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We remove the need for Laplace/inverse-Laplace transformations of experimental data, by presenting a direct and straightforward mathematical procedure for obtaining frequency-dependent storage and loss moduli ($G'(\omega)$ and $G"(\omega)$ respectively), from time-dependent experimental measurements. The procedure is applicable to ordinary rheological creep (stress-step) measurements, as well as all microrheological techniques, whether they access a Brownian mean-square displacement, or a forced compliance. Data can be substituted directly into our simple formula, thus eliminating traditional fitting and smoothing procedures that disguise relevant experimental noise., Comment: 4 pages

We calculate the form factor f_+(q^2) for B-meson semileptonic decay in unquenched lattice QCD with 2+1 flavors of light sea quarks. We use Asqtad-improved staggered light quarks and a Fermilab bottom quark on gauge configurations generated by the MILC Collaboration. We simulate with several light quark masses and at two lattice spacings, and extrapolate to the physical quark mass and continuum limit using heavy-light meson staggered chiral perturbation theory. We then fit the lattice result for f_+(q^2) simultaneously with that measured by the BABAR experiment using a parameterization of the form factor shape in q^2 which relies only on analyticity and unitarity in order to determine the CKM matrix element |V(ub)|. This approach reduces the total uncertainty in |V(ub)| by combining the lattice and experimental information in an optimal, model-independent manner. We find a value of |V(ub)| x 10^3 = 3.38 +/- 0.36., Comment: 59 pages, 11 figures v2: Added table with form factor covariance matrix. Added references. v3: Fixed typos. Corrected heavy-quark discretization errors and subsequent determination of Vub. Central value of Vub unchanged, but error in Vub changed in last decimal place. Version submitted to Phys. Rev. D

We present the first lattice QCD calculation of the form factor for B-> D* l nu with three flavors of sea quarks. We use an improved staggered action for the light valence and sea quarks (the MILC configurations), and the Fermilab action for the heavy quarks. The form factor is computed at zero recoil using a new double ratio method that yields the form factor more directly than the previous Fermilab method. Other improvements over the previous calculation include the use of much lighter light quark masses, and the use of lattice (staggered) chiral perturbation theory in order to control the light quark discretization errors and chiral extrapolation. We obtain for the form factor, F_{B-> D*}(1)=0.921(13)(20), where the first error is statistical and the second is the sum of all systematic errors in quadrature. Applying a 0.7% electromagnetic correction and taking the latest PDG average for F_{B-> D*}(1)|V_cb| leads to |V_cb|=(38.7 +/- 0.9_exp +/- 1.0_theo) x 10^-3., Comment: 48 pages, 9 figures. Sections VI and VII D clarified, minor typos corrected and references added. Version published in PRD

The dynamics of systems out of thermal equilibrium is usually treated on a case-by-case basis without knowledge of fundamental and universal principles. We address this problem for a class of driven steady states, namely those mechanically driven at the boundaries such as complex fluids under shear. From a nonequilibrium counterpart to detailed balance (NCDB) we derive a remarkably simple set of invariant quantities which remain unchanged when the system is driven. These new nonequilibrium relations are both exact and valid arbitrarily far from equilibrium. Furthermore, they enable the systematic calculation of transition rates in driven systems with state-spaces of arbitrary connectivity., Comment: 4 pages, 2 figures

The structure of spacetime, quantum field theory, and thermodynamics are all connected through the concepts of the Hawking and Unruh temperatures. The possible detection of the related radiation constitutes a fundamental test of such subtle connections. Here a scheme is presented for the detection of Unruh radiation based on currently available laser systems. By separating the classical radiation from the Unruh-response in frequency space, it is found that the detection of Unruh radiation is possible in terms of soft x-ray photons using current laser-electron beam technology. The experimental constraints are discussed and a proposal for an experimental design is given., Comment: 11 pages, 3 figures, 1 table

