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Academic literature on the topic 'NONLINEAR TREATMENT RATES'

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Published: 11 September 2023

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Journal articles on the topic "NONLINEAR TREATMENT RATES"

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Dochain, D., and M. Perrier. "Control Design for Nonlinear Wastewater Treatment Processes." Water Science and Technology 28, no. 11-12 (December 1, 1993): 283–93. http://dx.doi.org/10.2166/wst.1993.0668.

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This paper deals with the design of adaptive nonlinear control algorithms of biological wastewater treatment processes. The control design is based on the dynamical mass balance equations of the process and includes the on-line estimation of uncertain parameters (specific growth rates and yield coefficients). The procedure is illustrated by two examples (activated sludge process, anaerobic digestion).
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Upadhyay, Ranjit Kumar, Ashok Kumar Pal, Sangeeta Kumari, and Parimita Roy. "Dynamics of an SEIR epidemic model with nonlinear incidence and treatment rates." Nonlinear Dynamics 96, no. 4 (April 4, 2019): 2351–68. http://dx.doi.org/10.1007/s11071-019-04926-6.

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Kumar, Abhishek. "Stability of a Fractional-Order Epidemic Model with Nonlinear Incidences and Treatment Rates." Iranian Journal of Science and Technology, Transactions A: Science 44, no. 5 (August 27, 2020): 1505–17. http://dx.doi.org/10.1007/s40995-020-00960-x.

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Kumar, Abhishek, and Nilam. "Mathematical analysis of a delayed epidemic model with nonlinear incidence and treatment rates." Journal of Engineering Mathematics 115, no. 1 (March 7, 2019): 1–20. http://dx.doi.org/10.1007/s10665-019-09989-3.

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DUBEY, B., ATASI PATRA, P. K. SRIVASTAVA, and UMA S. DUBEY. "MODELING AND ANALYSIS OF AN SEIR MODEL WITH DIFFERENT TYPES OF NONLINEAR TREATMENT RATES." Journal of Biological Systems 21, no. 03 (September 2013): 1350023. http://dx.doi.org/10.1142/s021833901350023x.

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In this study, an SEIR epidemic model is proposed for treatment of infectives considering the development of acquired immunity in recovered individuals. We employed two different types of treatment functions. Stability analysis for disease-free as well as endemic equilibria is performed. It is observed that the existence of unique endemic equilibrium depends on the basic reproductive number R0as well as on treatment rate. Numerical simulations are performed on the proposed models to support and analyze theoretical findings.
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Li, Junhong, and Ning Cui. "Dynamic Behavior for an SIRS Model with Nonlinear Incidence Rate and Treatment." Scientific World Journal 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/209256.

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This paper considers an SIRS model with nonlinear incidence rate and treatment. It is assumed that susceptible and infectious individuals have constant immigration rates. We investigate the existence of equilibrium and prove the global asymptotical stable results of the endemic equilibrium. We then obtained that the model undergoes a Hopf bifurcation and existences a limit cycle. Some numerical simulations are given to illustrate the analytical results.
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Jin, Li, Yunxian Dai, Yu Xiao, and Yiping Lin. "RANK-ONE CHAOS IN A DELAYED SIR EPIDEMIC MODEL WITH NONLINEAR INCIDENCE AND TREATMENT RATES." Journal of Applied Analysis & Computation 11, no. 4 (2021): 1779–801. http://dx.doi.org/10.11948/20200190.

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Halder, Manisha, and Dr D. S. Sharma. "A Mathematical Analysis of Dynamical Behaviour of Epidemiological Models with Nonlinear Incidence Rates." International Journal of Scientific Research in Modern Science and Technology 2, no. 5 (May 31, 2023): 33–40. http://dx.doi.org/10.59828/ijsrmst.v2i5.86.

