Kinetic Path Summation, Multi--Sheeted Extension of Master Equation, and Evaluation of Ergodicity Coefficient

We study the Master equation with time--dependent coefficients, a linear kinetic equation for the Markov chains or for the monomolecular chemical kinetics. For the solution of this equation a path summation formula is proved. This formula represents the solution as a sum of solutions for simple kinetic schemes (kinetic paths), which are available in explicit analytical form. The relaxation rate is studied and a family of estimates for the relaxation time and the ergodicity coefficient is developed. To calculate the estimates we introduce the multi--sheeted extensions of the initial kinetics. This approach allows us to exploit the internal ("micro")structure of the extended kinetics without perturbation of the base kinetics.Comment: The final journal versio

c-Axis Transport and Resistivity Anisotropy of Lightly- to Moderately-Doped La_{2-x}Sr_{x}CuO_{4} Single Crystals: Implications on the Charge Transport Mechanism

Both the in-plane and the out-of-plane resistivities (\rho_{ab} and \rho_{c}) are measured in high-quality La_{2-x}Sr_{x}CuO_{4} (LSCO) single crystals in the lightly- to moderately-doped region, x = 0.01 to 0.10, and the resistivity anisotropy is determined. In all the samples studied, the anisotropy ratio \rho _{c}/\rho_{ab} quickly increases with decreasing temperature, although in non-superconducting samples the strong localization effect causes \rho _{c}/\rho_{ab} to decrease at low temperatures. Most notably, it is found that \rho_{c}/\rho_{ab} at moderate temperatures (100 - 300 K) is almost completely independent of doping in the non-superconducting regime (x = 0.01 to 0.05); this indicates that the same charge confinement mechanism that renormalizes the c-axis hopping rate is at work down to x = 0.01. It is discussed that this striking x-independence of \rho_{c}/\rho_{ab} is consistent with the idea that holes form a self-organized network of hole-rich regions, which also explains the unusually metallic in-plane transport of the holes in the lightly-doped region. Furthermore, the data for x > 0.05 suggest that the emergence of the superconductivity is related to an increase in the c-axis coupling.Comment: 7 pages, 5 figures, submitted to Phys. Rev.

Signal and System Approximation from General Measurements

In this paper we analyze the behavior of system approximation processes for stable linear time-invariant (LTI) systems and signals in the Paley-Wiener space PW_\pi^1. We consider approximation processes, where the input signal is not directly used to generate the system output, but instead a sequence of numbers is used that is generated from the input signal by measurement functionals. We consider classical sampling which corresponds to a pointwise evaluation of the signal, as well as several more general measurement functionals. We show that a stable system approximation is not possible for pointwise sampling, because there exist signals and systems such that the approximation process diverges. This remains true even with oversampling. However, if more general measurement functionals are considered, a stable approximation is possible if oversampling is used. Further, we show that without oversampling we have divergence for a large class of practically relevant measurement procedures.Comment: This paper will be published as part of the book "New Perspectives on Approximation and Sampling Theory - Festschrift in honor of Paul Butzer's 85th birthday" in the Applied and Numerical Harmonic Analysis Series, Birkhauser (Springer-Verlag). Parts of this work have been presented at the IEEE International Conference on Acoustics, Speech, and Signal Processing 2014 (ICASSP 2014

Dual boson approach to collective excitations in correlated fermionic systems

We develop a general theory of a boson decomposition for both local and non-local interactions in lattice fermion models which allows us to describe fermionic degrees of freedom and collective charge and spin excitations on equal footing. An efficient perturbation theory in the interaction of the fermionic and the bosonic degrees of freedom is constructed in so-called dual variables in the path-integral formalism. This theory takes into account all local correlations of fermions and collective bosonic modes and interpolates between itinerant and localized regimes of electrons in solids. The zero-order approximation of this theory corresponds to extended dynamical mean-field theory (EDMFT), a regular way to calculate nonlocal corrections to EDMFT is provided. It is shown that dual ladder summation gives a conserving approximation beyond EDMFT. The method is especially suitable for consideration of collective magnetic and charge excitations and allows to calculate their renormalization with respect to "bare" RPA-like characteristics. General expression for the plasmonic dispersion in correlated media is obtained. As an illustration it is shown that effective superexchange interactions in the half-filled Hubbard model can be derived within the dual-ladder approximation.Comment: Extended version, 17 pages, 5 figure

