Spreading due to heterogeneity in two-phase flow

Postprint (published version)

On a size-structured two-phase population model with infinite states-at-birth

In this work we introduce and analyze a linear size-structured population model with infinite states-at-birth. We model the dynamics of a population in which individuals have two distinct life-stages: an “active” phase when individuals grow, reproduce and die and a second “resting” phase when individuals only grow. Transition between these two phases depends on individuals’ size. First we show that the problem is governed by a positive quasicontractive semigroup on the biologically relevant state space. Then we investigate, in the framework of the spectral theory of linear operators, the asymptotic behavior of solutions of the model. We prove that the associated semigroup has, under biologically plausible assumptions, the property of asynchronous exponential growth.

Random assignment of intervention points in two phase single-case designs: data-division-specific distributions

The present study explores the statistical properties of a randomization test based on the random assignment of the intervention point in a two-phase (AB) single-case design. The focus is on randomization distributions constructed with the values of the test statistic for all possible random assignments and used to obtain p-values. The shape of those distributions is investigated for each specific data division defined by the moment in which the intervention is introduced. Another aim of the study consisted in testing the detection of inexistent effects (i.e., production of false alarms) in autocorrelated data series, in which the assumption of exchangeability between observations may be untenable. In this way, it was possible to compare nominal and empirical Type I error rates in order to obtain evidence on the statistical validity of the randomization test for each individual data division. The results suggest that when either of the two phases has considerably less measurement times, Type I errors may be too probable and, hence, the decision making process to be carried out by applied researchers may be jeopardized.

Comparative study of two needle models in terms of deflection during inferior alveolar nerve block

Objectives: The purpose of this study is to determine the possible differences in deflection between two needles of same length and external gauge but with different internal gauges during truncal block of the inferior alveolar nerve. The initial working hypothesis was that greater deflection may be expected with larger internal gauge needles. Study design: Four clinicians subjected 346 patients to inferior alveolar nerve block and infiltrating anesthesia of the buccal nerve trajectory for the surgical or conventional extraction of the lower third molar. A nonautoaspirating syringe system with 2 types of needle was used: a standard 27-gauge x 35-mm needle with an internal gauge of 0.215 mm or an XL Monoprotect® 27-gauge x 35-mm needle with an internal gauge of 0.265 mm. The following information was systematically recorded for each patient: needle type, gender, anesthetic technique (direct or indirect truncal block) and the number of bone contacts during the procedure, the patient-extraction side, the practitioner performing the technique, and blood aspiration (either positive or negative). Results: 346 needles were used in total. 190 were standard needles (27-gauge x 35-mm needle with an internal gauge of 0.215 mm) and 156 were XL Monoprotect®. Incidence of deflection was observed in 49.1% of cases (170 needles) where 94 were standard needles and 76 XL Monoprotect®. Needle torsion ranged from 0º and 6º. Conclusions: No significant differences were recorded in terms of deflection and internal gauge, operator, patient-extraction side, the anesthetic technique involved and the number of bone contacts during the procedure

Stability and asymptotic analysis of a fluid-particle interaction model

We are interested in coupled microscopic/macroscopic models describing the evolution of particles dispersed in a fluid. The system consists in a Vlasov-Fokker-Planck equation to describe the microscopic motion of the particles coupled to the Euler equations for a compressible fluid. We investigate dissipative quantities, equilibria and their stability properties and the role of external forces. We also study some asymptotic problems, their equilibria and stability and the derivation of macroscopic two-phase models.

Older people's university students in Spain: a comparison of motives and benefits between two models

This study examines both the motives for and the benefits of attending a uni- versity programme for older people (UPOP) in Spain, and how they vary with the type of UPOP. Two UPOP models were assessed: The"Older People"s Classes" of the University of Barcelona, which is organised as a lecture course, and the"University of Experience" at the University of Valencia, which is a three- or four- year variant of regular university degrees. A sample of 321 older students (mean age 67.5 years) was gathered from the two UPOPs, 161 participants from the former and 157 from the latter. The findings suggest that expressive motives such as acquiring knowledge, expanding the mind or learning for the joy of learning were the most important reasons for joining a UPOP, and that among the perceived benefits from taking classes at university featured"gaining more friends","enhanced self or life-satisfaction" and"joy in life". Perceived benefits were particularly high among the less educated and the older students. While students participating in the Older People"s Classes were older and included relatively more women, differences between the two models in motives and benefits did not exist or were slight. These results are discussed in the context of new strategies to improve university courses aimed at older students.

Epidemic models with an infected-infectious period

The introduction of an infective-infectious period on the geographic spread of epidemics is considered in two different models. The classical evolution equations arising in the literature are generalized and the existence of epidemic wave fronts is revised. The asymptotic speed is obtained and improves previous results for the Black Death plague

Risk management under a two-factor model of the term structure of interest rates

This paper presents several applications to interest rate risk managementbased on a two-factor continuous-time model of the term structure of interestrates previously presented in Moreno (1996). This model assumes that defaultfree discount bond prices are determined by the time to maturity and twofactors, the long-term interest rate and the spread (difference between thelong-term rate and the short-term (instantaneous) riskless rate). Several newmeasures of ``generalized duration" are presented and applied in differentsituations in order to manage market risk and yield curve risk. By means ofthese measures, we are able to compute the hedging ratios that allows us toimmunize a bond portfolio by means of options on bonds. Focusing on thehedging problem, it is shown that these new measures allow us to immunize abond portfolio against changes (parallel and/or in the slope) in the yieldcurve. Finally, a proposal of solution of the limitations of conventionalduration by means of these new measures is presented and illustratednumerically.