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An updated model of an epidemic is discussed, one in which incidence has plateaued but treatment has not been fully implemented. All equilibrium points are checked for existence. In this research, we examine how shifts from the SIR (susceptible-infectious-resistant) to the SIS (susceptible-infectious-susceptible) paradigm manifest in epidemiological models. These models hypothesize that the irresistible power is a nonlinear capability of the populace thickness of contaminated individuals. At last, this model might be utilized to research the elements of infection spread, provided that the two phenomena follow consistent patterns.
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Grey, T. L., D. C. Bridges, P. L. Raymer, and J. W. Davis. "Imazethapyr Rate Responses for Wild Radish, Conventional Canola, and Imidazolinone-tolerant Canola." Plant Health Progress 7, no. 1 (January 2006): 8. http://dx.doi.org/10.1094/php-2006-1018-01-rs.

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Greenhouse experiments were conducted to determine dose responses to imazethapyr for imidazolinone-tolerant canola (Brassica napus) Pioneer 45A71, conventional canola Oscar, and wild radish (Raphanus raphanistrum). Two weeks after treatment, foliar injury was rated and plants were harvested to determine plant dry weight. Plant responses to herbicide treatments were analyzed by nonlinear regression procedures using a modified Mitscherlich plant growth model for visual injury and the negative exponential growth function for plant dry weight. Pioneer 45A71 was tolerant of all rates of imazethapyr (0.055 to 0.60 g ai/liter). In contrast, wild radish and Oscar were sensitive to imazethapyr with significant injury and approximately 50% reduction in dry plant weight at rates of 0.275 g ai/liter and greater. For the model, increased injury from herbicide treatment resulted in significantly different asymptotic maximum (βo) injury for all plant types. The dry weight for the non-treated control was 1.3, 0.8, and 1.5 g/plant for wild radish, Pioneer 45A71, and Oscar, respectively. For the models, β1 parameters indicated significant differences in response to imazethapyr treatment between the Pioneer 45A71, wild radish, and Oscar dry weights. Accepted for publication 3 July 2006. Published 18 October 2006.
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Davies, Geraint R., Richard Brindle, Saye H. Khoo, and Leon J. Aarons. "Use of Nonlinear Mixed-Effects Analysis for Improved Precision of Early Pharmacodynamic Measures in Tuberculosis Treatment." Antimicrobial Agents and Chemotherapy 50, no. 9 (September 2006): 3154–56. http://dx.doi.org/10.1128/aac.00774-05.

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ABSTRACT Nonlinear mixed-effects analysis of serial sputum colony-counting data supports the existence of two bacillary subpopulations in sputum, eliminated at different rates. It distinguishes between combination regimens, removes bias, and greatly improves precision, with significant implications for the analysis of surrogate endpoints of “sterilization” in the development of new antituberculosis regimens.
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Dissertations / Theses on the topic "NONLINEAR TREATMENT RATES"

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KUMAR, ABHISHEK. "MATHEMATICAL MODELING IN EPIDEMIOLOGY." Thesis, 2019. http://dspace.dtu.ac.in:8080/jspui/handle/repository/16918.

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In the present thesis, various aspects of the transmission dynamics of epidemics are discussed through the mathematical models. We have proposed and analyzed the various mathematical models to control the spread of emerging/ re-emerging epidemics. We have investigated the facts and reasons behind the spread and control of infectious diseases/ epidemics. After analyzing several systems, various results obtained by analysis of the problem are discussed. The mathematical models have been analyzed for positiveness, boundedness, and stability. Locals stability, global stability, Routh-Hurwitz stability criterion, Descartes’ rule of signs, Lyapunov function, MATLAB 2012b (ODE 45, DDE 23), MATHEMATICA 11 are the main tools applied for analysis and simulations of mathematical models. We have studied two types of mathematical models: ordinary differential equations (ODEs) model and delay differential equations (DDEs) model. The time delay exists almost in every biological phenomenon and is responsible for the severity of the disease and hence in its treatment. Therefore, the importance of the DDE model cannot be ignored in the control and transmission dynamics of the epidemic. The DDE models have been developed for a better understanding of the transmission dynamics of epidemics.
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Book chapters on the topic "NONLINEAR TREATMENT RATES"

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Dubey, Preeti, Balram Dubey, and Uma S. Dubey. "An SIR Model with Nonlinear Incidence Rate and Holling Type III Treatment Rate." In Applied Analysis in Biological and Physical Sciences, 63–81. New Delhi: Springer India, 2016. http://dx.doi.org/10.1007/978-81-322-3640-5_4.

