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Stochastic modelling of the effects of interdependencies between critical infrastructure
An approach to Quantitative Interdependency Analysis, in the context of Large Complex Critical Infrastructures, is presented in this paper. A Discrete state–space, Continuous–time, Stochastic Process models the operation of critical infrastructure, taking interdependencies into account. Of primary interest are the implications of both model detail (that is, level of model abstraction) and model parameterisation for the study of dependencies. Both of these factors are observed to affect the distribution of cascade–sizes within and across infrastructure
Noncentrosymmetric plasmon modes and giant terahertz photocurrent in a two-dimensional plasmonic crystal
We introduce and theoretically study the plasmon-photogalvanic effect in the
planar noncentrosymmetric plasmonic crystal containing a homogeneous
two-dimensional electron system gated by a periodic metal grating with an
asymmetric unit cell. The plasmon-photogalvanic DC current arises due to the
two-dimensional electron drag by the noncentrosymmetric plasmon modes excited
under normal incidence of terahertz radiation. We show that the collective
plasmon modes of the planar plasmonic crystal become strongly
noncentrosymmetric in the weak coupling regime of their anticrossing. Large
plasmon wavevector (which is typically by two-three orders of magnitude greater
than the terahertz photon wavevector) along with strong near-field enhancement
at the plasmon resonance make the plasmonic drag a much stronger effect
compared to the photon drag observed in conventional two-dimensional electron
systems.Comment: 9 pages, 10 figures, submitted to Physical Review
KKbar molecules with momentum-dependent interactions
It is shown that the momentum-dependent kaon-antikaon interactions generated
via vector meson exchange from the standard SU_V(3) x SU_A(3) interaction
Lagrangian lead to a non-local potential in coordinate space that can be
incorporated without approximation into a non-relativistic version of the
Bethe-Salpeter wave equation containing a radial-dependent effective kaon mass
appearing in a fully symmetrized kinetic energy operator, in addition to a
local potential. Estimates of the mass and decay widths of f_0(980) and
a_0(980), considered as KKbar molecules of isospin 0 and 1, as well as for
K^+K^- atomic bound states (kaonium) are presented, and compared with previous
studies of a similar nature. It is argued that without a better knowledge of
hadronic form factors it is not possible to distinguish between the molecular
versus elementary particle models for the structure of the light scalar mesons.Comment: 14 pages, 2 tables, 5 figures. Added subsection on s-channel
exchange, additional remarks on the possible effect of gluon exchange, and 1
additional figur
Vortex mass in a superfluid at low frequencies
An inertial mass of a vortex can be calculated by driving it round in a
circle with a steadily revolving pinning potential. We show that in the low
frequency limit this gives precisely the same formula that was used by Baym and
Chandler, but find that the result is not unique and depends on the force field
used to cause the acceleration. We apply this method to the Gross-Pitaevskii
model, and derive a simple formula for the vortex mass. We study both the long
range and short range properties of the solution. We agree with earlier results
that the non-zero compressibility leads to a divergent mass. From the
short-range behavior of the solution we find that the mass is sensitive to the
form of the pinning potential, and diverges logarithmically when the radius of
this potential tends to zero.Comment: 4 page
Optical bistability in subwavelength apertures containing nonlinear media
We develop a self-consistent method to study the optical response of metallic
gratings with nonlinear media embedded within their subwavelength slits. An
optical Kerr nonlinearity is considered. Due to the large E-fields associated
with the excitation of the transmission resonances appearing in this type of
structures, moderate incoming fluxes result in drastic changes in the
transmission spectra. Importantly, optical bistability is obtained for certain
ranges of both flux and wavelength.Comment: 4 pages, 4 figure
The Zel'dovich effect and evolution of atomic Rydberg spectra along the Periodic Table
In 1959 Ya. B. Zel'dovich predicted that the bound-state spectrum of the
non-relativistic Coulomb problem distorted at small distances by a short-range
potential undergoes a peculiar reconstruction whenever this potential alone
supports a low-energy scattering resonance. However documented experimental
evidence of this effect has been lacking. Previous theoretical studies of this
phenomenon were confined to the regime where the range of the short-ranged
potential is much smaller than Bohr's radius of the Coulomb field. We go beyond
this limitation by restricting ourselves to highly-excited s states. This
