Modeling complex multi-component reactive-transport systems: towards a simulation environment based on the concept of a Knowledge Base

A modelling framework within which transport processes in the hydrosphere can be described and interfaced with relevant biogeochemical reactions is presented. Three key elements of this simulation environment are discussed: (1) a numerical engine for solving sets of coupled non-linear process equations; (2) an automated procedure for model code generation (`Automatic Code Generator'); (3) a Web-distributed Knowledge Base (KB) of processes. The Automatic Code Generator translates the information selected in the KB into computer algorithms using the principles defined in the numerical engine. The code CONTRASTE is a first attempt at developing such a modelling framework. It allows one to easily select, adapt and combine a specific set of biogeochemical processes relevant to a user-defined application. The workings of CONTRASTE are described by means of examples which demonstrate how the various components of the simulation environment are coupled and automated. Prospects for future developments towards a fully automated model generation procedure are discussed.     

A Stochastic Maximum Principle for a Stochastic Differential Game of a Mean-Field Type

We construct a stochastic maximum principle (SMP) which provides necessary conditions for the existence of Nash equilibria in a certain form of N-agent stochastic differential game (SDG) of a mean-field type. The information structure considered for the SDG is of a possible asymmetric and partial type. To prove our SMP we take an approach based on spike-variations and adjoint representation techniques, analogous to that of S.?Peng (SIAM J. Control Optim. 28(4):966?C979, 1990) in the optimal stochastic control context. In our proof we apply adjoint representation procedures at three points. The first-order adjoint processes are defined as solutions to certain mean-field backward stochastic differential equations, and second-order adjoint processes of a first type are defined as solutions to certain backward stochastic differential equations. Second-order adjoint processes of a second type are defined as solutions of certain backward stochastic equations of a type that we introduce in this paper, and which we term conditional mean-field backward stochastic differential equations. From the resulting representations, we show that the terms relating to these second-order adjoint processes of the second type are of an order such that they do not appear in our final SMP equations. A?comparable situation exists in an article by R.?Buckdahn, B.?Djehiche, and J.?Li (Appl. Math. Optim. 64(2):197?C216, 2011) that constructs a SMP for a mean-field type optimal stochastic control problem; however, the approach we take of using these second-order adjoint processes of a second type to deal with the type of terms that we refer to as the second form of quadratic-type terms represents an alternative to a development, to our setting, of the approach used in their article for their analogous type of term.     

Self-crossing Points of a Line Segment Process

This paper is devoted to planar stationary line segment processes. The segments are assumed to be independent, identically distributed, and independent of the locations (reference points). We consider a point process formed by self-crossing points between the line segments. Its asymptotic variance is explicitly expressed for Poisson segment processes. The main result of the paper is the central limit theorem for the number of intersection points in expanding rectangular sampling window. It holds not only for Poisson processes of reference points but also for stationary point processes satisfying certain conditions on absolute regularity (β-mixing) coefficients. The proof is based on the central limit theorem for β-mixing random fields. Approximate confidence intervals for the intensity of intersections can be constructed.     

Analysis of a new multispecies tumor growth model coupling 3D phase-fields with a 1D vascular network

In this work, we present and analyze a mathematical model for tumor growth incorporating ECM erosion, interstitial flow, and the effect of vascular flow and nutrient transport. The model is of phase-field or diffused-interface type in which multiple phases of cell species and other constituents are separated by smooth evolving interfaces. The model involves a mesoscale version of Darcy’s law to capture the flow mechanism in the tissue matrix. Modeling flow and transport processes in the vasculature supplying the healthy and cancerous tissue, one-dimensional (1D) equations are considered. Since the models governing the transport and flow processes are defined together with cell species models on a three-dimensional (3D) domain, we obtain a 3D–1D coupled model.     

On the tail behavior of a class of multivariate conditionally heteroskedastic processes

Conditions for geometric ergodicity of multivariate autoregressive conditional heteroskedasticity (ARCH) processes, with the so-called BEKK (Baba, Engle, Kraft, and Kroner) parametrization, are considered. We show for a class of BEKK-ARCH processes that the invariant distribution is regularly varying. In order to account for the possibility of different tail indices of the marginals, we consider the notion of vector scaling regular variation (VSRV), closely related to non-standard regular variation. The characterization of the tail behavior of the processes is used for deriving the asymptotic properties of the sample covariance matrices.     

