A Well-Balanced Positivity-Preserving Quasi-Lagrange Moving Mesh DG Method for the Shallow Water Equations

A high-order, well-balanced, positivity-preserving quasi-Lagrange moving mesh DG method is presented for the shallow water equations with non-flat bottom topography. The well-balance property is crucial to the ability of a scheme to simulate perturbation waves over the lake-at-rest steady state such as waves on a lake or tsunami waves in the deep ocean. The method combines a quasi-Lagrange moving mesh DG method, a hydrostatic reconstruction technique, and a change of unknown variables. The strategies in the use of slope limiting, positivity-preservation limiting, and change of variables to ensure the well-balance and positivity-preserving properties are discussed. Compared to rezoning-type methods, the current method treats mesh movement continuously in time and has the advantages that it does not need to interpolate flow variables from the old mesh to the new one and places no constraint for the choice of a update scheme for the bottom topography on the new mesh. A selection of one- and two-dimensional examples are presented to demonstrate the well-balance property, positivity preservation, and high-order accuracy of the method and its ability to adapt the mesh according to features in the flow and bottom topography.     

Working‐correlation‐structure identification in generalized estimating equations

Selecting an appropriate working correlation structure is pertinent to clustered data analysis using generalized estimating equations (GEE) because an inappropriate choice will lead to inefficient parameter estimation. We investigate the well‐known criterion of QIC for selecting a working correlation structure, and have found that performance of the QIC is deteriorated by a term that is theoretically independent of the correlation structures but has to be estimated with an error. This leads us to propose a correlation information criterion (CIC) that substantially improves the QIC performance. Extensive simulation studies indicate that the CIC has remarkable improvement in selecting the correct correlation structures. We also illustrate our findings using a data set from the Madras Longitudinal Schizophrenia Study. Copyright © 2008 John Wiley & Sons, Ltd.     

Suicide substrate reaction-diffusion equations: Varying the source

The suicide substrate reaction is a model for certain enzyme-inhibitingdrugs. This reaction system is examined assuming that the substratediffuses freely while the enzyme remains fixed. Two sets ofinitial and boundary conditions are examined: one modellingan instantaneous point source, akin to an injection of substrate,the other, a continuous point source, akin to a continuing influx,or intravenous drip, of substrate. The quasi-steady-state assumptionis applied to obtain analytical solutions for a limited parameterspace. Finally, further applications of numerical and analyticalexperimentation on pharmaceutical mechanisms are described.     

用化学计量法研究CO2—n—C7H16系的高压相平衡

测定了在温度３１０．６５Ｋ、３２３．１５Ｋ和压力３．１３～７．５４ＭＰａ条件下的气液平衡数据，实验结果与文献值具有较好的一致性。用ＴＲＫ状态方程对实验所得数据进行关联，取得了较满意的结果。     

Optimal control of non‐linear chemical reactors via an initial‐value Hamiltonian problem

The problem of designing strategies for optimal feedback control of non‐linear processes, specially for regulation and set‐point changing, is attacked in this paper. A novel procedure based on the Hamiltonian equations associated to a bilinear approximation of the dynamics and a quadratic cost is presented. The usual boundary‐value situation for the coupled state–costate system is transformed into an initial‐value problem through the solution of a generalized algebraic Riccati equation. This allows to integrate the Hamiltonian equations on‐line, and to construct the feedback law by using the costate solution trajectory. Results are shown applied to a classical non‐linear chemical reactor model, and compared against suboptimal bilinear‐quadratic strategies based on power series expansions. Since state variables calculated from Hamiltonian equations may differ from the values of physical states, the proposed control strategy is suboptimal with respect to the original plant. Copyright © 2005 John Wiley & Sons, Ltd.     

Using switching detection and variational equations for the shooting method

We study in this paper the resolution by single shooting of an optimal control problem with a bang‐bang control involving a large number of commutations. We focus on the handling of these commutations regarding the precise computation of the shooting function and its Jacobian. We first observe the impact of a switching detection algorithm on the shooting method results. Then, we study the computation of the Jacobian of the shooting function, by comparing classical finite differences to a formulation using the variational equations. We consider as an application a low thrust orbital transfer with payload maximization. This kind of problem presents a discontinuous optimal control, and involves up to 1800 commutations for the lowest thrust. Copyright © 2007 John Wiley & Sons, Ltd.     

