Modeling and simulation of thermal chlorine etching of gallium arsenide with application to real-time feedback control

A dynamic model for the simulation of thermal chlorine etching of gallium arsenide is developed. The primary motivation for the development of the simulation is the design and testing of real time adaptive feedback controllers which rely upon in-situ optical measurements of etch depth obtained via spectroscopic ellipsometry. The basis for the model is an empirically derived relationship between etch rate, chlorine pressure, and substrate temperature. The chlorine pressure in the chamber is regulated by a throttle valve which determines the effective pumping rate of a turbo-molecular pump which is used to evacuate chlorine pressure dynamics and a second-order damped harmonic oscillator with zero-order hold valve position command inputs is used to model the dynamics of the throttle valve. An output equation is used to model the fact that ellipsometry based etch depth and chamber pressure can be observed at discrete time intervals. Unmeasurable parameters which appear in the model are identified, and the model is validated using experimental data. An adaptive linear-quadratic Gaussian based controller based on our model which forces etching to precede at a desired rate while estimating the often difficult to measure substrate temperature is designed and then tested using our simulation.     

Modeling substrate concentration in skeletal muscle

We adapt an approach developed for modeling oxygen transport in skeletal muscle, which allows the inclusion of a large number of capillaries, to the modeling of substrate transport. The substrate concentration in the capillaries is determined from the solution of a set of algebraic equations. The tissue concentration in any region is sufficiently approximated by the concentration in a nearby capillary, diminished by a finite amount that is determined along with the solution to the equations for the capillary concentration. We find that differently perfused adjacent or nearby capillaries interact and affect each other, but that this interaction is fairly localized.     

A hybrid stimulation strategy for suppression of spiral waves in cardiac tissue

Atrial fibrillation (AF) is the most common cardiac arrhythmia whose mechanisms are thought to be mainly due to the self perpetuation of spiral waves (SW). To date, available treatment strategies (antiarrhythmic drugs, radiofrequency ablation of the substrate, electrical cardioversion) to restore and to maintain a normal sinus rhythm have limitations and are associated with AF recurrences. The aim of this study was to assess a way of suppressing SW by applying multifocal electrical stimulations in a simulated cardiac tissue using a 2D FitzHugh-Nagumo model specially convenient for AF investigations. We identified stimulation parameters for successful termination of SW. However, SW reinduction, following the electrical stimuli, leads us to develop a hybrid strategy based on sodium channel modification for the simulated tissue.     

Explicit asymptotic modelling of transient Love waves propagated along a thin coating

An explicit asymptotic model for transient Love waves is derived from the exact equations of anti-plane elasticity. The perturbation procedure relies upon the slow decay of low-frequency Love waves to approximate the displacement field in the substrate by a power series in the depth coordinate. When appropriate decay conditions are imposed on the series, one obtains a model equation governing the displacement at the interface between the coating and the substrate. Unusually, the model equation contains a term with a pseudo-differential operator. This result is confirmed and interpreted by analysing the exact solution obtained by integral transforms. The performance of the derived model is illustrated by numerical examples     

Explicit asymptotic modelling of transient Love waves propagated along a thin coating

An explicit asymptotic model for transient Love waves is derived from the exact equations of anti-plane elasticity. The perturbation procedure relies upon the slow decay of low-frequency Love waves to approximate the displacement field in the substrate by a power series in the depth coordinate. When appropriate decay conditions are imposed on the series, one obtains a model equation governing the displacement at the interface between the coating and the substrate. Unusually, the model equation contains a term with a pseudo-differential operator. This result is confirmed and interpreted by analysing the exact solution obtained by integral transforms. The performance of the derived model is illustrated by numerical examples     

Qualitative analysis of a chemostat model with inhibitory exponential substrate uptake

In this paper, we consider a simple chemostat model involving a single species feeding on redundant substrate with a constant yield term. Many experiments indicate that very high substrate concentrations actually inhibit growth. Instead of assuming the prevalent Monod kinetics for growth rate of cells, we use a non-monotonic functional response function to describe the inhibitory effect. A detailed qualitative analysis about the local and global stability of its equilibria (including all critical cases) is carried out. Numerical simulations are performed to show that the dynamical properties depend intimately upon the parameters.     

