New High-Resolution Central Schemes for Nonlinear Conservation Laws and Convection—Diffusion Equations

High resolution schemes for hyperbolic conservation laws

Let X(t) be the number of tumor cells at time t, and Pr{X(t) = n} = pn(t) is the density of X. A “birth”, i.e., an increase of one of the total population of cancer cells, can occur either by mutation of a normal cell caused by the action of the carcinogen, consisting of randomly (Poisson) distributed hits, or by reproduction of existing cancer cells. A death of a tumor cell occurs as an additive combination of non-immunological and immunological elements. Once a tumor is initiated by carcinogenic action, it undergoes a birth and death process with infinitesimal birth rate linear and infinitesimal death rate composed of a linear and a nonlinear term, the former due to non-immunological deaths, the latter to immunological feedback. The death rate per tumor cell due to immunological response is proportional to the total number of antigen-producing (tumor) cells; thus, the total death rate is quadratic. Although this assumes a very simple mechanism for the action of immunological feedback, it is nevertheless a first step.

The Mathematical Model

Water chemistry has been shown experimentally to affect the stability of water films and the sorption of organic oil components on mineral surfaces. When oil is displaced by water, water chemistry has been shown to impact oil recovery. At least two mechanisms could account for these effects, the water chemistry could change the charge on the rock surface and affect the rock wettability, and/or changes in the water chemistry could dissolve rock minerals and affect the rock wettability. The explanations need not be the same for oil displacement of water as for water imbibition and displacement of oil. This article investigates how water chemistry affects surface charge and rock dissolution in a pure calcium carbonate rock similar to the Stevns Klint chalk by constructing and applying a chemical model that couples bulk aqueous and surface chemistry and also addresses mineral precipitation and dissolution. We perform calculations for seawater and formation water for temperatures between 70 and 130°C. The model we construct accurately predicts the surface potential of calcite and the adsorption of sulfate ions from the pore water. The surface potential changes are not able to explain the observed changes in oil recovery caused by changes in pore water chemistry or temperature. On the other hand, chemical dissolution of calcite has the experimentally observed chemical and temperature dependence and could account for the experimental recovery systematics. Based on this preliminary analysis, we conclude that although surface potential may explain some aspects of the existing spontaneous imbibitions data set, mineral dissolution appears to be the controlling factor.

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The Impact of Pore Water Chemistry on Carbonate Surface Charge and Oil Wettability

Dean of Undergraduates John Hutchinson, the General Council and President David Leebron assembled the Working Group on University Responses to Federal Initiatives on Sexual Assault in June, according to Associate Vice Provost Matthew Taylor. The group formed in order to address federal measures as well as to continue changes already in progress. The federal government began releasing guidelines on how universities and colleges should address sexual assault beginning in April 2014. The White House task force report, Not Alone, features certain recommendations regarding training, prevention and adjudication of sexual assault. “The working group is looking at Rice’s policies, processes and communications about sexual violence and sexual harassment, in light of what the government is either recommending or requiring to make sure that we have a clear sense of the areas in which,” Taylor said. “We either exceed the recommendations or there are things that we need to do to meet the recommendations.” The working group consists of both undergraduate and graduate representatives, as well as leadership from the Student Wellbeing Office, Student Judicial Programs, the Rice University Police Department, the Rice Counseling Center, Athletics and Graduate and Post-Doctoral Studies, among others. There are approximately an equal number of males and females in the group. “I wouldn’t say [we have had] findings yet,” Taylor said. “We have tried to educate ourselves on the government’s recommendations.” According to Taylor, the working group focused on immediate shortterm issues for the summer. Many of the federal recommendations were already being met by Rice, and several aspects were already undergoing changes before the formation of the working group. Before the working group was formed, Associate Dean of Undergraduates Donald Ostdiek had already decided to hire a Title IX Resource Navigator, who will help students navigate the investigation if they choose to come forward and report a sexual assault. The main efforts of the working group are directed towards meeting federal guidelines that state that universities should designate employees to whom students can report sexual assault in confidence. Taylor said although Rice already has designated individuals, the policy’s language did not clearly outline whether those individuals are Title IX officers, responsible employees or non-disclosing employees. He said the new language encourages individuals to report cases. “The Title IX officers, in most cases, don’t have to report a student’s name, but we make it equally fair that, in some cases, the university would have to take action based on the law,” Taylor said. “Some of the people that we know students are most likely to go to for advice after a sexual assault are college masters, resident [associates] and college coordinators. We make it clear that they are responsible employees [who are] required to notify one of the Title IX coordinators if they are alerted by a student to a case of sexual assault or sexual violence.” Director of the Center for Student Wellbeing Kate Noonan and Wellbeing Advisor Saralyn Hernandez also contributed to the working group. Hernandez and Noonan said the Wellbeing Advisors are committed to providing trauma-informed support to students who have experienced sexual misconduct. “For survivors who prefer offcampus resources, Rice contracts with the Houston Area Women’s Center, [which] can provide support to Rice students outside the hedges,” Noonan and Hernandez said. Currently, new students undergo training during Orientation Week through Project Sexual Assault-Free Environment, presented by the Houston Area Women’s Resource Center and the Student Wellbeing Office. Although the working group did not have any influence on this year’s presentation of Project SAFE, the presentation already met federal recommendations by focusing on bystander prevention. The presentation discussed non-disclosing and responsible employees, although it did not talk about consequences for potential perpetrators. Colin Losey, a Martel College sophomore who transferred from the University of Chicago, said although he thought the presentation itself was satisfactory, he did not feel that all of the options for victims of sexual assault were covered, especially the option to report to police outside the university. “I’m a transfer student from a university that was recently hit with a major Title IX investigation, and a lot of what has come out from that is that the university’s adjudication process was used in a way to keep things internal,” Losey said. “Given what has happened at other college campuses across the country, students should be clear that this is criminal behavior, and they can press criminal charges.You don’t need to contact Rice first, and Rice need not be involved.” However, Taylor said offering Project SAFE only during O-Week is unsatisfactory and that there must Honor Council removes undergraduates from graduate cases, violates constitution

