Mean first-passage times for systems driven by gamma and McFadden dichotomous noise

We consider mean first-passage times (MFPTs) for systems driven by non-Markov gamma and McFadden dichotomous noises. A simplified derivation is given of the underlying integral equations and the theory for ordinary renewal processes is extended to modified and equilibrium renewal processes. The exact results are compared with the MFPT for Markov dichotomous noise and with the results of Monte Carlo simulations.

Statistics of depth probed by cw measurement of photons in a turbid medium

Photon migration in a turbid medium has been modeled in many different ways. The motivation for such modeling is based on technology that can be used to probe potentially diagnostic optical properties of biological tissue. Surprisingly, one of the more effective models is also one of the simplest. It is based on statistical properties of a nearest-neighbor lattice random walk. Here we develop a theory allowing one to calculate the number of visits by a photon to a given depth, if it is eventually detected at an absorbing surface. This mimics cw measurements made on biological tissue and is directed towards characterizing the depth reached by photons injected at the surface. Our development of the theory uses formalism based on the theory of a continuous-time random walk (CTRW). Formally exact results are given in the Fourier-Laplace domain, which, in turn, are used to generate approximations for parameters of physical interest.

Paperikoneen vesi- ja energiatehokkuuden parantaminen

Työn tavoitteena oli laatia reaaliaikaiset vesi- ja energiatasenäytöt Stora Enso PublicationPaper Veitsiluodon tehtaalle, paperikone 5:lle. Tavoitteena oli myös simuloida kyseisen paperikonelinjan vesitase. Aluksi työssä piirrettiin lohkokaaviot taseita varten paperikoneen kaikista vettä tai energiaa sisältävistä jakeista. Näitä yksinkertaistettuja lohkokaavioita hyväksi käyttäen laadittiin taseidenlaskentakaavat, jotka testattiin tarkastuslaskelmien avulla. Vesi- ja energiataseista tehtiin myös suunnitelmat prosessinohjausjärjestelmän tasenäytöiksi. FlowMac-simulointiohjelmalla rakennetun paperikone 5 vesitaseen simulointimallin tulosten oikeellisuutta arvioitiin herkkyysanalyysin avulla. Tehdyn herkkyysanalyysin tuloksien perusteella voidaan olettaa, että simulointimalli toimii luotettavasti. Tämän vesitaseen simulointimallin avulla tarkasteltiin kiekkosuotimien uudistamisen vaikutuksia paperikonelinjan vesitaseeseen. Tarkastelussa huomattiin, että vaihtamalla kiekkosuotimien syöttöventtiilit kolmea jaetta tuottaviksi, voitaisiin flotaatioallas ja suihkuveden kaarisihti poistaa käytöstä. Tulevaisuudessa simulointimallia voidaan käyttää myös monilla muilla eri tavoin hyödyksi kyseisellä paperikoneella. Työssä laaditut vesi- ja energiataseet saatiin niin tarkoiksi kuin se nykyisiä mittauksia hyödyntäen on mahdollista. Jostaseita haluttaisiin tarkentaa, olisi paperikonelinjalle syytä lisätä joitakin mittauksia. Myös työssä tehty vesitaseen simulointi FlowMac:lla onnistui hyvin mutta kyseisessä ohjelmassa havaittiin silti joitakin kehittämistarpeita. Työn tuloksien perusteella vettä ja energiaa voitaisiin mahdollisesti säästää paperikone 5:llä esimerkiksi laimennussäätöisen perälaatikon avulla, kiekkosuotimien uusimisella sekä kenkäpuristimen käyttöönotolla. Jatkotutkimuskohteita voisivat olla esimerkiksi paperikone 5:n lämpötase, kemiallisesti puhdistetun veden tulolämpötilan nostaminen, hiomon suodosveden ylimääräisen lämmön hyödyntäminen paperikone 5 kirkassuodoksen lämmittämisen jälkeen, lämmön talteenotossa lämmitysvesikennon ja prosessivesikennon järjestyksen vaihtaminen sekä vastaavien vesi- ja energiataseiden laatiminen paperikone 1:lle ja hiomolle.

