Is it really possible to grow isotropic on-lattice diffusion-limited aggregates?

In a recent paper (Bogoyavlenskiy V A 2002 \JPA \textbf{35} 2533), an algorithm aiming to generate isotropic clusters of the on-lattice diffusion-limited aggregation (DLA) model was proposed. The procedure consists of aggregation probabilities proportional to the squared number of occupied sites ($k^2$). In the present work, we analyzed this algorithm using the noise reduced version of the DLA model and large scale simulations. In the noiseless limit, instead of isotropic patterns, a $45^\circ$ ($30^\circ$) rotation in the anisotropy directions of the clusters grown on square (triangular) lattices was observed. A generalized algorithm, in which the aggregation probability is proportional to $k^\nu$, was proposed. The exponent $\nu$ has a nonuniversal critical value $\nu_c$, for which the patterns generated in the noiseless limit exhibit the original (axial) anisotropy for $\nu<\nu_c$ and the rotated one (diagonal) for $\nu>\nu_c$. The values $\nu_c = 1.395\pm0.005$ and $\nu_c = 0.82\pm 0.01$ were found for square and triangular lattices, respectively. Moreover, large scale simulations show that there are a nontrivial relation between noise reduction and anisotropy direction. The case $\nu=2$ (\bogo's rule) is an example where the patterns exhibit the axial anisotropy for small and the diagonal one for large noise reduction.Comment: 12 pages, 8 figure

Twist-3 Distribution Amplitudes of K* and phi Mesons

We present a systematic study of twist-3 light-cone distribution amplitudes of $K^*$ and $\phi$ mesons in QCD. The structure of SU(3)-breaking corrections is studied in detail. Non-perturbative input parameters are estimated from QCD sum rules. As a by-product, we update the parameters describing the twist-3 distribution amplitudes of the $\rho$ meson. We also review and update predictions for the twist-2 distribution amplitudes of $\rho$, $K^*$ and $\phi$.Comment: 27 page

Heavy to Light Meson Exclusive Semileptonic Decays in Effective Field Theory of Heavy Quark

We present a general study on exclusive semileptonic decays of heavy (B, D, B_s) to light (pi, rho, K, K^*) mesons in the framework of effective field theory of heavy quark. Transition matrix elements of these decays can be systematically characterized by a set of wave functions which are independent of the heavy quark mass except for the implicit scale dependence. Form factors for all these decays are calculated consistently within the effective theory framework using the light cone sum rule method at the leading order of 1/m_Q expansion. The branching ratios of these decays are evaluated, and the heavy and light flavor symmetry breaking effects are investigated. We also give comparison of our results and the predictions from other approaches, among which are the relations proposed recently in the framework of large energy effective theory.Comment: 18 pages, ReVtex, 5 figures, added references and comparison of results, and corrected signs in some formula

The social geography of childcare: 'making up' the middle class child

Childcare is a condensate of disparate social forces and social processes. It is gendered and classed. It is subject to an excess of policy and political discourse. It is increasingly a focus for commercial exploitation. This is a paper reporting on work in progress in an ESRC funded research project (R000239232) on the choice and provision of pre-school childcare by middle class (service class) families in two contrasting London locations. Drawing on recent work in class analysis the paper examines the relationships between childcare choice, middle class fractions and locality. It suggests that on the evidence of the findings to date, there is some evidence of systematic differences between fractions in terms of values, perspectives and preferences for childcare, but a more powerful case for intra-class similarities, particularly when it comes to putting preferences into practice in the 'making up of a middle class child' through care and education

Characterizing the Initial Phase of Epidemic Growth on some Empirical Networks

A key parameter in models for the spread of infectious diseases is the basic reproduction number $R_0$, which is the expected number of secondary cases a typical infected primary case infects during its infectious period in a large mostly susceptible population. In order for this quantity to be meaningful, the initial expected growth of the number of infectious individuals in the large-population limit should be exponential. We investigate to what extent this assumption is valid by performing repeated simulations of epidemics on selected empirical networks, viewing each epidemic as a random process in discrete time. The initial phase of each epidemic is analyzed by fitting the number of infected people at each time step to a generalised growth model, allowing for estimating the shape of the growth. For reference, similar investigations are done on some elementary graphs such as integer lattices in different dimensions and configuration model graphs, for which the early epidemic behaviour is known. We find that for the empirical networks tested in this paper, exponential growth characterizes the early stages of the epidemic, except when the network is restricted by a strong low-dimensional spacial constraint, such as is the case for the two-dimensional square lattice. However, on finite integer lattices of sufficiently high dimension, the early development of epidemics shows exponential growth.Comment: To be included in the conference proceedings for SPAS 2017 (International Conference on Stochastic Processes and Algebraic Structures), October 4-6, 201

Quantum Cournot equilibrium for the Hotelling-Smithies model of product choice

This paper demonstrates the quantization of a spatial Cournot duopoly model with product choice, a two stage game focusing on non-cooperation in locations and quantities. With quantization, the players can access a continuous set of strategies, using continuous variable quantum mechanical approach. The presence of quantum entanglement in the initial state identifies a quantity equilibrium for every location pair choice with any transport cost. Also higher profit is obtained by the firms at Nash equilibrium. Adoption of quantum strategies rewards us by the existence of a larger quantum strategic space at equilibrium.Comment: 13 pages, 6 tables, 8 figure

Heavy-to-Light Form Factors in the Final Hadron Large Energy Limit of QCD

We argue that the Large Energy Effective Theory (LEET), originally proposed by Dugan and Grinstein, is applicable to exclusive semileptonic, radiative and rare heavy-to-light transitions in the region where the energy release E is large compared to the strong interaction scale and to the mass of the final hadron, i.e. for q^2 not close to the zero-recoil point. We derive the Effective Lagrangian from the QCD one, and show that in the limit of heavy mass M for the initial hadron and large energy E for the final one, the heavy and light quark fields behave as two-component spinors. Neglecting QCD short-distance corrections, this implies that there are only three form factors describing all the pseudoscalar to pseudoscalar or vector weak current matrix elements. We argue that the dependence of these form factors with respect to M and E should be factorizable, the M-dependence (sqrt(M)) being derived from the usual heavy quark expansion while the E-dependence is controlled by the behaviour of the light-cone distribution amplitude near the end-point u=1. The usual expectation of the (1-u) behaviour leads to a 1/E^2 scaling law, that is a dipole form in q^2. We also show explicitly that in the appropriate limit, the Light-Cone Sum Rule method satisfies our general relations as well as the scaling laws in M and E of the form factors, and obtain very compact and simple expressions for the latter. Finally we note that this formalism gives theoretical support to the quark model-inspired methods existing in the literature.Comment: Latex2e, 25 pages, no figure. Slight changes in the title and the phrasing. Misprint in Eq. (25) corrected. To appear in Phys. Rev.