At equilibrium, a fluid element, within a larger heat bath, receives random impulses from the bath. Those impulses, which induce stochastic transitions in the system (the fluid element), respect the principle of detailed balance, because the bath is also at equilibrium. Under continuous shear, the fluid element adopts a non-equilibrium steady state. Because the surrounding bath of fluid under shear is also in a non-equilibrium steady state, the system receives stochastic impulses with a non-equilibrium distribution. Those impulses no longer respect detailed balance, but are nevertheless constrained by rules. The rules in question, which are applicable to a wide sub-class of driven steady states, were recently derived [R. M. L. Evans, Phys. Rev. Lett. {\bf 92}, 150601 (2004); J. Phys. A: Math. Gen. {\bf 38}, 293 (2005)] using information-theoretic arguments. In the present paper, we provide a more fundamental derivation, based on the uncontroversial, non-Bayesian interpretation of probabilities as simple ratios of countable quantities. We apply the results to some simple models of interacting particles, to investigate the nature of forces that are mediated by a non-equilibrium noise-source such as a fluid under shear., Comment: 14 pages, 7 figures

We report on the advances in our unquenched calculation of the matrix elements relevant for the analysis of B^0-\bar B^0 mixing using the Asqtad (light quark) and Fermilab (heavy quark) actions. We have calculated the hadronic parameters for the mass and width differences in the neutral B meson system. Preliminary results are presented for f_{B_q}^2 B_q as well as for the ratio \xi^2=f_{B_s}^2 B_{B_s}/f_{B_d}^2 B_{B_d}., Comment: 7 pages, talk at The XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, Germany

A new regime is described for Radiation Pressure Acceleration of a thin foil by an intense laser beam of above 10^20 W/cm^2. Highly monoenergetic proton beams extending to GeV energies can be produced with very high efficiency using circularly polarized light. The proton beams have a very small divergence angle (less than 4 degrees). This new method allows the construction of ultra-compact proton and ion accelerators with ultra-short particle bursts.

We present experimental evidence that the effective medium approximation (EMA), developed by D.C. Morse [Phys. Rev. E {\bf 63}, 031502, (2001)], provides the correct scaling law of the macroscopic plateau modulus $G^{0}\propto\rho^{4/3}L^{-1/3}_{p}$ (where $\rho$ is the contour length per unit volume and $L_{p}$ is the persistence length) of semi-flexible polymer solutions, in the highly entangled concentration regime. Competing theories, including a self-consistent binary collision approximation (BCA), have instead predicted $G^{0}\propto\rho^{7/5}L^{-1/5}_{p}$. We have tested both the EMA and BCA scaling predictions using actin filament (F-actin) solutions which permit experimental control of $L_p$ independently of other parameters. A combination of passive video particle tracking microrheology and dynamic light scattering yields independent measurements of the elastic modulus $G$ and $L_{p}$ respectively. Thus we can distinguish between the two proposed laws, in contrast to previous experimental studies, which focus on the (less discriminating) concentration functionality of $G$., Comment: 4 pages, 6 figures, Phys. Rev. Lett. (accepted)

Magnetic nanoparticles with Neel surface anisotropy, different internal structures, surface arrangements and elongation are modelled as many-spin systems. The results suggest that the energy of many-spin nanoparticles cut from cubic lattices can be represented by an effective one-spin potential containing uniaxial and cubic anisotropies. It is shown that the values and signs of the corresponding constants depend strongly on the particle's surface arrangement, internal structure and elongation. Particles cut from a simple cubic lattice have the opposite sign of the effective cubic term, as compared to particles cut from the face-centered cubic lattice. Furthermore, other remarkable phenomena are observed in nanoparticles with relatively strong surface effects: (i) In elongated particles surface effects can change the sign of the uniaxial anisotropy. (ii) In symmetric particles (spherical and truncated octahedral) with cubic core anisotropy surface effects can change its sign. We also show that the competition between the core and surface anisotropies leads to a new energy that contributes to both the 2nd- and 4th-order effective anisotropies., Comment: 15 PR pages, 19 Figure captions. Get the correct file from http://www.lehman.edu/faculty/dgaranin/EffectiveAnisotropies.pdf

We show that condensation in a capped capillary slit is a continuous interfacial critical phenomenon, related intimately to several other surface phase transitions. In three dimensions (3d), the adsorption and desorption branches correspond to the unbinding of the meniscus from the cap and opening, respectively and are equivalent to 2d-like complete-wetting transitions. For dispersion forces, the singularities on the two branches are distinct, owing to the different interplay of geometry and intermolecular forces. In 2d we establish precise connection, or covariance, with 2d critical-wetting and wedge-filling transitions, i.e. we establish that certain interfacial properties in very different geometries are identical. Our predictions of universal scaling and covariance in finite capillaries are supported by extensive Ising model simulation studies in 2d and 3d., Comment: (4 pages, 2 figures). Phys Rev Lett (accepted)