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Nilam. "Cause and Control Strategy for Infectious Diseases with Nonlinear Incidence and Treatment Rate." In Studies in Systems, Decision and Control, 61–81. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-49896-2_3.

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Srivastava, Akriti, and Prashant K. Srivastava. "Nonlinear Dynamics in an SIR Model with Ratio-Dependent Incidence and Holling Type III Treatment Rate Functions." In Trends in Biomathematics: Modeling Epidemiological, Neuronal, and Social Dynamics, 57–72. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-33050-6_4.

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Epstein, Irving R., and John A. Pojman. "Delays and Differential Delay Equations." In An Introduction to Nonlinear Chemical Dynamics. Oxford University Press, 1998. http://dx.doi.org/10.1093/oso/9780195096705.003.0016.

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Mathematically speaking, the most important tools used by the chemical kineticist to study chemical reactions like the ones we have been considering are sets of coupled, first-order, ordinary differential equations that describe the changes in time of the concentrations of species in the system, that is, the rate laws derived from the Law of Mass Action. In order to obtain equations of this type, one must make a number of key assumptions, some of which are usually explicit, others more hidden. We have treated only isothermal systems, thereby obtaining polynomial rate laws instead of the transcendental expressions that would result if the temperature were taken as a variable, a step that would be necessary if we were to consider thermochemical oscillators (Gray and Scott, 1990), for example, combustion reactions at metal surfaces. What is perhaps less obvious is that our equations constitute an average over quantum mechanical microstates, allowing us to employ a relatively small number of bulk concentrations as our dependent variables, rather than having to keep track of the populations of different states that react at different rates. Our treatment ignores fluctuations, so that we may utilize deterministic equations rather than a stochastic or a master equation formulation (Gardiner, 1990). Whenever we employ ordinary differential equations, we are making the approximation that the medium is well mixed, with all species uniformly distributed; any spatial gradients (and we see in several other chapters that these can play a key role) require the inclusion of diffusion terms and the use of partial differential equations. All of these assumptions or approximations are well known, and in all cases chemists have more elaborate techniques at their disposal for treating these effects more exactly, should that be desirable. Another, less widely appreciated idealization in chemical kinetics is that phenomena take place instantaneously—that a change in [A] at time t generates a change in [B] time t and not at some later time t + τ. On a microscopic level, it is clear that this state of affairs cannot hold.
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Guisinger, Shan. "Evolution, Chaos Theory, Narrative, and Dreaming." In Chaos and Nonlinear Psychology, 262–85. Oxford University Press, 2022. http://dx.doi.org/10.1093/oso/9780190465025.003.0014.