Multiscale cancer modeling: In the line of fast simulation and chemotherapy

Although Multiscale Cancer Modeling has a realistic view in the process of tumor growth, its numerical algorithm is time consuming. Therefore, it is problematic to run and to find the best treatment plan for chemotherapy, even in case of a small size of tissue. Using an artificial neural network, this paper simulates the multiscale cancer model faster than its numerical algorithm. In order to find the best treatment plan, it suggests applying a simpler avascular model called Gompertz. By using these proposed methods, multiscale cancer modeling may be extendable to chemotherapy for a realistic size of tissue.In order to simulate multiscale model, a hierarchical neural network called Nested Hierarchical Self Organizing Map (NHSOM) is used. The basis of the NHSOM is an enhanced version of SOM, with an adaptive vigilance parameter. Corresponding parameter and the overall bottom-up design guarantee the quality of clustering, and the embedded top-down architecture reduces computational complexity.Although by applying NHSOM, the process of simulation runs faster compared with that of the numerical algorithm, it is not possible to check a simple search space. As a result, a set containing the best treatment plans of a simpler model (Gompertz) is used. Additionally, it is assumed in this paper, that the distribution of drug in vessels has a linear relation with the blood flow rate. The technical advantage of this assumption is that by using a simple linear relation, a given diffusion of a drug dosage may be scaled to the desired one.By extracting a proper feature vector from the multiscale model and using NHSOM, applying the scaled-best treatment plans of Gompertz model is done for a small size of tissue. In addition, simulating the effect of stress reduction on normal tissue after chemotherapy is another advantage of using NHSOM, which is a kind of “emergent”.     

Modelling the growth of soil-borne fungi in response to carbon and nitrogen

Email: Angelique.Lamour{at}medew.fyto.wau.nl Growth of soil-borne fungi is poorly described and understood,largely because non-destructive observations on hyphae in soilare difficult to make. Mathematical modelling can help in theunderstanding of fungal growth. Except for a model by Paustian& Schnürer (1987a), fungal growth models do not considercarbon and nitrogen contents of the supplied substrate, althoughthese nutrients have considerable effects on hyphal extensionin soil. We introduce a fungal growth model in relation to soilorganic matter decomposition dealing with the detailed dynamicsof carbon and nitrogen. Substrate with a certain carbon: nitrogenratio is supplied at a constant rate, broken down and then takenup by fungal mycelium. The nutrients are first stored internallyin metabolic pools and then incorporated into structural fungalbiomass. Standard mathematical procedures were used to obtainoverall-steady states of the variables (implicitly from a cubicequation) and the conditions for existence. Numerical computationsfor a wide range of parameter combinations show that at mostone solution for the steady state is biologically meaningful,specified by the conditions for existence. These conditionsspecify a constraint, namely that the ‘energy’ (interms of carbon) invested in breakdown of substrate should beless than the ‘energy’ resulting from breakdownof substrate, leading to a positive carbon balance. The biologicalinterpretation of the conditions for existence is that for growththe ‘energy’ necessary for production of structuralfungal biomass and for maintenance should be less than the mentionedpositive carbon balance in the situation where all substrateis colonized. In summary, the analysis of this complicated fungalgrowth model gave results with a clear biological interpretation.     

Modeling of aerosol spray characteristics for synthesis of sensor thin film from solution

A model is developed of aerosol spray for synthesis of sensor film from solution. The synthesis technique considered involves atomization of a solution of mixed salts in methanol, spraying of solution droplets, droplet deposition on a heated substrate, evaporation and chemical reaction to produce mixed oxides, and subsequent film growth. The precise control of oxide nanoparticle size distribution and inter-particle spacing in the film is crucial to achieving high sensitivity. These in turn largely depend on the droplet characteristics prior to impingement on the substrate. This paper focuses on the development of a model to describe the atomization and spray processes prior to the film growth. Specifically, a mathematical model is developed utilizing computational fluid dynamics solution of the equations governing the transport of atomized droplets from the nozzle to the substrate in order to predict droplet characteristics in flight. The predictions include spatial distribution of droplet size and concentration, and the effect on these characteristics of swirling inlet flow at the spray nozzle.     