Integrating constructive feedback in personalised e-learning

When using e-learning material some students progress readily, others have difficulties. In a traditional classroom the teacher would identify those with difficulties and direct them to additional resources. This support is not easily available within e-learning. A new approach to providing constructive feedback is developed that will enable an e-learning system to identify areas of weakness and provide guidance on further study. The approach is based on the tagging of learning material with appropriate keywords that indicate the contents. Thus if a student performs poorly on an assessment on topic X, there is a need to suggest further study of X and participation in activities related to X such as forums. As well as supporting the learner this type of constructive feedback can also inform other stakeholders. For example a tutor can monitor the progress of a cohort; an instructional designer can monitor the quality of learning objects in facilitating the appropriate knowledge across many learners

Scale-free static and dynamical correlations in melts of monodisperse and Flory-distributed homopolymers: A review of recent bond-fluctuation model studies

It has been assumed until very recently that all long-range correlations are screened in three-dimensional melts of linear homopolymers on distances beyond the correlation length $\xi$ characterizing the decay of the density fluctuations. Summarizing simulation results obtained by means of a variant of the bond-fluctuation model with finite monomer excluded volume interactions and topology violating local and global Monte Carlo moves, we show that due to an interplay of the chain connectivity and the incompressibility constraint, both static and dynamical correlations arise on distances $r \gg \xi$. These correlations are scale-free and, surprisingly, do not depend explicitly on the compressibility of the solution. Both monodisperse and (essentially) Flory-distributed equilibrium polymers are considered.Comment: 60 pages, 49 figure

Cranked Relativistic Hartree-Bogoliubov Theory: Superdeformed Bands in the A∼190A\sim 190 Region

Cranked Relativistic Hartree-Bogoliubov (CRHB) theory is presented as an extension of Relativistic Mean Field theory with pairing correlations to the rotating frame. Pairing correlations are taken into account by a finite range two-body force of Gogny type and approximate particle number projection is performed by Lipkin-Nogami method. This theory is applied to the description of yrast superdeformed rotational bands observed in even-even nuclei of the $A\sim 190$ mass region. Using the well established parameter sets NL1 for the Lagrangian and D1S for the pairing force one obtains a very successful description of data such as kinematic ($J^{(1)}$) and dynamic ($J^{(2)}$) moments of inertia without any adjustment of new parameters. Within the present experimental accuracy the calculated transition quadrupole moments $Q_t$ agree reasonably well with the observed data.Comment: 6 pages including 4 PostScript figures, uses RevTex, revised version, Phys.Rev. C, Rapid Communications, in pres

Electric current circuits in astrophysics

Cosmic magnetic structures have in common that they are anchored in a dynamo, that an external driver converts kinetic energy into internal magnetic energy, that this magnetic energy is transported as Poynting fl ux across the magnetically dominated structure, and that the magnetic energy is released in the form of particle acceleration, heating, bulk motion, MHD waves, and radiation. The investigation of the electric current system is particularly illuminating as to the course of events and the physics involved. We demonstrate this for the radio pulsar wind, the solar flare, and terrestrial magnetic storms

A Review of Multi- Compartment Infectious Disease Models

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/156488/2/insr12402.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/156488/1/insr12402_am.pd

A Helicity-Based Method to Infer the CME Magnetic Field Magnitude in Sun and Geospace: Generalization and Extension to Sun-Like and M-Dwarf Stars and Implications for Exoplanet Habitability

Patsourakos et al. (Astrophys. J. 817, 14, 2016) and Patsourakos and Georgoulis (Astron. Astrophys. 595, A121, 2016) introduced a method to infer the axial magnetic field in flux-rope coronal mass ejections (CMEs) in the solar corona and farther away in the interplanetary medium. The method, based on the conservation principle of magnetic helicity, uses the relative magnetic helicity of the solar source region as input estimates, along with the radius and length of the corresponding CME flux rope. The method was initially applied to cylindrical force-free flux ropes, with encouraging results. We hereby extend our framework along two distinct lines. First, we generalize our formalism to several possible flux-rope configurations (linear and nonlinear force-free, non-force-free, spheromak, and torus) to investigate the dependence of the resulting CME axial magnetic field on input parameters and the employed flux-rope configuration. Second, we generalize our framework to both Sun-like and active M-dwarf stars hosting superflares. In a qualitative sense, we find that Earth may not experience severe atmosphere-eroding magnetospheric compression even for eruptive solar superflares with energies ~ 10^4 times higher than those of the largest Geostationary Operational Environmental Satellite (GOES) X-class flares currently observed. In addition, the two recently discovered exoplanets with the highest Earth-similarity index, Kepler 438b and Proxima b, seem to lie in the prohibitive zone of atmospheric erosion due to interplanetary CMEs (ICMEs), except when they possess planetary magnetic fields that are much higher than that of Earth.Comment: http://adsabs.harvard.edu/abs/2017SoPh..292...89