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This chapter explores anorexia nervosa as an unusually clear example of how instincts can self-organize as specific stories, and it also demonstrates a role for dreaming in the emergence of particular narratives. Human nature seems to emerge as beliefs and stories about our roles and our place in our community. Those who develop anorexia nervosa become obsessed by a story that demands that they restrict feeding and move hyperactively, which seems quite mad, because they starving. Anorexia symptoms are homogeneous and delusional and we can observe a clear correspondence between the manifestly insane cognitions and specific neurocircuit changes recently revealed by brain imaging studies. A wholescale reorganization of the brain’s response to feeding opportunities is triggered by a critical drop in the energy regulation hormone, leptin. Thus, serious weight loss in those with the genetic predisposition initiates anorexia nervosa. The symptoms of anorexia nervosa (AN) were probably selected during Paleolithic famines to help hunter-gatherers searching for better lands. Decreasing feeding, moving actively, and denying starvation would have helped individuals migrate. A bifurcation to the same behaviors has been described in starving rats and pigs. Moreover, post-pubescent girls are most vulnerable because ovarian hormones turn on the heritability of AN-related genes. This specific gene and environment interaction indicates that teenaged girls were the best candidates to search for better lands during famine, probably because they were more likely to survive to reproduce if they encountered an enemy band. Dreaming appears to help condition fear of food and consolidate anorexic beliefs. However, different neural modules also seem to use dreaming to help people to recover from anorexia nervosa. The hypothesis that anorexia nervosa is due to evolutionary adaptations to search for better lands during famine rather than learned habits or psychological issues has major treatment implications.
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J. Zhang, Jian. "In Search of Optimal Laser Settings for Lithotripsy by Numerical Response Surfaces of Ablation and Retropulsion." In Response Surface Methodology in Engineering Science [Working Title]. IntechOpen, 2021. http://dx.doi.org/10.5772/intechopen.96271.

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Even though ureteroscopic laser lithotripsy (URSL) has become the preferred treatment option for urolithiasis due to shorter operation time and a better stone-free rate, the optimum laser pulse settings for URSL with the shortest operative times remain unknown. In this chapter, two sets of design of experiments (DOE) were conducted with response surface methodology: 1) the quantitative responses of calculus ablation and retropulsion in terms of the pulse energy, pulse width, and the number of pulses of a prototype Chromium (Cr3+), Thulium (Tm3+), Holmium (Ho3+) triple doped yttrium aluminum garnet (CTH:YAG) laser system. The ablation or retropulsion is inversely proportional to the pulse width, and the pulse width has a higher impact coefficient for the ablation than for the retropulsion. The quadratic fit of the response surface for the volume of ablation has a nonlinear relationship with the pulse width and number of pulses. 2) the laser setting optimization of laser lithotripsy of a commercially available CTH: YAG laser system. The experimental setup is based on a benchtop model first introduced by Sroka’s group. Comparing to frequency, the laser pulse energy or peak power has a higher impact coefficient to stone retropulsion as compared to stone ablation in CTH: YAG laser lithotripsy. The most efficient way to curtail stone retropulsion during laser lithotripsy is to lower the laser pulse peak power.
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Conference papers on the topic "NONLINEAR TREATMENT RATES"

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Dunham, Eric M., Junwei Zhang, and Dan Moos. "Constraints on Pipe Friction and Perforation Cluster Efficiency from Water Hammer Analysis." In SPE Hydraulic Fracturing Technology Conference and Exhibition. SPE, 2023. http://dx.doi.org/10.2118/212337-ms.

