A practical analytic model for predicting the performance of an encapsulated polymer composite

A novel model is presented for simulating the characteristics of a micro-encapsulated composite. The procedure initiated utilizing particle size analysis (PSA) to obtain the volume based average diameter and average spacing between the microcapsules in the composite. Results of this procedure were verified by scanning electron microscopy (SEM). Then, a simple model was presented to predict the healing percent of a triangular crack propagating in the composite. In order to obtain more detailed results, a probabilistic model was also suggested for the planar and triangular cracks, which gave the probability of crack incidence for different number of capsules to be intersected. Results of this method were then validated in comparison with the results independently obtained using a simulation by computer programming. The comparison showed close agreement between the analytical results and the simulations which present the current model and simulations as a promising method for investigating the characteristics of the encapsulated self-healing composites.     

Stochastic binding of Ca2+ ions in the dyadic cleft; continuous vs random walk description of diffusion

Ca²⁺ signaling in the dyadic cleft in ventricular myocytes is fundamentally discrete and stochastic. In this paper we study the stochastic binding of single Ca²⁺ ions to receptors in the cleft using two different models of diffusion; a stochastic and discrete Random walk (RW) model, and a deterministic continuous model. We investigate if the latter model, together with a stochastic receptor model, can reproduce binding events registered in fully stochastic RW simulations. By evaluating the continuous model goodness-of-fit, we present evidences that it can. The large fluctuations in binding rate observed at the time level of single time steps are integrated and smoothed at the larger time scale of binding events, explaining the continuous model goodness-of-fit. With this we demonstrate that the stochasticity and discreteness of the Ca²⁺ signaling in the dyadic cleft, determined by single binding events, can be described with a deterministic model of Ca²⁺ diffusion together with a stochastic model of the binding events. Time consuming RW simulations can thus be avoided. We also present a new analytical model of bi-molecular binding probabilities that is used in the RW simulations, and in the statistical analysis. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Lagrangian relaxation approach for network inventory control of stochastic revenue management with perishable commodities

Airline seat inventory control is the allocation of seats in the same cabin to different fare classes such that the total revenue is maximized. Seat allocation can be modelled as dynamic stochastic programs, which are computationally intractable in network settings. Deterministic and probabilistic mathematical programming models are therefore used to approximate dynamic stochastic programs. The probabilistic model, which is the focus of this paper, has a nonlinear objective function, which makes the solution of large-scale practical instances with off-the-shelf solvers prohibitively time consuming. In this paper, we propose a Lagrangian relaxation (LR) method for solving the probabilistic model by exploring the fact that LR problems are decomposable. We show that the solutions of the LR problems admit a simple analytical expression which can be resolved directly. Both the booking limit policy and the bid-price policy can be implemented using this method. Numerical simulations demonstrate the effectiveness of the proposed method.     

Stabilization of planar discrete-time switched systems: Switched Lyapunov functional approach

In this paper, we investigate the problem of stabilization for single-input planar discrete-time switched systems by establishing necessary and/or sufficient conditions for the existence of switched quadratic Lyapunov functions of the closed-loop system. The results given in terms of a series of matrix inequalities generalize those results in our recent paper [Y.G. Sun, L. Wang, G. Xie, Necessary and sufficient conditions for stabilization of discrete-time planar switched systems, Nonlinear Anal.: Theory and Methods 65 (2006) 1039–1049] and clearly describe the set of switched quadratic Lyapunov functions for the system.     

Effect of localized input on bump solutions in a two-population neural-field model

We investigate a two-population Wilson–Cowan model extended with stationary and spatially dependent localized external inputs and study the existence and stability of localized stationary (bump) solutions. The generic situation for this model in the absence of external inputs corresponds to two bump pairs, one narrow and one broad pair. For spatially wide localized external inputs we find this generic picture to be unchanged. However, for strongly localized external inputs we find that three and even four bump pairs, all with symmetric activity profiles around the center of the localized external input, may coexist. We next investigate the stability of these bump pairs using two different techniques: a simplified phase–space reduction (Amari) technique and full stability analysis. Examples of models, i.e., choices of model parameters, exhibiting up to three stable bump pairs are found. The Amari technique is further found to be a poor predictor of stability in the case of strongly localized external inputs. The bump-pair states are also probed numerically using a fourth order Runge–Kutta method, and an excellent agreement is found between numerical simulations and the analytical predictions from full stability analysis.     