A new generation.

We study a viscous two-phase liquid-gas model relevant for well
and pipe flow modelling. The gas is assumed to be polytropic
whereas the liquid is treated as an incompressible fluid leading
to a pressure law which becomes singular when transition to
single-phase liquid flow occurs. In order to handle this
difficulty we reformulate the model in terms of Lagrangian
variables and study the model in a free-boundary setting where the
gas and liquid mass are of compact support initially and
discontinuous at the boundaries. Then, by applying an appropriate
variable transformation, point-wise control on masses can be
obtained which guarantees that no single-phase regions will occur
when the initial state represents a true mixture of both phases.
This paves the way for deriving a global existence result for a
class of weak solutions. The result requires that the viscous
coefficient depends on the volume fraction in an appropriate
manner. By assuming more regularity of the initial fluid velocity
a uniqueness result is obtained for an appropriate (smaller) class
of weak solutions.

https://www.aimsciences.org/article/exportPdf?id=6dc8c184-7bfb-45e7-b787-591d4094d0c4

Global weak solutions for a viscous liquid-gas model with singular pressure law

Numerical methods for the simulation of the settling of flocculated suspensions

On Strongly Degenerate Convection–Diffusion Problems Modeling Sedimentation–Consolidation Processes

We explore the relationship between two common two‐phase flow models, usually denoted as the two‐fluid and drift‐flux models. They differ in their mathematical description of momentum transfer between the phases. In this paper we provide a framework in which these two model formulations are unified. The drift‐flux model employs a mixture momentum equation and treats interphasic momentum exchange indirectly through the slip relation, which gives the relative velocity between the phases as a function of the flow parameters. This closure law is in general highly complex, which makes it difficult to analyze the model algebraically. To facilitate the analysis, we express the quasi‐linear formulation of the drift‐flux model as a function of three parameters: the derivatives of the slip with respect to the vector of unknown variables. The wave structure of this model is investigated using a perturbation technique. Then we rewrite the drift‐flux model with a general slip relation such that it is expressed in term...

On the Wave Structure of Two‐Phase Flow Models

The article was originally published at; http://dxdoiorg/101137/100813932; it is made available here with permission

/pdf/weak-solutions-for-a-gas-liquid-model-relevant-for-c0w4ihqhtg.pdf

Steinar Evje

Papers

Global weak solutions for a viscous liquid-gas model with singular pressure law

Numerical methods for the simulation of the settling of flocculated suspensions

On Strongly Degenerate Convection–Diffusion Problems Modeling Sedimentation–Consolidation Processes

On the Wave Structure of Two‐Phase Flow Models

Weak Solutions for a Gas-Liquid Model Relevant for Describing Gas-Kick in Oil Wells