Analytic calculation of scaling dimensions: Tricritical hard squares and critical hard hexagons

The finite-size corrections, central chargesc, and scaling dimensionsx of tricritical hard squares and critical hard hexagons are calculated analytically. This is achieved by solving the special functional equation or inversion identity satisfied by the commuting row transfer matrices of these lattice models at criticality. The results are expressed in terms of Rogers dilogarithms. For tricritical hard squares we obtainc=7/10,x=3/40, 1/5, 7/8, 6/5 and for hard hexagons we obtainc=4/5,x=2/15, 4/5, 17/15, 4/3, 9/5, in accord with the predictions of conformal and modular invariance.     

The use of polarization effects in electromagnetic inverse scattering problems

We consider the scattering of plane, time-harmonic electromagnetic waves by a perfect conductor D. We first show that the set ?_λ consisting of the span of a fixed linear combination of the electric and magnetic far-field patterns is dense in the space of square-integrable tangential vector fields defined on the unit sphere for all values of the wave number k ≠ 0 provided that Im k ≥0. We next consider the affine hull ??_λ of ?_λ and characterize the set ? in terms of electric Herglotz fields. This result is then used to derive an optimization scheme for solving the inverse scattering problem of determining D from a knowledge of ?_λ and it is shown that this (unconstrained) optimization scheme has zero as its greatest lower bound.     

Effective primality tests for integers of the formsN=k3 n +1 andN=k2 m 3 n +1

Using third roots of unity Proth's theorem for primality testing is generalized to integers of the formN=k3 ⁿ +1, avoiding the use of Lucas sequences which are more suitable ifN+1 is factored instead ofN–1. This approach has the advantage of being easily combined with Proth's test and gives polynomial time algorithms for testing integers of the formN=k2 ^m 3 ⁿ +1.     

Femtosecond laser-induced damage of gold films

Single- and multi-shot ablation thresholds of gold films in the thickness range of 31-1400 nm were determined employing a Ti:sapphire laser delivering pulses of 28 fs duration, 793 nm center wavelength at 1 kHz repetition rate. The gold layers were deposited on BK7 glass by an electron beam evaporation process and characterized by atomic force microscopy and ellipsometry. A linear dependence of the ablation threshold fluence F_th on the layer thickness d was found for d ≤ 180 nm. If a film thickness of about 180 nm was reached, the damage threshold remained constant at its bulk value. For different numbers of pulses per spot (N-on-1), bulk damage thresholds of ∼0.7 J cm⁻² (1-on-1), 0.5 J cm⁻² (10-on-1), 0.4 J cm⁻² (100-on-1), 0.25 J cm⁻² (1000-on-1), and 0.2 J cm⁻² (10000-on-1) were obtained experimentally indicating an incubation behavior. A characteristic layer thickness of L_c ≈ 180 nm can be defined which is a measure for the heat penetration depth within the electron gas before electron-phonon relaxation occurs. L_c is by more than an order of magnitude larger than the optical absorption length of α⁻¹ ≈ 12 nm at 793 nm wavelength.     

13C solid state NMR investigation of structural relaxation of the polymer backbone in poly (ethylmethacrylate)

Geometry and time scale of structural relaxation of poly(n-alkylmethacrylates) above the glass transition is studied by temperature dependent one- and two-dimensional 13C-NMR spectroscopy. The geometry of the isotropization of the polymer backbone as deduced from detailed analysis of spectral line shapes is identified as random angular jumps. Analysis of echo decays confirms that at a given temperature this isotropization can adequately be described with a single correlation time. The results are discussed in terms of conformational memory and local structure recently identified in these polymeric glasses.     

Towards the Evaluation of the Relevant Degrees of Freedom in Nonlinear Partial Differential Equations

We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical method providing the fundamental concepts of a numerical algorithm applicable to various dynamical systems. We examine dynamical scaling characteristics in the short-time and the long-time evolution regime providing only a reduced number of degrees of freedom to the evolution process.     

Colloidal Analysis of Particles Extracted from Microalloyed Steels

Different colloidal particle characterization methods are examined for their suitability to determine the particle size distribution of particles extracted from steels. Microalloyed steels are dissolved to extract niobium and titanium carbonitride particles that are important for the mechanical properties of these steels. Such particles have sizes ranging from several nanometers to hundreds of nanometers depending on the precipitation stage during the thermomechanically controlled rolling process. The size distribution of the particles is analyzed by dynamic light scattering (DLS), analytical ultracentrifugation (AUC), and hollow fiber flow field-flow fractionation (HF5) and compared to data obtained for reference particles as well as data from electron microscopy, the standard sizing technique used in metallurgy today. AUC and HF5 provide high-quality size distributions, average over large particle numbers that enables statistical analysis, and yield useful insights for alloy design; however, DLS fails due to a lack of resolution. Important aspects in the conversion and comparison of size distributions obtained for broadly distributed particle systems with different measurement principles and the role of surfactants used in sample preparation are discussed.     

Field-theoretic methods in strongly-coupled models of general gauge mediation

An often-exploited feature of the operator product expansion (OPE) is that it incorporates a splitting of ultraviolet and infrared physics. In this paper we use this feature of the OPE to perform simple, approximate computations of soft masses in gauge-mediated supersymmetry breaking. The approximation amounts to truncating the OPEs for hidden-sector current–current operator products. Our method yields visible-sector superpartner spectra in terms of vacuum expectation values of a few hidden-sector IR elementary fields. We manage to obtain reasonable approximations to soft masses, even when the hidden sector is strongly coupled. We demonstrate our techniques in several examples, including a new framework where supersymmetry breaking arises both from a hidden sector and dynamically. Our results suggest that strongly-coupled models of supersymmetry breaking are naturally split.