238 research outputs found
Control of scroll wave turbulence using resonant perturbations
Turbulence of scroll waves is a sort of spatio-temporal chaos that exists in
three-dimensional excitable media. Cardiac tissue and the Belousov-Zhabotinsky
reaction are examples of such media. In cardiac tissue, chaotic behaviour is
believed to underlie fibrillation which, without intervention, precedes cardiac
death. In this study we investigate suppression of the turbulence using
stimulation of two different types, "modulation of excitability" and "extra
transmembrane current". With cardiac defibrillation in mind, we used a single
pulse as well as repetitive extra current with both constant and feedback
controlled frequency. We show that turbulence can be terminated using either a
resonant modulation of excitability or a resonant extra current. The turbulence
is terminated with much higher probability using a resonant frequency
perturbation than a non-resonant one. Suppression of the turbulence using a
resonant frequency is up to fifty times faster than using a non-resonant
frequency, in both the modulation of excitability and the extra current modes.
We also demonstrate that resonant perturbation requires strength one order of
magnitude lower than that of a single pulse, which is currently used in
clinical practice to terminate cardiac fibrillation. Our results provide a
robust method of controlling complex chaotic spatio-temporal processes.
Resonant drift of spiral waves has been studied extensively in two dimensions,
however, these results show for the first time that it also works in three
dimensions, despite the complex nature of the scroll wave turbulence.Comment: 13 pages, 12 figures, submitted to Phys Rev E 2008/06/13. Last
version: 2008/09/18, after revie
Colouring triangle-free graphs with local list sizes
We prove two distinct and natural refinements of a recent breakthrough result
of Molloy (and a follow-up work of Bernshteyn) on the (list) chromatic number
of triangle-free graphs. In both our results, we permit the amount of colour
made available to vertices of lower degree to be accordingly lower. One result
concerns list colouring and correspondence colouring, while the other concerns
fractional colouring. Our proof of the second illustrates the use of the
hard-core model to prove a Johansson-type result, which may be of independent
interest.Comment: 16 pages; v2 includes minor corrections after review; to appear in
Random Structures & Algorithm
Existence of a rotating wave pattern in a disk for a wave front interaction model
[[abstract]]We study the rotating wave patterns in an excitable medium in a disk. This wave pattern is rotating along the given disk boundary with a constant angular speed. To study this pattern we use the wave front interaction model proposed by Zykov in 2007. This model is derived from the FitzHugh-Nagumo equation and it can be described by two systems of ordinary differential equations for wave front and wave back respectively. Using a delicate shooting argument with the help of the comparison principle, we derive the existence and uniqueness of rotating wave patterns for any admissible angular speed with convex front in a given disk.[[incitationindex]]SCI[[booktype]]紙本[[booktype]]電子
ТИПОЛОГИЯ СРЕДНЕВЕКОВЫХ ТОПОРОВ C СЕВЕРА ЗАПАДНОЙ СИБИРИ
The paper presents the results of the research on the Middle Ages iron axes found in different years in the north of Western Siberia and the Urals, excluding pole-axe (berdysh Rus.) that appear in large numbers in the study area with the growing of the Russian population. The relevance of such study has matured, since there are enough sources that need to be generalized and critically compiled. Taking into account the morphological features of the archaeological evidence, the authors propose to classify all currently known axes by 2 groups and 13 types. The first group including 3 types of minting axes were made exclusively for combat use. The second group includes 10 types of axes, classified as universal, which served both for the military and for economic purposes. The text with the description of the sites contains also table with the data on the basic parameters of axes (item length, blade width) and the time of their use (existence). For the first time, a new type of battle axe (type 13), accidentally found in the Khanty-Mansi Autonomous Okrug - Ugra, is published. We present analogues of this subject among the products of Russian blacksmiths of the 13th-14th centuries and explain the position on the dating and on origin of the axe. The paper discusses the evolution of certain types of objects, describes plots concerning the origin of certain items (imports from Volga Bulgaria, Russian lands, etc.) and the special attitude of the local population to this type of weapon, which could be stored for centuries in the holy places of the Ob Ugrians. The authors come to the conclusion that imported axes of the second group were used as a standard for Siberian blacksmiths. But local products, characterized by primitive technology (a multilayer package), low quality welding of iron strips and an abundance of slag inclusions, can be finally identified only after metallographic microstructural analysis. This research should be prolonged, because annual archaeological investigations replenish the source base, and, with no doubt, the typology of axes proposed in the article will be supplemented and adjusted. © 2020 Tyumen Scientific Centre of Siberian Branch of the Russian Academy of Sciences. All rights reserved.Работа выполнена по Программе УрО РАН № 18-6-6-15 «Археологические памятники как источники по реконструкции развития древних обществ Урала и севера Западной Сибири» (рук. д.и.н. А.Ф. Шорин)