A computationally efficient method for modeling flexible robots based on the assumed modes method

In this paper a simple method to obtain the analytical model of a flexible robot is presented, which turns out to be more efficient, from a computational point of view, than the classic assumed modes method.The presented method consists of using appropriate linear combinations of the modes of each link as basis functions to evaluate the deflection, in such a way as to minimize the dependency of the position of the generic link on the Lagrangian variables of the previous links. Hence, the number of terms of the inertia matrix and of the Coriolis and centrifugal vectors is significantly reduced. First, the model is derived, provided that the links are homogeneous and with constant cross-section, by analytically or otherwise by numerically calculating the parameters of the closed-form expression of the Lagrangian function of the generic link supposed free; afterwards, the analytical dynamic model of the whole robot is obtained by using an iterative interconnection algorithm, which can be easily implemented by using a symbolic manipulation language.The simplicity and efficiency of the proposed method is illustrated by considering the analytic expression of the kinetic energy of the end-effector in different cases and with significant comparison examples.     

Global Steady State Analytical Solution of Cadmium Uptake Model for Plant Roots

The concentration distribution of cadmium ion in soil is studied by the phytoavailability model. According to the states of the cadmium complex: fully inert, fully labile and partially labile, we establish three corresponding cadmium uptake sub-models, and derive respective global analytical solutions at steady state. In particular, when the complex is partially labile, we give the steady analytical solution of cadmium ion concentration in cylindrical geometry composed of the analytical solutions of partially labile complex and fully inert complex in planar geometry and fully inert complex in cylindrical geometry, that is, the ration approximation method. In this paper, the global analytical solutions are compared with the results of literature and numerical simulations. Therefore, the double check is realized to ensure the rationality of the analytical method. The global concentration profile of cadmium ions in the whole rhizosphere can be described by the steady state analytical solutions: the concentration of cadmium ion increases with the distance from the root surface and finally reaches the initial value; the change rate of cadmium ion concentration is the largest when the complex is fully labile; whatever the state of the complex is, cadmium ions never accumulate on the root surface. Finally, we discuss and compare the effects of moving and fixed right boundaries of the model on the results. The results show that it is more reasonable to take the fixed right boundary, and plant roots can uptake cadmium ions in a wider range.     

Deterministic and stochastic analysis of a delayed allelopathic phytoplankton model within fluctuating environment

In this paper, we consider a two-dimensional model for two competitive phytoplankton species where one species is toxic phytoplankton and other is non-toxic species. The logistic growth of both the species follows the Hutchinson type growth law. First, we briefly discuss basic dynamical properties of non-delayed and delayed model system within deterministic environment. Next we formulate the stochastic delay differential equation model system to study the effect of environmental driving forces on the dynamical behavior. We calculate population fluctuation intensity (variance) for both species by Fourier transform method. Numerical simulations are carried out to substantiate the analytical findings. Significant results of our analytical findings and their interpretations from ecological point of view are provided in concluding section.     

A geometric approach to characterize rigidity in proteins

Kinematic analysis, in contrast to sophisticated molecular dynamics simulations, can provide high-level insights into conformational diversity of proteins and other biomolecules, with broad implications for human health. Here, we model a protein as a kinematic linkage and present a new geometric method to characterize molecular rigidity. While existing combinatorial constraint counting is limited to generic structures, our geometric approach is also valid for non-generic linkages. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Time delay factor can be used as a key factor for preventing the outbreak of a disease—Results drawn from a mathematical study of a one season eco-epidemiological model

Chatterjee and Chattopadhyay [Role of migratory bird population in an simple eco-epidemiological model, Math. Comp. Model. Dyn. Syst., in press] proposed and analyzed a one season eco-epidemiological model of susceptible and infective prey together with their predators. In such systems, time lags due to the gestation of the infective prey are of importance. In this paper we modify and analyze their model by taking this factor into consideration. Our analysis shows that the outbreak of the disease can be controlled by a careful and suitable increment of the time lag factor. Moreover, to preserve the stability of the coexisting equilibrium, the time lag factor plays an important role. To substantiate our analytical results, extensive numerical simulations are performed for a hypothetical set of parameter values.     

Output feedback stabilization for planar switched nonlinear systems with asymmetric output constraints

In this paper, smooth output feedback controllers are presented to stabilize a class of planar switched nonlinear systems with asymmetric output constraints (AOCs). A new common barrier Lyapunov function (CBLF) is developed to prevent the switched system from violating AOCs. Combining the adding a power integrator technique (APIT) and the CBLF, state feedback controllers are designed. Then, reduced-order nonlinear observers are constructed and smooth output feedback controllers are proposed to globally stabilize planar switched nonlinear systems under arbitrary switchings. Meanwhile, the system output meets the prescribed AOCs during operation. The method proposed in this paper is a unified tool because it works not only for switched nonlinear systems with asymmetric or symmetric output constrains but also for those without output constraints. Simulations are presented to verify the proposed method.     

