476 research outputs found
Optimal antiviral treatment strategies and the effects of resistance
Recent pandemic planning has highlighted the importance of understanding the effect that widespread antiviral use will have on the emergence and spread of resistance. A number of recent studies have determined that if resistance to antiviral medication can evolve, then deploying treatment at a less than maximum rate often minimizes the outbreak size. This finding, however, involves the assumption that treatment levels remain constant during the entire outbreak. Using optimal control theory, we address the question of optimal antiviral use by considering a large class of time-varying treatment strategies. We prove that, contrary to previous results, it is always optimal to treat at the maximum rate provided that this treatment occurs at the right time. In general the optimal strategy is to wait some fixed amount of time and then to deploy treatment at the maximum rate for the remainder of the outbreak. We derive analytical conditions that characterize this optimal amount of delay. Our results show that it is optimal to start treatment immediately when one of the following conditions holds: (i) immediate treatment can prevent an outbreak, (ii) the initial pool of susceptibles is small, or (iii) when the maximum possible rate of treatment is low, such that there is little de novo emergence of resistant strains. Finally, we use numerical simulations to verify that the results also hold under more general conditions
Dynamical and thermal effects in nanoparticle systems driven by a rotating magnetic field
We study dynamical and thermal effects that are induced in nanoparticle
systems by a rotating magnetic field. Using the deterministic Landau-Lifshitz
equation and appropriate rotating coordinate systems, we derive the equations
that characterize the steady-state precession of the nanoparticle magnetic
moments and study a stability criterion for this type of motion. On this basis,
we describe (i) the influence of the rotating field on the stability of the
small-angle precession, (ii) the dynamical magnetization of nanoparticle
systems, and (iii) the switching of the magnetic moments under the action of
the rotating field. Using the backward Fokker-Planck equation, which
corresponds to the stochastic Landau-Lifshitz equation, we develop a method for
calculating the mean residence times that the driven magnetic moments dwell in
the up and down states. Within this framework, the features of the induced
magnetization and magnetic relaxation are elucidated.Comment: 18 pages, 5 figure
A smoothing monotonic convergent optimal control algorithm for NMR pulse sequence design
The past decade has demonstrated increasing interests in using optimal
control based methods within coherent quantum controllable systems. The
versatility of such methods has been demonstrated with particular elegance
within nuclear magnetic resonance (NMR) where natural separation between
coherent and dissipative spin dynamics processes has enabled coherent quantum
control over long periods of time to shape the experiment to almost ideal
adoption to the spin system and external manipulations. This has led to new
design principles as well as powerful new experimental methods within magnetic
resonance imaging, liquid-state and solid-state NMR spectroscopy. For this
development to continue and expand, it is crucially important to constantly
improve the underlying numerical algorithms to provide numerical solutions
which are optimally compatible with implementation on current instrumentation
and at same time are numerically stable and offer fast monotonic convergence
towards the target. Addressing such aims, we here present a smoothing
monotonically convergent algorithm for pulse sequence design in magnetic
resonance which with improved optimization stability lead to smooth pulse
sequence easier to implement experimentally and potentially understand within
the analytical framework of modern NMR spectroscopy
Mean first-passage times for an ac-driven magnetic moment of a nanoparticle
The two-dimensional backward Fokker-Planck equation is used to calculate the
mean first-passage times (MFPTs) of the magnetic moment of a nanoparticle
driven by a rotating magnetic field. It is shown that a magnetic field that is
rapidly rotating in the plane {\it perpendicular} to the easy axis of the
nanoparticle governs the MFPTs just in the same way as a static magnetic field
that is applied {\it along} the easy axis. Within this framework, the features
of the magnetic relaxation and net magnetization of systems composed of
ferromagnetic nanoparticles arising from the action of the rotating field are
revealed.Comment: 7 pages, 1 figur
Hopf Bifurcations in a Watt Governor With a Spring
This paper pursues the study carried out by the authors in "Stability and
Hopf bifurcation in a hexagonal governor system", focusing on the codimension
one Hopf bifurcations in the hexagonal Watt governor differential system. Here
are studied the codimension two, three and four Hopf bifurcations and the
pertinent Lyapunov stability coefficients and bifurcation diagrams, ilustrating
the number, types and positions of bifurcating small amplitude periodic orbits,
are determined. As a consequence it is found an open region in the parameter
space where two attracting periodic orbits coexist with an attracting
equilibrium point.Comment: 30 pages and 7 figure
Topological transversals to a family of convex sets
Let be a family of compact convex sets in . We say
that has a \emph{topological -transversal of index }
(, ) if there are, homologically, as many transversal
-planes to as -planes containing a fixed -plane in
.