A tidal ventilation model for oxygenation in respiratory failure

We develop tidal-ventilation pulmonary gas-exchange equations that allow pulmonary shunt to have different values during expiration and inspiration, in accordance with lung collapse and recruitment during lung dysfunction (Am. J. Respir. Crit. Care Med. 158 (1998) 1636). Their solutions are tested against published animal data from intravascular oxygen tension and saturation sensors. These equations provide one explanation for (i) observed physiological phenomena, such as within-breath fluctuations in arterial oxygen saturation and blood-gas tension; and (ii) conventional (time averaged) blood-gas sample oxygen tensions. We suggest that tidal-ventilation models are needed to describe within-breath fluctuations in arterial oxygen saturation and blood-gas tension in acute respiratory distress syndrome (ARDS) subjects. Both the amplitude of these oxygen saturation and tension fluctuations, and the mean oxygen blood-gas values, are affected by physiological variables such as inspired oxygen concentration, lung volume, and the inspiratory:expiratory (I:E) ratio, as well as by changes in pulmonary shunt during the respiratory cycle.     

Modelling HA protein-mediated interaction between an influenza virus and a healthy cell: pre-fusion membrane deformation.

We present a mathematical model for pre-fusion interaction between an influenza virus and a healthy cell. Our model describes the role played by hemagglutinin (HA) protein clusters in bringing the viral membrane into close contact with the host cell membrane as a first step of the fusion process between the two membranes. The viral membrane is modelled as a lipid bilayer with bending rigidity. Using the calculus of variations, we compute the deformation of the viral membrane under the influence of HA protein clusters. Our numerical results support the hypothesis of dimple formation in the fusion site proposed in the literature. The asymmetric nature of the protein molecules due to various reasons such as tilting is the primary cause for the dimple formation. We discuss the effects of spontaneous curvature, the protein cluster radius, fusion-site size and the bending moment exerted by the protein cluster. We also examine the effects of membrane tension and the presence of a host cell on the dimple shape. Our results support previous experimental observations.     

Assessment of cancer immunotherapy outcome in terms of the immune response time features.

A cytokine-based periodic immunotherapy treatment is included in a model of tumour growth with a delay. The effects of dose schedule are studied in the case of a weak immune system and a growing tumour. We find the existence of 'metastable' states (that may last for tens of years) induced by the treatment and also potentially adverse effects of the dosage frequency on the stabilization of the tumour. These two effects depend on the delay between the tumour growth and the immune system response, the cytokine dose burden, and other parameters considered in the model.     

An Epidemiology Model for Estimating the Numbers of US Patients With Multiple Myeloma by Line of Therapy and Treatment Exposure

ObjectivesEstimates on the distribution of patients with multiple myeloma (MM) by line of therapy (LOT) are scarce and get outdated quickly as new treatments become available. The objective of this study was to estimate the number of patients with MM by LOT and the number of patients who have received at least 4 previous LOTs including proteasome inhibitors, immunomodulatory agents, and anti-CD38 monoclonal antibodies (mAbs).MethodsA compartmental model was developed to calculate the number of patients by LOT. Two pathways were considered based on stem cell transplant eligibility, and at each pathway, treatments were stratified in 2 types: anti-CD38 mAbs or other. The model population was stratified into 4 subgroups based on age and cytogenetic risk. Model inputs were informed from real-world evidence.ResultsThe model estimated that, in 2020, 126 869 patients were living with MM in the United States. Of these, 105 701 received treatment in any LOT, with 56 959, 27 252, 11 258, and 5217 in lines 1 to 4, respectively, and 5015 in line 5 or beyond. The model estimated that 3497 patients received at least 4 previous LOTs including proteasome inhibitors, immunomodulatory agents, and anti-CD38 mAbs. The model overall prevalence predictions aligned well with publicly available estimates.ConclusionsThis study proposes a novel framework to estimate MM prevalence. It can assist clinicians to understand future trends in MM epidemiology, healthcare systems to plan for future resource use allocation, and payers to quantify the budget impact of new treatments.