Jack Wisdom

Bio: Jack Wisdom is an academic researcher from Massachusetts Institute of Technology. The author has contributed to research in topics: Chaotic & Enceladus. The author has an hindex of 43, co-authored 83 publications receiving 8714 citations. Previous affiliations of Jack Wisdom include University of California, Santa Barbara & California Institute of Technology.

Symplectic maps for the N-body problem.

Abstract: The present study generalizes the mapping method of Wisdom (1982) to encompass all gravitational n-body problems with a dominant central mass. The rationale for the generalized mapping method is discussed as well as details for the mapping for the n-body problem. Some refinements of the method are considered, and the relationship of the mapping method to other symplectic integration methods is shown. The method is used to compute the evolution of the outer planets for a billion years. The resulting evolution is compared to the 845 million year evolution of the outer planets performed on the Digital Orerry using standard numerical integration techniques. This calculation provides independent numerical confirmation of the result of Sussman and Wisdom (1988) that the motion of the planet Pluto is chaotic.

Cassini Observes the Active South Pole of Enceladus

Abstract: Cassini has identified a geologically active province at the south pole of Saturn's moon Enceladus. In images acquired by the Imaging Science Subsystem (ISS), this region is circumscribed by a chain of folded ridges and troughs at ∼55°S latitude. The terrain southward of this boundary is distinguished by its albedo and color contrasts, elevated temperatures, extreme geologic youth, and narrow tectonic rifts that exhibit coarse-grained ice and coincide with the hottest temperatures measured in the region. Jets of fine icy particles that supply Saturn's E ring emanate from this province, carried aloft by water vapor probably venting from subsurface reservoirs of liquid water. The shape of Enceladus suggests a possible intense heating epoch in the past by capture into a 1:4 secondary spin/orbit resonance.

The resonance overlap criterion and the onset of stochastic behavior in the restricted three-body problem

Abstract: The resonance overlap criterion for the onset of stochastic behavior is applied to the planar circular-restricted three-body problem with small mass ratio (mu). Its predictions for mu = 0.001, 0.0001, and 0.00001 are compared to the transitions observed in the numerically determined Kolmogorov-Sinai entropy and found to be in remarkably good agreement. In addition, an approximate scaling law for the onset of stochastic behavior is derived.

Decoherence, einselection, and the quantum origins of the classical

Abstract: as quantum engineering. In the past two decades it has become increasingly clear that many (perhaps all) of the symptoms of classicality can be induced in quantum systems by their environments. Thus decoherence is caused by the interaction in which the environment in effect monitors certain observables of the system, destroying coherence between the pointer states corresponding to their eigenvalues. This leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly nonlocal ''Schrodinger-cat states.'' The classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit. Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between the apparatus and the measured system with the classical correlation. Only the preferred pointer observable of the apparatus can store information that has predictive power. When the measured quantum system is microscopic and isolated, this restriction on the predictive utility of its correlations with the macroscopic apparatus results in the effective ''collapse of the wave packet.'' The existential interpretation implied by einselection regards observers as open quantum systems, distinguished only by their ability to acquire, store, and process information. Spreading of the correlations with the effectively classical pointer states throughout the environment allows one to understand ''classical reality'' as a property based on the relatively objective existence of the einselected states. Effectively classical pointer states can be ''found out'' without being re-prepared, e.g, by intercepting the information already present in the environment. The redundancy of the records of pointer states in the environment (which can be thought of as their ''fitness'' in the Darwinian sense) is a measure of their classicality. A new symmetry appears in this setting. Environment-assisted invariance or envariance sheds new light on the nature of ignorance of the state of the system due to quantum correlations with the environment and leads to Born's rules and to reduced density matrices, ultimately justifying basic principles of the program of decoherence and einselection.

A long-term numerical solution for the insolation quantities of the Earth

Abstract: We present here a new solution for the astronomical computation of the insolation quantities on Earth spanning from -250 Myr to 250 Myr. This solution has been improved with respect to La93 (Laskar et al. [CITE]) by using a direct integration of the gravitational equations for the orbital motion, and by improving the dissipative contributions, in particular in the evolution of the Earth–Moon System. The orbital solution has been used for the calibration of the Neogene period (Lourens et al. [CITE]), and is expected to be used for age calibrations of paleoclimatic data over 40 to 50 Myr, eventually over the full Palaeogene period (65 Myr) with caution. Beyond this time span, the chaotic evolution of the orbits prevents a precise determination of the Earth's motion. However, the most regular components of the orbital solution could still be used over a much longer time span, which is why we provide here the solution over 250 Myr. Over this time interval, the most striking feature of the obliquity solution, apart from a secular global increase due to tidal dissipation, is a strong decrease of about 0.38 degree in the next few millions of years, due to the crossing of the resonance (Laskar et al. [CITE]). For the calibration of the Mesozoic time scale (about 65 to 250 Myr), we propose to use the term of largest amplitude in the eccentricity, related to , with a fixed frequency of /yr, corresponding to a period of 405 000 yr. The uncertainty of this time scale over 100 Myr should be about , and over the full Mesozoic era.

A hybrid symplectic integrator that permits close encounters between massive bodies

Abstract: Mixed-variable symplectic integrators exhibit no long-term accumulation of energy error, beyond that owing to round-off, and they are substantially faster than conventional N-body algorithms. This makes them the integrator of choice for many problems in Solar system astronomy. However, in their original formulation, they become inaccurate whenever two bodies approach one another closely. This occurs because the potential energy term for the pair undergoing the encounter becomes comparable to the terms representing the unperturbed motion in the Hamiltonian. The problem can be overcome using a hybrid method, in which the close encounter term is integrated using a conventional integrator, whilst the remaining terms are solved symplectically. In addition, using a simple separable potential technique, the hybrid scheme can be made symplectic even though it incorporates a non-symplectic component.

Distilling Free-Form Natural Laws from Experimental Data

Abstract: For centuries, scientists have attempted to identify and document analytical laws that underlie physical phenomena in nature. Despite the prevalence of computing power, the process of finding natural laws and their corresponding equations has resisted automation. A key challenge to finding analytic relations automatically is defining algorithmically what makes a correlation in observed data important and insightful. We propose a principle for the identification of nontriviality. We demonstrated this approach by automatically searching motion-tracking data captured from various physical systems, ranging from simple harmonic oscillators to chaotic double-pendula. Without any prior knowledge about physics, kinematics, or geometry, the algorithm discovered Hamiltonians, Lagrangians, and other laws of geometric and momentum conservation. The discovery rate accelerated as laws found for simpler systems were used to bootstrap explanations for more complex systems, gradually uncovering the "alphabet" used to describe those systems.

Chaos: An Introduction to Dynamical Systems

Abstract: One-Dimensional Maps.- Two-Dimensional Maps.- Chaos.- Fractals.- Chaos in Two-Dimensional Maps.- Chaotic Attractors.- Differential Equations.- Periodic Orbits and Limit Sets.- Chaos in Differential Equations.- Stable Manifolds and Crises.- Bifurcations.- Cascades.- State Reconstruction from Data.