The phase structure of the two-dimensionalN=2 Wess-Zumino model

We construct a convergent cluster expansion for the two-dimensionalN=2 Wess-Zumino model, in a region of parameter space where there are multiple phase. As a result of this expansion, we are able to construct the infinite volume field theory and demonstrate exponential decay of correlations. We are also able to investigate the different phases of the model, develop the phase diagram, and show that the free energy of each phase vanishes.Supported in part by National Science Foundation grants DMS 90-08827, PHY/DMS 88-16214 and DMS 88-58073Supported in part by National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship DMS 88-07291     

Arbitrarily large solutions of the conformal scalar curvature problem at an isolated singularity

We study the conformal scalar curvature problem

where is a continuous function. We show that a necessary and sufficient condition on for this problem to have positive solutions which are arbitrarily large at is that be less than 1 on a sequence of points in which tends to .

     

A vanishing theorem for supersymmetric quantum field theory and finite size effects in multiphase cluster expansions

We apply cluster expansion methods to to theN=2 Wess-Zumino models in finite volume, in two space-time dimensions. We show that in the region of convergence of the cluster expansion, a vanishing theorem holds for the supercharge of the theory; that is, the dimension of the kernel of the Hamiltonian is equal to the index of the supercharge.Supported in part by National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship DMS 90-07206Supported in part by National Science Foundation Mathematical Sciences Postodoctoral Research Fellowship DmS 88-07291     

Recasting the (Synchrosqueezed) Short-Time Fourier Transform as an Instantaneous Spectrum

In a previous work, we proposed a time-frequency analysis called instantaneous spectral analysis (ISA), which generalizes the notion of the Fourier spectrum and in which instantaneous frequency is utilized to the fullest extent. In this paper, we recast both the Fourier transform (FT) and filterbank (FB) interpretations of the short-time Fourier transform (STFT) as instantaneous spectra. We show that to recast the FB interpretation of STFT as an instantaneous spectrum with valid structure, frequency reassignment is a fundamental necessity, thus demonstrating that this IS is closely related to the synchrosqueezed STFT. This result provides a new theoretical motivation for the synchrosqueezed STFT. Finally, we illustrate through example the instantaneous spectra corresponding to the FT and FB interpretations of STFT using two closed-form examples.     

A dynamical systems approach to mixing and segregation of granular materials in tumblers

The physics of granular matter is one of the big questions in science. Granular matter serves as a prototype of collective systems far from equilibrium and fundamental questions remain. At the same time, an understanding of granular matter has tremendous practical importance. Among practical problems, granular mixing and its interplay with segregation is arguably at the top of the list in terms of impact. Granular mixing in three-dimensional systems is complicated, as flow induces segregation by particle size or density. Several approaches and points of view for analysis are possible in principle, ranging from continuum to discrete. Flow and segregation in three-dimensional systems is seemingly complicated; however, to a reasonable approximation, all of the dynamics takes place in a thin flowing surface layer. This observation, coupled with key experimental results, leads to a simple, compact and extensible continuum-based dynamical systems framework applicable to time-periodic flow in quasi-two-dimensional tumblers and three-dimensional systems (such as spheres and cubes) rotated about one or more axes of rotation. The case of time-periodic systems, in its simplest version, can be viewed as a mapping of a domain into itself. The placement of periodic points can be investigated using symmetry concepts; the character of the periodic points and associated manifolds provides a skeleton for the flow and a template for segregation processes occurring in the flow.     

The not-so-peculiar case of calcium oxide: a weakness in atomic natural orbital basis sets for calcium

Atomic natural orbital (ANO) basis sets for calcium may produce surprisingly poor atomic and molecular properties and energetics. The weaknesses in these basis sets may be traced primarily to deficiencies within the sets of d functions which are incapable of effectively correlating the 3s and 3p electrons. Examples are given which show that addition of tight d functions to the ANO basis is required to achieve qualitatively correct energetics and structures for conventionally bonded calcium compounds.     

Sauna,sweat and science II – do we sweat what we drink?

ABSTRACT

Inspired by a previous ‘Sauna, sweat and science’ study [Zech et al. Isot Environ Health Stud. 2015;51(3):439–447] and out of curiosity and enthusiasm for stable isotope and sauna research we aimed at answering the question ‘do we sweat (isotopically) what we drink’? We, therefore, pulse-labelled five test persons in a sauna experiment with beverages that were ²H-enriched at about +25,600?‰. Sweat samples were collected during six sauna rounds and the hydrogen isotope composition δ²H_sweat was determined using an isotope ratio mass spectrometer. Before pulse labelling, δ²H_sweat – reflecting by approximation body water – ranged from –32 to –22?‰. This is ～35?‰ enriched compared to usual mid-European drinking water and can be explained with hydrogen-bearing food as well as with the respiratory loss of ²H-depleted vapour. The absence of a clearly detectable ²H pulse in sweat after pulse labelling and δ²H_sweat results of ≤+250?‰ due to a fast ²H equilibration with body water are moreover a clearly negative answer to our research question also in a short-term consideration. Given that the recovery of the tracer based on an isotope mass balance calculation is clearly below 100?%, we finally answer the question ‘where did the rest of the tracer go?’     

Meeting Reports: Energy-Recovering Linacs for Next-Generation Light Sources

Energy-recovering linear accelerators (ERLs) have the potential of providing two orders of magnitude increase in brightness over third-generation sources while offering bunch lengths as low as tens of femtoseconds for timing experiments. ERLs are different from storage rings in that the electron bunches circulate once only. Thus they are not at equilibrium, and in particular can be packed much more tightly than in storage rings, resulting in brighter sources. However, dumping a 100 mA, 3 GeV beam that carries 300 MW of energy is not practical, so the energy is recovered, and the devices are in some sense energystorage rings.     

The Fundamental Equations of Change in Statistical Ensembles and Biological Populations

A recent article in Nature Physics unified key results from thermodynamics, statistics, and information theory. The unification arose from a general equation for the rate of change in the information content of a system. The general equation describes the change in the moments of an observable quantity over a probability distribution. One term in the equation describes the change in the probability distribution. The other term describes the change in the observable values for a given state. We show the equivalence of this general equation for moment dynamics with the widely known Price equation from evolutionary theory, named after George Price. We introduce the Price equation from its biological roots, review a mathematically abstract form of the equation, and discuss the potential for this equation to unify diverse mathematical theories from different disciplines. The new work in Nature Physics and many applications in biology show that this equation also provides the basis for deriving many novel theoretical results within each discipline.