A second-order positivity preserving central-upwind scheme for chemotaxis and haptotaxis models

The paper is concerned with development of a new finite-volume method for a class of chemotaxis models and for a closely related haptotaxis model. In its simplest form, the chemotaxis model is described by a system of nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction-diffusion equation for the chemoattractant concentration. The first step in the derivation of the new method is made by adding an equation for the chemoattractant concentration gradient to the original system. We then show that the convective part of the resulting system is typically of a mixed hyperbolic-elliptic type and therefore straightforward numerical methods for the studied system may be unstable. The proposed method is based on the application of the second-order central-upwind scheme, originally developed for hyperbolic systems of conservation laws in Kurganov et al. (SIAM J Sci Comput 21:707–740, 2001), to the extended system of PDEs. We show that the proposed second-order scheme is positivity preserving, which is a very important stability property of the method. The scheme is applied to a number of two-dimensional problems including the most commonly used Keller–Segel chemotaxis model and its modern extensions as well as to a haptotaxis system modeling tumor invasion into surrounding healthy tissue. Our numerical results demonstrate high accuracy, stability, and robustness of the proposed scheme.     

Efficient finite-difference multi-scheme approach to the simulation of seismic waves in anisotropic media

This paper presents an original multi-scheme approach to the numerical simulation of seismic wave propagation in models with anisotropic formations. To simulate wave propagation in the anisotropic parts of the model, the Lebedev scheme is used. This scheme is rather universal, but highly expensive in terms of computational efficiency. In the main part of the model, a highly efficient standard staggered grid scheme is proposed. The two schemes are coupled to ensure convergence of the reflection/propagation coefficients with a prescribed order. The algorithm combines the universality of the Lebedev scheme and the efficiency of the standard staggered grid scheme.     

Indirect identification of continuous-time delay systems from step responses

In this paper, an indirect identification scheme is proposed for identifying the parameters of the continuous-time first-order plus time delay (FOPTD) model and the second-order plus time delay (SOPTD) model from step responses. Unlike the existing direct identification scheme, which identifies the parameters of the continuous-time FOPTD and SOPTD models directly from the continuous-time step response data, the proposed indirect scheme is to pre-identify discrete-time FOPTD and SOPTD models from the discretized continuous-time step response input–output data, then convert the obtained discrete-time models to the desirable continuous-time models. The proposed method is then extended to identify the afore-mentioned models from the step responses of the systems contaminated with input noise and constant output disturbance. The proposed simple alternative method exhibits good estimation performances in both the time domain and the frequency domain. Illustrative examples are presented to demonstrate the effectiveness of the proposed scheme.     

XTR-Kurosawa-Desmedt Scheme

This paper proposes an XTR version of the Kurosawa-Desmedt scheme. Our scheme is secure against adaptive chosen-ciphertext attack under the XTR version of the Decisional Diffie- Hellman assumption in the standard model. Comparing efficiency between the Kurosawa-Desmedt scheme and the proposed XTR-Kurosawa-Desmedt scheme, we find that the proposed scheme is more efficient than the Kurosawa-Desmedt scheme both in communication and computation without compromising security.     

XTR-Kurosawa-Desmedt Scheme

This paper proposes an XTR version of the Kurosawa-Desmedt scheme. Our scheme is secure against adaptive chosen-ciphertext attack under the XTR version of the Decisional Diffie-Hellman assumption in the standard model. Comparing efficiency between the Kurosawa-Desmedt scheme and the proposed XTR-Kurosawa-Desmedt scheme, we find that the proposed scheme is more efficient than the Kurosawa-Desmedt scheme both in communication and computation without compromising security.     

On an upwind difference scheme for strongly degenerate parabolic equations modelling the settling of suspensions in centrifuges and non-cylindrical vessels

We prove the convergence of an explicit monotone finite difference scheme approximating an initial-boundary value problem for a spatially one-dimensional quasilinear strongly degenerate parabolic equation, which is supplied with two zero-flux boundary conditions. This problem arises in a model of sedimentation–consolidation processes in centrifuges and vessels with varying cross-sectional area. We formulate the definition of entropy solution of the model in the sense of Kružkov and prove the convergence of the scheme to the unique BV entropy solution of the problem. The scheme and the model are illustrated by numerical examples.     

Integrable Discrete Model for One‐Dimensional Soil Water Infiltration

We propose an integrable discrete model of one‐dimensional soil water infiltration. This model is based on the continuum model by Broadbridge and White, which takes the form of nonlinear convection–diffusion equation with a nonlinear flux boundary condition at the surface. It is transformed to the Burgers equation with a time‐dependent flux term by the hodograph transformation. We construct a discrete model preserving the underlying integrability, which is formulated as the self‐adaptive moving mesh scheme. The discretization is based on linearizability of the Burgers equation to the linear diffusion equation, but the naïve discretization based on the Euler scheme which is often used in the theory of discrete integrable systems does not necessarily give a good numerical scheme. Taking desirable properties of a numerical scheme into account, we propose an alternative discrete model that produces solutions with similar accuracy to direct computation on the original nonlinear equation, but with clear benefits regarding computational cost.     

