Search results for "boundary"
showing 10 items of 1626 documents
The kite integral to all orders in terms of elliptic polylogarithms
2016
We show that the Laurent series of the two-loop kite integral in $D=4-2\varepsilon$ space-time dimensions can be expressed in each order of the series expansion in terms of elliptic generalisations of (multiple) polylogarithms. Using differential equations we present an iterative method to compute any desired order. As an example, we give the first three orders explicitly.
Spin Chains with Non-Diagonal Boundaries and Trigonometric SOS Model with Reflecting End
2011
In this paper we consider two a priori very different problems: construction of the eigenstates of the spin chains with non parallel boundary magnetic fields and computation of the partition function for the trigonometric solid-on-solid (SOS) model with one reflecting end and domain wall boundary conditions. We show that these two problems are related through a gauge transformation (so-called vertex-face transformation) and can be solved using the same dynamical reflection algebras.
Zero rest-mass fields and the Newman-Penrose constants on flat space
2020
Zero rest-mass fields of spin 1 (the electromagnetic field) and spin 2 propagating on flat space and their corresponding Newman-Penrose (NP) constants are studied near spatial infinity. The aim of this analysis is to clarify the correspondence between data for these fields on a spacelike hypersurface and the value of their corresponding NP constants at future and past null infinity. To do so, Friedrich's framework of the cylinder at spatial infinity is employed to show that, expanding the initial data in terms spherical harmonics and powers of the geodesic spatial distance $\rho$ to spatial infinity, the NP constants correspond to the data for the second highest possible spherical harmonic …
Quantum walk on a cylinder
2016
We consider the 2D alternate quantum walk on a cylinder. We concentrate on the study of the motion along the open dimension, in the spirit of looking at the closed coordinate as a small or "hidden" extra dimension. If one starts from localized initial conditions on the lattice, the dynamics of the quantum walk that is obtained after tracing out the small dimension shows the contribution of several components, which can be understood from the study of the dispersion relations for this problem. In fact, these components originate from the contribution of the possible values of the quasi-momentum in the closed dimension. In the continuous space-time limit, the different components manifest as …
Wick Theorem for General Initial States
2012
We present a compact and simplified proof of a generalized Wick theorem to calculate the Green's function of bosonic and fermionic systems in an arbitrary initial state. It is shown that the decomposition of the non-interacting $n$-particle Green's function is equivalent to solving a boundary problem for the Martin-Schwinger hierarchy; for non-correlated initial states a one-line proof of the standard Wick theorem is given. Our result leads to new self-energy diagrams and an elegant relation with those of the imaginary-time formalism is derived. The theorem is easy to use and can be combined with any ground-state numerical technique to calculate time-dependent properties.
A Model for high-cycle fatigue in polycrystals
2018
A grain-scale formulation for high-cycle fatigue inter-granular degradation in polycrystalline aggregates is presented. The aggregate is represented through Voronoi tessellations and the mechanics of individual bulk grains is modelled using a boundary integral formulation. The inter-granular interfaces degrade under the action of cyclic tractions and they are represented using cohesive laws embodying a local irreversible damage parameter that evolves according to high- cycle continuum damage laws. The consistence between cyclic and static damage, which plays an important role in the redistribution of inter-granular tractions upon cyclic degradation, is assessed at each fatigue solution jump…
Intergrain Effects in the AC Susceptibility of Polycrystalline LaFeAsO_{0.94}F_{0.06}
2010
The AC susceptibility, chi, at zero DC magnetic field of a polycrystalline sample of LaFeAsO_{0.94}F_{0.06} (Tc ≈ 24 K) has been investigated as a function of the temperature, the amplitude of the AC magnetic field (in the range Hac = 0.003 Oe - 4 Oe) and the frequency (in the range f = 10 kHz - 100 kHz). The chi(T) curve exhibits the typical two-step transition arising from the combined response of superconducting grains and intergranular weak-coupled medium. The intergranular part of chi strongly depends on both the amplitude and the frequency of the AC driving field, from few Kelvin below Tc down to T = 4.2 K. Our results show that, in the investigated sample, the intergrain critical cur…
Reconstruction of 3D grain boundaries from rock thin sections, using an advanced polarised-light microscopy method
2017
Grain boundaries play a significant role in materials by initiating reactions and collecting impurities. Here we present FAGO (Fabric Analyser Grain boundary recOnstruction), a first step towards the automatic determination of three-dimensional (3D) grain boundary geometry using polarised light. The trace of the grain boundaries from 2D rock thin sections are determined primarily from data acquired using an automatic fabric analyser microscope and the FAME software (fabric analyser-based microstructure evaluation; Peternell and colleagues and Hammes and Peternell). Based on the Fabric Analyser G50's unique arrangement of nine differently oriented light sources the retardation can be determi…
In search for a canonical design ABL stability class for wind farm turbines
2016
Production as well as loading of wake exposed wind turbines is known to depend significantly on stability of the Atmospheric Boundary Layer (ABL), which adds a new dimension to design of wind farm turbines. Adding this new aspect in wind turbine design makes the number of design cycle computations to blow up with a factor equal to the number of representative stability bin classes. The research question to be answered in this paper is: Can an ABL stability probability distribution in a meaningful way be collapsed into a representative design stability class as based on a (predefined) confidence level.
Another Look at Aspect in Thai
2007
The aim of the paper is twofold. The first aim is to analyse aspect in Thai in the framework of the selection-theory approach developed by Breu and Sasse (1991). The second aim is to study all possible co-occurrenc;es of each of the three aspect markers: lεεw, kamlaƞ, yùu with the four classes of verbs and with the verbs occurring with other strategies within the five classes of states of affairs. It was found that the selectional approach chosen helped explaining the inceptive-stative state of affairs in Thai clearly. It also pointed out that the Thai aspectuality focused on the initial boundary and terminative boundary of the state of affairs. It is here that combinations of the three asp…