A key-formula to compute the gravitational potential of inhomogeneous discs in cylindrical coordinates

We have established the exact expression for the gravitational potential of a homogeneous polar cell - an elementary pattern used in hydrodynamical simulations of gravitating discs. This formula, which is a closed-form, works for any opening angle and radial extension of the cell. It is valid at any point in space, i.e. in the plane of the distribution (inside and outside) as well as off-plane, thereby generalizing the results reported by Durand (1953) for the circular disc. The three components of the gravitational acceleration are given. The mathematical demonstration proceeds from the "incomplete version of Durand's formula" for the potential (based on complete elliptic integrals). We determine first the potential due to the circular sector (i.e. a pie-slice sheet), and then deduce that of the polar cell (from convenient radial scaling and subtraction). As a by-product, we generate an integral theorem stating that "the angular average of the potential of any circular sector along its tangent circle is 2/PI times the value at the corner". A few examples are presented. For numerical resolutions and cell shapes commonly used in disc simulations, we quantify the importance of curvature effects by performing a direct comparison between the potential of the polar cell and that of the Cartesian (i.e. rectangular) cell having the same mass. Edge values are found to deviate roughly like 2E-3 x N/256 in relative (N is the number of grid points in the radial direction), while the agreement is typically four orders of magnitude better for values at the cell's center. We also produce a reliable approximation for the potential, valid in the cell's plane, inside and close to the cell. Its remarkable accuracy, about 5E-4 x N/256 in relative, is sufficient to estimate the cell's self-acceleration.Comment: Accepted for publication in Celestial Mechanics and Dynamical Astronom

Discovery and Measurement of Sleptons, Binos, and Winos with a Z'

Extensions of the MSSM could significantly alter its phenomenology at the LHC. We study the case in which the MSSM is extended by an additional U(1) gauge symmetry, which is spontaneously broken at a few TeV. The production cross-section of sleptons is enhanced over that of the MSSM by the process $pp\to Z' \to \tilde{\ell} \tilde{\ell}^*$, so the discovery potential for sleptons is greatly increased. The flavor and charge information in the resulting decay, $\tilde{\ell} \to \ell + {LSP}$, provides a useful handle on the identity of the LSP. With the help of the additional kinematical constraint of an on-shell Z', we implement a novel method to measure all of the superpartner masses involved in this channel. For certain final states with two invisible particles, one can construct kinematic observables bounded above by parent particle masses. We demonstrate how output from one such observable, m_T2, can become input to a second, increasing the number of measurements one can make with a single decay chain. The method presented here represents a new class of observables which could have a much wider range of applicability.Comment: 20 pages, 15 figures; v2 references added and minor change

Width of Sunspot Generating Zone and Reconstruction of Butterfly Diagram

Based on the extended Greenwich-NOAA/USAF catalogue of sunspot groups it is demonstrated that the parameters describing the latitudinal width of the sunspot generating zone (SGZ) are closely related to the current level of solar activity, and the growth of the activity leads to the expansion of SGZ. The ratio of the sunspot number to the width of SGZ shows saturation at a certain level of the sunspot number, and above this level the increase of the activity takes place mostly due to the expansion of SGZ. It is shown that the mean latitudes of sunspots can be reconstructed from the amplitudes of solar activity. Using the obtained relations and the group sunspot numbers by Hoyt and Schatten (1998), the latitude distribution of sunspot groups ("the Maunder butterfly diagram") for the 18th and the first half of the 19th centuries is reconstructed and compared with historical sunspot observations.Comment: 16 pages, 11 figures; accepted by Solar Physics; the final publication will be available at www.springerlink.co

Probability distribution of the sizes of largest erased-loops in loop-erased random walks

We have studied the probability distribution of the perimeter and the area of the k-th largest erased-loop in loop-erased random walks in two-dimensions for k = 1 to 3. For a random walk of N steps, for large N, the average value of the k-th largest perimeter and area scales as N^{5/8} and N respectively. The behavior of the scaled distribution functions is determined for very large and very small arguments. We have used exact enumeration for N <= 20 to determine the probability that no loop of size greater than l (ell) is erased. We show that correlations between loops have to be taken into account to describe the average size of the k-th largest erased-loops. We propose a one-dimensional Levy walk model which takes care of these correlations. The simulations of this simpler model compare very well with the simulations of the original problem.Comment: 11 pages, 1 table, 10 included figures, revte

