5,504 research outputs found
On the MHD load and the MHD metage
In analogy with the load and the metage in hydrodynamics, we define
magnetohydrodynamic load and magnetohydrodynamic metage in the case of
magnetofluids. They can be used to write the magnetic field in MHD in Clebsch's
form. We show how these two concepts can be utilised to derive the magnetic
analogue of the Ertel's theorem and also, how in the presence of non-trivial
topology of the magnetic field in the magnetofluid one may associate the
linking number of the magnetic field lines with the invariant MHD loads. The
paper illustrates that the symmetry translation of the MHD metage in the
corresponding label space generates the conservation of cross helicity.Comment: Some issues in the paper are yet to be addressed. Constructive
critisicms are most welcom
Geometric inequalities from phase space translations
We establish a quantum version of the classical isoperimetric inequality
relating the Fisher information and the entropy power of a quantum state. The
key tool is a Fisher information inequality for a state which results from a
certain convolution operation: the latter maps a classical probability
distribution on phase space and a quantum state to a quantum state. We show
that this inequality also gives rise to several related inequalities whose
counterparts are well-known in the classical setting: in particular, it implies
an entropy power inequality for the mentioned convolution operation as well as
the isoperimetric inequality, and establishes concavity of the entropy power
along trajectories of the quantum heat diffusion semigroup. As an application,
we derive a Log-Sobolev inequality for the quantum Ornstein-Uhlenbeck
semigroup, and argue that it implies fast convergence towards the fixed point
for a large class of initial states.Comment: 37 pages; updated to match published versio
Randomized Composable Core-sets for Distributed Submodular Maximization
An effective technique for solving optimization problems over massive data
sets is to partition the data into smaller pieces, solve the problem on each
piece and compute a representative solution from it, and finally obtain a
solution inside the union of the representative solutions for all pieces. This
technique can be captured via the concept of {\em composable core-sets}, and
has been recently applied to solve diversity maximization problems as well as
several clustering problems. However, for coverage and submodular maximization
problems, impossibility bounds are known for this technique \cite{IMMM14}. In
this paper, we focus on efficient construction of a randomized variant of
composable core-sets where the above idea is applied on a {\em random
clustering} of the data. We employ this technique for the coverage, monotone
and non-monotone submodular maximization problems. Our results significantly
improve upon the hardness results for non-randomized core-sets, and imply
improved results for submodular maximization in a distributed and streaming
settings.
In summary, we show that a simple greedy algorithm results in a
-approximate randomized composable core-set for submodular maximization
under a cardinality constraint. This is in contrast to a known impossibility result for (non-randomized) composable core-set. Our
result also extends to non-monotone submodular functions, and leads to the
first 2-round MapReduce-based constant-factor approximation algorithm with
total communication complexity for either monotone or non-monotone
functions. Finally, using an improved analysis technique and a new algorithm
, we present an improved -approximation algorithm
for monotone submodular maximization, which is in turn the first
MapReduce-based algorithm beating factor in a constant number of rounds
The geometry of the two-component Camassa-Holm and Degasperis-Procesi equations
We use geometric methods to study two natural two-component generalizations
of the periodic Camassa-Holm and Degasperis-Procesi equations. We show that
these generalizations can be regarded as geodesic equations on the semidirect
product of the diffeomorphism group of the circle \Diff(S^1) with some space
of sufficiently smooth functions on the circle. Our goals are to understand the
geometric properties of these two-component systems and to prove local
well-posedness in various function spaces. Furthermore, we perform some
explicit curvature calculations for the two-component Camassa-Holm equation,
giving explicit examples of large subspaces of positive curvature.Comment: 31 page
Electricâfieldâinduced optical rectification in nitrobenzene
The first observation of dcâelectricâfieldâinduced$optical rectification is eported. In this process a dc polarization is produced in a medium (in this case nitrobenzene) by the simultaneous presence of dc and optical electric fields. The relation between this process and the Kerr effect is found to be consistent with that predicted by permutation symmetry. A bolometerlike response also seen in these experiments is discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70898/2/APPLAB-30-6-276-1.pd
Evaluation of electrospray differential mobility analysis for virus particle analysis: Potential applications for biomanufacturing.
The technique of electrospray differential mobility analysis (ES-DMA) was examined as a potential potency assay for routine virus particle analysis in biomanufacturing environments (e.g., evaluation of vaccines and gene delivery products for lot release) in the context of the International Committee of Harmonisation (ICH) Q2 guidelines. ES-DMA is a rapid particle sizing method capable of characterizing certain aspects of the structure (such as capsid proteins) and obtaining complete size distributions of viruses and virus-like particles. It was shown that ES-DMA can distinguish intact virus particles from degraded particles and measure the concentration of virus particles when calibrated with nanoparticles of known concentration. The technique has a measurement uncertainty of â20%, is linear over nearly 3 orders of magnitude, and has a lower limit of detection of â10(9)particles/mL. This quantitative assay was demonstrated for non-enveloped viruses. It is expected that ES-DMA will be a useful method for applications involving production and quality control of vaccines and gene therapy vectors for human use
Collider Interplay for Supersymmetry, Higgs and Dark Matter
We discuss the potential impacts on the CMSSM of future LHC runs and possible
electron-positron and higher-energy proton-proton colliders, considering
searches for supersymmetry via MET events, precision electroweak physics, Higgs
measurements and dark matter searches. We validate and present estimates of the
physics reach for exclusion or discovery of supersymmetry via MET searches at
the LHC, which should cover the low-mass regions of the CMSSM parameter space
favoured in a recent global analysis. As we illustrate with a low-mass
benchmark point, a discovery would make possible accurate LHC measurements of
sparticle masses using the MT2 variable, which could be combined with
cross-section and other measurements to constrain the gluino, squark and stop
masses and hence the soft supersymmetry-breaking parameters m_0, m_{1/2} and
A_0 of the CMSSM. Slepton measurements at CLIC would enable m_0 and m_{1/2} to
be determined with high precision. If supersymmetry is indeed discovered in the
low-mass region, precision electroweak and Higgs measurements with a future
circular electron-positron collider (FCC-ee, also known as TLEP) combined with
LHC measurements would provide tests of the CMSSM at the loop level. If
supersymmetry is not discovered at the LHC, is likely to lie somewhere along a
focus-point, stop coannihilation strip or direct-channel A/H resonance funnel.
We discuss the prospects for discovering supersymmetry along these strips at a
future circular proton-proton collider such as FCC-hh. Illustrative benchmark
points on these strips indicate that also in this case FCC-ee could provide
tests of the CMSSM at the loop level.Comment: 47 pages, 26 figure
- âŠ