Search results for "Conformal"
showing 10 items of 234 documents
Thermal form factors of the XXZ chain and the large-distance asymptotics of its temperature dependent correlation functions
2013
We derive expressions for the form factors of the quantum transfer matrix of the spin-1/2 XXZ chain which are suitable for taking the infinite Trotter number limit. These form factors determine the finitely many amplitudes in the leading asymptotics of the finite-temperature correlation functions of the model. We consider form-factor expansions of the longitudinal and transversal two-point functions. Remarkably, the formulae for the amplitudes are in both cases of the same form. We also explain how to adapt our formulae to the description of ground state correlation functions of the finite chain. The usefulness of our novel formulae is demonstrated by working out explicit results in the hig…
Mass-flux-based outlet boundary conditions for the lattice Boltzmann method
2009
We present outlet boundary conditions for the lattice Boltzmann method. These boundary conditions are constructed with a mass-flux-based approach. Conceptually, the mass-flux-based approach provides a mathematical framework from which specific boundary conditions can be derived by enforcing given physical conditions. The object here is, in particular, to explain the mass-flux-based approach. Furthermore, we illustrate, transparently, how boundary conditions can be derived from the emerging mathematical framework. For this purpose, we derive and present explicitly three outlet boundary conditions. By construction, these boundary conditions have an apparent physical interpretation which is fu…
Microscopic approach to a class of 1D quantum critical models
2015
Starting from the finite volume form factors of local operators, we show how and under which hypothesis the $c=1$ free boson conformal field theory in two-dimensions emerges as an effective theory governing the large-distance regime of multi-point correlation functions in a large class of one dimensional massless quantum Hamiltonians. In our approach, in the large-distance critical regime, the local operators of the initial model are represented by well suited vertex operators associated to the free boson model. This provides an effective field theoretic description of the large distance behaviour of correlation functions in 1D quantum critical models. We develop this description starting f…
Calibration of the Norwegian motion laboratory using conformal geometric algebra
2017
This paper applies Conformal Geometric Algebra (CGA) as a tool for calibrating the robotic equipment found in the Norwegian Motion Laboratory. By using the inner product of CGA to measure the distance between a point and the surface of a plane/sphere, the least-squares method can be used to solve for the unknown parameters describing the plane/sphere in an efficient and intuitive way given n measured points. Positional data samples were acquired from using a high precision Laser tracker (FARO Xi), and the overall calibration error was found to be no more than 4.90mm, and the maximum standard deviation 3.25mm. In addition, the applied least-squares algorithm using CGA was twice as fast, when…
Ricci-flow based conformal mapping of the proximal femur to identify exercise loading effects.
2018
AbstractThe causal relationship between habitual loading and adaptive response in bone morphology is commonly explored by analysing the spatial distribution of mechanically relevant features. In this study, 3D distribution of features in the proximal femur of 91 female athletes (5 exercise loading groups representing habitual loading) is contrasted with 20 controls. A femur specific Ricci-flow based conformal mapping procedure was developed for establishing correspondence among the periosteal surfaces. The procedure leverages the invariance of the conformal mapping method to isometric shape differences to align surfaces in the 2D parametric domain, to produce dense correspondences across an…
Surface homeomorphisms with zero dimensional singular set
1998
We prove that if f is an orientation-preserving homeomorphism of a closed orientable surface M whose singular set is totally disconnected, then f is topologically conjugate to a conformal transformation.
Quasi-Conformal Technique for Integrating and Validating Myocardial Tissue Characterization in MRI with Ex-Vivo Human Histological Data
2017
Ventricular tachycardia caused by a circuit of re-entry is one of the most critical arrhythmias. It is usually related with heterogeneous scar regions where slow velocity of conduction tissue is mixed with non-conductive tissue, creating pathways (CC) responsible for the tachycardia. Pre-operative DE-MRI can provide information on myocardial tissue viability and then improve therapy planning. However, the current DE-MRI resolution is not sufficient for identifying small CCs and therefore they have to be identified during the intervention, which requires considerable operator experience. In this work, we studied the relationship of histological data (with 10 \(\mu \)m resolution), with in-vi…
Annihilators of tensor density modules
2007
Abstract We describe the two-sided ideals in the universal enveloping algebras of the Lie algebras of vector fields on the line and the circle which annihilate the tensor density modules. Both of these Lie algebras contain the projective subalgebra, a copy of sl 2 . The restrictions of the tensor density modules to this subalgebra are duals of Verma modules (of sl 2 ) for Vec ( R ) and principal series modules (of sl 2 ) for Vec ( S 1 ) . Thus our results are related to the well-known theorem of Duflo describing the annihilating ideals of Verma modules of reductive Lie algebras. We find that, in general, the annihilator of a tensor density module of Vec ( R ) or Vec ( S 1 ) is generated by …