1,165 research outputs found
Torsional Alfvén waves: magneto-seismology in static and dynamic coronal plasmas
Aims: We study the properties of torsional Alfvén waves in coronal loops so that they may be exploited for coronal seismological applications.
Methods: The governing equation is obtained for standing torsional Alfvén waves of a dynamic, gravitationally stratified plasma. The footpoints are assumed to obey line-tying conditions necessary for standing oscillations. Solutions are found in a number of different but typical scenarios to demonstrate the possibilities for both temporal and spatial magneto-seismology exploitation of waveguides with the standing torsional Alfvén oscillations.
Results: It is found that the frequency of the standing Alfvén oscillation increases as the stratification of the plasma increases. The ratio of the periods of the fundamental modeand the first overtone is also found to change as the stratification of the plasma increases. Further, the eigenfunctions of the higher overtones of the standing oscillations are found to experience a shift of their anti-nodes. The influence of a dynamic plasma on the amplitudes of the mode is also investigated. The amplitude of the torsional Alfvén mode is found to increase as the plasma within the coronal loop experiences cooling
Dam Rain and Cumulative Gain
We consider a financial contract that delivers a single cash flow given by
the terminal value of a cumulative gains process. The problem of modelling and
pricing such an asset and associated derivatives is important, for example, in
the determination of optimal insurance claims reserve policies, and in the
pricing of reinsurance contracts. In the insurance setting, the aggregate
claims play the role of the cumulative gains, and the terminal cash flow
represents the totality of the claims payable for the given accounting period.
A similar example arises when we consider the accumulation of losses in a
credit portfolio, and value a contract that pays an amount equal to the
totality of the losses over a given time interval. An explicit expression for
the value process is obtained. The price of an Arrow-Debreu security on the
cumulative gains process is determined, and is used to obtain a closed-form
expression for the price of a European-style option on the value of the asset.
The results obtained make use of various remarkable properties of the gamma
bridge process, and are applicable to a wide variety of financial products
based on cumulative gains processes such as aggregate claims, credit portfolio
losses, defined-benefit pension schemes, emissions, and rainfall.Comment: 25 Pages, 1 Figur
The Open String Regge Trajectory and Its Field Theory Limit
We study the properties of the leading Regge trajectory in open string theory
including the open string planar one-loop corrections. With SU(N) Chan-Paton
factors, the sum over planar open string multi-loop diagrams describes the 't
Hooft limit N\to\infty. Our motivation is to improve the understanding of open
string theory at finite \alpha' as a model of gauge theories. SU(N) gauge
theories in D space-time dimensions are described by requiring open strings to
end on a stack of N Dp-branes of space-time dimension D=p+1. The large N
leading trajectory \alpha(t)=1+\alpha' t+\Sigma(t) can be extracted, through
order g^2, from the s\to-\infty limit, at fixed t, of the four open string tree
and planar loop diagrams. We analyze the t\to0 behavior with the result that
\Sigma(t)\sim-Cg^2(-\alpha' t)^{(D-4)/2}/(D-4). This result precisely tracks
the 1-loop Reggeized gluon of gauge theory in D>4 space-time dimensions. In
particular, for D\to4 it reproduces the known infrared divergences of gauge
theory in 4 dimensions with a Regge trajectory behaving as -\ln(-\alpha^\prime
t). We also study \Sigma(t) in the limit t\to-\infty and show that, when D<8,
it behaves as \alpha^\prime t/(\ln(-\alpha^\prime t))^{\gamma}, where \gamma>0
depends on D and the number of massless scalars. Thus, as long as 4<D<8, the
1-loop correction stays small relative to the tree trajectory for the whole
range -\infty<t<0. Finally we present the results of numerical calculations of
\Sigma(t) for all negative t.Comment: 19 pages, 5 figure
How Privacy Regulations Could Better Tackle Challenges Stemming from Combining Data Sets
Modern information and communication technology practices present novel
threats to privacy. This paper focuses on some shortcomings in current privacy
and data protection regulations' ability to adequately address the
ramifications of some AI-driven data processing practices, in particular where