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Abstract Pressure losses from pipe and perforation friction control the relation between wellhead pressure and pressure at the mouth (entrance) of hydraulic fractures. Because both pipe and perforation friction are proportional to flow rate squared, standard step-down tests that rely on the steady pressure response at a set of injection rates cannot uniquely determine pipe and perforation friction. We introduce a novel method to resolve this nonuniqueness by analyzing the water hammer response, measured by high-rate pressure sensors at the wellhead, following abrupt rate steps during shut-in following a stimulation treatment. Constraints on perforation friction permit quantification of the number of active perforations connecting to fractures and hence perforation cluster efficiency. Our method requires a shut-in procedure with abrupt drops in injection rate to produce water hammer oscillations (tube waves propagating between the wellhead and current stage). The rate drop is accompanied by a drop in wellhead pressure as a tube wave propagates away from the wellhead, decelerating the fluid behind it. Pipe friction attenuates this wave, such that the local flow rate remains higher at depth than near the wellhead. This expands the fluid, causing additional depressurization at the wellhead until the arrival of the reflected wave from the stage. The Darcy-Weisbach pipe friction factor is determined from the depressurization rate. At high background flow rates, the reflected wave amplitude is controlled by perforation friction with minimal sensitivity to fracture properties. The claims above are substantiated by numerical simulations of tube wave propagation and reflection from perforation clusters connected to hydraulic fractures. We then present two case studies in which the method is applied data from hydraulic fracturing treatments in two stages in different wells targeting the Wolfcamp and Bone Spring Formations, Permian Basin. The inferred pipe friction factor is 2×10−3, an order of magnitude smaller than for turbulent water flow, but consistent with the use of friction reducers and pumping company pressure loss tables. The measured perforation friction is higher than predictions based on a standard formula involving fluid density, discharge coefficient, entry hole diameter, and design number of holes. This suggests not all clusters connect to fractures; the inferred cluster efficiency is 67% (Case-A, Wolfcamp) and 84% (Case-B, Bone Spring). This work extends simulation and inversion capabilities utilizing wellhead data to nonlinear problems involving tube wave interactions with hydraulic fractures and perforations. The ability to independently constrain pipe and perforation friction resolves nonuniqueness of step rate tests. Rapid inversion enables us to deliver real-time measurements of perforation cluster efficiency, pipe and perforation friction that complement traditional fracture diagnostics. Combined with acoustic pulsing to quantify near-well flow resistance, the method provides a noninvasive, cost-effective means of monitoring of the critical connection between the well and fractures during simulation treatment. The method can be used to diagnose and treat problems such as uneven fluid distribution across clusters.
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Chen, Yue, Megan E. Poorman, David B. Comber, E. Bryn Pitt, Cindy Liu, Isuru S. Godage, Hong Yu, William A. Grissom, Eric J. Barth, and Robert J. Webster. "Treating Epilepsy via Thermal Ablation: Initial Experiments With an MRI-Guided Concentric Tube Robot." In 2017 Design of Medical Devices Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/dmd2017-3408.

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Epilepsy is a prevalent neurological disorder affecting 65 million people globally [1]. Anti-epileptic medications fail to provide effective seizure control for 30% of patients, placing them at a 7–17% risk of Sudden Unexplained Death in Epilepsy and recurrent seizures. Surgical resection of the seizure focus is a potentially curative treatment for patients with seizures that electrophysiologically correlate to a focal lesion. For these patients, focal surgical resection can result in 60–70% seizure-freedom rates [2]. However, open resection carries the risk of cognitive impairment or focal neurologic deficit [3]. Recent innovations in MRI enable high resolution soft tissue visualization, and real-time temperature monitoring, making MR-guided ablation therapy a promising minimally invasive technique to restrict the tissue destruction to just the seizure focus. Commercial products (e.g., Visualase, Medtronic Inc.; ClearPoint, MRI Interventions Inc.; NeuroBlate, Monteris Inc.) have recently been introduced for MR-guided laser-based thermal ablation. These products require the physician drill a hole into the skull for ablation probe placement, and may not always be able to ablate the entire seizure focus when the structure has a curved shape (such as the hippocampus) [4]. Incomplete ablation of the seizure focus would lead to seizure recurrence. We have recently proposed concentric-tube steerable needles as a means to address these challenges [4–7]. They enable nonlinear trajectories and offer the potential to enter the brain through the patient’s cheek via a natural opening in the skull base (i.e. the foramen ovale). We have designed and fabricated an MR-compatible robotic system to provide high resolution actuation for helical needle deployment [5]. We have shown in simulation that the curved medial axis of hippocampus can be accessed via a helical needle that delivers the ablation probe into the brain [4]. These preliminary results suggest that MR-guided robotic transforamenal thermal therapy could potentially provide a less invasive approach for potentially curative epilepsy treatment. In this paper we present our first results delivering heat along curved paths in brain phantoms and imaging the resulting treatment zones using MRI.
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Zou, Amy, and Louis J. Durlofsky. "Integrated Framework for Optimization of Horizontal/Deviated Well Placement and Control for Geological CO2 Storage." In SPE Reservoir Simulation Conference. SPE, 2023. http://dx.doi.org/10.2118/212228-ms.

