2,134 research outputs found
Analytic calculation of energies and wave functions of the quartic and pure quartic oscillators
Ground state energies and wave functions of quartic and pure quartic
oscillators are calculated by first casting the Schr\"{o}dinger equation into a
nonlinear Riccati form and then solving that nonlinear equation analytically in
the first iteration of the quasilinearization method (QLM). In the QLM the
nonlinear differential equation is solved by approximating the nonlinear terms
by a sequence of linear expressions. The QLM is iterative but not perturbative
and gives stable solutions to nonlinear problems without depending on the
existence of a smallness parameter. Our explicit analytic results are then
compared with exact numerical and also with WKB solutions and it is found that
our ground state wave functions, using a range of small to large coupling
constants, yield a precision of between 0.1 and 1 percent and are more accurate
than WKB solutions by two to three orders of magnitude. In addition, our QLM
wave functions are devoid of unphysical turning point singularities and thus
allow one to make analytical estimates of how variation of the oscillator
parameters affects physical systems that can be described by the quartic and
pure quartic oscillators.Comment: 8 pages, 12 figures, 1 tabl
Network Security Investment
Analysing potential risk and the allocation of resources for computer network security and
business continuity require strategic, long-term planning. Most companies tend to be reactive and
respond with quick infrastructure solutions. The purpose of risk analysis should be to assist managers
in making informed decisions about investment and developing risk management policies. High
countermeasures expenditure on every aspect of an information system is out of question in a
commercial organisation. Therefore, this expenditure must be directed to reduce corporate exposure to
information system risks in the context of overall business risks. The aim of this paper is to report the
on going research to justify funding for network security expenditure through risk assessment
practice
Masses and Mixings in a Grand Unified Toy Model
The generation of the fermion mass hierarchy in the standard model of
particle physics is a long-standing puzzle. The recent discoveries from
neutrino physics suggests that the mixing in the lepton sector is large
compared to the quark mixings. To understand this asymmetry between the quark
and lepton mixings is an important aim for particle physics. In this regard,
two promising approaches from the theoretical side are grand unified theories
and family symmetries. In this note we try to understand certain general
features of grand unified theories with Abelian family symmetries by taking the
simplest SU(5) grand unified theory as a prototype. We construct an SU(5) toy
model with family symmetry
that, in a natural way, duplicates the observed mass hierarchy and mixing
matrices to lowest approximation. The system for generating the mass hierarchy
is through a Froggatt-Nielsen type mechanism. One idea that we use in the model
is that the quark and charged lepton sectors are hierarchical with small mixing
angles while the light neutrino sector is democratic with larger mixing angles.
We also discuss some of the difficulties in incorporating finer details into
the model without making further assumptions or adding a large scalar sector.Comment: 21 pages, 2 figures, RevTeX, v2: references updated and typos
corrected, v3: updated top quark mass, comments on MiniBooNE result, and
typos correcte
Neutrino induced reactions related to the -process nucleosynthesis of Nb and Tc
It has recently been proposed that Nb and Tc may
have been formed in the -process. We investigate the neutrino induced
reactions related to the -process origin of the two odd-odd nuclei. The
main neutrino reactions for Nb are the charged-current (CC)
Zr()Nb and the neutral-current (NC) Nb( n)Nb reactions. The main
reactions for Tc, are the CC reaction
Mo()Tc and the NC reaction Ru( p)Tc. Our calculations are carried
out using the quasi-particle random phase approximation. Numerical results are
presented for the energy and temperature dependent cross sections. Since charge
exchange reactions by neutrons may also lead to the formation of
Nb and Tc, we discuss the feasibility of the
Mo(n,p)Nb and Ru(n,p)Tc reactions to produce these
nuclei.Comment: 21 pages, 8 figure
Information and network management security Investment
In today’s business environment it is difficult to obtain senior management approval for
the expenditure of valuable resources to “guarantee “that a potentially disastrous event will not occur
that could affect the organisation performance. Analysing potential risk and the allocation of
resources for computer network security and business continuity require strategic, long-term
planning. Most companies tend to be reactive and respond with quick infrastructure solutions. A
strategic approach to computer network security leads to a more efficient plan and a less expensive
risk-management strategy. Financial modelling is a fundamental component of all business
investment cases. IT security investment proposals have unique qualities that can pose expenditure
justification challenges. This paper aims to explore various financial models and to develop one that
IT managers can effectively use to support their business cases
On the Integrability, B\"Acklund Transformation and Symmetry Aspects of a Generalized Fisher Type Nonlinear Reaction-Diffusion Equation
The dynamics of nonlinear reaction-diffusion systems is dominated by the
onset of patterns and Fisher equation is considered to be a prototype of such
diffusive equations. Here we investigate the integrability properties of a
generalized Fisher equation in both (1+1) and (2+1) dimensions. A Painlev\'e
singularity structure analysis singles out a special case () as
integrable. More interestingly, a B\"acklund transformation is shown to give
rise to a linearizing transformation for the integrable case. A Lie symmetry
analysis again separates out the same case as the integrable one and
hence we report several physically interesting solutions via similarity
reductions. Thus we give a group theoretical interpretation for the system
under study. Explicit and numerical solutions for specific cases of
nonintegrable systems are also given. In particular, the system is found to
exhibit different types of travelling wave solutions and patterns, static
structures and localized structures. Besides the Lie symmetry analysis,
nonclassical and generalized conditional symmetry analysis are also carried
out.Comment: 30 pages, 10 figures, to appear in Int. J. Bifur. Chaos (2004
OligoWalk: an online siRNA design tool utilizing hybridization thermodynamics
Given an mRNA sequence as input, the OligoWalk web server generates a list of small interfering RNA (siRNA) candidate sequences, ranked by the probability of being efficient siRNA (silencing efficacy greater than 70%). To accomplish this, the server predicts the free energy changes of the hybridization of an siRNA to a target mRNA, considering both siRNA and mRNA self-structure. The free energy changes of the structures are rigorously calculated using a partition function calculation. By changing advanced options, the free energy changes can also be calculated using less rigorous lowest free energy structure or suboptimal structure prediction methods for the purpose of comparison. Considering the predicted free energy changes and local siRNA sequence features, the server selects efficient siRNA with high accuracy using a support vector machine. On average, the fraction of efficient siRNAs selected by the server that will be efficient at silencing is 78.6%. The OligoWalk web server is freely accessible through internet at http://rna.urmc.rochester.edu/servers/oligowalk
Direct Signals for Large Extra Dimensions in the Production of Fermion Pairs at Linear Colliders
We analyze the potentiality of the new generation of linear
colliders to search for large extra dimensions via the production of fermion
pairs in association with Kaluza-Klein gravitons (G), i.e. . This process leads to a final state exhibiting a significant amount
of missing energy in addition to acoplanar lepton or jet pairs. We study in
detail this reaction using full tree level contibutions due to the graviton
emission and the standard model backgrounds. After choosing the cuts to enhance
the signal, we show that a linear collider with a center-of-mass energy of 500
GeV will be able to probe quantum gravity scales from 0.96(0.86) up to 4.1(3.3)
TeV at 2(5) level, depending on the number of extra dimensions.Comment: 19 pages, 5 figures. Using RevTex, axodraw.sty. Discussion was
extended. No changes in the results. Accepted for publication by Phys. Rev.
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