39,546 research outputs found
CP Violation in Fourth Generation Quark Decays
We show that, if a fourth generation is discovered at the Tevatron or LHC,
one could study CP violation in b' \to s decays. Asymmetries could reach 30%
for b'\to sZ for m_{b'} \lesssim 350 GeV, while it could be greater than 50%
for b'\to s\gamma and extend to higher m_{b'}. Branching ratios are
10^{-3}--10^{-5}, and CPV measurement requires tagging. Once measured, however,
the CPV phase can be extracted with little theoretical uncertainty.Comment: 4 pages, 7 eps figure
The singular perturbation of surface tension in Hele-Shaw flows
Morphological instabilities are common to pattern formation problems such as the non-equilibrium growth of crystals and directional solidification. Very small perturbations caused by noise originate convoluted interfacial patterns when surface tension is small. The generic mechanisms in the formation of these complex patterns are present in the simpler problem of a Hele-Shaw interface. Amid this extreme noise sensitivity, what is then the role played by small surface tension in the dynamic formation and selection of these patterns? What is the asymptotic behaviour of the interface in the limit as surface tension tends to zero? The ill-posedness of the zero-surface-tension problem and the singular nature of surface tension pose challenging difficulties in the investigation of these questions. Here, we design a novel numerical method that greatly reduces the impact of noise, and allows us to accurately capture and identify the singular contributions of extremely small surface tensions. The numerical method combines the use of a compact interface parametrization, a rescaling of the governing equations, and very high precision. Our numerical results demonstrate clearly that the zero-surface-tension limit is indeed singular. The impact of a surface-tension-induced complex singularity is revealed in detail. The singular effects of surface tension are first felt at the tip of the interface and subsequently spread around it. The numerical simulations also indicate that surface tension defines a length scale in the fingers developing in a later stage of the interface evolution
Determination of a Type of Permutation Binomials over Finite Fields
Let f=a\x+\x^{3q-2}\in\Bbb F_{q^2}[\x], where . We
prove that is a permutation polynomial of if and only if one
of the following occurs: (i) , odd, and is a
primitive rd root of unity. (ii) belongs to a finite set which is
determined in the paper
On Singularity Formation of a Nonlinear Nonlocal System
We investigate the singularity formation of a nonlinear nonlocal system. This
nonlocal system is a simplified one-dimensional system of the 3D model that was
recently proposed by Hou and Lei in [13] for axisymmetric 3D incompressible
Navier-Stokes equations with swirl. The main difference between the 3D model of
Hou and Lei and the reformulated 3D Navier-Stokes equations is that the
convection term is neglected in the 3D model. In the nonlocal system we
consider in this paper, we replace the Riesz operator in the 3D model by the
Hilbert transform. One of the main results of this paper is that we prove
rigorously the finite time singularity formation of the nonlocal system for a
large class of smooth initial data with finite energy. We also prove the global
regularity for a class of smooth initial data. Numerical results will be
presented to demonstrate the asymptotically self-similar blow-up of the
solution. The blowup rate of the self-similar singularity of the nonlocal
system is similar to that of the 3D model.Comment: 28 pages, 9 figure
A characterization of positive linear maps and criteria of entanglement for quantum states
Let and be (finite or infinite dimensional) complex Hilbert spaces. A
characterization of positive completely bounded normal linear maps from
into is given, which particularly gives a
characterization of positive elementary operators including all positive linear
maps between matrix algebras. This characterization is then applied give a
representation of quantum channels (operations) between infinite-dimensional
systems. A necessary and sufficient criterion of separability is give which
shows that a state on is separable if and only if
for all positive finite rank elementary operators
. Examples of NCP and indecomposable positive linear maps are given and
are used to recognize some entangled states that cannot be recognized by the
PPT criterion and the realignment criterion.Comment: 20 page
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