Iterative approximation of <Emphasis Type="Italic">k</Emphasis>-limited polling systems

The present paper deals with the problem of calculating queue length distributions in a polling model with (exhaustive) k-limited service under the assumption of general arrival, service and setup distributions. The interest for this model is fueled by an application in the field of logistics. Knowledge of the queue length distributions is needed to operate the system properly. The multi-queue polling system is decomposed into single-queue vacation systems with k-limited service and state-dependent vacations, for which the vacation distributions are computed in an iterative approximate manner. These vacation models are analyzed via matrix-analytic techniques. The accuracy of the approximation scheme is verified by means of an extensive simulation study. The developed approximation turns out to be accurate, robust and computationally efficient. This research is supported by the Technology Foundation STW, applied science division of NWO and the technology programme of the Dutch Ministry of Economic Affairs.     

Mixed sensitivity minimization problems with rationall 1-optimal solutions

Up to this time, the only known method to solve the discrete-time mixed sensitivity minimization problem inl ¹ has been to use a certain infinite-dimensional linear programming approach, presented by Dahleh and Pearson in 1988 and later modified by Mendlovitz. That approach does not give in general true optimal solutions; only suboptimal ones are obtained. Here, for the first time, the truel ¹-optimal solutions are found for some mixed sensitivity minimization problems. In particular, Dahleh and Pearson construct an 11h order suboptimal compensator for a certain second-order plan with first-order weight functions; it is shown that the unique optimal compensator for that problem is rational and of order two. The author discovered this fact when trying out a new scheme of solving the infinite-dimensional linear programming system. This scheme is of independent interest, because when it is combined with the Dahleh-Pearson-Mendlovitz scheme, it gives both an upper bound and a lower bound on the optimal performance; hence, it provides the missing error bound that enables one to truncate the solution. Of course, truncation is appropriate only if the order of the optimal compensator is too high. This may indeed be the case, as is shown with an example where the order of the optimal compensator can be arbitrarily high.     

Multiround Unconditionally Secure Authentication

Authentication codes are used to protect communication against a malicious adversary. In this paper we investigate unconditionally secure multiround authentication schemes. In a multiround scheme a message is authenticated by passing back and forth several codewords between the sender and receiver. We define a multiround authentication model and show how to calculate the probability of a successful attack for this model. We prove the security for a 3-round scheme and give a construction for the 3-round scheme based on Reed-Solomom codes. This construction has a very small key size for even extremely large messages. Furthermore, a secure scheme for an arbitrary number of rounds is given. We give a new upper bound for the keys size of an n-round scheme.     

考虑繁忙率的多时段救护车优化布局研究

救护车布局对院前急救服务中需求的响应具有决定性作用。本文重点研究了考虑繁忙率的多时段救护车优化布局问题,在传统双覆盖模型基础上引入救护车繁忙率因素,提出改进后的双覆盖模型。首先计算考虑繁忙率的期望覆盖需求量,进而结合实际,将一天以早晚高峰划分为5个时段,探究不同时段下繁忙率差异带来的不同布局方案。以上海市松江区2014年数据为例,应用改进后的模型进行了系统深入的实证研究,并绘制繁忙率对需求覆盖率的影响曲线。结果表明,本文提出的布局方案比实际方案得到的期望覆盖需求量提高了3.19%,比传统双覆盖模型得到的期望覆盖需求量提高了0.54%,证明了改进后模型的有效性;需求覆盖率曲线随繁忙率增加而下降,与实际意义相符。该方法能够直观简洁地得出救护车布局方案,利于院前急救服务水平的提升,为社会安全提供有力保障。     

Geometric secret sharing schemes and their duals

Given a set of participants we wish to distribute information relating to a secret in such a way that only specified groups of participants can reconstruct the secret. We consider here a special class of such schemes that can be described in terms of finite geometries as first proposed by Simmons. We formalize the Simmons model and show that given a geometric scheme for a particular access structure it is possible to find another geometric scheme whose access structure is the dual of the original scheme, and which has the same average and worst-case information rates as the original scheme. In particular this shows that if an ideal geometric scheme exists then an ideal geometric scheme exists for the dual access structure.This work was supported by the Science and Engineering Research Council Grant GR/G 03359.This work was supported by the Australian Research Council.     

