Search results for "Singularity"
showing 10 items of 352 documents
Energy landscape properties studied using symbolic sequences
2006
We investigate a classical lattice system with $N$ particles. The potential energy $V$ of the scalar displacements is chosen as a $\phi ^4$ on-site potential plus interactions. Its stationary points are solutions of a coupled set of nonlinear equations. Starting with Aubry's anti-continuum limit it is easy to establish a one-to-one correspondence between the stationary points of $V$ and symbolic sequences $\bm{\sigma} = (\sigma_1,...,\sigma_N)$ with $\sigma_n=+,0,-$. We prove that this correspondence remains valid for interactions with a coupling constant $\epsilon$ below a critical value $\epsilon_c$ and that it allows the use of a ''thermodynamic'' formalism to calculate statistical prope…
Numerical Study of the semiclassical limit of the Davey-Stewartson II equations
2014
We present the first detailed numerical study of the semiclassical limit of the Davey–Stewartson II equations both for the focusing and the defocusing variant. We concentrate on rapidly decreasing initial data with a single hump. The formal limit of these equations for vanishing semiclassical parameter , the semiclassical equations, is numerically integrated up to the formation of a shock. The use of parallelized algorithms allows one to determine the critical time tc and the critical solution for these 2 + 1-dimensional shocks. It is shown that the solutions generically break in isolated points similarly to the case of the 1 + 1-dimensional cubic nonlinear Schrodinger equation, i.e., cubic…
Analysis of a slow–fast system near a cusp singularity
2016
This paper studies a slow fast system whose principal characteristic is that the slow manifold is given by the critical set of the cusp catastrophe. Our analysis consists of two main parts: first, we recall a formal normal form suitable for systems as the one studied here; afterwards, taking advantage of this normal form, we investigate the transition near the cusp singularity by means of the blow up technique. Our contribution relies heavily in the usage of normal form theory, allowing us to refine previous results. (C) 2015 Elsevier Inc. All rights reserved.
Bifurcations of cuspidal loops
1997
A cuspidal loop for a planar vector field X consists of a homoclinic orbit through a singular point p, at which X has a nilpotent cusp. This is the simplest non-elementary singular cycle (or graphic) in the sense that its singularities are not elementary (i.e. hyperbolic or semihyperbolic). Cuspidal loops appear persistently in three-parameter families of planar vector fields. The bifurcation diagrams of unfoldings of cuspidal loops are studied here under mild genericity hypotheses: the singular point p is of Bogdanov - Takens type and the derivative of the first return map along the orbit is different from 1. An analytic and geometric method based on the blowing up for unfoldings is propos…
Response properties with explicitly correlated coupled-cluster methods using a Slater-type correlation factor and cusp conditions
2009
The recently proposed extension of the explicitly correlated coupled-cluster ansatz using cusp conditions [A. Kohn, J. Chem. Phys. 130, 104104 (2009)] is tested for suitability in the calculation of response properties. For this purpose, static and dynamic electrical properties up to ESHG hyperpolarizabilities as well as optical rotations have been computed within the CCSD(F12) model. It is shown that effectively converged correlation contributions can reliably be obtained using augmented quadruple zeta basis sets already. The ansatz is optionally equipped with an extension capable of reducing the one-electron basis set error. A further simplification of the method specific Lagrangian aimed…
Mappings of finite distortion: Formation of cusps II
2007
For s > 0 s>0 given, we consider a planar domain Ω s \Omega _s with a rectifiable boundary but containing a cusp of degree s s , and show that there is no homeomorphism f : R 2 → R 2 f\colon \mathbb {R}^2\to \mathbb {R}^2 of finite distortion with exp ( λ K ) ∈ L l o c 1 ( R 2 ) \exp (\lambda K)\in L^1_{\mathrm {loc}}(\mathbb {R}^2) so that f ( B ) = Ω s f(B)=\Omega _s when λ > 4 / s \lambda >4/s and B B is the unit disc. On the other hand, for λ > 2 / s \lambda >2/s such an f f exists. The critical value for λ \lambda remains open.
A note to “Mappings of finite distortion: formation of cusps II”
2010
We consider planar homeomorphisms f : R 2 → R 2 f\colon \mathbb {R}^2\to \mathbb {R}^2 that are of finite distortion and map the unit disk onto a specific cusp domain Ω s \Omega _s . We study the relation between the degree s s of the cusp and the integrability of the distortion function K f K_f by sharpening a previous result where K f K_f is assumed to be locally exponentially integrable.
Explicitly correlated internally contracted multireference coupled-cluster singles and doubles theory: ic-MRCCSD(F12∗)
2013
Abstract An explicitly correlated ansatz employing Slater-type geminals and cusp conditions is developed for the internally contracted multireference coupled-cluster singles and doubles method. Only the most important geminal terms are retained in the spirit of earlier work for single-reference theory. Throughout all our test calculations, the new ic-MRCCSD(F12∗) method improves the basis set convergence of many properties, e.g., spectroscopic constants or singlet–triplet splittings, with only little extra computational cost. If a perturbative correction for connected triples is included (the ic-MRCCSD(F12∗)+(T) method), very accurate results can be obtained even with minimal active spaces.
Analysis of eta production using a generalized Lee model
1998
We have investigated the processes N($\pi$, $\pi$)N and N($\pi$, $\eta$)N close to eta threshold using a simple, nonrelativistic Lee model which has the advantage of being analytically solvable. It is then possible to study the Riemann sheets of the S-matrix and the behavior of its resonance poles especially close to threshold. A theoretical simulation of the experimental cusp effect at eta threshold leads to a characteristic distribution of poles on the Riemann sheets. We find a pole located in the $4^{th}$ Riemann sheet that up to now has not been discussed. It belongs to the cusp peak at eta threshold. In addition we obtain the surprising result using the Lee model that the resonance $S_…
Amplitude analysis ofB+→J/ψϕK+decays
2017
The first full amplitude analysis of B+→J/ψϕK+ with J/ψ→μ+μ−, ϕ→K+K− decays is performed with a data sample of 3 fb−1 of pp collision data collected at s√=7 and 8 TeV with the LHCb detector. The data cannot be described by a model that contains only excited kaon states decaying into ϕK+, and four J/ψϕ structures are observed, each with significance over 5 standard deviations. The quantum numbers of these structures are determined with significance of at least 4 standard deviations. The lightest is best described as a D±sD∗∓s cusp, but a resonant interpretation is also possible with mass consistent with, but width much larger than, previous measurements of the claimed X(4140) state. The mode…