Search results for " Nonlinear"
showing 10 items of 1224 documents
Low-temperature large-distance asymptotics of the transversal two-point functions of the XXZ chain
2014
We derive the low-temperature large-distance asymptotics of the transversal two-point functions of the XXZ chain by summing up the asymptotically dominant terms of their expansion into form factors of the quantum transfer matrix. Our asymptotic formulae are numerically efficient and match well with known results for vanishing magnetic field and for short distances and magnetic fields below the saturation field.
Ostrogradsky's Hamilton formalism and quantum corrections
2010
By means of a simple scalar field theory it is demonstrated that the Lagrange formalism and Ostrogradsky's Hamilton formalism in the presence of higher derivatives, in general, do not lead to the same results. While the two approaches are equivalent at the classical level, differences appear due to the quantum corrections.
Low-temperature spectrum of correlation lengths of the XXZ chain in the antiferromagnetic massive regime
2015
We consider the spectrum of correlation lengths of the spin-$\frac{1}{2}$ XXZ chain in the antiferromagnetic massive regime. These are given as ratios of eigenvalues of the quantum transfer matrix of the model. The eigenvalues are determined by integrals over certain auxiliary functions and by their zeros. The auxiliary functions satisfy nonlinear integral equations. We analyse these nonlinear integral equations in the low-temperature limit. In this limit we can determine the auxiliary functions and the expressions for the eigenvalues as functions of a finite number of parameters which satisfy finite sets of algebraic equations, the so-called higher-level Bethe Ansatz equations. The behavio…
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 …
Deformation of current algebras in 3+1 dimensions
1991
It was shown in an earlier paper that there is an Abelian extension \(\widehat{{\text{gl}}}_2 \) of the general linear algebra gl2, that contains the current algebra with anomaly in 3+1 dimensions. We construct a three-parameter family of deformations \(\widetilde{{\text{gl}}}_2 (t)\) of \(\widehat{{\text{gl}}}_2 \). For certain choices of the deformation parameters, we can construct unitary representations. We also construct highest-weight nonunitary representations for all choices of the parameters.
The glass transition in polymer-micronetwork colloids
1995
Dynamic light scattering experiments on a new, wore complex colloidal system reveal that the density fluctuations at high concentration follow a similar pattern as observed for molecular liquids an...
Granular chains for the assessment of thermal stress in slender structures
2015
Slender beams subjected to compressive stress are common in civil and mechanical engineering. The rapid in-situ measurement of this stress may prevent structural anomalies. In this paper, we describe the coupling mechanism between highly nonlinear solitary waves (HNSWs) propagating along an L-shaped granular system and a beam in contact with the granular medium. We evaluate the use of HNSWs as a tool to measure stress in thermally loaded structures and to estimate the neutral temperature, i.e. the temperature at which this stress is null. We investigated numerically and experimentally one and two L-shaped chains of spherical particles in contact with a prismatic beam subjected to heat. We f…
Iterated function systems and well-posedness
2009
Abstract Fractals and multivalued fractals play an important role in biology, quantum mechanics, computer graphics, dynamical systems, astronomy and astrophysics, geophysics, etc. Especially, there are important consequences of the iterated function (or multifunction) systems in several topics of applied sciences [see for example: El Naschie MS. Iterated function systems and the two-slit experiment of quantum mechanics. Chaos, Solitons & Fractals 1994;4:1965–8; Iovane G. Cantorian spacetime and Hilbert space: Part I-Foundations. Chaos, Solitons & Fractals 2006;28:857–78; Iovane G. Cantorian space-time and Hilbert space: Part II-Relevant consequences. Chaos, Solitons & Fractals 2006;29:1–22;…
Analysis of multilayer adsorption models without screening
1991
A class of recently introduced irreversible multilayer adsorption models without screening is analysed. The basic kinetic process of these models leads to power law behaviour for the decay of the jamming coverage as a function of height. The authors find the exact value for the power law exponent. An approximate analytical treatment of these models and previous Monte Carlo simulations are found to be in good agreement.
An immune system model in discrete time based on the analogy with the central nervous system
1988
Jerne's model for the immune system formulated in terms of a neural network recently proposed by Weisbuch and Atlan is generalized to interactions with continuous coupling coefficients. It is shown that even the extended model can be solved analytically without the aid of computer simulations and exhibits one additional attractor, which corresponds to a configuration with high concentrations of active killer cells eventually causing death of the organism.