A fully discrete scheme for diffusive-dispersive conservation laws

Summary.   We introduce a fully discrete (in both space and time) scheme for the numerical approximation of diffusive-dispersive hyperbolic conservation laws in one-space dimension. This scheme extends an approach by LeFloch and Rohde [4]: it satisfies a cell entropy inequality and, as a consequence, the space integral of the entropy is a decreasing function of time. This is an important stability property, shared by the continuous model as well. Following Hayes and LeFloch [2], we show that the limiting solutions generated by the scheme need not coincide with the classical Oleinik-Kruzkov entropy solutions, but contain nonclassical undercompressive shock waves. Investigating the properties of the scheme, we stress various similarities and differences between the continuous model and the discrete scheme (dynamics of nonclassical shocks, nucleation, etc). Received November 15, 1999 / Revised version received May 27, 2000 / Published online March 20, 2001     

How an added mass matrix estimation may dramatically improve FSI calculations for moving foils

This paper presents a corrected partitioned scheme for investigating fluid–structure interaction (FSI) that may be encountered by lifting devices immersed in heavy fluid such as liquids. The purpose of this model is to counteract the penalizing impact of the added mass effect on the classical partitioned FSI coupling scheme. This work is based on an added mass corrected version of the classical strongly coupled partitioned scheme presented in Song et al. (2013). Results show that this corrected version systematically allows convergence to the coupled solution. The fluid flow model considered here uses a non-stationary potential approach, commonly termed the Panel Method. The advantage of this kind of approach is twofold: first, in restricting itself to a boundary method and, second, in allowing an added mass matrix to be estimated as a post-processing phase. Whereas the classical scheme encounters an acceptable (no numerical oscillation) convergence limit for fluid densities higher than 8 kg/m³ for the considered case, our corrected scheme is not dependent on fluid density and converges with only 6 iterations. This makes it possible to investigate the dynamic behavior of a 2D foil immersed in heavy fluids such as water. For example, it recognizes that frequency shifting may occur as the consequence of a strong added mass effect.     

A multinomial spline approximation scheme using spline quasi-interpolants

This paper presents a multinomial spline approximation scheme based on spline quasi-interpolants. The scheme can be considered as an extension of the usual Bernstein approximation for complex exponentials. Error estimates and numerical examples are given to show that this new scheme could produce highly accurate results.     

Fast Identification of Parameters in Optical Systems

This paper presents a scheme for fast identification of parameters in systems that yield large-order measurement vectors. The method can be applied to real-time identification and control. In the paper, the scheme is applied to identification and control of an optical model of a space antenna. Both the mathematical models and numerical results are presented.     

A boundary element method for the Dirichlet eigenvalue problem of the Laplace operator

The solution of eigenvalue problems for partial differential operators by using boundary integral equation methods usually involves some Newton potentials which may be resolved by using a multiple reciprocity approach. Here we propose an alternative approach which is in some sense equivalent to the above. Instead of a linear eigenvalue problem for the partial differential operator we consider a nonlinear eigenvalue problem for an associated boundary integral operator. This nonlinear eigenvalue problem can be solved by using some appropriate iterative scheme, here we will consider a Newton scheme. We will discuss the convergence and the boundary element discretization of this algorithm, and give some numerical results.     

A note on an NSFD scheme for a mathematical model of respiratory virus transmission

We construct a non-standard finite difference (NSFD) scheme for an SIRS mathematical model of respiratory virus transmission. This discretization is in full compliance with the NSFD methodology as formulated by Mickens. By use of an exact conservation law satisfied by the SIRS differential equations, we are able to determine the corresponding denominator function for the discrete first-order time derivatives. Our scheme is dynamically consistent with the SIRS differential equations, since the conservation laws are preserved. Furthermore, the scheme is shown to satisfy a positivity condition for its solutions for all values of the time step size.     

An unconditionally stable uncoupled scheme for a triphasic Cahn–Hilliard/Navier–Stokes model

We propose an original scheme for the time discretization of a triphasic Cahn–Hilliard/Navier–Stokes model. This scheme allows an uncoupled resolution of the discrete Cahn–Hilliard and Navier‐Stokes system, which is unconditionally stable and preserves, at the discrete level, the main properties of the continuous model. The existence of discrete solutions is proved, and a convergence study is performed in the case where the densities of the three phases are the same. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq. 2013     

Quadratic optimal synchronization of uncertain chaotic systems

This paper investigates the quadratic optimal synchronization of uncertain chaotic systems with parameter mismatch, parametric perturbations and external disturbances on both master and slave systems. A robust control scheme based on Lyapunov stability theory and quadratic optimal control approach is derived to realize chaotic synchronization. The sufficient criterion for stability condition is formulated in a linear matrix inequality (LMI) form. The effect of uncertain parameters and external disturbance is suppressed to an H_∞ norm constraint. An adaptive algorithm is proposed to adjust the uncertain bound in the robust controller avoiding the chattering phenomena. The simulation results for synchronization of the Chua’s circuit system and the Lorenz system demonstrate the effectiveness of the proposed scheme.