We present a method of analyzing a set of N time signals f_i(t) that consist of local measurements of the same physical observable taken at N sequential locations Z_i along the length of an experimental device. The result is an algorithm for reconstructing an approximation F(z,t) of the field f(z,t) in the inaccessible regions between the points of measurement. We also explore the conditions needed for this approximation to hold, and test the algorithm under a variety of conditions. We apply this method to analyze the magnetic field measurements taken on the Compact Toroid Injection eXperiment (CTIX) plasma accelerator; providing a direct means of visualizing experimental data, quantifying global properties, and benchmarking simulation., Comment: 17 pages, 9 figures, some changes in notation since version 1

Using a simple mean-field density functional theory theory (DFT), we investigate the structure and phase behaviour of a model colloidal fluid composed of particles interacting via a pair potential which has a hard core of diameter $\sigma$, is attractive Yukawa at intermediate separations and repulsive Yukawa at large separations. We analyse the form of the asymptotic decay of the bulk fluid correlation functions, comparing results from our DFT with those from the self consistent Ornstein-Zernike approximation (SCOZA). In both theories we find rich crossover behaviour, whereby the ultimate decay of correlation functions changes from monotonic to long-wavelength damped oscillatory decay on crossing certain lines in the phase diagram, or sometimes from oscillatory to oscillatory with a longer wavelength. For some choices of potential parameters we find, within the DFT, a $\lambda$-line at which the fluid becomes unstable with respect to periodic density fluctuations. SCOZA fails to yield solutions for state points near such a $\lambda$-line. The propensity to clustering of particles, which is reflected by the presence of a long wavelength $\gg \sigma$, slowly decaying oscillatory pair correlation function, and a structure factor that exhibits a very sharp maximum at small but non zero wavenumbers, is enhanced in states near the $\lambda$-line. We present density profiles for the planar liquid-gas interface and for fluids adsorbed at a planar hard wall. The presence of a nearby $\lambda$-transition gives rise to pronounced long-wavelength oscillations in the one-body densities at both types of interface., Comment: 14 pages, 11 figures

We revisit the paradigm of an ideal gas under isothermal conditions. A moving piston performs work on an ideal gas in a container that is strongly coupled to a heat reservoir. The thermal coupling is modelled by stochastic scattering at the boundaries. In contrast to recent studies of an adiabatic ideal gas with a piston [R.C. Lua and A.Y. Grosberg, \textit{J. Phys. Chem. B} 109, 6805 (2005); I. Bena et al., \textit{Europhys. Lett.} 71, 879 (2005)], container and piston stay in contact with the heat bath during the work process. Under this condition the heat reservoir as well as the system depend on the work parameter $\lambda$ and microscopic reversibility is broken for a moving piston. Our model is thus not included in the class of systems for which the non-equilibrium work theorem has been derived rigorously either by Hamiltonian [C. Jarzynski, \textit{J. Stat. Mech.} P09005 (2004)] or stochastic methods [G.E. Crooks, \textit{J. Stat. Phys.} 90, 1481 (1998)]. Nevertheless the validity of the non-equilibrium work theorem is confirmed both numerically for a wide range of parameter values and analytically in the limit of a very fast moving piston, i.e. in the far non-equilibrium regime., Comment: 11 pages, 8 figures

The effective pair potential between mesoscopic charged particles in a neutralising background medium takes a Yukawa form $\exp(-\lambda r)/r$ with screening length $\lambda^{-1}$. We consider a dilute suspension of such Yukawa particles dispersed in a solvent with correlation length $\xi<\lambda^{-1}$ and show that the Yukawa interaction is `screened' if the pair potentials between solvent particles exhibit Yukawa decay with the same screening length $\lambda^{-1}$. However, if the solvent pair potentials are shorter ranged than the solute Yukawa potentials, then the effective potential between pairs of solute particles is `unscreened', i.e. the effective potential between the solute particles is equal to the bare potential at large particle separations., Comment: 4 pages, 2 figures, accepted for publication in Phys. Rev. E

We analyse the $r \to \infty$ asymptotic decay of the total correlation function, $h(r)$, for a fluid composed of particles interacting via a (point) Yukawa pair potential. Such a potential provides a simple model for dusty plasmas. The asymptotic decay is determined by the poles of the liquid structure factor in the complex plane. We use the hypernetted-chain closure to the Ornstein-Zernike equation to determine the line in the phase diagram, well-removed from the freezing transition line, where crossover occurs in the ultimate decay of $h(r)$, from monotonic to damped oscillatory. We show: i) crossover takes place via the same mechanism (coalescence of imaginary poles) as in the classical one-component plasma and in other models of Coulomb fluids and ii) leading-order pole contributions provide an accurate description of $h(r)$ at intermediate distances $r$ as well as at long range., Comment: 5 pages, 3 figures

