The momentum distribution and condensate fraction of liquid and solid 4He determined from Green's function Monte Carlo calculations using the HFDHE2 pair potential are described. The one-body density matrix and the momentum distribution for liquid 3He derived from variational and fixed-node Green's function Monte Carlo calculations are also reported.

Variational Monte Carlo and several many-fermion GreenVfunction Monte Carlo (GFMC) algorithms are used to study the ground state of liquid 3 He. We report the first mirror-potential GFMC calculations in a many-fermion problem, comparing them with transient estimation and fixed-node studies to illustrate the strengths and weaknesses of each. GFMC results with the Aziz HFDHE2 interaction are in good agreement with experiment, yielding energies within approximately 0.1 K per particle. In addition, each of these calculations predicts a kinetic energy per particle of between 12 and 12.5 K.

No abstract

No abstract

With advances in computing, agent-based models (ABMs) have become a feasible and appealing tool to study biological systems. ABMs are seeing increased incorporation into both the biology and mathematics classrooms as powerful modeling tools to study processes involving substantial amounts of stochasticity, nonlinear interactions, and/or heterogeneous spatial structures. Here we present a brief synopsis of the agent-based modeling approach with an emphasis on its use to simulate biological systems, and provide a discussion of its role and limitations in both the biology and mathematics classrooms.