Stability analysis of impulsive delayed switched systems and applications

In this paper, a general class of impulsive delayed switched systems is considered. By employing the Lyapunov–Razumikhin method and some analysis techniques, we established several global asymptotic stability and global exponential stability criteria for the considered impulsive delayed switched systems, which improve and extend some recent works. As an application, the result of global exponential stability are used to study a class of uncertain linear switched systems with time‐varying delays. Several LMI‐based conditions are proposed to guarantee the global robust stability and global exponential stabilization. The designed memoryless state feedback controller can be easily checked by the LMI toolbox in Matlab. Moreover, the dwell time constraint is imposed for the switching law. Finally, two numerical examples and their simulations are given to show the effectiveness of our proposed results. Copyright © 2012 John Wiley & Sons, Ltd.     

Novel analytical and numerical techniques for fractional temporal SEIR measles model

In this paper, a fractional temporal SEIR measles model is considered. The model consists of four coupled time fractional ordinary differential equations. The time-fractional derivative is defined in the Caputo sense. Firstly, we solve this model by solving an approximate model that linearizes the four time fractional ordinary differential equations (TFODE) at each time step. Secondly, we derive an analytical solution of the single TFODE. Then, we can obtain analytical solutions of the four coupled TFODE at each time step, respectively. Thirdly, a computationally effective fractional Predictor-Corrector method (FPCM) is proposed for simulating the single TFODE. And the error analysis for the fractional predictor-corrector method is also given. It can be shown that the fractional model provides an interesting technique to describe measles spreading dynamics. We conclude that the analytical and Predictor-Corrector schemes derived are easy to implement and can be extended to other fractional models. Fourthly, for demonstrating the accuracy of analytical solution for fractional decoupled measles model, we applied GMMP Scheme (Gorenflo-Mainardi-Moretti-Paradisi) to the original fractional equations. The comparison of the numerical simulations indicates that the solution of the decoupled and linearized system is close enough to the solution of the original system. And it also indicates that the linearizing technique is correct and effective.     

Dynastic cycle: a generic structure describing resource allocation in political economies,markets and firms

A generic system embodies basic principles and insights that are common to a set of diverse cases and situations. This paper presents a new generic system that we name the dynastic cycle structure. It is based on a stylized model of events from the Chinese history. The model describes resource allocation between social, asocial and control uses in political economies, markets and firms that experience cyclical behaviour and homeostasis symbolizing low levels of performance. Numerical simulations with the model are used to understand the internal dynamics and to test several policy scenarios.     

Low-complexity quantized switching controllers using approximate bisimulation

In this paper, we consider the problem of synthesizing low-complexity controllers for incrementally stable switched systems. For that purpose, we establish a new approximation result for the computation of symbolic models that are approximately bisimilar to a given switched system. The main advantage over existing results is that it allows us to design naturally quantized switching controllers for safety or reachability specifications; these can be pre-computed offline and therefore the online execution time is reduced. Then, we present a technique to reduce the memory needed to store the control law by borrowing ideas from algebraic decision diagrams for compact function representation and by exploiting the non-determinism of the synthesized controllers. We show the merits of our approach by applying it to a simple model of temperature regulation in a building.     

Global Existence for a Parabolic Chemotaxis Model with Prevention of Overcrowding

In this paper we study a version of the Keller–Segel model where the chemotactic cross-diffusion depends on both the external signal and the local population density. A parabolic quasi-linear strongly coupled system follows. By incorporation of a population-sensing (or “quorum-sensing”) mechanism, we assume that the chemotactic response is switched off at high cell densities. The response to high population densities prevents overcrowding, and we prove local and global existence in time of classical solutions. Numerical simulations show interesting phenomena of pattern formation and formation of stable aggregates. We discuss the results with respect to previous analytical results on the Keller–Segel model.     

Evaluation of time-varying availability in multi-echelon spare parts systems with passivation

The popular models for repairable item inventory, both in the literature as well as practical applications, assume that the demands for items are independent of the number of working systems. However this assumption can introduce a serious underestimation of availability when the number of working systems is small, the failure rate is high or the repair time is long. In this paper, we study a multi-echelon repairable item inventory system under the phenomenon of passivation, i.e. serviceable items are passivated (“switched off”) upon system failure. This work is motivated by corrective maintenance of high-cost technical equipment in the miltary. We propose an efficient approximation model to compute time-varying availability. Experiments show that our analytical model agrees well with Monte Carlo simulation.     

Modeling and optimization of CSMA/CA in VANET

In this paper, we propose a simple theoretical model to compute the maximum spatial reuse feasible in a VANET. We focus on the ad hoc mode of the IEEE 802.11p standard. Our model offers simple and closed-form formulas on the maximum number of simultaneous transmitters, and on the distribution of the distance between them. It leads to an accurate upper bound on the maximum capacity. In order to validate our approach, results from the analytical models are compared to simulations performed with the network simulator NS-3. We take into account different traffic distributions (traffic of vehicles), and study the impact of this traffic on capacity. An application of this work is the parameterization of the CSMA/CA mechanism. Such an optimization is developed at the end of this paper.