Controlling domain patterns far from equilibrium
A high degree of control over the structure and dynamics of domain patterns
in nonequilibrium systems can be achieved by applying nonuniform external
fields near parity breaking front bifurcations. An external field with a linear
spatial profile stabilizes a propagating front at a fixed position or induces
oscillations with frequency that scales like the square root of the field
gradient. Nonmonotonic profiles produce a variety of patterns with controllable
wavelengths, domain sizes, and frequencies and phases of oscillations.Comment: Published version, 4 pages, RevTeX. More at
http://t7.lanl.gov/People/Aric
Simultaneous Embeddability of Two Partitions
We study the simultaneous embeddability of a pair of partitions of the same
underlying set into disjoint blocks. Each element of the set is mapped to a
point in the plane and each block of either of the two partitions is mapped to
a region that contains exactly those points that belong to the elements in the
block and that is bounded by a simple closed curve. We establish three main
classes of simultaneous embeddability (weak, strong, and full embeddability)
that differ by increasingly strict well-formedness conditions on how different
block regions are allowed to intersect. We show that these simultaneous
embeddability classes are closely related to different planarity concepts of
hypergraphs. For each embeddability class we give a full characterization. We
show that (i) every pair of partitions has a weak simultaneous embedding, (ii)
it is NP-complete to decide the existence of a strong simultaneous embedding,
and (iii) the existence of a full simultaneous embedding can be tested in
linear time.Comment: 17 pages, 7 figures, extended version of a paper to appear at GD 201
Theory of spiral wave dynamics in weakly excitable media: asymptotic reduction to a kinematic model and applications
In a weakly excitable medium, characterized by a large threshold stimulus,
the free end of an isolated broken plane wave (wave tip) can either rotate
(steadily or unsteadily) around a large excitable core, thereby producing a
spiral pattern, or retract causing the wave to vanish at boundaries. An
asymptotic analysis of spiral motion and retraction is carried out in this
weakly excitable large core regime starting from the free-boundary limit of the
reaction-diffusion models, valid when the excited region is delimited by a thin
interface. The wave description is shown to naturally split between the tip
region and a far region that are smoothly matched on an intermediate scale.
This separation allows us to rigorously derive an equation of motion for the
wave tip, with the large scale motion of the spiral wavefront slaved to the
tip. This kinematic description provides both a physical picture and exact
predictions for a wide range of wave behavior, including: (i) steady rotation
(frequency and core radius), (ii) exact treatment of the meandering instability
in the free-boundary limit with the prediction that the frequency of unstable
motion is half the primary steady frequency (iii) drift under external actions
(external field with application to axisymmetric scroll ring motion in
three-dimensions, and spatial or/and time-dependent variation of excitability),
and (iv) the dynamics of multi-armed spiral waves with the new prediction that
steadily rotating waves with two or more arms are linearly unstable. Numerical
simulations of FitzHug-Nagumo kinetics are used to test several aspects of our
results. In addition, we discuss the semi-quantitative extension of this theory
to finite cores and pinpoint mathematical subtleties related to the thin
interface limit of singly diffusive reaction-diffusion models
Theory of Spike Spiral Waves in a Reaction-Diffusion System
We discovered a new type of spiral wave solutions in reaction-diffusion
systems --- spike spiral wave, which significantly differs from spiral waves
observed in FitzHugh-Nagumo-type models. We present an asymptotic theory of
these waves in Gray-Scott model. We derive the kinematic relations describing
the shape of this spiral and find the dependence of its main parameters on the
control parameters. The theory does not rely on the specific features of
Gray-Scott model and thus is expected to be applicable to a broad range of
reaction-diffusion systems.Comment: 4 pages (REVTeX), 2 figures (postscript), submitted to Phys. Rev.
Let
Dynamics of lattice spins as a model of arrhythmia
We consider evolution of initial disturbances in spatially extended systems
with autonomous rhythmic activity, such as the heart. We consider the case when
the activity is stable with respect to very smooth (changing little across the
medium) disturbances and construct lattice models for description of
not-so-smooth disturbances, in particular, topological defects; these models
are modifications of the diffusive XY model. We find that when the activity on
each lattice site is very rigid in maintaining its form, the topological
defects - vortices or spirals - nucleate a transition to a disordered,
turbulent state.Comment: 17 pages, revtex, 3 figure
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