A two-mean reverting-factor model of the term structure of interest rates

This paper presents a two--factor model of the term structure ofinterest rates. We assume that default free discount bond prices aredetermined by the time to maturity and two factors, the long--term interestrate and the spread (difference between the long--term rate and theshort--term (instantaneous) riskless rate). Assuming that both factorsfollow a joint Ornstein--Uhlenbeck process, a general bond pricing equationis derived. We obtain a closed--form expression for bond prices andexamine its implications for the term structure of interest rates. We alsoderive a closed--form solution for interest rate derivatives prices. Thisexpression is applied to price European options on discount bonds andmore complex types of options. Finally, empirical evidence of the model'sperformance is presented.

Hierarchical location-allocation models for congested systems

In this paper we address the issue of locating hierarchical facilities in the presence of congestion. Two hierarchical models are presented, where lower level servers attend requests first, and then, some of the served customers are referred to higher level servers. In the first model, the objective is to find the minimum number of servers and theirlocations that will cover a given region with a distance or time standard. The second model is cast as a Maximal Covering Location formulation. A heuristic procedure is then presented together with computational experience. Finally, some extensions of these models that address other types of spatial configurations are offered.

Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticality

A stochastic nonlinear partial differential equation is constructed for two different models exhibiting self-organized criticality: the Bak-Tang-Wiesenfeld (BTW) sandpile model [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] and the Zhang model [Phys. Rev. Lett. 63, 470 (1989)]. The dynamic renormalization group (DRG) enables one to compute the critical exponents. However, the nontrivial stable fixed point of the DRG transformation is unreachable for the original parameters of the models. We introduce an alternative regularization of the step function involved in the threshold condition, which breaks the symmetry of the BTW model. Although the symmetry properties of the two models are different, it is shown that they both belong to the same universality class. In this case the DRG procedure leads to a symmetric behavior for both models, restoring the broken symmetry, and makes accessible the nontrivial fixed point. This technique could also be applied to other problems with threshold dynamics.

Phase behavior and rheological analysis of reverse liquid crystals and W/I2, W/H2 gel emulsions using an amphiphilic block copolymer.

This article reports the phase behavior determi- nation of a system forming reverse liquid crystals and the formation of novel disperse systems in the two-phase region. The studied system is formed by water, cyclohexane, and Pluronic L-121, an amphiphilic block copolymer considered of special interest due to its aggregation and structural proper- ties. This system forms reverse cubic (I2) and reverse hexagonal (H2) phases at high polymer concentrations. These reverse phases are of particular interest since in the two-phase region, stable high internal phase reverse emulsions can be formed. The characterization of the I2 and H2 phases and of the derived gel emulsions was performed with small-angle X-ray scattering (SAXS) and rheometry, and the influence of temperature and water content was studied. TheH2 phase experimented a thermal transition to an I2 phase when temperature was increased, which presented an Fd3m structure. All samples showed a strong shear thinning behavior from low shear rates. The elasticmodulus (G0) in the I2 phase was around 1 order of magnitude higher than in theH2 phase. G0 was predominantly higher than the viscousmodulus (G00). In the gel emulsions,G0 was nearly frequency-independent, indicating their gel type nature. Contrarily to water-in-oil (W/O) normal emulsions, in W/I2 and W/H2 gel emulsions, G0, the complex viscosity (|η*|), and the yield stress (τ0) decreased with increasing water content, since the highly viscous microstructure of the con- tinuous phase was responsible for the high viscosity and elastic behavior of the emulsions, instead of the volumefraction of dispersed phase and droplet size. A rheological analysis, in which the cooperative flow theory, the soft glass rheology model, and the slip plane model were analyzed and compared, was performed to obtain one single model that could describe the non-Maxwellian behavior of both reverse phases and highly concentrated emulsions and to characterize their microstructure with the rheological properties.

Growth, habit formation, and catching-up\ with the Joneses

When habits are introduced multiplicatively in a capital accumulation model, the consumers' objective function might fail to be concave. In this paper we provide conditions aimed at guaranteeing the existence of interior solutions to the consumers' problem. We also characterize the equilibrium path of two growth models with multiplicative habits: the internal habit formation model, where individual habits coincide with own past consumption, and the external habit formation (or catching-up with the Joneses) model, where habits arise from the average past consumption in the economy. We show that the introduction of external habits makes the equilibrium path inefficient during the transition towards the balanced growth path. We characterize in this context the optimal tax policy.

Contractive probability metrics and asymptotic behavior of dissipative kinetic equations

The present notes are intended to present a detailed review of the existing results in dissipative kinetic theory which make use of the contraction properties of two main families of probability metrics: optimal mass transport and Fourier-based metrics. The first part of the notes is devoted to a self-consistent summary and presentation of the properties of both probability metrics, including new aspects on the relationships between them and other metrics of wide use in probability theory. These results are of independent interest with potential use in other contexts in Partial Differential Equations and Probability Theory. The second part of the notes makes a different presentation of the asymptotic behavior of Inelastic Maxwell Models than the one presented in the literature and it shows a new example of application: particle's bath heating. We show how starting from the contraction properties in probability metrics, one can deduce the existence, uniqueness and asymptotic stability in classical spaces. A global strategy with this aim is set up and applied in two dissipative models.