考虑磁通流动效应的超导薄膜基底结构界面断裂行为研究北大核心CSCD

超导薄膜是一种采用化学涂层制备而成的多层薄膜结构,作为性能优越的导电功能结构材料,其载流能力与结构完整性直接相关.在超导薄膜制备过程中,超导层与金属基底之间的界面裂纹很难避免.因此,在载流运行过程中,由于外磁场的存在,这类界面裂纹的强度问题成为关键.为此,该文针对超导薄膜结构,以磁通量子穿透薄膜理论和线弹性断裂理论为基础,建立了研究超导层与基底界面裂纹强度问题的解析模型.深入分析了外加磁场作用下界面裂纹强度问题,得到了超导磁通流动对裂纹尖端应力场和能量释放率的影响.结果表明:磁通流动速度越大,界面裂纹尖端处应力越大且能量释放率越大,这将导致界面更容易发生裂纹破坏.该文所得结果有助于分析相关的界面裂纹问题.     

Structural rheological model of two-phase interlayer shear flow

This paper presents a study of an epitropic liquid crystal layer formation at a metal substrate. Such layer structurization leads to non-Newtonian flow of thin interlayer with wall-adjacent orientation-ordered layers. Rheological characteristics of micron interlayers of n-hexadecane and Vaseline oil with surfactant addition are investigated. The features of structural “variable viscosity” layer are defined within the framework of a proposed rheological model. An increase in the rate of shear deformation leads to a reduction in near-surface layer viscosity due to molecular reorientation. Estimation of model parameters, performed on basis of the experimental rheological data, is carried out.     

Structural rheological model of two-phase interlayer shear flow

This paper presents a study of an epitropic liquid crystal layer formation at a metal substrate. Such layer structurization leads to non-Newtonian flow of thin interlayer with wall-adjacent orientation-ordered layers. Rheological characteristics of micron interlayers of n-hexadecane and Vaseline oil with surfactant addition are investigated. The features of structural “variable viscosity” layer are defined within the framework of a proposed rheological model. An increase in the rate of shear deformation leads to a reduction in near-surface layer viscosity due to molecular reorientation. Estimation of model parameters, performed on basis of the experimental rheological data, is carried out.     

考虑细胞外基质黏弹性行为的细胞黏附力学模型

细胞外基质由大量胶原蛋白和纤维蛋白组成,这些基质蛋白形成复杂的交联网络状结构,具有黏弹性力学特性.研究表明,黏弹性基质能显著影响细胞迁移、增殖和分化等生理行为,还能影响癌症转移和组织纤维化等疾病的发生与发展.然而,细胞感知细胞外基质黏弹性力学特性的分子机制仍不清楚.该文通过建立细胞黏附力学模型,从分子层次揭示细胞黏附在细胞响应外界黏弹性力学微环境中的作用.结果表明,细胞能通过调控细胞黏附动力学（包括黏附周期和黏附形成时间）响应细胞外基质的黏弹性力学特性.通过将模型计算结果与实验现象相比较,验证了模型的正确性.细胞黏附力学模型将为组织工程中细胞力学微环境的构建奠定理论基础.     

Bifurcations of phase portraits of a Singular Nonlinear Equation of the Second Class

The soliton dynamics is studied using the Frenkel Kontorova (FK) model with non-convex interparticle interactions immersed in a parameterized on-site substrate potential. The case of a deformable substrate potential allows theoretical adaptation of the model to various physical situations. Non-convex interactions in lattice systems lead to a number of interesting phenomena that cannot be produced with linear coupling alone. In the continuum limit for such a model, the particles are governed by a Singular Nonlinear Equation of the Second Class. The dynamical behavior of traveling wave solutions is studied by using the theory of bifurcations of dynamical systems. Under different parametric situations, we give various sufficient conditions leading to the existence of propagating wave solutions or dislocation threshold, highlighting namely that the deformability of the substrate potential plays only a minor role.     