Accounting for adsorption and desorption in Lattice Boltzmann simulations

We report a Lattice-Boltzmann scheme that accounts for adsorption and desorption in the calculation of mesoscale dynamical properties of tracers in media of arbitrary complexity. Lattice Boltzmann simulations made it possible to solve numerically the coupled Navier-Stokes equations of fluid dynamics and Nernst-Planck equations of electrokinetics in complex, heterogeneous media. With the moment propagation scheme, it became possible to extract the effective diffusion and dispersion coefficients of tracers, or solutes, of any charge, e.g., in porous media. Nevertheless, the dynamical properties of tracers depend on the tracer-surface affinity, which is not purely electrostatic and also includes a species-specific contribution. In order to capture this important feature, we introduce specific adsorption and desorption processes in a lattice Boltzmann scheme through a modified moment propagation algorithm, in which tracers may adsorb and desorb from surfaces through kinetic reaction rates. The method is validated on exact results for pure diffusion and diffusion-advection in Poiseuille flows in a simple geometry. We finally illustrate the importance of taking such processes into account in the time-dependent diffusion coefficient in a more complex porous medium.

Modellfehler und Greensche Funktionen in der Statik

Die vorliegende Arbeit befasst sich mit den Fehlern, die bei der Berechnung von Tragstrukturen auftreten können, dem Diskretisierungs- und dem Modellfehler. Ein zentrales Werkzeug für die Betrachtung des lokalen Fehlers in einer FE-Berechnung sind die Greenschen Funktionen, die auch in anderen Bereichen der Statik, wie man zeigen kann, eine tragende Rolle spielen. Um den richtigen Einsatz der Greenschen Funktion mit der FE-Technik sicherzustellen, werden deren Eigenschaften und die konsistente Generierung aufgezeigt. Mit dem vorgestellten Verfahren, der Lagrange-Methode, wird es möglich auch für nichtlineare Probleme eine Greensche Funktion zu ermitteln. Eine logische Konsequenz aus diesen Betrachtungen ist die Verbesserung der Einflussfunktion durch Verwendung von Grundlösungen. Die Greensche Funktion wird dabei in die Grundlösung und einen regulären Anteil, welcher mittels FE-Technik bestimmt wird, aufgespalten. Mit dieser Methode, hier angewandt auf die Kirchhoff-Platte, erhält man deutlich genauere Ergebnisse als mit der FE-Methode bei einem vergleichbaren Rechenaufwand, wie die numerischen Untersuchungen zeigen. Die Lagrange-Methode bietet einen generellen Zugang zur zweiten Fehlerart, dem Modellfehler, und kann für lineare und nichtlineare Probleme angewandt werden. Auch hierbei übernimmt die Greensche Funktion wieder eine tragende Rolle, um die Auswirkungen von Parameteränderungen auf ausgewählte Zielgrößen betrachten zu können.

Density profiles in the raise and peel model with and without a wall; physics and combinatorics

We consider the raise and peel model of a one-dimensional fluctuating interface in the presence of an attractive wall. The model can also describe a pair annihilation process in disordered unquenched media with a source at one end of the system. For the stationary states, several density profiles are studied using Monte Carlo simulations. We point out a deep connection between some profiles seen in the presence of the wall and in its absence. Our results are discussed in the context of conformal invariance ( c = 0 theory). We discover some unexpected values for the critical exponents, which are obtained using combinatorial methods. We have solved known ( Pascal`s hexagon) and new (split-hexagon) bilinear recurrence relations. The solutions of these equations are interesting in their own right since they give information on certain classes of alternating sign matrices.

Anomalous spin-related quantum phase in mesoscopic hole rings

We have obtained numerically exact results for the spin-related geometric quantum phases that arise in p-type semiconductor ring structures. The interplay between gate-controllable (Rashba) spin splitting and quantum-confinement-induced mixing between hole-spin states causes a much higher sensitivity of magnetoconductance oscillations to external parameters than previously expected. Our results imply a much-enhanced functionality of hole-ring spin-interference devices and shed new light on recent experimental findings.