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Abstract A general framework for optimizing the locations and time-varying injection rates of a set of monobore wells for geological carbon storage is presented and applied. Two objective functions, minimization of mobile CO2 fraction at the end of the operation, and maximization of storage efficiency, are considered. Appropriate linear and nonlinear constraints, involving the geometry of the well configuration, injection rates, and injected mass (for pressure management), are specified. Two derivative-free algorithms, particle swarm optimization (PSO) and differential evolution (DE), are applied and assessed. The various constraints are treated using a preprocessing repair procedure, penalty functions, and a filter method. The framework utilizes multifidelity optimization, in which increasing levels of grid resolution are applied during the course of the optimization run. For the minimization of mobile CO2 fraction, the multifidelity approach is compared with high-resolution optimization. This treatment is shown to outperform high-resolution PSO and DE optimization in terms of both solution quality and computational requirements. The multifidelity DE optimization case provides the best (feasible) solution, with 0.090 mobile CO2 fraction at 200 years, which represents a 68% improvement over a heuristic base-case. For the second objective function, multifidelity PSO provides a design that results in a storage efficiency of 0.074, which is about double the base-case value. For both objective functions, the optimized solutions contain horizontal and deviated wells placed near the bottom of the storage aquifer. The well configurations are much different for the two objective functions, with wells more closely spaced, resulting in a single merged plume, for the storage efficiency maximization case. For the mobile CO2 minimization case, by contrast, wells are separated and pulsed, which facilitates dissolution and residual trapping.
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Belenov, Edward M., and Peter P. Vasil’ev. "Coherent Effects in Ultrashort Pulse Generation by a Semiconductor Injection Laser." In Nonlinear Dynamics in Optical Systems. Washington, D.C.: Optica Publishing Group, 1990. http://dx.doi.org/10.1364/nldos.1990.tdsls57.

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Effects of coherent interaction of ultrashort pulses with an injection laser active medium are investigated both theoretically and experimentally. A breakup of the picosecond pulse envelop into subpulses and a train of coherent pulses with a repetition rate nearly 100 GHz are observed for the first time. The theoretical treatment of the laser dynamics is based on the Maxwell-Bloch equation taking into account the dependence of the intraband relaxation time on the electromagnetic field amplitude of the picosecond pulse, the inhomogenious line brodening mechanism and Raman scattering within the laser cavity.
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Oberleithner, Kilian, and Christian Oliver Paschereit. "Modeling Flame Describing Functions Based on Hydrodynamic Linear Stability Analysis." In ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/gt2016-57316.

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Combustion instabilities crucially affect the operational range of modern lean premixed gas turbine combustors and must be avoided or kept at low amplitudes. The main uncertainty of current prediction models is the flame describing function (FDF) that characterizes the flame response to high amplitude acoustic forcing. In this work, we present a new FDF model based on linear hydrodynamic stability analysis. This work is in continuation of an earlier study, where the frequency dependence and saturation of the FDF gain of a perfectly premixed flame was linked to the growth rates of the Kelvin–Helmholtz (KH) instability. In this work, we report on FDF measurements in a newly designed swirl-stabilized combustor. We identify two independent mechanisms that determine the flame response. The first stems from swirl-fluctuations that are generated in the swirler and the second stems from the KH instability. The swirl-fluctuations are approximated by a convective time lag model. The KH instability is predicted from linear hydrodynamic stability analysis based on the time-mean flow measured via PIV. A combination of both models leads to a good quantitative agreement with the measured FDF. Besides the practical advantages of predicting the FDF from stationary flow data, the model reveals the mechanisms driving the saturation of the FDF and guides the way out from the black-box treatment of the nonlinear flame response.
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Weidman, D. L., M. A. Newhouse, and D. W. Hall. "Thermal Effects in Ultrafast Photonic Switches." In Nonlinear Optical Properties of Materials. Washington, D.C.: Optica Publishing Group, 1988. http://dx.doi.org/10.1364/nlopm.1988.mf13.

