Long-term planetary integration with individual time steps

Reversible Long-Term Integration with Variable Stepsizes

The numerical integration of reversible dynamical systems is considered. A backward analysis for variable stepsize one-step methods is developed, and it is shown that the numerical solution of a symmetric one-step method, implemented with a reversible stepsize strategy, is formally equal to the exact solution of a perturbed differential equation, which again is reversible. This explains geometr...

Long-Term Contracting with Time-Inconsistent Agents∗

In many contractual relationships, consumers are allowed to terminate agreements at will. We study how removing commitment power from consumers affects equilibrium contracts and welfare when consumers have self-control problems. We show that removing commitment power is welfare improving when consumers are sufficiently dynamically inconsistent. Controlling for impatience, it is easier to sustai...

Successive Refinements in Long-term Integrations of Planetary Orbits

We report on accurate, long-term numerical simulations of the orbits of the major planets in our solar system. The equations of motion are directly integrated by a Störmer multi-step scheme, which is optimized to reduce round-off errors. The physical models are successively refined to include corrections due to general relativity and the finite size of the lunar orbit. In one case, the Earth– M...

Planetary Microlensing: Present Status and Long-term Goals

P19: Long-Term Potentiation

The term synaptic plasticity points to a series of persistent changes related to the activity of synapses. Long-term potentiation (LTP) is a reflection of synaptic plasticity that has an important role in learning and memory. LTP is a long-lasting increase of synaptic activity due to enhancement of excitatory synaptic transmission after a high-frequency train of electrical stimulations. Differe...