Two engineering applications of a constrained shortest-path model

This paper presents integer programming models for the determination of (a) optimal sequences of wastewater treatment processes, and (b) minimum cost, energy efficient composite wall and roof structures. The first model has been used to determine optimal sequences of wastewater treatment processes for a combined industrial and sanitary wastewater facility in Kuwait. The second model was used to assist design engineers in meeting government standards for the thermal resistance of building structures. Remarkably, the two models have essentially the same structure: a shortest path model with additional linear side constraints. The two practical applications are described and solved, and computational experience is discussed.     

Weighted branching and a pathwise renewal equation

This paper is devoted to the study of a pathwise renewal equation for stochastic processes which are functions of a weighted tree defined in a general weighted branching model. Motivated by applications in the analysis of certain stochastic fixed-point equations and in the theory of general (Crump–Mode–Jagers) branching processes, we analyze the solutions to the equation under several conditions, the main result being a characterization of the set of solutions satisfying appropriate integrability conditions.     

On the Exact Analysis of a Discrete-Time Queueing System with Autoregressive Inputs

In this paper, we provide an exact analysis of a discrete-time queueing system driven by a discrete autoregressive model of order 1 (DAR(1)) characterized by an arbitrary marginal batch size distribution and a correlation coefficient. Closed-form expressions for the probability generating function and mean queue length are derived. It is shown that the system performance is quite sensitive to the correlation of the arrival process. In addition, a comparison with traditional Markovian processes shows that arrival processes of DAR(1) type exhibit larger queue length as compared with the traditional Markovian processes when the marginal densities and correlation coefficients are matched.     

Stochastic processes determined by a general success-breeds-success principle

The general “success-breeds-success” (SBS) principle as introduced in a previous paper extends the classical SBS principle in that the allocation of items over sources is determined by a more general rule than in the classical case. In this article we study the time evolution of the total number of sources, the average number of items per source and the number of sources with n items at time t, in the general SBS framework. Conditional as well as absolute expectations are calculated. Moreover, we investigate if and when these processes are martingales, supermartingales or submartingales. Stability results for the stochastic processes are obtained in the sense that we are able to determine when these processes converge. The article also studies the evolution of the expected average number of items per source.     

Finite element simulation for material accumulation and welding processes including a free melt surface

A modeling and simulation approach for problems with solid-liquid-solid phase transitions and a free surface, feasible for material accumulation processes based on laser-based free form heading and welding processes for joining different metallic materials is presented. Both named processes are modeled within the framework of continuum mechanics by coupling the Stefan problem with the Navier-Stokes equations including a free capillary surface. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Conservative markov processes on a topological space

A Markov operator preservingC(X) is known to induce a decomposition of the locally compact spaceX to conservative and dissipative parts. Two notions of ergodicity are defined and the existence of subprocesses is studied. A sufficient condition for the existence of a conservative subprocess is given, and then the process is assumed to be conservative. When it has no subprocesses, sufficient conditions for the existence of a σ-finite invariant measure are given, and are extended to continuous-time processes. When the invariant measure is unique, ratio limit theorems are proved for the discrete and continuous time processes. Examples show that some combinations of conservative processes are not necessarily conservative. This paper is a part of the authors’s Ph.D. thesis prepared at the Hebrew University under the direction of Professor S. R. Foguel, to whom the author is grateful for his helpful advice and kind encouragement.     

Strong approximations for a Kumar-Seidman network under a priority service discipline

In this paper,we derive the strong approximations for a four-class two station multi-class queuing network（Kumar-Seidman network） under a priority service discipline.Within a group,jobs are served in the order of arrival,that is,a first-in-first-out disciple,and among groups,jobs are served under a pre-emptiveresume priority disciple.We show that if the input data（i.e.,the arrival and service processe） satisfy an approximation（such as the functional law-of-iterated logarithm approximation or the strong approximation）,the output data（the departure processes） and the performance measures（such as the queue length,the work load and the sojourn time process） satisfy a similar approximation.     

Implementation processes: a Boolean analysis

Implementing new operating procedures into organisations is problematic. It requires consideration of the socialisation processes needed to encourage implementers to creatively adopt and adapt the new procedure. The four main explanations of why organisational change occurs are teleology (group emerged action), evolution, dialectic and life cycles (growth stages). These have been mapped onto the corresponding organisational socialisation processes of job rotation, benchmarking with continuous improvement, competition and the use of champions. It has been claimed that successful implementation requires a mix of all four of these processes. This paper tests that claim by comparing the implementation of Total Quality Management into 32 independent and geographically dispersed bulk grain handling sites located around South Australia. Using Boolean Analysis it was found that successful implementation was achieved using either (a) self managed problem-solving teams and a review teams or, (b) champions with job rotation and site visits. Both of these mixes of socialisation processes worked; doing both was not necessary. The implications of this finding are discussed.     