data sets are combined and processed by AI systems. We raise attention to two
regulatory anomalies related to two fundamental assumptions underlying
traditional privacy and data protection approaches: (1) Only personally
identifiable information (PII)/personal data require privacy protection:
Privacy and data protection regulations are only triggered with respect to
PII/personal data, but not anonymous data. This is not only problematic because
determining whether data falls in the former or latter category is no longer
straightforward, but also because privacy risks associated with data processing
may exist whether or not an individual can be identified. (2) Given sufficient
information provided in a transparent and understandable manner, individuals
are able to adequately assess the privacy implications of their actions and
protect their privacy interests: We show that this assumption corresponds to
the current societal consensus on privacy protection. However, relying on human
privacy expectations fails to address some important privacy threats, because
those expectations are increasingly at odds with the actual privacy
implications of data processing practices, as most people lack the necessary
technical literacy to understand the sophisticated technologies at play, not to
mention correctly assess their privacy implications.Comment: 18 page
The effect of twisted magnetic field on the resonant absorption of MHD waves in coronal loops
The standing quasi modes in a cylindrical incompressible flux tube with
magnetic twist that undergoes a radial density structuring is considered in
ideal magnetohydrodynamics (MHD). The radial structuring is assumed to be a
linearly varying density profile. Using the relevant connection formulae, the
dispersion relation for the MHD waves is derived and solved numerically to
obtain both the frequencies and damping rates of the fundamental and
first-overtone modes of both the kink (m=1) and fluting (m=2,3) waves. It was
found that a magnetic twist will increase the frequencies, damping rates and
the ratio of the oscillation frequency to the damping rate of these modes. The
period ratio P_1/P_2 of the fundamental and its first-overtone surface waves
for kink (m=1) and fluting (m=2,3) modes is lower than 2 (the value for an
untwisted loop) in the presence of twisted magnetic field. For the kink modes,
particularly, the magnetic twists B_{\phi}/B_z=0.0065 and 0.0255 can achieve
deviations from 2 of the same order of magnitude as in the observations.
Furthermore, for the fundamental kink body waves, the frequency bandwidth
increases with increasing the magnetic twist.Comment: 18 pages, 9 figure
Sum rules for correlation functions of ionic mixtures in arbitrary dimension
The correlations in classical multi-component ionic mixtures with spatial
dimension are studied by using a restricted grand-canonical ensemble
and the associated hierarchy equations for the correlation functions. Sum rules
for the first few moments of the two-particle correlation function are derived
and their dependence on is established. By varying continuously near
it is shown how the sum rules for the two-dimensional mixture are related
to those for mixtures at higher .Comment: 19 page
Solar feature tracking in both spatial and temporal domains
A new method for automated coronal loop tracking, in both spatial and temporal
domains, is presented. The reliability of this technique was tested with TRACE 171A observations.
The application of this technique to a flare-induced kink-mode oscillation, revealed a
3500 km spatial periodicity which occur along the loop edge. We establish a reduction in oscillatory
power, for these spatial periodicities, of 45% over a 322 s interval. We relate the reduction
in oscillatory power to the physical damping of these loop-top oscillations
Nonlinear effects in resonant layers in solar and space plasmas
The present paper reviews recent advances in the theory of nonlinear driven
magnetohydrodynamic (MHD) waves in slow and Alfven resonant layers. Simple
estimations show that in the vicinity of resonant positions the amplitude of
variables can grow over the threshold where linear descriptions are valid.
Using the method of matched asymptotic expansions, governing equations of
dynamics inside the dissipative layer and jump conditions across the
dissipative layers are derived. These relations are essential when studying the
efficiency of resonant absorption. Nonlinearity in dissipative layers can
generate new effects, such as mean flows, which can have serious implications
on the stability and efficiency of the resonance
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