Cyclotomic integers, fusion categories, and subfactors

Dimensions of objects in fusion categories are cyclotomic integers, hence number theoretic results have implications in the study of fusion categories and finite depth subfactors. We give two such applications. The first application is determining a complete list of numbers in the interval (2, 76/33) which can occur as the Frobenius-Perron dimension of an object in a fusion category. The smallest number on this list is realized in a new fusion category which is constructed in the appendix written by V. Ostrik, while the others are all realized by known examples. The second application proves that in any family of graphs obtained by adding a 2-valent tree to a fixed graph, either only finitely many graphs are principal graphs of subfactors or the family consists of the A_n or D_n Dynkin diagrams. This result is effective, and we apply it to several families arising in the classification of subfactors of index less then 5.Comment: 47 pages, with an appendix by Victor Ostri

The position of graptolites within Lower Palaeozoic planktic ecosystems.

An integrated approach has been used to assess the palaeoecology of graptolites both as a discrete group and also as a part of the biota present within Ordovician and Silurian planktic realms. Study of the functional morphology of graptolites and comparisons with recent ecological analogues demonstrates that graptolites most probably filled a variety of niches as primary consumers, with modes of life related to the colony morphotype. Graptolite coloniality was extremely ordered, lacking any close morphological analogues in Recent faunas. To obtain maximum functional efficiency, graptolites would have needed varying degrees of coordinated automobility. A change in lifestyle related to ontogenetic changes was prevalent within many graptolite groups. Differing lifestyle was reflected by differing reproductive strategies, with synrhabdosomes most likely being a method for rapid asexual reproduction. Direct evidence in the form of graptolithophage 'coprolitic' bodies, as well as indirect evidence in the form of probable defensive adaptations, indicate that graptolites comprised a food item for a variety of predators. Graptolites were also hosts to a variety of parasitic organisms and provided an important nutrient source for scavenging organisms

Measures of process harmonization

Context Many large organizations juggle an application portfolio that contains different applications that fulfill similar tasks in the organization. In an effort to reduce operating costs, they are attempting to consolidate such applications. Before consolidating applications, the work that is done with these applications must be harmonized. This is also known as process harmonization. Objective The increased interest in process harmonization calls for measures to quantify the extent to which processes have been harmonized. These measures should also uncover the factors that are of interest when harmonizing processes. Currently, such measures do not exist. Therefore, this study develops and validates a measurement model to quantify the level of process harmonization in an organization. Method The measurement model was developed by means of a literature study and structured interviews. Subsequently, it was validated through a survey, using factor analysis and correlations with known related constructs. Results As a result, a valid and reliable measurement model was developed. The factors that are found to constitute process harmonization are: the technical design of the business process and its data, the resources that execute the process, and the information systems that are used in the process. In addition, strong correlations were found between process harmonization and process standardization and between process complexity and process harmonization. Conclusion The measurement model can be used by practitioners, because it shows them the factors that must be taken into account when harmonizing processes, and because it provides them with a means to quantify the extent to which they succeeded in harmonizing their processes. At the same time, it can be used by researchers to conduct further empirical research in the area of process harmonization

\sqrt{s}_min: a global inclusive variable for determining the mass scale of new physics in events with missing energy at hadron colliders

We propose a new global and fully inclusive variable \sqrt{s}_{min} for determining the mass scale of new particles in events with missing energy at hadron colliders. We define \sqrt{s}_{min} as the minimum center-of-mass parton level energy consistent with the measured values of the total calorimeter energy E and the total visible momentum \vec{P}. We prove that for an arbitrary event, \sqrt{s}_{min} is simply given by the formula \sqrt{s}_{min}=\sqrt{E^2-P_z^2}+\sqrt{\met^2+M_{inv}^2}, where M_{inv} is the total mass of all invisible particles produced in the event. We use t\bar{t} production and several supersymmetry examples to argue that the peak in the \sqrt{s}_{min} distribution is correlated with the mass threshold of the parent particles originally produced in the event. This conjecture allows a determination of the heavy superpartner mass scale (as a function of the LSP mass) in a completely general and model-independent way, and without the need for any exclusive event reconstruction. In our SUSY examples of several multijet plus missing energy signals, the accuracy of the mass measurement based on \sqrt{s}_{min} is typically at the percent level, and never worse than 10%. After including the effects of initial state radiation and multiple parton interactions, the precision gets worse, but for heavy SUSY mass spectra remains 10%.Comment: 33 pages, 36 figures, discussion on effect of ISR and MPI adde