Squares of characters with few irreducible constituents in finite groups

The research of the first author was partially supported by a grant from NSF.     

The dynamical role of solvent on the ICN photodissociation reaction: connecting experimental observables directly with molecular dynamics simulations

The ICN photodissociation reaction is the prototype system for understanding energy disposal and curve crossing in small molecule bond-breaking. The wide knowledge base on this reaction in the gas phase makes it an excellent test case to explore and understand the influence of a liquid solvent on the photo-induced reaction dynamics. Molecular dynamics simulations that include surface-hopping have addressed numerous aspects of how the solvent should influence non-adiabatic transitions and energy flow and ultimately determine product branching for this reaction system. In this paper, we report femtosecond transient absorption work directly combined with new molecular dynamics simulations that make direct connection with the spectroscopic observables. The full spectral evolution after initiating ICN photodissociation at 266 nm in water and ethanol is recorded with unprecedented time resolution, fast enough to see the nascent products emerge before interacting with the solvent cage. Use of a 266 nm pump maximizes the probability of subsequent caging on the upper diabat while launching large rotational energy release for trajectories emerging on the lower diabat. The 2D dataset yields a map of the different products and how they interconvert. In particular, information on the branching ratio and spectral evolution of the product bands is revealed as the products relax their electronic and rotational degrees of freedom. An evolution from rotationally hot gas-phase like CN (sharp band, at 390 nm) to equilibrated and solvated CN radicals (broad, at 326 nm in water and 415 nm in ethanol) is clearly observed in both solvents, and signals assignable to I* are also captured. The non-adiabatic molecular dynamics simulations focus on identifying when trajectories curve cross, filtering the trajectory ensemble into spectroscopically distinct sub-populations and analyzing the rotational energy for the CN product population. The experimental results, taken together with the MD simulations, establish the initial surface crossing probability and suggest multiple passes through the curve crossing region determine the final product yields and provide a source of freshly torqued CN radicals that continues to top up the population of rotationally hot photoproduct over the first few picoseconds.     

Acoustic centering of sources measured by surrounding spherical microphone arrays

The radiation patterns of acoustic sources have great significance in a wide range of applications, such as measuring the directivity of loudspeakers and investigating the radiation of musical instruments for auralization. Recently, surrounding spherical microphone arrays have been studied for sound field analysis, facilitating measurement of the pressure around a sphere and the computation of the spherical harmonics spectrum of the sound source. However, the sound radiation pattern may be affected by the location of the source inside the microphone array, which is an undesirable property when aiming to characterize source radiation in a unique manner. This paper presents a theoretical analysis of the spherical harmonics spectrum of spatially translated sources and defines four measures for the misalignment of the acoustic center of a radiating source. Optimization is used to promote optimal alignment based on the proposed measures and the errors caused by numerical and array-order limitations are investigated. This methodology is examined using both simulated and experimental data in order to investigate the performance and limitations of the different alignment methods.     

11th Annual BNL Accelerator Test Facility Program Committee and Users' Meeting

The Seventh Annual Users' Meeting of the Canadian Light Source was a great success, as the world's newest synchrotron welcomed close to 400 researchers and students from across Canada, the U.S., Europe and Australia to the University of Saskatchewan on November 17–21, 2004. The plenary session of the Users' Meeting, held November 20, was preceded by five workshops: “XAFS Analysis Using Ifeffit, Athena and Artemis,” “SR Applications in Environmental Science,” “Medical Imaging,” “Protein Crystallography,” and “Applications of Elliptically Polarized Synchrotron Radiation.” Meetings of the Beamline Advisory Committee and beamline teams were held on November 21.

After welcoming remarks by Dr. Alan Anderson, Chair of the CLS User Advisory Committee, the meeting opened with a briefing by CLS Executive Director William Thomlinson regarding the accomplishments made by the CLS over the preceding year.     

Noise-induced linewidth in frequency combs

Frequency combs generated by trains of pulses emitted from mode-locked lasers are analyzed when the center time and phase of the pulses undergo noise-induced random walk, which broadens the comb lines. Asymptotic analysis and computation reveal that, when the standard deviation of the center-time jitter of the nth pulse scales as n(p/2) where p is a jitter exponent, the linewidth of the kth comb line scales as k(2/p). The linear-dispersionless (p=1) and pure-soliton (p=3) dynamics in lasers are derived as special cases of this time-frequency duality relation. In addition, the linewidth induced by phase jitter decreases with power P(out), as (P(out))(-1/p).     

Percolation in living neural networks

We study living neural networks by measuring the neurons' response to a global electrical stimulation. Neural connectivity is lowered by reducing the synaptic strength, chemically blocking neurotransmitter receptors. We use a graph-theoretic approach to show that the connectivity undergoes a percolation transition. This occurs as the giant component disintegrates, characterized by a power law with an exponent beta approximately or = 0.65. Beta is independent of the balance between excitatory and inhibitory neurons and indicates that the degree distribution is Gaussian rather than scale free.     

Cuts,Trees and ℓ<Subscript>1</Subscript>-Embeddings of Graphs*

Motivated by many recent algorithmic applications, this paper aims to promote a systematic study of the relationship between the topology of a graph and the metric distortion incurred when the graph is embedded into ₁ space. The main results are:1. Explicit constant-distortion embeddings of all series-parallel graphs, and all graphs with bounded Euler number. These are the first natural families known to have constant distortion (strictly greater than 1). Using the above embeddings, algorithms are obtained which approximate the sparsest cut in such graphs to within a constant factor.2. A constant-distortion embedding of outerplanar graphs into the restricted class of ₁-metrics known as dominating tree metrics. A lower bound of (log n) on the distortion for embeddings of series-parallel graphs into (distributions over) dominating tree metrics is also presented. This shows, surprisingly, that such metrics approximate distances very poorly even for families of graphs with low treewidth, and excludes the possibility of using them to explore the finer structure of ₁-embeddability.* A preliminary version of this work appeared in Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science, 1999, pp. 399–408. This work was done while the author was at the University of California, Berkeley. Supported in part by NSF grants CCR-9505448 and CCR-9820951.