We investigate the structure of a binary mixture of particles interacting via purely repulsive (point) Yukawa pair potentials with a common inverse screening length $\lambda$. Using the hyper-netted chain closure to the Ornstein-Zernike equations, we find that for a system with `ideal' (Berthelot mixing rule) pair potential parameters for the interaction between unlike species, the asymptotic decay of the total correlation functions crosses over from monotonic to damped oscillatory on increasing the fluid total density at fixed composition. This gives rise to a Kirkwood line in the phase diagram. We also consider a `non-ideal' system, in which the Berthelot mixing rule is multiplied by a factor $(1+\delta)$. For any $\delta>0$ the system exhibits fluid-fluid phase separation and remarkably the ultimate decay of the correlation functions is now monotonic for all (mixture) state points. Only in the limit of vanishing concentration of either species does one find oscillatory decay extending to $r = \infty$. In the non-ideal case the simple random phase approximation provides a good description of the phase separation and the accompanying Lifshitz line., Comment: 11 pages, 6 figures. Accepted for publication in J. Chem. Phys

We present a density-functional study of a binary phase-separating mixture of soft core particles immersed in a random matrix of quenched soft core particles of larger size. This is a model for a binary polymer mixture immersed in a crosslinked rigid polymer network. Using the replica `trick' for quenched-annealed mixtures we derive an explicit density functional theory that treats the quenched species on the level of its one-body density distribution. The relation to a set of effective external potentials acting on the annealed components is discussed. We relate matrix-induced condensation in bulk to the behaviour of the mixture around a single large particle. The interfacial properties of the binary mixture at a surface of the quenched matrix display a rich interplay between capillary condensation inside the bulk matrix and wetting phenomena at the matrix surface., Comment: 20 pages, 5 figures. Accepted for Phys. Rev. E

We study various manifestations of structural crossover in the properties of a binary mixture of hard-spheres. For homogeneous mixtures that are sufficiently asymmetric, there is a crossover line in the phase diagram such that for thermodynamic states that lie on one side, the decay of the three bulk pair correlation functions is oscillatory with a common wavelength approximately equal to the diameter of the smaller spheres, and for states on the other side, the common wavelength is approximately the diameter of the bigger spheres. Using density functional theory we show that structural crossover manifests itself in the intermediate range decay of i) the one-body density profiles of a hard-sphere mixture adsorbed at planar walls, ii) the effective (depletion) potential between two big hard-spheres immersed in the same binary mixture and iii) the solvation force, or excess pressure, of the same mixture confined between two planar hard-walls. We determine exactly the structural crossover line for a one-dimensional binary mixture of hard-rods and present evidence, based on density functional theory calculations and Monte-Carlo simulations, for structural crossover in homogeneous binary mixtures of hard-disks in two dimensions. By considering a multicomponent mixture of hard-spheres, with an appropriate bimodal distribution of diameters, we argue that structural crossover should still occur in the presence of polydispersity and that our results could be relevant to colloidal mixtures where correlation functions can be measured using real-space techniques., Comment: 18 pages, 11 figures, submitted to Mol. Phys

Using density functional theory we calculate the density profiles of a binary solvent adsorbed around a pair of big solute particles. All species interact via repulsive Gaussian potentials. The solvent exhibits fluid-fluid phase separation and for thermodynamic states near to coexistence the big particles can be surrounded by a thick adsorbed `wetting' film of the coexisting solvent phase. On reducing the separation between the two big particles we find there can be a `bridging' transition as the wetting films join to form a fluid bridge. The potential between the two big particles becomes long ranged and strongly attractive in the bridged configuration. Within our mean-field treatment the bridging transition results in a discontinuity in the solvent mediated force. We demonstrate that accounting for the phenomenon of bridging requires the presence of a non-zero bridge function in the correlations between the solute particles when our model fluid is described within a full mixture theory based upon the Ornstein-Zernike equations., Comment: 28 pages, 8 figures

