Colloquium Spring 1998
No Colloquium: Martin Luther King Day, University Holiday
January 30 Note Special Day and Time: 2:00 pm. Room: SLH 100
The asymptotic behavior of a physical system depends on its parameters. Mathematically, such a behavior is determined by some asymptotic set in the phase space of the system. The asymptotic set can be either regular (e.g., periodic) or chaotic. When the asymptotic set is chaotic, the system exhibits sensitive dependence on initial conditions. That is, small changes in the initial state of the system can cause large changes in the final state. A chaotic set can be either attracting or nonattracting, the former corresponds to a chaotic attractor and the latter to a chaotic saddle which leads to transient chaos. When the asymptotic set is a chaotic attractor, the state of the system appears random all the time. When the asymptotic set is a nonattracting chaotic saddle, the system's state usually behaves randomly for a finite amount of time but eventually becomes regular. In the phase space, a chaotic saddle is typically a fractal set (Cantor-like set) of points with an infinite number of gaps of all scales in between. As a system parameter changes, qualitative changes in the asymptotic set of the system can occur. These changes can be, for example, from a chaotic attractor to a chaotic saddle, or from a chaotic set to a regular set, or vice versa.
The focus of this talk is on sudden changes in chaotic attractors as a system parameter changes. This is referred to as a "crisis." We will describe sudden enlargement of chaotic attractors, an event called the interior crisis. Before the crisis, the asymptotic set of the system is a small chaotic attractor. An interior crisis is triggered by the collision of a small chaotic attractor with a coexisting nonattracting chaotic saddle. After the crisis, the asymptotic set of the system is a larger chaotic attractor, and the original chaotic saddle is converted into part of the larger chaotic attractor. The gaps in-between various pieces of the chaotic saddle are densely filled after the crisis. This is referred to as "gap filling." We argue that gap filling is caused by the birth of an infinite number of unstable periodic orbits which do not exist before the crisis. As a consequence, we expect the topological entropy, which quantifies the number of periodic orbits of a chaotic set, to grow after the crisis. We give a quantitative scaling theory for the growth of the topological entropy. The theory is confirmed by numerical experiments, and it is expected to be universal, i.e., it holds regardless details of the system.
I will motivate this topic by discussing the two limits of temperature: the highest conceivable temperature as well as the very lowest temperature attained in a physics laboratory. I will then review the development of temperature scales, touching briefly on the biographies of the two most important contributors: William Thompson (later, Lord Kelvin) and Daniel Fahrenheit. I will then discuss the present issue in thermometry: The current international temperature scale, ITS-90, does not extend below 0.65 K. Many low-temperature experiments have been conducted far below this limit and call for an extension of this scale to a temperature at least as low as 0.001 K. The status of the international effort to achieve this goal is reviewed.
February 6 Note Special Day and Time: 2:00 pm. Room: SLH 100
The origin and nature of particles at the high end of the cosmic ray spectrum is unknown. This mystery attracts increasing attention since anticipated experiments such as the international Pierre Auger Project promise a strongly growing amount of data in the near future. Detailed testable predictions within theoretical scenarios therefore increasingly employ computational methods, for example, to model cosmic ray propagation. Proposed source mechanisms range from conventional shock acceleration to the decay of supermassive Grand Unification scale particles released from topological defects. These scenarios often link several subfields, from the astrophysics of gamma rays, neutrinos, and cosmic magnetic fields to the theory of particle interactions beyond accelerator energies. We present an overview of this quickly growing field.
February 13 Note Special Day and Time: 2:00 pm. Room: SLH 100
No Colloquium: President's Day, University Holiday
February 20 Note Special Day. Tentative Time: 2:00 pm. Room: SLH 100
This talk will be devoted to some recent calculations of the density expansion of the thermodynamical functions for a classical multicomponent system made of charged particles interacting via the hard sphere Coulomb potential. The general method of this virial expansion has been already studied in previous papers [1-3] in the more general situation of a quantum Coulomb plasma. Here, the diagrammatic expansion is the analog of the familiar Abe-Meeron [4,5] expansion for a classical one-component plasma. The exact density expansion of the free energy and of the pressure are explicitly calculated up to the power of density rho(5/2). The corresponding expressions include, in a systematic and coherent way, the contributions of the various physical effects such as corrections beyond the Debye screening and creation of dipolar pairs. Long range correction terms proportional to rho(p/2)*log(rho) (p=4,5) have been also derived and indicate the behavior of the Coulomb potential in the mechanism of pair creation. The range of validity of this expansion is controlled by selective rules preventing the collapse of big neutral entities.
 A. Alastuey and A. Perez, Europhys. Lett. 20, 19 (1992)
 A. Alastuey, F. Cornu and A. Perez, Phys. Rev. E 51, 1725 (1995)
 A. Alastuey and A. Perez, Phys. Rev. E 53, 5714 (1996)
 R. Abe, Progr. Theor. Phys. 22, 213 (1959)
 E.Meeron, J. Chem. Phys. 28, 630 (1958)
Recent advances in laser cooling and trapping of atoms have produced exciting new results including the observation of Bose-Einstein condensation and prospects for atom lasers. These advances, believed to be a sample of many more to come, hold the promise for providing the physics community with exciting new areas of research, as well as significant future technological applications. Despite these prospects in the laboratory, many interesting research problems in laser cooling and atomic physics require the micro-gravity environment of space. This talk will cover some of the relevant aspects of laser cooling and trapping, and will introduce the current plans by NASA to support space based research in this area. Opportunities for graduate student research at JPL in laser cooling and trapping will also be discussed.
Science Policy in China, Challenges for Basic Research
Fudan University, China
The insurance and reinsurance industries take on a variety of kinds of risk in exchange for a premium. The risk is traditionally determined by the past history of insured losses through an actuarial approach. In reality, some kinds of risks cannot be determined by such an actuarial analysis and require true forecasts. This is notably true of risks that are either rare or where the likelihood of occurrence changes through time. The most important of these are tropical cyclones and earthquakes and in some cases environmental pollution and product liability. As this industry has becomes aware of the value of the underlying science in these areas, it has forced them into creative interactions with the academic community. Shared risks and external regulations also give a unique value to public, peer-reviewed information in many of these contexts that enhances the possibility of mutually-beneficial links with academia. As insurance companies merge with other areas of the financial markets, it has also lead to new finance products that again require academic expertise to develop.
I will focus on climate science and insurance risk as the main topic of the discussion because of a unique pilot program that I co-founded in Bermuda. It illustrates the basic issues in joint projects between scientists and businesses where the "product" is public understanding rather than a patentable item. I will then present some of the new areas that we are currently developing at USC to expand this type of interaction into other scientific fields. The demand for academic expertise in these areas is great and it promises to be a valuable source of jobs for natural scientists in the future.
For additional background information, please see:
Michaels, A., D. Malmquist, A. Knap and A. Close. 1997. "Climate Science and Insurance Risk" Nature 389:225-227