7,297 research outputs found
Embeddings of rearrangement invariant spaces that are not strictly singular
We give partial answers to the following conjecture: the natural embedding of
a rearrangement invariant space E into L_1([0,1]) is strictly singular if and
only if G does not embed into E continuously, where G is the closure of the
simple functions in the Orlicz space L_Phi with Phi(x) = exp(x^2)-1.Comment: Also available at http://www.math.missouri.edu/~stephen/preprint
Capacitively-coupled rf discharge with a large amount of microparticles: spatiotemporal emission pattern and microparticle arrangement
The effect of micron-sized particles on a low-pressure capacitively-coupled
rf discharge is studied both experimentally and using numerical simulations. In
the laboratory experiments, microparticle clouds occupying a considerable
fraction of the discharge volume are supported against gravity with the help of
the thermophoretic force. The spatiotemporally resolved optical emission
measurements are performed with different arrangements of microparticles. The
numerical simulations are carried out on the basis of a one-dimensional hybrid
(fluid-kinetic) discharge model describing the interaction between plasma and
microparticles in a self-consistent way. The study is focused on the role of
microparticle arrangement in interpreting the spatiotemporal emission
measurements. We show that it is not possible to reproduce simultaneously the
observed microparticle arrangement and emission pattern in the framework of the
considered one-dimensional model. This disagreement is discussed and attributed
to two-dimensional effects, e.g., radial diffusion of the plasma components
Weak ferromagnetism of antiferromagnetic domains in graphene with defects
Magnetic properties of graphene with randomly distributed magnetic
defects/vacancies are studied in terms of the Kondo Hamiltonian in the mean
field approximation. It has been shown that graphene with defects undergoes a
magnetic phase transition from a paramagnetic to a antiferromagnetic (AFM)
phase once the temperature reaches the critical point . The defect
straggling is taken into account as an assignable cause of multiple nucleation
into AFM domains. Since each domain is characterized by partial compensating
magnetization of the defects associated with different sublattices, together
they reveal a super-paramagnetic behavior in a magnetic field. Theory
qualitatively describe the experimental data provided the temperature
dependence of the AFM domain structure.Comment: 8 pages, 2 figure
Mixed Quantum/Classical Approach for Description of Molecular Collisions in Astrophysical Environments
An efficient and accurate mixed quantum/classical theory approach for computational treatment of inelastic scattering is extended to describe collision of an atom with a general asymmetric-top rotor polyatomic molecule. Quantum mechanics, employed to describe transitions between the internal states of the molecule, and classical mechanics, employed for description of scattering of the atom, are used in a self-consistent manner. Such calculations for rotational excitation of HCOOCH3 in collisions with He produce accurate results at scattering energies above 15 cm–1, although resonances near threshold, below 5 cm–1, cannot be reproduced. Importantly, the method remains computationally affordable at high scattering energies (here up to 1000 cm–1), which enables calculations for larger molecules and at higher collision energies than was possible previously with the standard full-quantum approach. Theoretical prediction of inelastic cross sections for a number of complex organic molecules observed in space becomes feasible using this new computational tool
A DC Programming Approach for Solving Multicast Network Design Problems via the Nesterov Smoothing Technique
This paper continues our effort initiated in [9] to study Multicast
Communication Networks, modeled as bilevel hierarchical clustering problems, by
using mathematical optimization techniques. Given a finite number of nodes, we
consider two different models of multicast networks by identifying a certain
number of nodes as cluster centers, and at the same time, locating a particular
node that serves as a total center so as to minimize the total transportation
cost through the network. The fact that the cluster centers and the total
center have to be among the given nodes makes this problem a discrete
optimization problem. Our approach is to reformulate the discrete problem as a
continuous one and to apply Nesterov smoothing approximation technique on the
Minkowski gauges that are used as distance measures. This approach enables us
to propose two implementable DCA-based algorithms for solving the problems.
Numerical results and practical applications are provided to illustrate our
approach
Classification of All Poisson-Lie Structures on an Infinite-Dimensional Jet Group
A local classification of all Poisson-Lie structures on an
infinite-dimensional group of formal power series is given. All
Lie bialgebra structures on the Lie algebra {\Cal G}_{\infty} of
are also classified.Comment: 11 pages, AmSTeX fil
Equivariant Symplectic Geometry of Gauge Fixing in Yang-Mills Theory
The Faddeev-Popov gauge fixing in Yang-Mills theory is interpreted as
equivariant localization. It is shown that the Faddeev-Popov procedure amounts
to a construction of a symplectic manifold with a Hamiltonian group action. The
BRST cohomology is shown to be equivalent to the equivariant cohomology based
on this symplectic manifold with Hamiltonian group action. The ghost operator
is interpreted as a (pre)symplectic form and the gauge condition as the moment
map corresponding to the Hamiltonian group action. This results in the
identification of the gauge fixing action as a closed equivariant form, the sum
of an equivariant symplectic form and a certain closed equivariant 4-form which
ensures convergence. An almost complex structure compatible with the symplectic
form is constructed. The equivariant localization principle is used to localize
the path integrals onto the gauge slice. The Gribov problem is also discussed
in the context of equivariant localization principle. As a simple illustration
of the methods developed in the paper, the partition function of N=2
supersymmetric quantum mechanics is calculated by equivariant localizationComment: 46 pages, added remarks, typos and references correcte
Electron spin relaxation in carbon nanotubes
The long standing problem of inexplicably short spin relaxation in carbon
nanotubes (CNTs) is examined. The curvature-mediated spin-orbital interaction
is shown to induce fluctuating electron spin precession causing efficient
relaxation in a manner analogous to the Dyakonov-Perel mechanism. Our
calculation estimates longitudinal (spin-flip) and transversal (decoherence)
relaxation times as short as 150 ps and 110 ps at room temperature,
respectively, along with a pronounced anisotropic dependence. Interference of
electrons originating from different valleys can lead to even faster dephasing.
The results can help clarify the measured data, resolving discrepancies in the
literature.Comment: 9 pages, 3 figure
Mixed Quantum/Classical Calculations of Total and Differential Elastic and Rotationally Inelastic Scattering Cross Sections for Light and Heavy Reduced Masses in a Broad Range of Collision Energies
The mixed quantum/classical theory (MQCT) for rotationally inelastic scattering developed recently [A. Semenov and D. Babikov, J. Chem. Phys.139, 174108 (2013)] is benchmarked against the full quantum calculations for two molecular systems: He + H2 and Na + N2. This allows testing new method in the cases of light and reasonably heavy reduced masses, for small and large rotational quanta, in a broad range of collision energies and rotational excitations. The resultant collision cross sections vary through ten-orders of magnitude range of values. Both inelastic and elastic channels are considered, as well as differential (over scattering angle) cross sections. In many cases results of the mixed quantum/classical method are hard to distinguish from the full quantum results. In less favorable cases (light masses, larger quanta, and small collision energies) some deviations are observed but, even in the worst cases, they are within 25% or so. The method is computationally cheap and particularly accurate at higher energies, heavier masses, and larger densities of states. At these conditions MQCT represents a useful alternative to the standard full-quantum scattering theory
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