Series Expansion Calculation of Persistence Exponents

We consider an arbitrary Gaussian Stationary Process X(T) with known correlator C(T), sampled at discrete times T_n = n \Delta T. The probability that (n+1) consecutive values of X have the same sign decays as P_n \sim \exp(-\theta_D T_n). We calculate the discrete persistence exponent \theta_D as a series expansion in the correlator C(\Delta T) up to 14th order, and extrapolate to \Delta T = 0 using constrained Pad\'e approximants to obtain the continuum persistence exponent \theta. For the diffusion equation our results are in exceptionally good agreement with recent numerical estimates.Comment: 5 pages; 5 page appendix containing series coefficient

High precision measurement of the associated strangeness production in proton proton interactions

A new high precision measurement of the reaction pp -> pK+Lambda at a beam momentum of 2.95 GeV/c with more than 200,000 analyzed events allows a detailed analysis of differential observables and their inter-dependencies. Correlations of the angular distributions with momenta are examined. The invariant mass distributions are compared for different regions in the Dalitz plots. The cusp structure at the N Sigma threshold is described with the Flatt\'e formalism and its variation in the Dalitz plot is analyzed.Comment: accepted for publication in Eur. Phys. J.

First Model-Independent Measurement of the Spin Triplet pΛp\Lambda Scattering Length from Final State Interaction in the p⃗p→pK+Λ\vec{p}p \rightarrow pK^{+}\Lambda Reaction

The $\vec{p}p \rightarrow pK^{+}\Lambda$ reaction has been measured with the COSY-TOF detector at a beam momentum of $2.7\,\mathrm{GeV}/c$. The polarized proton beam enables the measurement of the beam analyzing power by the asymmetry of the produced kaon ($A_N^{K}$). This observable allows the $p\Lambda$ spin triplet scattering length to be extracted for the first time model independently from the final-state interaction in the reaction. The obtained value is $a_{t} = (-2.55 ^{+0.72}_{-1.39} {}_{\textrm{stat.}} \pm 0.6_{\textrm{syst.}} \pm 0.3_{\textrm{theo.}})\mathrm{fm}$. This value is compatible with theoretical predictions and results from model-dependent analyses.Comment: Revised version as accepted for publication in PR

Painlev\'e V and time dependent Jacobi polynomials

In this paper we study the simplest deformation on a sequence of orthogonal polynomials, namely, replacing the original (or reference) weight $w_0(x)$ defined on an interval by $w_0(x)e^{-tx}.$ It is a well-known fact that under such a deformation the recurrence coefficients denoted as $\alpha_n$ and $\beta_n$ evolve in $t$ according to the Toda equations, giving rise to the time dependent orthogonal polynomials, using Sogo's terminology. The resulting "time-dependent" Jacobi polynomials satisfy a linear second order ode. We will show that the coefficients of this ode are intimately related to a particular Painlev\'e V. In addition, we show that the coefficient of $z^{n-1}$ of the monic orthogonal polynomials associated with the "time-dependent" Jacobi weight, satisfies, up to a translation in $t,$ the Jimbo-Miwa $\sigma$-form of the same $P_{V};$ while a recurrence coefficient $\alpha_n(t),$ is up to a translation in $t$ and a linear fractional transformation $P_{V}(\alpha^2/2,-\beta^2/2, 2n+1+\alpha+\beta,-1/2).$ These results are found from combining a pair of non-linear difference equations and a pair of Toda equations. This will in turn allow us to show that a certain Fredholm determinant related to a class of Toeplitz plus Hankel operators has a connection to a Painlev\'e equation

A quasi classical approach to electron impact ionization

A quasi classical approximation to quantum mechanical scattering in the Moeller formalism is developed. While keeping the numerical advantage of a standard Classical--Trajectory--Monte--Carlo calculation, our approach is no longer restricted to use stationary initial distributions. This allows one to improve the results by using better suited initial phase space distributions than the microcanonical one and to gain insight into the collision mechanism by studying the influence of different initial distributions on the cross section. A comprehensive account of results for single, double and triple differential cross sections for atomic hydrogen will be given, in comparison with experiment and other theories.Comment: 21 pages, 10 figures, submitted to J Phys