A Porous Media Model to Describe the Behaviour of Brain Tissue

The human brain is a very sensitive organ. Even small changes in the cranium cavity can cause life–threatening effects. In case of medical intervention, biomechanics can assist the therapy decisions by simulating the physical behaviour of brain tissue, e.g., the coupled interaction of the fluid motion and the deformation of the brain tissue. In the context of the Theory of Porous Media (TPM), a convenient model of the brain is introduced, which is able to simulate essential mechanical effects in the porous structure of the brain material. The fluid–saturated brain can be treated as an immiscible binary mixture of constituents. In this macroscopic biphasic model, the mixture consists of a solid phase (brain tissue) and a fluid phase (interstitial fluid or blood plasma). Both constituents are assumed to be materially incompressible. The resulting set of coupled partial differential equations is then spatially discretised using mixed finite elements with a backward Euler time integration. Numerical examples are presented illustrating the fundamental effects on the brain tissue under heart–rate dependent pulsative pressure variations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling and simulation of micro-well formation

Physico-chemical processes on the micro-scale require new modelling concepts because some effects become dominating that are negligible for macroscopic systems. This is illustrated by a new method for the production of micro-wells based on the placement of a small drop of toluene on a plate of polystyrene. After droplet evaporation, a micro-well is left. A mathematical model has been developed to understand the elementary processes of the micro-well formation. The model accounts for: (1) growth of the drop on the substrate, (2) evaporation process of the solvent, (3) dissolution of the substrate, (4) flow rate in the evaporating drop caused by the pinning effect, including the vertical velocity profile, and (5) increase in the concentration of dissolved material followed by precipitation. In the modelling and simulation process, it could be shown that the method of drop production also has a significant influence on the shape of the micro-wells.     

The dynamic behaviour of aerated continuous flow stirred tank bioreactor

The dynamics of continuous stirred tank bioreactors (CSTB), in which microbial growth is subjected to gaseous substrate limitation, is analysed. The growth process is supposed to obey the classical model proposed by Monod for substrate limitation, or the hump exponential model, which considers the occurrence of both substrate limitation and inhibition. The yield coefficient is supposed to be a linear function of substrate concentration. The influence of mass transfer on the system behaviour is considered. The developments produced here are shown to include the particular case of a nongaseous limiting substrate, identified in a previous study [1]. Besides the purely analytical results, numerical bifurcation diagrams and phase portraits are given to show the influence of the system parameters on the bioreactor behaviour.     

On the repulsion of an interface above a correlated substrate

We analyze a model of an interface fluctuating above a rough substrate. It is based on harmonic crystals, or lattice free fields, indexed by ^d , d 3. The phenomenon for which we want to get precise quantitative estimates is the repulsion effect of the substrate on the interface: the substrate is itself a random field, but its randomness is quenched (this generalizes the widely considered case of a flat deterministic substrate). With respect to [2] in which the substrate has been taken to be an IID field, here the substrate is an harmonic crystal, as the interface, and as such it is strongly correlated. We obtain the leading asymptotic behavior of the model in the limit of a very extended substrate: we show in particular that, to leading order, the effect of an IID substrate cannot be distinguished from the effect of an harmonic crystal substrate. We observe however that, unlike in the IID substrate case, annealed and quenched models display sharply different features.     

A model for monolayer deposition with interacting particles

We present a very versatile three-dimensional growth model with random initial conditions for the deposition of a monolayer of particles out of a gas beam on a substrate. The flexibility of the model is guaranteed by the inclusion of parameters like the substrate temperature and the chemical binding whose variation changes strongly the lateral diffusion and the morphology of the developing disordered structure. In the modelling of the potential we can use in principle data coming from experiment and quantum mechanical computations. The use of short-range potentials allows to apply the model to covalent systems. We find a variety of patterns which resemble structures found in the experiment and in other theoretical models. The important parameters have simple physical and chemical interpretations, whereas the simulation of static properties may be done with more complicated potentials for specific materials. Our approach allows to look for particular growth conditions and dynamical processes of large structures with moderate use of computational resources.