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The performance of a nonlinear device may be significantly altered by thermal effects. The heat generated by the absorption of power from the switching laser can induce thermal index changes which may overwhelm the photonic index changes. Here a model of these thermal effects is presented, and expressions for the relationship of thermal to photonic index changes are derived. Previous workers have considered heating due to a single pulse.1 Our treatment snows that, for the appropriate material and device parameter ranges, cumulative thermal build-up will be important in the envisioned high-data-rate systems. Using these results, we compare the potential performance characteristics of various materials, including experimental heavy-metal glasses which show large nonlinear effects.
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Franc, Jacques, Olav Møyner, and Hamdi A. Tchelepi. "Coupling-Strength Criteria for Sequential Implicit Formulations." In SPE Reservoir Simulation Conference. SPE, 2021. http://dx.doi.org/10.2118/203909-ms.

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Abstract Sequential Fully Implicit (SFI) schemes have been proposed as an alternative to the Fully Implicit Method (FIM). A significant advantage of SFI is that one can employ scalable strategies to the flow and transport problems. However, the primary disadvantage of using SFI compared with FIM is the fact that the splitting errors induced by the decoupling operator, which separates the pressure from the saturation(s), can lead to serious convergence difficulties of the overall nonlinear problem. Thus, it is important to quantify the coupling strength in an adaptive manner in both space and time. We present criteria that localize the computational cells where the pressure and saturation solutions are tightly coupled. The approach is using terms in the FIM Jacobian matrix, we quantify the sensitivity of the mass and volume-balance equations to changes in the pressure and the saturations. We identify three criteria that provide a measure of the coupling strength across the equations and variables. The standard CFL stability criteria, which are based entirely on the saturation equations, are a subset of the new criteria. Here, the pressure equation is solved using Algebraic MultiGrid (AMG), or a multiscale solver, such as the Multiscale Restricted-Smooth Basis (MsRSB) approach. The transport equations are then solved using a fixed total-velocity. These ‘coupling strength’ criteria are used to identify the cells where the pressure-saturation coupling is strong. The applicability of the derived coupling-strength criteria is tested using several test cases. The first test is using a gravitational immiscible dead-oil lock-exchange under a unit mobility ratio and large differences in density. For this case, the SFI algorithm fails to converge to the fully coupled solution due to the large splitting errors. Introducing a fully coupled solution stage on the local subdomains as an additional correction step restores nonlinear convergence. Detailed analysis of the ‘coupling strength’ criteria indicates that the criteria related to the sensitivity of the mass balance to changes in the pressure and the sensitivity of the volume balance to changes in the saturations are the most important ones to satisfy. Other test cases include an alternate gas-water-gas injection in a top layer of the SPE 10 test case and an injection-production scenario in a three-dimensional reservoir with layered lognormally distributed permeability. We propose novel criteria to estimate the strength of coupling between pressure and saturation. These CFL-like numbers are used to identify the cells that require fully implicit treatment in the nonlinear solution strategy. These criteria can also be used to improve the nonlinear convergence rates of Adaptive Implicit Methods (AIM).
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Dimitriu, Gabriel, Vasile lucian Boiculese, Mihaela Moscalu, and Cristina gena Dascalu. "GLOBAL SENSITIVITY ANALYSIS APPLIED TO A CANCER IMMUNOTHERAPY MODEL." In eLSE 2019. Carol I National Defence University Publishing House, 2019. http://dx.doi.org/10.12753/2066-026x-19-177.