allows us to demonstrate that along the Periodic Table of elements the
Zel'dovich effect manifests itself as systematic periodic variation of the
Rydberg spectra with a period proportional to the cubic root of the atomic
number. This dependence, which is supported by analysis of experimental and
numerical data, has its origin in the binding properties of the ionic core of
the atom.Comment: 17 pages, 12 figure
Non-Abelian Vortices, Super-Yang-Mills Theory and Spin(7)-Instantons
We consider a complex vector bundle E endowed with a connection A over the
eight-dimensional manifold R^2 x G/H, where G/H = SU(3)/U(1)xU(1) is a
homogeneous space provided with a never integrable almost complex structure and
a family of SU(3)-structures. We establish an equivalence between G-invariant
solutions A of the Spin(7)-instanton equations on R^2 x G/H and general
solutions of non-Abelian coupled vortex equations on R^2. These vortices are
BPS solitons in a d=4 gauge theory obtained from N=1 supersymmetric Yang-Mills
theory in ten dimensions compactified on the coset space G/H with an
SU(3)-structure. The novelty of the obtained vortex equations lies in the fact
that Higgs fields, defining morphisms of vector bundles over R^2, are not
holomorphic in the generic case. Finally, we introduce BPS vortex equations in
N=4 super Yang-Mills theory and show that they have the same feature.Comment: 14 pages; v2: typos fixed, published versio
NUMERICAL SIMULATION OF DYNAMICS OF BLOCK MEDIA BY MOVABLE LATTICE AND MOVABLE AUTOMATA METHODS
Two versions of modified Burridge-Knopoff model including state dependent friction, elastic force and thermal conductivity are derived. The friction model describes a velocity weakening of friction and elasticity between moving blocks and an increase of both static friction and rigidity during stick periods as well their weakening during motion. It provides a simplified but qualitatively correct behavior including the transition from smooth sliding to stick-slip behavior, which is often observed in various tribological and tectonic systems. Attractor properties of the model dynamics is studied also. The alternative versions of the model are proposed which apply a simulation of the motion of interacting elastically connected mesh elements and motion of relatively large solid blocks, utilizing technique of the movable cellular automata. First version of the model was already basically studied before. Its advanced version here involves all components of the real system: state-depending friction and changeable rigidity, as well as heat production and thermal conductivity. Model based on the movable automata also involves the components included into traditional lattice model. It has its own ad-vantages and disadvantages which are also discussed in the paper
Bloch oscillations in one-dimensional spinor gas
A force applied to a spin-flipped particle in a one-dimensional spinor gas
may lead to Bloch oscillations of particle's position and velocity. The
existence of Bloch oscillations crucially depends on the viscous friction force
exerted by the rest of the gas on the spin excitation. We evaluate the friction
in terms of the quantum fluid parameters. In particular, we show that the
friction is absent for integrable cases, such as SU(2) symmetric gas of bosons
or fermions. For small deviations from the exact integrability the friction is
very weak, opening the possibility to observe Bloch oscillations.Comment: 4 pages, 2 figure
Quantum dynamics and entanglement of a 1D Fermi gas released from a trap
We investigate the entanglement properties of the nonequilibrium dynamics of
one-dimensional noninteracting Fermi gases released from a trap. The gas of N
particles is initially in the ground state within hard-wall or harmonic traps,
then it expands after dropping the trap. We compute the time dependence of the
von Neumann and Renyi entanglement entropies and the particle fluctuations of
spatial intervals around the original trap, in the limit of a large number N of
particles. The results for these observables apply to one-dimensional gases of
impenetrable bosons as well.
We identify different dynamical regimes at small and large times, depending
also on the initial condition, whether it is that of a hard-wall or harmonic
trap. In particular, we analytically show that the expansion from hard-wall
traps is characterized by the asymptotic small-time behavior of the von Neumann entanglement entropy, and the relation
where V is the particle variance, which are analogous to
the equilibrium behaviors whose leading logarithms are essentially determined
by the corresponding conformal field theory with central charge . The time
dependence of the entanglement entropy of extended regions during the expansion
from harmonic traps shows the remarkable property that it can be expressed as a
global time-dependent rescaling of the space dependence of the initial
equilibrium entanglement entropy.Comment: 19 pages, 18 fig
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