Model building with multiple dependent variables and constraints

The most widely used method for finding relationships between several quantities is multiple regression. This however is restricted to a single dependent variable. We present a more general method which allows models to be constructed with multiple variables on both sides of an equation and which can be computed easily using a spreadsheet program. The underlying principle (originating from canonical correlation analysis) is that of maximising the correlation between the two sides of the model equation. This paper presents a fitting procedure which makes it possible to force the estimated--model to satisfy constraint conditions which it is required to possess, these may arise from--theory, prior knowledge or be intuitively obvious. We also show that the least squares approach--to the problem is inadequate as it produces models which are not scale invariant.Peer reviewe

Device for in-situ cleaving of hard crystals

Cleaving crystals in a vacuum chamber is a simple method for obtaining atomically flat and clean surfaces for materials that have a preferential cleaving plane. Most in-situ cleavers use parallel cutting edges that are applied from two sides on the sample. We found in ambient experiments that diagonal cutting pliers, where the cleavage force is introduced in a single point instead of a line work very well also for hard materials. Here, we incorporate the diagonal cutting plier principle in a design compatible with ultra-high vacuum requirements. We show optical microscopy (mm scale) and atomic force microscopy (atomic scale) images of NiO(001) surfaces cleaved with this device.Comment: 7 pages, 3 figures Submitted to Review of Scientific Instruments (2005

Area law violation for the mutual information in a nonequilibrium steady state

We study the nonequilibrium steady state of an infinite chain of free fermions, resulting from an initial state where the two sides of the system are prepared at different temperatures. The mutual information is calculated between two adjacent segments of the chain and is found to scale logarithmically in the subsystem size. This provides the first example of the violation of the area law in a quantum many-body system outside a zero temperature regime. The prefactor of the logarithm is obtained analytically and, furthermore, the same prefactor is shown to govern the logarithmic increase of mutual information in time, before the system relaxes locally to the steady state.Comment: 7 pages, 5 figures, final version, references adde

Classification of Planetary Nebulae by their Departure from Axisymmetry

We propose a scheme to classify planetary nebulae (PNe) according to their departure from axisymmetric structure. We consider only departure along and near the equatorial plane, i.e., between the two sides perpendicular to the symmetry axis of the nebula. We consider 6 types of departure from axisymmetry: (1) PNe whose central star is not at the center of the nebula; (2) PNe having one side brighter than the other; (3) PNe having unequal size or shape of the two sides; (4) PNe whose symmetry axis is bent, e.g., the two lobes in bipolar PNe are bent toward the same side; (5) PNe whose main departure from axisymmetry is in the outer regions, e.g., an outer arc; (6) PNe which show no departure from axisymmetry, i.e., any departure, if it exists, is on scales smaller than the scale of blobs, filaments, and other irregularities in the nebula. We discuss the connection between departure types and the physical mechanisms that may cause them, mainly due to the influence by a stellar binary companion. We find that about 50 percents of all PNe possess large-scale departure from axisymmetry. This number is larger than that expected from the influence of binary companions, namely 25-30 percents. We argue that this discrepancy comes from many PNe whose departure from axisymmetry, mainly unequal size, shape, or intensity, results from the presence of long-lived and large, hot or cool, spots on the surface of their AGB progenitors. Such spots locally enhance mass loss rate, leading to a deparure from axisymmetry, mainly near the equator, in the descendant PN.Comment: 10 pages + 1 table. Submitted to MNRA

Critical Percolation in Finite Geometries

The methods of conformal field theory are used to compute the crossing probabilities between segments of the boundary of a compact two-dimensional region at the percolation threshold. These probabilities are shown to be invariant not only under changes of scale, but also under mappings of the region which are conformal in the interior and continuous on the boundary. This is a larger invariance than that expected for generic critical systems. Specific predictions are presented for the crossing probability between opposite sides of a rectangle, and are compared with recent numerical work. The agreement is excellent.Comment: 10 page

A universal result on central charges in the presence of double-trace deformations

We study large N conformal field theories perturbed by relevant double-trace deformations. Using the auxiliary field trick, or Hubbard-Stratonovich transformation, we show that in the infrared the theory flows to another CFT. The generating functionals of planar correlators in the ultraviolet and infrared CFT's are shown to be related by a Legendre transform. Our main result is a universal expression for the difference of the scale anomalies between the ultraviolet and infrared fixed points, which is of order 1 in the large N expansion. Our computations are entirely field theoretic, and the results are shown to agree with predictions from AdS/CFT. We also remark that a certain two-point function can be computed for all energy scales on both sides of the duality, with full agreement between the two and no scheme dependence.Comment: 15 pages, latex2e, no figures. v2: references adde

The transverse magnetoresistance of the two-dimensional chiral metal

We consider the two-dimensional chiral metal, which exists at the surface of a layered, three-dimensional sample exhibiting the integer quantum Hall effect. We calculate its magnetoresistance in response to a component of magnetic field perpendicular to the sample surface, in the low temperature, but macroscopic, regime where inelastic scattering may be neglected. The magnetoresistance is positive, following a Drude form with a field scale, $B_0=\Phi_0/al_{\text{el}}$, given by the transverse field strength at which one quantum of flux, $\Phi_0$, passes through a rectangle with sides set by the layer-spacing, $a$, and the elastic mean free path, $l_{\text{el}}$. Experimental measurement of this magnetoresistance may therefore provide a direct determination of the elastic mean free path in the chiral metal.Comment: submitted to Phys Rev