On the Fixed-Point Structure of Scalar Fields

In a recent Letter (K.Halpern and K.Huang, Phys. Rev. Lett. 74 (1995) 3526), certain properties of the Local Potential Approximation (LPA) to the Wilson renormalization group were uncovered, which led the authors to conclude that $D>2$ dimensional scalar field theories endowed with {\sl non-polynomial} interactions allow for a continuum of renormalization group fixed points, and that around the Gaussian fixed point, asymptotically free interactions exist. If true, this could herald very important new physics, particularly for the Higgs sector of the Standard Model. Continuing work in support of these ideas, has motivated us to point out that we previously studied the same properties and showed that they lead to very different conclusions. Indeed, in as much as the statements in hep-th/9406199 are correct, they point to some deep and beautiful facts about the LPA and its generalisations, but however no new physics.Comment: Typos corrected. A Comment - to be published in Phys. Rev. Lett. 1 page, 1 eps figure, uses LaTeX, RevTex and eps

Convergence of derivative expansions of the renormalization group

We investigate the convergence of the derivative expansion of the exact renormalization group, by using it to compute the beta function of scalar field theory. We show that the derivative expansion of the Polchinski flow equation converges at one loop for certain fast falling smooth cutoffs. The derivative expansion of the Legendre flow equation trivially converges at one loop, but also at two loops: slowly with sharp cutoff (as a momentum-scale expansion), and rapidly in the case of a smooth exponential cutoff. Finally, we show that the two loop contributions to certain higher derivative operators (not involved in beta) have divergent momentum-scale expansions for sharp cutoff, but the smooth exponential cutoff gives convergent derivative expansions for all such operators with any number of derivatives.Comment: Latex inc axodraw. 20 page

Properties of derivative expansion approximations to the renormalization group

Approximation only by derivative (or more generally momentum) expansions, combined with reparametrization invariance, turns the continuous renormalization group for quantum field theory into a set of partial differential equations which at fixed points become non-linear eigenvalue equations for the anomalous scaling dimension $\eta$. We review how these equations provide a powerful and robust means of discovering and approximating non-perturbative continuum limits. Gauge fields are briefly discussed. Particular emphasis is placed on the r\^ole of reparametrization invariance, and the convergence of the derivative expansion is addressed.Comment: (Minor touch ups of the lingo.) Invited talk at RG96, Dubna, Russia; 14 pages including 2 eps figures; uses LaTeX, epsf and sprocl.st

Sensitivity of Nonrenormalizable Trajectories to the Bare Scale

Working in scalar field theory, we consider RG trajectories which correspond to nonrenormalizable theories, in the Wilsonian sense. An interesting question to ask of such trajectories is, given some fixed starting point in parameter space, how the effective action at the effective scale, Lambda, changes as the bare scale (and hence the duration of the flow down to Lambda) is changed. When the effective action satisfies Polchinski's version of the Exact Renormalization Group equation, we prove, directly from the path integral, that the dependence of the effective action on the bare scale, keeping the interaction part of the bare action fixed, is given by an equation of the same form as the Polchinski equation but with a kernel of the opposite sign. We then investigate whether similar equations exist for various generalizations of the Polchinski equation. Using nonperturbative, diagrammatic arguments we find that an action can always be constructed which satisfies the Polchinski-like equation under variation of the bare scale. For the family of flow equations in which the field is renormalized, but the blocking functional is the simplest allowed, this action is essentially identified with the effective action at Lambda = 0. This does not seem to hold for more elaborate generalizations.Comment: v1: 23 pages, 5 figures, v2: intro extended, refs added, published in jphy

Fatigue testing a plurality of test specimens and method

Described is a fatigue testing apparatus for simultaneously subjecting a plurality of material test specimens to cyclical tension loading to determine the fatigue strength of the material. The fatigue testing apparatus includes a pulling head having cylinders defined therein which carry reciprocating pistons. The reciprocation of the pistons is determined by cyclical supplies of pressurized fluid to the cylinders. Piston rods extend from the pistons through the pulling head and are attachable to one end of the test specimens, the other end of the test specimens being attachable to a fixed base, causing test specimens attached between the piston rods and the base to be subjected to cyclical tension loading. Because all the cylinders share a common pressurized fluid supply, the breaking of a test specimen does not substantially affect the pressure of the fluid supplied to the other cylinders nor the tension applied to the other test specimens

Pump less wearable microfluidic device for real time pH sweat monitoring

This paper presents the fabrication and the performance of a novel, wearable, robust, flexible and disposable microfluidic device which incorporates micro-Light Emitting Diodes (μ-LEDs) as a detection system, for monitoring in real time mode the pH of the sweat generated during an exercising period

Strong coupling of magnons in a YIG sphere to photons in a planar superconducting resonator in the quantum limit

We report measurements of a superconducting coplanar waveguide resonator (CPWR) coupled to a sphere of yttrium-iron garnet. The non-uniform CPWR field allows us to excite various magnon modes in the sphere. Mode frequencies and relative coupling strengths are consistent with theory. Strong coupling is observed to several modes even with, on average, less than one excitation present in the CPWR. The time response to square pulses shows oscillations at the mode splitting frequency. These results indicate the feasibility of combining magnonic and planar superconducting quantum devices.Comment: 5 pages, 4 figure

An Extended Star Formation History for the Galactic Center from Hubble Space Telescope/NICMOS Observations

We present Hubble Space Telescope (HST) Near-Infrared Camera and Multiobject Spectrometer (NICMOS) observations as evidence that continuous star formation has created much of the central stellar cusp of the Galaxy. The data are the deepest ever obtained for a Galactic Center (GC) population, being $>$50% complete for \mnk$<19.3$, or initial stellar masses $\gtrsim$2 \Msun. We use Geneva and Padova stellar evolution models to produce synthetic luminosity functions for burst and continuous star formation scenarios, finding that the observations are fit best by continuous star formation at a rate that is consistent with the recent star formation activity that produced the three massive young clusters in the central 50 \pc. Further, it is not possible to fit the observations with ancient burst models, such as would be appropriate for an old population like that in Baade's Window or NGC6528