268 research outputs found
The Dielectric Skyrme model
We consider a version of the Skyrme model where both the kinetic term and the
Skyrme term are multiplied by field-dependent coupling functions. For suitable
choices, this "dielectric Skyrme model" has static solutions saturating the
pertinent topological bound in the sector of baryon number (or topological
charge) but not for higher . This implies that higher charge
field configurations are unbound, and loosely bound higher skyrmions can be
achieved by small deformations of this dielectric Skyrme model. We provide a
simple and explicit example for this possibility. Further, we show that the
BPS sector continues to exist for certain generalizations of the model
like, for instance, after its coupling to a specific version of the BPS Skyrme
model, i.e., the addition of the sextic term and a particular potential.Comment: Latex file, 13 pages, no figure
Mechanism of the Verwey transition in magnetite
By combining {\it ab initio} results for the electronic structure and phonon
spectrum with the group theory, we establish the origin of the Verwey
transition in FeO. Two primary order parameters with and
symmetries are identified. They induce the phase transformation from
the high-temperature cubic to the low-temperature monoclinic structure. The
on-site Coulomb interaction between 3d electrons at Fe ions plays a crucial
role in this transition -- it amplifies the coupling of phonons to conduction
electrons and thus opens a gap at the Fermi energy. {\it Published in Phys.
Rev. Lett. {\bf 97}, 156402 (2006).}Comment: 5 pages, 3 figure
Magnetic and orbital ordering in cuprates and manganites
The mechanisms of magnetic and orbital interactions due to double exchange
(DE) and superexchange (SE) in transition metal oxides with degenerate e_g
orbitals are presented. Specifically, we study the effective spin-orbital
models derived for the d^9 ions as in KCuF_3, and for the d^4 ions as in
LaMnO_3, for spins S=1/2 and S=2, respectively. Such models are characterized
by three types of elementary excitations: spin waves, orbital waves, and
spin-and-orbital waves. The SE interactions between Cu^{2+} (d^9) ions are
inherently frustrated, which leads to a new mechanism of spin liquid which
operates in three dimensions. The SE between Mn^{3+} (d^4) ions explains the
A-type antiferromagnetic order in LaMnO_3 which coexists with the orbital
order. In contrast, the ferromagnetic metallic phase and isotropic spin waves
observed in doped manganites are explained by DE for degenerate e_g orbitals.
It is shown that although a hole does not couple to spin excitations in
ferromagnetic planes of LaMnO_3, the orbital excitations change the energy
scale for the coherent hole propagation and cause a large redistribution of
spectral weight. Finally, we point out some open problems in the present
understanding of doped manganites.Comment: 155 pages, 66 figure
Classical frustration and quantum disorder in spin-orbital models
The most elementary of all physical spin-orbital models is the Kugel-Khomskii
model describing a S=1/2, degenerate Mott-insulator. Recent theoretical
work is reviewed revealing that the classical limit is characterized by a point
of perfect dynamical frustration. It is suggested that this might give rise to
a quantum disordered ground state.Comment: 7 pages Revtex, 3 ps figures, proceedings 1998 NEC symposium, Nasu,
Japa
Searching for the optimal control strategy of epidemics spreading on different types of networks
The main goal of my studies has been to search for the optimal control strategy of controlling epidemics when taking into account both economical and social costs of the disease. Three control scenarios emerge with treating the whole population (global strategy, GS), treating a small number of individuals in a well-defined neighbourhood of a detected case (local strategy, LS) and allowing the disease to spread unchecked (null strategy, NS). The choice of the optimal strategy is governed mainly by a relative cost of palliative and preventive treatments. Although the properties of the pathogen might not be known in advance for emerging diseases, the prediction of the optimal strategy can be made based on economic analysis only.
The details of the local strategy and in particular the size of the optimal treatment neighbourhood weakly depends on disease infectivity but strongly depends on other epidemiological factors (rate of occurring the symptoms, spontaneously recovery. The required extent of prevention is proportional to the size of the infection neighbourhood, but this relationship depends on time till detection and time till treatment in a non-nonlinear (power) law.
The spontaneous recovery also affects the choice of the control strategy. I have extended my results to two contrasting and yet complementary models, in which individuals that have been through the disease can either be treated or not. Whether the removed individuals (i.e., those who have been through the disease but then spontaneously recover or die) are part of the treatment plan depends on the type of the disease agent. The key factor in choosing the right model is whether it is possible - and desirable - to distinguish such individuals from those who are susceptible. If the removed class is identified with dead individuals, the distinction is very clear. However, if the removal means recovery and immunity, it might not be possible to identify those who
are immune. The models are similar in their epidemiological part, but differ in how the removed/recovered individuals are treated. The differences in models affect choice of the strategy only for very cheap treatment and slow spreading disease. However for the combinations of parameters that are important from the epidemiological perspective (high infectiousness and expensive treatment) the models give similar results. Moreover, even where the choice of the strategy is different, the total cost spent on controlling the epidemic is very similar for both models.
Although regular and small-world networks capture some aspects of the structure of real networks of contacts between people, animals or plants, they do not include the effect of clustering noted in many real-life applications. The use of random clustered networks in epidemiological modelling takes an impor- tant step towards application of the modelling framework to realistic systems. Network topology and in particular clustering also affects the applicability of the control strategy
Quantum disorder versus order-out-of-disorder in the Kugel-Khomskii model
The Kugel-Khomskii model, the simplest model for orbital degenerate magnetic
insulators, exhibits a zero temperature degeneracy in the classical limit which
could cause genuine quantum disorder. Khaliullin and Oudovenko [Phys. Rev. B
56, R14 243 (1997)] suggested recently that instead a particular classical
state could be stabilized by quantum fluctuations. Here we compare their
approach with standard random phase approximation and show that it strongly
underestimates the strength of the quantum fluctuations, shedding doubts on the
survival of any classical state.Comment: 4 pages, ReVTeX, 4 figure
Kink-antikink collisions in a weakly interacting model
We study kink-antikink scattering in a one-parameter variant of the
theory where the model parameter controls the static intersoliton force. We
interpolate between the limit of no static force (BPS limit) and the regime
where the static interaction is small (non-BPS). This allows us to study the
impact of the strength of the intersoliton static force on the soliton
dynamics.
In particular, we analyze how the transition of a bound mode through the mass
threshold affects the soliton dynamics in a generic process, i.e., when a
static intersoliton force shows up. We show that the thin, precisely localized
spectral wall which forms in the limit of no static force, broadens in a
well-defined manner when a static force is included, giving rise to what we
will call a thick spectral wall. This phenomenon just requires that a discrete
mode crosses into the continuum at some intermediate stage of the dynamics and,
therefore, should be observable in many soliton-antisoliton collisions.Comment: version accepted in Phys. Rev.
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