Trotter Derivation of Algorithms for Brownian and Dissipative Particle Dynamics

This paper focuses on the temporal discretization of the Langevin dynamics, and on different resulting numerical integration schemes. Using a method based on the exponentiation of time dependent operators, we carefully derive a numerical scheme for the Langevin dynamics, that we found equivalent to the proposal of Ermak, and not simply to the stochastic version of the velocity-Verlet algorithm. However, we checked on numerical simulations that both algorithms give similar results, and share the same ``weak order two'' accuracy. We then apply the same strategy to derive and test two numerical schemes for the dissipative particle dynamics (DPD). The first one of them was found to compare well, in terms of speed and accuracy, with the best currently available algorithms.Comment: to be published in J.Chem.Phy

Injected Power Fluctuations in 1D Dissipative Systems

Using fermionic techniques, we compute exactly the large deviation function (ldf) of the time-integrated injected power in several one-dimensional dissipative systems of classical spins. The dynamics are T=0 Glauber dynamics supplemented by an injection mechanism, which is taken as a Poissonian flipping of one particular spin. We discuss the physical content of the results, specifically the influence of the rate of the Poisson process on the properties of the ldf.Comment: 18 pages, 8 figure

Entropic Elasticity of Phantom Percolation Networks

A new method is used to measure the stress and elastic constants of purely entropic phantom networks, in which a fraction $p$ of neighbors are tethered by inextensible bonds. We find that close to the percolation threshold $p_c$ the shear modulus behaves as $(p-p_c)^f$, where the exponent $f\approx 1.35$ in two dimensions, and $f\approx 1.95$ in three dimensions, close to the corresponding values of the conductivity exponent in random resistor networks. The components of the stiffness tensor (elastic constants) of the spanning cluster follow a power law $\sim(p-p_c)^g$, with an exponent $g\approx 2.0$ and 2.6 in two and three dimensions, respectively.Comment: submitted to the Europhys. Lett., 7 pages, 5 figure

Persistence distributions for non gaussian markovian processes

We propose a systematic method to derive the asymptotic behaviour of the persistence distribution, for a large class of stochastic processes described by a general Fokker-Planck equation in one dimension. Theoretical predictions are compared to simple solvable systems and to numerical calculations. The very good agreement attests the validity of this approach.Comment: 7 pages, 1 figure, to be published in Europhysics Letter

Chapter 2: Where the children are: Exploring quality, community, and support for family, friend and neighbor child care

This chapter describes two studies examining quality of care in Family, Friend, and Neighbor (FFN) child care settings in two separate communities. The findings from two studies are shared and discussed through the use of a socio-cultural theoretical lens that necessitates an exploration of specific communities’ histories as well as current political context. We explicitly list and describe implications for designing successful and culturally responsive professional development initiatives and policies that are responsive to this hard-to-reach group of providers and the families they serve