What Makes a Theory of Infinitesimals Useful? A View by Klein and Fraenkel

Felix Klein and Abraham Fraenkel each formulated a criterion for a theory of infinitesimals to be successful, in terms of the feasibility of implementation of the Mean Value Theorem. We explore the evolution of the idea over the past century, and the role of Abraham Robinson's framework therein

The equation of state at high temperatures from lattice QCD

We present results for the equation of state upto previously unreachable, high temperatures. Since the temperature range is quite large, a comparison with perturbation theory can be done directly.Comment: 7 pages, 5 figures, Lattice 200

The nature of the finite temperature QCD transition as a function of the quark masses

The finite temperature QCD transition for physical quark masses is a crossover. For smaller quark masses a first-order phase transition is expected. Using Symanzik improved gauge and stout improved fermion action for 2+1 flavour staggered QCD we give estimates/bounds for the phase line separating the first-order region from the crossover one. The calculations are carried out on two different lattice spacings. Our conclusion for the critical mass is $m_0 \lesssim 0.07 \cdot m_{phys}$ for $N_T=4$ and $m_0 \lesssim 0.12 \cdot m_{phys}$ for $N_T=6$ lattices.Comment: Talk presented at the XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, Germany. 7 pages, 6 figure

probing the atmosphere with high power, high resolution radars

Observations of radar echoes from the clear atmosphere are presented and the scattering mechanisms responsible for the two basic types of clear-air echoes are discussed. The commonly observed dot echo originates from a point in space and usually shows little variation in echo intensity over periods of about 0.1 second. The second type of clear-air radar echo appears diffuse in space, and signal intensities vary considerably over periods of less than 0.1 second. The echoes often occur in thin horizontal layers or as boundaries of convective activity; these are characterized by sharp gradients of refractive index. Some features of clear-air atmospheric structures as observed with radar are presented. These structures include thin stable inversions, convective thermals, Benard convection cells, breaking gravity waves, and high tropospheric layers which are sufficiently turbulent to affect aircraft

On the p-adic geometry of traces of singular moduli

The aim of this article is to show that p-adic geometry of modular curves is useful in the study of p-adic properties of traces of singular moduli. In order to do so, we partly answer a question by Ono. As our goal is just to illustrate how p-adic geometry can be used in this context, we focus on a relatively simple case, in the hope that others will try to obtain the strongest and most general results. For example, for p=2, a result stronger than Thm.1 is proved in [Boylan], and a result on some modular curves of genus zero can be found in [Osburn] . It should be easy to apply our method, because of its local nature, to modular curves of arbitrary level, as well as to Shimura curves.Comment: 3 pages, Late

A simple method for designing or analyzing an optical communication link

A simple method is described for determining the performance of a free space optical communication link. The method can be used either in the system design (synthesis) mode or in the performance evaluation (analysis) mode. Although restricted to photo counting based detection of pulse position modulated signals, the method is still sufficiently general to accommodate space-based, as well as ground-based, reception

Integral Constraints On cosmological Perturbations and their Energy

We show the relation between Traschen's integral equations and the energy, and ``position of the centre of mass'', of the matter perturbations in a Robertson-Walker spacetime. When the perturbations are ``localised'' we get a set of integral constraints that includes hers. We illustrate them on a simple example.Comment: 19 pages, Tex file, submitted to Classical and Quantum Gravit

The curvature of the QCD phase transition line

We determine the curvature of the phase transition line in the mu-T plane through an analysis of various observables, including the Polyakov loop, the quark number susceptibilities and the susceptibility of the chiral condensate. The second derivative of these quantities with respect to mu was calculated. The measurements were carried out on N_T = 4,6,8 and 10 lattices generated with a Symanzik improved gauge and stout-link improved 2+1 flavour staggered fermion action using physical quark masses.Comment: Talk presented at the XXVI International Symposium on Lattice Field Theory, July 14 - 19, 2008, Williamsburg, Virginia, USA. 7 pages, 6 figure

Mesoscopic Mechanical Resonators as Quantum Non-Inertial Reference Frames

An atom attached to a micrometer-scale wire that is vibrating at a frequency of 100 MHz and with displacement amplitude 1 nm experiences an acceleration magnitude 10^9 ms^-2, approaching the surface gravity of a neutron star. As one application of such extreme non-inertial forces in a mesoscopic setting, we consider a model two-path atom interferometer with one path consisting of the 100 MHz vibrating wire atom guide. The vibrating wire guide serves as a non-inertial reference frame and induces an in principle measurable phase shift in the wave function of an atom traversing the wire frame. We furthermore consider the effect on the two-path atom wave interference when the vibrating wire is modeled as a quantum object, hence functioning as a quantum non-inertial reference frame. We outline a possible realization of the vibrating wire, atom interferometer using a superfluid helium quantum interference setup.Comment: Published versio

Lattice SU(3) thermodynamics and the onset of perturbative behaviour

We present the equation of state (pressure, trace anomaly, energy density and entropy density) of the SU(3) gauge theory from lattice field theory in an unprecedented precision and temperature range. We control both finite size and cut-off effects. The studied temperature window ($0.7... 1000 T_c$) stretches from the glueball dominated system into the perturbative regime, which allows us to discuss the range of validity of these approaches. From the critical couplings on fine lattices we get T_c/\Lambdamsbar=1.26(7) and use this ratio to express the perturbative free energy in $T_c$ units. We also determine the preferred renormalization scale of the Hard Thermal Loop scheme and we fit the unknown $g^6$ order perturbative coefficient at extreme high temperatures $T>100T_c$. We furthermore quantify the nonperturbative contribution to the trace anomaly using two simple functional forms.Comment: 7 pages, Contribution to the The XXVIII International Symposium on Lattice Field Theory; June 14 - 19, 2010, Villasimius, Sardinia, Ital