Comparing the adaptive control methodology (ACM) to the financial planning practice of a large international group

The present paper is a contribution to the validation of the newly developed methodological framework called “adaptive control methodology” (ACM) introduced in a previous paper. ACM is a tool for planning and on-line control of complex socio-economic processes. It combines the techniques of adaptive control theory with system dynamics (SD) and group multicriteria decision aid (GMCDA). In the following, the usefulness and practical use of this framework are set in perspective by comparing it with recurrent planning and control of financial processes in the BSN/DANONE group. As a result of this comparison, some lessons drawn on the way of practical implementation of the theoretical framework can be eased. As by-product recommendations are made on how to influence in a constructive way common planning processes in the real world.     

Derivation of the cost equation of a dual replenishment inventory model with two order levels

This paper investigates an inventory control system where a single product can be ordered in two separate and independent processes within an inventory cycle. The cost equation is developed by deriving the steady-state probabilities for each level of inventory and using those probabilities to define (a) the average level of inventory, (b) time between replenishments and (c) the units acquired using each replenishment. The terms of the equation are represented as a function of two order levels: the least-order level, used to determine the need for two replenishment processes, and the maximum-order level, which represents the highest level of inventory allowed.     

Functional limit theorems for a new class of non-stationary shot noise processes

We study a class of non-stationary shot noise processes which have a general arrival process of noises with non-stationary arrival rate and a general shot shape function. Given the arrival times, the shot noises are conditionally independent and each shot noise has a general (multivariate) cumulative distribution function (c.d.f.) depending on its arrival time. We prove a functional weak law of large numbers and a functional central limit theorem for this new class of non-stationary shot noise processes in an asymptotic regime with a high intensity of shot noises, under some mild regularity conditions on the shot shape function and the conditional (multivariate) c.d.f. We discuss the applications to a simple multiplicative model (which includes a class of non-stationary compound processes and applies to insurance risk theory and physics) and the queueing and work-input processes in an associated non-stationary infinite-server queueing system. To prove the weak convergence, we show new maximal inequalities and a new criterion of existence of a stochastic process in the space $\mathbb{D}$ given its consistent finite dimensional distributions, which involve a finite set function with the superadditive property.     

Local asymptotic normality of a sequential model for marked point processes and its applications

This paper deals with statistical inference problems for a special type of marked point processes based on the realization in random time intervals [0,_u]. Sufficient conditions to establish the local asymptotic normality (LAN) of the model are presented, and then, certain class of stopping times _u satisfying them is proposed. Using these stopping rules, one can treat the processes within the framework of LAN, which yields asymptotic optimalities of various inference procedures. Applications for compound Poisson processes and continuous time Markov branching processes (CMBP) are discussed. Especially, asymptotically uniformly most powerful tests for criticality of CMBP can be obtained. Such tests do not exist in the case of the non-sequential approach. Also, asymptotic normality of the sequential maximum likelihood estimators (MLE) of the Malthusian parameter of CMBP can be derived, although the non-sequential MLE is not asymptotically normal in the supercritical case.     

Unsteady flow and heat transfer of a second grade fluid over a stretching sheet

The problem of unsteady boundary layer flow of a second grade over a stretching sheet is investigated in this paper. The governing equations of motion are reduced into a partial differential equation with two independent variables by using similarity transformations. The heat transfer analysis has been also carried out for two heating processes namely the prescribed surface temperature (PST case) and prescribed surface heat flux (PHF case). The series solutions of the problem are developed by employing homotopy analysis method (HAM). Convergence of the obtained series solutions are analyzed. It is noted that the present solutions of a second grade are valid for all dimensionless times. Finally, the results are obtained and discussed through graphs for various parameters of interest.     

Optimum Allocation of Processes in a Distributed Environment: A Process-to-Process Approach

The process allocation problem (PAP) concerned with the assignment of a number of communicating processes to a certain number (not known a priori) of identical processors in a telecommunications environment is examined. The objective is to minimize the total message-passing between processes residing on different processors subject to constraints on the processing power and storage capacity (code-, data-storage and occupancy) of the processors. Constraints imposed on the co-location of certain processes on the same processor are also included. The problem is formulated as a 0-1 linear maximization problem, taking into account only the number of processes involved, while the number of processors required is produced automatically with the optimum solution. An implicit enumeration algorithm is developed which produces an optimum message-passing allocation. Computational results of a set of random problems which have similar characteristics to a real-world application in telecommunications are also presented.