Propriedades críticas do modelo z(4) em sistemas bi e tridimensionais

A real space renormalization group method is used to investigate the criticality (phase diagrams, critical expoentes and universality classes) of Z(4) model in two and three dimensions. The values of the interaction parameters are chosen in such a way as to cover the complete phase diagrams of the model, which presents the following phases: (i) Paramagnetic (P); (ii) Ferromagnetic (F); (iii) Antiferromagnetic (AF); (iv) Intermediate Ferromagnetic (IF) and Intermediate Antiferromagnetic (IAF). In the hierarquical lattices, generated by renormalization the phase diagrams are exact. It is also possible to obtain approximated results for square and simple cubic lattices. In the bidimensional case a self-dual lattice is used and the resulting phase diagram reproduces all the exact results known for the square lattice. The Migdal-Kadanoff transformation is applied to the three dimensional case and the additional phases previously suggested by Ditzian et al, are not found

Excitations and finite-size properties of an integrable supersymmetric electronic model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

BOUND HYDROGENIC STATES IN A MAGNETIC FIELD: A FINITE-DIFFERENCE APPROACH

A finite-difference scheme is used to calculate bound electronic states of an electron in a hydrogen atom subject to a magnetic field. The numerical results are in good agreement with exact results, in the absence of the magnetic field, and with a two-parameters variational calculation, when the magnetic field is applied.

Modal transformation analyses for double three-phase transmission lines

Eigenvector and eigenvalue analyses are carried out for double three-phase transmission lines, studying the application of a constant and real phase-mode transformation matrix and the errors of this application to mode line models. Employing some line transposition types, exact results are obtained with a single real transformation matrix based on Clarke's matrix and line geometrical characteristics. It is shown that the proposed technique leads to insignificant errors when a nontransposed case is considered. For both cases, transposed and nontransposed, the access to the electrical values (voltage and current, for example) is provided through a simple matrix multiplication without convolution methods. Using this facility, an interesting model for transmission line analysis is obtained even though the nontransposed case errors are not eliminated. The main advantages of the model are related to the transformation matrix: single, real, frequency independent, and identical for voltage and current.

s-wave approximation for asymmetry in nonmesonic decay of finite hypernuclei

We establish the bridge between the commonly used Nabetani-Ogaito-Sato-Kishimoto (NOSK) formula for the asymmetry parameter a(Lambda) in the Lambda p -> np emission of polarized hypernuclei, and the shell-model (SM) formalism for finite hypernuclei. We demonstrate that the s-wave approximation leads to a SM formula for a(Lambda) that is as simple as the NOSK one and that reproduces the exact results for (5)(Lambda)He and (12)(Lambda)C better than initially expected. The simplicity achieved here is indeed remarkable. The new formalism makes the theoretical evaluation of a(Lambda) more transparent and explains clearly why the one-meson exchange model is unable to account for the experimental data of (5)(Lambda)He.

Induced variational method from supersymmetric quantum mechanics and the screened Coulomb potential

The formalism of supersymmetric quantum mechanics supplies a trial wave function to be used in the variational method. The screened Coulomb potential is analyzed within this approach. Numerical and exact results for energy eigenvalues are compared.

Linearização dos coeficientes de reflexão de ondas qP em meios anisotrópicos

Os coeficientes de reflexão de onda qP em uma interface plana que separa dois meios anisotrópicos dependem dos parâmetros elásticos dos meios envolvidos de maneira não linear. Aproximações lineares para a refletividade de ondas qP pressupondo fraco contraste de impedância e fraca anisotropia levam a uma forma simples para se fazer à análise de AVO/AVD. Neste trabalho a solução das equações de Zoeppritz é rescrita explicitamente em função de matrizes de impedância e polarização. Além disso, utilizando-se esta abordagem, é apresentada uma metodologia geral mais simples para se obter as formas linearizadas. Estas formas linearizadas para os coeficientes de reflexão da onda qP e das ondas convertidas para uma onda qP incidente apresentam resultados muito próximos da formulação exata para ângulos de incidência menores que 30° considerando-se um contraste de impedância moderado e anisotropia em limites geologicamente aceitáveis.

Renormalization-group calculation of dynamical properties for impurity models

The numerical renormalization-group method was originally developed to calculate the thermodynamical properties of impurity Hamiltonians. A recently proposed generalization capable of computing dynamical properties is discussed. As illustrative applications, essentially exact results for the impurity specttral densities of the spin-degenerate Anderson model and of a model for electronic tunneling between two centers in a metal are presented. © 1991.