Fluctuation, time-correlation function and geometric Phase

We establish a fluctuation-correlation theorem by relating the quantum fluctuations in the generator of the parameter change to the time integral of the quantum correlation function between the projection operator and force operator of the ``fast'' system. By taking a cue from linear response theory we relate the quantum fluctuation in the generator to the generalised susceptibility. Relation between the open-path geometric phase, diagonal elements of the quantum metric tensor and the force-force correlation function is provided and the classical limit of the fluctuation-correlation theorem is also discussed.Comment: Latex, 12 pages, no figures, submitted to J. Phys. A: Math & Ge

Energies of S^2-valued harmonic maps on polyhedra with tangent boundary conditions

A unit-vector field n:P \to S^2 on a convex polyhedron P \subset R^3 satisfies tangent boundary conditions if, on each face of P, n takes values tangent to that face. Tangent unit-vector fields are necessarily discontinuous at the vertices of P. We consider fields which are continuous elsewhere. We derive a lower bound E^-_P(h) for the infimum Dirichlet energy E^inf_P(h) for such tangent unit-vector fields of arbitrary homotopy type h. E^-_P(h) is expressed as a weighted sum of minimal connections, one for each sector of a natural partition of S^2 induced by P. For P a rectangular prism, we derive an upper bound for E^inf_P(h) whose ratio to the lower bound may be bounded independently of h. The problem is motivated by models of nematic liquid crystals in polyhedral geometries. Our results improve and extend several previous results.Comment: 42 pages, 2 figure

Topology and Bistability in liquid crystal devices

We study nematic liquid crystal configurations in a prototype bistable device - the Post Aligned Bistable Nematic (PABN) cell. Working within the Oseen-Frank continuum model, we describe the liquid crystal configuration by a unit-vector field, in a model version of the PABN cell. Firstly, we identify four distinct topologies in this geometry. We explicitly construct trial configurations with these topologies which are used as initial conditions for a numerical solver, based on the finite-element method. The morphologies and energetics of the corresponding numerical solutions qualitatively agree with experimental observations and suggest a topological mechanism for bistability in the PABN cell geometry

Solid--on--Solid Model for Adsorption on Self--Affine Substrate: A Transfer Matrix Approach

We study a $d=2$ discrete solid--on--solid model of complete wetting of a rough substrate with random self--affine boundary, having roughness exponent $\zeta_s$. A suitable transfer matrix approach allows to discuss adsorption isotherms, as well as geometrical and thermal fluctuations of the interface. For $\zeta_s\leq 1/2$ the same wetting exponent $\psi=1/3$ as for flat substrate is obtained for the dependence of the coverage, $\theta$, on the chemical potential, $h$ ($\theta\sim h^{-\psi}$ for $h\to 0$). The expected existence of a zero temperature fixed point, leading to $\psi=\zeta_s /(2-\zeta_s)$ for $\zeta_s>1/2$, is verified numerically in spite of an unexpected, very slow convergence to asymptotics.Comment: Standard TeX, 13 pages. 5 PostScript figures available on request. Preprint UDPHIR 94/04/G

Dynamic sampling schemes for optimal noise learning under multiple nonsmooth constraints

We consider the bilevel optimisation approach proposed by De Los Reyes, Sch\"onlieb (2013) for learning the optimal parameters in a Total Variation (TV) denoising model featuring for multiple noise distributions. In applications, the use of databases (dictionaries) allows an accurate estimation of the parameters, but reflects in high computational costs due to the size of the databases and to the nonsmooth nature of the PDE constraints. To overcome this computational barrier we propose an optimisation algorithm that by sampling dynamically from the set of constraints and using a quasi-Newton method, solves the problem accurately and in an efficient way

Les Filles De Cadix (The Maids of Cadiz) / music by Leo Delibes; words by Alfred De Musset

Cover: Photo of Jeanette Mac Donald; Publisher: Robbins Music Corporation (New York)https://egrove.olemiss.edu/sharris_e/1071/thumbnail.jp

Summer Moon

https://digitalcommons.library.umaine.edu/mmb-vp/4882/thumbnail.jp

Soil Health Beneath Amended Switchgrass: Effects of Biochar and Nitrogen on Active Carbon and Wet Aggregate Stability

Perennial crops, like switchgrass (Panicum virgatum L.), are important for bioenergy production and long-term carbon sequestration. Biochar, a byproduct of certain bioenergy production processes, is also identified as a potential tool for carbon sequestration and soil quality improvements, especially in marginal soils. Despite the focus on switchgrass, soil health characteristics under switchgrass production for biomass are unclear. This study focused on identifying the effects of four N rates (0, 17, 34, and 67 kg N ha−1) and biochar application (0 and 9 Mg ha−1) in a 3-year switchgrass field study on a silt loam soil. Soil active carbon (AC) and wet aggregate stability (WAS) were the indicators used to assess soil health. Our results indicated a decline in both AC and WAS over the study period, similar to other studies. Wet aggregate stability declined from 32% in 2018 to 15% in 2019. There were some significant differences between treatments, but no defined trends were observed. A decline in AC from 301 mg C kg soil−1 to 267 mg C kg soil−1 was also observed over the three-year period. Nitrogen rate also affected AC in the last year of study. Several possible explanations for the observed changes are proposed; however, a definitive mechanism is still unknown, thus future research is essential to improve our understanding and provide wider acceptance

Elliptic Quantum Billiard

The exact and semiclassical quantum mechanics of the elliptic billiard is investigated. The classical system is integrable and exhibits a separatrix, dividing the phasespace into regions of oscillatory and rotational motion. The classical separability carries over to quantum mechanics, and the Schr\"odinger equation is shown to be equivalent to the spheroidal wave equation. The quantum eigenvalues show a clear pattern when transformed into the classical action space. The implication of the separatrix on the wave functions is illustrated. A uniform WKB quantization taking into account complex orbits is shown to be adequate for the semiclassical quantization in the presence of a separatrix. The pattern of states in classical action space is nicely explained by this quantization procedure. We extract an effective Maslov phase varying smoothly on the energy surface, which is used to modify the Berry-Tabor trace formula, resulting in a summation over non-periodic orbits. This modified trace formula produces the correct number of states, even close to the separatrix. The Fourier transform of the density of states is explained in terms of classical orbits, and the amplitude and form of the different kinds of peaks is analytically calculated.Comment: 33 pages, Latex2e, 19 figures,macros: epsfig, amssymb, amstext, submitted to Annals of Physic