Sequences, modular forms and cellular integrals

It is well-known that the Ap\'ery sequences which arise in the irrationality proofs for $\zeta(2)$ and $\zeta(3)$ satisfy many intriguing arithmetic properties and are related to the $p$th Fourier coefficients of modular forms. In this paper, we prove that the connection to modular forms persists for sequences associated to Brown's cellular integrals and state a general conjecture concerning supercongruences.Comment: 26 pages, to appear in Mathematical Proceedings of the Cambridge Philosophical Societ

An analytical and experimental assessment of flexible road ironwork support structures

This paper describes work undertaken to investigate the mechanical performance of road ironwork installations in highways, concentrating on the chamber construction. The principal aim was to provide the background research which would allow improved designs to be developed to reduce the incidence of failures through improvements to the structural continuity between the installation and the surrounding pavement. In doing this, recycled polymeric construction materials (Jig Brix) were studied with a view to including them in future designs and specifications. This paper concentrates on the Finite Element (FE) analysis of traditional (masonry) and flexible road ironwork structures incorporating Jig Brix. The global and local buckling capacity of the Jig Brix elements was investigated and results compared well with laboratory measurements. FE models have also been developed for full-scale traditional (masonry) and flexible installations in a surrounding flexible (asphalt) pavement structure. Predictions of response to wheel loading were compared with full-scale laboratory measurements. Good agreement was achieved with the traditional (masonry) construction but poorer agreement for the flexible construction. Predictions from the FE model indicated that the use of flexible elements significantly reduces the tensile horizontal strain on the surface of the surrounding asphaltic material which is likely to reduce the incidence of surface cracking

Lessons Learned about Change Capital in the Arts: Reflections on a four-year evaluation of Nonprofit Finance Fund's Leading for the Future initiative

This report takes stock of a four-year evaluation of Leading for the Future: Innovative Support for Artistic Excellence (LFF), an experimental $15 million funding initiative administered by Nonprofit Finance Fund (NFF) with support from the Doris Duke Charitable Foundation (DDCF). The purpose of this analysis is to reflect critically on what was learned from the initiative for the benefit of funders, individual philanthropists and others with an interest in the theory and practice of capitalization as applied to nonprofit arts organizations.The LFF initiative was unique in its exclusive focus on change capital – substantial, flexible, multi-year capital intended to transform how an organization operates and delivers its programs, with the long-term goal of increasing reliable revenue, net of costs. By definition, change capital aims to strengthen an organization's financial position.Ten performing arts organizations received$1 million in change capital, drawn down according to individual plans for change, and an additional $75,000 in planning funds. Exit grants of up to$225,000 were awarded to organizations that made the most progress on their change efforts, for the purpose of advancing ongoing change efforts or seeding new plans.1 The 10 grantees invested LFF change capital in a wide variety of "business model transformations" ranging from building technologies with the potential to attract new donors and audiences, to experimenting with different models for touring, to investing in marketing and development capacities.NFF has previously published a series of working papers, case studies and video highlights from the LFF initiative, exploring the concepts of capital and financial reporting for capital, and documenting the 10 grantees' experiences.2 We will avoid citing the accomplishments and challenges of specific grantees in this report, and focus instead on program level issues and ideas that might be helpful to future investors of change capital. Indeed, the LFF initiative has played out against the backdrop of a national dialogue about capitalization in the nonprofit arts sector, both learning from, and contributing to, a good deal of productive thinking about capital.While the LFF initiative involved large grants, much was learned that might be of value to funders with more modest resources who are interested in exploring the role of capital in the artistic and financial health of the sector

Solving the electrical control of magnetic coercive field paradox

The ability to tune magnetic properties of solids via electric voltages instead of external magnetic fields is a physics curiosity of great scientific and technological importance. Today, there is strong published experimental evidence of electrical control of magnetic coercive fields in composite multiferroic solids. Unfortunately, the literature indicates highly contradictory results. In some studies, an applied voltage increases the magnetic coercive field and in other studies the applied voltage decreases the coercive field of composite multiferroics. Here, we provide an elegant explanation to this paradox and we demonstrate why all reported results are in fact correct. It is shown that for a given polarity of the applied voltage, the magnetic coercive field depends on the sign of two tensor components of the multiferroic solid: magnetostrictive and piezoelectric coefficient. For a negative applied voltage, the magnetic coercive field decreases when the two material parameters have the same sign and increases when they have opposite signs, respectively. The effect of the material parameters is reversed when the same multiferroic solid is subjected to a positive applied voltage

Reversal Modes of Simulated Iron Nanopillars in an Obliquely Oriented Field

Stochastic micromagnetic simulations are employed to study switching in three-dimensional magnetic nanopillars exposed to highly misaligned fields. The switching appears to proceed through two different decay modes, characterized by very different average lifetimes and different average values of the transverse magnetization components.Comment: 3 pages, 4 figure

The Structural Estimation of Principal-Agent Models by Least Squares: Evidence from Land Tenancy in Madagascar

We develop a method to structurally estimate principal-agent models by ordinary least squares (OLS). We set up a general principal-agent model which explicitly incorporates the wealth levels of each party and the opportunity cost to the agent of entering the contract. This yields an optimal contract that is linearized by way of an Nth order Taylor approximation. This in turn imposes N(3N-1)/2 restrictions on the parameters and yields an empirical test of the canonical principal-agent model. In the application, we consider the case where N = 2 and apply our method to a sample of land tenancy contracts in rural Madagascar. Empirical tests lead to consistent failure to reject the hypotheses derived from our structural model, which lends support to our structural method as well as to the canonical principal-agent model.Principal-Agent Models, Contract Theory, Structural Estimations, Risk and Uncertainty, C12, C13, D86, O12, Q12,

Molecular dynamics simulations of reflection and adhesion behavior in Lennard-Jones cluster deposition

We conduct molecular dynamics simulations of the collision of atomic clusters with a weakly-attractive surface. We focus on an intermediate regime, between soft-landing and fragmentation, where the cluster undergoes deformation on impact but remains largely intact, and will either adhere to the surface (and possibly slide), or be reflected. We find that the outcome of the collision is determined by the Weber number, We i.e. the ratio of the kinetic energy to the adhesion energy, with a transition between adhesion and reflection occurring as We passes through unity. We also identify two distinct collision regimes: in one regime the collision is largely elastic and deformation of the cluster is relatively small but in the second regime the deformation is large and the adhesion energy starts to depend on the kinetic energy. If the transition between these two regimes occurs at a similar kinetic energy to that of the transition between reflection and adhesion, then we find that the probability of adhesion for a cluster can be bimodal. In addition we investigate the effects of the angle of incidence on adhesion and reflection. Finally we compare our findings both with recent experimental results and with macroscopic theories of particle collisions.Comment: 18 pages, 13 figure

Tunable magnetization damping in transition metal ternary alloys

We show that magnetization damping in Permalloy, Ni80Fe20 (``Py''), can be enhanced sufficiently to reduce post-switching magnetization precession to an acceptable level by alloying with the transition metal osmium (Os). The damping increases monotonically upon raising the Os-concentration in Py, at least up to 9% of Os. Other effects of alloying with Os are suppression of magnetization and enhancement of in-plane anisotropy. Magnetization damping also increases significantly upon alloying with the five other transition metals included in this study (4d-elements: Nb, Ru, Rh; 5d-elements: Ta, Pt) but never as strongly as with Os.Comment: 4 pages, submitted to Appl. Phys. Let