1,910 research outputs found
Fourth SM Family Manifestations at CLIC
The latest electroweak precision data allow the existence of additional
chiral generations in the standard model. We study prospects of search for the
fourth standard model family fermions and quarkonia at and options of CLIC. It is shown that CLIC will be powerfull machine for
discovery and investigation of both fourth family leptons and quarkonia.
Moreover, the formation of the fourth family quarkonia will give a new
opportunity to investigate Higgs boson properties.Comment: 7 pages, 6 Table
Spectral characteristics for a spherically confined -1/r + br^2 potential
We consider the analytical properties of the eigenspectrum generated by a
class of central potentials given by V(r) = -a/r + br^2, b>0. In particular,
scaling, monotonicity, and energy bounds are discussed. The potential is
considered both in all space, and under the condition of spherical confinement
inside an impenetrable spherical boundary of radius R. With the aid of the
asymptotic iteration method, several exact analytic results are obtained which
exhibit the parametric dependence of energy on a, b, and R, under certain
constraints. More general spectral characteristics are identified by use of a
combination of analytical properties and accurate numerical calculations of the
energies, obtained by both the generalized pseudo-spectral method, and the
asymptotic iteration method. The experimental significance of the results for
both the free and confined potential V(r) cases are discussed.Comment: 16 pages, 4 figure
Solutions for certain classes of Riccati differential equation
We derive some analytic closed-form solutions for a class of Riccati equation
y'(x)-\lambda_0(x)y(x)\pm y^2(x)=\pm s_0(x), where \lambda_0(x), s_0(x) are
C^{\infty}-functions. We show that if \delta_n=\lambda_n
s_{n-1}-\lambda_{n-1}s_n=0, where \lambda_{n}=
\lambda_{n-1}^\prime+s_{n-1}+\lambda_0\lambda_{n-1} and
s_{n}=s_{n-1}^\prime+s_0\lambda_{k-1}, n=1,2,..., then The Riccati equation has
a solution given by y(x)=\mp s_{n-1}(x)/\lambda_{n-1}(x). Extension to the
generalized Riccati equation y'(x)+P(x)y(x)+Q(x)y^2(x)=R(x) is also
investigated.Comment: 10 page
Solvable Systems of Linear Differential Equations
The asymptotic iteration method (AIM) is an iterative technique used to find
exact and approximate solutions to second-order linear differential equations.
In this work, we employed AIM to solve systems of two first-order linear
differential equations. The termination criteria of AIM will be re-examined and
the whole theory is re-worked in order to fit this new application. As a result
of our investigation, an interesting connection between the solution of linear
systems and the solution of Riccati equations is established. Further, new
classes of exactly solvable systems of linear differential equations with
variable coefficients are obtained. The method discussed allow to construct
many solvable classes through a simple procedure.Comment: 13 page
Two-dimensional random walk in a bounded domain
In a recent Letter Ciftci and Cakmak [EPL 87, 60003 (2009)] showed that the
two dimensional random walk in a bounded domain, where walkers which cross the
boundary return to a base curve near origin with deterministic rules, can
produce regular patterns. Our numerical calculations suggest that the
cumulative probability distribution function of the returning walkers along the
base curve is a Devil's staircase, which can be explained from the mapping of
these walks to a non-linear stochastic map. The non-trivial probability
distribution function(PDF) is a universal feature of CCRW characterized by the
fractal dimension d=1.75(0) of the PDF bounding curve.Comment: 4 pages, 7 eps figures, revtex
- …