New bounds on the Lieb-Thirring constants

Improved estimates on the constants $L_{\gamma,d}$, for $1/2<\gamma<3/2$, $d\in N$ in the inequalities for the eigenvalue moments of Schr\"{o}dinger operators are established

A diagnostic model framework for water use in rice-based irrigation systems

Models / Crop-based irrigation / Rice / Water use / Irrigation management / Constraints / Water availability / Water balance / Sensitivity analysis / Irrigation requirements / Ivory Coast / Loka Catchment Area

LpL^p-approximation of the integrated density of states for Schr\"odinger operators with finite local complexity

We study spectral properties of Schr\"odinger operators on \RR^d. The electromagnetic potential is assumed to be determined locally by a colouring of the lattice points in \ZZ^d, with the property that frequencies of finite patterns are well defined. We prove that the integrated density of states (spectral distribution function) is approximated by its finite volume analogues, i.e.the normalised eigenvalue counting functions. The convergence holds in the space $L^p(I)$ where $I$ is any finite energy interval and $1\leq p< \infty$ is arbitrary.Comment: 15 pages; v2 has minor fixe

Connectivity and tree structure in finite graphs

Considering systems of separations in a graph that separate every pair of a given set of vertex sets that are themselves not separated by these separations, we determine conditions under which such a separation system contains a nested subsystem that still separates those sets and is invariant under the automorphisms of the graph. As an application, we show that the $k$-blocks -- the maximal vertex sets that cannot be separated by at most $k$ vertices -- of a graph $G$ live in distinct parts of a suitable tree-decomposition of $G$ of adhesion at most $k$, whose decomposition tree is invariant under the automorphisms of $G$. This extends recent work of Dunwoody and Kr\"on and, like theirs, generalizes a similar theorem of Tutte for $k=2$. Under mild additional assumptions, which are necessary, our decompositions can be combined into one overall tree-decomposition that distinguishes, for all $k$ simultaneously, all the $k$-blocks of a finite graph.Comment: 31 page

Eigenvalue Bounds for Perturbations of Schrodinger Operators and Jacobi Matrices With Regular Ground States

We prove general comparison theorems for eigenvalues of perturbed Schrodinger operators that allow proof of Lieb--Thirring bounds for suitable non-free Schrodinger operators and Jacobi matrices.Comment: 11 page

Conservative Space and Time Regularizations for the ICON Model

In this article, we consider two modified (regularized) versions of the shallow water equations which are of potential interest for the construction of global oceanic and atmospheric models. The first modified system is the Lagrangian averaged shallow water system, which involves the use of a regularized advection velocity and which has been recently proposed as a turbulence parametrization for ocean models in order to avoid an excessive damping of the computed solution. The second modified system is the pressure regularized shallow water system, which provides an alternative to traditional semi-implicit time integration schemes and which results in larger freedom in the design of the time integrator and in a better treatment of nearly geostrophic flows. The two modified systems are both nondissipative, in that they do not result in an increase of the overall dissipation of the flow. We first show how the numerical discretization of the two regularized equation sets can be constructed in a natural way within the finite difference formulation adopted for the ICON general circulation model currently under developed at the Max Planck Institute for Meteorology and at the German Weather Service. The resulting scheme is then validated on a set of idealized tests in both planar and spherical geometry, and the effects of the considered regularizations on the computed solution are analyzed concerning: stability properties and maximum allowable time steps, similarities and differences in the behavior of the solutions, discrete conservation of flow invariants such as total energy and enstrophy. Our analysis should be considered as a first step toward the use of the regularization ideas in the simulation of more complex and more realistic flows

Lieb-Thirring inequalities for geometrically induced bound states

We prove new inequalities of the Lieb-Thirring type on the eigenvalues of Schr\"odinger operators in wave guides with local perturbations. The estimates are optimal in the weak-coupling case. To illustrate their applications, we consider, in particular, a straight strip and a straight circular tube with either mixed boundary conditions or boundary deformations.Comment: LaTeX2e, 14 page

Optimizing the total energy consumption and CO₂ emissions by distributing computational workload among worldwide dispersed data centers

Major internet service providers have built and are currently building the world's largest data centres (DCs), which has already resulted in significant global energy consumption. Energy saving measures, from chip to building level, have been introduced gradually in recent decades. However, there is further potential for savings by assessing the performance of different DCs on a wider scale and evaluating information technology (IT) workload distribution strategies among these DCs. This paper proposes a methodology to optimize the electricity consumption and CO2 emissions by distributing IT workload across multiple imaginary DCs. The DCs are modelled and controlled in a virtual test environment based on a building energy simulation (BES) tool (TRNSYS). A controller tool (Matlab) is used to support testing and tuning of the optimization algorithm. A case study, consisting of the distribution of IT workload across four different types of data centers in multiple locations with different climate conditions, is presented. The case study will illustrate.</p