Strong solutions for stochastic porous media equations with jumps

We prove global well-posedness in the strong sense for stochastic generalized porous media equations driven by locally square integrable martingales with stationary independent increments.

Numerical methods for strong solutions of stochastic differential equations: an overview

This paper gives a review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations. We give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications, and give the necessary analytical tools for understanding some of the important concepts associated with stochastic processes. We present the stochastic Taylor series expansion as the fundamental mechanism for constructing effective numerical methods, give general results that relate local and global order of convergence and mention the Magnus expansion as a mechanism for designing methods that preserve the underlying structure of the problem. We also present various classes of explicit and implicit methods for strong solutions, based on the underlying structure of the problem. Finally, we discuss implementation issues relating to maintaining the Brownian path, efficient simulation of stochastic integrals and variable-step-size implementations based on various types of control.

Classical solutions for a logarithmic fractional diffusion equation

We prove global existence and uniqueness of strong solutions to the logarithmic porous medium type equation with fractional diffusion ?tu + (?)1/2 log(1 + u) = 0, posed for x ? R, with nonnegative initial data in some function space of LlogL type. The solutions are shown to become bounded and C? smooth in (x, t) for all positive times. We also reformulate this equation as a transport equation with nonlocal velocity and critical viscosity, a topic of current relevance. Interesting functional inequalities are involved.

Existence and weak-strong uniqueness for the Navier-Stokes-Smoluchowski system over moving domains

This dissertation concerns the well-posedness of the Navier-Stokes-Smoluchowski system. The system models a mixture of fluid and particles in the so-called bubbling regime. The compressible Navier-Stokes equations governing the evolution of the fluid are coupled to the Smoluchowski equation for the particle density at a continuum level. First, working on fixed domains, the existence of weak solutions is established using a three-level approximation scheme and based largely on the Lions-Feireisl theory of compressible fluids. The system is then posed over a moving domain. By utilizing a Brinkman-type penalization as well as penalization of the viscosity, the existence of weak solutions of the Navier-Stokes-Smoluchowski system is proved over moving domains. As a corollary the convergence of the Brinkman penalization is proved. Finally, a suitable relative entropy is defined. This relative entropy is used to establish a weak-strong uniqueness result for the Navier-Stokes-Smoluchowski system over moving domains, ensuring that strong solutions are unique in the class of weak solutions.

Numerical simulation of stochastic ordinary differential equations in biomathematical modelling

In this work we discuss the effects of white and coloured noise perturbations on the parameters of a mathematical model of bacteriophage infection introduced by Beretta and Kuang in [Math. Biosc. 149 (1998) 57]. We numerically simulate the strong solutions of the resulting systems of stochastic ordinary differential equations (SDEs), with respect to the global error, by means of numerical methods of both Euler-Taylor expansion and stochastic Runge-Kutta type. (C) 2003 IMACS. Published by Elsevier B.V. All rights reserved.

Using the max-sum algorithm for supply chain emergence in dynamic multiunit environments

Supply chain formation (SCF) is the process of determining the set of participants and exchange relationships within a network with the goal of setting up a supply chain that meets some predefined social objective. Many proposed solutions for the SCF problem rely on centralized computation, which presents a single point of failure and can also lead to problems with scalability. Decentralized techniques that aid supply chain emergence offer a more robust and scalable approach by allowing participants to deliberate between themselves about the structure of the optimal supply chain. Current decentralized supply chain emergence mechanisms are only able to deal with simplistic scenarios in which goods are produced and traded in single units only and without taking into account production capacities or input-output ratios other than 1:1. In this paper, we demonstrate the performance of a graphical inference technique, max-sum loopy belief propagation (LBP), in a complex multiunit unit supply chain emergence scenario which models additional constraints such as production capacities and input-to-output ratios. We also provide results demonstrating the performance of LBP in dynamic environments, where the properties and composition of participants are altered as the algorithm is running. Our results suggest that max-sum LBP produces consistently strong solutions on a variety of network structures in a multiunit problem scenario, and that performance tends not to be affected by on-the-fly changes to the properties or composition of participants.

On a Stochastic Partial Differential Equation with a Noisy Term

2000 Mathematics Subject Classification: 60H15, 60H40

Adsorption Isotherms for Removal of Linoleic Acid from Ethanolic Solutions Using the Strong Anion Exchange Resin Amberlyst A26 OH

Adsorption isotherms for the removal of linoleic acid from aqueous ethanol were measured using a strong anion exchange resin (Amberlyst A26 OH). The data for linoleic acid were compared with previously published results for oleic acid. The equilibrium data were correlated using the Langmuir and Freundlich isotherms. Lower average deviations between experimental and calculated results were obtained with the Langmuir model. The capacity of the resin for adsorbing linoleic acid was evaluated at different water contents in ethanol, 100 w = 0.50 to 15.27, and at 298.15 K. The water content in ethanol does not influence significantly the equilibrium behavior, and the strong anion exchange resin has a good performance in the removal of linoleic acid from the liquid phase.

