Search results for "singular"
showing 10 items of 589 documents
Form-perturbation theory for higher-order elliptic operators and systems by singular potentials
2020
We give a form-perturbation theory by singular potentials for scalar elliptic operators onL2(Rd)of order 2mwith Hölder continuous coefficients. The form-bounds are obtained from anL1functional analytic approach which takes advantage of both the existence ofm-gaussian kernel estimates and the holomorphy of the semigroup inL1(Rd).We also explore the (local) Kato class potentials in terms of (local) weak compactness properties. Finally, we extend the results to elliptic systems and singular matrix potentials.This article is part of the theme issue ‘Semigroup applications everywhere’.
Singular quasilinear elliptic systems involving gradient terms
2019
Abstract In this paper we establish the existence of at least one smooth positive solution for a singular quasilinear elliptic system involving gradient terms. The approach combines the sub-supersolutions method and Schauder’s fixed point theorem.
Deterministic and Random Vibration of Linear Systems with Singular Parameter Matrices and Fractional Derivative Terms
2021
Both time- and frequency-domain solution techniques are developed for determining the response of linear multi-degree-of-freedom systems exhibiting singular parameter matrices and endowed with derivative terms of noninteger orders modeled as rational numbers. This is done based on the Moore-Penrose matrix inverse theory, in conjunction with a state variable formulation and with a complex modal analysis treatment. It is worth noting that, for the class of systems considered herein, this treatment also yields decoupled governing equations, thus facilitating further their numerical solution. Next, a generalization of the standard frequency-domain input-output (excitation-response) relationship…
Modal Analysis of Multi-Degrees-of-Freedom Systems with Singular Matrices: Analytical Dynamics Approach
2017
Complex mechanical (e.g., multibody) systems with different types of constraints are generally performed through analytical dynamics methods. In some cases, however, it is possible that the (augmented) mass and/or stiffness matrices may derive to be singular; consequently, modal analysis, which is used extensively in the classical dynamics literature, fails. In this paper, if the uniqueness condition is satisfied by the constraints, a properly modified modal analysis is elucidated into analytical dynamics leading to the evaluation of the natural frequencies in a simple and straightforward way. Under that framework, advances of both classical and analytical dynamics are taken into considerat…
Use of Automated Photoelasticity to Determine Stress Intensity Factors of Bimaterial Joints
2005
A new systematic experimental procedure has been developed to obtain the stress intensity factors governing the singular stress field that occurs near the intersection between the interface and free edges of bimaterial joints. A preliminary theoretical study of the singular stress field is carried out by the well-known Airy stress function method. The obtained stress laws are properly combined with the basic law of photoelasticity in order to define a procedure that permits the zone dominated by the singularity to be located and the stress intensity factors (SIFs) to be computed on the basis of full field data provided from automated photoelasticity. In particular, a systematic error analys…
Smooth and non-smooth traveling wave solutions of some generalized Camassa–Holm equations
2014
In this paper we employ two recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a recently-derived integrable family of generalized Camassa-Holm (GCH) equations. A recent, novel application of phase-plane analysis is employed to analyze the singular traveling wave equations of three of the GCH NLPDEs, i.e. the possible non-smooth peakon, cuspon and compacton solutions. Two of the GCH equations do not support singular traveling waves. The third equation supports four-segmented, non-smooth $M$-wave solutions, while the fourth supports both solitary (peakon) and periodic (cuspon) cusp waves in different parameter regimes. Moreover, sm…
Regular and singular pulse and front solutions and possible isochronous behavior in the short-pulse equation: Phase-plane, multi-infinite series and …
2014
In this paper we employ three recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a family of so-called short-pulse equations (SPE). A recent, novel application of phase-plane analysis is first employed to show the existence of breaking kink wave solutions in certain parameter regimes. Secondly, smooth traveling waves are derived using a recent technique to derive convergent multi-infinite series solutions for the homoclinic (heteroclinic) orbits of the traveling-wave equations for the SPE equation, as well as for its generalized version with arbitrary coefficients. These correspond to pulse (kink or shock) solutions respectively o…
Singularity tracking for Camassa-Holm and Prandtl's equations
2006
In this paper we consider the phenomenon of singularity formation for the Camassa-Holm equation and for Prandtl's equations. We solve these equations using spectral methods. Then we track the singularity in the complex plane estimating the rate of decay of the Fourier spectrum. This method allows us to follow the process of the singularity formation as the singularity approaches the real axis.
Large-photon-number limit and the essential singularity in finite quantum electrodynamics
1976
It is shown that the essential singularity in finite quantum electrodynamics can be located by considering only those diagrams with a large number of photons exchanged in the single-fermion loop, without photons emitted and absorbed on a fermion line. (AIP)
Critical behavior of short range Potts glasses
1993
We study by means of Monte Carlo simulations and the numerical transfer matrix technique the critical behavior of the short rangep=3 state Potts glass model in dimensionsd=2,3,4 with both Gaussian and bimodal (±J) nearest neighbor interactions on hypercubic lattices employing finite size scaling ideas. Ind=2 in addition the degeneracy of the glass ground state is computed as a function of the number of Potts states forp=3, 4, 5 and compared to that of the antiferromagnetic ground state. Our data indicate a transition into a glass phase atT=0 ind=2 with an algebraic singularity, aT=0 transition ind=3 with an essential singularity of the form χ∼exp(const.T−2), and an algebraic singularity atT…