1,721,053 research outputs found
Towards a unified field theory for classical electrodynamics
No full textIn this paper we introduce a model which describes the relation of matter and
the electromagnetic field from a unitarian standpoint in the spirit of ideas of Born
and Infeld. In this model, based on a semilinear perturbation of Maxwell equations,
the particles are finite-energy solitary waves due to the presence of the nonlinearity.
In this respect the matter and the electromagnetic field have the same nature.
Finite energy means that particles have finite mass and this makes electrodynamics
consistent with the special relativity. We analyze the invariants of the motion of
the semilinear Maxwell equations (SME) and their static solutions. In the magnetostatic
case (i.e., when the electric field E = 0 and the magnetic field H does not
depend on time) SME are reduced to the semilinear equation
∇ ×∇ ×A = f
(A), (1)
where ∇× denotes the curl operator, f
is the gradient of a strictly convex smooth
function f : R3 → R and A : R3 → R3 is the gauge potential related to the magnetic
fieldH (H = ∇×A). Due to the presence of the curl operator, (1) is a strongly
degenerate elliptic equation. Moreover, physical considerations impel f to be flat
at zero (f
(0) = 0) and this fact leads us to study the problem in a functional
setting related to the Orlicz space Lp + Lq . The existence of a nontrivial finiteenergy
solution of (1) is proved under suitable growth conditions on f. The proof is
carried out by using a suitable variational framework related to the Hodge splitting
of the vector field A
Solitary waves in the nonlinear wave equation and in gauge theories
No full textRoughly speaking a solitary wave is a solution of a field equation whose energy travels as a localized packet and which preserves this localization in time. This paper is an introduction to the study of solitary waves relative to the Nonlinear Wave Equation and to the Abelian Gauge Theories. Abelian Gauge Theories consist of a class of field equations obtained by coupling in a suitable way the nonlinear wave equation with the Maxwell equations. They provide a model for the interaction of matter with the electromagnetic field. One of the motivations of this study relies in the fact that the Nonlinear Wave Equation and the Abelian Gauge Theories are the simplest equations which satisfy the basic principles of Modern Phyics
A minimization method and applications to the study of solitons
No full textas a localized packet and which preserves this localization in time. A soliton is a solitary
wave which exhibits some strong form of stability so that it has a particle-like behavior.
In this paper, we prove a general, abstract theorem (Theorem 26) which allows to prove
the existence of a class of solitons. Such solitons are suitable minimizers of a constrained
functional and they are called hylomorphic solitons. Then we apply the abstract theory
to problems related to the nonlinear Schrödinger equation (NSE) and to the nonlinear
Klein–Gordon equation (NKG)
Solitary waves in abelian gauge theories
No full textAbelian gauge theories consist of a class of ?eld equations which pro-
vide a model for the interaction between matter and electromagnetic ?elds.
In this paper we analyze the existence of solitary waves for these theo-
ries. We assume that the lower order term W is positive and we prove
the existence of solitary waves if the coupling between matter and elec-
tromagnetic ?eld is small. We point out that the positiveness assumption
on W implies that the energy is positive: this fact makes these theories
more suitable to model physical phenomena
Solitary waves of the nonlinear Klein-Gordon equation coupled with the Maxwell equations
No full textInfluence of the familiarity with the handler on the dog's paw preference
No full textThe term laterally refers to the preference most mammals show for one body side over the other. The aim of this study was to evaluate the reproducibility of the First-stepping test (Tomkins et al., 2010b) in relation to the familiarity with the handler. Thirty-eight adult dogs (22 females, 16 males, different breeds) were tested twice in a modified version of Tomkins' test (30 repetitions instead of 50), once with the owner and once with an unfamiliar handler, one day apart. The paw preference (PP) for each dog in both tests was determined as suggested by Tomkins et al. (2010), calculating the lateralization index and considering a significant preference for Z-scores < - 1.96 (left PP) or > + 1.96 (right PP). There was a low concordance between the Z-scores of the two tests (Cohens' Kappa coefficient = 0.44). In detail, the Z-score of 14 dogs was different in relation to the familiarity with the handler: 1 dog showed a right PP with the owner and a left PP with the unfamiliar handler; 9 dogs showed a non-significant Z-score with the owner and a significant Z-score with the unfamiliar handler; 4 dogs showed a significant Z-score with the owner and a non-significant Z-score with the unfamiliar handler. Previous literature on dogs and other mammals reports that laterality is strongly task-dependent. The current findings suggest that PP may be influenced by other factors, such as the familiarity with the handler, which should be taken into account when testing animals for motor laterality
Existence of solitons in the nonlinear beam equation
No full textThis paper concerns the existence of solitons, namely stable
solitary waves in the nonlinear beam equation with a suitable nonlinearity.
An equation of this type has been introduced in [P. J. McKenna
and W. Walter, Arch. Ration. Mech. Anal., 98 (1987), 167–177] as a
model of a suspension bridge. We prove both the existence of solitary
waves for a large class of nonlinearities and their stability. As far as we
know this is the first result about stability of solitary waves in nonlinear
beam equation
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