The vertex-cover polynomial of a graph

In this paper we define the vertex-cover polynomial Ψ(G,τ) for a graph G. The coefficient of τ^r in this polynomial is the number of vertex covers V′ of G with |V′|=r. We develop a method to calculate Ψ(G,τ). Motivated by a problem in biological systematics, we also consider the mappings f from {1, 2,…,m} into the vertex set V(G) of a graph G, subject to f⁻¹(x)f⁻¹(y)≠ for every edge xy in G. Let F(G,m) be the number of such mappings f. We show that F(G,m) can be determined from Ψ(G,τ).     

μSR at new accelerators

In this paper I speculate upon the potential of muon spin rotation/relaxation/resonance (μSR) for future refinement and/or exploitation at large accelerators like KAON, which might generate muon beams a hundred times more intense than today's best. Several schemes for efficient utilisation of such beams might be well worth implementing on existing muon channels. Work supported by NRC and NSERC.     

Experiments on the interaction of current channels in a laboratoryplasma: relaxation to the force-free state

A series of experiments on the dynamic interaction of two current channels has been performed in the large plasma device, a laboratory device at UCLA. The two current channels are formed by coating the cathode source nonuniformly and then biasing it with respect to an anode 10 m away. The experiment consists of two phases, one in which a net current is drawn through the plasma, and one in which the net current is zero. The current channels twist about each other, merge, and evolve toward a force-free state when a net current is drawn through the plasma. When the net current is zero the interaction between the channels is greatly reduced. The dynamics of the system are dominated by electron pressure and associated electrostatic fields. However, as the currents twist, a small amount of magnetic helicity is generated. The helicity and its temporal rate of change are computed and found to compare within experimental uncertainty to the predicted rate     

SPM-induced spectral compression of picosecond pulses in a single-mode Yb-doped fiber amplifier

In a fiber amplifier, spectral compression due to self-phase modulation is demonstrated for ultrashort pulses. We report the generation of near-transform-limited picosecond pulses with peak powers of several kW at a repetition rate of 74 MHz and diffraction-limited beam quality in a Yb-doped fiber amplifier when seeding with a negative chirped pulse. Received: 17 September 2001 / Revised version: 22 November 2001 / Published online: 17 January 2002     

Elasticity in nanocrystalline Nd2Fe14B+αFe magnetic composites

The dynamic Young modulus (E) of magnetic Nd₂Fe₁₄B+αFe nanocomposites is investigated with mechanical spectroscopy techniques (vibrating reed configuration, f≈1.5 kHz <10⁻⁶). Reduced values of E are obtained (88–152 GPa) as compared with that predicted by the rule of mixtures for the composite (164 GPa). Three contributions to this reduction are briefly discussed: a large volume fraction of the specimen with grain boundary like structure; internal pores, resulting from the high cooling rate during processing (10⁶ K/min) and magneto-mechanical effects. Even when porosity is identified as the principal cause of modulus reduction, magnetic effects are also detected.     

Effects of Au coating on thermal stresses in stainless-to-Kovar packages

A finite-element method (FEM) analysis has been carried out on the thermally-induced stresses generated when stainless steel covers are laser-welded to Au-coated Kovar TO headers during the packaging of semiconductor lasers. In particular, the effect of varying the Au coating thickness of these stresses was investigated. Maximum stresses were found to be reduced as the Au thickness increased. This effect is attributed to the reduction in thermal gradient in the weld region provided by the increased thermal conduction of thicker Au. The result suggests that adequate Au coating thickness is important for ensuring good reliability of opto-electronic packages having laser-welded caps. This revised version was published online in June 2006 with corrections to the Cover Date.     

Glass-forming liquids,anomalous liquids,and polyamorphism in liquids and biopolymers

Summary Glass formation in nature and materials science is reviewed and the recent recognition of polymorphism within the glassy state, polyamorphism, is discussed. The process by which the glassy state originates during the continuous cooling or viscous slowdown process, is examined and the three canonical characteristics of relaxing liquids are correlated through the fragility. The conversion of strong liquids to fragile liquids by pressure-induced coordination number increases is discussed, and then it is shown that for the same type of system it is possible to have the same conversion accomplished via a first-order transition within the liquid state. The systems in which this can happen are of the same type which exhibit polyamorphism, and the whole phenomenology can be accounted for by a recent simple modification of the van der Waals model for tetrahedrally bonded liquids. The concept of complex amorphous systems which can lose a significant number of degrees of freedom through weak first-order transitions is then used to discuss the relation between native and denatured hydrated proteins, since the latter have much in common with plasticized chain polymer systems. Finally, we close the circle by taking a short-time-scale phenomenon given much attention by protein physicists,viz., the onset of an anomaly in the Debye-Waller factor with increasing temperature, and showing that for a wide variety of liquids, including computer-simulated strong and fragile ionic liquids, this phenomenon is closely correlated with the experimental glass transition temperature. This implies that the latter owes its origin to the onset of strong anharmonicity in certain components of the vibrational density of states (evidently related to the boson peak) which then permits the system to gain access to its configurational degrees of freedom. The more anharmonic these vibrational components, the closer to the Kauzmann temperature will commence the exploration of configuration space and, for a given configurational microstate degeneracy, the more fragile the liquid will be. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Strong interactions at low energies

The lectures review some of the basic concepts relevant for an understanding of the low energy properties of the strong interactions: chiral symmetry, spontaneous symmetry breakdown, Goldstone bosons, quark condensate. The effective field theory used to analyze the low energy structure is briefly sketched. As an illustration, I discuss the implications of the recent data on the decay K→ππeν for the magnitude of the quark condensate.