1,895 research outputs found
Emergence of chaotic attractor and anti-synchronization for two coupled monostable neurons
The dynamics of two coupled piece-wise linear one-dimensional monostable maps
is investigated. The single map is associated with Poincare section of the
FitzHugh-Nagumo neuron model. It is found that a diffusive coupling leads to
the appearance of chaotic attractor. The attractor exists in an invariant
region of phase space bounded by the manifolds of the saddle fixed point and
the saddle periodic point. The oscillations from the chaotic attractor have a
spike-burst shape with anti-phase synchronized spiking.Comment: To be published in CHAO
Stochastic Flux-Freezing and Magnetic Dynamo
We argue that magnetic flux-conservation in turbulent plasmas at high
magnetic Reynolds numbers neither holds in the conventional sense nor is
entirely broken, but instead is valid in a novel statistical sense associated
to the "spontaneous stochasticity" of Lagrangian particle tra jectories. The
latter phenomenon is due to the explosive separation of particles undergoing
turbulent Richardson diffusion, which leads to a breakdown of Laplacian
determinism for classical dynamics. We discuss empirical evidence for
spontaneous stochasticity, including our own new numerical results. We then use
a Lagrangian path-integral approach to establish stochastic flux-freezing for
resistive hydromagnetic equations and to argue, based on the properties of
Richardson diffusion, that flux-conservation must remain stochastic at infinite
magnetic Reynolds number. As an important application of these results we
consider the kinematic, fluctuation dynamo in non-helical, incompressible
turbulence at unit magnetic Prandtl number. We present results on the
Lagrangian dynamo mechanisms by a stochastic particle method which demonstrate
a strong similarity between the Pr = 1 and Pr = 0 dynamos. Stochasticity of
field-line motion is an essential ingredient of both. We finally consider
briefly some consequences for nonlinear MHD turbulence, dynamo and reconnectionComment: 29 pages, 10 figure
Atom trapping and guiding with a subwavelength-diameter optical fiber
We suggest using an evanescent wave around a thin fiber to trap atoms. We
show that the gradient force of a red-detuned evanescent-wave field in the
fundamental mode of a silica fiber can balance the centrifugal force when the
fiber diameter is about two times smaller than the wavelength of the light and
the component of the angular momentum of the atoms along the fiber axis is in
an appropriate range. As an example, the system should be realizable for Cesium
atoms at a temperature of less than 0.29 mK using a silica fiber with a radius
of 0.2 m and a 1.3-m-wavelength light with a power of about 27 mW.Comment: 5 pages, 5 figure
Magnetic Field Amplification by Small-Scale Dynamo Action: Dependence on Turbulence Models and Reynolds and Prandtl Numbers
The small-scale dynamo is a process by which turbulent kinetic energy is
converted into magnetic energy, and thus is expected to depend crucially on the
nature of turbulence. In this work, we present a model for the small-scale
dynamo that takes into account the slope of the turbulent velocity spectrum
v(l) ~ l^theta, where l and v(l) are the size of a turbulent fluctuation and
the typical velocity on that scale. The time evolution of the fluctuation
component of the magnetic field, i.e., the small-scale field, is described by
the Kazantsev equation. We solve this linear differential equation for its
eigenvalues with the quantum-mechanical WKB-approximation. The validity of this
method is estimated as a function of the magnetic Prandtl number Pm. We
calculate the minimal magnetic Reynolds number for dynamo action, Rm_crit,
using our model of the turbulent velocity correlation function. For Kolmogorov
turbulence (theta=1/3), we find that the critical magnetic Reynolds number is
approximately 110 and for Burgers turbulence (theta=1/2) approximately 2700.
Furthermore, we derive that the growth rate of the small-scale magnetic field
for a general type of turbulence is Gamma ~ Re^((1-theta)/(1+theta)) in the
limit of infinite magnetic Prandtl numbers. For decreasing magnetic Prandtl
number (down to Pm approximately larger than 10), the growth rate of the
small-scale dynamo decreases. The details of this drop depend on the
WKB-approximation, which becomes invalid for a magnetic Prandtl number of about
unity.Comment: 13 pages, 8 figures; published in Phys. Rev. E 201
Development of Requirements for a Basic Standardized Mathematical Model of Geokhod
The article revealed the shortcomings of existing mathematical models geokhods, the necessity of a new approach to modeling the processes of internal and external geokhods interaction, formulated the task of building flexible mathematical models
Importance of Resultant Action of the Mining Machine Actuator for Stresses in Impact Zone of a Separate Cutter
Two stress levels are considered in the general pattern of stress-strain state of the rock destroyed by the mining machine. The authors also ground the necessity of considering the interaction of all cutters of the actuating device when calculating the process of cutting with a separate cutter
Features of martensitic transformation and fine structure of intermetallic compound Ni50Mn50
Transmission and scanning electron microscopy and Xray and electron diffraction are used to investigate the martensitic transformation and martensitic phase structure of the Ni50Mn50 alloy. Its resistivity and coefficient of thermal expansion are measured over a wide temperature range. © 2013 Pleiades Publishing, Ltd
A Unified treatment of small and large- scale dynamos in helical turbulence
Helical turbulence is thought to provide the key to the generation of
large-scale magnetic fields. Turbulence also generically leads to rapidly
growing small-scale magnetic fields correlated on the turbulence scales. These
two processes are usually studied separately. We give here a unified treatment
of both processes, in the case of random fields, incorporating also a simple
model non-linear drift. In the process we uncover an interesting plausible
saturated state of the small-scale dynamo and a novel analogy between quantum
mechanical (QM) tunneling and the generation of large scale fields. The steady
state problem of the combined small/large scale dynamo, is mapped to a
zero-energy, QM potential problem; but a potential which, for non-zero mean
helicity, allows tunneling of bound states. A field generated by the
small-scale dynamo, can 'tunnel' to produce large-scale correlations, which in
steady state, correspond to a force-free 'mean' field.Comment: 4 pages, 1 figure, Physical Review Letters, in pres
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