We investigate the solvation of a hard spherical cavity, of radius $R$, immersed in a fluid for which the interparticle forces are short ranged. For thermodynamic states lying close to the liquid binodal, where the chemical potential deviation $\delta \mu\equiv \mu - \mu_{co}(T)$ is very small and positive, complete wetting by gas (drying) occurs and two regimes of interfacial behavior can be identified. These are characterized by the length scale $R_c=2 \gamma_{gl}^\infty/(\Delta \rho \delta \mu)$, where $\gamma_{gl}^\infty$ is the planar gas-liquid surface tension and $\Delta \rho$ is the difference in coexisting densities at temperature $T$. For $R>R_c$, the interfacial free energy and the density profile of the fluid near the hard wall can be expanded in powers of the curvature $R^{-1}$, in keeping with the analysis of Stillinger and Cotter, J. Chem. Phys. {\bf 55}, 3449 (1971). In the other regime, $R

When modelling driven steady states of matter, it is common practice either to choose transition rates arbitrarily, or to assume that the principle of detailed balance remains valid away from equilibrium. Neither of those practices is theoretically well founded. Hypothesising ergodicity constrains the transition rates in driven steady states to respect relations analogous to, but different from the equilibrium principle of detailed balance. The constraints arise from demanding that the design of any model system contains no information extraneous to the microscopic laws of motion and the macroscopic observables. This prevents over-description of the non-equilibrium reservoir, and implies that not all stochastic equations of motion are equally valid. The resulting recipe for transition rates has many features in common with equilibrium statistical mechanics., Comment: Replaced with minor revisions to introduction and conclusions. Accepted for publication in Journal of Physics A

The global requirements for energy are increasing rapidly as the global population increases and the under-developed nations become more advanced. The traditional fuels used in their traditional ways will become increasingly unable to meet the demand. The need for a review of the energy sources available is paramount, although the subsequent need to develop a realistic strategy to deal with all local and global energy requirements is almost as important. Here attention will be restricted to examining some of the claims and problems of using nuclear power to attempt to solve this major question., Comment: 11 pages; to appear in "Progress in Energy", Nova Science Publishers,Inc., New York

We present an alternative derivation of the dynamical density functional theory for the one body density profile of a classical fluid developed by Marconi and Tarazona [J. Chem. Phys., 110, 8032 (1999)]. Our derivation elucidates further some of the physical assumptions inherent in the theory and shows that it is not restricted to fluids composed of particles interacting solely via pair potentials; rather it applies to general, multi-body interactions. The starting point for our derivation is the Smoluchowski equation and the theory is therefore one for Brownian particles and as such is applicable to colloidal fluids. In the second part of this paper we use the dynamical density functional theory to derive a theory for spinodal decomposition that is applicable at both early and intermediate times. For early stages of spinodal decomposition our non-linear theory is equivalent to the (generalised) linear Cahn-Hilliard theory, but for later times it incorporates coupling between different Fourier components of the density fluctuations (modes) and therefore goes beyond Cahn-Hilliard theory. We describe the results of calculations for a model (Yukawa) fluid which show that the coupling leads to the growth of a second maximum in the density fluctuations, at a wavenumber larger than that of the main peak., Comment: 23 pages, 3 figures

Attention is drawn to the fact that the well-known expression for the red-shift of spectral lines due to a gravitational field may be derived with no recourse to the theory of general relativity. This raises grave doubts over the inclusion of the measurement of this gravitational red-shift in the list of crucial tests of the theory of general relativity., Comment: 3 pages

Just as transition rates in a canonical ensemble must respect the principle of detailed balance, constraints exist on transition rates in driven steady states. I derive those constraints, by maximum information-entropy inference, and apply them to the steady states of driven diffusion and a sheared lattice fluid. The resulting ensemble can potentially explain nonequilibrium phase behaviour and, for steady shear, gives rise to stress-mediated long-range interactions., Comment: 4 pages. To appear in Physical Review Letters