Molecular dynamics simulation of the order-disorder phase transition in solid NaNO2_2

We present molecular dynamics simulations of solid NaNO$_2$ using pair potentials with the rigid-ion model. The crystal potential surface is calculated by using an \emph{a priori} method which integrates the \emph{ab initio} calculations with the Gordon-Kim electron gas theory. This approach is carefully examined by using different population analysis methods and comparing the intermolecular interactions resulting from this approach with those from the \emph{ab initio} Hartree-Fock calculations. Our numerics shows that the ferroelectric-paraelectric phase transition in solid NaNO$_2$ is triggered by rotation of the nitrite ions around the crystallographical c axis, in agreement with recent X-ray experiments [Gohda \textit{et al.}, Phys. Rev. B \textbf{63}, 14101 (2000)]. The crystal-field effects on the nitrite ion are also addressed. Remarkable internal charge-transfer effect is found.Comment: RevTeX 4.0, 11 figure

Worker remittances and the global preconditions of ‘smart development’

With the growing environmental crisis affecting our globe, ideas to weigh economic or social progress by the ‘energy input’ necessary to achieve it are increasingly gaining acceptance. This question is intriguing and is being dealt with by a growing number of studies, focusing on the environmental price of human progress. Even more intriguing, however, is the question of which factors of social organization contribute to a responsible use of the resources of our planet to achieve a given social result (‘smart development’). In this essay, we present the first systematic study on how migration – or rather, more concretely, received worker remittances per GDP – helps the nations of our globe to enjoy social and economic progress at a relatively small environmental price. We look at the effects of migration on the balance sheets of societal accounting, based on the ‘ecological price’ of the combined performance of democracy, economic growth, gender equality, human development, research and development, and social cohesion. Feminism in power, economic freedom, population density, the UNDP education index as well as the receipt of worker remittances all significantly contribute towards a ‘smart overall development’, while high military expenditures and a high world economic openness are a bottleneck for ‘smart overall development’

Coevolution of Glauber-like Ising dynamics on typical networks

We consider coevolution of site status and link structures from two different initial networks: a one dimensional Ising chain and a scale free network. The dynamics is governed by a preassigned stability parameter $S$, and a rewiring factor $\phi$, that determines whether the Ising spin at the chosen site flips or whether the node gets rewired to another node in the system. This dynamics has also been studied with Ising spins distributed randomly among nodes which lie on a network with preferential attachment. We have observed the steady state average stability and magnetisation for both kinds of systems to have an idea about the effect of initial network topology. Although the average stability shows almost similar behaviour, the magnetisation depends on the initial condition we start from. Apart from the local dynamics, the global effect on the dynamics has also been studied. These parameters show interesting variations for different values of $S$ and $\phi$, which helps in determining the steady-state condition for a given substrate.Comment: 8 pages, 10 figure

Single-Pion Production in pp Collisions at 0.95 GeV/c (II)

The single-pion production reactions $pp\to d\pi^+$, $pp\to np\pi^+$ and $pp\to pp\pi^0$ were measured at a beam momentum of 0.95 GeV/c ($T_p \approx$ 400 MeV) using the short version of the COSY-TOF spectrometer. The central calorimeter provided particle identification, energy determination and neutron detection in addition to time-of-flight and angle measurements from other detector parts. Thus all pion production channels were recorded with 1-4 overconstraints. Main emphasis is put on the presentation and discussion of the $np\pi^+$ channel, since the results on the other channels have already been published previously. The total and differential cross sections obtained are compared to theoretical calculations. In contrast to the $pp\pi^0$ channel we find in the $np\pi^+$ channel a strong influence of the $\Delta$ excitation already at this energy close to threshold. In particular we find a $(3 cos^2\Theta + 1)$ dependence in the pion angular distribution, typical for a pure s-channel $\Delta$ excitation and identical to that observed in the $d\pi^+$ channel. Since the latter is understood by a s-channel resonance in the $^1D_2$ $pn$ partial wave, we discuss an analogous scenario for the $pn\pi^+$ channel