Hamiltonian Formalism in Quantum Mechanics

Heisenberg motion equations in Quantum mechanics can be put into the Hamilton form. The difference between the commutator and its principal part, the Poisson bracket, can be accounted for exactly. Canonical transformations in Quantum mechanics are not, or at least not what they appear to be; their properties are formulated in a series of Conjectures

Inter- and intragrain currents in bulk melt-grown YBaCuO rings

A simple contactless method suitable to discern between the intergrain (circular) current, which flows in the thin superconducting ring, and the intragrain current, which does not cross the weakest link, has been proposed. At first, we show that the intergrain current may directly be estimated from the magnetic flux density $B(\pm z_0)$ measured by the Hall sensor positioned in the special points $\pm z_0$ above/below the ring center. The experimental and the numerical techniques to determine the value $z_0$ are discussed. Being very promising for characterization of a current flowing across the joints in welded YBaCuO rings (its dependencies on the temperature and the external magnetic field as well as the time dissipation), the approach has been applied to study corresponding properties of the intra- and intergrain currents flowing across the $a$-twisted grain boundaries which are frequent in bulk melt-textured YBaCuO samples. We present experimental data related to the flux penetration inside a bore of MT YBaCuO rings both in the non-magnetized, virgin state and during the field reversal. The shielding properties and their dependence on external magnetic fields are also studied. Besides, we consider the flux creep effects and their influence on the current re-distribution during a dwell.Comment: 13 pages, 16 figures (EPS), RevTeX4. In the revised version, corrections to perturbing effects near the weak links are introduced, one more figure is added. lin

The influence of gene expression time delays on Gierer-Meinhardt pattern formation systems

There are numerous examples of morphogen gradients controlling long range signalling in developmental and cellular systems. The prospect of two such interacting morphogens instigating long range self-organisation in biological systems via a Turing bifurcation has been explored, postulated, or implicated in the context of numerous developmental processes. However, modelling investigations of cellular systems typically neglect the influence of gene expression on such dynamics, even though transcription and translation are observed to be important in morphogenetic systems. In particular, the influence of gene expression on a large class of Turing bifurcation models, namely those with pure kinetics such as the Gierer–Meinhardt system, is unexplored. Our investigations demonstrate that the behaviour of the Gierer–Meinhardt model profoundly changes on the inclusion of gene expression dynamics and is sensitive to the sub-cellular details of gene expression. Features such as concentration blow up, morphogen oscillations and radical sensitivities to the duration of gene expression are observed and, at best, severely restrict the possible parameter spaces for feasible biological behaviour. These results also indicate that the behaviour of Turing pattern formation systems on the inclusion of gene expression time delays may provide a means of distinguishing between possible forms of interaction kinetics. Finally, this study also emphasises that sub-cellular and gene expression dynamics should not be simply neglected in models of long range biological pattern formation via morphogens

Finding a moral homeground: appropriately critical religious education and transmission of spiritual values

Values-inspired issues remain an important part of the British school curriculum. Avoiding moral relativism while fostering enthusiasm for spiritual values and applying them to non-curricular learning such as school ethos or children's home lives are challenges where spiritual, moral, social and cultural (SMSC) development might benefit from leadership by critical religious education (RE). Whether the school's model of spirituality is that of an individual spiritual tradition (schools of a particular religious character) or universal pluralistic religiosity (schools of plural religious character), the pedagogy of RE thought capable of leading SMSC development would be the dialogical approach with examples of successful implementation described by Gates, Ipgrave and Skeie. Marton's phenomenography, is thought to provide a valuable framework to allow the teacher to be appropriately critical in the transmission of spiritual values in schools of a particular religious character as evidenced by Hella's work in Lutheran schools