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Sensitivity analysis methods have a long history and have been widely applied in different fields, such as environmental modeling, economical modeling for decision making, parameter estimation and control, chemical kinetics, and biological modeling analysis, with metabolic networks, signaling pathways and genetic circuits. Cancer immunotherapy is based on the idea of immune surveillance. Immunotherapy, also named biologic therapy, represents a type of cancer treatment that boosts the body's natural defenses to fight cancer. It uses substances made by the body or in a laboratory to improve or restore immune system function. The aim of this paper is to perform a global sensitivity analysis applied to a mathematical model for the tumor-immune interaction. Global sensitivity analysis quantifies the importance of model inputs and their interactions with respect to model output. It provides an overall view on the influence of inputs on outputs as opposed to a local view of partial derivatives as in local sensitivity analysis. The model under investigation is specialized for autologous dendritic cell transfection therapy. It consists of a system of five nonlinear ordinary differential equations which define the rates of change for the following key immune cell populations: the tumor-specific CD4 T helper cells, the tumor-specific CD8 T cells or CTLs cytotoxic cells, the cancer cells that expose the tumor-associated antigens or TAAs, the mature dendritic cells loaded with the TAAs, and the IL-2 secreted by the tumor-specific CD4 T helper cells and responsible for T cell growth. We show how to globally analyze the sensitivity of this complex system by means of several graphical objects: sensitivity heat map, singular spectrum plot, and parameter sensitivity spectrum.
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Zheng, B., H. D. Yu, X. Wang, and X. M. Lai. "Effect of Surface Roughness and Residual Stress Induced by High Speed Milling Process on Short Crack Growth." In ASME 2016 11th International Manufacturing Science and Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/msec2016-8503.

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Surface scratches and residual stresses inevitably appear on the surface of the component as a result of the machining process. The damage evolution of surface scratch due to the combined effect of cyclic loading and residual stresses will be significantly different from the case where only the cyclic loading is considered. In the damage evolution of surface scratch, the short crack growth is of great importance owing to its apparently anomalous behaviors compared with the long-crack growth. In this paper, the effect of the surface roughness and the residual stress on the short crack growth is studied. Firstly, the surface roughness and the residual stress of 7075-T6 aluminum alloy induced by the high speed milling process with various cutting speeds and feed rates are investigated with the experimental method. The maximum height roughness parameter is measured, which is regarded as the surface defect induced by the milling process. The residual stress on the specimen surface is measured with the X-ray diffraction. Results show that the surface roughness becomes higher with the increase of the feed rate. However, the influence of the cutting speed on the surface roughness is not significant. The residual stresses on the specimen surface are all in the compressive state. The residual stress is more compressive as the feed rate increases. The effects of the process parameters on the surface roughness and the residual stress are described by the fitted formulas. Then a modified model is built to characterize short fatigue crack growth behaviors with the consideration of the residual stress. This model is proved to provide a realistic treatment of the short crack growth, as reflected by comparison with experimental fatigue crack growth data of medium carbon steel and 7075-T6 aluminum alloy published in literature. The effect of surface roughness and residual stress caused by the milling process on the short crack growth is also investigated by using the proposed model. The growth of the scratch is nonlinear when it is subjected to the cyclic load. The compressive residual stress reduces the growth rate of the crack. The crack with larger initial surface roughness grows faster than that with smaller roughness. The correlation of surface roughness, residual stress and crack growth length is obtained by the polynomial fitting. The investigations in this paper can help the damage tolerance design of structures and improve the awareness of the effect of the residual stress and surface roughness induced by the machining process on the short crack growth.
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10

Smith, Joshua H., and Jose Jaime García. "A Nonlinear Biphasic Model for Fluid Transport and Tissue Deformation During Constant Flow Rate Infusion Into Brain Tissue." In ASME 2009 Summer Bioengineering Conference. American Society of Mechanical Engineers, 2009. http://dx.doi.org/10.1115/sbc2009-204506.

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The delivery of therapeutic agents into the brain is impeded by the blood-brain barrier, preventing adequate treatment of diseases of the central nervous system. Convection enhanced delivery was developed as a means to deliver therapeutic agents directly into brain tissue and to transport the drugs in the extracellular space using convective flow. Poroelastic or biphasic models have been used to study the concomitant fluid transport and tissue deformation that occurs during infusion, however previous studies have been limited by the assumption of linear elasticity of the solid phase [1].
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