Clearly, if has a -transversal plane, then
has a topological -transversal of index for and . The converse is not true in general.
We prove that for a family of compact convex sets in
a topological -transversal of index implies an
ordinary -transversal. We use this result, together with the
multiplication formulas for Schubert cocycles, the Lusternik-Schnirelmann
category of the Grassmannian, and different versions of the colorful Helly
theorem by B\'ar\'any and Lov\'asz, to obtain some geometric consequences
Null Energy Condition Violation and Classical Stability in the Bianchi I Metric
The stability of isotropic cosmological solutions in the Bianchi I model is
considered. We prove that the stability of isotropic solutions in the Bianchi I
metric for a positive Hubble parameter follows from their stability in the
Friedmann-Robertson-Walker metric. This result is applied to models inspired by
string field theory, which violate the null energy condition. Examples of
stable isotropic solutions are presented. We also consider the k-essence model
and analyse the stability of solutions of the form .Comment: 27 pages, references added, accepted for publication in Phys. Rev.
Rapidly driven nanoparticles: Mean first-passage times and relaxation of the magnetic moment
We present an analytical method of calculating the mean first-passage times
(MFPTs) for the magnetic moment of a uniaxial nanoparticle which is driven by a
rapidly rotating, circularly polarized magnetic field and interacts with a heat
bath. The method is based on the solution of the equation for the MFPT derived
from the two-dimensional backward Fokker-Planck equation in the rotating frame.
We solve these equations in the high-frequency limit and perform precise,
numerical simulations which verify the analytical findings. The results are
used for the description of the rates of escape from the metastable domains
which in turn determine the magnetic relaxation dynamics. A main finding is
that the presence of a rotating field can cause a drastic decrease of the
relaxation time and a strong magnetization of the nanoparticle system. The
resulting stationary magnetization along the direction of the easy axis is
compared with the mean magnetization following from the stationary solution of
the Fokker-Planck equation.Comment: 24 pages, 4 figure
General Framework for phase synchronization through localized sets
We present an approach which enables to identify phase synchronization in
coupled chaotic oscillators without having to explicitly measure the phase. We
show that if one defines a typical event in one oscillator and then observes
another one whenever this event occurs, these observations give rise to a
localized set. Our result provides a general and easy way to identify PS, which
can also be used to oscillators that possess multiple time scales. We
illustrate our approach in networks of chemically coupled neurons. We show that
clusters of phase synchronous neurons may emerge before the onset of phase
synchronization in the whole network, producing a suitable environment for
information exchanging. Furthermore, we show the relation between the localized
sets and the amount of information that coupled chaotic oscillator can
exchange
General critical states in type-II superconductors
The magnetic flux dynamics of type-II superconductors within the critical
state regime is posed in a generalized framework, by using a variational theory
supported by well established physical principles. The equivalence between the
variational statement and more conventional treatments, based on the solution
of the differential Maxwell equations together with appropriate conductivity
laws is shown. Advantages of the variational method are emphasized, focusing on
its numerical performance, that allows to explore new physical scenarios. In
particular, we present the extension of the so-called double critical state
model to three dimensional configurations in which only flux transport
(T-states), cutting (C-states) or both mechanisms (CT-states) occur. The theory
is applied to several problems. First, we show the features of the transition
from T to CT states. Second, we give a generalized expression for the flux
cutting threshold in 3-D and show its relevance in the slab geometry. In
addition, several models that allow to treat flux depinning and cutting
mechanisms are compared. Finally, the longitudinal transport problem (current
is applied parallel to the external magnetic field) is analyzed both under T
and CT conditions. The complex interaction between shielding and transport is
solved.Comment: 21 figures, submitted for publicatio
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