Observation of charge-dependent azimuthal correlations and possible local strong parity violation in heavy-ion collisions

Parity (P)-odd domains, corresponding to nontrivial topological solutions of the QCD vacuum, might be created during relativistic heavy-ion collisions. These domains are predicted to lead to charge separation of quarks along the orbital momentum of the system created in noncentral collisions. To study this effect, we investigate a three-particle mixed-harmonics azimuthal correlator which is a P-even observable, but directly sensitive to the charge-separation effect. We report measurements of this observable using the STAR detector in Au + Au and Cu + Cu collisions at root s(NN) = 200 and 62 GeV. The results are presented as a function of collision centrality, particle separation in rapidity, and particle transverse momentum. A signal consistent with several of the theoretical expectations is detected in all four data sets. We compare our results to the predictions of existing event generators and discuss in detail possible contributions from other effects that are not related to P violation.

Azimuthal Charged-Particle Correlations and Possible Local Strong Parity Violation

Parity-odd domains, corresponding to nontrivial topological solutions of the QCD vacuum, might be created during relativistic heavy-ion collisions. These domains are predicted to lead to charge separation of quarks along the system's orbital momentum axis. We investigate a three-particle azimuthal correlator which is a P even observable, but directly sensitive to the charge separation effect. We report measurements of charged hadrons near center-of-mass rapidity with this observable in Au+Au and Cu+Cu collisions at s(NN)=200 GeV using the STAR detector. A signal consistent with several expectations from the theory is detected. We discuss possible contributions from other effects that are not related to parity violation.

Preparative ion exchange for salt solutions

Työssä tutkittiin moniarvoisten metalliformiaattien valmistusta ioninvaihto-menetelmällä. Kirjallisuustutkimus käsitteleetunnettuja alumiiniformiaatin ja rautaformiaatin valmistusmenetelmiä, kationinvaihtohartsien ominaisuuksia, ioninvaihtohartsien selektiivisyyttä ja alumiinin, raudan, magnesiumin ja sinkin vesikemiaa. Laboratoriokokeiden avulla tutkittiin sinkki-, magnesium-, rauta(II)- ja alumiiniformiaattien valmistusta ioninvaihdolla. Kokeet suoritettiin kolonnissa, joka oli pakattu makrohuokoisella tai geelimäisellä vahvalla kationin-vaihtohartsilla. Hartsi vaihdettiin natriummuodosta metallimuotoon metallikloridi- tai metallisulfaattiliuoksella.Metalli eluoitiin hartsista natriumformiaatilla. Formiaattien valmistus onnistui makrohuokoista vahvaa kationinvaihtohartsia käyttämällä. Rauta(II)formiaatin valmistus oli vaikeampaa kuin muiden formiaattien, koska rauta(II) hapettui osittain rauta(III):ksi valmistuksen aikana. Alumiiniformiaattia valmistettiin käyttäen sekä makrohuokoista että geelimäistä hartsia. Makrohuokoisen hartsin havaittiin soveltuvan geelimäistä hartsia paremmin alumiiniformiaatin valmistukseen. Kungeelimäistä hartsia käytettiin, noin 30 % alumiinista jäi kiinni hartsiin eikä siten eluoitunut. Ioninvaihdon selektiivisyyskertoimien saamiseksi suoritettiin tasapainokokeita. Selektiivisyyskertoimia käytettiin ioninvaihtokolonnin dynaamisessa simuloinnissa. Ioninvaihdon simuloiminen dynaamisella kolonnimallilla onnistui hyvin.

Comparative electron impact and fast atom bombardment mass spectrometric studies of some HMPA adducts of phenyltin and phenyllead halides and studies of strong hydrogen bonding by FAB-MS

The fragmentation patterns and mass spectra of some phenyl tin and -lead halide adducts with hexamethylphosphoramide are compared by subjecting them t~ electron impact and fast atom bombardment ionization in a mass spectrometer. This comparison is restricted to the metal-containing ions. Ligand-exchange mechanisms of some of the metal-containing species are explored by FAB-MS. Several moisturesensitive organo-metallics and H-bonded systems have been examined by FAB for attempted characterization, but without any success. Scavenging and trapping of water molecules by complex aggregates in solutions of quaternary ammonium fluorides and hydroxides are investigated by FAB to complement previous NMR-studies.

Testing solutions in grass-dominated landscapes: a review of current research

In this paper we review the experimental development of agri-environment measures for use on grasslands. Sward structure has been shown to have a strong influence on birds' ability to forage in grasslands, but the effects of food abundance on foraging behaviour are poorly understood and this hinders development of grassland conservation measures. The experiments described have a dual purpose: to investigate the foraging ecology of birds on grasslands and to test candidate management measures. Most of the work featured focuses on increasing invertebrate food resources during the summer by increasing habitat heterogeneity. We also identify important gaps in the habitats provided by existing or experimental measures, where similar dual-purpose experiments are required.