Measurement of beauty production in deep inelastic scattering at HERA

The beauty production cross section for deep inelastic scattering events with at least one hard jet in the Breit frame together with a muon has been measured, for photon virtualities Q^2 > 2 GeV^2, with the ZEUS detector at HERA using integrated luminosity of 72 pb^-1. The total visible cross section is sigma_b-bbar (ep -> e jet mu X) = 40.9 +- 5.7 (stat.) +6.0 -4.4 (syst.) pb. The next-to-leading order QCD prediction lies about 2.5 standard deviations below the data. The differential cross sections are in general consistent with the NLO QCD predictions; however at low values of Q^2, Bjorken x, and muon transverse momentum, and high values of jet transverse energy and muon pseudorapidity, the prediction is about two standard deviations below the data.Comment: 18 pages, 4 figure

Measurement of three-jet differential cross sections d sigma-3jet / d M-3jet in p anti-p collisions at sqrt(s)=1.96 TeV

We present the first measurement of the inclusive three-jet differential cross section as a function of the invariant mass of the three jets with the largest transverse momenta in an event in p anti-p collisions at sqrt(s) = 1.96 TeV. The measurement is made in different rapidity regions and for different jet transverse momentum requirements and is based on a data set corresponding to an integrated luminosity of 0.7 fb^{-1} collected with the D0 detector at the Fermilab Tevatron Collider. The results are used to test the three-jet matrix elements in perturbative QCD calculations at next-to-leading order in the strong coupling constant. The data allow discrimination between parametrizations of the parton distribution functions of the proton.Comment: 10 pages, 4 figures, 2 tables, submitted to Phys. Lett. B, corrected chi2 values for NNPD

Measurement of the ttbar production cross section using dilepton events in ppbar collisions

We present a measurement of the ttbar production cross section sigma(ttbar) in ppbar collisions at sqrt{s} = 1.96 TeV using 5.4 fb-1 of integrated luminosity collected with the D0 detector. We consider final states with at least two jets and two leptons (ee, emu, mumu), and events with one jet for the the emu final state as well. The measured cross section is sigma(ttbar)= 7.36 +0.90-0.79 (stat + syst) pb. This result combined with the cross section measurement in the lepton + jets final state yields sigma(ttbar)=7.56 +0.63-0.56 (stat + syst) pb, which agrees with the standard model expectation. The relative precision of 8% of this measurement is comparable to the latest theoretical calculations.Comment: 9 pages, published in Phys. Lett.

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

Photoproduction of D∗±D^{*\pm} mesons associated with a leading neutron

The photoproduction of $D^{*\pm} (2010)$ mesons associated with a leading neutron has been observed with the ZEUS detector in $ep$ collisions at HERA using an integrated luminosity of 80 pb$^{-1}$. The neutron carries a large fraction, {$x_L>0.2$}, of the incoming proton beam energy and is detected at very small production angles, {$\theta_n<0.8$ mrad}, an indication of peripheral scattering. The $D^*$ meson is centrally produced with pseudorapidity {$|\eta| 1.9$ GeV}, which is large compared to the average transverse momentum of the neutron of 0.22 GeV. The ratio of neutron-tagged to inclusive $D^*$ production is $8.85\pm 0.93({\rm stat.})^{+0.48}_{-0.61}({\rm syst.})\%$ in the photon-proton center-of-mass energy range {$130 <W<280$ GeV}. The data suggest that the presence of a hard scale enhances the fraction of events with a leading neutron in the final state.Comment: 28 pages, 4 figures, 2 table

Measurement of the open-charm contribution to the diffractive proton structure function

Production of D*+/-(2010) mesons in diffractive deep inelastic scattering has been measured with the ZEUS detector at HERA using an integrated luminosity of 82 pb^{-1}. Diffractive events were identified by the presence of a large rapidity gap in the final state. Differential cross sections have been measured in the kinematic region 1.5 < Q^2 < 200 GeV^2, 0.02 < y < 0.7, x_{IP} < 0.035, beta 1.5 GeV and |\eta(D*+/-)| < 1.5. The measured cross sections are compared to theoretical predictions. The results are presented in terms of the open-charm contribution to the diffractive proton structure function. The data demonstrate a strong sensitivity to the diffractive parton densities.Comment: 35 pages, 11 figures, 6 table