry breaking envisaged in recent theories of the structural glass transition. Estimates for translational correlation lengths in the multi-domain glass indicate that they can be far larger than the interline spacing for weak disorder, suggesting a plausible mechanism by which signals of a two-step transition can be obscured. Calculations of the Bragg glass-multi-domain glass and the multi-domain glass-disordered liquid phase boundaries are presented and compared to experimental data. We argue that these proposals provide a unified picture of the available experimental data on both high-T$_c$ and low-T$_c$ materials, simulations and current theoretical understanding., Comment: 70 pages, 9 postscript figures, modified title and minor changes in published version

A universal phase diagram for type-II superconductors with weak point pinning disorder is proposed. In this phase diagram, two thermodynamic phase transitions generically separate a ``Bragg glass'' from the disordered liquid. Translational correlations in the intervening ``multi-domain glass'' phase are argued to exhibit a significant degree of short-range order. This phase diagram differs significantly from the currently accepted one but provides a more accurate description of experimental data on high and low-T$_c$ materials, simulations and current theoretical understanding., Comment: 15 pages including 2 postscript figures, minor changes in published version