10,263 research outputs found
A family of rotation numbers for discrete random dynamics on the circle
We revisit the problem of well-defining rotation numbers for discrete random
dynamical systems on the circle. We show that, contrasting with deterministic
systems, the topological (i.e. based on Poincar\'{e} lifts) approach does
depend on the choice of lifts (e.g. continuously for nonatomic randomness).
Furthermore, the winding orbit rotation number does not agree with the
topological rotation number. Existence and conversion formulae between these
distinct numbers are presented. Finally, we prove a sampling in time theorem
which recover the rotation number of continuous Stratonovich stochastic
dynamical systems on out of its time discretisation of the flow.Comment: 15 page
Robustness of the O() universality class
We calculate the critical exponents for Lorentz-violating O()
scalar field theories by using two independent methods. In
the first situation we renormalize a massless theory by utilizing normalization
conditions. An identical task is fulfilled in the second case in a massive
version of the same theory, previously renormalized in the BPHZ method in four
dimensions. We show that although the renormalization constants, the
and anomalous dimensions acquire Lorentz-violating quantum corrections, the
outcome for the critical exponents in both methods are identical and
furthermore they are equal to their Lorentz-invariant counterparts. Finally we
generalize the last two results for all loop levels and we provide symmetry
arguments for justifying the latter
Rod-like Polyelectrolytes in Presence of Monovalent Salt
We investigate the properties of rigid polyelectrolyte solutions in presence
of monovalent salt. The free energy within the Debye-H\"uckel-Bjerrum (DHBj)
theory [M. E.
Fisher and Y. Levin, {\it Phys. Rev. Lett.} 71, 3826 (1993)] is constructed.
It is found that at thermodynamic equilibrium the polyelectrolyte solution
consists of clusters composed of one polyion and various counterions. The
distribution of the cluster densities is determined by finding the minimum of
the Helmholtz free energy. The osmotic pressure and the average charge of the
cluster are found and their dependence on Manning parameter is
elucidated. A good agreement with the experimental results is obtained.Comment: 11 pages, Revtex (using twocolumn style), 15 figures and postscript
file. Submitted to Macromomelecule
Amphiphile Adsorption on Rigid Polyelectrolytes
A theory is presented which quantitatively accounts for the cooperative
adsorption of cationic surfactants to anionic polyelectrolytes. For high salt
concentration we find that the critical adsorption concentration (CAC) is a
bilinear function of the polyion monomer and salt concentrations, with the
coefficients dependent only on the type of surfactant used. The results
presented in the paper might be useful for designing more efficient gene
delivery systems
Unfolding spinor wavefunctions and expectation values of general operators: Introducing the unfolding-density operator
We show that the spectral weights used for the
unfolding of two-component spinor eigenstates can be decomposed as the sum of the
partial spectral weights calculated for each
component independently, effortlessly turning a possibly
complicated problem involving two coupled quantities into two independent
problems of easy solution. Furthermore, we define the unfolding-density
operator , which unfolds the
primitive cell expectation values of any
arbitrary operator according to
. As a proof of concept, we apply the method to
obtain the unfolded band structures, as well as the expectation values of the
Pauli spin matrices, for prototypical physical systems described by
two-component spinor eigenfunctions
Systematic evaluation of software product line architectures
The architecture of a software product line is one of its most important artifacts as it represents an abstraction of the products that can be generated. It is crucial to evaluate the quality attributes of a product line architecture in order to: increase the productivity of the product line process and the quality of the products; provide a means to understand the potential behavior of the products and, consequently, decrease their time to market; and, improve the handling of the product line variability. The evaluation of product line architecture can serve as a basis to analyze the managerial and economical values of a product line for software managers and architects. Most of the current research on the evaluation of product line architecture does not take into account metrics directly obtained from UML models and their variabilities; the metrics used instead are difficult to be applied in general and to be used for quantitative analysis. This paper presents a Systematic Evaluation Method for UML-based Software Product Line Architecture, the SystEM-PLA. SystEM-PLA differs from current research as it provides stakeholders with a means to: (i) estimate and analyze potential products; (ii) use predefined basic UML-based metrics to compose quality attribute metrics; (iii) perform feasibility and trade-off analysis of a product line architecture with respect to its quality attributes; and, (iv) make the evaluation of product line architecture more flexible. An example using the SEI’s Arcade Game Maker (AGM) product line is presented as a proof of concept, illustrating SystEM-PLA activities. Metrics for complexity and extensibility quality attributes are defined and used to
perform a trade-off analysis
- …