1,428 research outputs found
Spiraling Solitons: a Continuum Model for Dynamical Phyllotaxis and Beyond
A novel, protean, topological soliton has recently been shown to emerge in
systems of repulsive particles in cylindrical geometries, whose statics is
described by the number-theoretical objects of phyllotaxis. Here we present a
minimal and local continuum model that can explain many of the features of the
phyllotactic soliton, such as locked speed, screw shift, energy transport and,
for Wigner crystal on a nanotube, charge transport. The treatment is general
and should apply to other spiraling systems. Unlike e.g. Sine-Gornon-like
systems, our solitons can exist between non-degenerate structure, imply a power
flow through the system, dynamics of the domains it separates; we also predict
pulses, both static and dynamic. Applications include charge transport in
Wigner Crystals on nanotubes or A- to B-DNA transitions.Comment: 8 Pages, 6 Figures, Phys Rev E in pres
Kink dynamics in the MSTB model
Producción CientÃficaIn this paper kink scattering processes are investigated in the Montonen–Sarker–Trullinger–Bishop (MSTB) model. The MSTB model is in fact a one-parametric family of relativistic scalar field theories living in a one-time one-space Minkowski space-time which encompasses two coupled scalar fields. Among the static solutions of the model two kinds of topological kinks are distinguished in a precise range of the family parameter. In that regime there exists one unstable kink exhibiting only one non-null component of the scalar field. Another type of topological kink solutions, stable in this case, includes two different kinks for which the two components of the scalar field are non-null. Both one-component and two-component topological kinks are accompanied by their antikink partners. The decay of the unstable kink to one of the stable solutions plus radiation is numerically computed. The pair of stable two-component kinks living
respectively on upper and lower semi-ellipses in the field space belongs to the same topological sector in the configuration space and provides an ideal playground to address several scattering events involving one kink and either its own antikink or the antikink of the other stable kink. By means of numerical analysis we shall find and describe interesting physical phenomena. Bion (kink–antikink oscillations) formation, kink reflection, kink–antikink annihilation, kink transmutation and resonances are examples of these types of events. The appearance of these phenomena emerging in the kink–antikink scattering depends critically on the initial collision velocity and the chosen value of the coupling constant parametrizing the family of MSTB models.MINDECO grant MTM2014-57129-C2-1-P and Junta de Castilla y León grants VA057U16 and BU229P18
Asymmetric kink scattering in a two-component scalar field theory model
Producción CientÃficaIn this paper the kink scattering in a two-component scalar field theory model in (1+1)-Minkowskian
space-time is addressed. The potential term U(fi_1; fi_2) is given by a polynomial of fourth degree in the
first field component and of sixth degree in the second one. The novel characteristic of this model is
that the kink variety describes two different types of extended particles. These particles are characterized
by its topological charge but also by a new feature determined by a discrete charge L = 0,1,-1.
For this reason, the kink scattering involves a very rich variety of processes, which comprises kink
annihilation, reflection, charge exchange, transmutation, etc. It has been found that not only the final
velocity of the scattered kinks, but also the final nature of the emerging lumps after the collision are
very sensitive on the initial velocities. Asymmetric scattering processes arise when Type I and Type
II particles are obliged to collide. In this case, ten different final scenarios are possible. Symmetric
scattering events are also discussed.In this paper the kink scattering in a two-component scalar field theory model in (1+1)-Minkowskian space-time is addressed. The potential term U(Ï•1, Ï•2) is given by a polynomial of fourth degree in the first field component and of sixth degree in the second one. The novel characteristic of this model is that the kink variety describes two different types of extended particles. These particles are characterized by its topological charge but also by a new feature determined by a discrete charge . For this reason, the kink scattering involves a very rich variety of processes, which comprises kink annihilation, reflection, charge exchange, transmutation, etc. It has been found that not only the final velocity of the scattered kinks, but also the final nature of the emerging lumps after the collision are very sensitive on the initial velocities. Asymmetric scattering processes arise when Type I and Type II particles are obliged to collide. In this case, ten different final scenarios are possible. Symmetric scattering events are also discussed.Ministerio de EconomÃa, Ciencia y Competitividad (grant MTM2014-57129-C2-1-P)Junta de Castilla y Leon (grant VA057U16
Sine-Gordon solitons, auxiliary fields, and singular limit of a double pendulums chain
We consider the continuum version of an elastic chain supporting topological
and non-topological degrees of freedom; this generalizes a model for the
dynamics of DNA recently proposed and investigated by ourselves. In a certain
limit, the non-topological degrees of freedom are frozen, and the model reduces
to the sine-Gordon equations and thus supports well-known topological soliton
solutions. We consider a (singular) perturbative expansion around this limit
and study in particular how the non-topological field assume the role of an
auxiliary field. This provides a more general framework for the slaving of this
degree of freedom on the topological one, already observed elsewhere in the
context of the mentioned DNA model; in this framework one expects such
phenomenon to arise in a quite large class of field-theoretical models.Comment: 18 pages, 2 figure
Solving linear and nonlinear klein-gordon equations by new perturbation iteration transform method
We present an effective algorithm to solve the Linear and Nonlinear KleinGordon equation, which is based on the Perturbation Iteration Transform Method (PITM). The Klein-Gordon equation is the name given to the equation of motion of a quantum scalar or pseudo scalar field, a field whose quanta are spin-less particles. It describes the quantum amplitude for finding a point particle in various places, the relativistic wave function, but the particle propagates both forwards and backwards in time. The Perturbation Iteration Transform Method (PITM) is a combined form of the Laplace Transform Method and Perturbation Iteration Algorithm. The method provides the solution in the form of a rapidly convergent series. Some numerical examples are used to illustrate the preciseness and effectiveness of the proposed method. The results show that the PITM is very efficient, simple and can be applied to other nonlinear problems.Publisher's Versio
Kink Dynamics in a Topological Phi^4 Lattice
It was recently proposed a novel discretization for nonlinear Klein-Gordon
field theories in which the resulting lattice preserves the topological
(Bogomol'nyi) lower bound on the kink energy and, as a consequence, has no
Peierls-Nabarro barrier even for large spatial discretizations (h~1.0). It was
then suggested that these ``topological discrete systems'' are a natural choice
for the numerical study of continuum kink dynamics. Giving particular emphasis
to the phi^4 theory, we numerically investigate kink-antikink scattering and
breather formation in these topological lattices. Our results indicate that,
even though these systems are quite accurate for studying free kinks in coarse
lattices, for legitimate dynamical kink problems the accuracy is rather
restricted to fine lattices (h~0.1). We suggest that this fact is related to
the breaking of the Bogomol'nyi bound during the kink-antikink interaction,
where the field profile loses its static property as required by the
Bogomol'nyi argument. We conclude, therefore, that these lattices are not
suitable for the study of more general kink dynamics, since a standard
discretization is simpler and has effectively the same accuracy for such
resolutions.Comment: RevTeX, 4 pages, 4 figures; Revised version, accepted to Physical
Review E (Brief Reports
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