The density profile and Gibbs adsorption of a near-critical fluid confined between two identical planar walls is studied by means of Monte Carlo simulation and by density functional theory for a Lennard-Jones fluid. By reducing the strength of wall-fluid interactions relative to fluid-fluid interactions we observe a crossover from behaviour characteristic of the normal surface universality class, strong critical adsorption, to behaviour characteristic of a 'neutral' wall. The crossover is reminiscent of that which occurs near the ordinary surface transition in Ising films subject to vanishing surface fields. For the 'neutral' wall the density profile, away from the walls, is almost constant throughout the slit capillary and gives rise to an adsorption that is constant along the critical isochore. The same 'neutral' wall yields a line of capillary coexistence that is almost identical to the bulk coexistence line. In the crossover regime we observe features in the density profile similar to those found in the magnetisation profile of the critical Ising film subject to weak surface fields, namely two smooth maxima, located away from the walls, which merge into a single maximum at midpoint as the strength of the wall-fluid interaction is reduced or as the distance between walls is decreased. We discuss similarities and differences between the surface critical behaviour of fluids and of Ising magnets., Comment: 34 pages, 10 figures, submitted to the Journ. Chem. Phys

We argue that for complete wetting at a curved substrate (wall) the wall-fluid surface tension is non-analytic in $R_i^{-1}$, the curvature of the wall and that the density profile of the fluid near the wall acquires a contribution proportional to the gas-liquid surface tension $\times R_i^{-1}$ plus higher-order contributions which are non-analytic in $R_i^{-1}$. These predictions are confirmed by results of density functional calculations for the square-well model of a liquid adsorbed on a hard sphere and on a hard cylinder where complete wetting by gas (drying) occurs. The implications of our results for the solvation of big solvophobic particles are discussed., Comment: 7 pages, 3 figures; to appear in Europhysics Letters

We show that a general density functional approach for calculating the force between two big particles immersed in a solvent of smaller ones can describe systems that exhibit fluid-fluid phase separation: the theory captures effects of strong adsorption (wetting) and of critical fluctuations in the solvent. We illustrate the approach for the Gaussian core model, a simple model of a polymer mixture in solution and find extremely attractive, long ranged solvent mediated potentials between the big particles for state points lying close to the binodal, on the side where the solvent is poor in the species which is favoured by the big particles., Comment: 7 pages, 3 figures, submitted to Europhysics Letters

We examine the geometry of the spaces between particles in diffusion-limited cluster aggregation, a numerical model of aggregating suspensions. Computing the distribution of distances from each point to the nearest particle, we show that it has a scaled form independent of the concentration phi, for both two- (2D) and three-dimensional (3D) model gels at low phi. The mean remoteness is proportional to the density-density correlation length of the gel, xi, allowing a more precise measurement of xi than by other methods. A simple analytical form for the scaled remoteness distribution is developed, highlighting the geometrical information content of the data. We show that the second moment of the distribution gives a useful estimate of the permeability of porous media., Comment: 4 pages

We show that the formal procedure of integrating out the degrees of freedom of the small spheres in a binary hard-sphere mixture works equally well for non-additive as it does for additive mixtures. For highly asymmetric mixtures (small size ratios) the resulting effective Hamiltonian of the one-component fluid of big spheres, which consists of an infinite number of many-body interactions, should be accurately approximated by truncating after the term describing the effective pair interaction. Using a density functional treatment developed originally for additive hard-sphere mixtures we determine the zero, one, and two-body contribution to the effective Hamiltonian. We demonstrate that even small degrees of positive or negative non-additivity have significant effect on the shape of the depletion potential. The second virial coefficient $B_2$, corresponding to the effective pair interaction between two big spheres, is found to be a sensitive measure of the effects of non-additivity. The variation of $B_2$ with the density of the small spheres shows significantly different behavior for additive, slightly positive and slightly negative non-additive mixtures. We discuss the possible repercussions of these results for the phase behavior of binary hard-sphere mixtures and suggest that measurements of $B_2$ might provide a means of determining the degree of non-additivity in real colloidal mixtures.

Unlike atoms, colloidal particles are not identical, but can only be synthesised within a finite size tolerance. Colloids are therefore polydisperse, i.e. mixtures of infinitely many components with sizes drawn from a continuous distribution. We model the crystallisation of hard-sphere colloids (with/without attractions) from an initially amorphous phase. Though the polydisperse hard-sphere phase diagram has been widely studied, it is not straightforwardly applicable to real colloidal crystals, since they are inevitably out of equilibrium. The process by which colloidal crystals form determines the size distribution of the particles that comprise them. Once frozen into the crystal lattice, the particles are caged so that the composition cannot subsequently relax to the equilibrium optimum. We predict that the mean size of colloidal particles incorporated into a crystal is smaller than anticipated by equilibrium calculations. This is because small particles diffuse fastest and therefore arrive at the crystal in disproportionate abundance., Comment: 12 pages, 5 figures