48,603 research outputs found
Meson Mass Spectrum of Heavy-Light Quarks Combinations with Dirac Equation
We use the Dirac equation to study the mass spectrum of mesons with
heavy-light quark combinations. First we study the Dirac equation with
spherically symmetry and funnel potential, and apply them on the hydrogen-like
atom problem to check the correctness of our numerical program. Then we test
the parameters in Olsson's paper. We show that Olsson's parameters are good in
fitting the averaged central mass, but fail to get correct energy fine
splitting. Finally we fit the mass spectrum data of D, D_s, B and B_s mesons
with our parameters by solve the Dirac equation and funnel potential, calculate
the energy splitting of the S and P states. Our parameters can fit the mass and
fine splitting with errors in less than 7 MeV.Comment: 23 pages, 13 fig. v3, correct typo, add fig, add average dat
Convergence of the largest eigenvalue of normalized sample covariance matrices when p and n both tend to infinity with their ratio converging to zero
Let
where 's are independent and identically distributed (i.i.d.) random
variables with and . It is showed
that the largest eigenvalue of the random matrix
tends to 1 almost surely as with
.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ381 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
The effect of electromechanical coupling on the strain in AlGaN/GaN heterojunction field effect transistors
The strain in AlGaN/GaN heterojunction field-effect transistors (HFETs) is
examined theoretically in the context of the fully-coupled equation of state
for piezoelectric materials. Using a simple analytical model, it is shown that,
in the absence of a two-dimensional electron gas (2DEG), the out-of-plane
strain obtained without electromechanical coupling is in error by about 30% for
an Al fraction of 0.3. This result has consequences for the calculation of
quantities that depend directly on the strain tensor. These quantities include
the eigenstates and electrostatic potential in AlGaN/GaN heterostructures. It
is shown that for an HFET, the electromechanical coupling is screened by the
2DEG. Results for the electromechanical model, including the 2DEG, indicate
that the standard (decoupled) strain model is a reasonable approximation for
HFET calculataions. The analytical results are supported by a self-consistent
Schr\"odinger-Poisson calculation that includes the fully-coupled equation of
state together with the charge-balance equation.Comment: 6 figures, revte
Turbulence-Induced Relative Velocity Of Dust Particles. III. The Probability Distribution
Motivated by its important role in the collisional growth of dust particles in protoplanetary disks, we investigate the probability distribution function (PDF) of the relative velocity of inertial particles suspended in turbulent flows. Using the simulation from our previous work, we compute the relative velocity PDF as a function of the friction timescales, tau(p1) and tau(p2), of two particles of arbitrary sizes. The friction time of the particles included in the simulation ranges from 0.1 tau(eta) to 54T(L), where tau(eta) and T-L are the Kolmogorov time and the Lagrangian correlation time of the flow, respectively. The relative velocity PDF is generically non-Gaussian, exhibiting fat tails. For a fixed value of tau(p1), the PDF shape is the fattest for equal-size particles (tau(p2) = tau(p1)), and becomes thinner at both tau(p2) tau(p1). Defining f as the friction time ratio of the smaller particle to the larger one, we find that, at a given f in (1/2) less than or similar to f less than or similar to 1, the PDF fatness first increases with the friction time tau(p,h) of the larger particle, peaks at tau(p,h) similar or equal to tau(eta), and then decreases as tp, h increases further. For 0 > T-L). These features are successfully explained by the Pan & Padoan model. Using our simulation data and some simplifying assumptions, we estimated the fractions of collisions resulting in sticking, bouncing, and fragmentation as a function of the dust size in protoplanetary disks, and argued that accounting for non-Gaussianity of the collision velocity may help further alleviate the bouncing barrier problem.Astronom
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